Igcse core papers 2002 2014

The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.

This document consists of 11 printed pages and 1 blank page.

© UCLES 2012 [Turn over

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

MATHEMATICS 0580/01

Paper 1 (Core) For Examination from 2015

SPECIMEN PAPER 1 hour

Candidates answer on the Question Paper.

Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional)

READ THESE INSTRUCTIONS FIRST

Write your Centre number, candidate number and name on all the work you hand in.

Write in dark blue or black pen.

You may use an HB pencil for any diagrams or graphs.

Do not use staples, paper clips, glue or correction fluid.

Answer all questions.

If working is needed for any question it must be shown below that question.

Electronic calculators should be used.

If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.

For π, use either your calculator value or 3.142.

At the end of the examination, fasten all your work securely together.

The number of marks is given in brackets [ ] at the end of each question or part question.

The total of the marks for this paper is 56.

2

© UCLES 2012 0580/01/SP/15

1

A

S

The diagram shows the map of part of an orienteering course. Sanji runs from the start, S, to the point A.

Write as a column vector.

Answer

[1]

2 When Ali takes a penalty, the probability that he will score a goal is 5

4.

Ali takes 30 penalties. Find how many times he is expected to score a goal. Answer [2]

3 The ratio of Anne’s height : Ben’s height is 7 : 9. Anne’s height is 1.4 m. Find Ben’s height. Answer m [2]

3

© UCLES 2012 0580/01/SP/15 [Turn over

4 The distance between the centres of two villages is 8 km. A map on which they are shown has a scale of 1 : 50 000. Calculate the distance between the centres of the two villages on the map. Give your answer in centimetres. Answer cm [2]

5

10

8

6

4

2

0Black Silver Red

Favourite colour

Green Blue

Frequency

The bar chart shows the favourite colours of students in a class. (a) How many students are in the class? Answer(a) [1]

(b) Write down the modal colour.

Answer(b) [1]

4

© UCLES 2012 0580/01/SP/15

6 Use your calculator to find 1.53.1

5.7545

+

×.

Answer [2]

7 (a) Calculate 60% of 200. Answer(a) [1]

(b) Write 0.36 as a fraction. Give your answer in its lowest terms. Answer(b) [2]

8 A circle has a radius of 50 cm. (a) Calculate the area of the circle in cm2. Answer(a) cm2 [2]

(b) Write your answer to part (a) in m2. Answer(b) m2 [1]

5


9

30

25

20

15

10

5

06 am 9 am Midday

Time

3 pm 6 pm

Temperature(°C)

The graph shows the temperature in Paris from 6 am to 6 pm one day. (a) What was the temperature at 9 am? Answer(a) °C [1]

(b) Between which two times was the temperature decreasing? Answer(b) and [1]

(c) Work out the difference between the maximum and minimum temperatures shown. Answer(c) °C [1]

10 (a) Write down the mathematical name of a quadrilateral that has exactly two lines of symmetry. Answer(a) [1]

(b) Write down the mathematical name of a triangle with exactly one line of symmetry. Answer(b) [1]

(c) Write down the order of rotational symmetry of a regular pentagon. Answer(c) [1]

6

© UCLES 2012 0580/01/SP/15

11 Without using your calculator, work out

+

4

1

3

2

2

1.

Show all your working clearly and give your answer as a fraction. Answer [3]

12

y

x10– 1– 2– 3– 4 2

9

8

7

6

5

4

3

2

1

The diagram shows the graph of y = (x + 1)2 for −4 Y x Y 2. (a) On the same grid, draw the line y = 3. [1] (b) Use your graph to find the solutions of (x + 1)2 = 3. Give each solution correct to 1 decimal place. Answer(b) x = or x = [2]

7


13

NOT TOSCALE

The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size. Calculate the size of one of these angles. Answer [3]

14 (a) Expand and simplify. 2(3x – 2) + 3(x – 2) Answer(a) [2]

(b) Expand. x(2x2 – 3) Answer(b) [2]

8

© UCLES 2012 0580/01/SP/15

15

50

40

30

20

10

0 10 20 30 40Mathematics test mark

Engl

ish

test

mar

k

50 60 70 80

The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an English

test by 15 students. (a) Describe the correlation. Answer(a) [1]

(b) The mean for the Mathematics test is 47.3 . The mean for the English test is 30.3 . Plot the mean point (47.3, 30.3) on the scatter diagram above. [1] (c) (i) Draw the line of best fit on the diagram above. [1] (ii) One student missed the English test. She received 45 marks in the Mathematics test. Use your line to estimate the mark she might have gained in the English test. Answer(c)(ii) [1]

9


16 (a)

A B

C

D E

110°NOT TOSCALE

In the diagram, AB is parallel to DE. Angle ABC = 110°. Find angle BDE. Answer(a) Angle BDE = [2]

(b)

t °

y°

z°50°

OB

A T

NOT TOSCALE

TA is a tangent at A to the circle, centre O. Angle OAB = 50°. Find the value of (i) y, Answer(b)(i) y = [1]

(ii) z, Answer(b)(ii) z = [1]

(iii) t. Answer(b)(iii) t = [1]

10

© UCLES 2012 0580/01/SP/15

17

y°

8 m

3 m

NOT TOSCALE

The diagram shows a ladder, of length 8 m, leaning against a vertical wall. The bottom of the ladder stands on horizontal ground, 3 m from the wall. (a) Find the height of the top of the ladder above the ground. Answer(a) m [3]

(b) Use trigonometry to calculate the value of y. Answer(b) y = [2]

11

© UCLES 2012 0580/01/SP/15

18 (a) Lucinda invests $500 at a rate of 5% per year simple interest. Calculate the interest Lucinda has after 3 years. Answer(a) $ [2]

(b) Andy invests $500 at a rate of 5% per year compound interest. Calculate how much more interest Andy has than Lucinda after 3 years. Answer(b) $ [4]

12

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.

Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2012 0580/01/SP/15

BLANK PAGE

The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.

This document consists of 16 printed pages.

© UCLES 2012 [Turn over

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

MATHEMATICS 0580/03

Paper 3 (Core) For Examination from 2015

SPECIMEN PAPER 2 hours






You may use an HB pencil for any diagrams or graphs.

Do not use staples, paper clips, glue or correction fluid.





For π , use either your calculator value or 3.142.




2

© UCLES 2012 0580/03/SP/15

1 (a) Write twenty five million in figures. Answer(a) [1]

(b) Write the following in order of size, starting with the smallest.

3

2 65% 0.6

Answer(b) I I [1]

(c) In a sale a coat costing $250 is reduced to $200. Find the percentage decrease in the cost. Answer(c) % [3]

(d)

Basketball

Tennis

90°150°Football

NOT TOSCALE

120 students are asked to choose their favourite sport. The results are shown in the pie chart. Calculate the number of students who chose

(i) basketball, Answer(d)(i) [1]

(ii) football. Answer(d)(ii) [2]

3


2 The distance between Geneva and Gstaad is 150 km. (a) Write 150 in standard form. Answer(a) [1]

(b) A car took 12

1 hours to travel from Geneva to Gstaad.

Calculate the average speed of the car. Answer(b) km/h [1]

(c) A bus left Gstaad at 10 15. It arrived in Geneva at 12 30. Calculate the time, in hours and minutes, that the bus took for the journey. Answer(c) h min [1]

(d) Another bus left Geneva at 13 55. It travelled at an average speed of 60 km/h. Find the time it arrived in Gstaad. Answer(d) [2]

(e) The distance of 150 km is correct to the nearest 10 km. Complete the statement for the distance, d km, from Geneva to Gstaad. Answer(e) Y d I [2]

4

© UCLES 2012 0580/03/SP/15

3 36 29 41 45 15 10 13 Use the numbers in the list above to answer all the following questions.

(a) Write down (i) two even numbers, Answer(a)(i) , [1]

(ii) two prime numbers, Answer(a)(ii) , [2]

(iii) a square number, Answer(a)(iii) [1]

(iv) two factors of 90 . Answer(a)(iv) , [2]

(b) (i) Calculate the mean of the seven numbers. Answer(b)(i) [2]

(ii) Find the median. Answer(b)(ii) [2]

(iii) Find the range. Answer(b)(iii) [1]

5


(c) A number from the list is chosen at random. Find the probability that the number is (i) even, Answer(c)(i) [1]

(ii) a multiple of 5. Answer(c)(ii) [1]

6

© UCLES 2012 0580/03/SP/15

4 (a) Using the exchange rates $1 = 0.70 Euros and $1 = 90 Yen change (i) $100 to Euros, Answer(a)(i) Euros [1]

(ii) 100 Yen to dollars. Answer(a)(ii) $ [2]

(b) Tania went on holiday to Switzerland. The exchange rate was $1 = 1.04 Swiss francs (CHF). She changed $1500 to Swiss francs and paid 1% commission. (i) How much commission, in dollars, did she pay? Answer(b)(i) $ [1]

(ii) Show that she received CHF 1544.40. Answer (b)(ii) [2] (c) Tania spent CHF 950 on her holiday. She converted the remaining Swiss francs back into dollars. She paid CHF 10 to make the exchange. Calculate the amount, in dollars, Tania received. Answer(c) $ [3]

7


5 y

x

6

5

4

3

2

1

–1

–2

–3

0 1 2 3 4 5 6–1–2–3–4

l

(a) Find the gradient of the line l. Answer(a) [2]

(b) (i) Complete the table below for x + 2y = 6 .

x 0 2

y 0

[3]

(ii) On the grid, draw the line x + 2y = 6 for −4 Y x Y 6 . [2] (c) The equation of the line l is 4x + 3y = 4. Use your diagram to solve the simultaneous equations 4x + 3y = 4 and x + 2y = 6 . Answer(c) x =

y = [2]

8

© UCLES 2012 0580/03/SP/15

6 (a)

A B The line AB is drawn above. Parts (i), (iii), and (v) must be completed using a ruler and compasses only.

All construction arcs must be clearly shown. (i) Construct triangle ABC with AC = 7 cm and BC = 6 cm. [2] (ii) Measure angle BAC. Answer(a)(ii) Angle BAC = [1]

(iii) Construct the bisector of angle ABC. [2] (iv) The bisector of angle ABC meets AC at T. Measure the length of AT. Answer(a)(iv) AT = cm [1]

(v) Construct the perpendicular bisector of the line BC. [2] (vi) Shade the region that is

• nearer to B than to C and

• nearer to BC than to AB. [1]

9


(b) A ship sails 40 km on a bearing of 040° from P to Q. (i) Using a scale of 1 centimetre to represent 5 kilometres, make a scale drawing of the path of the

ship. Mark the point Q.

North

P

Scale: 1 cm = 5 km [2] (ii) At Q the ship changes direction and sails 30 km on a bearing of 160° to the point R. Draw the path of the ship. [2] (iii) Find how far, in kilometres, the ship is from the starting position P. Answer(b)(iii) km [1]

(iv) Measure the bearing of P from R. Answer(b)(iv) [1]

10

© UCLES 2012 0580/03/SP/15

7 (a) Solve the equation 2(x + 4) = 3(x + 2) + 8 . Answer(a) x = [3]

(b) Make z the subject of za + b = 3 . Answer(b) z = [2]

(c) Find x when 2x3 = 54 . Answer(c) x = [2]

11


(d) A rectangular field has a length of x metres. The width of the field is (2x – 5) metres. (i) Show that the perimeter of the field is (6x – 10) metres. Answer (d)(i) [2] (ii) The perimeter of the field is 50 metres. Find the length of the field. Answer(d)(ii) length =

m [2]

12

© UCLES 2012 0580/03/SP/15

8

A

B

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

The diagram shows two shapes A and B. (a) Describe fully the single transformation which maps A onto B. Answer(a) [2]

(b) On the grid, draw the line x = 2. [1] (c) On the grid, draw the image of shape A after the following transformations. (i) Reflection in the line x = 2. Label the image C. [1] (ii) Enlargement, scale factor 2, centre (0, 0). Label the image D. [2]

13


9 (a) Factorise completely 3x2 + 12x. Answer(a) [2]

(b) Find the value of a3 + 3b2 when a = 2 and b = −2 . Answer(b) [2]

(c) Simplify 3x4 × 2x3. Answer(c) [2]

14

© UCLES 2012 0580/03/SP/15

10

2 m

5 m

10 m

x m

NOT TOSCALE

The diagram shows a ramp in the form of a triangular prism. The cross-section is a right-angled triangle of length 5 m and height 2 m. (a) Find the value of x. Give your answer correct to 1 decimal place. Answer(a) x = [3]

(b) Find the area of the cross-section. Answer(b) m2 [2]

(c) The ramp is 10 m long. Calculate the volume of the ramp. Answer(c) m3 [1]

15


(d) Calculate the total surface area of all five faces of the ramp. Answer(d) m2 [3]

(e) Each face of the ramp is painted. Paint costs $2.25 per square metre. Calculate the total cost of the paint. Answer(e) $ [1]

Question 11 is printed on the next page.

16



© UCLES 2012 0580/03/SP/15

11

Diagram 1 Diagram 2 Diagram 3 The diagrams show a sequence of shapes. (a) On the grid, draw Diagram 4. [1] (b) Complete the table showing the number of lines in each diagram.

Diagram (n) Number of lines

1 6

2 11

3

4

5

[3] (c) Work out the number of lines in Diagram 8. Answer(c) [1]

(d) Write down an expression, in terms of n, for the number of lines in Diagram n. Answer(d) [2]

(e) Work out the number of lines in Diagram 100. Answer(e) [1]

(f) The number of lines in Diagram p is 66. Find the value of p. Answer(f) p = [2]


Write your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use an HB pencil for any diagrams or graphs.Do not use staples, paper clips, glue or correction fl uid.DO NOT WRITE IN ANY BARCODES.

Answer all questions.If working is needed for any question it must be shown below that question.Electronic calculators should be used.If the degree of accuracy is not specifi ed in the question, and if the answer is not exact, give the answer to three signifi cant fi gures. Give answers in degrees to one decimal place.For π, use either your calculator value or 3.142.

At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.The total of the marks for this paper is 56.

MATHEMATICS 0580/11

Paper 1 (Core) May/June 2014

1 hour



Cambridge International ExaminationsCambridge International General Certifi cate of Secondary Education


[Turn overIB14 06_0580_11/2RP© UCLES 2014

*1477753275*

The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certifi cate.

2

0580/11/M/J/14© UCLES 2014

1 Work out. 10 – 3 × 2

Answer ................................................ [1]__________________________________________________________________________________________

2 Write down the prime numbers between 20 and 30.

Answer ................................................ [1]__________________________________________________________________________________________

3

NOT TOSCALE

163°59° x°

(a) Find the value of x.

Answer(a) x = ................................................ [1]

(b) One of the angles is 163°.

What type of angle is this?

Answer(b) ................................................ [1]__________________________________________________________________________________________

4 A city has a population of fi ve hundred and six thousand.

Write the size of the population

(a) in fi gures,

Answer(a) ................................................ [1]

(b) in standard form.

Answer(b) ................................................ [1]__________________________________________________________________________________________

3

0580/11/M/J/14© UCLES 2014 [Turn over

5 p = 16.834.8 1.98276#

(a) In the spaces provided, write each number in this calculation correct to 1 signifi cant fi gure.

Answer(a)............ × ............

............[1]

(b) Use your answer to part (a) to estimate the value of p.

Answer(b) ................................................ [1]__________________________________________________________________________________________

6 Solve the equation. 8n

2- = 11

Answer n = ................................................ [2]__________________________________________________________________________________________

7 a = 3-

4e o b =

15

-e o

Work out a – 2b.

Answer f p [2]

__________________________________________________________________________________________

8 The width, w cm, of a carpet is 455 cm, correct to the nearest centimetre.

Complete the statement about the value of w.

Answer ............................ Ğ w < ............................ [2]__________________________________________________________________________________________

4

0580/11/M/J/14© UCLES 2014

9 y = 2x

x2+2

2

Find the value of y when x = 6. Give your answer as a mixed number in its simplest form.

Answer y = ................................................ [2]__________________________________________________________________________________________

10 Use your calculator to work out 43 + 2–1.

Give your answer correct to 2 decimal places.

Answer ................................................ [2]__________________________________________________________________________________________

11 The diagram shows a cuboid.

8 cm

15 cmh

NOT TOSCALE

The volume of this cuboid is 720 cm3. The width is 8 cm and the length is 15 cm.

Calculate h, the height of the cuboid.

Answer h = .......................................... cm [2]__________________________________________________________________________________________

5


12 The scatter diagram shows the rainfall and the average temperature in a city for the month of June, over a period of 10 years.

30

25

20

15

10

5

0 5 10 15

Rainfall (cm)

Temperature (°C)

20 25 30

(a) What type of correlation does this scatter diagram show?

Answer(a) ................................................ [1]

(b) Describe the relationship between the rainfall and the average temperature.

Answer(b) ...........................................................................................................................................

............................................................................................................................................................. [1]__________________________________________________________________________________________

6

0580/11/M/J/14© UCLES 2014

13 The graph can be used to convert between miles and kilometres.

80

70

60

50

40

30

20

10

0 10 20 30

Miles

Kilometres

40 50

A train travels 24 miles in 20 minutes.

Find its average speed in kilometres per hour.

Answer ....................................... km/h [2]__________________________________________________________________________________________

7


14

127°

a°b°

A

D

E

BC

NOT TOSCALE

The diagram shows an isosceles triangle ABC. DCB is a straight line and is parallel to AE. Angle DCA = 127°.

Find the value of

(a) a,

Answer(a) a = ................................................ [2]

(b) b.

Answer(b) b = ................................................ [1]__________________________________________________________________________________________

15 Carlo changed 800 euros (€) into dollars for his holiday when the exchange rate was €1 = $1.50 . His holiday was then cancelled. He changed all his dollars back into euros and he received €750.

Find the new exchange rate.

Answer €1 = $ ................................................. [3]__________________________________________________________________________________________

8

0580/11/M/J/14© UCLES 2014

16 (a) Simplify the expressions.

(i) p 3 × p

7

Answer(a)(i) ................................................ [1]

(ii) t 5 ÷ t

8

Answer(a)(ii) ................................................ [1]

(b) (h3)k = h12

Find the value of k.

Answer(b) k = ................................................ [1]__________________________________________________________________________________________

17

OP R

Q

17 cm9 cm

NOT TOSCALE

The diagram shows a circle, centre O. P, Q and R are points on the circumference. PQ = 17 cm and QR = 9 cm.

(a) Explain why angle PQR is 90°.

Answer(a) ...........................................................................................................................................

............................................................................................................................................................. [1]

(b) Calculate the length PR.

Answer(b) PR = .......................................... cm [2]__________________________________________________________________________________________

9


18 In this question, do not use your calculator and show all the steps in your working.

(a) Show that 3 51 – 2 8

5 = 4023 .

Answer(a)

[2]

(b) Work out 87 ÷ 40

23 .

Give your answer as a mixed number in its simplest form.

Answer(b) ................................................ [2]__________________________________________________________________________________________

19 The table shows the average monthly temperature (°C) for Fairbanks, Alaska.

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Temperature (°C) –23.4 –19.8 –11.7 –0.8 9.2 15.4 16.9 13.8 7.5 –5.8 –21.4 –21.8

(a) Find

(i) the difference between the highest and the lowest temperatures,

Answer(a)(i) ........................................... °C [1]

(ii) the median.

Answer(a)(ii) ........................................... °C [2]

(b) A month is chosen at random from the table.

Find the probability that its average temperature is below zero.

Answer(b) ................................................ [1]__________________________________________________________________________________________

10

0580/11/M/J/14© UCLES 2014

20 A bus company in Dubai has the following operating times.

Day Starting time

Finishing time

Saturday 06 00 24 00

Sunday 06 00 24 00

Monday 06 00 24 00

Tuesday 06 00 24 00

Wednesday 06 00 24 00

Thursday 06 00 24 00

Friday 13 00 24 00

(a) Calculate the total number of hours that the bus company operates in one week.

Answer(a) ............................................. h [3]

(b) Write the starting time on Friday in the 12-hour clock.

Answer(b) ................................................ [1]__________________________________________________________________________________________

11


21

The diagram shows a circle inside a square. The circumference of the circle touches all four sides of the square.

(a) Calculate the area of the circle when the side of the square is 15 cm.

Answer(a) ......................................... cm2 [2]

(b) Draw all the lines of symmetry on the diagram. [2]__________________________________________________________________________________________


12

0580/11/M/J/14© UCLES 2014

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Everyreasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included the publisher will be pleased to make amends at the earliest possible opportunity.


22

B

C

A27 m

34 m

NorthNOT TOSCALE

In the diagram, B is 27 metres due east of A. C is 34 metres from A and due south of B.

(a) Using trigonometry, calculate angle ACB.

Answer(a) Angle ACB = ................................................ [2]

(b) Find the bearing of C from A.

Answer(b) ................................................ [2]





MATHEMATICS 0580/12


1 hour





*5359060919*



2

0580/12/M/J/14© UCLES 2014

1 Simplify the expression. p + p + p + p

Answer ................................................ [1]__________________________________________________________________________________________

2 Calculate 216

1.3

3

.

Answer ................................................ [1]__________________________________________________________________________________________

3 Write down in fi gures

(a) three hundred and forty thousand,

Answer(a) ................................................ [1]

(b) the number that is one less than one million.

Answer(b) ................................................ [1]__________________________________________________________________________________________

4 Write the following numbers in order, starting with the smallest.

115 0.2 45.4% 20

9

Answer ...................... < ...................... < ...................... < ...................... [2]__________________________________________________________________________________________

3


5 (a) The temperature on Monday was –6°C. On Tuesday the temperature was 3 degrees lower.

Write down the temperature on Tuesday.

Answer(a) ........................................... °C [1]

(b) The temperature on Saturday was –2°C. The temperature on Sunday was 8°C.

Write down the difference in these two temperatures.

Answer(b) ........................................... °C [1]__________________________________________________________________________________________

6 (a) Write 569 000 correct to 2 signifi cant fi gures.

Answer(a) ................................................ [1]

(b) Write 569 000 in standard form.

Answer(b) ................................................ [1]__________________________________________________________________________________________

7 Find three numbers which have a mode of 4 and a mean of 6.

Answer ...................... , ...................... , ...................... [2]__________________________________________________________________________________________

4

0580/12/M/J/14© UCLES 2014

8

lP

NOT TOSCALE

y

x0

The equation of the line l in the diagram is y = 5 – x .

(a) The line cuts the y-axis at P.

Write down the co-ordinates of P.

Answer(a) (...................... , ......................) [1]

(b) Write down the gradient of the line l.

Answer(b) ................................................ [1]__________________________________________________________________________________________

9 Solve the simultaneous equations. 2x – y = 7 3x + y = 3

Answer x = ................................................

y = ................................................ [2]__________________________________________________________________________________________

5


10C

B A

8 cm

28°

NOT TOSCALE

Calculate the length of AB.

Answer AB = .......................................... cm [2]__________________________________________________________________________________________

11 The height of Mount Everest is 8800 m, correct to the nearest hundred metres.

Complete the statement about the height, h metres, of Mount Everest.

Answer ......................... Ğ h < ......................... [2]__________________________________________________________________________________________

12 Colin is travelling from Sydney, Australia, to Auckland, New Zealand.

(a) Colin’s bus leaves for Sydney airport at 12 38. The bus arrives at the airport at 13 24.

How many minutes does the bus journey take?

Answer(a) ......................................... min [1]

(b) Colin’s fl ight from Sydney to Auckland leaves at 14 45 local time and takes 3 hours 20 minutes. The time in Auckland is 2 hours ahead of the time in Sydney.

What is the local time in Auckland when his fl ight arrives?

Answer(b) ................................................ [2]__________________________________________________________________________________________

6

0580/12/M/J/14© UCLES 2014

13 (a) The scale drawing shows the positions of two villages, A and B. The scale is 1 centimetre represents 200 metres.

North

North

B

A Scale: 1 cm to 200 m

(i) Measure the bearing of B from A.

Answer(a)(i) ................................................ [1]

(ii) Work out the actual distance from A to B.

Answer(a)(ii) ............................................ m [1]

(b) The post box in Village A has a volume of 84 000 cm3. The post box in Village B has a volume of 0.1 m3.

Which post box has the greater volume? Show how you decide.

Answer(b) Post box in Village ............... [1]__________________________________________________________________________________________

7


14 V = 31 Ah

(a) Find V when A = 15 and h = 7 .

Answer(a) V = ................................................ [1]

(b) Make h the subject of the formula.

Answer(b) h = ................................................ [2]__________________________________________________________________________________________

15 At the beginning of July, Kim had a mass of 63 kg. At the end of July, his mass was 61 kg.

Calculate the percentage loss in Kim’s mass.

Answer ............................................ % [3] __________________________________________________________________________________________

16 Without using your calculator, work out 65 – 2 2

1 11#` j.

Write down all the steps of your working.

Answer ................................................ [3]__________________________________________________________________________________________

8

0580/12/M/J/14© UCLES 2014

17 A plane is travelling at 180 metres per second.

How many minutes will it take the plane to travel 800 km? Give your answer correct to the nearest minute.

Answer ......................................... min [4]__________________________________________________________________________________________

18 (a) The probability that FC Victoria wins the cup is 0.18 .

Work out the probability that they do not win the cup.

Answer(a) ................................................ [1]

(b) After training, the shirts are washed. There are 5 red, 3 blue and 6 green shirts. One shirt is taken from the washing machine at random.

Find the probability that it is

(i) red,

Answer(b)(i) ................................................ [1]

(ii) blue or green,

Answer(b)(ii) ................................................ [1]

(iii) white.

Answer(b)(iii) ................................................ [1]__________________________________________________________________________________________

9


19 similar acute line perpendicular radius

refl ex obtuse parallel congruent isosceles

Choose the correct word from this box to complete each of these statements.

(a)

Angle A is ..................................... [1]

(b)

Angle B is ..................................... [1]

(c)

These lines are ..................................... [1]

(d)

These lines are ..................................... [1]__________________________________________________________________________________________

A

B

10

0580/12/M/J/14© UCLES 2014

20

6.7 cm

NOT TOSCALE

Each edge of this cube is 6.7 cm long.

Work out

(a) the volume,

Answer(a) ......................................... cm3 [2]

(b) the surface area.

Answer(b) ......................................... cm2 [2]__________________________________________________________________________________________

11


21

O63°

A

B

C

NOT TOSCALE

The diagram shows a circle, centre O with diameter AB = 15 cm. AC is a tangent to the circle at A and angle AOC = 63°.

(a) Calculate the area of the circle.

Answer(a) ......................................... cm2 [2]

(b) (i) Work out the size of angle ACO.

Answer(b)(i) Angle ACO = ................................................ [2]

(ii) Give one geometrical reason for your answer to part (b)(i).

Answer(b)(ii) ...............................................................................................................................

..................................................................................................................................................... [1]__________________________________________________________________________________________

12

0580/12/M/J/14© UCLES 2014



BLANK PAGE





MATHEMATICS 0580/13


1 hour




[Turn overIB14 06_0580_13/RP© UCLES 2014

*7662998175*



2

0580/13/M/J/14© UCLES 2014

1–3°C 8°C –19°C 42°C –7°C

Write down the lowest temperature from this list.

Answer ........................................... °C [1]__________________________________________________________________________________________

2 Change 6450 cm into metres.

Answer ............................................ m [1]__________________________________________________________________________________________

3

52°

x°

NOT TOSCALE

In the diagram, a straight line intersects two parallel lines.

Find the value of x.

Answer x = ................................................ [1]__________________________________________________________________________________________

4 Calculate.

0.256.2 34.8

-

-

Answer ................................................ [1]__________________________________________________________________________________________

5 Write down the value of 70.

Answer ................................................ [1]__________________________________________________________________________________________

3


6 Write 45 000 in standard form.

Answer ................................................ [1]__________________________________________________________________________________________

7 Four faces of a cube are drawn on the grid.

Complete the net of this cube.

[1]__________________________________________________________________________________________

8 Write down all the prime numbers that are greater than 30 and less than 40.

Answer ................................................ [1]__________________________________________________________________________________________

9 a =

43-

e o b = 26e o

Write each of the following as a single vector.

(a) 2a

Answer(a) f p [1]

(b) a – b

Answer(b) f p [1]

__________________________________________________________________________________________

4

0580/13/M/J/14© UCLES 2014

10 (a)1 4 8 12 27 40

Write down the number from this list which is both a cube number and has a factor of 4.

Answer(a) ................................................ [1]

(b) 1258 is a multiple of 34.

Write down a different multiple of 34 between 1200 and 1300.

Answer(b) ................................................ [1]__________________________________________________________________________________________

11–3 –5 1 0 3

Three different numbers from the list are added together to give the smallest possible total.

Complete the sum below.

................. + ................. + ................. = .................[2]

__________________________________________________________________________________________

12 The area of a square is 36 cm2.

Calculate the perimeter of this square.

Answer .......................................... cm [2]__________________________________________________________________________________________

13 The mean of fi ve numbers is 6. Four of the numbers are 3, 4, 5, and 10.

Work out the number that is missing from the list.

Answer ................................................ [2]__________________________________________________________________________________________

5


14 Find the value of 3a – 5b when a = –4 and b = 2 .

Answer ................................................ [2]__________________________________________________________________________________________

15 Celine buys a bag of 24 tulip bulbs. There are 8 red bulbs and 5 white bulbs. All of the other bulbs are yellow.

Celine chooses a bulb at random from the bag.

(a) Write down the probability that the bulb is red or white.

Answer(a) ................................................ [1]

(b) Write down the probability that the bulb is yellow.

Answer(b) ................................................ [1]__________________________________________________________________________________________

16 Find the fraction that is half-way between 21 and 3

2 .

Answer ................................................ [2]__________________________________________________________________________________________

6

0580/13/M/J/14© UCLES 2014

17 Using a straight edge and compasses only, construct the perpendicular bisector of AB. All construction arcs must be clearly shown.

A

B

[2]__________________________________________________________________________________________

18 Michelle sells ice cream. The table shows how many of the different fl avours she sells in one hour.

Flavour Vanilla Strawberry Chocolate Mango

Number sold 6 8 9 7

Michelle wants to show this information in a pie chart.

Calculate the sector angle for mango.

Answer ................................................ [2]__________________________________________________________________________________________

7


19 Chris changes $1350 into euros (€) when €1 = $1.313 .

Calculate how much he receives.

Answer € ................................................. [2]__________________________________________________________________________________________

20

A

y

x

7

6

5

4

3

2

1

–1

–2

–3

0–1 1 2 3 4 5–2–3–4–5–6–7

Draw the image of triangle A after a translation by the vector 43

-e o. [2]

__________________________________________________________________________________________

8

0580/13/M/J/14© UCLES 2014

21 Each exterior angle of a regular polygon is 30°.

Work out the number of sides the polygon has.

Answer ................................................ [2]__________________________________________________________________________________________

22

46°

74° 60°46°

x°

9.65 cm9.65 cm

8.69 cm

7.22 cmy cm

NOT TOSCALE

These two triangles are congruent. Write down the value of

(a) x,

Answer(a) x = ................................................ [1]

(b) y.

Answer(b) y = ................................................ [1]__________________________________________________________________________________________

9


23 Without using a calculator, work out 1 41 – 9

7 .

Write down all the steps in your working.

Answer ............................................... [3]__________________________________________________________________________________________

24 Solve the simultaneous equations. 2x + 3y = 29 5x + y = 27

Answer x = ................................................

y = ................................................ [3]__________________________________________________________________________________________

10

0580/13/M/J/14© UCLES 2014

25

10 00 10 04 10 08 10 12 10 16

Time

Distance(km)

10 20 10 24 10 28 10 32

4

3

2

1

0

Town

Home

William Toby

Toby and William cycled into town. Their journeys are shown on the travel graph.

(a) For how many minutes did Toby stop on his journey into town?

Answer(a) ......................................... min [1]

(b) Explain what happened at 10 20.

Answer(b) ........................................................................................................................................... [1]

(c) Work out how long William took to cycle into town.

Answer(c) ......................................... min [1]

(d) Calculate William’s speed in km/h.

Answer(d) ....................................... km/h [2]__________________________________________________________________________________________

11


26 (a) Factorise completely. 15a3 – 5ab

Answer(a) ................................................ [2]

(b) Simplify. 3x2y3 × x4y

Answer(b) ................................................ [2]

(c) Multiply out the brackets and simplify. 3(x – 2) – 4(2x – 3)

Answer(c) ................................................ [2]

(d) Solve the equation. 8x + 9 = 3(x + 8)

Answer(d) x = ................................................ [3]__________________________________________________________________________________________

12

0580/13/M/J/14© UCLES 2014



BLANK PAGE





MATHEMATICS 0580/31


2 hours






*0224327052*


2

0580/31/M/J/14© UCLES 2014

1 (a) The angles in a triangle are in the ratio 3 : 4 : 8 .

(i) Show that the smallest angle of the triangle is 36°.

Answer(a)(i)

[2]

(ii) Work out the other two angles of the triangle.

Answer(a)(ii) ............................. and ............................. [2]

(b) Another triangle ABC has angle BAC = 35° and angle ABC = 65°.

(i) Using a protractor and straight edge complete an accurate drawing of the triangle ABC. The side AB has been drawn for you.

A B[2]

(ii) Measure the length, in centimetres, of the shortest side of your triangle.

Answer(b)(ii) .......................................... cm [1]

(c) A different triangle has base 7.0 cm and height 5.6 cm. Calculate the area of this triangle, giving the units of your answer.

Answer(c) ....................... ..................... [3]__________________________________________________________________________________________

3


2 (a) From the integers 50 to 100, fi nd

(i) a multiple of 43,

Answer(a)(i) ................................................ [1]

(ii) a factor of 165,

Answer(a)(ii) ................................................ [1]

(iii) an odd number that is also a square number,

Answer(a)(iii) ................................................ [1]

(iv) a number which is a square number and also a cube number.

Answer(a)(iv) ................................................. [1]

(b) (i) Find the square root of 5929.

Answer(b)(i) ................................................ [1]

(ii) Find the lowest common multiple of 24 and 30.

Answer(b)(ii) ................................................ [2]

(c) Elena goes on a journey to the North Pole. She leaves home at 7 am on 15 July and arrives at the North Pole at 10 pm on 27 July.

How long, in days and hours, did her journey take?

Answer(c) ....................... days ....................... hours [2]__________________________________________________________________________________________

4

0580/31/M/J/14© UCLES 2014

3

S

P

T

y

x–2 20 4 6 81 3 5 7–4–6–8 –1–3–5–7

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

The diagram shows two shapes, S and T, on a 1 cm2 grid. P is the point (–2, 0).

5


(a) (i) Write down the mathematical name of shape S.

Answer(a)(i) ................................................ [1]

(ii) How many lines of symmetry does shape S have?

Answer(a)(ii) ................................................ [1]

(b) Describe the single transformation that maps shape S onto shape T.

Answer(b) ...........................................................................................................................................

............................................................................................................................................................. [2]

(c) On the grid,

(i) draw the refl ection of shape S in the y-axis, [2]

(ii) draw the rotation of shape S about (0, 0) through 90° anti-clockwise. [2]

(d) On the grid, draw the enlargement of shape S with scale factor 2 and centre P (–2, 0). Label the image E. [2]

(e) (i) Work out the area of shape S.

Answer(e)(i) ......................................... cm2 [2]

(ii) How many shapes, identical to shape S, will fi ll shape E completely?

Answer(e)(ii) ................................................ [1]

(iii) Work out the area of shape E.

Answer(e)(iii) ......................................... cm2 [1]__________________________________________________________________________________________

6

0580/31/M/J/14© UCLES 2014

4 Denzil grows tomatoes. He selects a random sample of 25 tomatoes. The mass of each tomato, to the nearest 5 grams, is shown below.

55 65 50 75 6580 70 70 55 6070 60 65 50 7565 70 75 80 7055 65 70 80 55

(a) (i) Complete the frequency table. You may use the tally column to help you.

Mass(grams) Tally Frequency

50

55

60

65

70

75

80

[2]

(ii) Write down the mode.

Answer(a)(ii) ............................................. g [1]

(iii) Find the range.

Answer(a)(iii) ............................................. g [1]

(iv) Show that the mean mass is 66 g.

Answer(a)(iv)

[2]

7


(b) Denzil picks 800 tomatoes. 4% of the 800 tomatoes are damaged.

How many of these tomatoes are not damaged?

Answer(b) ................................................ [2]

(c) Denzil sells 750 of his tomatoes.

(i) The mean mass of a tomato is 66 g.

Calculate the mass of the 750 tomatoes in kilograms.

Answer(c)(i) ........................................... kg [3]

(ii) Denzil sells his tomatoes at $1.40 per kilogram.

Calculate the total amount he receives from selling all the 750 tomatoes.

Answer(c)(ii) $ ................................................ [1]

(iii) The cost of growing these tomatoes was $33.

Calculate his percentage profi t.

Answer(c)(iii) ............................................ % [3]__________________________________________________________________________________________

8

0580/31/M/J/14© UCLES 2014

5 Use a ruler and compasses only in parts (a), (c) and (d) of this question. Show all your construction arcs.

A

B

C

D

E

P

100 m

100 m

120 m

150 m

Scale: 1 cm to 20 m

Maria owns a farm. The scale drawing shows part of the boundary of the farm. The scale is 1 centimetre represents 20 metres.

9


(a) The point F is such that AF = 140 m and EF = 160 m. Angle BAF and angle DEF are both obtuse angles.

Complete the scale drawing of the farm boundary ABCDEF. [2]

(b) Write down the name of the polygon ABCDEF.

Answer(b) ................................................ [1]

(c) (i) Construct the perpendicular bisector of the side CD. [2]

(ii) Construct the bisector of angle ABC. [2]

(iii) All the farm buildings are within a region that is

● nearer to C than to D and ● nearer to BC than to BA.

Shade the region containing the farm buildings. [1]

(d) A fence post, P, is shown on the boundary DE.

(i) Construct the locus of points that are 50 m from P and also inside the farm boundary. [2]

(ii) A region for keeping pigs is within 50 m of P and inside the farm boundary.

Calculate the actual area for keeping pigs.

Answer(d)(ii) ........................................... m2 [2]__________________________________________________________________________________________

10

0580/31/M/J/14© UCLES 2014

6 (a) (i) Complete the table of values for y = x8 , x ≠ 0 .

x –8 –4 –2 –1 1 2 4 8

y –2 2

[3]

(ii) On the grid, draw the graph of y = x8 for –8 Ğ x Ğ –1 and 1 Ğ x Ğ 8 .

y

x

8

6

4

2

–2

–4

–6

–8

0–2–4–6–8 6 842

[4]

11


(iii) Write down the order of rotational symmetry of your graph.

Answer(a)(iii) ................................................ [1]

(b) (i) Complete this table of values for y = 1.5x + 3 .

x –6 –4 –2 0 2

y –6 3

[2]

(ii) On the grid, draw the graph of y = 1.5x + 3 . [1]

(c) Use your graphs to solve the equation x8 = 1.5x + 3 .

Answer(c) x = .......................... or x = .......................... [2]

(d) Write down the gradient of the graph of y = 1.5x + 3 .

Answer(d) ................................................ [1]__________________________________________________________________________________________

12

0580/31/M/J/14© UCLES 2014

7 120 people are asked how they travel to work. The pie chart shows the results.

Bus

Car

Cycle

Walk

(a) (i) Show that 45 people travel by car.

Answer(a)(i)

[2]

(ii) A person is chosen at random from the 120 people.

Find the probability that this person travels to work by bus or by car.

Answer(a)(ii) ................................................ [2]

13


(b) One year later, the same 120 people were again asked how they travel to work.

Here is the information.

Number of people

Walk x

Cycle 31

Bus 17 more than the number of people who walk

Car 2 times the number of people who walk

(i) Use this information to complete the following equation, in terms of x.

............................................................................................. = 120 [3]

(ii) Solve the equation to fi nd the number of people who walk to work.

Answer(b)(ii) ................................................ [3]__________________________________________________________________________________________

14

0580/31/M/J/14© UCLES 2014

8 (a) Write down an expression for the total mass of c cricket balls, each weighing 160 grams, and f footballs, each weighing 400 grams.

Answer(a) ...................................... grams [2]

(b) Expand and simplify. 3(2x – 5y) – 4(x – 2y)

Answer(b) ................................................ [2]

(c) Factorise completely. 5x2y – 20x

Answer(c) ................................................ [2]

(d) Solve the simultaneous equations. 3x + 4y = 7 4x – 3y = 26

Answer(d) x = ................................................

y = ................................................ [4]__________________________________________________________________________________________

15


9 (a) For these sequences, write down the next two terms and the rule for fi nding the next term.

(i) 84, 75, 66, 57, . . .

Answer(a)(i) ................. , ................. rule .................................................................................. [3]

(ii) 2, 6, 18, 54, . . .

Answer(a)(ii) ................. , ................. rule ................................................................................. [3]

(b) For the sequence in part (a)(i),

(i) write down an expression, in terms of n, for the n th term,

Answer(b)(i) ................................................ [2]

(ii) fi nd the 21st term.

Answer(b)(ii) ................................................ [2]__________________________________________________________________________________________

16

0580/31/M/J/14© UCLES 2014



BLANK PAGE





MATHEMATICS 0580/32


2 hours





*4942783219*



2

0580/32/M/J/14© UCLES 2014

1 (a) Here is a list of numbers.

2 4 5 8 9 12

Write down all the numbers from this list which are

(i) odd,

Answer(a)(i) ................................................ [1]

(ii) square,

Answer(a)(ii) ................................................ [1]

(iii) cube,

Answer(a)(iii) ................................................ [1]

(iv) prime.

Answer(a)(iv) ................................................ [1]

(b) Write one of these symbols >, < or = to make each statement true.

π .................... 722

2^ h2 .................... 2

1 11+ .................... 2

(–1)2 .................... –1[2]

(c) Put one pair of brackets in each statement to make it true.

(i) 16 + 8 ÷ 4 – 2 = 4 [1]

(ii) 16 + 8 ÷ 4 – 2 = 20 [1]

3


(d) (i) Write 84 as a product of its prime factors.

Answer(d)(i) ................................................ [2]

(ii) Find the highest common factor of 84 and 24.

Answer(d)(ii) ................................................ [2]

(iii) Find the lowest common multiple of 84 and 24.

Answer(d)(iii) ................................................ [2]

(e) Here are the fi rst four terms of a sequence.

3 7 11 15

(i) Write down the next term in this sequence.

Answer(e)(i) ................................................ [1]

(ii) Explain how you found your answer.

Answer(e)(ii) ............................................................................................................................... [1]

(iii) Write down an expression for the n th term of this sequence.

Answer(e)(iii) ................................................ [2]

(iv) Explain why 125 is not in this sequence.

Answer(e)(iv) ..............................................................................................................................

..................................................................................................................................................... [1]__________________________________________________________________________________________

4

0580/32/M/J/14© UCLES 2014

2

A

D C

B

180 cm

120 cm

240 cm

NOT TOSCALE

The diagram shows the cross section ABCD of a shed. AD = 180 cm, DC = 120 cm and BC = 240 cm.

(a) (i) Write down the mathematical name of the cross section ABCD.

Answer(a)(i) ................................................ [1]

(ii) Calculate the area of the cross section ABCD. Give the units of your answer.

Answer(a)(ii) ........................... .............. [3]

(iii) The shed is a prism of length 2.5 metres.

Calculate the volume of the shed. Give your answer in cubic metres.

Answer(a)(iii) ........................................... m3 [2]

5


(iv) Calculate the length AB.

Answer(a)(iv) AB = .......................................... cm [3]

(b) Here is a scale drawing of a garden, GHIJ. The scale is 1 centimetre represents 5 metres.

I

H

G J

Scale: 1 cm to 5 m

The shed is placed in the garden so that it is

● nearer to GJ than to IJ and ● within 20 m of H.

Using a ruler and compasses only, construct and shade the region where the shed can be placed. Show all your construction arcs. [5]__________________________________________________________________________________________

6

0580/32/M/J/14© UCLES 2014

3 (a) Draw the line of symmetry on the shape below.

[1]

(b) Write down the order of rotational symmetry of the shape below.

Answer(b) ................................................ [1]

(c) (i)

x°157°

72° NOT TOSCALE

Work out the value of x.

Answer(c)(i) x = ................................................ [1]

(ii)

y°

49°

54°

NOT TOSCALE

Work out the value of y.

Answer(c)(ii) y = ................................................ [2]

7


(d)A

B C

O34°

NOT TOSCALE

AC is a diameter of the circle, centre O.

Calculate angle ACB.

Answer(d) Angle ACB = ................................................ [2]

(e) The diagram below shows parts of shape P and shape Q. Shape P is a regular hexagon and shape Q is another regular polygon. The two shapes have one side in common.

100°

100°

QP

NOT TOSCALE

Find the number of sides in shape Q. Show each step of your working.

Answer(e) ................................................ [5]__________________________________________________________________________________________

8

0580/32/M/J/14© UCLES 2014

4 Paolo’s football team played 46 games. The pictogram shows some information about the number of goals scored by Paolo’s football team. They did not score any goals in fi ve games.

Numberof goals Number of games

0

1

2

3

4

5

6

Key: = .................. games

(a) (i) Complete the key. [1]

(ii) Paolo’s team scored 2 goals in each of nine games.

Complete the pictogram. [1]

(b) (i) Write down the modal number of goals.

Answer(b)(i) ................................................ [1]

(ii) Find the median number of goals.

Answer(b)(ii) ................................................ [1]

(iii) Find the range.

Answer(b)(iii) ................................................ [1]

(iv) One of the 46 games is chosen at random.

Work out the probability that Paolo’s team scored at least 4 goals.

Answer(b)(iv) ................................................ [2]

9


(c) The table shows the total goals scored and the total points gained by 10 teams.

Team A B C D E F G H I J

Goals 31 40 46 50 43 92 60 84 68 87

Points 36 35 52 56 72 78 59 70 61 75

(i) Complete the scatter diagram. The fi rst six points have been plotted for you. [2]

80

70

60

50

40

3030 40 50 60 70

Goals

80 90 100

Points

(ii) Draw the line of best fi t. [1]

(iii) What type of correlation is shown?

Answer(c)(iii) ................................................ [1]

(iv) Use your line of best fi t to estimate the total points gained by a team scoring 75 goals.

Answer(c)(iv) ................................................ [1]

(v) Which team only scores a few goals but gains a lot of points?

Answer(c)(v) ................................................ [1]__________________________________________________________________________________________

10

0580/32/M/J/14© UCLES 2014

5 (a) Jasmine works for 38 hours each week and she earns $12.15 each hour.

(i) Calculate her earnings in one week.

Answer(a)(i) $ ................................................ [1]

(ii) Jasmine pays 14% of her earnings in tax.

Calculate how much money she has left after tax is paid.

Answer(a)(ii) $ ................................................ [2]

(iii) She pays 31 of the money she has left after tax in rent.

Calculate how much rent she pays in one year (52 weeks).

Answer(a)(iii) $ ................................................ [2]

(iv) In one week she spends $140 on food and electricity in the ratio

food : electricity = 3 : 2 .

Calculate how much she spends on food.

Answer(a)(iv) $ ................................................ [2]

(b) Jasmine buys a watch for 10 000 Japanese Yen (¥). The exchange rate is $1 = ¥ 80.4 .

Calculate the cost of this watch in dollars, giving your answer correct to the nearest dollar.

Answer(b) $ ................................................ [3]__________________________________________________________________________________________

11


6 (a) Complete the table of values for y = x2 + 2x – 3 .

x –4 –3 –2 –1 0 1 2 3 4

y 0 –3 –4 –3 0 5 21[2]

(b) On the grid, draw the graph of y = x2 + 2x – 3 for –4 Ğ x Ğ 4 .

y

x

25

20

15

10

5

–5

0 1 2 3 4–1–2–3–4

[4]

(c) On the grid, draw the line y = 10 . [1]

(d) Use your graphs to solve the equation x2 + 2x – 3 = 10 for –4 Y x Y 4 .

Answer(d) x = ................................................ [1]__________________________________________________________________________________________

12

0580/32/M/J/14© UCLES 2014

7 (a)

5p + 3r7p – 6r

p + 2r

NOT TOSCALE

Write an expression for the perimeter of this triangle. Give your answer in its simplest form.

Answer(a) ................................................ [2]

(b) Another triangle has a perimeter 12w – 2z .

Calculate this perimeter when w = 16 and z = –3.

Answer(b) ................................................ [2]

(c) Solve.

(i) 5a = 32

Answer(c)(i) a = ................................................ [1]

(ii) 5b + 23 = 8

Answer(c)(ii) b = ................................................ [2]

(iii) 5c + 7 = 2(c – 10)

Answer(c)(iii) c = ................................................ [3]

13


(d) (i) Multiply out the brackets. 8(2x + 3)

Answer(d)(i) ................................................ [1]

(ii) Factorise completely. 6x2 – 12x

Answer(d)(ii) ................................................ [2]

(e) Write each expression in its simplest form.

(i) 3q4 × 5q2

Answer(e)(i) ................................................ [2]

(ii) t 8 ÷ t

2

Answer(e)(ii) ................................................ [1]__________________________________________________________________________________________

14

0580/32/M/J/14© UCLES 2014

8 (a) Work out.

(i) 5 3-

2e o

Answer(a)(i) f p [1]

(ii) 5

4

-e o +

1

3

-e o

Answer(a)(ii) f p [1]

(b) A translation moves the point (6, 3) to the point (2, 8).

Work out the vector which represents this translation.

Answer(b) f p [1]

15


(c) A point P is translated by the vector 3

4-e o to the point (7, –2).

Find the co-ordinates of P. You may use the grid below to help you.

Answer(c) (.................... , ....................) [1]

__________________________________________________________________________________________


16

0580/32/M/J/14© UCLES 2014



9

A

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6–7 –5 –4 –3 –2 –1 10 2 3 4 5 6 7x

y

B

(a) On the grid, draw the image of triangle A after the following transformations.

(i) Refl ection in the x-axis. [1]

(ii) Rotation about (0, 0) through 180°. [2]

(iii) Translation by the vector 5-

3e o. [2]

(b) Describe fully the single transformation that maps triangle A onto triangle B.

Answer(b) ...........................................................................................................................................

............................................................................................................................................................. [3]





MATHEMATICS 0580/33


2 hours





*9994985227*



2

0580/33/M/J/14© UCLES 2014

1 (a)

D

A

B

C

y

x

7

6

5

4

3

2

1

–1

–2

–3

–4

0–1 1 2 3 4 5 6–2–3–4

Four shapes, A, B, C and D, are shown on the grid.

Describe fully the single transformation that maps shape A onto

(i) shape B,

Answer(a)(i) ................................................................................................................................

..................................................................................................................................................... [2]

(ii) shape C,

Answer(a)(ii) ...............................................................................................................................

..................................................................................................................................................... [3]

(iii) shape D.

Answer(a)(iii) ..............................................................................................................................

..................................................................................................................................................... [3]

3


(b) (i)

Shade in one more square so that this shape has rotational symmetry of order 2. [1]

(ii)

Refl ect this shape in the line of symmetry shown. [2]__________________________________________________________________________________________

4

0580/33/M/J/14© UCLES 2014

2 A group of students take part in their school’s sports day.

(a) (i) The length, l m, that Anna throws the javelin is 23.6 metres correct to the nearest 10 centimetres.

Complete the statement about l.

Answer(a)(i) .......................... Y l < .......................... [2]

(ii) Billy throws the hammer a distance of 8 metres on his fi rst throw. His second throw is 15% further.

Calculate the distance of his second throw.

Answer(a)(ii) ............................................ m [2]

(iii) Carl runs 100 metres at a speed of 8 m/s.

Calculate the time it takes him to run 100 m.

Answer(a)(iii) .............................................. s [1]

(iv) Change Carl’s speed of 8 m/s into km/h.

Answer(a)(iv) ....................................... km/h [2]

(b) Ten students take part in both the long jump and 100 m hurdles competitions. The results are shown in the table below.

Student A B C D E F G H I J

Distance in long jump (metres) 3.25 3.60 3.75 3.90 4.10 4.20 4.30 4.40 4.65 4.70

Time for 100 m hurdles (seconds) 17.3 17.4 16.7 16.1 16.5 15.8 15.3 14.8 15.5 15.0

5


(i) Complete the scatter diagram. The fi rst six points have been plotted for you.

18.0

17.0

16.0

15.0

14.03.5 4.0 4.5 5.0 5.53.0

Distance in long jump (metres)

Time for100 m hurdles(seconds)

[2]

(ii) What type of correlation does this scatter diagram show?

Answer(b)(ii) ................................................ [1]

(iii) Describe the relationship between the distance in the long jump and the time for the 100 m hurdles.

Answer(b)(iii) .............................................................................................................................. [1]

(iv) On the grid, draw the line of best fi t. [1]

(v) Another student jumps 3.50 m in the long jump.

Use your line of best fi t to estimate the time for this student in the 100 m hurdles.

Answer(b)(v) .............................................. s [1]

(vi) A different student jumps 5.20 m in the long jump.

Explain why you should not use your scatter diagram to estimate their time in the 100 m hurdles.

Answer(b)(vi) .............................................................................................................................. [1]__________________________________________________________________________________________

6

0580/33/M/J/14© UCLES 2014

3 The Wong family spend the day at the zoo.

(a) The Wong family has 2 adults and 3 children aged 2, 5 and 11 years old.

Admission

Adults $8.50Children 11-16 years $6.00Children 3-10 years $4.50Children under 3 years FREE

Mr Wong pays for his family to go into the zoo using a $50 note.

Work out the change he receives.

Answer(a) $ ................................................ [3]

(b) The dolphin show fi nishes at 11 05. It lasts for 1 hour and 20 minutes.

Write down the time the dolphin show starts.

Answer(b) ................................................ [1]

(c) Torty the tortoise was born on 27 December 1898.

Work out how many years old she was on 3 January 2003.

Answer(c) ....................................... years [1]

(d) Last year, the ratio snakes : lizards = 3 : 5 . There were 45 lizards.

(i) Work out how many snakes there were last year.

Answer(d)(i) ................................................ [2]

(ii) This year, there are 3 more snakes and the same number of lizards.

Write down the new ratio snakes : lizards. Give your answer in its simplest form.

Answer(d)(ii) ....................... : ....................... [2]

(e) Mr Wong hires a vehicle to drive around the zoo. The cost is $25 for the fi rst hour and $7.50 for every extra half hour. He pays $85 altogether.

For how long does he hire the vehicle?

Answer(e) ...................................... hours [3]

7


(f) Mrs Wong wants to buy some food for the giraffes.

Small Bag

225g

60 cents

Medium Bag

250g

70 cents

Large Bag

325g

90 cents

Work out which bag is the best value for money. Show how you decide.

Answer(f) ................................................ [3]

(g) The diagram shows a map of the zoo. The scale is 1 centimetre represents 50 metres.

North

Entrance

Flamingos

North

Exit

Scale: 1 cm to 50 m

(i) Measure the bearing of the fl amingos from the entrance.

Answer(g)(i) ................................................ [1]

(ii) Xanthe looks after all the animals within 200 m of the exit.

Draw accurately the locus of points inside the zoo which are 200 m from the exit. [2]

(iii) A shop, S, is on a bearing of 212° from the entrance and a bearing of 293° from the exit.

Mark the point S on the map. [3]__________________________________________________________________________________________

8

0580/33/M/J/14© UCLES 2014

4 The ages of 15 children who go to a swimming club are shown below.

10 11 10 12 12 13 11 12 12 12 12 10 11 11 11

(a) Complete the frequency table. You may use the tally column to help you.

Age Tally Frequency

10

11

12

13[2]

(b) For the ages of the 15 children, fi nd

(i) the range,

Answer(b)(i) ................................................ [1]

(ii) the mode,

Answer(b)(ii) ................................................ [1]

(iii) the median,

Answer(b)(iii) ................................................ [1]

(iv) the mean.

Answer(b)(iv) ................................................ [2]

(c) One child is chosen at random from the group.

Write down the probability that the child’s age is

(i) 10,

Answer(c)(i) ................................................ [1]

(ii) more than 13.

Answer(c)(ii) ................................................ [1]__________________________________________________________________________________________

9


5 (a) (i) Write down the name of a solid which is not a prism.

Answer(a)(i) ................................................ [1]

(ii) A prism has a cross-sectional area, A, and height, h.

Write down an expression, in terms of A and h, for the volume of the prism.

Answer(a)(ii) ................................................ [1]

(b) The volume, V, of a cylinder with radius r and height h is V = πr2h .

(i) Calculate the volume of a cylinder with radius 3 cm and height 12 cm.

Answer(b)(i) ......................................... cm3 [2]

(ii) Ravi puts 150 identical marbles in the cylinder. He fi lls the cylinder to the top with 160 cm3 of water.

Find the volume of one marble. Give your answer correct to 2 signifi cant fi gures.

Answer(b)(ii) ......................................... cm3 [4]

(iii) Make r the subject of the formula V = πr2h .

Answer(b)(iii) r = ................................................ [2]__________________________________________________________________________________________

10

0580/33/M/J/14© UCLES 2014

6y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

0–1 1 2 3 4 5 6–2–3–4–5–6

(a) On the grid, draw the graphs of

(i) y = 5, [1]

(ii) x = –3. [1]

(b) (i) Write down the co-ordinates of the point of intersection of y = 5 and x = –3.

Answer(b)(i) (...................... , ......................) [1]

(ii) Write down the equation of a line parallel to y = 5.

Answer(b)(ii) ................................................ [1]

11


(c) (i) Complete the table of values for the function y = x2 – 3x .

x –2 –1 0 1 2 3 4 5

y 4 0 0 4[2]

(ii) On the grid, draw the graph of y = x2 – 3x for –2 Y x Y 5 .

y

x

11

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

0–1 1 2 3 4 5 6–2–3

[4]

(iii) Write down the co-ordinates of the lowest point of the graph.

Answer(c)(iii) (...................... , ......................) [1]__________________________________________________________________________________________

12

0580/33/M/J/14© UCLES 2014

7 Today it is Simon’s birthday.

(a) Simon is x years old. Katy is twice as old as Simon. Bob is 8 years younger than Simon.

(i) Write expressions, in terms of x, for the ages of Katy and Bob.

Answer(a)(i) Katy ................................................

Bob ................................................ [2]

(ii) The sum of their three ages is 40 years.

Write an equation in terms of x.

Answer(a)(ii) ................................................ [1]

(iii) Solve your equation for x.

Answer(a)(iii) x = ................................................ [2]

(b) Simon’s birthday cake weighs 600 grams.

He eats 81 of the cake.

Katy eats 25% of the cake. Bob eats 0.3 of the cake.

Find the weight of the cake that is left.

Answer(b) ............................................. g [4]

13


(c) Aunty Millie gives Simon $150 for his birthday. He invests the money in a bank at a rate of 6% per year compound interest.

Calculate the total amount Simon will have after 3 years.

Answer(c) $ ................................................. [3]

(d) One of Simon’s presents is a bag of sweets. He decides to eat the sweets in a sequence. On day 1 he eats 1 sweet, on day 2 he eats 5 sweets, on day 3 he eats 9 sweets and so on.

(i) Describe in words the rule for continuing the sequence 1, 5, 9, 13, 17 ..... .

Answer(d)(i) ................................................................................................................................ [1]

(ii) Write down an expression for the number of sweets he eats on day n.

Answer(d)(ii) ................................................ [2]__________________________________________________________________________________________

14

0580/33/M/J/14© UCLES 2014

8 (a)

h

10 cm

NOT TOSCALE

The triangle has an area of 30 cm2 and a base of 10 cm.

Calculate the perpendicular height h of the triangle.

Answer(a) h = ......................................... cm [2]

(b)NOT TOSCALE

D C

A B

8 cm

14 cm

7 cm

AB is parallel to CD. AB is 14 cm and CD is 8 cm. The perpendicular distance between AB and CD is 7 cm.

(i) Write down the mathematical name for the quadrilateral ABCD.

Answer(b)(i) ................................................ [1]

(ii) Calculate the area of ABCD.

Answer(b)(ii) ......................................... cm2 [2]

15


(c) An isosceles triangle has an angle of 40°. Tikka draws the triangle with angles 40°, 70° and 70°. Kanwarpreet draws a different correct triangle.

What angles did Kanwarpreet use?

Answer(c) 40°, .............. , .............. [2]__________________________________________________________________________________________


16

0580/33/M/J/14© UCLES 2014



9

A

C

B

O

NOT TOSCALE

The diagram shows a circle with diameter AB and centre O. C is a point on the circumference of the circle.

(a) Explain how you know that angle ACB is 90° without having to measure it.

Answer(a) ........................................................................................................................................... [1]

(b) AB = 13 cm and AC = 5 cm.

Calculate the length BC.

Answer(b) BC = .......................................... cm [3]

(c) Calculate angle ABC.

Answer(c) Angle ABC = ................................................ [2]





MATHEMATICS 0580/11

Paper 1 (Core) October/November 2014

1 hour







*9883604560*

2

0580/11/O/N/14© UCLES 2014

1y

x

5

4

3

2

1

–1

–2

–3

–4

–5

0–1 1 2 3 4–2–3–4–5–6

A

B

Points A and B are shown on the grid.

Write as a column vector.Answer f p [1]

__________________________________________________________________________________________

2 Write 15.0782 correct to

(a) one decimal place,

Answer(a) ................................................ [1]

(b) the nearest 10.

Answer(b) ................................................ [1]__________________________________________________________________________________________

3

0580/11/O/N/14© UCLES 2014 [Turn over

3

Write down the letters in the word above that have

(a) exactly one line of symmetry,

Answer(a) ................................................ [1]

(b) rotational symmetry of order 2.

Answer(b) ................................................ [1]__________________________________________________________________________________________

4

A

B

C

105°

k°

98°

NOT TOSCALE

In the diagram, all four lines are straight. Angle A = 105°, angle B = 90° and angle C = 98°.

Find the value of k.

Answer k = ................................................ [2]__________________________________________________________________________________________

4

0580/11/O/N/14© UCLES 2014

5 These are the heights, correct to the nearest centimetre, of 12 children.

132 114 151 130 132 145 163 142 153 170 132 125

Find the median height.

Answer .......................................... cm [2]__________________________________________________________________________________________

6 Write the following in order of size, smallest fi rst.

π 3.14 722 3.142 3

Answer ..................... < ..................... < ..................... < ..................... < ..................... [2] smallest__________________________________________________________________________________________

7 Without using a calculator, work out 41 + 6

1 .

Write down all the steps in your working and give your answer as a fraction in its simplest form.

Answer ................................................ [2]__________________________________________________________________________________________

5


8 Factorise completely. 8w2x – 12wy

Answer ................................................ [2]__________________________________________________________________________________________

9 A cylinder has radius 3.6 cm and height 16 cm.

Calculate the volume of the cylinder.

Answer ......................................... cm3 [2]__________________________________________________________________________________________

10 Cheryl recorded the midday temperatures in Seoul for one week in January.

Day Mon Tue Wed Thu Fri Sat Sun

Temperature (°C) –4 –5 –3 –11 –8 –3 –1

(a) Write down the mode.

Answer(a) ........................................... °C [1]

(b) On how many days was the temperature lower than the mode?

Answer(b) ................................................ [1]__________________________________________________________________________________________

6

0580/11/O/N/14© UCLES 2014

11 Simplify. 10x – 15 – 6x + 8

Answer ................................................ [2]__________________________________________________________________________________________

12 (a) Write down a 2-digit odd number that is a factor of 182.

Answer(a) ................................................ [1]

(b) Find all the prime factors of 182.

Answer(b) ................................................ [2]__________________________________________________________________________________________

13 (a) Write 2.8 × 102 as an ordinary number.

Answer(a) ................................................ [1]

(b) Work out 2.5 × 108 × 2 × 10–2. Give your answer in standard form.

Answer(b) ................................................ [2]__________________________________________________________________________________________

7


14 To hire a bicycle it costs $6 for each day, plus a fi xed charge of $15.

(a) Maria pays $39 to hire a bicycle.

How many days does she hire it for?

Answer(a) ........................................ days [2]

(b) Write down a formula for the cost, C dollars, to hire a bicycle for d days.

Answer(b) C = ................................................ [1]__________________________________________________________________________________________

15

140°

NOT TOSCALE

A B

C

The diagram shows two sides, AB and BC, of a regular polygon. Angle ABC = 140°.

Find the number of sides of this regular polygon.

Answer ................................................ [3]__________________________________________________________________________________________

8

0580/11/O/N/14© UCLES 2014

16

OA

B

E

C

D

x°

y°

24°

NOT TOSCALE

The diagram shows a circle with centre O. ED is a tangent to the circle at C. AB is parallel to ED and angle ACO = 24°.

Find the value of

(a) x,

Answer(a) x = ................................................ [1]

(b) y.

Answer(b) y = ................................................ [2]__________________________________________________________________________________________

9


17 Dominic invests $850 at a rate of 3.5% per year compound interest.

Calculate the total amount he has after 3 years.

Answer $ ................................................. [3]__________________________________________________________________________________________

18 On a ship, the price of a gift is 24 euros (€) or $30.

What is the difference in the price on a day when the exchange rate is €1 = $1.2378? Give your answer in dollars, correct to the nearest cent.

Answer $ ................................................. [3]__________________________________________________________________________________________

10

0580/11/O/N/14© UCLES 2014

19

4 cm

7 cm

NOT TOSCALE

The diagram shows a prism. The cross section is an equilateral triangle.

On the grid, draw an accurate net of the prism. The base is drawn for you.

[3]__________________________________________________________________________________________

11


20 Solve the simultaneous equations. 5x + 2y = 16 3x – 4y = 7

Answer x = ................................................

y = ................................................ [3]__________________________________________________________________________________________

21 (a) Find the value of 5x2 when x = –4.

Answer(a) ................................................ [2]

(b) Make x the subject of the formula y = 5x2.

Answer(b) x = ................................................ [2]__________________________________________________________________________________________


12

0580/11/O/N/14© UCLES 2014



22

Q

P16 km

9 km

North

NOT TOSCALE

The diagram shows the route of a ship that leaves a port, P. It travels due west for 16 km and then changes course to due south for 9 km.

(a) Calculate the straight line distance PQ.

Answer(a) PQ = .......................................... km [2]

(b) Use trigonometry to calculate the bearing of P from Q.

Answer(b) ................................................ [2]





MATHEMATICS 0580/12


1 hour




This document consists of 10 printed pages and 2 blank pages.



*5594379073*

2

0580/12/O/N/14© UCLES 2014

1 Insert one pair of brackets only to make the following statement correct.

6 + 5 × 10 – 8 = 16[1]

__________________________________________________________________________________________

2 Calculate 1.26 0.728.24 2.56

-

+ .

Answer ................................................ [1]__________________________________________________________________________________________

3

Write down the order of rotational symmetry of this shape.

Answer ................................................ [1]__________________________________________________________________________________________

4 (a) Write down two whole numbers that have a product of –15.

Answer(a) ..................... and .................... [1]

(b) During one year, the temperature in Ulaanbaatar varied from –33 °C to 27 °C.

Find the range of the temperatures during that year.

Answer(b) ........................................... °C [1]__________________________________________________________________________________________

3


5 Work out the value of 34 ÷ 3–2. Give your answer as an ordinary number.

Answer ................................................ [2]__________________________________________________________________________________________

6 Indira measures the length, l centimetres, of her desk as 95.6 cm, correct to the nearest millimetre.

Complete the statement about the value of l.

Answer ................... Y l < ................... [2]__________________________________________________________________________________________

7 (a) Complete the following list of factors of 30.

1, 2, ........... , 5, ........... , 10, ........... , 30[1]

(b) Write down the prime factors of 30.

Answer(b) ................................................ [1]__________________________________________________________________________________________

8 (a) Write 640 000 in standard form.

Answer(a) ................................................ [1]

(b) Write 7.82 × 10–4 as an ordinary number.

Answer(b) ................................................ [1]__________________________________________________________________________________________

4

0580/12/O/N/14© UCLES 2014

9 Make y the subject of the formula. 8 + 5y – 3x = 0

Answer y = ................................................ [2]__________________________________________________________________________________________

10y

x

4

3

2

1

–1

–2

–3

–4

0–1 1 2 3 4–2–3–4A

B

Points A and B are shown on the grid.

(a) Write as a column vector.

Answer(a) = f p [1]

(b) Write 3 as a column vector.

Answer(b) 3 = f p [1]

__________________________________________________________________________________________

5


11 Write the following in order of size, starting with the smallest.

3715 0.41 40.4% 42

17

Answer ...................... < ...................... < ...................... < ...................... [2]__________________________________________________________________________________________

12 (a) Simplify 5k – 7k + 4k.

Answer(a) ................................................ [1]

(b) Find the value of 8x – 3y when x = –2 and y = –5.

Answer(b) ................................................ [2]__________________________________________________________________________________________

13 For her holiday, Alyssa changed 2800 Malaysian Ringgits (MYR) to US dollars ($) when the exchange rate was 1 MYR = $0.325 .

At the end of her holiday she had $210 left.

(a) How many dollars did she spend?

Answer(a) $ ................................................. [2]

(b) She changed the $210 for 750 MYR.

What was the exchange rate in dollars for 1 MYR?

Answer(b) 1 MYR = $ ................................................. [1]__________________________________________________________________________________________

6

0580/12/O/N/14© UCLES 2014

14 Without using a calculator, work out 1 61 ÷ 8

7 .

Show all your working and give your answer as a fraction in its lowest terms.

Answer ................................................ [3]__________________________________________________________________________________________

15 Solve the simultaneous equations. You must show all your working. 9x + 2y = 8 5x + 6y = –20

Answer x = ................................................

y = ................................................ [3]__________________________________________________________________________________________

7


16 A bag contains different coloured counters. Sasha takes a counter at random, records its colour, and replaces it. She does this 90 times and records her results in the pie chart below.

136°148°

Red

Green

Blue

(a) Write down the relative frequency of Sasha choosing a red counter.

Answer(a) ................................................ [1]

(b) Work out the number of times a green counter is chosen.

Answer(b) ................................................ [3]__________________________________________________________________________________________

8

0580/12/O/N/14© UCLES 2014

17 The scatter diagram shows the results of height plotted against shoe size for 8 people.

200

192

184

176

168

160

152

144

136

128

1202826 30 32 34

Shoe size36 38 40 42 44

Height(cm)

(a) Four more results are recorded.

Shoe size 28 31 38 43

Height (cm) 132 156 168 198

Plot these 4 results on the scatter diagram. [2]

(b) Draw a line of best fi t on the scatter diagram. [1]

(c) What type of correlation is shown by the scatter diagram?

Answer(c) ................................................ [1]__________________________________________________________________________________________

9


18 Find

(a) the cube root of 729,

Answer(a) ................................................ [1]

(b) the two square roots of 225,

Answer(b) ..................... and .................... [2]

(c) a common multiple of 6 and 9,

Answer(c) ................................................ [1]

(d) (–4)2.

Answer(d) ................................................ [1]__________________________________________________________________________________________

19

z°

x°

y°

24°A

BE

CD

NOT TOSCALE

The points B, C, D and E lie on a circle. AB and AC are equal length tangents to the circle. BD is a diameter of the circle and BC is parallel to ED. Angle BDE = 24°.

Calculate the value of

(a) x,

Answer(a) x = ................................................ [2]

(b) y,

Answer(b) y = ................................................ [1]

(c) z.

Answer(c) z = ................................................ [2]__________________________________________________________________________________________

10

0580/12/O/N/14© UCLES 2014

20 The diagram shows the plan, ABCD, of a park. The scale is 1 centimetre represents 20 metres.

D

A

C

B

Scale: 1 cm to 20 m

(a) Find the actual distance BC. Answer(a) ............................................ m [2]

(b) A fountain, F, is to be placed

● 160 m from C and ● equidistant from AB and AD.

On the diagram, using a ruler and compasses only, construct and mark the position of F. Leave in all your construction lines. [5]__________________________________________________________________________________________

11

0580/12/O/N/14© UCLES 2014

BLANK PAGE

12

0580/12/O/N/14© UCLES 2014

BLANK PAGE







MATHEMATICS 0580/13


1 hour






*6293220431*


2

0580/13/O/N/14© UCLES 2014

1 Write 0.13 as a fraction.

Answer ................................................ [1]__________________________________________________________________________________________

2 (a) Write in fi gures the number three hundred and four thousand six hundred and twenty.

Answer(a) ................................................ [1]

(b) Write your answer to part (a) correct to 3 signifi cant fi gures.

Answer(b) ................................................ [1]__________________________________________________________________________________________

3

(a) Write down the order of rotational symmetry of the diagram.

Answer(a) ................................................ [1]

(b) Draw the lines of symmetry on the diagram. [1]__________________________________________________________________________________________

4 Calculate 3.71

9.25 26.4+ .


Answer ................................................ [2]__________________________________________________________________________________________

3


5 A bag contains 20 counters. One counter is taken from the bag at random. The arrow on the probability scale shows the probability that this counter is blue.

0 0.5 1

(a) Work out the number of blue counters in the bag.

Answer(a) ................................................ [1]

(b) Find the probability that the counter is not blue.

Answer(b) ................................................ [1]__________________________________________________________________________________________

6 The temperature in a freezer is –20.5 °C.

(a) The temperature in a fridge is 2.8 °C.

Find the difference between the temperature in the fridge and the temperature in the freezer.

Answer(a) ........................................... °C [1]

(b) The temperature in the freezer rises by 5 °C.

Find the temperature in the freezer now.

Answer(b) ........................................... °C [1]__________________________________________________________________________________________

7 Find the value of

(a) 27443 ,

Answer(a) ................................................ [1]

(b) 64.

Answer(b) ................................................ [1]__________________________________________________________________________________________

4

0580/13/O/N/14© UCLES 2014

8 m = 5

2-e o n =

36

-e o

Work out

(a) m + n,

Answer(a) f p [1]

(b) 3n.

Answer(b) f p [1]

__________________________________________________________________________________________

9 Without using a calculator, work out 54 – 3

2 . Give your answer as a fraction and show each step of your working.

Answer ................................................ [2]__________________________________________________________________________________________

10 Make x the subject of the formula y = 6x – 1.

Answer x = ................................................ [2]__________________________________________________________________________________________

5



0.34 0.6 0.62 0.73

Answer ..................... < ..................... < ..................... < ..................... [2] smallest__________________________________________________________________________________________

12 Work out 4 × 10–5 × 6 × 1012. Give your answer in standard form.

Answer ................................................ [2]__________________________________________________________________________________________

13 The four sector angles in a pie chart are 2x°, 3x°, 4x° and 90°.


Answer x = ................................................ [2]__________________________________________________________________________________________

14 A train takes 65 minutes to travel 52 km.

Calculate the average speed of the train in kilometres per hour.

Answer ....................................... km/h [2]__________________________________________________________________________________________

6

0580/13/O/N/14© UCLES 2014

15 (a) A parcel is in the shape of a cuboid of length 18 cm, width 10 cm and height 8 cm.

Calculate the volume of the parcel.

Answer(a) ......................................... cm3 [2]

(b) The mass of the parcel is 1.7 kilograms.

Change 1.7 kilograms to grams.

Answer(b) ............................................. g [1]__________________________________________________________________________________________

16 (a) Simplify. 5j + 2k + j – 3k

Answer(a) ................................................ [2]

(b) Factorise. 5p + 10

Answer(b) ................................................ [1]__________________________________________________________________________________________

17 (a) Paolo thinks of a number. It has two digits. It is a common factor of 36 and 48.

Write down Paolo’s number.

Answer(a) ................................................ [1]

(b) Maria thinks of a number. It has two digits. It is a common multiple of 15 and 20.

Write down Maria’s number.

Answer(b) ................................................ [1]

(c) Kemar thinks of a number. It is between 1 and 2. It is an irrational number.

Write down a number he could be thinking of.

Answer(c) ................................................ [1]__________________________________________________________________________________________

7


18 Solve the equation. 3

2 5x + = 8

Answer x = ................................................ [3]__________________________________________________________________________________________

19 The scatter diagram shows the heights and masses of some fi ve-year-old boys.

30

25

20

15

1090 95 100 105 110 115

Height (cm)

Mass(kg)

120 125 130 135

(a) The height of one of the boys is likely to have been recorded incorrectly.

Write down the mass of this boy.

Answer(a) ........................................... kg [1]

(b) What type of correlation does the scatter diagram show?

Answer(b) ................................................ [1]

(c) (i) Draw a line of best fi t on the scatter diagram. [1]

(ii) Another boy had a height of 108 cm. His mass was not recorded.

Use your line of best fi t to estimate the boy’s mass.

Answer(c)(ii) ........................................... kg [1]__________________________________________________________________________________________

8

0580/13/O/N/14© UCLES 2014

20D

A

C

B

E

(a) Draw the locus of the points which are 3 cm from E. [1]

(b) Using a straight edge and compasses only, construct the bisector of angle DCB. [2]

(c) Shade the region which is

● less than 3 cm from E and ● nearer to CB than to CD. [1]__________________________________________________________________________________________

9


21C

B

A

8 cm

5 cm

32°

NOT TOSCALE

A, B and C lie on a circle with diameter AB. Angle CAB = 32°, AC = 8 cm and BC = 5 cm.

(a) Work out the size of angle CBA.

Answer(a) Angle CBA = ................................................ [2]

(b) Work out the length of AB.

Answer(b) AB = .......................................... cm [2]__________________________________________________________________________________________

10

0580/13/O/N/14© UCLES 2014

22 This is an accurate drawing of quadrilateral ABCD.

D C

A B

(a) Write down the mathematical name for quadrilateral ABCD.

Answer(a) ................................................ [1]

(b) Measure the size of the acute angle.

Answer(b) ................................................ [1]

(c) By taking suitable measurements from the diagram, work out the area of ABCD.

Answer(c) ......................................... cm2 [3]__________________________________________________________________________________________

11

0580/13/O/N/14© UCLES 2014

BLANK PAGE

12

0580/13/O/N/14© UCLES 2014



BLANK PAGE





MATHEMATICS 0580/31


2 hours






*3336153480*


2

0580/31/O/N/14© UCLES 2014

1 A carton of fruit juice contains apple, orange, pineapple and tropical juices.

(a) They are mixed in the ratio

apple : orange : pineapple : tropical = 9 : 7 : 4 : 5.

The carton contains 540 millilitres of apple juice.

(i) Show that the total amount of fruit juice in the carton is 1.5 litres.

Answer(a)(i)

[3]

(ii) Calculate the amount of tropical juice in the carton. Give your answer in millilitres.

Answer(a)(ii) ........................................... ml [2]

(iii) 70% of the tropical juice is mango.

Calculate the amount of mango juice in the carton.

Answer(a)(iii) ........................................... ml [2]

3


(b) A shopkeeper pays $36 for 16 cartons.

(i) How much does he pay for one carton?

Answer(b)(i) $ ................................................. [1]

(ii) He sells 87 of the 16 cartons for $3.40 each and the rest for $2.50 each.

Calculate the total amount he receives from selling the cartons.

Answer(b)(ii) $ ................................................. [2]

(iii) Calculate his percentage profi t.

Answer(b)(iii) .............................................% [3]__________________________________________________________________________________________

4

0580/31/O/N/14© UCLES 2014

2y

x

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–9

0–1 1 2 3 4 5 6–2–3–4–5–6–7–8

G

H

P

Two congruent quadrilaterals, G and H, and a point P are shown on this 1 cm2 grid.

(a) (i) Write down the mathematical name of the shaded quadrilateral.

Answer(a)(i) ................................................ [1]

5


(ii) Calculate the area of the shaded quadrilateral. Give the units of your answer.

Answer(a)(ii) .................................. ........... [3]

(b) Describe fully the single transformation that maps quadrilateral G onto quadrilateral H.

Answer(b) ...........................................................................................................................................

............................................................................................................................................................. [3]

(c) On the grid, draw the images of quadrilateral G after the following transformations.

(i) Refl ection in the line y = 0. [2]

(ii) Translation by the vector 5-

7e o. [2]

(iii) Enlargement by scale factor 0.5 with centre P. [2]

(d) On quadrilateral H mark, with an arc, an obtuse angle. [1]__________________________________________________________________________________________

6

0580/31/O/N/14© UCLES 2014

3 12 athletes took part in the 100 metres race. 11 of these athletes also took part in the long jump. The times and distances, each measured correct to 3 signifi cant fi gures, for these athletes are shown in the

table.

Athlete A B C D E F G H I J K L

100 m time (seconds) 12.1 10.3 12.8 10.7 12.6 11.2 12.0 12.4 10.6 12.7 11.8 11.1

Long jump (metres) × 7.60 5.15 7.25 6.72 6.30 5.60 6.20 6.90 5.70 6.85 6.70

(a) The scatter diagram shows the times and distances for athletes B to H.

(i) Plot the times and distances for athletes I, J, K and L.

8.0

7.5

7.0

6.5

6.0

5.5

5.010.510.0 11.0 11.5 12.0 12.5 13.0

100 m time (seconds)

Long jump(metres)

[2]

7


(ii) On the scatter diagram, draw a line of best fi t. [1]

(iii) Athlete A did not take part in the long jump.

Use your line of best fi t to estimate a long jump distance for athlete A.

Answer(a)(iii) ............................................ m [1]

(iv) What type of correlation is shown on the scatter diagram?

Answer(a)(iv) ................................................ [1]

(v) Describe in words the relationship between the time for 100 metres and the distance in the long jump.

Answer(a)(v) ...............................................................................................................................

..................................................................................................................................................... [1]

(b) Use the table of times and distances to work out

(i) the mean of the 100 metres times,

Answer(b)(i) .............................................. s [2]

(ii) the percentage of athletes who ran 100 metres in less than 11.5 seconds,

Answer(b)(ii) ............................................ % [2]

(iii) the range of the distances jumped by the 11 athletes, B to L.

Answer(b)(iii) ............................................ m [1]__________________________________________________________________________________________

8

0580/31/O/N/14© UCLES 2014

4

30 cm

50 cm

20 cm

x cm

x cm

180 cm

480 cm

NOT TOSCALE

The diagram shows the cross section of a medal presentation platform.

(a) Show that x = 150.

Answer(a)

[2]

(b) Work out the perimeter of the cross section.

Answer(b) .......................................... cm [2]

(c) (i) Calculate the area of the cross section.

Answer(c)(i) ......................................... cm2 [2]

(ii) The platform is a prism, 170 cm deep.

Find the volume of the platform.

Answer(c)(ii) ......................................... cm3 [1]

(iii) The prism is completely fi lled with a light material. 1 cubic metre of this material has mass 16 kg.

Calculate the mass of the material used.

Answer(c)(iii) ........................................... kg [2]__________________________________________________________________________________________

9


5 (a) Write in fi gures six million three thousand and seventy six.

Answer(a) ................................................ [1]

(b) (i) Work out the value of p when p = –0.6 ÷ 1.6 .

Answer(b)(i) p = ................................................ [1]

(ii) Work out the value of q when q = –0.6 – 1.6 .

Answer(b)(ii) q = ................................................ [1]

(iii) Use one of the symbols >, <, [, Y, = to complete this statement.

p ........................ q[1]

(c) Mount Robson in Canada has a height of 3950 metres, correct to the nearest 10 metres.

Complete the following statement about the height, h m, of Mount Robson.

Answer(c) .................... Y h < .................... [2]

(d) Calculate 2 121 ÷ 1 4

1 .

Give your answer as a decimal, correct to 4 signifi cant fi gures.

Answer(d) ................................................ [2]

(e) (i) Write down the value of 80.

Answer(e)(i) ................................................ [1]

(ii) Work out 5–3. Write your answer as a fraction.

Answer(e)(ii) ................................................ [1]

(iii) Simplify the expression. 8x5 × 3x4

Answer(e)(iii) ................................................ [2]__________________________________________________________________________________________

10

0580/31/O/N/14© UCLES 2014

6 (a) (i) Complete the table of values for y = 8 – x2.

x –3 –2 –1 0 1 2 3

y –1 8 7 –1

[2]

(ii) On the grid, draw the graph of y = 8 – x2 for –3 Y x Y 3 .

y

x

12

11

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

0–1–2–3 321

[4]

11


(iii) Write down the equation of the line of symmetry of the graph.

Answer(a)(iii) ................................................ [1]

(iv) Use your graph to solve the equation 8 – x2 = 0.

Answer(a)(iv) x = .......................... or x = .......................... [2]

(b) (i) On the grid, plot the points (–2, 8) and (2.5, –1). Draw a straight line through these points. [2]

(ii) Find the equation of your line in the form y = mx + c.

Answer(b)(ii) y = ................................................ [3]

(iii) Write down the co-ordinates of the point of intersection of your line with y = 8 – x2.

Answer(b)(iii) (..................... , .....................) [1]__________________________________________________________________________________________

12

0580/31/O/N/14© UCLES 2014

7 The scale drawing represents the positions of 3 towns, A, B and C. The scale is 1 centimetre represents 4 kilometres.

North

A

B

C

Scale: 1 cm to 4 km

13


(a) Measure the bearing of B from A. Answer(a) ................................................ [1]

(b) A transmitter is placed near to the 3 towns.

(i) The transmitter is equidistant from A and B.

Using a straight edge and compasses only, construct the locus of points equidistant from A and B. [2]

(ii) The transmitter is also on the bisector of angle ABC.

Using a straight edge and compasses only, construct the bisector of angle ABC. [2]

(iii) Mark the position, T, of the transmitter on the scale drawing. [1]

(c) Work out the actual distance, in kilometres, of town A from T.

Answer(c) .......................................... km [2]

(d) The signal from the transmitter has a range of 30 kilometres in all directions.

On the scale drawing, construct the locus of points 30 kilometres from T. [2]

(e) Would the signal from the transmitter reach town C ? Give a reason for your answer.

Answer(e) .................... because .........................................................................................................

............................................................................................................................................................. [1]__________________________________________________________________________________________

14

0580/31/O/N/14© UCLES 2014

8 (a) One day a survey is taken of the ages of 120 children at a fairground. The results are shown in the frequency table.

Age in completed years Number of children

1 to 3 12

4 to 6 19

7 to 9 32

10 to 12 41

13 to 15 9

16 to 18 7

(i) On the grid, draw a bar chart for this data. Complete the scale on the frequency axis.

Frequency

Age in completed years

1 to 3 4 to 6 7 to 9 10 to 12 13 to 15 16 to 18

[3]

15


(ii) What is the modal age group?

Answer(a)(ii) ................................................ [1]

(iii) One of the 120 children is chosen at random.

Write down the probability that the child is aged 4 to 6.

Answer(a)(iii) ................................................ [1]

(b) Lalia says the probability of taking a yellow bead from a bag containing yellow beads and blackbeads is 5

7 .

Explain why 57 cannot be a correct probability.

Answer(b) ........................................................................................................................................... [1]

(c) Another bag contains 9 green marbles and 11 red marbles. A marble is taken at random.

Write down the probability that the marble is

(i) green,

Answer(c)(i) ................................................ [1]

(ii) blue.

Answer(c)(ii) ................................................ [1]__________________________________________________________________________________________


16

0580/31/O/N/14© UCLES 2014



9

Diagram 4Diagram 3Diagram 2Diagram 1

Diagrams 1 to 4 show a sequence of shapes made up of lines and dots at the intersections of lines.

(a) (i) Complete the table showing the number of dots in each diagram.

Diagram 1 2 3 4 5 6

Dots 3 8 13

[3]

(ii) Write down the rule for continuing the sequence of dots.

Answer(a)(ii) ............................................................................................................................... [1]

(iii) Write down an expression, in terms of n, for the number of dots in Diagram n.

Answer(a)(iii) ................................................ [2]

(iv) Find the number of dots in Diagram 15.

Answer(a)(iv) ................................................ [1]

(b) The dots are joined by sloping lines and horizontal lines.

(i) Diagram 1 has 2 sloping lines and Diagram 2 has 6 sloping lines.

Find the number of sloping lines in Diagrams 3 and 4.

Answer(b)(i) Diagram 3 ................................................

Diagram 4 ................................................ [2]

(ii) Write down an expression, in terms of n, for the number of sloping lines in Diagram n.

Answer(b)(ii) ................................................ [2]





MATHEMATICS 0580/32


2 hours






*8150616039*


2

0580/32/O/N/14© UCLES 2014

1 A building company buys 4 square kilometres of land. On the land the company builds houses, shops and a school.

(a) Show that 4 square kilometres is equivalent to 4 000 000 square metres.

Answer(a)

[1]

(b) The company uses 5% of the land for roads and paths.

Show that the remaining area of land is 3 800 000 m2.

Answer(b)

[1]

(c) The 3 800 000 m2 of land is divided in the ratio houses : shops : school = 11 : 5 : 3.

(i) Show that the area for the school is 600 000 m2.

Answer(c)(i)

[2]

(ii) Calculate the area for houses.

Answer(c)(ii) ........................................... m2 [1]

(iii) 140 m2 is needed for each house.

Calculate, correct to the nearest 10, the number of houses that can be built.

Answer(c)(iii) ................................................ [2]

3


(d) 53 of the school area is for classrooms and 8

1 is for other rooms.

The remainder is for sporting facilities.

(i) Without using a calculator, and showing all your working, fi nd the fraction of the school area for sporting facilities.

Answer(d)(i) ................................................ [3]

(ii) The school has an area of 600 000 m2.

Work out the area for sporting facilities.

Answer(d)(ii) ........................................... m2 [1]

(e) To pay for materials, the building company borrows $250 000 from a bank for 3 years. The bank charges compound interest at a rate of 4% per year.

Calculate the total amount the company must pay back at the end of 3 years.

Answer(e) $ ................................................ [3]__________________________________________________________________________________________

4

0580/32/O/N/14© UCLES 2014

2 (a) Write down the mathematical name of a polygon with 8 sides.

Answer(a) ................................................ [1]

(b) Calculate the interior angle of a regular 8-sided polygon.

Answer(b) ................................................ [3]

(c)

Diagram 1 Diagram 2 Diagram 3

The pattern of diagrams above forms a sequence.

(i) Complete the table.

Diagram 1 2 3 4 5

Number of dots 8 15

[2]

(ii) Find an expression, in terms of n, for the number of dots in Diagram n.

Answer(c)(ii) ................................................ [2]

(iii) Find the number of dots in Diagram 10.

Answer(c)(iii) ................................................ [1]

(iv) Find the value of n for a diagram with 92 dots.

Answer(c)(iv) ................................................ [2]__________________________________________________________________________________________

5


3

O

A B

(a) Describe fully two single transformations that each map the shaded triangle onto the unshaded triangle.

Answer(a) Transformation 1 ...............................................................................................................

...........................................................................................................................................

Transformation 2 ...............................................................................................................

........................................................................................................................................... [5]

(b) On the grid, draw the image of

(i) the shaded triangle after a translation by the vector 27

-e o, [2]

(ii) the shaded triangle after an enlargement with scale factor 3 and centre O. [2]

(c) Draw the line of symmetry of the enlarged triangle in part (b)(ii). [1]__________________________________________________________________________________________

6

0580/32/O/N/14© UCLES 2014

4

07 00 07 30 08 00 08 30 09 00

Time

09 30 10 00 10 30 11 00

600

550

500

450

400

350

300

250

200

150

100

50

0

Distance fromMadrid (km)

Seville

Cordoba

Madrid

7


(a) A train leaves Madrid at 07 00. It arrives at Cordoba at 08 40 and stays at the station for 10 minutes. It then continues to Seville arriving at 09 40.

(i) Show this journey on the grid opposite. [3]

(ii) Write down, in hours and minutes, the total time for this journey.

Answer(a)(ii) .................. h .................. min [1]

(iii) Calculate, in kilometres per hour, the average speed for the whole journey.

Answer(a)(iii) ....................................... km/h [2]

(b) Another train leaves Seville at 07 45. It travels to Madrid without stopping at an average speed of 200 km/h.

(i) Calculate, in hours and minutes, the time taken for this journey.

Answer(b)(i) .................. h .................. min [2]

(ii) Show this journey on the grid. [2]

(c) How far from Madrid were the trains when they passed each other?

Answer(c) .......................................... km [1]__________________________________________________________________________________________

8

0580/32/O/N/14© UCLES 2014

59 cm 50 cm

70 cm12 cm

52 cm

A

E

D H C

BGF

NOT TOSCALE

The diagram shows a rectangle ABCD divided into three sections by the lines EF and HG. AF = 9 cm, GB = 50 cm, DH = 12 cm, HC = 70 cm and HG = 52 cm.

(a) Write down the mathematical name of

(i) quadrilateral BCHG,

Answer(a)(i) ................................................ [1]

(ii) the shaded polygon.

Answer(a)(ii) ................................................ [1]

(b) (i) Show by calculation that BC = 48 cm.

Answer(b)(i)

[2]

(ii) Calculate the area of rectangle ABCD.

Answer(b)(ii) ......................................... cm2 [2]

9


(c) Calculate

(i) the perimeter of BCHG,

Answer(c)(i) .......................................... cm [1]

(ii) the area of BCHG.

Answer(c)(ii) ......................................... cm2 [2]

(d) E is the midpoint of AD.

Find the area of triangle AEF.

Answer(d) ......................................... cm2 [3]

(e) Work out the area of the shaded polygon.

Answer(e) ......................................... cm2 [1]__________________________________________________________________________________________

10

0580/32/O/N/14© UCLES 2014

6 (a) (i) Complete the table of values for y = 20x

.

x –8 –5 –4 –2.5 2.5 4 5 8

y –2.5 –4 8 4

[2]

(ii) On the grid, draw the graph of y = 20x for –8 Y x Y –2.5 and 2.5 Y x Y 8.

y

x

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–9

0–2–4–6–8 –1–3–5–7 6 842 5 731

[4]

11


(iii) By drawing a suitable line on your graph solve the equation 20x = 6.

Answer(a)(iii) x = ................................................ [2]

(b)

x –8 0 8

y

(i) Complete the table for y = 21 x – 1. [2]

(ii) On the grid, draw the graph of y = 21 x – 1 for –8 Y x Y 8. [1]

(iii) Write down the gradient of y = 21 x – 1.

Answer(b)(iii) ................................................ [1]

(c) Write down the values of x at the points of intersection of the graphs of y = 20x and y = 2

1 x – 1.

Answer(c) x = ...................... and x = ...................... [2]__________________________________________________________________________________________

12

0580/32/O/N/14© UCLES 2014

7 (a) 21 11 7 29 3 20 24 8 18 14

For these numbers

(i) calculate the mean,

Answer(a)(i) ................................................ [2]

(ii) fi nd the median,

Answer(a)(ii) ................................................ [2]

(iii) fi nd the range.

Answer(a)(iii) ................................................ [1]

(b) The table shows the number of births for each month of 2013 in a hospital.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

319 299 336 309 334 336 348 363 351 347 331 335

(i) On the grid opposite, complete the bar chart. The fi rst 6 months have been drawn for you. [2]

(ii) Write down the modal month.

Answer(b)(ii) ................................................ [1]

(iii) A month is chosen at random.

Find the probability that the number of births in that month is greater than 340.

Answer(b)(iii) ................................................ [1]

13


370

360

350

340

330

320

310

300

290

Number ofbirths

Jan Feb Mar Apr May Jun

Month

Jul Aug Sep Oct Nov Dec

__________________________________________________________________________________________

14

0580/32/O/N/14© UCLES 2014

8

North

North

P

Q

48 km

(a) The scale drawing shows a ship’s voyage from port P to port Q. The straight line distance from P to Q is 48 km.

(i) Measure the bearing of Q from P.

Answer(a)(i) ................................................ [1]

(ii) Complete the following statement.

The scale of the drawing is 1 centimetre represents ........................ kilometres. [2]

(b) From port Q, the ship sails on a bearing of 125° for 76 km to port R.

Show this part of the voyage on the scale drawing. [3]

15


(c)

North

297°P

L

W

8.5 kmNOT TOSCALE

Another ship leaves port P and sails on a bearing of 297° to a lighthouse, L. PL = 8.5 km.

(i) Show that angle LPW = 27°.

Answer(c)(i)

[1]

(ii) Using trigonometry, calculate PW. Give your answer correct to 2 signifi cant fi gures.

Answer(c)(ii) PW = .......................................... km [3]

(d) The diagram shows the positions of two beacons, A and B. A ship sails on a course that is the perpendicular bisector of the line AB.

Using a straight edge and compasses only, construct the ship’s course.

A

B

[2]__________________________________________________________________________________________

16

0580/32/O/N/14© UCLES 2014



9 Adriano hires a car. The cost of hiring the car is $36 per day plus 24 cents for each kilometre travelled. He hires the car for 5 days and travels a total of 660 km.

(a) (i) Calculate the cost to hire the car.

Answer(a)(i) $ ................................................ [3]

(ii) 15% tax is then added to this cost. Calculate the total cost of hiring the car including tax.

Answer(a)(ii) $ ................................................ [2]

(b) The car uses one litre of fuel to travel 11 km. Fuel costs $1.80 per litre.

(i) Work out the number of litres used to travel the 660 km.

Answer(b)(i) ....................................... litres [1]

(ii) Work out the cost of this fuel.

Answer(b)(ii) $ ................................................ [1]

(iii) Find the total cost of hiring the car including tax and the fuel used.

Answer(b)(iii) $ ................................................ [1]

(c) During the 5 days Adriano earns $1600.

What percentage of his earnings is your answer to part (b)(iii)? Give your answer correct to the nearest whole number.

Answer(c) .............................................% [2]





MATHEMATICS 0580/33


2 hours






*6233172548*


2

0580/33/O/N/14© UCLES 2014

1 (a) A group of 20 boys were asked which type of movie they liked best. Each boy’s choice is shown below.

Action Science Fiction Comedy Drama ComedyHorror Action Science Fiction Science Fiction Comedy

Comedy Horror Comedy Horror ComedyHorror Action Action Horror Drama

(i) Complete the frequency table for the results. You may use the tally column to help you.

Type of movie Tally Frequency

Action

Horror

Science Fiction

Comedy

Drama

Total 20[2]

(ii) Draw a bar chart to show this information. Complete the scale on the frequency axis.

Action Horror ScienceFiction

Comedy Drama

Frequency

[3]

3


(b) A group of 24 girls were also asked which type of movie they liked best. The results are shown in the table below.

Type of movie Frequency

Action 5

Horror 3

Science Fiction 2

Comedy 6

Drama 8

One of these girls is picked at random.

Find the probability that she liked comedy or drama best.

Answer(b) ................................................ [1]

(c) Khalid says:

Comedy movies are equally popular with boys and girls.

Is he correct? Give a reason for your answer.

Answer(c) ...................... because ......................................................................................................

............................................................................................................................................................. [1]

(d) A group of 25 people were asked how many movies they had watched in the last two weeks. The results are shown in the table below.

Number of movies 0 1 2 3 4 5 6

Frequency 4 6 5 3 5 0 2

(i) Find the median.

Answer(d)(i) ................................................ [2]

(ii) Calculate the mean.

Answer(d)(ii) ................................................ [3]__________________________________________________________________________________________

4

0580/33/O/N/14© UCLES 2014

2 (a) Lei earns $6.75 per hour. One week she works for 37 hours.

How much does she earn this week?

Answer(a) $ ................................................. [1]

(b) One month Lei earns $1080. 20% of her earnings are taken off for tax.

Show that the amount of money she has left is $864.

Answer(b)

[1]

(c) Lei divides $864 in the ratio bills : spending money : savings = 9 : 4 : 2.

(i) Work out how much spending money she has.

Answer(c)(i) $ ................................................. [2]

(ii) What fraction of the $864 does she use for bills? Give your answer in its simplest form.

Answer(c)(ii) ................................................ [2]

5


(d) Lei wants to buy a computer.

(i)

Computer$425 + sales tax

The sales tax is 15%.

Work out the total cost of this computer.

Answer(d)(i) $ ................................................. [2]

(ii) Lei goes on holiday to London. The exchange rate between dollars and pounds (£) is $1 = £0.52 . The total cost of the same computer in London is £235.

Work out how much less, in pounds, the computer costs in London.

Answer(d)(ii) £ ................................................. [2]

(e) Lei inherits $1400. She spends $175 on a camera.

(i) Work out $175 as a percentage of $1400.

Answer(e)(i) ............................................ % [1]

(ii) Lei invests the remaining $1225 for 3 years at a rate of 4.5% per year compound interest.

How much interest does she receive after 3 years?

Answer(e)(ii) $ ................................................. [3]__________________________________________________________________________________________

6

0580/33/O/N/14© UCLES 2014

3 Sylvain leaves his house at 09 30 to cycle to Southfi eld Lake. He cycles for 4 km then waits for his friend Michel. Both boys then cycle to the lake together. The travel graph shows Sylvain’s journey.

20

18

16

14

12

10

8

6

4

2

009 30 10 00 10 30 11 00 11 30 12 00 12 30 13 00 13 30 14 00

Time

Distance(km)

SouthfieldLake

(a) Write down how long Sylvain waits for Michel.

Answer(a) ......................................... min [1]

(b) Is Sylvain’s speed faster before or after he meets Michel? Explain how you know.

Answer(b) ...................................... because .......................................................................................

............................................................................................................................................................. [1]

(c) Write down the time Sylvain and Michel arrive at the lake.

Answer(c) ................................................ [1]

7


(d) Sylvain and Michel stay at the lake for 50 minutes. They then cycle back to Sylvain’s house at a speed of 10 km/h.

(i) Find how long it takes them to cycle the 18 km back to Sylvain’s house. Give your answer in hours and minutes.

Answer(d)(i) ............................ h .......................... min [2]

(ii) Complete the travel graph. [2]

(e) Manon plans to go to Southfi eld Lake by bus from High Street. Here is the bus timetable.

Railway Station 08 45 09 15 09 45 10 15 10 45 11 15

High Street 08 57 09 27 09 57 10 27 10 57 11 27

Hospital 09 12 09 42 10 12 10 42 11 12 11 42

Southfi eld Lake 09 21 09 51 10 21 10 51 11 21 11 51

Country Park 09 50 10 20 10 50 11 20 11 50 12 20

(i) Manon arrives at Southfi eld Lake just before 11 30.

Write down the time of the bus she caught from High Street.

Answer(e)(i) ................................................ [1]

(ii) How long does the journey from High Street to Southfi eld Lake take?

Answer(e)(ii) ......................................... min [1]

(f) Southfi eld Lake is 13 km from Manon’s house on a bearing of 110°. Mark the position of the lake on the scale drawing below. Use a scale of 1 centimetre represents 4 kilometres.

North

Manon’shouse

[2]__________________________________________________________________________________________

8

0580/33/O/N/14© UCLES 2014

4 (a)

A

B

G

C

D

E F

H

85°

30° NOT TOSCALE

In the diagram, ABC and DEC are triangles. AB = BE and BED is parallel to GFH. Angle AEB = 85° and angle CBE = 30°.

(i) Find angle EAB.

Answer(a)(i) Angle EAB = ................................................ [1]

(ii) Find angle ABE.

Answer(a)(ii) Angle ABE = ................................................ [1]

(iii) Find refl ex angle ABC.

Answer(a)(iii) Angle ABC = ................................................ [1]

(iv) Find angle BEC.

Answer(a)(iv) Angle BEC = ................................................ [1]

(v) Find angle EFH.

Answer(a)(v) Angle EFH = ................................................ [1]

(vi) Find angle BCE.

Answer(a)(vi) Angle BCE = ................................................ [1]

9


(vii) Complete the following statement.

Triangle .......................... is similar to triangle .......................... [1]

(b) For a regular 12-sided polygon, fi nd the size of

(i) an exterior angle,

Answer(b)(i) ................................................ [2]

(ii) an interior angle.

Answer(b)(ii) ................................................ [1]__________________________________________________________________________________________

10

0580/33/O/N/14© UCLES 2014

5y

x

8

6

4

2

–2

–4

–6

–8

–10

0–1–2–3–4 321

L

(a) The line L is drawn on the grid.

(i) Work out the gradient of L.

Answer(a)(i) ................................................ [2]

(ii) Write down the equation of L in the form y = mx + c.

Answer(a)(ii) y = ................................................ [1]

11


(b) (i) Complete the table of values for y = 6 – 2x – x2.

x –4 –3 –2 –1 0 1 2 3

y –2 3 3 –2[3]

(ii) On the grid opposite, draw the graph of y = 6 – 2x – x2 for –4 Y x Y 3. [4]

(iii) Use your graph to solve the equation 6 – 2x – x2 = 0.

Answer(b)(iii) x = .................... or x = .................... [2]

(c) Write down the co-ordinates of the points of intersection of L with your graph.

Answer(c) (................ , ................) and (................ , ................) [2]__________________________________________________________________________________________

12

0580/33/O/N/14© UCLES 2014

6 In this question all lengths are in centimetres.

ABC is an isosceles triangle. AC = 2x – 3 and BC = x + 2.

(a) Write down an expression for AB.

Answer(a) AB = ................................................ [1]

(b) Write down and simplify an expression for the perimeter of the triangle.

Answer(b) .......................................... cm [2]

(c) A rectangle has length 3(x – 4) and width (14 – x).

(i) Write down and simplify an expression for the perimeter of this rectangle.

Answer(c)(i) .......................................... cm [2]

(ii) The triangle and the rectangle have the same perimeter.

Write down an equation and use it to fi nd x.

Answer(c)(ii) x = ................................................ [2]

(d) Find the length and width of the rectangle.

Answer(d) Length = .......................................... cm

Width = .......................................... cm [2]

(e) Work out the area of the rectangle.

Answer(e) ......................................... cm2 [1]__________________________________________________________________________________________

A

B C

2x – 3

x + 2

NOT TOSCALE

13


7 Tables and chairs can be arranged in two different patterns.

Pattern A

Pattern B

1 table 2 tables 3 tables

(a) Complete the following table.

Number of tables 1 2 3 4 8

Number of chairsin Pattern A 6 8

Number of chairs inPattern B 6 10

[5]

(b) How many chairs are needed with n tables

(i) in Pattern A,

Answer(b)(i) ................................................ [2]

(ii) in Pattern B ?

Answer(b)(ii) ................................................ [2]

(c) Sofi a needs to arrange tables to seat 66 people.

Which pattern uses the least number of tables and by how many?

Answer(c) Pattern ................ by ............................ tables [3]__________________________________________________________________________________________

14

0580/33/O/N/14© UCLES 2014

8 (a)

Sweets are packed in a box. The cross section of the box is an equilateral triangle with side 4 cm. The length of the box is 8 cm.

(i) Write down the mathematical name for the box.

Answer(a)(i) ................................................ [1]

(ii) Draw an accurate net for the box. Side AB has been drawn for you.

A B

[3]

A

B

8 cm4 cm

NOT TOSCALE

15


(iii) The surface area of the box is 10 986 mm2.

Change this surface area to square centimetres.

Answer(a)(iii) ......................................... cm2 [1]

(iv) The box contains 120 g of sweets, correct to the nearest 10 g.

Write down the lower bound of the mass of sweets in the box.

Answer(a)(iv) ............................................. g [1]

(b)

3 cm

4 cm

10 cm

NOT TOSCALE

Another box of sweets is in the shape of a cylinder. The cylinder has diameter 3 cm and length 10 cm.

(i) Calculate the volume of the cylinder.

Answer(b)(i) ......................................... cm3 [3]

(ii) A label of width 4 cm fi ts around the cylinder with no overlap.

Calculate the area of the label.

Answer(b)(ii) ......................................... cm2 [3]__________________________________________________________________________________________


16

0580/33/O/N/14© UCLES 2014



9

A

C

B

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–6–7 –5 –4 –3 –2 –1 10 2 3 4 5 6 7

y

x

(a) On the grid,

(i) draw the line x = 1, [1]

(ii) refl ect fl ag A in the line x = 1, [1]

(iii) rotate fl ag A through 90° anticlockwise about the origin. [2]

(b) Describe fully the single transformation that maps

(i) fl ag A onto fl ag B,

Answer(b)(i) ................................................................................................................................

..................................................................................................................................................... [2]

(ii) fl ag A onto fl ag C.

Answer(b)(ii) ...............................................................................................................................

..................................................................................................................................................... [3]


Write your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fl uid.DO NOT WRITE IN ANY BARCODES.



MATHEMATICS 0580/11


1 hour



UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSInternational General Certifi cate of Secondary Education



*1495681373*

2

0580/11/M/J/13© UCLES 2013

ForExaminer's

Use

1 Write 45% as a fraction in its simplest form.

Answer ............................................... [1]_____________________________________________________________________________________

2 One January day in Munich, the temperature at noon was 3°C. At midnight the temperature was –8°C.

Write down the difference between these two temperatures.

Answer .......................................... °C [1]_____________________________________________________________________________________

3 (a) Calculate 5.7 – 1.032 .

Write down all the numbers displayed on your calculator.

Answer(a) ............................................... [1]

(b) Write your answer to part (a) correct to 3 decimal places.

Answer(b) ............................................... [1]_____________________________________________________________________________________

4 Pedro and Eva do their homework. Pedro takes 84 minutes to do his homework.

The ratio Pedro’s time : Eva’s time = 7 : 6.

Work out the number of minutes Eva takes to do her homework.

Answer ........................................ min [2]_____________________________________________________________________________________

5 Write each of the following as a single vector.

(a) 61e o +

4-

2e o

Answer(a) e o [1]

(b) 43-

2e o

Answer(b) e o [1]

_____________________________________________________________________________________

3


ForExaminer's

Use

6

50°

a°

55°NOT TOSCALE

Use the information in the diagram to fi nd the value of a.

Answer a = ............................................... [2]_____________________________________________________________________________________

7 Show that 1 21 ÷ 16

3 = 8.

Do not use a calculator and show all the steps of your working.

Answer

[2]_____________________________________________________________________________________

8 Sebastian ran a race in 11.4 seconds, correct to 1 decimal place.

Complete the statement about the time, t seconds, that Sebastian took to run the race.

Answer ....................... Ğ t < ....................... [2]_____________________________________________________________________________________

4

0580/11/M/J/13© UCLES 2013

ForExaminer's

Use

9 Rearrange this equation to make b the subject.

a = 5b – 9

Answer b = ............................................... [2]_____________________________________________________________________________________

10 Here are the fi rst four terms of a sequence.

4 11 18 25

Write down an expression for the nth term.

Answer ............................................... [2]_____________________________________________________________________________________

11 x and y are integers.

(a) Find the value of x when –7 < x < –5 .

Answer(a) x = ............................................... [1]

(b) Find the value of y when 43

< y

16 < 87

.

Answer(b) y = ............................................... [2]_____________________________________________________________________________________

12 The probability of Sachin’s team winning any match is 0.45.

(a) Write down the probability of Sachin’s team not winning any match.

Answer(a) ............................................... [1] (b) In a season there are 40 matches.

How many matches should Sachin’s team expect to win in a season?

Answer(b) ............................................... [2]_____________________________________________________________________________________

5


ForExaminer's

Use

13 Complete each statement with the correct mathematical term.

(a)

This solid is a ........................................................ [1]

(b)

This polygon is a regular ............................................... [1] (c)

Angle ABC is an ............................................. angle [1]_____________________________________________________________________________________

14 (a) The perimeter of a square is 28 mm.

Work out the length of one side of the square.

Answer(a) ........................................ mm [1]

(b) Calculate the volume of a cylinder with radius 5.2 cm and height 15 cm.

Answer(b) ........................................ cm3 [2]_____________________________________________________________________________________

15 Bruce invested $420 at a rate of 4% per year compound interest.

Calculate the total amount Bruce has after 2 years. Give your answer correct to 2 decimal places.

Answer $ ...................................... [3]_____________________________________________________________________________________

A

B C

6

0580/11/M/J/13© UCLES 2013

ForExaminer's

Use

16 Martina changed 200 Swiss francs (CHF) into euros (€). The exchange rate was €1 = 1.14 CHF.

Calculate how much Martina received. Give your answer correct to the nearest euro.

Answer € ...................................... [3]_____________________________________________________________________________________

17 In this question use a straight edge and compasses only. Leave in all your construction arcs.

(a) Construct the bisector of angle ABC.

A

B

C[2]

(b) Construct the perpendicular bisector of the line DE.

E

D

[2]_____________________________________________________________________________________

7


ForExaminer's

Use

18 (a) Which two of these have the same value?

5–2 52

2

21

c m 2

52

c m 0.22

Answer(a) ........................ and ........................ [2]

(b) Simplify.

(i) a6 × a3

Answer(b)(i) ............................................... [1]

(ii) 24b16 ÷ 6b4

Answer(b)(ii) ............................................... [2]_____________________________________________________________________________________

19 (a) Multiply out the brackets. 5 ( x + 3 )

Answer(a) ............................................... [1]

(b) Factorise completely. 12xy – 3x2

Answer(b) ............................................... [2]

(c) Solve. 5x – 24 = 51

Answer(c) x = ............................................... [2]_____________________________________________________________________________________


8

0580/11/M/J/13


University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2013

ForExaminer's

Use

20 Marco throws a six-sided dice 27 times. The bar chart shows his results.

8

7

6

5

4

3

2

1

01 2 3 4 5 6

Score on dice

Frequency


Answer(a) ............................................... [1]

(b) Work out the probability that Marco throws a number less than 5.

Answer(b) ............................................... [2]

(c) Calculate the mean.

Answer(c) ............................................... [3]





MATHEMATICS 0580/12


1 hour






*0071500764*

2

0580/12/M/J/13© UCLES 2013

ForExaminer's

Use

1

0 0.5 1.0

Write down the number the arrow points to on the scale.

Answer ............................................... [1]_____________________________________________________________________________________

2

100 164 200 343 999

Write down the cube number from this list.

Answer ............................................... [1]_____________________________________________________________________________________

3 Write down the next prime number after 23.

Answer ............................................... [1]_____________________________________________________________________________________

4 Calculate the number of seconds in 3 hours.

Answer ............................................ s [1] _____________________________________________________________________________________

3


ForExaminer′s

Use

5

The diagram shows the net of a solid.

Write down the mathematical name of this solid.

Answer ............................................... [1]_____________________________________________________________________________________

6 Bryony asks her friends how many pets they have. She is going to use this table to record her results.

Number of pets Frequency

0 – 1

1 – 2

2 – 3

3 or more

Explain what is wrong with this frequency table.

Answer .....................................................................................................................................................

........................................................................................................................................................... [1]_____________________________________________________________________________________

7 (a) Draw an acute angle. Label the acute angle with the letter a.

[1] (b) Write down the mathematical name of angle b.

b

Answer(b) ............................................... [1]_____________________________________________________________________________________

4

0580/12/M/J/13© UCLES 2013

ForExaminer's

Use

8

3 rows2 rows1 row

Complete the table for 4 rows and 5 rows.

Number of rows 1 2 3 4 5

Number of cans 1 3 6[2]

_____________________________________________________________________________________

9 The probability that the school hockey team will win its next match is 0.45 . The probability that it will lose its next match is 0.3 .

Work out the probability that the school hockey team will draw its next match.

Answer ............................................... [2]_____________________________________________________________________________________

10

a = 47e o b =

5-

2e o

Write each of the following as a single vector.

(a) 6a

Answer(a) e o [1]

(b) a + b

Answer(b) e o [1]

_____________________________________________________________________________________

5


ForExaminer′s

Use

11A

B C

8 cm

NOT TOSCALE

Triangle ABC has a height of 8 cm and an area of 42 cm².

Calculate the length of BC.

Answer BC = ......................................... cm [2]_____________________________________________________________________________________

12 (a) Use your calculator to work out 65 – 1.72 .

Write down all the numbers displayed on your calculator.

Answer(a) ............................................... [1]

(b) Write your answer to part (a) correct to 2 signifi cant fi gures.

Answer(b) ............................................... [1]_____________________________________________________________________________________

6

0580/12/M/J/13© UCLES 2013

ForExaminer's

Use

13 The exterior angle of a regular pentagon is 72°.

(a) Write down the interior angle of a regular pentagon.

Answer(a) ............................................... [1]

(b)

The diagram shows three pentagons which fi t together. Uta thinks that three regular pentagons will fi t together in the same way.

Explain how you know she is wrong.

Answer(b) ........................................................................................................................................

................................................................................................................................................... [1]_____________________________________________________________________________________

14

B

A

11

10

9

8

7

6

5

4

3

2

1

10 2 3 4 5 6 7 8 9 10 11 12 13

y

x

Describe fully the single transformation that maps shape A onto shape B.

Answer .............................................................................................................................................. [3]_____________________________________________________________________________________

7


ForExaminer′s

Use

15 (a)

128°

x°

NOT TOSCALE

A straight line intersects two parallel lines as shown.


Answer(a) x = ................................................ [2]

(b)

30°

128° y°

NOT TOSCALE

Calculate the value of y.

Answer(b) y = ............................................... [1]_____________________________________________________________________________________

16 (a) The average distance of the Moon from the Earth is 384 400 km.

Write this distance in standard form.

Answer(a) ......................................... km [1]

(b) Calculate (4.3 × 108 ) + (2.5 × 107 ) .

Give your answer in standard form.

Answer(b) ............................................... [2]_____________________________________________________________________________________

8

0580/12/M/J/13© UCLES 2013

ForExaminer's

Use

17

= < > Write one of the three symbols between each pair of numbers.

Each symbol can be used more than once.

(a) 30% ............ 31

[1]

(b) –2 ............ –3 [1]

(c) π ............ 10 [1]_____________________________________________________________________________________

18 (a)

–3 – 4 –7 2 5 Choose three different numbers from the list to complete this calculation.

.............. + .............. + .............. = – 6 [1]

(b) Find the value of 5x – 3y when x = –2 and y = 4.

Answer(b) ............................................... [2]_____________________________________________________________________________________

9


ForExaminer′s

Use19 Without using a calculator, work out 7

6 ÷ 1 32 .

Write down all the steps in your working.

Answer ............................................... [3]_____________________________________________________________________________________

20

A

BC

ONOT TOSCALE

A, B and C are points on the circumference of a circle centre O. AC is a straight line.

(a) Explain why angle ABC is 90°.

Answer(a) ................................................................................................................................. [1]

(b) The diameter of the circle is 3 cm.

Calculate the area of this circle.

Answer(b) ........................................ cm2 [2]_____________________________________________________________________________________

10

0580/12/M/J/13© UCLES 2013

ForExaminer's

Use

21 Carol invests $6250 at a rate of 2% per year compound interest.

Calculate the total amount Carol has after 3 years.

Answer $ ............................................... [3]_____________________________________________________________________________________

22 Solve the equation. 5(2y – 17) = 60

Answer y = ............................................... [3]_____________________________________________________________________________________

23 (a) Simplify y 0.

Answer(a) ............................................... [1]

(b) Make v the subject of E = 2

1 mv 2.

Answer(b) v = ............................................... [3]_____________________________________________________________________________________

11


ForExaminer′s

Use

24

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–6–7–8–9 –5 –4 –3 –2 –1 10 2 3 4 5 6 7 8 9

y

x

S

(a) On the grid

(i) plot the point (–5 , –2) and label it P, [1]

(ii) draw the line y = 2x. [1]

(b) (i) Write down the order of rotational symmetry of shape S.

Answer(b)(i) ............................................... [1]

(ii) Draw the image of shape S after a rotation through 90° clockwise about (0, 0). [2]_____________________________________________________________________________________

12

0580/12/M/J/13



BLANK PAGE

© UCLES 2013





MATHEMATICS 0580/13


1 hour






*5726780475*

2

0580/13/M/J/13© UCLES 2013

ForExaminer′s

Use

1 The table shows the distances by road, in kilometres, between some towns in New Zealand.

126

426

368

235

657

300

242

109

531

415

229

332

319

356460

AucklandHamiltonNapier

New PlymouthRotoruaWellington

Write down the distance between Rotorua and Hamilton.

Answer ......................................... km [1]_____________________________________________________________________________________

2 Find the value of 1.473. Give your answer correct to 3 decimal places.

Answer ............................................... [2]_____________________________________________________________________________________

3 The time in Lisbon is the same as the time in Funchal. A plane left Lisbon at 08 30 and arrived in Funchal at 10 20. It then left Funchal at 12 55 and returned to Lisbon. The return journey took 15 minutes more.

What time did the plane arrive in Lisbon?

Answer ............................................... [2]_____________________________________________________________________________________

3


ForExaminer′s

Use

4 The Ocean View Hotel has 300 rooms numbered from 100 to 399. A room is chosen at random.

Find the probability that the room number ends in zero.

Answer ............................................... [2]_____________________________________________________________________________________

5 Solve the equation 3x – 5 = 16 .

Answer x = ............................................... [2]_____________________________________________________________________________________

6 A television screen size, S cm, is 80 cm correct to the nearest centimetre.

Complete the statement for S in the answer space.

Answer ......................... Y S I ......................... [2]_____________________________________________________________________________________

4

0580/13/M/J/13© UCLES 2013

ForExaminer′s

Use

7 Sheila can pay her hotel bill in Euros (€) or Pounds (£). The bill was €425 or £365 when the exchange rate was £1 = €1.14 .

In which currency was the bill cheaper? Show all your working.

Answer ............................................... [2]_____________________________________________________________________________________

8 Without using a calculator, show that 35

3 ÷ 2 4

1 = 15

3 .

You must show each step of your working.

Answer

[2]_____________________________________________________________________________________

9 Factorise completely. 6xy2 – 8y

Answer ............................................... [2]_____________________________________________________________________________________

5


ForExaminer′s

Use

10 Use a calculator to fi nd

(a) 5 24

5 ,

Answer(a) ............................................... [1]

(b) °407

cos .

Answer(b) ............................................... [1]_____________________________________________________________________________________

11

81°87°

63°O

B

CD

ANOT TOSCALE

(a) Calculate the size of angle AOB.

Answer(a) Angle AOB = ............................................... [1]

(b) What type of angle is angle AOB?

Answer(b) ............................................... [1]_____________________________________________________________________________________

6

0580/13/M/J/13© UCLES 2013

ForExaminer′s

Use

12y

x

6

5

4

3

2

1

–1

–2

–3

–4

0–1 1 2 3 4 5 6 7 8–2–3–4

P

Q

The points P and Q are marked on the grid.

(a) Work out the vector .

Answer(a) = f p [1]

(b) = 8

1-

-e o

Find the co-ordinates of the point R.

Answer(b) (................ , ................) [1]_____________________________________________________________________________________

13 Huy borrowed $4500 from a bank at a rate of 5% per year compound interest. He paid back the money and interest at the end of 2 years.

How much interest did he pay?

Answer $ ............................................... [3]_____________________________________________________________________________________

7


ForExaminer′s

Use

144 cm

18 cm

5 cm10 cm

NOT TOSCALE

The shaded shape has rotational symmetry of order 2.

Work out the shaded area.

Answer ........................................ cm2 [3]_____________________________________________________________________________________

15 (a) 5x × 53 = 510


Answer(a) x = ............................................... [1]

(b) Simplify. 12h3 ÷ 4h–2

Answer(b) ............................................... [2]_____________________________________________________________________________________

16 Calculate, giving your answers in standard form,

(a) 2 × (5.5 × 104) ,

Answer(a) ............................................... [2]

(b) (5.5 × 104) – (5 × 104) .

Answer(b) ............................................... [2]_____________________________________________________________________________________

8

0580/13/M/J/13© UCLES 2013

ForExaminer′s

Use

17

C

A B

F

ED

6 cm

4 cm

NOT TOSCALE

The diagram shows a triangular prism. Triangle ABC is equilateral. AB = 4 cm and BE = 6 cm.

(a) Write down the size of angle ABC.

Answer(a) Angle ABC = ............................................... [1]

(b) On the 1 cm2 grid, draw an accurate net of the prism. The line BE has been drawn for you.

B E

[3]_____________________________________________________________________________________

9


ForExaminer′s

Use

18 On the fi rst day of each month, a café owner records the midday temperature (°C) and the number of hot meals sold.

Month J F M A M J J A S O N D

Temperature (°C) 2 4 9 15 21 24 28 27 23 18 10 5

Number of hot meals 38 35 36 24 15 10 4 5 12 20 18 32

(a) Complete the scatter diagram. The results for January to June have been plotted for you.

40

35

30

25

20

15

10

5

0 5 10 15Temperature (°C)

20 25 30

Number ofhot meals

[2]

(b) On the grid, draw the line of best fi t. [1]

(c) What type of correlation does this scatter diagram show?

Answer(c) ............................................... [1]_____________________________________________________________________________________

10

0580/13/M/J/13© UCLES 2013

ForExaminer′s

Use

19y

x0 1 2 3 4

8

7

6

5

4

3

2

1

A

The point A (1, 3.5) is plotted on the grid.

(a) Plot the point B (3, 6.5) and draw the straight line through A and B. [1]

(b) (i) Find the gradient of the line in part (a).

Answer(b)(i) ............................................... [2]

(ii) Write down the equation of the line in the form y = mx + c.

Answer(b)(ii) y = ............................................... [2]

(c) On the grid, draw a line through the point (2, 5) that is perpendicular to the line in part (a). [1]_____________________________________________________________________________________

11


ForExaminer′s

Use

20

17 cm

6 cm

B

C

A

NOT TOSCALE

In the diagram, AB is a diameter of the circle and C is a point on the circumference. AB = 17 cm and AC = 6 cm.

(a) Calculate the area of the circle.

Answer(a) ........................................ cm2 [2]

(b) (i) Explain why angle ACB = 90°.

Answer(b)(i) ...................................................................................................................... [1]

(ii) Calculate BC.

Answer(b)(ii) BC = ......................................... cm [3]_____________________________________________________________________________________

12

0580/13/M/J/13



BLANK PAGE

© UCLES 2013





MATHEMATICS 0580/31


2 hours






*8443737097*

2

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

1 (a) On a map, the height of Hillibar Station is 1047 m and the height of Sular Junction is 297 m.

(i) Calculate the difference in these heights.

Answer(a)(i) ........................................... m [1]

(ii) The temperature falls by 1°C for every 100 m increase in height. One day the temperature in Sular Junction is 19°C.

Work out the temperature at Hillibar Station.

Answer(a)(ii) .......................................... °C [1]

(iii) Write 297 correct to the nearest ten.

Answer(a)(iii) ............................................... [1]

(iv) Write 1047 correct to the nearest hundred.

Answer(a)(iv) ............................................... [1]

(b) (i) Kim arrives at Hillibar Station at 12 35. The taxi to her hotel takes 27 minutes.

Work out the time Kim arrives at her hotel.

Answer(b)(i) ............................................... [1]

(ii) Henry takes 17 minutes to walk from his home to Sular Junction. He must arrive there by 10 43.

Work out the latest time he can leave home.

Answer(b)(ii) ............................................... [1]

3


ForExaminer′s

Use

(c) Here is part of a train timetable. Each journey from Sular Junction to Hillibar Station takes the same time.

Sular Junction departs 10 59 12 32 14 48

Hillibar Station arrives 12 35 14 08

(i) Complete the timetable. [2]

(ii) The distance between Sular Junction and Hillibar Station is 64 km.

Calculate the average speed, in kilometres per hour, of a train between these two stations.

Answer(c)(ii) ...................................... km/h [2]

(iii) Joel arrives at Sular Junction at 11 48.

At what time is the next train to Hillibar Station due to depart?

Answer(c)(iii) ............................................... [1]_____________________________________________________________________________________

4

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

2 (a)

43° 108° p°A B

NOT TOSCALE

AB is a straight line.

Find the value of p.

Answer(a) p = ............................................... [1]

(b)

123°

107°88°q°

NOT TOSCALE

Find the value of q.

Answer(b) q = ............................................... [1]

(c)

48°

r°s°

NOT TOSCALE

D C B

A

DCB is a straight line and AB = AC.

Find the values of r and s.

Answer(c) r = ...............................................

s = ............................................... [2]

5


ForExaminer′s

Use

(d)

NOT TOSCALE

B

A

t°

130°

The straight line AB crosses two parallel lines.

Find the value of t.

Answer(d) t = ............................................... [1]

(e)

NOT TOSCALE

u°124°

C

A

B

O

A and B lie on a circle, centre O. AC and BC are tangents to the circle.

Find the value of u.

Answer(e) u = ............................................... [2]_____________________________________________________________________________________

6

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

3 (a) On each of the following shapes draw any lines of symmetry.

(i)

[1]

(ii)

[2]

(b) Complete this shape by shading one square so that it has rotational symmetry of order 2.

[1]

7


ForExaminer′s

Use

(c)

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–6–7 –5 –4 –3 –2 –1 10 2 3 4 5 6 7

y

x

B

AT

On the grid, draw the image of triangle T after a

(i) refl ection in the line x = 4, [2]

(ii) translation by the vector 4

5

-

-e o , [2]

(iii) rotation, centre (4, 1) through 180°. [2]

(d) Describe fully the single transformation that maps

(i) triangle T onto triangle A,

Answer(d)(i) ...................................................................................................................... [3]

(ii) triangle T onto triangle B.

Answer(d)(ii) ..................................................................................................................... [2]_____________________________________________________________________________________

8

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

4 The table shows a summary of the types of employment for 90 people.

Employment Frequency Pie chart sector angle

Retail 18 72°

Leisure industry 12 48°

Public service 35

Other 25

(a) (i) Complete the table. [2]

(ii) Complete the pie chart and label the sectors.

Retail

Leisure industry

[2]

9


ForExaminer′s

Use

(b) Here are the ages of the people working in the leisure industry.

16 17 19 23 23 24 27 31 33 40 45 56

(i) Work out the range.

Answer(b)(i) ...................................... years [1]

(ii) Calculate the mean.

Answer(b)(ii) ...................................... years [2]

(iii) Sabrina wants to interview someone working in the leisure industry. She chooses one person at random.

Write down the probability that the person chosen is under 30 years old.

Answer(b)(iii) ............................................... [1]_____________________________________________________________________________________

10

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

5 The table shows the height, in metres, above sea-level and the temperature, in °C, at midday for some places on a mountain.

Height above sea-level (m) 420 540 660 820 960 1100 1240 1580

Temperature (°C) 29.8 28.3 27.7 27.2 25.4 25.0 24.2 21.0

(a) Complete the scatter diagram for these results. The fi rst four points have been plotted for you.

30

29

28

27

26

25

24

23

22

21

20400 600 800 1000

Height (m)

1200 1400 1600

Temperature(°C)

[2]

(b) What type of correlation does this scatter diagram show?

Answer(b) ............................................... [1]

(c) On the grid, draw the line of best fi t. [1]

(d) Use your line of best fi t to estimate the temperature at a height of 1400 m.

Answer(d) .......................................... °C [1]_____________________________________________________________________________________

11


ForExaminer′s

Use

6 (a) (i) Write down all the factors of 22.

Answer(a)(i) ............................................... [2]

(ii) Write down a multiple of 13 between 30 and 50.

Answer(a)(ii) ............................................... [1]

(b) 1 2 6 9 15 17 19 21 27

(i) Write down all the prime numbers in this list.

Answer(b)(i) ............................................... [2]

(ii) Write down a cube number from this list.

Answer(b)(ii) ............................................... [1]

(c) (i) Write 0.0035 in standard form.

Answer(c)(i) ............................................... [1]

(ii) Calculate (6.3 × 106) ÷ (1.5 × 102). Write your answer in standard form.

Answer(c)(ii) ............................................... [2]_____________________________________________________________________________________

12

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

7

B

A 82 km

27 km

C

North

NOT TOSCALE

The diagram shows the positions of three towns A, B and C. B is 27 km north of A and the distance between A and C is 82 km.

(a) Calculate BC.

Answer(a) BC = ......................................... km [2]

(b) Write down the three fi gure bearing of C from A.

Answer(b) ............................................... [1]

(c) (i) Use trigonometry to calculate angle ABC.

Answer(c)(i) Angle ABC = ............................................... [2]

(ii) Work out the bearing of C from B.

Answer(c)(ii) ............................................... [1]

13


ForExaminer′s

Use

(d) (i) Calculate the area of triangle ABC.

Answer(d)(i) ........................................ km2 [2]

(ii) The land forming the triangle ABC is valued at $8400 for each square kilometre.

Calculate the value of this land.

Answer(d)(ii) $ ................................................ [1]_____________________________________________________________________________________

14

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

8 Ben and Ruth own a company.

(a) The company’s profi ts of $43 680 are shared in the ratio Ben : Ruth = 2 : 5 .

Calculate Ruth’s share of the profi ts.

Answer(a) $ ................................................ [2]

(b) Ruth invests $15 000 at a rate of 4% per year simple interest.

Calculate how much her investment is worth at the end of 3 years.

Answer(b) $ ................................................ [3]

(c) The company employs 450 people. 14% of these people work in sales.

Calculate the number of people who work in sales.

Answer(c) ............................................... [2]

15


ForExaminer′s

Use

(d) Every year Ben travels 32 000 km on business.

(i)

Car-rentCost ($) = 600 + 0.35d

where d is the distance travelled in kilometres

Calculate the cost of hiring a car from Car-rent to travel 32 000 km.

Answer(d)(i) $ ................................................ [2]

(ii)

Drive-easy

Cost = $100 plus $4 for every 10 km travelled

Calculate the cost of hiring a car from Drive-easy to travel 32 000 km.

Answer(d)(ii) $ ................................................ [2]_____________________________________________________________________________________

16

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

9 (a) (i) Complete the table of values for y = x2 + x .

x –3 –2 –1 0 1 2 3

y 6 0 0 6[2]

(ii) On the grid, draw the graph of y = x2 + x for –3 Ğ x Ğ 3 .

y

x

14

13

12

11

10

9

8

7

6

5

4

3

2

1

–1

–2

0 1 2 3–1–2–3

[4]

(iii) On the grid, draw the line y = 10. [1]

(iv) Use both your graphs to solve x2 + x = 10 for –3 Ğ x Ğ 3 .

Answer(a)(iv) x = ............................................... [1]

17


ForExaminer′s

Use (b) Another line, L, has the equation y =

3

2 x – 5 .

(i) Write down the gradient of L.

Answer(b)(i) ............................................... [1]

(ii) Write down the equation of a straight line that is parallel to L.

Answer(b)(ii) ............................................... [1]

(c)y

x

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

0–1 1 2 3 4–2

K

Write the equation of the line, K, in the form y = mx + c .

Answer(c) y = ............................................... [3]_____________________________________________________________________________________

18

0580/31/M/J/13© UCLES 2013

ForExaminer′s

Use

10 (a) In 2001 Arnold was x years old. Ken is 34 years younger than Arnold.

(i) Complete the table, in terms of x, for Arnold’s and Ken’s ages.

2001 2013

Arnold’s age x

Ken’s age[3]

(ii) In 2013 Arnold is three times as old as Ken.

Write down an equation in x and solve it.

Answer(a)(ii) x = ............................................... [4]

19


ForExaminer′s

Use

(b) Solve the simultaneous equations.

3x + 2y = 18 2x – y = 19

Answer(b) x = ...............................................

y = ............................................... [3]_____________________________________________________________________________________


20

0580/31/M/J/13



© UCLES 2013

ForExaminer′s

Use

11 (a) Calculate the area of a circle of radius 6 cm.

Answer(a) ........................................ cm2 [2]

(b)

6 cmNOT TOSCALE

Each circle in this rectangle has a radius of 6 cm. The circles fi t exactly in the rectangle.

Calculate the shaded area.

Answer(b) ........................................ cm2 [4]





MATHEMATICS 0580/32


2 hours






*4956619265*

2

0580/32/M/J/13© UCLES 2013

ForExaminer′s

Use

1 (a)

3 5 8 10 10 For the numbers above, fi nd

(i) the mean,

Answer(a)(i) ............................................... [2]

(ii) the mode, Answer(a)(ii) ............................................... [1]

(iii) the median, Answer(a)(iii) ............................................... [1]

(iv) the range. Answer(a)(iv) ............................................... [1]

(v) A sixth number, 11, is added to the list.

Write down which one of the mean, the mode, the median and the range will stay the same.

Answer(a)(v) ............................................... [1]

(b) The table shows the results of asking 24 children their favourite colour.

Colour Red Blue Yellow Green Pink

Number of children 4 8 2 3 7

Write down the probability, as a fraction, that the favourite colour of a child chosen at random is

(i) blue, Answer(b)(i) ............................................... [1]

(ii) not pink. Answer(b)(ii) ............................................... [1]

(c) The information in part (b) is to be shown in a pie chart.

Work out the sector angle for green. Do not draw the pie chart.

Answer(c) ............................................... [2]_____________________________________________________________________________________

3


ForExaminer′s

Use

2 Three children have some marbles. Shireen has m marbles. Nazaneen has three times as many marbles as Shireen. Karly has 4 more marbles than Shireen.

(a) Write down an expression, in terms of m, for

(i) the number of marbles Nazaneen has,

Answer(a)(i) ............................................... [1]

(ii) the number of marbles Karly has.

Answer(a)(ii) ............................................... [1]

(b) The three children have a total of 84 marbles between them.

(i) Write down an equation in m.

Answer(b)(i) ............................................... [1]

(ii) Solve your equation.

Answer(b)(ii) m = ............................................... [2]

(c) Shireen weighs the 84 identical marbles. Their total weight is 4.2 kg.

Calculate, in grams, the weight of one marble.

Answer(c) ............................................ g [2]

(d) The children now decide to share the 84 marbles in the ratio

Shireen : Nazaneen : Karly = 2 : 7 : 3 .

Calculate the number of marbles each receives.

Answer(d) Shireen ...............................................

Nazaneen ...............................................

Karly ............................................... [3]_____________________________________________________________________________________

4

0580/32/M/J/13© UCLES 2013

ForExaminer′s

Use

3 (a) A shop has maps arranged in bookcases.

(i) The length of one wall in the shop is 7.35 m. Each bookcase is 120 cm wide.

Work out the maximum number of bookcases that will fi t along this wall.

Answer(a)(i) ............................................... [2]

(ii) Each bookcase weighs 45 kg correct to the nearest 5 kg.

Write down the upper bound for the weight of a bookcase.

Answer(a)(ii) .......................................... kg [1]

(b) During July and August the shop sells a total of 160 maps. Some of these maps are driving maps and the rest are walking maps.

(i) Complete the table below.

Driving maps Walking maps Total

July 15

August 65

Total 40 160[2]

(ii) Write down the fraction of the total number of walking maps that are sold in July. Give your answer in its simplest form.

Answer(b)(ii) ............................................... [2]

5


ForExaminer′s

Use

(c) The shopkeeper buys each map for $5.50 . He sells each map for $6.60 .

(i) Calculate his percentage profi t.

Answer(c)(i) ........................................... % [3]

(ii) Each map has a price in dollars ($) and euros (€). The price is $6.60 or €3.52 .

Work out the exchange rate for €1 .

Answer(c)(ii) €1 = $ ............................................... [2]

(d) The shop is open for 312 days each year. The shopkeeper pays 3 employees $47.66 each per day.

The total annual wage bill for the three employees is given by

3 × 312 × 47.66 .

(i) Rewrite this calculation so that each number is rounded to 1 signifi cant fi gure.

3 × ........... × ........... [1]

(ii) Use your answer to part (d)(i) to work out an estimate for the total annual wage bill.

Answer(d)(ii) $ ............................................... [1]_____________________________________________________________________________________

6

0580/32/M/J/13© UCLES 2013

ForExaminer′s

Use

4 The diagram is part of a map showing the position of two towns Anderro, A, and Bratena, B. The scale is 1 centimetre represents 10 kilometres.

North

North

A

B

Scale: 1 cm to 10 km

(a) Work out the distance, in kilometres, from Anderro to Bratena.

Answer(a) ......................................... km [2]

(b) Measure the bearing of Bratena from Anderro.

Answer (b) ............................................... [1]

(c) Carribon is 80 km from Anderro. The bearing of Carribon from Anderro is 304°.

Mark the position of Carribon on the diagram. Label it C. [2]_____________________________________________________________________________________

7


ForExaminer′s

Use

5

A

B

C D

E

(a) In this part, all constructions must be completed using a straight edge and compasses only. All construction arcs must be clearly shown.

(i) Construct the perpendicular bisector of DE. [2]

(ii) Mark the midpoint of DE with the letter M. [1]

(iii) Construct the bisector of angle BCD. Label the point, F, where this line crosses the line you have drawn in part (a)(i). [2]

(iv) Write down the mathematical name of the quadrilateral CDMF.

Answer(a)(iv) ............................................... [1]

(b) (i) Draw the locus of points which are 4 cm from A. [1]

(ii) Draw the locus of points which are 3 cm from E. [1]

(iii) Shade the region which is less than 3 cm from E and more than 4 cm from A. [1]_____________________________________________________________________________________

8

0580/32/M/J/13© UCLES 2013

ForExaminer′s

Use

6 Finn is going camping. The diagram shows his tent.

2.5 m

1.5 m1.2 m

M CA

B NOT TOSCALE

ABC is an isosceles triangle. M is the midpoint of AC. AB = 1.5 m and BM = 1.2 m.

(a) Show that AM = 0.9 m.

Answer(a)

[2]

(b) Use trigonometry to calculate angle ABM.

Answer(b) Angle ABM = ............................................... [2]

9


ForExaminer′s

Use

(c) The tent is a prism of length 2.5 m. The area of triangle ABC is 1.08 m2.

Calculate the volume of the tent. Give the units of your answer.

Answer(c) ............................ .............. [2]

(d) Calculate the surface area of the tent, including the base.

Answer(d) .......................................... m2 [3]_____________________________________________________________________________________

10

0580/32/M/J/13© UCLES 2013

ForExaminer′s

Use

7 (a) Complete the table of values for the function y = x2 – 5x + 2 .

x –1 0 1 2 3 4 5

y –2 –4 –4 2[2]

(b) On the grid, draw the graph of y = x2 – 5x + 2 for –1 Ğ x Ğ=5 .

y

x

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

0–1–2–3–4–5–6 5 64321

[4]

11


ForExaminer′s

Use

(c) (i) Write down the co-ordinates of the lowest point of the graph of y = x2 – 5x + 2 .

Answer(c)(i) (.................. , ..................) [1]

(ii) On the grid, draw the line y = –1 . [1]

(iii) Write down the x co-ordinates of the two points where y = –1 crosses the graph of y = x2 – 5x + 2 .

Answer(c)(iii) x = .................. and x = .................. [2]

(d) The point (5, 2) is refl ected in the y-axis.

Write down the co-ordinates of the image of the point.

Answer(d) (.................. , ..................) [1]

(e) Write down the equation of the line, l, drawn on the grid below. Give your answer in the form y = mx + c .

y

x

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

0–1 1 2 3 4 5–2–3

l

Answer(e) y = ............................................... [3]_____________________________________________________________________________________

12

0580/32/M/J/13© UCLES 2013

ForExaminer′s

Use

8

5

4

3

2

1

014 10 14 20 14 30 14 40 14 50 15 00

Time15 10 15 20 15 30 15 40

Distance(km)

Sweetshop

Home

(a) Jono walked from his home to a sweet shop.

Use the travel graph to calculate his walking speed in kilometres per hour.

Answer(a) ...................................... km/h [2]

(b) Jono stayed in the sweet shop for 20 minutes. He then ran home at a steady speed of 12 km/h.

(i) On the grid above, complete the travel graph for Jono. [2]

(ii) Write down the time Jono arrived home.

Answer(b)(ii) ............................................... [1]

13


ForExaminer′s

Use

(c) The sweet shop owner records how much time and how much money children spend in his shop.

Time in shop (min) 3 6 7 9 10 11 12 14 15 15 20

Money spent ($) 0.50 1.20 1.10 1.60 2.00 1.70 2.00 2.80 2.30 2.90 3.00

05 10 15 20 25

Time in shop (min)

Moneyspent ($)

3

2

1

(i) Complete the scatter diagram. The fi rst seven points have been plotted for you. [2]

(ii) What type of correlation does this scatter diagram show?

Answer(c)(ii) ............................................... [1]

(iii) On the grid, draw the line of best fi t. [1]

(iv) A child spent $2.50 in the shop. Use your line of best fi t to estimate how long the child was in the shop.

Answer(c)(iv) ........................................ min [1]_____________________________________________________________________________________

14

0580/32/M/J/13© UCLES 2013

ForExaminer′s

Use

9 A family of 2 adults and 3 children are on holiday. They each hire a mountain bike from the hotel.

Large mountain bike Small mountain bike

First hour Each extra hour First hour Each extra hour

$6 $2 $3.60 $1.20

(a) The family hire 2 large and 3 small mountain bikes for 5 hours.

(i) Work out the total cost.

Answer(a)(i) $ ............................................... [3]

(ii) The hotel gives the family a discount of 15% on the total cost. Work out how much the family pays.

Answer(a)(ii) $ ............................................... [2]

(b) A wheel of a large bike has a radius of 32 cm.

(i) Calculate the circumference of a wheel of a large bike.

Answer(b)(i) ......................................... cm [2]

15


ForExaminer′s

Use

(ii) The family cross a bridge which is 24 m long.

Calculate how many complete turns a wheel of a large bike makes to cross the bridge.

Answer(b)(ii) ............................................... [2]

(c) The diagram shows part of a wheel of a large bike. There is an angle of 9° between two metal spokes. Each spoke is 29 cm long.

Calculate the total length of metal, in metres, needed to make the spokes for one wheel.

Answer(c) ........................................... m [3]_____________________________________________________________________________________


9°NOT TOSCALE

16

0580/32/M/J/13



© UCLES 2013

ForExaminer′s

Use

10 (a) (i) Find the highest common factor (HCF) of 24 and 36.

Answer(a)(i) ............................................... [2]

(ii) Factorise. 24x + 36y

Answer(a)(ii) ............................................... [1]

(b) Simplify.

(i) w + 8k – 5w + 2k

Answer(b)(i) ............................................... [2]

(ii) (x4)5

Answer(b)(ii) ............................................... [1]

(c) Here are the fi rst four terms of a sequence.

7 11 15 19

Find the nth term of this sequence.

Answer(c) ............................................... [2]

(d) Solve the simultaneous equations.

3x + y = 8 x + 5y = 5

Answer(d) x = ...............................................

y = ............................................... [3]





MATHEMATICS 0580/33


2 hours






*0303734794*

2

0580/33/M/J/13© UCLES 2013

ForExaminer′s

Use

1 (a) Kasem earns $900 each month. 14% of this amount is deducted for tax and insurance.

Show that he receives $774 each month.

Answer(a)

[2]

(b) He pays 92 of the $774 in rent.

Calculate the amount of rent he pays.

Answer(b) $ ............................................... [1]

(c) Kasem spends $480 each month on food, entertainment and clothes. He shares this in the ratio

food : entertainment : clothes = 9 : 3 : 4.

Calculate how much he spends on food each month.

Answer(c) $ ............................................... [2]

(d) Kasem saves the rest of his money.

Work out the amount he saves as a percentage of $774.

Answer(d) ........................................... % [2]_____________________________________________________________________________________

3


ForExaminer′s

Use

2 (a) 2 12 144 40 .6 25 110 11 4 80 0.25

From this list of numbers, write down

(i) a two-digit odd number,

Answer(a)(i) ............................................... [1]

(ii) a square number,

Answer(a)(ii) ............................................... [1]

(iii) the value of 2–2,

Answer(a)(iii) ............................................... [1]

(iv) an irrational number,

Answer(a)(iv) ............................................... [1]

(v) the lowest common multiple of 8 and 10,

Answer(a)(v) ............................................... [2]

(vi) the cube root of 8.

Answer(a)(vi) ............................................... [1]

(b) (i) Find the smallest factor, apart from 1, of 2013.

Answer(b)(i) ............................................... [1]

(ii) Write 2013 as the product of its prime factors.

Answer(b)(ii) ................. × ................. × ................. [2]_____________________________________________________________________________________

4

0580/33/M/J/13© UCLES 2013

ForExaminer′s

Use

3

AB

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–9

–6–7–8 –5 –4 –3 –2 –1 10 2 3 4 5 6 7 8

y

x

(a) Write down the order of rotational symmetry of shape A.

Answer(a) ............................................... [1]

(b) Describe fully the single transformation which maps shape A onto shape B.

Answer(b) ................................................................................................................................. [2]

(c) (i) Translate shape A by the vector . Label the image C. [2]

(ii) Rotate shape A through 90° clockwise about the origin. Label the image D. [2]

5

7

-

-e o

5


ForExaminer′s

Use

(d) Triangle LMN is drawn on the 1 cm2 grid below.

(i) Enlarge triangle LMN by scale factor 3 from the centre P.

L M

N

P

[2]

(ii) Write down the length of the base, LM, and the height of triangle LMN.

Answer(d)(ii) LM = ......................................... cm

Height = ......................................... cm [2]

(iii) Calculate the area of triangle LMN.

Answer(d)(iii) ........................................ cm2 [2]

(iv) Find the area of the enlarged triangle.

Answer(d)(iv) ........................................ cm2 [2]_____________________________________________________________________________________

6

0580/33/M/J/13© UCLES 2013

ForExaminer′s

Use

4 (a) The table shows some values of y = x2 – 2x – 1.

x –3 –2 –1 0 1 2 3 4

y 14 2 –1 –2 7

(i) Complete the table. [2]

(ii) On the grid, draw the graph of y = x2 – 2x – 1 for –3 Y x Y 4.

y

x

16

14

12

10

8

6

4

2

–2

–4

0 1 2 3 4–1–2–3

[4]

7


ForExaminer′s

Use

(b) Write down the equation of the line of symmetry of the graph.

Answer(b) ............................................... [1]

(c) The point with co-ordinates (–3, 7) lies on the line y = –x + 4 .

(i) Write down the co-ordinates of two other points on this line. Use x co-ordinates so that –3 < x Y 4 .

Answer(c)(i) (............... , ...............) and (............... , ...............) [2]

(ii) On the grid, draw the line y = –x + 4 for –3 Y x Y 4 . [1]

(iii) Use both graphs to fi nd the solutions of the equation x2 – 2x – 1 = –x + 4 .

Answer(c)(iii) x = ................. or x = ................. [2]_____________________________________________________________________________________

8

0580/33/M/J/13© UCLES 2013

ForExaminer′s

Use

5 (a)

North

North

B

C

D

AScale: 1 cm to 12 km

The diagram shows four towns, A, B, C and D, joined by straight roads AB, BC and BD. The scale is 1 centimetre represents 12 kilometres.

(i) Measure the bearing of B from A.

Answer(a)(i) ............................................... [1]

(ii) Work out the distance in kilometres from A to B.

Answer(a)(ii) ......................................... km [2]

(iii) Saraswati takes 1 hour 30 minutes to drive from A to B.

Calculate her average speed, in kilometres per hour, for this journey.

Answer(a)(iii) ...................................... km/h [1]

9


ForExaminer′s

Use

(b) At B, Saraswati follows another straight road which is equidistant from BC and BD.

Using a straight edge and compasses only and leaving in all your construction lines, construct the line of this road on the diagram. [2]

(c) Another motorist, Leah, leaves C and drives on a bearing of 165° to meet Saraswati at town E. Town E is on the road in part (b).

Show Leah’s journey on the diagram and mark the town E. [1]

(d) Saraswati travelled from B to E at an average speed of 55 km/h.

Calculate the time, in hours and minutes, that she took.

Answer(d) ......................... h ......................... min [4]

(e) There is a speed limit of 50 km/h on all roads within 30 km of town D.

On the diagram, show the boundary of the region where this speed limit applies. [2]_____________________________________________________________________________________

10

0580/33/M/J/13© UCLES 2013

ForExaminer′s

Use

6

Felix rolls two fair dice, each numbered from 1 to 6, and adds the numbers shown. He repeats the experiment 70 times and records the results in a frequency table.

The fi rst 60 results are shown in the tally column of the table. The last 10 results are 6, 8, 9, 2, 6, 4, 7, 9, 6, 10 .

Total Tally Frequency

2

3

4

5

6

7

8

9

10

11

12

(a) (i) Complete the frequency table to show all his results. [2]

(ii) Write down the relative frequency of a total of 5.

Answer(a)(ii) ............................................... [1]

11


ForExaminer′s

Use

(b) (i) Write down the mode.

Answer(b)(i) ............................................... [1]

(ii) Write down the range.

Answer(b)(ii) ............................................... [1]

(iii) Work out the median.

Answer(b)(iii) ............................................... [2]

(iv) Calculate the mean.

Answer(b)(iv) ............................................... [3]

(c) (i) Complete this table showing how different totals can be made when rolling two dice.

Dice 2

Dice 1

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6

3

4 7

5 7 9

6 12

[1]

(ii) Explain why 7 is the most likely total.

Answer(c)(ii) ..................................................................................................................... [1]_____________________________________________________________________________________

12

0580/33/M/J/13© UCLES 2013

ForExaminer′s

Use

7 (a)B C

DA

h

8.4 cm

12.5 cm

5.5 cm

70°

NOT TOSCALE

In the quadrilateral ABCD, BC is parallel to AD. AB = 5.5 cm, BC = 8.4 cm, AD = 12.5 cm and angle BAD = 70°. The height of the quadrilateral is h.

(i) Write down the mathematical name of the quadrilateral ABCD.

Answer(a)(i) ............................................... [1]

(ii) Use trigonometry to show that h = 5.2 cm, correct to 1 decimal place.

Answer(a)(ii)

[2]

(iii) Calculate the area of the quadrilateral ABCD.

Answer(a)(iii) ........................................ cm2 [2]

13


ForExaminer′s

Use

(iv) The quadrilateral forms the cross section of a prism with length 6.8 cm.

Calculate the volume of the prism. Give your answer correct to 2 signifi cant fi gures.

Answer(a)(iv) ........................................ cm3 [2]

(b)

C

B

A

E D

y°z°

w° x°64°

95° NOT TOSCALE

The diagram shows a pentagon, ABCDE. AB is parallel to DC. A straight line, parallel to ED, passes through the vertex C.

(i) Find the values of w, x and y.

Answer(b)(i) w = ...............................................

x = ...............................................

y = ............................................... [3]

(ii) The sum of the angles of a pentagon is 540°.

Find the value of z.

Answer(b)(ii) z = ............................................... [2]_____________________________________________________________________________________

14

0580/33/M/J/13© UCLES 2013

ForExaminer′s

Use

8 (a) Simplify the following expressions.

(i) 3m – 5m + 6m

Answer(a)(i) ............................................... [1]

(ii) 5e – 4f – 3e – 6f

Answer(a)(ii) ............................................... [2]

(b) s = u + at

(i) Calculate the value of s when u = 27, a = –2 and t = 15.

Answer(b)(i) s = ............................................... [2]

(ii) Make t the subject of the formula s = u + at.

Answer(b)(ii) t = ............................................... [2]

(c) Solve the simultaneous equations.

5x + 2y = 4 4x – y = 11

Answer(c) x = ................................................

y = ................................................ [3]_____________________________________________________________________________________

15


ForExaminer′s

Use

9 (a) Write down the next term and the rule for fi nding the next term for the following sequences.

(i) 3, 9, 27, 81, ...

Answer(a)(i) Next term .................. rule ......................................................................... [2]

(ii) 2, 3, 6, 11, 18, ...

Answer(a)(ii) Next term .................. rule ....................................................................... [2]

(iii) 4, 2, 1, 21 , ...

Answer(a)(iii) Next term .................. rule ...................................................................... [2]

(iv) 5, –10, 20, –40, ...

Answer(a)(iv) Next term .................. rule ....................................................................... [2]

(b) (i) Write down the next two terms of this sequence.

5, 13, 21, 29, ............. , ............. [2] (ii) Write down the nth term of this sequence.

Answer(b)(ii) ............................................... [2]

(iii) Find the 100th term.

Answer(b)(iii) ............................................... [1]_____________________________________________________________________________________

16

0580/33/M/J/13



BLANK PAGE

© UCLES 2013





MATHEMATICS 0580/11


1 hour






*1288077579*

2

0580/11/O/N/13© UCLES 2013

ForExaminer′s

Use

1 Write in fi gures the number one hundred and twenty one thousand and forty two.

Answer ............................................... [1]_____________________________________________________________________________________

2 Write down the number of centimetres in 22

1 metres.

Answer ......................................... cm [1]_____________________________________________________________________________________

3 Work out 72 cents as a percentage of 83 cents.

Answer ........................................... % [1]_____________________________________________________________________________________

4 There were 41 524 people at a football match.

(a) Write 41 524 correct to the nearest thousand.

Answer(a) ............................................... [1]

(b) One quarter of the 41 524 people left before the end of the game.

Find the number of people who left before the end of the game.

Answer(b) ............................................... [1]_____________________________________________________________________________________

5 (a) Write down the order of rotational symmetry of this shape.

Answer(a) ............................................... [1]

(b) Draw the lines of symmetry on this shape.

[1]_____________________________________________________________________________________

3


ForExaminer′s

Use

6y

x

5

4

3

2

1

–1

–2

0–1 1 2 3 4 5–2–3

A

(a) Write down the co-ordinates of point A.

Answer(a) (...................... , ......................) [1]

(b) On the grid, plot the point (–1, 3). [1]_____________________________________________________________________________________

7 Simplify the following expression.5a – 3b – 2a – b

Answer ............................................... [2]_____________________________________________________________________________________

8 Calculate . .. .

4 89 4 075 27 0 93

-

- .

Give your answer correct to 4 signifi cant fi gures.

Answer ............................................... [2]_____________________________________________________________________________________

4

0580/11/O/N/13© UCLES 2013

ForExaminer′s

Use

9

55° p°

NOT TOSCALE

Find the value of p.

Answer p = ............................................... [2]_____________________________________________________________________________________

10 Calculate 17.5% of 44 kg.

Answer .......................................... kg [2]_____________________________________________________________________________________

11 Find the value of

(a) 94,

Answer(a) ............................................... [1]

(b) 60.

Answer(b) ............................................... [1]_____________________________________________________________________________________

5


ForExaminer′s

Use

12 Solve the equation. 5 – 2x = 3x – 19

Answer x = ............................................... [2]_____________________________________________________________________________________

13 Yim knows one angle of an isosceles triangle is 48°. He says one of the other angles must be 66°.

Explain why Yim is wrong.

Answer ..............................................................................................................................................

........................................................................................................................................................... [2]_____________________________________________________________________________________

14

S P A C E S

One of the 6 letters is taken at random.

(a) Write down the probability that the letter is S.

Answer(a) ............................................... [1]

(b) The letter is replaced and again a letter is taken at random. This is repeated 600 times.

How many times would you expect the letter to be S?

Answer(b) ............................................... [1]_____________________________________________________________________________________

6

0580/11/O/N/13© UCLES 2013

ForExaminer′s

Use

15 The length, p cm, of a car is 440 cm, correct to the nearest 10 cm.

Complete the statement about p.

Answer ....................... Ğ p < ....................... [2]_____________________________________________________________________________________

168 15 7 8 7 15 4 13 4 3 10 2 9 4 5


Answer(a) ............................................... [1]

(b) Work out the median.

Answer(b) ............................................... [2]_____________________________________________________________________________________

17 Bruce invested $800 at a rate of 3% per year simple interest.

Calculate the total amount he has after 6 years.

Answer $ ............................................... [3]_____________________________________________________________________________________

7


ForExaminer′s

Use

18

A

P

B C

(a) On the diagram above, draw a line perpendicular to the line AB, through the point P. [1]

(b) Using a straight edge and compasses only, construct the locus of points that are equidistant from A and from C. [2]

_____________________________________________________________________________________

8

0580/11/O/N/13© UCLES 2013

ForExaminer′s

Use

19 The diagram shows a ladder of length 8 m leaning against a vertical wall.

56°

8 m

NOT TOSCALE

h

Use trigonometry to calculate h. Give your answer correct to 2 signifi cant fi gures.

Answer h = ............................................ m [3]_____________________________________________________________________________________

20 a = 43e o b =

2

0

-e o c =

5-

1e o

Find

(a) 4a,

Answer(a) f p [2]

(b) b – c.

Answer(b) f p [2]

_____________________________________________________________________________________

9


ForExaminer′s

Use

21 Do not use a calculator in this question and show all the steps of your working.

Give each answer as a fraction in its lowest terms.

Work out.

(a) 43

– 121

Answer(a) ............................................... [2]

(b) 22

1 × 25

4

Answer(b) ............................................... [2]_____________________________________________________________________________________

22 (a) Factorise completely. 6ab – 24bc

Answer(a) ............................................... [2]

(b) Rearrange the following formula to make m the subject.

j = nm – k

Answer(b) m = ............................................... [2]_____________________________________________________________________________________

10

0580/11/O/N/13© UCLES 2013

ForExaminer′s

Use

23 (a) Here are the fi rst four terms of a sequence.

27 23 19 15

(i) Write down the next term in the sequence.

Answer(a)(i) ............................................... [1]

(ii) Explain how you worked out your answer to part (a)(i).

Answer(a)(ii) ..................................................................................................................... [1]

(b) The nth term of a different sequence is 4n – 2 .

Write down the fi rst three terms of this sequence.

Answer(b) ................. , ................. , ................. [1]

(c) Here are the fi rst four terms of another sequence.

–1 2 5 8

Write down the nth term of this sequence.

Answer(c) ............................................... [2]_____________________________________________________________________________________

11

BLANK PAGE

0580/11/O/N/13© UCLES 2013

12

0580/11/O/N/13



BLANK PAGE

© UCLES 2013





MATHEMATICS 0580/12


1 hour






*1262666784*

2

0580/12/O/N/13© UCLES 2013

ForExaminer′s

Use

1 Put one pair of brackets into this equation to make it correct.

3 + 5 × 4 – 2 = 13[1]

_____________________________________________________________________________________

2 p = 3

2-e o q =

4

1-e o

Work out p + q.

Answer f p [1]

_____________________________________________________________________________________

3 Zingon make light bulbs.

The probability that a Zingon light bulb is faulty is 201

.

Gina tests 240 of these light bulbs.

How many of them would she expect to be faulty?

Answer ............................................... [1]_____________________________________________________________________________________

4 The pictogram shows information about the numbers of different drinks sold in a café in one hour.

Coffee

Tea

Hot chocolate

Juice

Key: represents 4 cups

(a) In this hour, 14 cups of hot chocolate were sold. Complete the pictogram using this information. [1]

(b) How many more cups of coffee than cups of tea were sold?

Answer(b) ............................................... [1]_____________________________________________________________________________________

3


ForExaminer′s

Use


19% 51 .0 038 sin 11.4° 0.7195

Answer ......................... < ......................... < ......................... < ......................... < ......................... [2]_____________________________________________________________________________________

6 Use a calculator to work out the following.

(a) 3 (– 4 × 62 – 5)

Answer(a) ............................................... [1]

(b) 3 × tan 30° + 2 × sin 45°

Answer(b) ............................................... [1]_____________________________________________________________________________________

7 Find the circumference of a circle of radius 2.5 cm.

Answer ......................................... cm [2]_____________________________________________________________________________________

8 Bruce plays a game of golf. His scores for each of the 18 holes are shown below.

2 3 4 5 4 6 2 3 4

4 5 3 4 3 5 4 4 4

The information is to be shown in a pie chart.

Calculate the sector angle for the score of 4.

Answer ............................................... [2]_____________________________________________________________________________________

4

0580/12/O/N/13© UCLES 2013

ForExaminer′s

Use

9 (a) Add one line to the diagram so that it has two lines of symmetry.

[1]

(b) Add two lines to the diagram so that it has rotational symmetry of order 2.

[1]_____________________________________________________________________________________

10

4.6 cm

7.2 cmA C

BNOT TOSCALE

Calculate AB.

Answer ......................................... cm [2]_____________________________________________________________________________________

5


ForExaminer′s

Use

11 The table shows how the dollar to euro conversion rate changed during one day.

Time 10 00 11 00 12 00 13 00 14 00 15 00 16 00

$1 €1.3311 €1.3362 €1.3207 €1.3199 €1.3200 €1.3352 €1.3401

Khalil changed $500 into euros (€).

How many more euros did Khalil receive if he changed his money at the highest rate compared to the lowest rate?

Answer € ................................................ [3]_____________________________________________________________________________________

12 Pam wins the student of the year award in New Zealand. She sends three photographs of the award ceremony by post to her relatives.

● one of size 13 cm by 23 cm to her uncle in Australia ● one of size 15 cm by 23 cm to her sister in China ● one of size 23 cm by 35 cm to her mother in the UK

Maximum lengths Australia Rest of the world

13 cm by 23.5 cm $1.90 $2.50

15.5 cm by 23.5 cm $2.40 $2.90

23 cm by 32.5 cm $2.80 $3.40

26 cm by 38.5 cm $3.60 $5.20

The cost of postage is shown in the table above. Use this information to calculate the total cost.

Answer $ ................................................ [3]_____________________________________________________________________________________

6

0580/12/O/N/13© UCLES 2013

ForExaminer′s

Use

13 (a) Complete the following statement.

The two common factors of 15 and 20 are 1 and ......................... . [1]

(b) Write down the next square number that is greater than 169.

Answer(b) ............................................... [1]

(c) Write down a prime number between 90 and 100.

Answer(c) ............................................... [1]_____________________________________________________________________________________

14 The straight line, L, has the equation y = 5 – 2x .

Write down

(a) the co-ordinates of the point where the line crosses the y-axis,

Answer(a) (....................... , .......................) [1]

(b) the gradient of the line,

Answer(b) ............................................... [1]

(c) the equation of a line parallel to L. Give your answer in the form y = mx + c.

Answer(c) y = ............................................... [1]_____________________________________________________________________________________

7


ForExaminer′s

Use

15 c = 10d + 3

(a) Find the value of c when d = 2.3 .

Answer(a) c = ............................................... [1]

(b) Make d the subject of the formula.

Answer(b) d = ............................................... [2]_____________________________________________________________________________________

16

10 cm

6 cm

NOT TOSCALE

This shape is made from a rectangle and a semicircle. The rectangle measures 10 cm by 6 cm.

Work out the area of the shape.

Answer ........................................ cm2 [3]_____________________________________________________________________________________

8

0580/12/O/N/13© UCLES 2013

ForExaminer′s

Use

17 Solve the simultaneous equations.2x + 5y = 264x + 3y = 24

Answer x = ...............................................

y = ............................................... [3]_____________________________________________________________________________________

18 Simplify the following.

(a) x5 × x2

Answer(a) ............................................... [1]

(b) 20y4 ÷ 4y–2

Answer(b) ............................................... [2]_____________________________________________________________________________________

9


ForExaminer′s

Use

19 Mario says that 5 gallons = 22.5 litres.

(a) On the grid, draw a straight line to show the conversion rate that Mario uses.

25

20

15

10

5

01 2 3

Gallons

Litres

4 5

[2]

(b) Use your graph to fi nd

(i) the number of litres equivalent to 4 gallons,

Answer(b)(i) ...................................... litres [1]

(ii) the number of gallons equivalent to 15 litres.

Answer(b)(ii) .................................. gallons [1]_____________________________________________________________________________________

10

0580/12/O/N/13© UCLES 2013

ForExaminer′s

Use

20

The diagram shows part of the net of a cuboid. It is drawn full size.

(a) Complete the net of the cuboid. [2]

(b) Work out the volume of the cuboid. Write down the units of your answer.

Answer(b) ................................ .............. [3]_____________________________________________________________________________________

11


ForExaminer′s

Use

21 Use a straight edge and compasses only for the constructions in parts (a) and (b). Leave in all your construction arcs.

A

B

C

(a) Construct the bisector of angle ABC. [2]

(b) Construct the perpendicular bisector of AB. [2]

(c) Shade the region inside triangle ABC containing points that are

● less than 7 cm from C and ● closer to A than to B. [2]_____________________________________________________________________________________

12

0580/12/O/N/13



BLANK PAGE

© UCLES 2013





MATHEMATICS 0580/13


1 hour






*3349079136*

2

0580/13/O/N/13© UCLES 2013

ForExaminer′s

Use

1 The table shows the daily takings, correct to the nearest dollar, of a shop during one week.

Day Mon Tue Wed Thu Fri Sat Sun

Takings ($) 153 201 178 231 164 147 156

Find the range.

Answer $ ................................................ [1]_____________________________________________________________________________________

2 Factorise. 2a2 – 5a

Answer ............................................... [1]_____________________________________________________________________________________

3 The table shows the average monthly temperatures in Ulaanbaatar, Mongolia.


Temperature (°C) –25 –30 –12 –2 6 13 17 10 7 0 –13 –22

By how many degrees does the temperature rise between March and July?

Answer .......................................... °C [1]_____________________________________________________________________________________

4 Christa had a music lesson every week for one year. Each of the 52 lessons lasted for 45 minutes.

Calculate the total time that Christa spent in music lessons. Give your time in hours.

Answer ............................................ h [2]_____________________________________________________________________________________

3


ForExaminer′s

Use

5 (a) Write 2563 correct to the nearest 100.

Answer(a) ............................................... [1]

(b) Write 0.0584 correct to 2 signifi cant fi gures.

Answer(b) ............................................... [1]_____________________________________________________________________________________

6A B C D E F G H I J K

(a) A letter is chosen at random from the list above.

Write down, as a fraction, the probability that the letter has no curved parts.

Answer(a) ............................................... [1]

(b) On the probability scale, mark an arrow to show this probability.

0 0.5 1

[1]_____________________________________________________________________________________

7 Three of the vertices of a parallelogram are at (4, 12), (8, 4) and (16, 16).

4 8–8 –4 12 16 20 240

y

x

24

20

16

12

8

4

Write down the co-ordinates of two possible positions of the fourth vertex.

Answer (........... , ...........) and (........... , ...........) [2]_____________________________________________________________________________________

4

0580/13/O/N/13© UCLES 2013

ForExaminer′s

Use

8 (a) A train leaves Hamilton at 9.50 am and arrives in Wellington at 7.25 pm.

Work out, in hours and minutes, the time taken for this journey.

Answer(a) ................. h ................. min [1]

(b) Write 7.25 pm using the 24-hour clock.

Answer(b) ............................................... [1]_____________________________________________________________________________________

9

For the diagram, write down

(a) the number of lines of symmetry,

Answer(a) ............................................... [1]

(b) the order of rotational symmetry.

Answer(b) ............................................... [1]_____________________________________________________________________________________

10 Write these numbers in order of size, starting with the smallest.

0.41 73

229

π7 43%

Answer ................... < ................... < ................... < ................... < ................... [2]_____________________________________________________________________________________

5


ForExaminer′s

Use

11 The diagram shows two points, A and B.

8

7

6

5

4

3

2

1

–1

–2

–5 –4 –3 –2 –1 10 2 3

y

x

B

A

Write as column vectors

(a) ,

Answer(a) f p [1]

(b) 3 .

Answer(b) f p [1]

_____________________________________________________________________________________

12 Write down the type of correlation you would expect when values for the following are plotted.

(a) Total amount of time spent training for long distance races and time taken to run a marathon.

Answer(a) ............................................... [1]

(b) Total amount of time spent training for throwing the javelin and the distance the javelin is thrown.

Answer(b) ............................................... [1]_____________________________________________________________________________________

6

0580/13/O/N/13© UCLES 2013

ForExaminer′s

Use

13

Point B is 5.5 cm from point A on a bearing of 132°.

Draw accurately the line AB. [2]_____________________________________________________________________________________

14 Solve the equation. 4x + 3 = 10

Answer x = ............................................... [2]_____________________________________________________________________________________

15 Without using a calculator, work out 3 17

1

5

2- .

Give your answer as a fraction in its lowest terms. You must show each step of your working.

Answer ............................................... [3]_____________________________________________________________________________________

A

North

7


ForExaminer′s

Use

16

15°

h628 m NOT TO

SCALE

Calculate the length h. Give your answer correct to 2 signifi cant fi gures.

Answer h = ........................................... m [3]_____________________________________________________________________________________

1712 cm

12 cm

NOT TOSCALE

The diagram shows a circle inside a square of side 12 cm. The circle touches each side of the square.

Calculate the area of the shaded part of the diagram.

Answer ........................................ cm2 [3]_____________________________________________________________________________________

8

0580/13/O/N/13© UCLES 2013

ForExaminer′s

Use

18 Solve the simultaneous equations. 5x + 6y = 3 4x – 3y = 18

Answer x = ...............................................

y = ............................................... [3]_____________________________________________________________________________________

19 Write the answer to the following calculations in standard form.

(a) 600 ÷ 8000

Answer(a) ............................................... [2]

(b) 108 – 7 × 106

Answer(b) ............................................... [2]_____________________________________________________________________________________

9


ForExaminer′s

Use

20

A

(a) Construct the locus of all the points which are 3 cm from vertex A and outside the rectangle. [2]

(b) Construct, using a straight edge and compasses only, one of the lines of symmetryof the rectangle. [2]

_____________________________________________________________________________________

21 (a) Simplify. 3x – 5y + 8x – 2y

Answer(a) ............................................... [2]

(b) Expand and simplify. 4(2a – 3b) – 5(a – 2b)

Answer(b) ............................................... [2]_____________________________________________________________________________________

10

0580/13/O/N/13© UCLES 2013

ForExaminer′s

Use

22 The travel graph shows Natasha’s visit to her friend’s house. She starts by walking and then runs. She stays at her friend’s house until 11 10 before returning home.

2000

1800

1600

1400

1200

1000

800

600

400

200

010 30 10 40 10 50 11 00 11 10

Time

Distancefrom home(metres)

11 20 11 30 11 40

Friend’shouse

Home

(a) (i) How far does Natasha walk on the journey to her friend’s house?

Answer(a)(i) ........................................... m [1]

(ii) Find Natasha’s average speed, in metres per minute, on the journey to her friend’s house.

Answer(a)(ii) .................................... m/min [2]

(iii) How long does Natasha stay at her friend’s house?

Answer(a)(iii) ........................................ min [1]

11


ForExaminer′s

Use

(b) Natasha returns home at a constant speed of 64 metres per minute.

(i) Complete the travel graph. [2]

(ii) Write down the time she arrives home.

Answer(b)(ii) ............................................... [1]_____________________________________________________________________________________

12

0580/13/O/N/13



BLANK PAGE

© UCLES 2013





MATHEMATICS 0580/31


2 hours






*0871794379*

2

0580/31/O/N/13© UCLES 2013

ForExaminer′s

Use

1 Pedro is on a cruise ship.

(a) The ship has a climbing wall. These are the number of attempts that each of 30 people made at climbing the wall.

29 27 11 3 12 4 29 9 16 17 30 29 38 36 18

2 15 24 36 3 33 26 21 9 38 4 28 23 19 27

(i) Find the range.

Answer(a)(i) ............................................... [1]

(ii) Complete the frequency table. You may use the tally column to help you.

Number of attempts Tally Frequency

1 – 5

6 – 10

11 – 15

16 – 20

21 – 25

26 – 30

31 – 35

36 – 40[2]

(iii) Draw a bar chart to show this information. Complete the scale on the frequency axis.

1 – 5 6 – 10 11 – 15 16 – 20

Number of attempts

21 – 25 26 – 30 31 – 35 36 – 40

Frequency

[3]

3


ForExaminer′s

Use

(iv) Write down the modal group.

Answer(a)(iv) ............................................... [1]

(b) Pedro left the ship in Cadiz at 08 45. He returned to the ship at 16 10. Find how long Pedro was in Cadiz.

Answer(b) ....................... hours ....................... minutes [1]

(c)

Exchange Rate

$1 = €1.428

(i) Pedro changed $167 into euros (€).

Calculate how many euros Pedro received. Give your answer correct to 2 decimal places.

Answer(c)(i) € ............................................... [2]

(ii) Later, Pedro changed €107.10 back into dollars ($) using the same exchange rate.

Calculate how many dollars Pedro received.

Answer(c)(ii) $ ............................................... [2]_____________________________________________________________________________________

4

0580/31/O/N/13© UCLES 2013

ForExaminer′s

Use

2 (a) (i) 1 and 120 are factors of 120.

Write down another factor of 120.

Answer(a)(i) ............................................... [1]

(ii) Find the highest common factor of 120 and 900.

Answer(a)(ii) ............................................... [2]

(b) 2 5 15 24 49 60 258 512

From the list, write down

(i) a multiple of 30,

Answer(b)(i) ............................................... [1]

(ii) a square number,

Answer(b)(ii) ............................................... [1]

(iii) the cube root of 8.

Answer(b)(iii) ............................................... [1]

(c) Give an example to show that the following statements are not true.

(i) An odd number multiplied by an even number gives an odd number.

Answer(c)(i) ..................................................................... [1]

(ii) The cube of a negative number is positive.

Answer(c)(ii) ..................................................................... [1]

(d) Use < , > , or = to complete the following statements. Each symbol may be used more than once.

(i) 0.5 ................................ 83 [1]

(ii) 1.5 ................................ 105% [1]

(iii) 0.78 .............................. 1411 [1]

_____________________________________________________________________________________

5


ForExaminer′s

Use

3 (a) The diagram shows the position of town A and town B, on a map.

A

B

North

(i) Measure the length, in millimetres, of the line AB.

Answer(a)(i) ........................................ mm [1]

(ii) Measure the bearing of town B from town A.

Answer(a)(ii) ............................................... [1]

(b) A triangular fi eld has sides of length 550 m, 300 m and 400 m.

(i) Construct the triangle, using a ruler and compasses only. Use a scale of 1 cm to represent 50 m. The side of length 550 m has been drawn for you.

550 m[3]

(ii) By making a suitable measurement on your diagram, calculate the area of the fi eld. Give your answer in square metres.

Answer(b)(ii) .......................................... m2 [3]_____________________________________________________________________________________

6

0580/31/O/N/13© UCLES 2013

ForExaminer′s

Use

4

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–5 –4–6 –3 –2 –1 10 2 3 4 5 6 7 8

y

x

B

A

C

(a) (i) Describe fully the single transformation which maps shape B onto shape A.

Answer(a)(i) ......................................................................................................................

........................................................................................................................................... [2]

(ii) Describe fully the single transformation which maps shape B onto shape C.

Answer(a)(ii) .....................................................................................................................

........................................................................................................................................... [3]

(b) (i) Refl ect shape B in the y-axis. Label the image D. [1]

(ii) Rotate shape B through 90° anticlockwise about the origin. Label the image E. [2]_____________________________________________________________________________________

7


ForExaminer′s

Use

5 (a) The cost, $C, of a party for n people is calculated using the following formula.

C = 130 + 4n

(i) Calculate C when n = 25.

Answer(a)(i) ............................................... [2]

(ii) Eurdley has a party which costs $1138. How many people is this party for?

Answer(a)(ii) ............................................... [2]

(b) Solve the following equations.

(i) 3x = 27

Answer(b)(i) x = ............................................... [1]

(ii) 8y – 4 = 24

Answer(b)(ii) y = ............................................... [2]

(iii) 4(5q – 2) = 72

Answer(b)(iii) q = ............................................... [3]

(c) Solve the simultaneous equations. 6x + 8y = –31

14x – 5y = 46

Answer(c) x = ...............................................

y = ............................................... [4]_____________________________________________________________________________________

8

0580/31/O/N/13© UCLES 2013

ForExaminer′s

Use

630 m

17 m

B

C

A

D

NOT TOSCALE

HOUSE

The rectangle ABCD shows Mr Liu’s garden.

(a) Mr Liu puts a fence around three sides of his garden, AB, BC and CD. The fence costs $3.28 per metre.

Calculate the cost of the fence.

Answer(a) $ ............................................... [2]

(b) (i) Calculate the area of Mr Liu’s garden.

Answer(b)(i) .......................................... m2 [2]

(ii) Mr Liu uses an area of 408 m2 in his garden for a lawn, fl owers and vegetables. He divides this area into three parts, in the ratio

lawn : fl owers : vegetables = 5 : 3 : 4 .

Calculate the area used for each part.

Answer(b)(ii) Lawn ................................................. m2

Flowers ............................................. m2

Vegetables ........................................ m2 [3]

9


ForExaminer′s

Use

(c) Mr Liu walks in a straight line across his garden from A to C.

Calculate the distance Mr Liu walks.

Answer(c) ........................................... m [3]

(d) Mr Liu has a circular pond, radius 4.5 m, in his garden.

(i) Calculate the area of the pond.

Answer(d)(i) .......................................... m2 [2]

(ii) The pond is fi lled with water to a depth of 2 metres.

Calculate the volume of water in the pond.

Answer(d)(ii) .......................................... m3 [1]_____________________________________________________________________________________

10

0580/31/O/N/13© UCLES 2013

ForExaminer′s

Use

7 (a) Complete the table of values for y = x2 – x + 2 .

x –3 –2 –1 0 1 2 3 4

y 8 2 4[3]

(b) On the grid, draw the graph of y = x2 – x + 2 for −3 Y x Ğ 4 .

0–1 1 3 42–2–3x

y

16

14

12

10

8

6

4

2

[4]

11


ForExaminer′s

Use

(c) Write down the equation of the line of symmetry of the graph.

Answer(c) ............................................... [1]

(d) (i) On the grid, draw the line y = 9 . [1]

(ii) Solve the equation x2 – x + 2 = 9 .

Answer(d)(ii) x = ....................... or x = ....................... [2]_____________________________________________________________________________________

12

0580/31/O/N/13© UCLES 2013

ForExaminer′s

Use

8


Average temperature in °C –4.4 –4.2 –2.7 0.3 4.8 9.1 11.8 10.8 6.7 2.7 –1.1 –3.3

The table shows the average temperature for Tromso, Norway each month.

(a) (i) Write down the month which had the highest average temperature.

Answer(a)(i) ............................................... [1]

(ii) How much warmer was it in September than in February?

Answer(a)(ii) .......................................... °C [1]

(iii) The lowest temperature in October was 12.3°C below the average temperature for thatmonth.

Work out the lowest temperature in October.

Answer(a)(iii) .......................................... °C [1]

(b) In a survey, some tourists were asked how they had travelled to Norway. The pie chart shows the results.

Boat

Plane

Train

Road

13


ForExaminer′s

Use

(i) 150 of these tourists travelled by boat.

Show that 600 tourists took part in the survey.

Answer(b)(i)

[1]

(ii) Calculate the number of these tourists who travelled by plane.

Answer (b)(ii) ............................................... [3]

(c) A train ticket from Oslo to Stavanger costs 885 krone. There is a discount of 12% on the total cost of the tickets for a group of 10 or more people.

Calculate the cost of tickets for a group of 15 people.

Answer(c) ..................................... krone [3]

(d) On 1 January 2000, the population of Norway was 4 480 000, correct to 3 signifi cant fi gures.

(i) Write this number in standard form.

Answer(d)(i) ............................................... [1]

(ii) On 1 January 2011, the population of Norway was 4 920 000, correct to 3 signifi cant fi gures.

Calculate the percentage increase in the population.

Answer(d)(ii) ........................................... % [3]_____________________________________________________________________________________

14

0580/31/O/N/13© UCLES 2013

ForExaminer′s

Use

9

B

G

H

A

F

E

C

D

Ox°

y°

24°

78°

NOT TOSCALE

A, B, C and D are points on the circumference of a circle, centre O. EF is a tangent to the circle at A. GH is a straight line through the point A. Angle CBD = 24° and angle OAG = 78°.

(a) (i) Write down the mathematical names of lines BC and OA.

Answer(a)(i) BC is a .............................................................

OA is a ............................................................. [2]

(ii) Find the value of x, giving a reason for your answer.

Answer(a)(ii) x = ............................ because ...................................................................

........................................................................................................................................... [2]

(iii) Find the value of y, giving a reason for your answer.

Answer(a)(iii) y = ............................ because ..................................................................

........................................................................................................................................... [3]

15


ForExaminer′s

Use

(b) The diagram shows a regular polygon, centre O.

NOT TOSCALE

w°

O

(i) Write down the name of this polygon.

Answer(b)(i) ............................................... [1]

(ii) Find the value of w. Show all your working.

Answer(b)(ii) w = ............................................... [3]

(c) The exterior angle of another regular polygon is 24°.

Calculate the number of sides this polygon has.

Answer(c) ............................................... [2]_____________________________________________________________________________________

16

0580/31/O/N/13



BLANK PAGE

© UCLES 2013





MATHEMATICS 0580/32


2 hours






*6778759382*

2

0580/32/O/N/13© UCLES 2013

ForExaminer′s

Use

1

B

A

C

y

x

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

0–1 1 2 3 4 5 6 7 8–2–3–4–5–6

Triangles A, B and C are shown on a 1 cm2 grid.

(a) Write down the mathematical name for triangle A.

Answer(a) ............................................... [1]

(b) Complete the following statement.

Triangles A, B and C are ................................ triangles because they are the same shape and size.[1]

3


ForExaminer′s

Use

(c) Describe fully the single transformation that maps

(i) triangle A onto triangle B,

Answer(c)(i) ......................................................................................................................

........................................................................................................................................... [2]

(ii) triangle A onto triangle C.

Answer(c)(ii) .....................................................................................................................

........................................................................................................................................... [3]

(d) Refl ect triangle A in the x-axis. Label the image P. [1]

(e) Enlarge triangle A, scale factor 2, centre (0, 0). Label the image Q. [2]

(f) Calculate the area of triangle Q.

Answer(f) ........................................ cm2 [2]_____________________________________________________________________________________

4

0580/32/O/N/13© UCLES 2013

ForExaminer′s

Use

2 Ravi sells cars.

(a) He has a total of 144 cars for sale.

(i) 64 of these cars are 3 or more years old.

What fraction of the cars are less than 3 years old? Give your answer in its simplest form.

Answer(a)(i) ............................................... [2]

(ii) Some of the 144 cars use petrol, some use diesel and some are electric cars. The ratio of petrol to diesel to electric cars is 6 : 5 : 1 .

Work out the number of these cars that use diesel.

Answer(a)(ii) ............................................... [2]

(b) Lola buys a car from Ravi.

There are two ways she can pay for the car.

Option 1: one payment of $5200 .

Option 2: a payment of 52

of $5200 plus 24 monthly payments, each of $175 .

Work out how much more Lola pays using Option 2 than Option 1.

Answer(b) $ ............................................... [3]

(c) For one week, Ravi reduces all his car prices by 15%. The price of a car was $3450.

Show that the reduced price of the car is $2932.50 .

Answer(c)

[2]

(d) Ravi buys a car for $2500 . He sells it for $3300 .

Calculate his percentage profi t.

Answer(d) ........................................... % [3]_____________________________________________________________________________________

5


ForExaminer′s

Use

3 (a) Sweets are sold in packets. There are n sweets in each packet.

(i) Maya has 4 packets of sweets and 21 extra sweets.

Write an expression, in terms of n, for the number of sweets Maya has.

Answer(a)(i) ............................................... [1]

(ii) Tassos has 5n + 3 sweets. Roma has 3n + 27 sweets. Tassos and Roma each have the same number of sweets.

Write down an equation, in terms of n, and solve it.

Answer(a)(ii) n = ............................................... [3]

(iii) Work out the number of sweets Tassos and Roma have altogether.

Answer(a)(iii) ............................................... [1]

(b) A different packet of sweets contains 6 red sweets, 10 yellow sweets and 4 green sweets. Simon takes one sweet from the packet at random.

(i) Write down the colour of sweet Simon is most likely to take.

Answer(b)(i) ............................................... [1]

(ii) On the probability scale, draw an arrow to show the probability that Simon’s sweet is yellow.

0 1

[1]

(iii) Write down the probability that Simon’s sweet is green.

Answer(b)(iii) ............................................... [1]

(iv) Write down the probability that Simon’s sweet is red or yellow.

Answer (b)(iv) ............................................... [1]_____________________________________________________________________________________

6

0580/32/O/N/13© UCLES 2013

ForExaminer′s

Use

4 (a)

North

North

A

B

Sea

The scale drawing shows the position of two airfi elds, A and B. The scale is 1 cm represents 50 km.

(i) Find the actual distance between A and B. Give your answer in kilometres.

Answer(a)(i) ......................................... km [2]

(ii) Measure the bearing of B from A.

Answer(a)(ii) ............................................... [1]

(iii) A third airfi eld, C, is 525 km from airfi eld A and 350 km from airfi eld B.

On the scale drawing, construct the position of airfi eld C. [2]

(iv) Measure the bearing of B from C.

Answer(a)(iv) ............................................... [1]

7


ForExaminer′s

Use

(b) A plane is at airfi eld C at 10 40. It fl ies 525 km to airfi eld A at a speed of 700 km/h.

Work out the time when the plane reaches airfi eld A.

Answer(b) ............................................... [3]

(c) This plane has a maximum take-off weight of 4173 kg.

Write 4173 kg correct to the nearest hundred kilograms.

Answer(c) .......................................... kg [1]

(d) The plane can fl y at a maximum height of 13 107 m.

Write 13 107 m in kilometres, correct to 3 signifi cant fi gures.

Answer(d) ......................................... km [2]

(e) In one week, the plane fl ies a total distance of 8520 km, correct to the nearest ten kilometres.

Write down the lower bound of this distance.

Answer(e) ......................................... km [1]_____________________________________________________________________________________

8

0580/32/O/N/13© UCLES 2013

ForExaminer′s

Use5 (a) Complete the table of values for y = x5

.

x –5 –4 –3 –2 –1 1 2 3 4 5

y –1.67 –2.5 –5 5 1.67 1.25[2]

(b) On the grid, draw the graph of y = x5

for –5 Y x Y –1 and 1 Y x Y 5.

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

0–1 1 2 3 4 5 6–2–3–4–5–6

[4]

(c) Use your graph to solve the equation x5 = 4 .

Answer(c) x = ............................................... [1]

(d) (i) On the grid, draw the line x = –3.5 . [1]

(ii) On the grid, plot the point (5, –3) and label it P. [1]

(iii) Draw the line that passes through P and is perpendicular to x = –3.5 . [1]_____________________________________________________________________________________

9


ForExaminer′s

Use

6 (a) Here are three different sequences. Write the missing terms in the spaces provided.

(i) 2, 8, 14, 20, ................ [1]

(ii) 1, 4, 9, ................ , 25 [1]

(iii) ................ , 12, 7, 2, ................ [2]

(b) Here is the rule for fi nding the next term in another sequence.

Double the previous term and subtract 1.

The fi rst two terms in this sequence are 3 and 5.

(i) Work out the next two terms in the sequence.

Answer(b)(i) ................... , ................... [2]


All the terms in this sequence are .............................................. numbers. [1]

(c) Here is the start of a sequence of stick patterns.

Pattern 18 sticks

Pattern 213 sticks

Pattern 318 sticks

(i) Find the number of sticks in Pattern 4.

Answer(c)(i) ............................................... [1]

(ii) Write down an expression for the number of sticks in Pattern n.

Answer(c)(ii) ............................................... [2]

(iii) One pattern in the sequence has 98 sticks.

Which pattern number is this?

Answer(c)(iii) ............................................... [2]_____________________________________________________________________________________

10

0580/32/O/N/13© UCLES 2013

ForExaminer′s

Use

7 12 people each solved the same puzzle. The table shows their ages and the time they each took to solve the puzzle.

Age (years) 19 24 28 16 25 20 15 22 32 30 68 16

Time (seconds) 36 38 42 36 45 42 32 40 40 46 56 38

(a) Find the median age.

Answer(a) ...................................... years [2]

(b) For these 12 people, explain why the mean age may not be an appropriate average.

Answer(b) .................................................................................................................................

................................................................................................................................................... [1]

(c) Calculate the mean time taken.

Answer(c) ................................. seconds [2]

11


ForExaminer′s

Use

(d) (i) Complete the scatter diagram. The fi rst six points have been plotted for you.

70

60

50

40

30

20

10

010 20 30 40 50 60 70

Time(seconds)

Age (years)[2]

(ii) What type of correlation does the scatter diagram show?

Answer(d)(ii) ............................................... [1]

(iii) Draw a line of best fi t on the scatter diagram. [1]

(iv) Would it be sensible to use your line of best fi t to estimate the time taken by a child aged 8 to solve the puzzle?

Explain your answer.

Answer(d)(iv) .................... because ........................................................................................

........................................................................................................................................... [1]_____________________________________________________________________________________

12

0580/32/O/N/13© UCLES 2013

ForExaminer′s

Use

8 (a) Complete the table.

Name of polygon Number of sides

Quadrilateral 4

Heptagon

5[2]

(b)

55°

23°

B C D

EA

NOT TOSCALE

In the diagram, AB is parallel to EC and BCD is parallel to AE. Angle BAE = 55° and angle CED = 23°.

(i) Complete the following statement.

The mathematical name for quadrilateral ABDE is ............................................ . [1]

(ii) Work out the size of angle ABC.

Answer(b)(ii) Angle ABC = ............................................... [1]

(iii) Work out the size of angle CDE.

Answer(b)(iii) Angle CDE = ............................................... [2]

13


ForExaminer′s

Use

(c)

35°

52°

NOT TOSCALE

B

C

O

A

D

Points A, B and C lie on a circle with centre O. DA is a tangent to the circle at A. Angle BAC = 35° and angle ADC = 52°.

(i) Write down the size of angle ABC giving a reason for your answer.

Answer(c)(i) Angle ABC = ............... because ..................................................................

........................................................................................................................................... [2]

(ii) Work out the size of angle BCA.

Answer(c)(ii) Angle BCA = ............................................... [1]

(iii) Work out the size of angle BCD.

Answer(c)(iii) Angle BCD = ............................................... [3]_____________________________________________________________________________________

14

0580/32/O/N/13© UCLES 2013

ForExaminer′s

Use

9 (a) The table shows some information about minimum and maximum temperatures in Moscow one January and February.

Temperature January February

Maximum –9°C 2°C

Minimum –16°C

(i) Find the difference between the maximum and minimum temperatures in January.

Answer(a)(i) ...........................................°C [1]

(ii) The difference between the maximum and minimum temperatures in February was 34°C.

Find the minimum temperature in February.

Answer(a)(ii) ...........................................°C [1]

(iii) The minimum temperature in Moscow in December was 5°C higher than the minimum temperature in January.

Work out the minimum temperature in December.

Answer(a)(iii) ...........................................°C [1]

15


ForExaminer′s

Use

(b) The table shows the population of some cities in Russia.

City Population

Kaliningrad 4.30 × 105

Moscow

Novosibirsk 1.40 × 106

Omsk 1.13 × 106

Saint Petersburg 4.58 × 106

(i) The population of Moscow is 10 500 000.

Complete the table by writing the population of Moscow in standard form. [1]

(ii) Write the population of Saint Petersburg as an ordinary number.

Answer(b)(ii) ............................................... [1]

(iii) Which city has the smallest population?

Answer(b)(iii) ............................................... [1]

(iv) Find the difference between the population of Novosibirsk and the population of Omsk. Give your answer in standard form.

Answer(b)(iv) ............................................... [2]_____________________________________________________________________________________


16

0580/32/O/N/13



© UCLES 2013

ForExaminer′s

Use

10 (a) Solve the equation. 6(x – 2) = 9

Answer(a) x = ............................................... [2]

(b) Expand and simplify. 8(n – 1) – 2(3n + 5)

Answer(b) ............................................... [2]

(c) Factorise completely. 10p2 + 5p3

Answer(c) ............................................... [2]





MATHEMATICS 0580/33


2 hours






*4932585116*

2

0580/33/O/N/13© UCLES 2013

ForExaminer′s

Use

1 Adam owns a farm.

(a) He plans to keep twenty hens. He works out what he thinks this will cost.

Complete the following table.

Item Cost ($)

Equipment 500

20 hens costing $12 each

3 years supply of feedcosting $25 per month

TOTAL

[3]

(b) The equipment actually costs $600.

The ratio of costs is equipment : hens : feed = 5 : 3 : 9 .

(i) Show that the total cost is now $2040.

Answer(b)(i)

[2]

(ii) Adam actually buys more than 20 hens, each costing $12.

How many hens does he buy?

Answer(b)(ii) ............................................... [2]

3


ForExaminer′s

Use

(c) Adam makes $2920 from selling his hens’ eggs.

Calculate his percentage profi t on the $2040.

Answer(c) ........................................... % [2]

(d) Adam borrows $1500 for 3 years at a rate of 5.5% per year compound interest.

Calculate the interest he will pay, correct to the nearest cent.

Answer(d) $ ................................................ [3]_____________________________________________________________________________________

4

0580/33/O/N/13© UCLES 2013

ForExaminer′s

Use

2 The diagram shows four quadrilaterals drawn on a 1 cm2 grid.

y

x

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

0–1 1 2 3 4 5 6 7 8–2–3–4–5–6–7–8

X

A

CB

(a) Write down the mathematical name of the quadrilateral X.

Answer(a) ............................................... [1]

5


ForExaminer′s

Use

(b) Describe fully the single transformation that maps quadrilateral X onto quadrilateral

(i) A,

Answer(b)(i) ......................................................................................................................

........................................................................................................................................... [3]

(ii) B,

Answer(b)(ii) .....................................................................................................................

........................................................................................................................................... [2]

(iii) C.

Answer(b)(iii) ....................................................................................................................

........................................................................................................................................... [3]

(c) (i) Calculate the length of the longest side of quadrilateral X. Show that your answer rounds to 3.16 cm, correct to 3 signifi cant fi gures.

Answer(c)(i)

[2]

(ii) Calculate the perimeter of quadrilateral X.

Answer(c)(ii) ......................................... cm [3]

(iii) Find the perimeter of quadrilateral C.

Answer(c)(iii) ......................................... cm [1]_____________________________________________________________________________________

6

0580/33/O/N/13© UCLES 2013

ForExaminer′s

Use

3 (a) Using only the integers from 1 to 50, fi nd

(i) a multiple of both 4 and 7,

Answer(a)(i) ............................................... [1]

(ii) a square number that is odd,

Answer(a)(ii) ............................................... [1]

(iii) an even prime number,

Answer(a)(iii) ............................................... [1]

(iv) a prime number which is one less than a multiple of 5.

Answer(a)(iv) ............................................... [1]

(b) Find the value of

(i) 25^ h ,

Answer(b)(i) ............................................... [1]

(ii) 2–3 × 63.

Answer(b)(ii) ............................................... [2]_____________________________________________________________________________________

7


ForExaminer′s

Use

4 (a) A regular polygon has 9 sides. For this polygon, calculate

(i) the size of one exterior angle,

Answer(a)(i) ............................................... [2]

(ii) the size of one interior angle.

Answer(a)(ii) ............................................... [1]

(b)

F

A

E

D

C

B

O

w°

x°

24°

z°

y° NOT TOSCALE

In the diagram, A, B, C and D are points on the circumference of a circle, centre O. AB is the diameter and EF is a tangent to the circle at A. AB is parallel to DC and angle ACD = 24°.

Find

(i) w, Answer(b)(i) w = ............................................... [1]

(ii) x, Answer(b)(ii) x = ............................................... [1]

(iii) y.

Answer(b)(iii) y = ............................................... [1]

(c) Complete the statement.

z = ............................... because ................................................................................................

................................................................................................................................................... [2]_____________________________________________________________________________________

8

0580/33/O/N/13© UCLES 2013

ForExaminer′s

Use

5 (a) (i) Complete the table for y = 5 + 3x – x2.

x –2 –1 0 1 2 3 4 5

y –5 5 7 5 –5[3]

(ii) On the grid, draw the graph of y = 5 + 3x – x2 for –2 Y x Y 5.

y

x

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

0 1 2 3 4 5–1–2

[4]

(b) Use your graph to solve the equation 5 + 3x – x2 = 0 .

Answer(b) x = ..................... or x = ..................... [2]

9


ForExaminer′s

Use

(c) (i) On the grid, draw the line of symmetry of y = 5 + 3x – x2. [1]

(ii) Write down the equation of this line of symmetry.

Answer(c)(ii) ............................................... [1]

(d) (i) On the grid, draw a straight line from (–1, 1) to (3, 5). [1]

(ii) Work out the gradient of this line.

Answer(d)(ii) ............................................... [2]

(iii) Write down the equation of this line in the form y = mx + c.

Answer(d)(iii) y = ............................................... [1]_____________________________________________________________________________________

10

0580/33/O/N/13© UCLES 2013

ForExaminer′s

Use

6 Alison scored the following number of runs in 15 cricket matches.

12 3 27 35 0

7 52 4 18 30

18 7 94 61 7

(a) For these scores,

(i) work out the median,

Answer(a)(i) ............................................... [2]

(ii) write down the mode,

Answer(a)(ii) ............................................... [1]

(iii) calculate the mean.

Answer(a)(iii) ............................................... [2]

(b) These are the averages for the number of runs scored by Bethan in the 15 matches.

Median = 21 Mode = 13 Mean = 20

Alison says that her scores are better than Bethan’s scores. Bethan says that her scores are better than Alison’s scores.

Explain how they could both be correct.

Answer(b) .................................................................................................................................

...................................................................................................................................................

................................................................................................................................................... [2]

11


ForExaminer′s

Use

(c) Alison puts her 15 scores into 4 groups and shows them in a pie chart.


Score Frequency Sector Angle

0 to 25 9 216°

26 to 50

51 to 75

76 to 100[3]

(ii) Complete the pie chart and label the sectors.

0 to 25

[3]

(d) Estimate the probability that in the next match Alison will score more than 25 runs. Give your answer as a fraction in its simplest form.

Answer(d) ............................................... [2]_____________________________________________________________________________________

12

0580/33/O/N/13© UCLES 2013

ForExaminer′s

Use

7D

A B

CE

1.0 m

1.5 m

2.25 m

NOT TOSCALE

The diagram shows a trapezium ABCD. AB = 1.0 m, AD = 2.25 m, BC = 1.5 m and angle DEC = 90°.

(a) Using trigonometry, calculate angle DCE.

Answer(a) Angle DCE = ............................................... [3]

(b) Calculate the area of the trapezium ABCD.

Answer(b) .......................................... m2 [2]

(c) ABCD is the cross-section of a box. The box is 2 m long.

Calculate the volume of the box.

Answer(c) .......................................... m3 [1]

2 m

A

B

CD

13


ForExaminer′s

Use

(d) On the grid, complete the net of the box. The base and one face of the box have been drawn for you.

The scale is 2 cm to 1 m.

[4]_____________________________________________________________________________________

14

0580/33/O/N/13© UCLES 2013

ForExaminer′s

Use

8 Here is a sequence of patterns made using identical polygons.

Pattern 2Pattern 1 Pattern 3

(a) Write down the mathematical name of the polygon in Pattern 1.

Answer(a) ............................................... [1]

(b) Complete the table for the number of vertices (corners) and the number of lines in Pattern 3, Pattern 4 and Pattern 7.

Pattern 1 2 3 4 7

Number of vertices 8 14

Number of lines 8 15

[5]

(c) (i) Find an expression for the number of vertices in Pattern n.

Answer(c)(i) ............................................... [2]

(ii) Work out the number of vertices in Pattern 23.

Answer(c)(ii) ............................................... [1]

15


ForExaminer′s

Use

(d) Find an expression for the number of lines in Pattern n.

Answer(d) ............................................... [2]

(e) Work out an expression, in its simplest form, for

(number of lines in Pattern n) – (number of vertices in Pattern n).

Answer(e) ............................................... [2]_____________________________________________________________________________________


16

0580/33/O/N/13



© UCLES 2013

ForExaminer′s

Use9 (a) The formula for the volume, V, of a cone with radius r, and height h, is V =

3

1 πr2h .

(i) To make r the subject of this formula, the fi rst step is 3V = πr2h.

Show the remaining steps to make r the subject of this formula.

Answer(a)(i) r = ............................................... [2]

(ii) An ice-cream cone has a volume of 141 cm3 and height 15 cm.

Show that the radius of the cone is 3 cm, correct to the nearest whole number.

Answer(a)(ii)

[2]

(b) The open end of an ice-cream cone is a circle of radius 3 cm.

Calculate the circumference of this circle.

Answer(b) ......................................... cm [2]

(c) The volume of a ball of ice-cream is 113 cm3. The ball of ice-cream costs $2.15 .

Calculate the cost of 1 cm3 of the ice-cream. Give your answer in cents, correct to 1 decimal place.

Answer(c) ...................................... cents [3]


IB12 06_0580_11/6RP © UCLES 2012 [Turn over

*1195964981*

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

MATHEMATICS 0580/11


1 hour


Additional Materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional)




You may use a pencil for any diagrams or graphs.

Do not use staples, paper clips, highlighters, glue or correction fluid.

DO NOT WRITE IN ANY BARCODES.









2

© UCLES 2012 0580/11/M/J/12

For

Examiner's

Use

1 Kyle scores 84 marks out of 96 in an examination. Work out his percentage mark. Answer % [1]

2

The lengths of each side of this triangle are the same. (a) Write down the mathematical name for this triangle. Answer(a) [1]

(b) Write down the number of lines of symmetry for the triangle. Answer(b) [1]

3 Work out the number of minutes from 18 27 on Tuesday to 03 19 on Wednesday. Answer min [2]

3

© UCLES 2012 0580/11/M/J/12 [Turn over

For

Examiner's

Use

4 Gregor changes $700 into euros (€) when the rate is €1 = $1.4131 . Calculate the amount he receives. Answer € [2]

5 w = 3a – 5b Calculate w when a = 2 and b = –3. Answer w = [2]

6 One bracelet costs 85 cents and one necklace costs $7.50 . Write down an expression, in dollars, for the total cost of b bracelets and n necklaces. Answer $ [2]

4

© UCLES 2012 0580/11/M/J/12

For

Examiner's

Use

7 (a) A quadrilateral has four sides of equal length and two pairs of equal angles. Write down the mathematical name for this quadrilateral. Answer(a) [1]

(b)

74°

92°

63°

NOT TOSCALE

Three of the angles in a quadrilateral are 63°, 74° and 92°. Work out the size of the fourth angle. Answer(b) [1]

8 Solve the equation 4x – 2 = 7 . Answer x = [2]

9 The temperature at the top of a mountain is –12°C. The temperature at the bottom of the mountain is 18°C. (a) Work out the difference in these temperatures. Answer(a) °C [1]

(b) 18°C is given correct to the nearest degree. Write down the upper bound for this temperature. Answer(b) °C [1]

5


For

Examiner's

Use

10

x cm29 cm

53.2°

NOT TOSCALE

Calculate the value of x. Answer x = [2]

11 (a) Write down all the factors of 15. Answer(a) [1]

(b) Factorise completely. 15p2 + 24pt Answer(b) [2]

12 Triangle ABC has sides AB = 40 m, BC = 25 m and AC = 35 m. Using a scale of 1 cm to represent 5 m, construct triangle ABC. The construction must be completed using a ruler and compasses only.

All construction arcs must be clearly shown. Answer

A B [3]

6

© UCLES 2012 0580/11/M/J/12

For

Examiner's

Use

13 Shania invests $750 at a rate of 2 2

1% per year simple interest.

Calculate the total amount Shania has after 5 years. Answer $ [3]

14 Without using your calculator, work out 16

5+10

9 .

You must show your working and give your answer as a mixed number in its simplest form.

Answer [3]

7


For

Examiner's

Use

15 (a) Find the value of x.

x°

51°

NOT TOSCALE

Answer(a) x = [1]

(b) EF is a diameter of the circle. Find the value of y.

y°63°E

F

NOT TOSCALE

Answer(b) y = [1]

(c) Find the value of z in this isosceles triangle.

z°

48° NOT TOSCALE

Answer(c) z = [1]

8

© UCLES 2012 0580/11/M/J/12

For

Examiner's

Use

16 Solve the simultaneous equations. 3x + 5y = 24 x + 7y = 56

Answer x =

y = [3]

9


For

Examiner's

Use

17 y

x

7

6

5

4

3

2

1

–1

–2

–3

–4

–5 –4 –3 –2 –1 0 1 2 3 4 5

A

B

(a) Write down the co-ordinates of point A.

Answer(a) ( , ) [1]

(b) Write as a column vector.

Answer(b) =

[1]

(c) =

3

2

Write down the co-ordinates of C.

Answer(c) ( , ) [1]

10

© UCLES 2012 0580/11/M/J/12

For

Examiner's

Use

18 (a) Write 326.413 correct to 2 significant figures. Answer(a) [1]

(b) Find the square root of one million. Answer(b) [2]

(c) Calculate

3.655.2

7.46564.3

−

+.

Answer(c) [1]

19 (a) Simplify 4p + 3q + 5p –7q. Answer(a) [2]

(b) Make x the subject of this formula. g = 2x + y Answer(b) x = [2]

11


For

Examiner's

Use

20

A

B

(a) Using a straight edge and compasses only, construct the perpendicular bisector of AB. Show all your construction arcs. [2] (b) Draw the locus of points that are 4 cm from A. [1] (c) Shade the region which is less than 4 cm from A and nearer to B than to A. [1]


12



© UCLES 2012 0580/11/M/J/12

For

Examiner's

Use

21

13 17 13 17 19 13 31 21 29 (a) For the numbers above, find (i) the range, Answer(a)(i) [1]

(ii) the median. Answer(a)(ii) [2]

(b) Write down the only number in the list which is not a prime number. Answer(b) [1]



*7644698688*


MATHEMATICS 0580/12


1 hour

















2

© UCLES 2012 0580/12/M/J/12

For

Examiner's

Use

1 Work out the value of 4.63.519.1

48

×−

.

Answer [1]


0.83 6

5 82%

28

23

Answer < < < [2]

3 The ferry from Helsinki to Travemunde leaves Helsinki at 17 30 on a Tuesday. The journey takes 28 hours 45 minutes. Work out the day and time that the ferry arrives in Travemunde.

Answer Day Time [2]

4 T R I G O N O M E T R Y From the above word, write down the letters which have (a) exactly two lines of symmetry, Answer(a) [1]

(b) rotational symmetry of order 2. Answer(b) [1]

3


For

Examiner's

Use

5 The table shows the average monthly temperatures in Beijing.


Average temperature (°C)

– 4.6 –2.2 4.5 13.1 19.8 24.0 25.8 24.4 19.4 12.4 4.1 –2.7

(a) Work out how many degrees higher the temperature is in December than in January. Answer(a) °C [1]

(b) Find the range.

Answer(b) °C [1]

6 a =

− 3

5 b =

−

7

2

Work out 3a + b.

Answer

[2]

7 12

1 +

3

1 +

4

1 =

12

p

Work out the value of p. Show all your working. Answer p = [2]

4

© UCLES 2012 0580/12/M/J/12

For

Examiner's

Use

8 A lake has an area of 63 800 000 000 square metres. Write this area in square kilometres, correct to 2 significant figures. Answer km2 [2]

9 (a) Simplify a–3 × a8. Answer(a) [1]

(b) Work out the value of 5–2. Answer(b) [1]

10 The number of people, n, who attended a concert was 12 600 to the nearest 100. Complete the statement about n. Answer Y n I= [2]

11 Keiko travels from Tokyo to London for the Olympic Games. On the internet, a flight costs £767. (a) Use the exchange rate £1 = 143 Japanese Yen to find the cost of the flight in Japanese Yen. Answer(a) Yen [1]

(b) Write your answer to part (a) in standard form. Answer(b) [1]

5


For

Examiner's

Use

12 8 cm

6 cm rNOT TOSCALE

The perimeter of the rectangle is the same length as the circumference of the circle. Calculate the radius, r, of the circle. Answer r = cm [3]

13 (a) Factorise xy – y2. Answer(a) [1]

(b) Solve 4x − 7 = 12. Answer(b) x = [2]

6

© UCLES 2012 0580/12/M/J/12

For

Examiner's

Use

14 Scatter diagrams are drawn to compare sets of data from each team in a hockey league during a year. Write down the type of correlation you would expect to see when the data recorded is (a) the number of games won and the total points scored, Answer(a) [1]

(b) the number of games drawn and the average height of the team, Answer(b) [1]

(c) the number of goals scored and the final position in the league. Answer(c) [1]

15

The diagram shows a quadrilateral drawn on a 1 cm square grid. (a) Write down the mathematical name of the quadrilateral. Answer(a) [1]

(b) Find the area of the quadrilateral and give the units. Answer(b) [2]

7


For

Examiner's

Use

16 The shirt colour of the teams in a football league are shown in the following table.

Colour Frequency

Red 8

White 3

Blue 7

Gold 2

The pie chart shows some of this information. The sectors for red shirts and white shirts have been drawn.

Red

White

(a) Calculate the angle of the sector for blue shirts. Answer(a) [2]

(b) Complete the pie chart. [1]

8

© UCLES 2012 0580/12/M/J/12

For

Examiner's

Use

17 Solve the simultaneous equations. 6x + 2y = 22 4x − y = 3 Answer x =

y = [3]

18 The taxi fare in a city is $3 and then $0.40 for every kilometre travelled.

(a) A taxi fare is $9. How far has the taxi travelled? Answer(a) km [2]

(b) Taxi fares cost 30 % more at night. How much does a $9 daytime journey cost at night? Answer(b) $ [2]

9


For

Examiner's

Use

19

O

E

A

C BD58°

x°

y°

NOT TOSCALE

AC is a diameter of a circle, centre O. BCD is a tangent to the circle and E is a point on the circumference. Angle ECD = 58°. Work out the value of (a) x, Answer(a) x = [2]

(b) y. Answer(b) y = [2]

10

© UCLES 2012 0580/12/M/J/12

For

Examiner's

Use

20 C

BA

34 cm 30 cm

16 cm

NOT TOSCALE

(a) Write down all your working to show that angle ABC is a right angle. Answer(a)

[2] (b) Use trigonometry to calculate angle CAB. Answer(b) Angle CAB = [2]

11

© UCLES 2012 0580/12/M/J/12

For

Examiner's

Use

21 (a) Show that the sum of the interior angles of a regular pentagon is 540°. Answer(a)

[2] (b)

x° y°

y°76°

B C

D

EA

NOT TOSCALE

The diagram shows a pentagon ABCDE. BC is parallel to AE and angle CDE is a right angle. Find the values of x and y. Answer(b) x =

y = [3]

12



© UCLES 2012 0580/12/M/J/12

BLANK PAGE



*6617826257*


MATHEMATICS 0580/13


1 hour

















2

© UCLES 2012 0580/13/M/J/12

For

Examiner's

Use

1 Write 5

2 as a percentage.

Answer %[1]

2 Change 5.2 square metres into square centimetres. Answer cm2 [1]

3 Mohinder changes $240 into Rupees. The exchange rate is $1 = 46.2875 Rupees. Calculate how many Rupees he receives. Answer Rupees [1]

4 (a) Write down the next prime number after 47. Answer(a) [1]

(b) Write down the next square number after 49. Answer(b) [1]

3


For

Examiner's

Use

5 I K =

Choose one of these symbols to make each statement correct. (a) −15 −5 [1]

(b) (−5)2 25 [1]

6 Hans invests $750 for 8 years at a rate of 2% per year simple interest. Calculate the interest Hans receives. Answer $ [2]

7

B

C D E

A

120°

82°

73°

x°

NOT TOSCALE

The diagram shows a quadrilateral ABCD. CDE is a straight line. Calculate the value of x. Answer x = [2]

4

© UCLES 2012 0580/13/M/J/12

For

Examiner's

Use

8 Work out

(a)

3

5 −

− 2

6,

Answer(a)

[1]

(b) 5

− 4

3.

Answer(b)

[1]

9 Simplify (a) a0

, Answer(a) [1]

(b) b3 × b-5

. Answer(b) [1]

10 During her holiday, Hannah rents a bike. She pays a fixed cost of $8 and then a cost of $4.50 per day. Hannah pays with a $50 note and receives $10.50 change. Calculate for how many days Hannah rents the bike. Answer days [3]

5


For

Examiner's

Use

11 ED F

A CBa°

b°52°

NOT TOSCALE

In the diagram lines AC and DF are parallel and AE = EB. Angle AEB = 52°.

(a) Write down the mathematical name for triangle AEB. Answer(a) [1]

(b) Work out the value of a. Answer(b) a = [1]

(c) Explain why a = b. Answer(c) [1]

12 Solve the simultaneous equations. 4x + y = 18 5x + 3y = 19 Answer x =

y = [3]

6

© UCLES 2012 0580/13/M/J/12

For

Examiner's

Use

13 (a) Write 0.000 64 in standard form. Answer(a) [1]

(b) Calculate, writing the answer in standard form.

4

7

105.84

108.18

×

×

Answer(b) [2]

14

7 3 8 2 5 1

5 3 4 6 2 3

For the numbers above work out the (a) mode, Answer(a) [1]

(b) median, Answer(b) [2]

(c) range. Answer(c) [1]

7


For

Examiner's

Use

15 Without using your calculator, work out the following. Show all the steps of your working and give each answer as a fraction in its simplest form.

(a) 12

11 −

3

1

Answer(a) [2]

(b) 4

1 ÷

13

11

Answer(b) [2]

16 (a) Solve the equation 5(x − 3) = 21 . Answer(a) x = [2]

(b) Make x the subject of the equation y = 3x − 2 . Answer(b) x = [2]

8

© UCLES 2012 0580/13/M/J/12

For

Examiner's

Use

17 12 cm

12 cm

34 cm

4 cm

18 cm 18 cmNOT TOSCALE

For the shape above, work out (a) the perimeter, Answer(a) cm [2]

(b) the area. Answer(b) cm2 [2]

18 (a) Find the value of 7p – 3q when p = 8 and q = O5 . Answer(a) [2]

(b) Factorise completely. 3uv + 9vw Answer(b) [2]

9


For

Examiner's

Use

19

28°

North

North

A

B

C

74 km

26 km NOT TOSCALE

(a) Work out the bearing of A from C. Answer(a) [2]

(b) Calculate the distance AB. Answer(b) km [2]

10

© UCLES 2012 0580/13/M/J/12

For

Examiner's

Use

20 (a) Colin has some seeds. The probability a seed will grow is 0.85 . Find the probability that a seed will not grow. Answer(a) [1]

(b) Richard grows flowers. Some of his flowers are chosen at random. The colours are recorded in the table below.

Colour of flower

Frequency Relative

Frequency

Red 20 0.16

Blue 15

Yellow 35

Other 55

(i) Complete the table to show the relative frequency of each colour. [2] (ii) Richard grows 800 flowers in total. Estimate how many of these flowers are red. Answer(b)(ii) [2]

11

© UCLES 2012 0580/13/M/J/12

BLANK PAGE

12



© UCLES 2012 0580/13/M/J/12

BLANK PAGE



*9282554543*


MATHEMATICS 0580/31


2 hours

















2

© UCLES 2012 0580/31/M/J/12

For

Examiner's

Use

1 (a) Vince and Wendy share $2000 in the ratio Vince : Wendy = 19 : 21. Calculate the amount of money that Vince receives. Answer(a) $ [2]

(b) Wendy has $265 to spend on some chairs. The chairs cost $37 each. Work out the largest number of chairs she can buy. Answer(b) [2]

(c) Wendy shares $200 between her three children Jake, Karl and Lana.

She gives 27% of the money to Jake and 5

2 of the money to Karl.

Work out the amount of money she gives to Lana. Answer(c) $ [3]

(d) Wendy invests $500 at a rate of 4% per year compound interest. Calculate the total amount of interest she receives at the end of 2 years. Give your answer correct to the nearest dollar. Answer(d) $ [4]

3


For

Examiner's

Use

2

8

6

4

2

–2

–4

–6

–8

–2 20 4 6 8–4–6

A

D

y

x

Two shapes A and D are shown on the grid. (a) (i) Reflect shape A in the line x = 0. Label this image B. [2] (ii) Rotate shape A through 180° about (2, 4). Label this image C. [2] (iii) Enlarge shape A with scale factor 2 and centre (3, 7). Label this image E. [2] (b) Describe fully the single transformation that maps shape D onto (i) shape B, Answer(b)(i) [2]

(ii) shape C. Answer(b)(ii) [2]

4

© UCLES 2012 0580/31/M/J/12

For

Examiner's

Use

3 (a) Jon spins this 6-sided spinner.

The probability that the spinner lands on any of the six sides is equally likely. Write down the probability that the spinner lands on (i) the number 6, Answer(a)(i) [1]

(ii) a prime number, Answer(a)(ii) [1]

(iii) a number less than 11. Answer(a)(iii) [1]

(b) Felix has a 12-sided spinner with the numbers 2, 4, 5, 7 and 9 written on it. It is equally likely to land on any side. The table shows the probability of the spinner landing on each number.

Number on spinner 2 4 5 7 9

Probability 4

1

3

1

6

1

6

1

12

1

The diagram of the spinner has been completed for the number 2. Complete the diagram for the numbers 4, 5, 7 and 9.

222

[3] (c) Felix says that his spinner is more likely to land on a 2 than Jon’s spinner. Explain why he is wrong. Answer(c)

[1]

2

68

10

4

2

5


For

Examiner's

Use

(d) Felix spins his 12-sided spinner 60 times and records the results.

Number on spinner Frequency Pie chart sector angle

2 15 90°

4 20 120°

5 5 30°

7 12

9 8

(i) Complete the table by working out the sector angles for the numbers 7 and 9 . [3] (ii) Complete the pie chart.

2

4

[2] (iii) Write down the mode. Answer(d)(iii) [1]

(iv) Calculate the mean. Answer(d)(iv) [3]

6

© UCLES 2012 0580/31/M/J/12

For

Examiner's

Use

4 In this question all the measurements are in centimetres.

2x + 3

3x

11 – x NOT TOSCALE

The diagram shows a triangle with sides of length 2x + 3, 11 – x and 3x. (a) Explain why x must be less than 11.

Answer(a)

[1] (b) Write down an expression, in terms of x, for the perimeter of the triangle. Give your answer in its simplest possible form. Answer(b) [2]

(c) The perimeter of the triangle is 32 cm. (i) Write down an equation in terms of x and solve it. Answer(c)(i) x = [3]

(ii) Work out the length of the shortest side of the triangle. Answer(c)(ii) cm [2]

7


For

Examiner's

Use

5

Diagram 1 Diagram 2 Diagram 3 Diagram 4 The number of crosses in each Diagram forms a sequence. (a) On the grid draw Diagram 4. [1] (b) Write down the number of crosses needed to draw Diagram 5. Answer(b) [1]

(c) Diagram 1 has 1 row of 3 crosses. Diagram 2 has 2 rows of 4 crosses. (i) Complete this statement for Diagram n.

Diagram n has n rows of crosses. [1] (ii) Write down, in terms of n, how many crosses are needed to draw Diagram n. Answer(c)(ii) [1]

(iii) Find the number of crosses needed to draw Diagram 20. Answer(c)(iii) [1]

8

© UCLES 2012 0580/31/M/J/12

For

Examiner's

Use

6

6

4

2

–2

–4

–6

–2 20 4 6 8 10 12–4

y

xA E

B

C

Triangle ABC is drawn on a 1cm2 grid. E is the point (0, 0). (a) Write down the gradient of the line AB. Answer(a) [2]

(b) The gradient of BC is – 0.5 . Write down the equation of the line BC in the form y = mx + c. Answer(b) y = [2]

9


For

Examiner's

Use

(c) Write down the ratio AE : EC. Give your answer in its simplest form. Answer(c) : [2]

(d) Measure angle ABE. Answer(d) Angle ABE = [1]

(e) Triangle ABE is similar to triangle BCE. Explain what the word similar tells you about the triangles ABE and BCE.

Answer(e)

[2] (f) Calculate the area of triangle ABC. Answer(f) cm2 [3]

(g) ABCD is a rectangle. (i) Mark point D on the grid. [1] (ii) Write down the co-ordinates of D. Answer(g)(ii) ( , ) [1]

10

© UCLES 2012 0580/31/M/J/12

For

Examiner's

Use

7

6

5

4

3

2

1

010 00 10 15 10 30 10 45 11 00 11 15 11 30

Distancefrom home

(km)

Sasha’shome

Café

Home

Time Poppy and Toni go to a café which is 3 km from their home. They take the same route. Poppy leaves home at 10 00 and walks. Toni leaves home at 10 10 and cycles. These journeys are shown on the travel graph. (a) (i) How long does Toni wait at the café before Poppy arrives? Answer(a)(i) min [1]

(ii) The graphs cross at 10 15. Describe what this means.

Answer(a)(ii)

[1]

(iii) Calculate Toni’s average speed from home to the café in kilometres per hour. Answer(a)(iii) km/h [2]

11


For

Examiner's

Use

(b) Poppy and Toni stay at the café until 10 50. (i) At 10 50 Poppy walks to visit her friend Sasha. Sasha’s home is 5 km from Poppy’s home. Poppy walks at the same speed as before. Complete the travel graph for Poppy. [2] (ii) At 10 50 Toni starts to cycle home. At 10 55, when she has travelled half the distance home, her bicycle has a puncture. She then walks the rest of the way home at 4.5 km/h. Complete the travel graph for Toni. [2] (iii) Calculate the average speed for Toni’s journey home from the café. Answer(b)(iii) km/h [3]

12

© UCLES 2012 0580/31/M/J/12

For

Examiner's

Use

8 North

P

Q R

S

y°

120 m

50 m

NOT TOSCALE

The diagram shows a rectangular field, PQRS. QR = 120 m, PQ = 50 m and P is due North of Q. Bill and Said run from P to R. Bill runs along the sides PQ and QR. Said runs directly from P to R. (a) Calculate how far (i) Bill runs, Answer(a)(i) m [1]

(ii) Said runs. Answer(a)(ii) m [2]

(b) Bill takes 34 seconds to reach R. Calculate Bill’s average speed. Answer(b) m/s [1]

13


For

Examiner's

Use

(c) Said runs at 4 m / s. Who arrives at R first and by how many seconds? Answer(c) arrives at R first by seconds. [3]

(d) (i) Use trigonometry to calculate the size of the angle marked y. Answer(d)(i) [2]

(ii) Find the bearing of R from P. Answer(d)(ii) [1]

(e) Calculate the area of the field in square kilometres. Give your answer in standard form. Answer(e) km2 [4]

14

© UCLES 2012 0580/31/M/J/12

For

Examiner's

Use

9 (a) 3 cm

8 cm

NOT TOSCALE

A cylindrical drinking glass has radius 3 cm and height 8 cm. (i) Calculate the volume of water the glass holds when it is filled to the top. Give the units of your answer. Answer(a)(i) [3]

(ii) Water is poured into a number of these glasses from a jug containing 1.5 litres. Each glass has a horizontal line 2 cm from the top. Calculate how many of these glasses can be filled up to the line from the jug. Answer(a)(ii) [4]

(b) A cylindrical pipe has a circumference of 16 cm. Calculate the diameter of the pipe. Answer(b) cm [2]

15

© UCLES 2012 0580/31/M/J/12

For

Examiner's

Use

(c) A cuboid measures 6 cm by 5 cm by 4 cm.

4 cm

5 cm

6 cm

NOT TOSCALE

Work out the surface area of the cuboid. Answer(c) cm2 [3]

(d) 1m3 of copper has a mass of m kg. The volume of one copper sphere is v m3. Write down an expression for (i) the mass, in kilograms, of one sphere,

Answer(d)(i) kg [1] (ii) the mass, in kilograms, of s spheres, Answer(d)(ii) kg [1]

(iii) the mass, in grams, of s spheres. Answer(d)(iii) g [1]

16



© UCLES 2012 0580/31/M/J/12

BLANK PAGE



*2901534127*


MATHEMATICS 0580/32


2 hours

















2

© UCLES 2012 0580/32/M/J/12

For

Examiner's

Use

1 (a) Indira buys 1250 square metres of land to build a hotel. Each square metre of land costs $12 . Calculate the cost of the land. Answer(a) $ [1]

(b) The cost of the land is 3% of the cost of the hotel. Calculate the cost of the hotel. Answer(b) $ [2]

(c) The hotel has 84 rooms. The types of room are in the ratio family : double : single = 3 : 5 : 4 . Calculate the number of double rooms. Answer(c) [2]

(d) Each single room is a cuboid, 4.5 m long, 3.2 m wide and 2.8 m high. Calculate the volume of a single room. Answer(d) m3 [2]

3


For

Examiner's

Use

(e) The total hotel income for the first year was $992 000 .

(i) The hotel spent 8

3 of the total hotel income on staff wages.

Calculate the staff wages. Answer(e)(i) $ [1]

(ii) The hotel also spent $420 000 on food. Calculate how much of the total hotel income was left. Answer(e)(ii) $ [2]

(iii) Calculate $420 000 as a percentage of $992 000 . Give your answer correct to 1 decimal place. Answer(e)(iii) % [2]

(f) To make improvements, Indira borrows $3 500 at a rate of 6% per year simple interest. She pays back all the amount at the end of 3 years. Calculate the total amount she needs to repay. Answer(f) $ [3]

4

© UCLES 2012 0580/32/M/J/12

For

Examiner's

Use

2

8

6

4

2

–2

–4

–6

–8

–2 20 4 6 8–4–6–8

y

x

A

B

CD

(a) Describe fully the single transformation that maps A onto (i) B, Answer(a)(i) [2]

(ii) C, Answer(a)(ii) [3]

(iii) D. Answer(a)(iii) [2]

(b) On the grid, draw the enlargement of A, scale factor 2

1

, centre (0, 0). [2]

5


For

Examiner's

Use

3 (a) Calculate (i) 33, Answer(a)(i) [1]

(ii) 2

12

81

,

Answer(a)(ii) [1]

(iii) the cube root of 4913. Answer(a)(iii) [1]

(b) Find (i) all the square numbers between 6 and 40, Answer(b)(i) [2]

(ii) four factors of 76, Answer(b)(ii) [2]

(iii) a prime factor of 35, Answer(b)(iii) [1]

(iv) the lowest common multiple of 6 and 8, Answer(b)(iv) [2]

(v) the highest common factor of 56 and 70. Answer(b)(v) [2]

6

© UCLES 2012 0580/32/M/J/12

For

Examiner's

Use

4 (a) The table shows some values of y =x

10.

x –8 –5 –4 –2 –1 1 2 4 5 8

y –1.25 –5 10 2


(ii) On the grid opposite, draw the graph of y = x

10 for −8 Y x Y −1 and 1 Y x Y=8 . [4]

(b) (i) On the same grid, draw the straight line through the points (−3, −5) and (1, 3). Extend the line to the edges of the grid. [2]

(ii) Find the co-ordinates of the points of intersection of this line with the graph of y = x

10.

Answer(b)(ii) ( , ) and ( , ) [2]

(c) For the line in part (b)(i)

(i) work out the gradient, Answer(c)(i) [2]

(ii) write down the equation in the form y = mx + c . Answer(c)(ii) y = [1]

7


For

Examiner's

Use

y

x

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

–1–2–3–4–5–6–7–8 876543210

8

© UCLES 2012 0580/32/M/J/12

For

Examiner's

Use

5 (a) A = 2

1(a + b)h

Work out the value of A when a = 9.6, b = 12.4 and h = 7.5 . Answer(a) [2]

(b) (i) Expand x(x2 – 3y). Answer(b)(i) [2]

(ii) Expand and simplify 4(2w – 3) + 5(w – 2). Answer(b)(ii) [2]

(c) A quadrilateral has sides x, 2x, y and 3y. (i) Write down and simplify a formula for the perimeter, p, of the quadrilateral. Answer(c)(i) p = [2]

9


For

Examiner's

Use

(ii) Make y the subject of the formula in part (c)(i). Answer(c)(ii) y = [2]

(d) Joseph is 3 times as old as Amy. In 5 years time Joseph will be 2 times as old as Amy. (i) Amy is now n years old. Write down an equation in n connecting the ages of Joseph and Amy in 5 years time. Answer(d)(i) [2]

(ii) Solve the equation to find n.

Answer(d)(ii) n = [3]

10

© UCLES 2012 0580/32/M/J/12

For

Examiner's

Use

6 The total distance, to the nearest kilometre, travelled by a taxi each day for 24 days is shown below.

100 98 95 98 97 99 96 98

97 98 97 99 100 96 97 99

100 250 97 99 98 95 97 96

(a) (i) Complete the frequency table. You may use the tally column to help you.

Distance travelled (km) Tally Number of days

95

96

97

98

99

100

250

[2]

11


For

Examiner's

Use


Answer(a)(ii) km [1]

(iii) Find the median. Answer(a)(iii) km [2]

(iv) Calculate the mean. Answer(a)(iv) km [3]

(v) Which of the mean or the median best represents the average distance the taxi travels

each day? Give a reason for your answer.

Answer(a)(v) because

[1]

(b) Find the probability that, on a day chosen at random, the taxi travels 98 km or more. Answer(b) [2]

12

© UCLES 2012 0580/32/M/J/12

For

Examiner's

Use

7 The scale drawing shows the positions of three airports A, B and C. The scale is 1 centimetre represents 100 kilometres.

North

North

North

B

A

C

Scale: 1 cm to 100 km (a) Measure the bearing of airport A from airport B. Answer(a) [1]

13


For

Examiner's

Use

(b) The flight path of an aeroplane is a straight line equidistant from A and from B. Using a straight edge and compasses only, construct the flight path of this aeroplane. [2] (c) An aeroplane takes off from airport A and flies on a bearing of 020°. It crosses the flight path of the aeroplane in part (b) at D. (i) Draw the straight line path of this aeroplane and mark the point D. [1] (ii) Write down the actual distance from A to D. Answer(c)(ii) km [2]

(d) An aeroplane takes off from airport C. It flies a distance of 1230 km in 2 hours 45 minutes. Calculate the average speed of the aeroplane. Answer(d) km/h [2]

14

© UCLES 2012 0580/32/M/J/12

For

Examiner's

Use

8

D C

A B

V

6.5 cm

6.5 cm

5 cm

5 cm

NOT TOSCALE

The diagram shows a pyramid, ABCDV, on a square base. All the sloping faces are congruent triangles. AB = 5 cm and VA = 6.5 cm. (a) Write down the mathematical name of triangle VAB.

Answer(a) [1] (b) (i) Using a ruler and compasses only, construct the triangle VAB. Show your construction arcs. [2] (ii) By making any necessary measurements, calculate the area of triangle VAB. Answer(b)(ii) cm2 [3]

(iii) Calculate the total surface area of the pyramid, including the base. Answer(b)(iii) cm2 [2]

15


For

Examiner's

Use

(iv) Work out the total length of all the edges of the pyramid. Answer(b)(iv) cm [2]

(c) On the grid, draw an accurate net of the pyramid. The line AB has been drawn.

A B

[3]


16



© UCLES 2012 0580/32/M/J/12

For

Examiner's

Use

9

Diagram 1 Diagram 2 Diagram 3 Diagram 4 (a) The pattern of diagrams above forms a sequence. (i) On the grid, draw Diagram 4. [1] (ii) Complete the table.

Diagram 1 2 3 4 5

Number of dots 4 6

[2] (b) Find the number of dots in Diagram n. Answer(b) [2]

(c) Find the number of dots in Diagram 48. Answer(c) [1]

(d) There are 3 one centimetre squares in Diagram 2. Find the number of one centimetre squares in Diagram 5. Answer(d) [2]



*5603526471*


MATHEMATICS 0580/33


2 hours

















2

© UCLES 2012 0580/33/M/J/12

For

Examiner's

Use

1 (a) The minimum temperatures at Beijing Airport, for five days, are given in this table.

Day Monday Tuesday Wednesday Thursday Friday

Temperature (°C) –3 5 –1 2 –4

(i) Write down the lowest temperature. Answer(a)(i) °C [1]

(ii) Write these temperatures in order, starting with the lowest. Answer(a)(ii) < < < < [1]

(iii) What is the difference between the temperatures on Monday and Tuesday? Answer(a)(iii) °C [1]

(b) The table shows part of the timetable for flights from Beijing to Hong Kong.

Beijing 07 45 08 00 09 30

Hong Kong 11 20 11 40 13 05

(i) At what time does the first plane after midday arrive in Hong Kong? Answer(b)(i) [1]

(ii) How long, in hours and minutes, does the 07 45 flight from Beijing to Hong Kong take? Answer(b)(ii) h min [1]

(c) A plane travels 1708 km in 3.5 hours. Work out the average speed of the plane. Give the units of your answer. Answer(c) [2]

3


For

Examiner's

Use

2 (a) Find all the factors of 28 . Answer(a) [2]

(b) Write down a multiple of 8 that is greater than 20 . Answer(b) [1]

(c) Work out 183

. Answer(c) [1]

(d) p and q are prime numbers. p3 × q2 = 200 Find the values of p and q. Answer(d) p =

q = [2] (e) A town has two bus companies.

Buses from Western Travel stop at the Town Hall every 8 minutes.

Buses from Eastern Travel stop at the Town Hall every 14 minutes.

(i) Write down the lowest common multiple of 8 and 14 . Answer(e)(i) [2]

(ii) A bus from each company stops at the Town Hall at 08 00. When is the next time that a bus from each company stop together at the Town Hall? Answer(e)(ii) [1]

(iii) The cost of an adult ticket on Western Travel is $a and the cost of a child’s ticket is $c.

One day 84 adult tickets and 36 child tickets are sold. Write an expression, in terms of a and c, for the total cost of these tickets. Answer(e)(iii) $ [2]

4

© UCLES 2012 0580/33/M/J/12

For

Examiner's

Use

3 Here is a scale drawing of a shop floor, EFGH. The scale is 1 centimetre represents 2 metres.

E

F G

H

Scale: 1 cm to 2 m

(a) What is the mathematical name of the shape EFGH? Answer(a) [1]

(b) What type of angle is angle EFG? Answer(b) [1]

(c) Find the actual length, in metres, of the side EH. Answer(c) m [2]

(d) Measure angle FEH. Answer(d) Angle FEH = [1]

(e) Complete this part using ruler and compasses only.

All construction arcs must be clearly shown.

A table is placed • nearer to E than to H

and • less than 14 m from H. By constructing two loci on the scale drawing, find and label the region R, where the table is

placed. [5] (f) The shop sells shoes which are packed in boxes. Each box is a cuboid 33.2 cm long, 16.8 cm wide and 11 cm high. Calculate the volume of one of these shoe boxes. Answer(f) cm3 [2]

5


For

Examiner's

Use

4 (a) In a café the price of an adult’s meal is $24 and the price of a child’s meal is $16. A 12% service charge is added to the costs of the meals. Calculate the total cost of meals for 2 adults and 3 children. Answer(a) $ [3]

(b) On a Saturday night the adult meal price of $24 is increased by 20%. Calculate the increased price of this meal. Answer(b) $ [2]

(c) The price of a large cup of coffee increases from $3.00 to $3.42 . Calculate the percentage increase in the price. Answer(c) % [3]

6

© UCLES 2012 0580/33/M/J/12

For

Examiner's

Use

5 (a) Draw all the lines of symmetry on this rectangle.

[2] (b) Shade one square so that the shaded shape has rotational symmetry of order 2.

[1] (c) On the grid below, draw an enlargement of the triangle with a scale factor of 2.

[2]

7


For

Examiner's

Use

(d)

A

D

P

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–3–4–5–6 –2 –1 10 2 3 4 5 6

(i) Write down the co-ordinates of the point P. Answer(d)(i) ( , ) [1]

(ii) Reflect triangle A in the y-axis. Label the image B. [1]

(iii) Translate triangle A by the vector

− 3

1.

Label the image C. [2] (iv) Describe the single transformation that maps triangle A onto triangle D. Answer(d)(iv) [3]

8

© UCLES 2012 0580/33/M/J/12

For

Examiner's

Use

6 James and Wei have a car. Each year James drives 3 600 km and Wei drives 4 800 km. (a) Write 3 600 : 4 800 as a ratio in its simplest form. Answer(a) : [1]

(b) A garage charges $420 to service the car. James and Wei share the $420 in the ratio James : Wei = 2 : 3 . Find the amount that James pays. Answer(b) $ [2]

(c) On a 268 km journey the car uses 22.8 litres of fuel. By writing these numbers to 1 significant figure, estimate the distance travelled

using one litre of fuel. Show all your working. Answer(c) km [2]

(d) On another journey the car uses 46.3 litres of fuel. Fuel costs $1.48 per litre. Work out the cost of the fuel for this journey. Answer(d) $ [2]

9


For

Examiner's

Use

(e) The table shows some information about the car.

Fuel tank capacity 64 litres (to the nearest litre)

Width 1810 mm (to 3 significant figures)

(i) Write down the upper bound of the fuel tank capacity. Answer(e)(i) litres [1]

(ii) Write down the minimum width of the car. Answer(e)(ii) mm [1]

10

© UCLES 2012 0580/33/M/J/12

For

Examiner's

Use

7 The table shows the marks for ten students in their Chemistry papers for Unit A and Unit B.

Unit A 32 78 45 63 36 73 58 41 68 54

Unit B 43 81 49 58 40 74 60 50 72 59

(a) On the grid, complete the scatter diagram for these results. The first six points have been plotted for you.

90

80

70

60

50

40

3030 40 50 60 70 80 90

Unit A

Unit B

[2] (b) What type of correlation does the scatter diagram show? Answer(b) [1]

11


For

Examiner's

Use

(c) (i) Calculate the mean of the marks for Unit A. Answer(c)(i) [2]

(ii) Work out the range of the marks for Unit A. Answer(c)(ii) [1]

(iii) The mean for Unit B is 58.6 . Which unit did the students find more difficult? Give a reason for your answer. Answer(c)(iii) Unit because

[1] (d) (i) Draw a line of best fit on the grid. [1] (ii) Lee scored 48 on Unit A but she was absent for Unit B. Use your line of best fit to estimate her score on Unit B. Answer(d)(ii) [1]

(e) Find how many students scored more than 65 marks on both units. Answer(e) [1]

12

© UCLES 2012 0580/33/M/J/12

For

Examiner's

Use

8 (a) Complete the table of values for y = x2 – 2x + 5 .

x –3 –2 –1 0 1 2 3 4 5

y 20 8 8 20

[3]

(b) On the grid, draw the graph of y = x2 – 2x + 5 for −3 Y x Y 5 .

–4 –2 0 2 4 6–3 –1 1 3 5

y

x

22

20

18

16

14

12

10

8

6

4

2

[4] (c) (i) On the grid, draw the line of symmetry of the graph. [1] (ii) Write down the equation of the line of symmetry. Answer(c)(ii) [1]

13


For

Examiner's

Use

(d) (i) On the grid, draw the line y = 12 . [1] (ii) Use your graph to solve the equation x2 – 2x + 5 = 12 . Answer(d)(ii) x = or x = [2]

(e) The equation of a straight line is y = 6 – 3x . (i) Write down the gradient of this line. Answer(e)(i) [1]

(ii) Write down the co-ordinates of the point where this line crosses the y-axis. Answer(e)(ii) ( , ) [1]

(iii) Write down the equation of a line parallel to y = 6 – 3x . Answer(e)(iii) [1]

(f) Simplify 3(2x + 1) O=2(6 – 3x) . Answer(f) [2]

14

© UCLES 2012 0580/33/M/J/12

For

Examiner's

Use

9 The diagram shows a regular hexagon inside a circle, centre O and radius 8 cm. Each vertex of the hexagon is on the circumference of the circle. A and B are two vertices of the hexagon and M is the midpoint of AB.

O

A BM

8 cm

NOT TOSCALE

(a) Calculate (i) angle AOB, Answer(a)(i) Angle AOB = [1]

(ii) angle AOM. Answer(a)(ii) Angle AOM = [1]

(b) Write down the length AB. Answer(b) AB = cm [1]

(c) Show that the length of OM = 6.93 cm, correct to 3 significant figures. Answer(c) [2]

15


For

Examiner's

Use

(d) Calculate the area of triangle AOB. Answer(d) cm2 [2]

(e) Calculate the shaded area. Answer(e) cm2 [4]


16



© UCLES 2012 0580/33/M/J/12

For

Examiner's

Use

10 The Patterns shown below form a sequence.

Pattern 1 has 6 dots and 6 lines. Pattern 2 has 10 dots and 11 lines.

Pattern 1

Pattern 2

Pattern 3

Pattern 4

(a) On the grid, draw Pattern 4. [1] (b) (i) Find the number of dots in Pattern 5. Answer(b)(i) [1]

(ii) Explain how you worked out your answer in part (b)(i). Answer(b)(ii) [1]

(c) Write down an expression, in terms of n, for the number of dots in Pattern n. Answer(c) [2]

(d) The number of dots in Pattern n is 62 . Find n. Answer(d) n = [2]



*8270368766*


MATHEMATICS 0580/11


1 hour

















2

© UCLES 2012 0580/11/O/N/12

For

Examiner's

Use

1 Shade two more squares so that this pattern has rotational symmetry of order 2.

[1]

2 Write three hundredths as a decimal.

Answer [1]

3

87°36°

75°

x

NOT TOSCALE

(a) Find angle x.

Answer(a) Angle x = [1]

(b) What type of angle is x ?

Answer(b) [1]

3

© UCLES 2012 0580/11/O/N/12 [Turn over

For

Examiner's

Use

4 A football ground seats 28 750 people when it is full.

(a) Write 28 750 correct to the nearest thousand.

Answer(a) [1]

(b) One day 17 250 people attended a football match.

Work out 17 250 as a percentage of 28 750.

Answer(b) % [1]

5 Solve the following equations.

(a) x + 9 = 16

Answer(a) x = [1]

(b) 6y = 27

Answer(b) y = [1]

6 On a mountain, the temperature decreases by 6.5 °C for every 1000 metres increase in height.

At 2000 metres the temperature is 10 °C.

Find the temperature at 6000 metres.

Answer °C [2]

4

© UCLES 2012 0580/11/O/N/12

For

Examiner's

Use

7 Simplify the following expression.

3j – 4k – 2 + 5j + k – 6

Answer [2]

8 The train fare from Bangkok to Chiang Mai is 768 baht.

The exchange rate is £1 = 48 baht.

Calculate the train fare in pounds (£).

Answer £ [2]

9 Use your calculator to find the value of

6.28.12

4.36.28.1222

××

−+.

Answer [2]

5


For

Examiner's

Use

10 (a) Write 230 000 in standard form.

Answer(a) [1]

(b) Write 4.8 × 10O4 as an ordinary number.

Answer(b) [1]

11 Write down all your working to show that the following statement is correct.

2

1

9

8

2

1

+

+

= 45

34

Answer

[2]

12

6 cmNOT TOSCALE

The diagram shows a circular disc with radius 6 cm.

In the centre of the disc there is a circular hole with radius 0.5 cm.

Calculate the area of the shaded section.

Answer cm2 [3]

6

© UCLES 2012 0580/11/O/N/12

For

Examiner's

Use

13 (a) Factorise 9y + 12 .

Answer(a) [1]

(b) Expand a(a2 – 7) .

Answer(b) [2]

14 Ying spins a spinner 75 times.

The table shows her results.

Red

Blue

Green

Yellow

Colour Red Blue Green Yellow

Frequency 17 24 20 14

(a) Write down the relative frequency of the spinner stopping on blue.

Answer(a) [1]

(b) Tony spins the same spinner 450 times.

Find the expected number of times the spinner stops on yellow.

Answer(b) [2]

7


For

Examiner's

Use

15 The table shows how 45 students each travel to college.

Method of travel Walk Bus Cycle

Frequency 20 18 7

This information can be displayed in a pie chart.

(a) Show that the sector angle for students who walk is 160°.

Answer(a)

[1]

(b) Calculate the sector angle for students who travel by bus.

Answer(b) [1]

(c) Complete the pie chart and label the sectors.

[2]

8

© UCLES 2012 0580/11/O/N/12

For

Examiner's

Use

16

=

9

0p

−

=

5

3q

=

−

3

4r

Calculate

(a) 7p ,

Answer(a)

[2]

(b) q – r .

Answer(b)

[2]

9


For

Examiner's

Use

17

A BC

AB is the diameter of a circle.

C is a point on AB such that AC = 4 cm.

(a) Using a straight edge and compasses only, construct

(i) the locus of points which are equidistant from A and from B, [2]

(ii) the locus of points which are 4 cm from C. [1]

(b) Shade the region in the diagram which is

• nearer to B than to A

and

• less than 4 cm from C. [1]

10

© UCLES 2012 0580/11/O/N/12

For

Examiner's

Use

18

x

y L

0–2

(4, 10)NOT TOSCALE

Line L passes through the point (4, 10).

(a) Find the gradient of line L.

Answer(a) [2]

(b) Write down the equation of line L, in the form y = mx + c.

Answer(b) y = [1]

(c) Line P passes through the point (0, 0).

Line P is parallel to line L.

Write down the equation of line P.

Answer(c) y = [1]

11


For

Examiner's

Use

19 B

DA C

9.3 cm6.5 cm

7.4 cm

NOT TOSCALE

(a) Calculate AD.

Answer(a) AD = cm [3]

(b) Use trigonometry to calculate angle BCD.

Answer(b) Angle BCD =

[2]


12



© UCLES 2012 0580/11/O/N/12

For

Examiner's

Use

20

14121086420

14 00 14 30 15 00 15 30 16 00 16 30 17 00 17 30

Distance fromLola’s house (km)

Sarah’s house

Lola’s house

Time

The travel graph shows Lola’s journey from her house to Sarah’s house.

(a) Lola stopped at a shop on the way to Sarah’s house.

For how many minutes did she stop?

Answer(a) min [1]

(b) Write down the time she arrived at Sarah’s house.

Answer(b) [1]

(c) Calculate Lola’s average speed from leaving the shop to arriving at Sarah’s house.

Give your answer in kilometres per hour.

Answer(c) km/h [2]

(d) Lola stayed at Sarah’s house for 1 hour 20 minutes.

She then cycled home without stopping.

Her journey took 50 minutes.

Complete the travel graph. [2]



*7301883916*


MATHEMATICS 0580/12


1 hour

















2

© UCLES 2012 0580/12/O/N/12

For

Examiner's

Use

1 Work out 8

5

7

3× .

Give your answer as a fraction. Answer [1]

2 Amisi travelled from Johannesburg to Cairo. She changed 500 Egyptian pounds (EGP) to South African rand (ZAR) when the exchange rate was

1 EGP = 1.24 ZAR. Calculate the amount she received. Answer ZAR [1]

3 Write the following numbers correct to one significant figure. (a) 7682 Answer(a) [1]

(b) 0.07682 Answer(b) [1]

4 Mars is ninety-one million, seven hundred thousand kilometres from Earth. (a) Write this number in figures. Answer(a) [1]

(b) Write your answer to part (a) in standard form. Answer(b) [1]

3


For

Examiner's

Use

5 A bowl of fruit contains only 8 peaches, 5 oranges and 6 apples. One piece of fruit is chosen at random. Write down the probability that it is (a) an orange, Answer(a) [1]

(b) not a peach. Answer(b) [1]

6 The formula for changing a temperature in Celsius to a temperature in Fahrenheit is F = 1.8C + 32 . Make C the subject of the formula. Answer C = [2]

7 a =

−1

4 b =

−

−

3

2

Work out a + 3b.

Answer

[2]

4

© UCLES 2012 0580/12/O/N/12

For

Examiner's

Use

8 Work out. (a) 4 – 5 – 6 Answer(a) [1]

(b) 2

8

−

−

Answer(b) [1]

9 Patrick buys some bananas for $35. He sells all the bananas for $40.60 . Calculate his percentage profit. Show all your working. Answer % [3]

10 12 13 14 15 16 17 18 From the list of numbers, write down (a) a factor of 36, Answer(a) [1]

(b) a multiple of 8, Answer(b) [1]

(c) a prime factor of 52. Answer(c) [1]

5


For

Examiner's

Use

11 An athlete runs 1500 metres in 4 minutes. Calculate her average speed in (a) metres per minute, Answer(a) m/min [1]

(b) kilometres per hour. Answer(b) km/h [2]

12 In a traffic survey of 125 cars the number of people in each car was recorded.

Number of people in each car 1 2 3 4 5

Frequency 50 40 10 20 5

Find (a) the range, Answer(a) [1]

(b) the median, Answer(b) [1]

(c) the mode. Answer(c) [1]

6

© UCLES 2012 0580/12/O/N/12

For

Examiner's

Use

13

0.65 m

85 km

NOT TOSCALE

A water pipeline in Australia is a cylinder with radius 0.65 metres and length 85 kilometres. Calculate the volume of water the pipeline contains when it is full. Give your answer in cubic metres. Answer m3 [3]

14 A shop is open during the following hours.

Monday to Friday Saturday Sunday

Opening time 06 45 07 30 08 45

Closing time 17 30 17 30 12 00

(a) Write the closing time on Saturday in the 12-hour clock time. Answer(a) [1]

(b) Calculate the total number of hours the shop is open in one week. Answer(b) h [2]

7


For

Examiner's

Use

15 The diagram shows an isosceles triangle between two parallel lines.

115°

p°q°

NOT TOSCALE

Calculate (a) the value of p, Answer(a) p = [2]

(b) the value of q. Answer(b) q = [1]

16 Musa borrows $600 for 2 years at a rate of 7.5% per year compound interest. At the end of the 2 years she repays the amount owing in full. Calculate the total amount she has to repay. Give your answer correct to the nearest dollar. Answer $ [3]

8

© UCLES 2012 0580/12/O/N/12

For

Examiner's

Use

17 (a) Factorise completely. 6x2 – 8xy Answer(a) [2]

(b) Simplify the following expression.

28a5 Q 4aO2

Answer(b) [2]

9


For

Examiner's

Use

18 A company sends out ten different questionnaires to its customers. The table shows the number sent and replies received for each questionnaire.

Questionnaire A B C D E F G H I J

Number sent out 100 125 150 140 70 105 100 90 120 130

Number of replies 24 30 35 34 15 25 22 21 30 31

40

35

30

25

20

15

10

5

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Num

ber o

f rep

lies

Number sent out (a) Complete the scatter diagram for these results. The first two points have been plotted for you. [2] (b) Describe the correlation between the two sets of data. Answer(b) [1]

(c) Draw the line of best fit. [1]

10

© UCLES 2012 0580/12/O/N/12

For

Examiner's

Use

19 D

A CB

NOT TOSCALE

5.6 m 7.8 m

2.9 m (a) Calculate BD. Answer(a) BD = m [3]

(b) DC = 7.8 m . Use trigonometry to calculate angle BCD. Answer(b) Angle BCD = [2]

11

© UCLES 2012 0580/12/O/N/12

For

Examiner's

Use

20

34°

68°

AB

E

DC

NOT TOSCALE

The points A, B, C, D and E lie on a circle with diameter BD. AE is parallel to BD. Angle BDE = 68° and angle DBC = 34°. (a) Give the reason why angle BCD is 90°. Answer(a) [1]

(b) Find (i) angle BDC, Answer(b)(i) [1]

(ii) angle DEA. Answer(b)(ii) [1]

(c) Find the sum of the angles of the pentagon ABCDE. Answer(c) [2]

12



© UCLES 2012 0580/12/O/N/12

BLANK PAGE



*3457337604*


MATHEMATICS 0580/13


1 hour

















2

© UCLES 2012 0580/13/O/N/12

For

Examiner's

Use

1

x° 196°

NOT TOSCALE


Answer x = [1]

2 (a) Write down the order of rotational symmetry of this letter.

H

Answer(a) [1]

(b) Draw the line of symmetry on this letter.

A

[1]

3 Work out.

43 O 49

Answer [2]

3


For

Examiner's

Use

4 Simplify.

(a) 5t O 2t + 4t Answer(a) [1]

(b) r5 × r8 Answer(b) [1]

5 Samantha invests $600 at a rate of 2% per year simple interest. Calculate the interest Samantha earns in 8 years. Answer $ [2]

6 Show that 10

1

2

+ 5

2

2

= 0.17.

Write down all the steps in your working. Answer

[2]

7 Pens cost p cents and rulers cost r cents. Write down an expression, in terms of p and r, for the cost of 5 pens and 11 rulers. Answer cents [2]

4

© UCLES 2012 0580/13/O/N/12

For

Examiner's

Use

8 Jamie needs 300 g of flour to make 20 cakes. How much flour does he need to make 12 cakes? Answer g [2]

9 Expand the brackets.

y(3 O y3) Answer [2]

10 Maria pays $84 rent. The rent is increased by 5%. Calculate Maria’s new rent. Answer $ [2]

11 A carton contains 250 ml of juice, correct to the nearest millilitre. Complete the statement about the amount of juice, j ml, in the carton. Answer Y j I [2]

5


For

Examiner's

Use 12 98

19.784.72+

(a) Rewrite this calculation with each number written correct to 1 significant figure. Answer(a)

[1] (b) Work out the answer to your calculation in part (a). Do not use a calculator and show all your working. Answer(b) [1]

13 Factorise completely. 4xy + 12yz Answer [2]

14

Using a straight edge and compasses only, construct the locus of points which are equidistant from

R and from T. [2]

T

R

6

© UCLES 2012 0580/13/O/N/12

For

Examiner's

Use

15 Find the value of 10.9511.8

7.2

−

.

Give your answer correct to 4 significant figures. Answer [2]

16 Calculate the interior angle of a regular pentagon. You must show all your working. Answer [3]


5

1

8

3

25 −.

Give your answer as a fraction in its lowest terms. You must show all your working. Answer [3]

7


For

Examiner's

Use

18 14 children played a game. The age of each child and the number of points they scored are plotted on the scatter diagram.

76 8 9 10 11 12 13 14 15 16

14

13

12

11

10

9

8

7

6

5

4

Pointsscored

Age of child (a) Write down the number of points the child aged 11 scored. Answer(a) [1]

(b) Draw a line of best fit on the scatter diagram. [1] (c) What type of correlation is shown? Answer(c) [1]

8

© UCLES 2012 0580/13/O/N/12

For

Examiner's

Use

19 y

x10 2 3 4 5 6–6 –5 –4 –3 –2 –1

5

4

3

2

1

–1

–2

–3

–4

B

L

(a) On the grid mark the point (5, 1). Label it A. [1] (b) Write down the co-ordinates of the point B. Answer(b) ( , ) [1]

(c) Find the gradient of the line L. Answer(c) [2]

9


For

Examiner's

Use

20 (a) The probability that the school bus is late is 0.29 . Write down the probability that the school bus is not late. Answer(a) [1]

(b) A fridge contains 12 beef pies, 3 vegetable pies and 5 chicken pies. One pie is taken at random from the fridge. Find the probability that it is (i) a vegetable pie, Answer(b)(i) [1]

(ii) a beef pie or a vegetable pie, Answer(b)(ii) [1]

(iii) a lamb pie. Answer(b)(iii) [1]

10

© UCLES 2012 0580/13/O/N/12

For

Examiner's

Use

21 C

A B

8 cm9 cm

12 cm

NOT TOSCALE

(a) (i) Construct an accurate drawing of triangle ABC. [2] (ii) On your drawing, mark accurately the midpoint of the side AB. Label it M. [1]

11


For

Examiner's

Use

(b) (i) Sketch the quadrilateral that has

• opposite sides which are equal in length and parallel and

• opposite angles which are equal and

• diagonals which bisect each other at 90°. [1] (ii) Write down the mathematical name of this quadrilateral. Answer(b)(ii) [1]


12



© UCLES 2012 0580/13/O/N/12

For

Examiner's

Use

22 (a) In the diagram, the line AC touches the circle at B.

A

B

C (i) Measure the length of the line AC. Answer(a)(i) AC = cm [1]

(ii) Write down the mathematical name for the line AC. Answer(a)(ii) [1]

(iii) Mark a point D on the circumference of the circle. [1] (b) The diameter of another circle is 3.6 cm. Calculate the circumference of this circle. Answer(b) cm [2]



*0719272774*


MATHEMATICS 0580/31


2 hours

















2

© UCLES 2012 0580/31/O/N/12

For

Examiner's

Use

1 (a) (i) Write down two numbers that are multiples of 10. Answer(a)(i) and [1]

(ii) Find the lowest common multiple of 10 and 15. Answer(a)(ii) [2]

(b) 4 6 9 15 23 27 32 36 From the list above, write down (i) a factor of 18, Answer(b)(i) [1]

(ii) a cube number, Answer(b)(ii) [1]

(iii) a prime number. Answer(b)(iii) [1]

(c) Give an example to show that each of these statements is not true. (i) All square numbers are even. Answer(c)(i) [1]

(ii) When two prime numbers are added the answer is always even. Answer(c)(ii) [1]

(d) Write the following in order of size, starting with the smallest.

25 80 4–2 169

Answer(d) I I I [2]

3


For

Examiner's

Use

2 (a) Luka earns $475 each week. (i) He works for 38 hours each week. How much does he earn for each hour he works? Answer(a)(i) $ [1]

(ii) Luka pays $175 in rent each week. Write the amount he pays in rent as a fraction of his weekly earnings. Give your answer in its lowest terms. Answer(a)(ii) [2]

(iii) He spends 20

7 of his weekly earnings on bills.

How much money does he have left after paying rent and bills? Answer(a)(iii) $ [2]

(b) Luka’s weekly earnings of $475 are increased by 6%. Calculate his new weekly earnings. Answer(b) $ [2]

(c) Luka has saved $350. He invests this for 2 years at a rate of 4% per year compound interest. How much interest does he receive after 2 years? Answer(c) $ [3]

4

© UCLES 2012 0580/31/O/N/12

For

Examiner's

Use

3 (a) Amir asked 15 friends how many hours they spent playing sport last weekend. His results are shown in the table below.

Number of hours 0 1 2 3 4 5

Frequency 6 2 3 1 2 1

(i) Write down the mode. Answer(a)(i) hours [1]

(ii) Find the median. Answer(a)(ii) hours [1]

(iii) Calculate the mean. Answer(a)(iii) hours [3]

(iv) On the grid, draw a bar chart to show the information given in the table.

Frequency

Number of hours [4]

5


For

Examiner's

Use

(b) Amir also asked these 15 friends which was their favourite sport. His results are shown in the table below.

Football 4

Cricket 5

Basketball 2

Badminton 4

Amir picks one of these friends at random. Write down the probability that his friend’s favourite sport is (i) cricket, Answer(b)(i) [1]

(ii) not football, Answer(b)(ii) [1]

(iii) basketball or badminton. Answer(b)(iii) [1]

6

© UCLES 2012 0580/31/O/N/12

For

Examiner's

Use

4 (a)

70°

40°

C

D

E

A

B

NOT TOSCALE

In the diagram, ACE is a triangle. B is a point on AC and D is a point on CE. AE is parallel to BD, angle ACE = 70° and angle CBD = 40°. (i) Find angle BDC. Answer(a)(i) Angle BDC = [1]

(ii) Write down the mathematical name of triangle BCD. Answer(a)(ii) [1]

(iii) Find angle CAE. Give a reason for your answer. Answer(a)(iii) Angle CAE = because

[2] (iv) Complete the following statement. Triangle ACE and triangle BCD are [1]

7


For

Examiner's

Use

(b)

55°

A

B

OC

NOT TOSCALE

In the diagram, A and B lie on a circle, centre O. AC and BC are tangents to the circle and angle ACB = 55°. (i) Work out reflex angle ACB. Answer(b)(i) Reflex angle ACB = [1]

(ii) Give a reason why angle OAC = angle OBC = 90°. Answer(b)(ii) [1]

(iii) Work out angle AOB. Answer(b)(iii) Angle AOB = [1]

(iv) Write down the mathematical name of quadrilateral OACB. Answer(b)(iv) [1]

8

© UCLES 2012 0580/31/O/N/12

For

Examiner's

Use

5

B

A D

C20 m

32 m

15 m

NOT TOSCALE

The diagram shows a plot of land, ABCD, in the shape of a trapezium. (a) Show that CD = 19.2 m, correct to 1 decimal place. Answer(a)

[2] (b) A fence is built around the perimeter of the plot of land. The cost of the fence is $35 for each metre. Calculate the total cost of the fence. Answer(b) $ [2]

(c) Calculate the area of the plot of land. Give your answer in square metres. Answer(c) m2 [2]

9


For

Examiner's

Use

(d) A house is built on the plot of land. The area of the plot is divided in the ratio house : grounds = 3 : 7 . Calculate the area of the grounds. Answer(d) m2 [2]

(e) (i) In the space below, make a scale drawing of the plot of land. Use a scale of 1 centimetre to represent 4 metres. The side AB has been drawn for you.

B

A [2] (ii) Measure angle ADC. Answer(e)(ii) Angle ADC = [1]

(iii) Use your diagram to find the actual length BD in metres. Answer(e)(iii) BD = m [1]

10

© UCLES 2012 0580/31/O/N/12

For

Examiner's

Use

6

Diagram 1 Diagram 2 Diagram 3 Diagram 4 A sequence of diagrams is made from black counters and white counters. The first four diagrams in the sequence are shown. (a) Complete the table.

Diagram 1 2 3 4 5

Number of black counters 1 4

Number of white counters 1 4

[4] (b) Complete the statement.

The numbers of black counters are all numbers. [1] (c) How many white counters are needed for (i) Diagram 8, Answer(c)(i) [1]

(ii) Diagram n? Answer(c)(ii) [2]

11


For

Examiner's

Use

(d) Diagram p contains 58 white counters. (i) Find the value of p. Answer(d)(i) p = [2]

(ii) Find the number of black counters in Diagram p. Answer(d)(ii) [1]

12

© UCLES 2012 0580/31/O/N/12

For

Examiner's

Use

7 (a) The cost, $C, of hiring a meeting room for n people is calculated using the formula C = 80 + 5n. (i) Calculate C when n = 12. Answer(a)(i) [2]

(ii) Maria pays $230 to hire the meeting room. Work out the number of people at the meeting. Answer(a)(ii) [2]

(iii) Make n the subject of the formula C = 80 + 5n. Answer(a)(iii) n = [2]

(b) Expand and simplify 2(3x + 4) – 3(2 – x) . Answer(b) [2]

(c) Solve the simultaneous equations. 3x + y = 13 2x + 3y = 18 Answer(c) x =

y = [3]

13


For

Examiner's

Use

8 (a) A water tank in the shape of a cuboid measures 55 cm by 40 cm by 75 cm. (i) Find the volume of the tank. Answer(a)(i) cm3 [2]

(ii) Write down the volume of the tank in litres. Answer(a)(ii) litres [1]

(b) Another water tank contains 260 litres. (i) The tank is emptied at a rate of 25 litres per minute. Work out the time taken to completely empty the tank. Give your answer in minutes and seconds. Answer(b)(i) minutes seconds [2]

(ii) 260 litres is given correct to the nearest 10 litres. Write down the lower bound of this amount. Answer(b)(ii) litres [1]

(c) A different tank is in the shape of a cube. It has a volume of 27 000 cm3. Find the height of this tank. Answer(c) cm [2]

14

© UCLES 2012 0580/31/O/N/12

For

Examiner's

Use

9 (a) Complete the table of values for y = 8 + 3x – x2.

x –3 –2 –1 0 1 2 3 4 5 6

y –10 8 10 10 –10

[3]

(b) On the grid, draw the graph of y = 8 + 3x – x2 for –3 Y x Y 6 .

y

x

12

10

8

6

4

2

–2

–4

–6

–8

–10

10 2 3 4 5 6–1–2–3

[4] (c) Write down the equation of the line of symmetry of the graph. Answer(c) [1]

(d) (i) On the grid, draw the graph of y = 6 . [1] (ii) Use your graphs to solve the equation 8 + 3x – x2 = 6 . Answer(d)(ii) x = or x = [2]

15

© UCLES 2012 0580/31/O/N/12

For

Examiner's

Use

10

A

B

C

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–6 –5 –4 –3 –2 –1 10 2 3 4 5 6

y

x

Shapes A, B and C are shown on the grid. (a) Describe fully the single transformation which maps (i) shape A onto shape B, Answer(a)(i) [3]

(ii) shape A onto shape C. Answer(a)(ii) [3]

(b) On the grid, draw the image of shape A after

(i) translation by the vector

− 4

3, [2]

(ii) reflection in the line y = –1. [2]

16



© UCLES 2012 0580/31/O/N/12

BLANK PAGE



*4405903504*


MATHEMATICS 0580/32


2 hours

















2

© UCLES 2012 0580/32/O/N/12

For

Examiner's

Use

1 An area of 94 500 m2 in a city is developed.

(a) The area is divided into housing, shops and a park in the ratio

housing : shops : park = 7 : 6 : 5 .

(i) Show that the area of the park is 26 250 m2.

Answer(a)(i)

[2]

(ii) Calculate the area for housing.

Answer(a)(ii) m2 [1]

(b) The diagram shows the children’s playground in the park.

100 m

45 m

76 m

NOT TOSCALE

(i) Calculate the area of the playground.

Answer(b)(i) m2 [2]

(ii) What fraction of the area of the park does the playground occupy?

Answer(b)(ii) [1]

3


For

Examiner's

Use

(c) Buildings occupy 30 625 m2 of the area for housing.

Calculate the percentage of the area for housing occupied by buildings.

Answer(c) % [1]

(d) Of the buildings, 12

5 are bungalows and

8

3 are houses.

The rest of the buildings are apartments.

(i) Complete these equivalent fractions.

2412

5=

248

3= [2]

(ii) Show that 24

5 of the buildings are apartments.

Answer(d)(ii)

[1]

(iii) There are 120 buildings altogether.

Work out the number of houses.

Answer(d)(iii) [1]

4

© UCLES 2012 0580/32/O/N/12

For

Examiner's

Use

2 (a) The table shows some values of the function y = x O x

8.

x O8 O6 O5 O4 O2 O1

1 2 4 5 6 8

y O7 O4.7 O3.4 O2 7

O2 3.4 4.7 7


(ii) On the grid on the opposite page, draw the graph of y = x O x

8 for

O8 Y x Y O1, 1 Y x Y 8 . [5]

(iii) Write down the order of rotational symmetry of the graph.

Answer(a)(iii) [1]

(iv) Use your graph to solve the equation x O x

8 = 0 .

Answer(a)(iv) x = or x = [2]

(b) (i) Write down the gradient of the line y = 2

1x + 1 .

Answer(b)(i) [1]

(ii) Complete the table below for the line y = 2

1x + 1 .

x O8 O4 0 4 8

y O3 3

[2]

(iii) On the grid, draw the line y = 2

1x + 1 for O8 Y x Y 8 . [1]

(c) Write down the co-ordinates of the points of intersection of y = x O x

8 and y =

2

1x + 1 .

Answer(c) ( , ) and ( , ) [2]

5


For

Examiner's

Use

x

y

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–8 –7 –6 –5 –4 –3 –2 –1 10 2 3 4 5 6 7 8

6

© UCLES 2012 0580/32/O/N/12

For

Examiner's

Use

3 l

A

B

C

D

E

F

P

(a) Describe fully the single transformation that maps triangle ABC onto triangle DEF.

Answer(a) [2]

(b) (i) Reflect triangle ABC in the line l.

Label the image M. [1]

(ii) Rotate triangle ABC through 90° clockwise about vertex A.

Label the image T. [2]

(c) Triangle DEF is enlarged by scale factor 2.

The image of vertex D is the point labelled P on the grid.

Mark the image of vertex E. Label this point Q.

Mark the image of vertex F. Label this point R. [2]

7


For

Examiner's

Use

4 (a)

A B C D

Complete the table for each of the different quadrilaterals A, B, C and D.

Quadrilateral Mathematical name Number of lines of symmetry

A

B

C

D

[8]

(b)

AB

C

14 cm

21 cm10 cm

6 cm

9 cm

120°120°

R

P

Q

NOT TOSCALE

The two triangles are similar.

(i) Write down the angle in triangle PQR that corresponds to angle B in triangle ABC.

Answer(b)(i) Angle [1]

(ii) Work out PQ.

Answer(b)(ii) PQ = cm [2]

8

© UCLES 2012 0580/32/O/N/12

For

Examiner's

Use

5 (a) The colours of the cars at a car centre are red, blue, green, black and white.

The pie chart shows some information about the number of cars of each colour.

Red

Blue

Green

(i) There are 60 red cars.

Show that the total number of cars is 270.

Answer(a)(i)

[2]

(ii) Calculate the number of blue cars and the number of green cars.

Answer(a)(ii) Blue

Green [3]

9


For

Examiner's

Use

(b) There are 39 black cars.

(i) Calculate the sector angle in the pie chart for the black cars.

Answer(b)(i) [2]

(ii) Complete the pie chart.

Label each of your sectors. [2]

(c) The manager asked 100 people which colour of car they prefer.

The results are shown in the table.

Red Blue Green Black White

25 40 6 16 13

(i) On the grid, draw a bar chart to show this information.

Complete the scale on the frequency axis.

Red Blue Green Black White

Frequency

[3]

(ii) The manager uses the results when she orders 900 cars, in these colours, for the next year.

How many blue cars do you expect her to order?

Answer(c)(ii) [2]

10

© UCLES 2012 0580/32/O/N/12

For

Examiner's

Use

6 Johno travelled from his home on the North Island of New Zealand to Blenheim on the South Island.

He left home at 06 30 and drove 50 km to Wellington where he waited for the 08 20 ferry.

(a) Use information from the travel graph opposite to write down

(i) the time Johno arrived at Wellington,

Answer(a)(i) [1]

(ii) the number of hours and minutes that he waited in Wellington for the 08 20 ferry.

Answer(a)(ii) h min [1]

(b) The ferry left Wellington at 08 20 and sailed 92 km to Picton on the South Island.

The ferry arrived at 11 40.

On the travel graph, show the ferry journey. [1]

(c) Johno waited 20 minutes to get off the ferry.

He then drove for 30 minutes at an average speed of 40 km/h to Blenheim.

Complete the travel graph for his journey.

[3]

(d) Calculate his average speed, in km/h, for the whole journey from his home to Blenheim.

Answer(d) km/h [2]

(e) Another ferry left Picton at 10 10 and arrived at Wellington at 13 20.

(i) On the travel graph, show the journey of this ferry. [2]

(ii) How far were the two ferries from Wellington when they passed each other?

Answer(e)(ii) km [1]

11


For

Examiner's

Use

180

170

160

150

140

130

120

110

100

90

80

70

60

50

40

30

20

10

006 00 07 00 08 00 09 00 10 00

Time11 00 12 00 13 00 14 00

Distancefrom home

(km)

Wellington

Home

12

© UCLES 2012 0580/32/O/N/12

For

Examiner's

Use

7 The diagram shows the plan of a field QRST.

The scale is 1 centimetre represents 10 metres.

(a) Nothing is grown within 35 metres of T.

Construct the boundary, inside QRST, of the region where nothing is grown. [2]

T

S

Q R

Scale: 1 cm = 10 m

13


For

Examiner's

Use

(b) Use a straight edge and compasses only for the constructions in parts (b)(i) and (b)(ii).

Leave in all your construction arcs.

(i) Construct the bisector of angle RQT.

Draw your line to meet the side ST. [2]

(ii) Construct the locus of points equidistant from Q and from R.

Draw your line to meet the side ST. [2]

(c) Flowers are grown in the region

• nearer to QR than to QT

and

• nearer to Q than to R.

(i) Label this region F. [1]

(ii) Calculate the actual area in which flowers are grown.

Give your answer in square metres.

Answer(c)(ii) m2 [4]

14

© UCLES 2012 0580/32/O/N/12

For

Examiner's

Use

8

Diagram 1 Diagram 2 Diagram 3 Diagram 4

(a) This pattern of diagrams forms a sequence.

(i) On the grid, draw Diagram 4. [1]

(ii) Complete this table.

Diagram 1 2 3 4 5

Number of dots 7 12

[2]

(b) How many dots will there be in

(i) Diagram n,

Answer(b)(i) [2]

(ii) Diagram 29.

Answer(b)(ii) [1]

15


For

Examiner's

Use

(c) There are either 2 lines or 3 lines meeting at the dots in the Diagrams.

In Diagram 1 there are 0 dots where 3 lines meet.

In Diagram 2 there are 4 dots where 3 lines meet.

Complete the statements.

(i) In Diagram 3 there are dots where 3 lines meet. [1]

(ii) In Diagram n there are dots where 3 lines meet. [2]

(d) Find the number of dots where 2 lines meet in Diagram n.

Answer(d) [1]


16



© UCLES 2012 0580/32/O/N/12

For

Examiner's

Use

9 (a) Each day from Monday to Saturday Caroline buys a newspaper, costing d cents.

On Sunday she buys a newspaper costing 160 cents.

The total amount she spends on newspapers in a week is 430 cents.

(i) Write down an equation in d, to show this information.

Answer(a)(i) [1]

(ii) Solve your equation to find d.

Answer(a)(ii) d = [2]

(iii) The price of the Sunday newspaper is increased by 15%.

Calculate the price of the Sunday newspaper after this increase.

Answer(a)(iii) cents [2]

(b) Potatoes cost p cents per kilogram and carrots cost c cents per kilogram.

(i) Bernard buys 3 kilograms of potatoes and 2 kilograms of carrots.

An expression for the amount he spends is 3p + 2c.

He spends 92 cents on these items.

Write down an equation, in p and c, to show this.

Answer(b)(i) [1]

(ii) Eleanor buys 2 kilograms of potatoes and 5 kilograms of carrots.

She spends 153 cents on these items.

Write down an equation, in p and c, to show this.

Answer(b)(ii) [2]

(iii) Solve your equations to find p and c.

Answer(b)(iii) p =

c = [4]



*6997528550*


MATHEMATICS 0580/33


2 hours

















2

© UCLES 2012 0580/33/O/N/12

For

Examiner's

Use

1 (a) Angelica goes to watch a football match. She entered the stadium at 19 20 and left at 22 05. Work out the number of hours and minutes she was in the stadium. Answer(a) hours minutes [1]

(b) The number of people watching the football match was 25 926. Write 25 926 correct to the nearest thousand. Answer(b) [1]

(c) The football club buys lemonade in 5 litre bottles. Work out the number of 250 millilitre drinks that can be poured from one bottle.

Answer(c) [2]

(d) The table shows the number of goals scored in each match by Mathsletico Rangers.

Number of goals scored Number of matches

0 4

1 11

2 6

3 3

4 2

5 1

6 2

3


For

Examiner's

Use

(i) Draw a bar chart to show this information. Complete the scale on the frequency axis.

0 1 2 3 4 5 6

Frequency

Number of goals scored [3] (ii) Write down the mode. Answer(d)(ii) [1]

(iii) Calculate the mean. Answer(d)(iii) [3]

4

© UCLES 2012 0580/33/O/N/12

For

Examiner's

Use

2 (a) The travel graph shows Helva’s journey from her home to the airport.

08 00 10 00 12 00 14 00 16 00

Distancefrom home

(km)

Time

200

180

160

140

120

100

80

60

40

20

0

airport

home

(i) What happened at 09 30? Answer(a)(i) [1]

(ii) Work out the time taken to travel from home to the airport. Give your answer in hours and minutes Answer(a)(ii) hours minutes [1]

(iii) Calculate Helva’s average speed for the whole journey from home to the airport. Answer(a)(iii) km/h [2]

(iv) Between which two times was Helva travelling fastest? Answer(a)(iv) and [1]

(v) Helva’s husband left their home at 11 00 and travelled directly to the airport. He arrived at 15 30. Complete the travel graph for his journey. [1]

5


For

Examiner's

Use

(b) (i) Helva and her husband are flying from Finland to India. Their plane takes off at 17 00 and arrives in India 7 hours 25 minutes later.

The time in India is 32

1 hours ahead of the time in Finland.

What is the local time in India when the plane arrives? Answer(b)(i) [2]

(ii) The temperature is O3°C in Finland and 23°C in India. Write down the difference between these two temperatures. Answer(b)(ii) °C [1]

(c) Helva exchanged 7584 rupees for euros (€). The exchange rate was 1€ = 56 rupees. How many euros did Helva receive? Give your answer correct to 2 decimal places. Answer(c) € [2]

6

© UCLES 2012 0580/33/O/N/12

For

Examiner's

Use

3 Mrs Ali sold her house for $600 000.

(a) She gives 5

2 of the money to her son.

Work out how much her son receives. Answer(a)$ [1]

(b) Mrs Ali gives $2400 to her grandchildren Elize, Sam and Juan in the ratio Elize : Sam : Juan = 8 : 3 : 5 . Calculate how much they each receive. Answer(b) Elize $

Sam $

Juan $ [3]

(c) Mrs Ali invests $200 000 for 3 years at a rate of 4% per year compound interest. Calculate the total amount of money she will have at the end of the 3 years. Give your answer correct to the nearest dollar. Answer(c) $ [3]

7


For

Examiner's

Use

(d) Mrs Ali spends a total of $9000 on the following items.

Amount spent ($) Angle in pie chart

Holiday 4050 162°

Television 90°

Clothes 1800 72°

Computer

(i) Complete the table. [3] (ii) Complete the pie chart. Label each of your sectors.

Holiday

[2]

8

© UCLES 2012 0580/33/O/N/12

For

Examiner's

Use

4 (a) Solve the following equations.

(i) 6x O 2 = 2x + 8 Answer(a)(i) x = [2]

(ii) 4(2y O 3) = 24 Answer(a)(ii) y = [3]


5x + 9y = O21

12x O 2y = 44 Answer(b) x =

y = [4]

9


For

Examiner's

Use

5

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–6 –5 –4 –3 –2 –1 10 2 3 4 5 6 7 8 9 10

y

x

A

B

(a) What special type of quadrilateral is shape A? Answer(a) [1]

(b) Describe fully the single transformation which maps shape A onto shape B. Answer(b) [3]

(c) On the grid (i) reflect shape A in the y-axis and label the image C, [2]

(ii) translate shape A by

−

−

4

6 and label the image D, [2]

(iii) enlarge shape A by scale factor 2, with centre (0, 0) and label the image E. [2]

10

© UCLES 2012 0580/33/O/N/12

For

Examiner's

Use

6 (a) These are the first four terms of a sequence.

19 15 11 7 (i) Write down the next two terms of this sequence. Answer(a)(i) and [2]

(ii) Write down the rule for finding the next term of this sequence. Answer(a)(ii) [1]

(iii) Find an expression for the nth term of this sequence. Answer(a)(iii) [2]

(b) The nth term of another sequence is 2n + 6 . Write down the first three terms of this sequence. Answer(b) , , [2]

(c) The first three diagrams of a different sequence are shown below.

Diagram 1 Diagram 2 Diagram 3 Complete the table.

Diagram 1 2 3

8

n

Number of lines 6 9 12

[3]

11


For

Examiner's

Use

7

117°

H

FA

D

B

EI

C K G

J

NOT TOSCALE

The points F, G, H and I lie on a circle, centre C. FG is a diameter and DE is a tangent to the circle at I. DE is parallel to AB and angle GKI = 117°. Complete the following statements.

(a) Angle FKI = because

[2]

(b) Angle FHG = because

[2]

(c) Angle EIJ = because

[2]

(d) Angle CIE = because

[2]

12

© UCLES 2012 0580/33/O/N/12

For

Examiner's

Use

8

H

E CF

D

G A B2 m 12 m

8.5 m6 m

42°

NOT TOSCALE

The diagram shows a house, built on level ground. ABCE is a rectangle with AB = 12 m and BC = 8.5 m. CDE is an isosceles triangle. (a) Use trigonometry to calculate DF. Answer(a) DF = m [2]

(b) Calculate the area of triangle CDE. Answer(b) m2 [2]

(c) A ladder, GH, of length 6 m, leans against the house wall. The foot of the ladder is 2 m from this wall. Calculate AH. Answer(c) AH = m [3]

13


For

Examiner's

Use

(d) This diagram shows the plan of the driveway to the house.

3 m

14 m

12 mHOUSE

18 m

NOT TOSCALE

Work out the perimeter of the driveway. Answer(d) m [2]

(e) The driveway is made from concrete. The concrete is 15 cm thick. Calculate the volume of concrete used for the driveway. Give your answer in cubic metres. Answer(e) m3 [4]

14

© UCLES 2012 0580/33/O/N/12

For

Examiner's

Use

9 (a) Complete the table of values for y = x2 + 2x O=4 .

x O4 O3 O2 O1 0 1 2 3

y 4 O4 O4 11

[3]

(b) On the grid, draw the graph of y = x2 + 2x O=4 for O4 Y x Y 3 .

y

x

12

11

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

1 2 3–1–2–3–4 0

[4]

15


For

Examiner's

Use

(c) (i) Draw the line of symmetry on the graph. [1] (ii) Write down the equation of this line of symmetry. Answer(c)(ii) [1]

(d) Use your graph to solve the equation x2 + 2x O=4 = 3 Answer(d) x = or x = [2]


16



© UCLES 2012 0580/33/O/N/12

For

Examiner's

Use

10 (a) The diagram shows the positions of three towns A, B and C. The scale is 1 cm represents 2 km.

NorthNorth

North

AC

B

Scale: 1 cm = 2 km (i) Find the distance in kilometres from A to B. Answer(a)(i) km [2]

(ii) Town D is 9 km from A on a bearing of 135°. Mark the position of town D on the diagram. [2] (iii) Measure the bearing of A from C. Answer(a)(iii) [1]

(b) The population of town C is 324 100. (i) Write this number in standard form. Answer(b)(i) [1]

(ii) The population of town D is 7.64 × 104. Which town, C or D, has the larger population and by how much? Give your answer in standard form. Answer(b)(ii) Town by [3]



*6492030672*


MATHEMATICS 0580/11


1 hour

















2

© UCLES 2011 0580/11/M/J/11

For

Examiner's

Use

1 A concert hall has 1540 seats. Calculate the number of people in the hall when 55% of the seats are occupied. Answer [1]

2 (a) Write down in figures the number twenty thousand three hundred and seventy six. Answer(a) [1]

(b) Write your answer to part (a) correct to the nearest hundred. Answer(b) [1]

3 For an equilateral triangle, write down (a) the number of lines of symmetry, Answer(a) [1]

(b) the order of rotational symmetry. Answer(b) [1]

4

A B

Write down the geometrical name for

(a) shape A, Answer(a) [1]

(b) shape B. Answer(b) [1]

3


For

Examiner's

Use

5 Mark and Naomi share $600 in the ratio Mark : Naomi = 5 : 1. Calculate how much money Naomi receives. Answer $ [2]

6 Calculate the area of a circle with radius 6.28 centimetres. Answer cm2 [2]

7 The scale on a map is 1 : 20 000. Calculate the actual distance between two points which are 2.7 cm apart on the map. Give your answer in kilometres. Answer km [2]

8 (a) Find m when 4m × 42 = 412. Answer(a) m = [1]

(b) Find p when 6

p ÷ 67 = 62. Answer(b) p = [1]

4

© UCLES 2011 0580/11/M/J/11

For

Examiner's

Use

9

A B

C D

2x°

5x° x°

NOT TOSCALE

AB is parallel to CD. Calculate the value of x. Answer x = [3]

10 Solve the simultaneous equations. 3x + y = 30 2x – 3y = 53 Answer x =

y = [3]

11 Without using your calculator, and leaving your answer as a fraction, work out

26

1 –

12

7.

You must show all your working. Answer [3]

5


For

Examiner's

Use

12 (a) Write 1738.279 correct to 1 decimal place. Answer(a) [1]

(b) Write 28 700 in standard form. Answer(b) [1]

(c) The mass of a ten-pin bowling ball is 7 kg to the nearest kilogram. Write down the lower bound of the mass of the ball. Answer(c) kg [1]

13 Paulo invests $3000 at a rate of 4% per year compound interest. Calculate the total amount Paulo has after 2 years. Give your answer correct to the nearest dollar. Answer $ [3]

14 A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reach Paris. (a) Calculate the time the next day when the train arrives in Paris. Answer(a) [1]

(b) The distance from Barcelona to Paris is 827 km. Calculate the average speed of the train in kilometres per hour. Answer(b) km/h [3]

6

© UCLES 2011 0580/11/M/J/11

For

Examiner's

Use

15 (a) The table shows part of a railway timetable.

arrival time 12 58 13 56 14 54 15 52 Peartree Station

departure time 13 07 14 05 15 03 16 01

(i) Each train waits the same number of minutes at Peartree Station. Write down how many minutes each train waits. Answer(a)(i) min [1]

(ii) Janine is at Peartree Station at 3 pm. At what time does the next train depart? Answer(a)(ii) [1]

(b) The average temperature each month in Moscow and Helsinki is recorded. The table shows this information from January to June.

January February March April May June

Temperature in

Moscow (°C) −16 −14 −8 1 8 11

Temperature in

Helsinki (°C) −9 −10 −7 −1 4 10

(i) Find the difference in temperature between Moscow and Helsinki in January. Answer(b)(i) °C [1]

(ii) Find the increase in temperature in Helsinki from March to June. Answer(b)(ii) °C [1]

7


For

Examiner's

Use

16

96°60°

120°

BlueRed

YellowGreen

NOT TOSCALE

In a survey a number of people chose their favourite colour. The results are shown in the pie chart. (a) Calculate the size of the sector angle for green. Answer(a) [1]

(b) The number of people who chose red is 16. Calculate the number who chose yellow. Answer(b) [1]

(c) Calculate the total number of people in the survey. Answer(c) [1]

(d) Write down the fraction who chose red. Answer(d) [1]

8

© UCLES 2011 0580/11/M/J/11

For

Examiner's

Use

17 y

x

4

3

2

1

–1

–2

–3

–3 –2 –1 10 2 3 4 5 6 7

B

A

(a) Write down the vector .

Answer(a)

[1]

(b) =

−

1

3

Mark the point C on the grid. [1] (c) Work out

(i)

−

1

3 +

− 4

7,

Answer(c)(i)

[1]

(ii) 4 ×

−

1

3.

Answer(c)(ii)

[1]

9


For

Examiner's

Use

18 C

A

BO

T24°

NOT TOSCALE

A, B and C are points on a circle, centre O. TA is a tangent to the circle at A and OBT is a straight line.

AC is a diameter and angle OTA = 24°. Calculate (a) angle AOT, Answer(a) Angle AOT = [2]

(b) angle BOC, Answer(b) Angle BOC = [1]

(c) angle OCB. Answer(c) Angle OCB = [1]

10

© UCLES 2011 0580/11/M/J/11

For

Examiner's

Use

19 Piet, Rob and Sam collect model aeroplanes. Piet has x aeroplanes. Rob has 7 more aeroplanes than Piet. Sam has three times as many aeroplanes as Piet. (a) Write down an expression, in terms of x, for (i) the number of aeroplanes Rob has, Answer(a)(i) [1]

(ii) the number of aeroplanes Sam has. Answer(a)(ii) [1]

(b) The total number of aeroplanes is 32. (i) Use the information in part (a) to write down an equation in x. Answer(b)(i) [1]

(ii) Solve your equation. Answer(b)(ii) x = [2]

(c) Write down the number of aeroplanes Rob has. Answer(c) [1]

11

© UCLES 2011 0580/11/M/J/11

BLANK PAGE

12



© UCLES 2011 0580/11/M/J/11

BLANK PAGE



*5523010966*


MATHEMATICS 0580/12


1 hour

















2

© UCLES 2011 0580/12/M/J/11

For

Examiner's

Use

1 One square number between 50 and 100 is also a cube number. Write down this number. Answer [1]

2

52°

x°NOT TOSCALE

A straight line intersects two parallel lines as shown in the diagram. Find the value of x. Answer x = [1]

3 A letter is chosen at random from the following word.

S T A T I S T I C S

Write down the probability that the letter is

(a) A or I ,

Answer(a) [1]

(b) E.

Answer(b) [1]

4 Ingrid throws a javelin a distance of 58.3 metres, correct to 1 decimal place. Complete the statement about the distance, d metres, the javelin is thrown. Answer Y d I [2]

3


For

Examiner's

Use

5 Show that 19

5 ÷ 1

9

7 =

8

7 .

Write down all the steps in your working. Answer

[2]

6 5

3 I p I

3

2

Which of the following could be a value of p?

27

16 0.67 60% (0.8)2

9

4

Answer [2]

7 Calculate 324 × 17. Give your answer in standard form, correct to 3 significant figures. Answer [2]

4

© UCLES 2011 0580/12/M/J/11

For

Examiner's

Use

8 A meal on a boat costs 6 euros (€) or 11.5 Brunei dollars ($). In which currency does the meal cost less, on a day when the exchange rate is €1 = $1.9037? Write down all the steps in your working. Answer [2]

9 Simplify 32x

8 ÷ 8x

32. Answer [2]

10

C

BA 17 cm

9 cmNOT TOSCALE

In the triangle ABC, AB = 17 cm, BC = 9 cm and angle ACB = 90°. Calculate AC. Answer AC = cm [3]

5


For

Examiner's

Use

11 The table shows the opening and closing times of a café.

Mon Tue Wed Thu Fri Sat Sun

Opening time 0600 0600 0600 0600 0600 (a) 0800

Closing time 2200 2200 2200 2200 2200 2200 1300

(a) The café is open for a total of 100 hours each week. Work out the opening time on Saturday. Answer(a) [2]

(b) The owner decides to close the café at a later time on Sunday. This increases the total number

of hours the café is open by 4%. Work out the new closing time on Sunday. Answer(b) [1]

12 =

−1

3 and =

−

4

5

(a) Find . You may use the grid below to help if you wish.

Answer(a) =

[2]

(b) Work out .

Answer(b) =

[1]

6

© UCLES 2011 0580/12/M/J/11

For

Examiner's

Use

13 (a) Rewrite this calculation with all the numbers rounded to 1 significant figure.

4.33.821.9

77.8

×−

Answer(a) [1]

(b) Use your answer to part (a) to work out an estimate for the calculation.

Answer(b) [1]

(c) Use your calculator to find the actual answer to the calculation in part (a). Give your answer correct to 1 decimal place. Answer(c) [2]

14 (a) Complete the list to show all the factors of 18.

1, 2, , , , 18 [2]

(b) Write down the prime factors of 18. Answer(b) [1]

(c) Write down all the multiples of 18 between 50 and 100. Answer(c) [1]

7


For

Examiner's

Use

15 (a) Expand the brackets and simplify.

3(2x O 5y) O 4(x O y) Answer(a) [2]

(b) Factorise completely.

6x2 O 9xy

Answer(b) [2]

16

38°

D

BA C47.1 m

28.5 m

NOT TOSCALE

A flagpole, BD, is attached to level horizontal ground by ropes, AD and CD. AD = 28.5 m, BC = 47.1 m and angle DAB = 38°. Calculate

(a) BD, the height of the flagpole, Answer(a) BD = m [2]

(b) angle BCD.

Answer(b) Angle BCD = [2]

8

© UCLES 2011 0580/12/M/J/11

For

Examiner's

Use

17 (a)

A

C

B

NOT TOSCALE

Points A, B and C lie on the circumference of the circle shown above. When angle BAC is 90° write down a statement about the line BC.

Answer(a) [1] (b)

54°

D

O

B

A

C

NOT TOSCALE

O is the centre of a circle and the line ABC is a tangent to the circle at B. D is a point on the circumference and angle BOD = 54°. Calculate angle DBC. Answer(b) Angle DBC = [3]

9


For

Examiner's

Use

18

A

B

C

(a) On the diagram above, using a straight edge and compasses only, construct (i) the bisector of angle ABC, [2] (ii) the locus of points which are equidistant from A and from B. [2] (b) Shade the region inside the triangle which is nearer to A than to B and nearer to AB than to BC.

[1]

10

© UCLES 2011 0580/12/M/J/11

For

Examiner's

Use

19 (a) The travel graph on the opposite page shows Joel’s journey to his school. He walks to the bus stop and waits for the bus, which takes him to the school.

(i) How long did Joel wait for the bus? Answer(a)(i) min [1]

(ii) Find the distance from the bus stop to the school.


(b) Joel’s sister, Samantha, leaves home 14 minutes later than Joel to cycle to the same school. She cycles at a constant speed and arrives at the school at 08 16. (i) On the grid, show her journey. [1] (ii) At what time did the bus pass Samantha? Answer(b)(ii) [1]

(iii) How far from the school was she when the bus passed her? Answer(b)(iii) km [1]

(iv) How many minutes after Joel did Samantha arrive at the school? Answer(b)(iv) min [1]

11

© UCLES 2011 0580/12/M/J/11

For

Examiner's

Use

10

9

8

7

6

5

4

3

2

1

0Home

School

07 00 07 10 07 20 07 30 07 40

Time

07 50 08 00 08 10 08 20

Distance(km)

12



© UCLES 2011 0580/12/M/J/11

BLANK PAGE



*2493042725*


MATHEMATICS 0580/13


1 hour

















2

© UCLES 2011 0580/13/M/J/11

For

Examiner's

Use

1 (a) Write down ten thousand and seventy three in figures. Answer(a) [1]

(b) Work out 13 + 5 × 4 – 2. Write down all the steps of your working. Answer(b) [1]

2 Write down the next term in each sequence.

(a) 1, 2, 4, 8, 16, [1]

(b) 23, 19, 15, 11, 7, [1]

3 Write down the time and date which is 90 hours after 20 30 on May 31st. Answer Time

Date [2]

4 Factorise completely. 2xy – 4yz Answer [2]

5 Insert I= or K or = in the spaces provided to make correct statements.

(a)

11

3

0.273 [1]

(b) 1.1 111% [1]

6 Make x the subject of the formula. 53+=

xy

Answer x = [2]

3


For

Examiner's

Use

7


(a) the number of lines of symmetry, Answer(a) [1]


Answer(b) [1]

8

4

3

2

1

–1

–2

–5 –4 –3 –2 –1 O 1 2

y

x

P

In the diagram O is the origin and P is the point (–2, 1).


Answer(a) =

[1]

(b) =

− 2

3

Mark the point Q on the diagram. [1]

9 Using integers between 10 and 30, write down (a) an odd multiple of 7, Answer(a) [1]

(b) a cube number. Answer(b) [1]

4

© UCLES 2011 0580/13/M/J/11

For

Examiner's

Use

10

27°AC

B

12 cmNOT TOSCALE

In triangle ABC, AB = 12 cm, angle C = 90° and angle A = 27°. Calculate the length of AC. Answer AC = cm [2]

11

A B

D C

12 cm

9 cm

NOT TOSCALE

In the rectangle ABCD, AB = 9 cm and BD = 12 cm. Calculate the length of the side BC. Answer BC = cm [3]

12 (a) Write 16 460 000 in standard form. Answer(a) [1]

(b) Calculate 7.85 ÷ (2.366 × 102), giving your answer in standard form. Answer(b) [2]

5


For

Examiner's

Use

13 (a) Find the value of x when x

27

24

18=

.

Answer(a) x = [1]

(b) Show that 3

2 ÷ 1

6

1 =

7

4.

Write down all the steps in your working. Answer(b)

[2]

14 (a) A drinking glass contains 55 cl of water. Write 55 cl in litres. Answer(a) litres [1]

(b) The mass of grain in a sack is 35 kg. The grain is divided equally into 140 bags. Calculate the mass of grain in each bag. Give your answer in grams.

Answer(b) g [2]

15 (a) Write 67.499 correct to the nearest integer. Answer(a) [1]

(b) Write 0.003040506 correct to 3 significant figures.

Answer(b) [1]

(c) d = 56.4, correct to 1 decimal place. Write down the lower bound of d. Answer(c) [1]

6

© UCLES 2011 0580/13/M/J/11

For

Examiner's

Use

16 Solve the simultaneous equations. x + 2y = 3 2x – 3y = 13 Answer x =

y = [3]

17 (a)

What type of angle is shown by the arc on the diagram? Answer(a) [1]

(b) ABCD is a quadrilateral.

• AB is parallel to DC.

• BC is longer than AD. (i) Draw a possible quadrilateral ABCD. Answer(b)(i) [1] (ii) Write down the geometrical name for the quadrilateral ABCD. Answer(b)(ii) [1]

7


For

Examiner's

Use

18 Eva invests $120 at a rate of 3% per year compound interest. Calculate the total amount Eva has after 2 years. Give your answer correct to 2 decimal places. Answer $ [3]

19 At a ski resort the temperature, in °C, was measured every 4 hours during one day. The results were –12°, –13°, –10°, 4°, 4°, –6°. (a) Find the difference between the highest and the lowest of these temperatures. Answer(a) °C [1]

(b) Find (i) the mean, Answer(b)(i) °C [2]

(ii) the median, Answer(b)(ii) °C [2]

(iii) the mode. Answer(b)(iii) °C [1]


8



© UCLES 2011 0580/13/M/J/11

For

Examiner's

Use

20

900

800

700

600

500

400

300

200

100

008 00 08 05 08 10 08 15

Time

Distance(metres)

08 20 08 25 08 30Home

Friend’s house

School

The graph shows part of Ali’s journey from home to his school. The school is 900 m from his home. He walks 200 m to his friend’s house and waits there. He then takes 20 minutes to walk with his friend to their school. (a) Complete the travel graph showing Ali’s journey. [1] (b) How long does he wait at his friend’s house? Answer(b) min [1]

(c) Calculate the average speed for Ali’s complete journey from home to his school. Give your answer in kilometres per hour. Answer(c) km/h [4]



*2833932865*


MATHEMATICS 0580/31


2 hours

















2

© UCLES 2011 0580/31/M/J/11

For

Examiner's

Use

1 Mr and Mrs Clark and their three children live in the USA and take a holiday in Europe. (a) Mr Clark changes $500 into euros (€) when the exchange rate is €1 = $1.4593. Calculate how much he receives. Give your answer correct to 2 decimal places. Answer(a) € [2]

(b) Tickets for an amusement park cost €62 for an adult and €52 for a child. Work out the cost for Mr and Mrs Clark and their three children to visit the park. Answer(b) € [3]

(c) Mr Clark sees a notice:

SPECIAL OFFER!

Family ticket €200

Work out €200 as a percentage of your answer to part (b). Answer(c) % [1]

3


For

Examiner's

Use

(d) Mrs Clark buys 6 postcards at €0.98 each. She pays with a €10 note. Calculate how much change she will receive. Answer(d) € [2]

(e) Children under a height of 130 cm are not allowed on one of the rides in the park. Helen Clark is 50 inches tall. Use 1 inch = 2.54 cm to show that she will not be allowed on this ride. Answer(e)

[1]

4

© UCLES 2011 0580/31/M/J/11

For

Examiner's

Use

2

The shape above is the net of a solid drawn on a 1 cm square grid. (a) Write down the geometrical name of the solid. Answer(a) [1]

(b) Find the perimeter of the net. Answer(b) cm [1]

5


For

Examiner's

Use

(c) Work out (i) the area of one of the triangles, Answer(c)(i) cm2 [2]

(ii) the volume of the solid. Answer(c)(ii) cm3 [2]

(d) A cuboid of length 4 cm and width 3 cm has the same volume as the solid. Calculate the height of the cuboid. Answer(d) cm [2]

6

© UCLES 2011 0580/31/M/J/11

For

Examiner's

Use

3 (a) x = 3m – k Find the value of

(i) x when m = 2 and k = −4, Answer(a)(i) [2]

(ii) m when x = 19 and k = 5. Answer(a)(ii) [3]

(b) Expand the brackets. g(7f – g2) Answer(b) [2]

(c) Factorise completely. 18h2 – 12hj Answer(c) [2]

(d) Make m the subject of the formula. t = 8m + 15 Answer(d) m = [2]

(e) Solve the equation. p + 3 = 3(p – 5) Answer(e) p = [3]

7


For

Examiner's

Use

4

5

4

3

2

1

00 20 40 60

Time (minutes)

Distance(kilometres)

80 100 120 140Home

Bus stop

Library

Sonia travels from home to the library. She walks to the bus stop and waits for a bus to take her to the library. (a) Write down

(i) the distance to the bus stop, Answer(a)(i) km [1]

(ii) how many minutes Sonia waits for a bus, Answer(a)(ii) min [1]

(iii) how many minutes the bus journey takes to the library. Answer(a)(iii) min [1]

(b) Calculate, in kilometres per hour, (i) Sonia’s walking speed, Answer(b)(i) km/h [1]

(ii) the speed of the bus, Answer(b)(ii) km/h [2]

(iii) the average speed for Sonia’s journey from home to the library. Answer(b)(iii) km/h [3]

(c) Sonia works in the library for one hour. Then she travels home by car. The average speed of the car is 30 km/h. Complete the travel graph. [2]

8

© UCLES 2011 0580/31/M/J/11

For

Examiner's

Use

5 y

x

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–3 –2 –1 0 1 2 3 4

A

B

(a) (i) Find the gradient of the line AB. Answer(a)(i) [2]

(ii) Write down the equation of the line AB in the form y = mx + c. Answer(a)(ii) y = [2]

9


For

Examiner's

Use

(b) The table shows some values of the function y = x2 O 2.

x −3 −2 −1 0 1 2 3

y 7 −1 −1 7


(ii) On the grid, draw the graph of y = x2 O 2 for −3 Y x Y 3. [4]

(iii) Use your graph to solve the equation x2 O 2 = 0. Answer(b)(iii) x = or x = [2]

(c) Write down the co-ordinates of the points where your graph meets the line AB. Answer(c)( , ) and ( , ) [2]

10

© UCLES 2011 0580/31/M/J/11

For

Examiner's

Use

6 (a) 103 112 125 132 144 159 161 From the list above, write down (i) a square number, Answer(a)(i) [1]

(ii) a cube number, Answer(a)(ii) [1]

(iii) a prime number, Answer(a)(iii) [1]

(iv) an odd number which is a multiple of 3. Answer(a)(iv) [1]

(b) Write 88 as a product of prime numbers. Answer(b) [2]

(c) Find the highest common factor of 72 and 96. Answer(c) [2]

(d) Find the lowest common multiple of 15 and 20. Answer(d) [2]

11


For

Examiner's

Use

7 (a) B

A

P T

(i) Reflect triangle T in the line AB. Label your image X. [1]

(ii) Rotate triangle T through 90° clockwise about the point P. Label your image Y. [2]

(b)

Describe the single transformation which maps

(i) flag P onto flag Q, Answer(b)(i) [3]

(ii) flag P onto flag R. Answer(b)(ii) [2]

8

7

6

5

4

3

2

1

–1

–1 10 2 3 4 5 6 7 8 9 10 11 12

y

x

P

Q

R

12

© UCLES 2011 0580/31/M/J/11

For

Examiner's

Use

8 30 students took a vocabulary test. The marks they scored are shown below.

7 8 5 8 3 2

6 6 3 3 6 2

7 1 5 10 2 6

6 5 8 1 2 7

3 1 5 3 10 3 (a) Complete the frequency table below. The first five frequencies have been completed for you. You may use the tally column to help you.

Mark Tally Frequency

1 3

2 4

3 6

4 0

5 4

6

7

8

9

10

[3]

13


For

Examiner's

Use

(b) (i) Find the range. Answer(b)(i) [1]

(ii) Write down the mode. Answer(b)(ii) [1]

(iii) Find the median. Answer(b)(iii) [2]

(iv) Calculate the mean. Answer(b)(iv) [3]

(c) A student is chosen at random. Find the probability that the student scored (i) 1 mark, Answer(c)(i) [1]

(ii) 4 marks, Answer(c)(ii) [1]

(iii) fewer than 6 marks. Answer(c)(iii) [1]

14

© UCLES 2011 0580/31/M/J/11

For

Examiner's

Use

9 (a) In the space below, construct the triangle ABC with AB = 10 cm and AC = 12 cm. Leave in your construction arcs. The line BC is already drawn.

B C [2]

15


For

Examiner's

Use

(b) Measure angle ABC. Answer(b) Angle ABC = [1]

(c) (i) Using a straight edge and compasses only, and leaving in your construction arcs,

construct the perpendicular bisector of BC. [2] (ii) This bisector cuts AC at P. Mark the position of P on the diagram and measure AP. Answer(c)(ii) AP = cm [1]

(d) Construct the locus of all the points inside the triangle which are 5 cm from A. [1] (e) Shade the region inside the triangle which is


• less than 5 cm from A. [2]


16



© UCLES 2011 0580/31/M/J/11

For

Examiner's

Use

10 (a)

B is 120 m from A on a bearing of 053°. Calculate (i) the distance d, Answer(a)(i) d = m [2]

(ii) the bearing of A from B. Answer(a)(ii) [1]

(b)

20 m 9 m

24 mG HA

F

NOT TOSCALE

A vertical flagpole, AF, is 9 m high. It is held in place by two straight wires FG and FH. FG = 20 m and AH = 24 m. G, A and H lie in a straight line on horizontal ground. Calculate (i) angle FHA, Answer(b)(i) Angle FHA = [2]

(ii) the distance GA.

Answer(b)(ii) GA = m [3]

53°

A

B

120 m

NorthNorth

d

NOT TOSCALE



*5006791848*


MATHEMATICS 0580/32


2 hours

















2

© UCLES 2011 0580/32/M/J/11

For

Examiner's

Use

1 Falla buys 3000 square metres of land for a house and garden. The garden is divided into areas for flowers, vegetables and grass. He divides the land in the following ratio. house : flowers : vegetables : grass = 4 : 7 : 8 : 5 (a) (i) Show that the area of land used for flowers is 875 m2. Answer(a)(i)

[2] (ii) Calculate the area of land used for the house. Answer(a)(ii) m2 [2]

(b) Write down the fraction of land used for vegetables. Give your answer in its simplest form. Answer(b) [2]

3


For

Examiner's

Use

(c) During the first year Falla plants flowers in 64% of the 875 m2. Calculate the area he plants with flowers. Answer(c) m2 [2]

(d) Falla sells some of the vegetables he grows. These vegetables cost $85 to grow. He sells them for $105. Calculate his percentage profit. Answer(d) % [3]

(e) To buy the land Falla borrowed $5000 at a rate of 6.4% compound interest for 2 years. Calculate the total amount he pays back at the end of the 2 years. Give your answer correct to the nearest dollar. Answer(e) $ [3]

4

© UCLES 2011 0580/32/M/J/11

For

Examiner's

Use

2

A

B

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–5–6 –4 –3 –2 –1 10 2 3 4 5 6

y

x

The diagram shows two triangles drawn on a 1 cm square grid.

(a) (i) Describe fully the single transformation which maps triangle A onto triangle B.

Answer(a)(i) [3] (ii) Calculate the area of triangle A. Answer(a)(ii) cm2 [2]

(iii) Find the perimeter of triangle A.

Answer(a)(iii) cm [1]

(b) Reflect triangle A in the x-axis. Label the image P. [1] (c) Rotate triangle A through 90° clockwise about (0, 0). Label the image Q. [2]

(d) Describe fully the single transformation which maps triangle P onto triangle Q.

Answer(d) [2]

5


For

Examiner's

Use

3 The colours of 30 cars in a car park are shown in the frequency table.

Colour Frequency

Red 5

Silver 15

Black 6

White 4

(a) Complete the bar chart to represent this information.

Frequency

Colour

Red Silver Black White

[3] (b) Write down the mode. Answer(b) [1]

6

© UCLES 2011 0580/32/M/J/11

For

Examiner's

Use

4 (a) An electrician is paid a fixed amount of $12 and then $6.50 for each hour she works. (i) The electrician works for 7 hours. Calculate how much she is paid for this work. Answer(a)(i) $ [2]

(ii) The electrician works for n hours. Write down an expression, in terms of n, for how much she is paid. Answer(a)(ii) [1]

(iii) The electrician is paid $44.50 for her work. Calculate the number of hours she worked. Answer(a)(iii) [2]


3x O y = 22 5x + 3y = 4 Answer(b) x =

y = [3]

7


For

Examiner's

Use

5 (a) The table below shows how many sides different polygons have. Complete the table.

Name of polygon Number of sides

3

Quadrilateral 4

5

Hexagon 6

Heptagon 7

8

Nonagon 9

[3] (b) Two sides, AB and BC, of a regular nonagon are shown in the diagram below.

x°A B

C

NOT TOSCALE

(i) Work out the value of x, the exterior angle. Answer(b)(i) x = [2]

(ii) Find the value of angle ABC, the interior angle of a regular nonagon. Answer(b)(ii) Angle ABC = [1]

8

© UCLES 2011 0580/32/M/J/11

For

Examiner's

Use

6 The number of ice-creams sold in a shop each month is shown in the table.


Number of ice-creams sold

1300 1200 1700 1800 2300 2500 2800 2600 1500 1600 1100 1900

(a) (i) Find the range. Answer(a)(i) [1]

(ii) Calculate the mean. Answer(a)(ii) [2]

(iii) Find the median. Answer(a)(iii) [2]

(b) The numbers of chocolate, strawberry and vanilla ice-creams sold are shown in the table.

Flavour Number of ice-creams Pie chart sector angle

Chocolate 4200 140°

Strawberry 3600

Vanilla 3000

(i) Complete the table by working out the sector angles for strawberry and vanilla. [3] (ii) Complete the pie chart below and label the sectors.

[2]

9


For

Examiner's

Use

(c) The table shows the average temperature and the number of ice-creams sold each month.


Temperature (°C)

5.6 5.7 7.0 11.4 16.0 23.3 23.4 20.0 15.5 11.5 8.0 14.0

Number of ice-creams sold

1300 1200 1700 1800 2300 2500 2800 2600 1500 1600 1100 1900

(i) Complete the scatter diagram for the months August to December. The points for January to July are plotted for you.

3000

2500

2000

1500

10005 10 15

Average temperature (°C)20 25

Number ofice-creams sold

[2] (ii) What type of correlation does the scatter diagram show? Answer(c)(ii) [1]

(iii) Write down a statement connecting the number of ice-creams sold to the average monthly

temperature.

Answer(c)(iii) [1]

10

© UCLES 2011 0580/32/M/J/11

For

Examiner's

Use

7 (a) The table shows some values of the function y = x2 + x O 3.

x O4 O3 O2 O1

0 1 2 3

y 9 3 O3 O1 9


(ii) On the grid, draw the graph of y = x2 + x O 3 for O4 Y x Y 3.

y

x

10

8

6

4

2

–2

–4

0–1 1 2 3–2–3–4

A

B

[4]

(iii) Use your graph to solve the equation x2 + x O 3 = 0. Answer(a)(iii) x = or x = [2]

11


For

Examiner's

Use

(b) (i) Draw the line of symmetry of the graph. [1] (ii) Write down the equation of the line of symmetry. Answer(b)(ii) [1]

(c) Two points, A and B, are marked on the grid. (i) Draw the straight line through the points A and B extending it to the edges of the grid. [1]

(ii) Write down the co-ordinates of the points of intersection of this line with y = x2 + x O 3. Answer(c)(ii) ( , ) and ( , ) [2]

(iii) Work out the gradient of the straight line through points A and B. Answer(c)(iii) [2]

(iv) Write down the equation of the straight line through points A and B, in the form y = mx + c. Answer(c)(iv) y = [2]

12

© UCLES 2011 0580/32/M/J/11

For

Examiner's

Use

8 Manuel rows his boat from A to B, a distance of 3 kilometres. The scale diagram below shows his journey. 1 centimetre represents 0.5 kilometres.

North

North

A

B

3 km

(a) (i) Measure the bearing of B from A. Answer(a)(i) [1]

(ii) The journey from A to B takes him 30 minutes. Calculate his average speed in kilometres per hour. Answer(a)(ii) km/h [1]

(b) From B, Manuel rows 3.5 kilometres in a straight line, on a bearing of 145°, to a point C. On the diagram, draw accurately this journey and label the point C. [2]

13


For

Examiner's

Use

(c) Manuel then rows from C to A.

(i) Measure CA. Answer(c)(i) cm [1]

(ii) Work out the actual distance from C to A.

Answer(c)(ii) km [1]

(iii) By measuring a suitable angle, find the bearing of A from C. Answer(c)(iii) [1]

(d) Two buoys, P and Q, are on opposite sides of the line AB. Each buoy is 2 km from A and 1.5 km from B. (i) On the diagram, construct and mark the positions of P and Q. [2] (ii) Measure the distance between P and Q. Answer(d)(ii) cm [1]

(iii) Find the actual distance, PQ, in kilometres. Answer(d)(iii) km [1]

14

© UCLES 2011 0580/32/M/J/11

For

Examiner's

Use

9 60 cm

18 cm

18 cm

NOT TOSCALE

The diagram shows the net of a box. (a) (i) Calculate the total surface area of the box. Answer(a)(i) cm2 [2]

(ii) Calculate the volume of the box. Answer(a)(ii) cm3 [2]

15


For

Examiner's

Use

(b) A cylinder with diameter 18 cm and length 60 cm just fits inside the box.

18 cm

60 cm

NOT TOSCALE

(i) Calculate the volume of the cylinder. Answer(b)(i) cm3 [2]

(ii) Find the volume of space outside the cylinder but inside the box. Answer(b)(ii) cm3 [1]

(iii) Calculate the curved surface area of the cylinder.

Answer(b)(iii) cm2 [2]

Question 10 is printed on the following page.

16



© UCLES 2011 0580/32/M/J/11

For

Examiner's

Use

10 (a) Write down the next two terms in each of the following sequences.

(i) 71, 64, 57, 50, , [1]

(ii) O17, O13, O9, O5, , [2]

(b) The nth term of the sequence in part (a)(i) is 78 O 7n. Find the value of the 15th term. Answer(b) [1]

(c) Write down an expression for the nth term of the sequence in part (a)(ii). Answer(c) [2]

(d) For one value of n, both sequences in part (a) have a term with the same value. Use parts (b) and (c) to find (i) the value of n, Answer(d)(i) n = [2]

(ii) the value of this term. Answer(d)(ii) [2]



*5608091386*


MATHEMATICS 0580/33


2 hours

















2

© UCLES 2011 0580/33/M/J/11

For

Examiner's

Use

1 At a theatre, adult tickets cost $5 each and child tickets cost $3 each. (a) Find the total cost of 110 adult tickets and 85 child tickets. Answer(a) $ [2]

(b) The total cost of some tickets is $750. There are 120 adult tickets. Work out the number of child tickets. Answer(b) [2]

(c) The ratio of the number of adults to the number of children during one performance is adults : children = 3 : 2. (i) The total number of adults and children in the theatre is 150. Find the number of adults in the theatre. Answer(c)(i) [2]

(ii) For this performance, find the ratio total cost of adult tickets : total cost of child tickets. Give your answer in its simplest form. Answer(c)(ii) : [3]

(d) The $5 cost of an adult ticket is increased by 30%. Calculate the new cost of an adult ticket. Answer(d) $ [2]

(e) The cost of a child ticket is reduced from $3 to $2.70. Calculate the percentage decrease in the cost of a child ticket. Answer(e) % [3]

3


For

Examiner's

Use

2

P Q (a) In the space above, construct triangle PQR with QR = 9 cm and PR = 7 cm. Leave in your construction arcs. The line PQ is already drawn. [2] (b) Using a straight edge and compasses only, construct (i) the perpendicular bisector of PR, [2] (ii) the bisector of angle QPR. [2] (c) Shade the region inside the triangle PQR which is nearer to P than to R and nearer to PQ than to PR. [1] (d) Triangle PQR is a scale drawing with a scale 1 : 50 000. Find the actual distance QR. Give your answer in kilometres. Answer(d) km [2]

4

© UCLES 2011 0580/33/M/J/11

For

Examiner's

Use

3 288 students took part in a quiz. There were three questions in the quiz. Each correct answer scored 1 point. The pie chart shows the results.

1 point

0 points

3 points

2 points120°

100°t °

(a) Find the value of t. Answer(a) t = [1]

(b) Find the number of students who scored 2 points. Answer(b) [2]

(c) Find the modal number of points. Answer(c) [1]

5


For

Examiner's

Use

(d) (i) Use the information in the pie chart to complete the frequency table for the 288 students.

Number of points 0 1 2 3

Number of students

[2] (ii) Calculate the mean number of points. Answer(d)(ii) [3]

(e) One student is chosen at random. Find the probability that this student scored (i) 3 points, Answer(e)(i) [1]

(ii) at least 1 point, Answer(e)(ii) [2]

(iii) more than 3 points. Answer(e)(iii) [1]

(f) 1440 students took part in the same quiz. How many students would be expected to score 3 points? Answer(f) [1]

6

© UCLES 2011 0580/33/M/J/11

For

Examiner's

Use

4

0.8 m

1.4 m

NOT TOSCALE

The diagram shows part of a trench. The trench is made by removing soil from the ground. The cross-section of the trench is a rectangle. The depth of the trench is 0.8 m and the width is 1.4 m. (a) Calculate the area of the cross-section. Answer(a) m2 [2]

(b) The length of the trench is 200 m. Calculate the volume of soil removed. Answer(b) m3 [1]

7


For

Examiner's

Use

(c)

0.25 m

NOT TOSCALE

A pipe is put in the trench. The pipe is a cylinder of radius 0.25 m and length 200 m. (i) Calculate the volume of the pipe. [The volume, V, of a cylinder of radius r and length l is V = πr2l.] Answer(c)(i) m3 [2]

(ii) The trench is then filled with soil. Find the volume of soil put back into the trench. Answer(c)(ii) m3 [1]

(iii) The soil which is not used for the trench is spread evenly over a horizontal area of

8000 m2. Calculate the depth of this soil. Give your answer in millimetres, correct to 1 decimal place. Answer(c)(iii) mm [3]

8

© UCLES 2011 0580/33/M/J/11

For

Examiner's

Use

5 (a) (i) Complete the table for the function y = x

6, x ≠ 0.

x –6 –5 –4 –3 –2 –1 1 2 3 4 5 6

y –1 –1.2 –2 –3 –6 6 3 1.2 1

[2]

(ii) On the grid, draw the graph of y = x

6 for O6 Y x Y O1 and 1 Y x Y 6.

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–6 –5 –4 –3 –2 –1 10 2 3 4 5 6

[4]

9


For

Examiner's

Use

(b) (i) Complete the table for the function y = 2

2x

O2.

x –4 –3 –2 –1 0 1 2 3 4

y 6 2.5 –2 2.5 6

[2]

(ii) On the grid opposite, draw the graph of y = 2

2x

O2 for O4 Y x Y 4. [4]

(c) Write down the co-ordinates of the point of intersection of the two graphs. Answer(c)( , ) [2]

10

© UCLES 2011 0580/33/M/J/11

For

Examiner's

Use

6 (a)

p°B

C

DA140°

NOT TOSCALE

The diagram shows a triangle ABC with BA extended to D. AB = AC and angle CAD = 140°. Find the value of p. Answer(a) p = [2]

(b)

NOT TOSCALE

72°

q°

Find the value of q. Answer(b) q = [2]

(c)

NOT TOSCALE

108° 104°

94°

x°

Find the value of x. Answer(c) x = [1]

11


For

Examiner's

Use

(d)

A

C

B22°

NOT TOSCALE

In triangle ABC, angle A = 90° and angle B = 22°. Calculate angle C. Answer(d) Angle C = [1]

(e)

10 cm

8 cm

10 cm

X

P

Y Z

Q

NOT TOSCALE

In triangle XYZ, P is a point on XY and Q is a point on XZ. PQ is parallel to YZ. (i) Complete the statement.

Triangle XPQ is to triangle XYZ. [1]

(ii) PQ = 8 cm, XQ = 10 cm and YZ = 10 cm. Calculate the length of XZ. Answer(e)(ii) XZ = cm [2]

12

© UCLES 2011 0580/33/M/J/11

For

Examiner's

Use

7 (a) Solve the equations.

(i) 2x + 3 = 15 O x Answer(a)(i) x = [2]

(ii) 73

12=

−y

Answer(a)(ii) y = [2]

(iii) 2 = 1

1

−u

Answer(a)(iii) u = [3]

13


For

Examiner's

Use

(b) Write down equations to show the following. (i) p is equal to r plus two times q. Answer(b)(i) [1]

(ii) k is equal to the square of the sum of l and m. Answer(b)(ii) [2]

(c) Pierre walks for 2 hours at w km/h and then for another 3 hours at (w –1) km/h. The total distance of Pierre’s journey is 11.5 km. Find the value of w. Answer(c) w = [4]

14

© UCLES 2011 0580/33/M/J/11

For

Examiner's

Use

8 y

x

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9

C

B A

(a) On the grid, draw the images of the following transformations of shape A. (i) Reflection in the x-axis [1]

(ii) Translation by the vector

4

3 [2]

(iii) Rotation, centre (0, 0), through 180° [2] (b) Describe fully the single transformation that maps (i) shape A onto shape B, Answer(b)(i) [2]

(ii) shape A onto shape C. Answer(b)(ii) [3]

15

© UCLES 2011 0580/33/M/J/11

For

Examiner's

Use

9

Diagram 3Diagram 2Diagram 1 Diagram 4 Diagram 5 The Diagrams above form a pattern. (a) Draw Diagram 5 in the space provided. [1] (b) The table shows the numbers of dots in some of the diagrams. Complete the table.

Diagram 1 2 3 4 5 10 n

Number of dots 3 5

[5] (c) What is the value of n when the number of dots is 737? Answer(c) [2]

(d) Complete the table which shows the total number of dots in consecutive pairs of diagrams. For example, the total number of dots in Diagram 2 and Diagram 3 is 12.

Diagrams 1 and 2 2 and 3 3 and 4 4 and 5 10 and 11 n and n + 1

Total number of

dots 8 12 16

[3]

16



© UCLES 2011 0580/33/M/J/11

BLANK PAGE



*7634568734*


MATHEMATICS 0580/11


1 hour

















2

© UCLES 2011 0580/11/O/N/11

For

Examiner's

Use

1

A

S

The diagram shows the map of part of an orienteering course. Sanji runs from the start, S, to the point A.


Answer

[1]

2 When Ali takes a penalty, the probability that he will score a goal is 5

4.

Ali takes 30 penalties. Find how many times he is expected to score a goal. Answer [2]

3 The ratio of Anne’s height : Ben’s height is 7 : 9. Anne’s height is 1.4 m. Find Ben’s height. Answer m [2]

3


For

Examiner's

Use

4 The distance between the centres of two villages is 8 km. A map on which they are shown has a scale of 1 : 50 000. Calculate the distance between the centres of the two villages on the map. Give your answer in centimetres. Answer cm [2]

5

10

8

6

4

2

0Black Silver Red

Favourite colour

Green Blue

Frequency

The bar chart shows the favourite colours of students in a class. (a) How many students are in the class? Answer(a) [1]

(b) Write down the modal colour.

Answer(b) [1]

4

© UCLES 2011 0580/11/O/N/11

For

Examiner's

Use

6 Use your calculator to find 1.53.1

5.7545

+

×.

Answer [2]

7 (a) Calculate 60% of 200. Answer(a) [1]

(b) Write 0.36 as a fraction. Give your answer in its lowest terms. Answer(b) [2]

8 A circle has a radius of 50 cm. (a) Calculate the area of the circle in cm2. Answer(a) cm2 [2]

(b) Write your answer to part (a) in m2. Answer(b) m2 [1]

5


For

Examiner's

Use

9

30

25

20

15

10

5

06 am 9 am Noon

Time

3 pm 6 pm

Temperature(°C)

The graph shows the temperature in Paris from 6 am to 6 pm one day. (a) What was the temperature at 9 am? Answer(a) °C [1]

(b) Between which two times was the temperature decreasing? Answer(b) and [1]

(c) Work out the difference between the maximum and minimum temperatures shown. Answer(c) °C [1]

10 (a) Write down the mathematical name of a quadrilateral that has exactly two lines of symmetry. Answer(a) [1]

(b) Write down the mathematical name of a triangle with exactly one line of symmetry. Answer(b) [1]

(c) Write down the order of rotational symmetry of a regular pentagon. Answer(c) [1]

6

© UCLES 2011 0580/11/O/N/11

For

Examiner's

Use


+

4

1

3

2

2

1.

Show all your working clearly and give your answer as a fraction. Answer [3]

12

y

x10– 1– 2– 3– 4 2

9

8

7

6

5

4

3

2

1

The diagram shows the graph of y = (x + 1)2 for −4 Y x Y 2. (a) On the same grid, draw the line y = 3. [1] (b) Use your graph to find the solutions of (x + 1)2 = 3. Give each solution correct to 1 decimal place. Answer(b) x = or x = [2]

7


For

Examiner's

Use

13

NOT TOSCALE

The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size. Calculate the size of one of these angles. Answer [3]

14 (a) Expand and simplify. 2(3x – 2) + 3(x – 2) Answer(a) [2]

(b) Expand. x(2x2 – 3) Answer(b) [2]

8

© UCLES 2011 0580/11/O/N/11

For

Examiner's

Use

15

50

40

30

20

10

0 10 20 30 40Mathematics test mark

Engl

ish

test

mar

k

50 60 70 80

The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an

English test by 15 students. (a) Describe the correlation. Answer(a) [1]

(b) The mean for the Mathematics test is 47.3 . The mean for the English test is 30.3 . Plot the mean point (47.3, 30.3) on the scatter diagram above. [1] (c) (i) Draw the line of best fit on the diagram above. [1] (ii) One student missed the English test. She received 45 marks in the Mathematics test. Use your line to estimate the mark she might have gained in the English test. Answer(c)(ii) [1]

9


For

Examiner's

Use

16 (a)

A B

C

D E

110°NOT TOSCALE

In the diagram, AB is parallel to DE. Angle ABC = 110°. Find angle BDE. Answer(a) Angle BDE = [2]

(b)

t °

y°

z°50°

OB

A T

NOT TOSCALE

TA is a tangent at A to the circle, centre O. Angle OAB = 50°. Find the value of (i) y, Answer(b)(i) y = [1]

(ii) z, Answer(b)(ii) z = [1]

(iii) t. Answer(b)(iii) t = [1]

10

© UCLES 2011 0580/11/O/N/11

For

Examiner's

Use

17

y°

8 m

3 m

NOT TOSCALE

The diagram shows a ladder, of length 8 m, leaning against a vertical wall. The bottom of the ladder stands on horizontal ground, 3 m from the wall. (a) Find the height of the top of the ladder above the ground. Answer(a) m [3]

(b) Use trigonometry to calculate the value of y. Answer(b) y = [2]

11

© UCLES 2011 0580/11/O/N/11

For

Examiner's

Use

18 (a) Lucinda invests $500 at a rate of 5% per year simple interest. Calculate the interest Lucinda has after 3 years. Answer(a) $ [2]

(b) Andy invests $500 at a rate of 5% per year compound interest. Calculate how much more interest Andy has than Lucinda after 3 years. Answer(b) $ [4]

12



© UCLES 2011 0580/11/O/N/11

BLANK PAGE



*5352163886*


MATHEMATICS 0580/12


1 hour

















2

© UCLES 2011 0580/12/O/N/11

For

Examiner's

Use

1 The temperature on Monday is 3 °C. On Tuesday it is 5 °C lower. Find the temperature on Tuesday. Answer °C [1]

2 Joseph changed 120 New Zealand dollars (NZ$) into Australian dollars (A$) when the exchange rate

was NZ$1 = A$0.796 . Calculate the exact amount he received. Answer A$ [1]

3 A bus leaves a port every 15 minutes, starting at 09 00. The last bus leaves at 17 30. How many times does a bus leave the port during one day? Answer [2]


8

9 1.2 115% 1

6

1

Answer I I I [2]

3


For

Examiner's

Use

5 Mortar is a mixture of cement, sand and lime in the ratio cement : sand : lime = 1 : 5 : 2. Calculate how much sand there is in a 12 kg bag of this mortar. Answer kg [2]

6 Find the cube root of 96. Give your answer correct to 2 decimal places. Answer [2]

7 Write these numbers in standard form. (a) 734 000 000 Answer(a) [1]

(b) 0.000587 Answer(b) [1]

4

© UCLES 2011 0580/12/O/N/11

For

Examiner's

Use

8 The population, P, of Brunei in 2008 was 400 000 correct to the nearest 1000. Complete the statement about the value of P. Answer Y P I [2]

9 Use your calculator to find the value of (a) 30 × 2.52, Answer(a) [1]

(b) 2.5

– 2. Answer(b) [1]

5


For

Examiner's

Use

10

A

C

D

B E115°

20°

y°x°

NOT TOSCALE

In the diagram, AB is parallel to CDE. Find the value of (a) x, Answer(a) x = [1]


11

75° x°

2x°2x°

NOT TOSCALE

(a) For the diagram above, write down an equation in x. Answer(a) [1]

(b) Solve your equation. Answer(b) x = [2]

6

© UCLES 2011 0580/12/O/N/11

For

Examiner's

Use

12 Jiwan incorrectly wrote 1 + 2

1 +

3

1 +

4

1 = 1

9

3.

Show the correct working and write down the answer as a mixed number. Answer [3]

13 Solve these simultaneous equations. 5x – 2y = 17 2x + y = 5 Answer x =

y = [3]

7


For

Examiner's

Use

14 A bag contains only red, yellow and blue counters. Bashira picks a counter at random from the bag, records its colour, and puts it back in the bag. She does this 60 times. (a) Complete the table for her results.

Colour Frequency Relative frequency

Red 19

Yellow

Blue 28

[2] (b) Gita picks a counter at random from the same bag. Which colour counter is she most likely to pick? Answer(b) [1]

15 A cruise ship travels at 22 knots. [1 knot is 1.852 kilometres per hour.] Convert this speed into metres per second. Answer m/s [3]

8

© UCLES 2011 0580/12/O/N/11

For

Examiner's

Use

16 (a) Write down a common multiple of 8 and 14. Answer(a) [1]

(b) (i) Complete the list of factors of 81. 1, , , , 81 [2]

(ii) Write down the prime factor of 81. Answer(b)(ii) [1]

9


For

Examiner's

Use

17 y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

0–1–2–3–4–5–6 5 64321

B

A

The diagram shows two straight lines, A and B, drawn on a grid. (a) Write down the equation of line A. Answer(a) [1]

(b) The equation of line B is y = 3x – 1 . (i) Draw a line parallel to line B that passes through the point (0, 2). [1] (ii) Write down the equation of your line in the form y = mx + c. Answer(b)(ii) y = [2]

10

© UCLES 2011 0580/12/O/N/11

For

Examiner's

Use

18 O

A B75°

NOT TOSCALE

(a) Triangle AOB is isosceles. OA = OB. Calculate angle AOB. Answer(a) Angle AOB = [1]

(b)

O

A B

NOT TOSCALE

75°

AB is one side of a regular polygon with n sides. (i) Calculate n. Answer(b)(i) n = [2]

(ii) Find the size of an interior angle of this polygon. Answer(b)(ii) [1]

11


For

Examiner's

Use

19 (a)

8

7

6

5

4

3

2

1

1 2 3 4 5 6 7 80

A

B C

y

x

Three vertices of the quadrilateral ABCD are shown in the diagram. (i) Write down the co-ordinates of the point B. Answer(a)(i) ( , ) [1]

(ii) On the grid, plot and label the point D so that quadrilateral ABCD has rotational symmetry

of order 2. [1] (iii) Draw the quadrilateral ABCD. Draw in all the lines of symmetry on your quadrilateral. [1] (b) Write down the mathematical names of these quadrilaterals.

P Q

Answer(b) P Q [2]


12



© UCLES 2011 0580/12/O/N/11

For

Examiner's

Use

20 In a survey of 60 cars, the type of fuel that they use is recorded in the table below. Each car only uses one type of fuel.

Petrol Diesel Liquid Hydrogen Electricity

40 12 2 6

(a) Write down the mode. Answer(a) [1]

(b) Olav drew a pie chart to illustrate these figures. Calculate the angle of the sector for Diesel. Answer(b) [2]

(c) Calculate the probability that a car chosen at random uses Electricity. Write your answer as a fraction in its simplest form. Answer(c) [2]



*7602060251*


MATHEMATICS 0580/13


1 hour

















2

© UCLES 2011 0580/13/O/N/11

For

Examiner's

Use

1 During April the probability that it will rain on any one day is 6

5.

On how many of the 30 days in April would it be expected to rain? Answer [1]

2 (a) Write, in figures, the number one hundred and five thousand and two. Answer(a) [1]

(b) Write your answer to part (a) correct to the nearest ten thousand. Answer(b) [1]

3 Simplify the expression. 7x + 11y + x – 6y Answer [2]

4 Insert one pair of brackets into each calculation to make the answer correct. (a) 7 × 6 – 3 + 5 = 26 [1] (b) 8 – 6 × 4 – 1 = –10 [1]

3


For

Examiner's

Use


0.525 21

11

211

111 52.4%

Answer I I I [2]

6 Thomas fills glasses from a jug containing 2.4 litres of water. Each glass holds 30 centilitres. How many glasses can Thomas fill? Answer [2]

7 Martha divides $240 between spending and saving in the ratio spending : saving = 7 : 8 . Calculate the amount Martha has for spending. Answer $ [2]

4

© UCLES 2011 0580/13/O/N/11

For

Examiner's

Use

8 210 211 212 213 214 215 216 From the list of numbers, find (a) a prime number, Answer(a) [1]

(b) a cube number. Answer(b) [1]

9 Calculate the selling price of a bicycle bought for $120 and sold at a profit of 15%. Answer $ [2]

10 Solve the simultaneous equations. x + 5y = 22 x + 3y = 12 Answer x =

y = [2]

5


For

Examiner's

Use

11 Solve the equation.

2

32 −x

= 2

Answer x = [2]

12 The population of a city is 128 000, correct to the nearest thousand. (a) Write 128 000 in standard form. Answer(a) [1]

(b) Write down the upper bound of the population. Answer(b) [1]

13 Pedro invested $800 at a rate of 5% per year compound interest. Calculate the total amount he has after 2 years. Answer $ [2]

6

© UCLES 2011 0580/13/O/N/11

For

Examiner's

Use

14 Factorise completely. 5g2h + 10hj Answer [2]

15 For her holiday, Dina changed 500 Swiss francs (CHF) into pounds (£). The rate was £1 = CHF 1.6734 . Calculate how much Dina received in pounds. Give your answer correct to 2 decimal places. Answer £ [2]

16 Simplify 4x4 × 5x5. Answer [2]

7


For

Examiner's

Use

17 The scale of a map is 1 : 500 000. On the map the centres of two cities are 26 cm apart. Calculate the actual distance, in kilometres, between the centres of the two cities. Answer km [2]

18 Show that 3

–2 + 2

–2 = 36

13.

Write down all the steps of your working. Answer

[2]

8

© UCLES 2011 0580/13/O/N/11

For

Examiner's

Use

19 In Vienna, the mid-day temperatures, in °C, are recorded during a week in December. This information is shown below. –2 2 1 –3 –1 –2 0 Calculate (a) the difference between the highest temperature and the lowest temperature, Answer(a) °C [1]

(b) the mean temperature. Answer(b) °C [2]

20

2.5 m

8 m

8 m

NOT TOSCALE

The diagram shows a circular pool of radius 2.5 m. A square piece of land surrounds the pool. Each side of the square is 8 m long. Calculate the shaded area of the land that surrounds the pool. Answer m2 [3]

9


For

Examiner's

Use

21

40°58°

A B

C

D

NOT TOSCALE

In the quadrilateral ABCD, AB = AD and CB = CD. Angle BAD = 40° and angle CBD = 58°. (a) Calculate (i) angle ABD, Answer(a)(i) Angle ABD = [1]

(ii) angle BCD. Answer(a)(ii) Angle BCD = [1]

(b) Write down the mathematical name for the quadrilateral ABCD. Answer(b) [1]

10

© UCLES 2011 0580/13/O/N/11

For

Examiner's

Use

22 (a) Calculate 3

28.6

700 .

Answer(a) [1]

(b) Work out (8 × 106)2, giving your answer in standard form. Answer(b) [2]

11


For

Examiner's

Use

23 y

x

3

2

1

–1

–2

–3

–4

–5

0 1–1–2–3–4–5 2 3 4 5

A

M

The diagram shows two points A (–5, 2) and M (2, –3). (a) B is the point (5, –2). (i) On the grid, mark the point B. [1]

(ii) Write as a column vector.

Answer(a)(ii) =

[1]

(b) M is the midpoint of the line BD. Find the co-ordinates of D. Answer(b) ( , ) [2]


12



© UCLES 2011 0580/13/O/N/11

For

Examiner's

Use

24

A BD

C

13 cm7 cm

12 cm

NOT TOSCALE

In triangle ABC, D is on AB so that angle ADC = angle BDC = 90°. AC = 13 cm, BC = 12 cm and CD = 7 cm. (a) Calculate the length of DB. Answer(a) DB = cm [3]

(b) Use trigonometry to calculate angle CAD. Answer(b) Angle CAD = [2]



*6953510778*


MATHEMATICS 0580/31


2 hours

















2

© UCLES 2011 0580/31/O/N/11

For

Examiner's

Use

1 (a) Write twenty five million in figures. Answer(a) [1]

(b) Write the following in order of size, starting with the smallest.

3

2 65% 0.6

Answer(b) I I [1]

(c) In a sale a coat costing $250 is reduced to $200. Find the percentage decrease in the cost. Answer(c) % [3]

(d)

Basketball

Tennis

90°150°Football

NOT TOSCALE

120 students are asked to choose their favourite sport. The results are shown in the pie chart. Calculate the number of students who chose

(i) basketball, Answer(d)(i) [1]

(ii) football. Answer(d)(ii) [2]

3


For

Examiner's

Use

2 The distance between Geneva and Gstaad is 150 km. (a) Write 150 in standard form. Answer(a) [1]

(b) A car took 12

1 hours to travel from Geneva to Gstaad.

Calculate the average speed of the car. Answer(b) km/h [1]

(c) A bus left Gstaad at 10 15. It arrived in Geneva at 12 30. Calculate the time, in hours and minutes, that the bus took for the journey. Answer(c) h min [1]

(d) Another bus left Geneva at 13 55. It travelled at an average speed of 60 km/h. Find the time it arrived in Gstaad. Answer(d) [2]

(e) The distance of 150 km is correct to the nearest 10 km. Complete the statement for the distance, d km, from Geneva to Gstaad. Answer(e) Y d I [2]

4

© UCLES 2011 0580/31/O/N/11

For

Examiner's

Use

3 36 29 41 45 15 10 13 Use the numbers in the list above to answer all the following questions.

(a) Write down (i) two even numbers, Answer(a)(i) , [1]

(ii) two prime numbers, Answer(a)(ii) , [2]


(iv) two factors of 90 . Answer(a)(iv) , [2]

(b) (i) Calculate the mean of the seven numbers. Answer(b)(i) [2]

(ii) Find the median. Answer(b)(ii) [2]

(iii) Find the range. Answer(b)(iii) [1]

5


For

Examiner's

Use

(c) A number from the list is chosen at random. Find the probability that the number is (i) even, Answer(c)(i) [1]

(ii) a multiple of 5. Answer(c)(ii) [1]

6

© UCLES 2011 0580/31/O/N/11

For

Examiner's

Use

4 (a) Using the exchange rates $1 = 0.70 Euros and $1 = 90 Yen change (i) $100 to Euros, Answer(a)(i) Euros [1]

(ii) 100 Yen to dollars. Answer(a)(ii) $ [2]

(b) Tania went on holiday to Switzerland. The exchange rate was $1 = 1.04 Swiss francs (CHF). She changed $1500 to Swiss francs and paid 1% commission. (i) How much commission, in dollars, did she pay? Answer(b)(i) $ [1]

(ii) Show that she received CHF 1544.40. Answer (b)(ii) [2] (c) Tania spent CHF 950 on her holiday. She converted the remaining Swiss francs back into dollars. She paid CHF 10 to make the exchange. Calculate the amount, in dollars, Tania received. Answer(c) $ [3]

7


For

Examiner's

Use

5 y

x

6

5

4

3

2

1

–1

–2

–3

0 1 2 3 4 5 6–1–2–3–4

l

(a) Find the gradient of the line l. Answer(a) [2]

(b) (i) Complete the table below for x + 2y = 6 .

x 0 2

y 0

[3]

(ii) On the grid, draw the line x + 2y = 6 for −4 Y x Y 6 . [2] (c) The equation of the line l is 4x + 3y = 4. Use your diagram to solve the simultaneous equations 4x + 3y = 4 and x + 2y = 6 . Answer(c) x =

y = [2]

8

© UCLES 2011 0580/31/O/N/11

For

Examiner's

Use

6 (a)

A B The line AB is drawn above. Parts (i), (iii), and (v) must be completed using a ruler and compasses only.

All construction arcs must be clearly shown. (i) Construct triangle ABC with AC = 7 cm and BC = 6 cm. [2] (ii) Measure angle BAC. Answer(a)(ii) Angle BAC = [1]

(iii) Construct the bisector of angle ABC. [2] (iv) The bisector of angle ABC meets AC at T. Measure the length of AT. Answer(a)(iv) AT = cm [1]

(v) Construct the perpendicular bisector of the line BC. [2] (vi) Shade the region that is


• nearer to BC than to AB. [1]

9


For

Examiner's

Use

(b) A ship sails 40 km on a bearing of 040° from P to Q. (i) Using a scale of 1 centimetre to represent 5 kilometres, make a scale drawing of the path of

the ship. Mark the point Q.

North

P

Scale: 1 cm = 5 km [2] (ii) At Q the ship changes direction and sails 30 km on a bearing of 160° to the point R. Draw the path of the ship. [2] (iii) Find how far, in kilometres, the ship is from the starting position P. Answer(b)(iii) km [1]

(iv) Measure the bearing of P from R. Answer(b)(iv) [1]

10

© UCLES 2011 0580/31/O/N/11

For

Examiner's

Use

7 (a) Solve the equation 2(x + 4) = 3(x + 2) + 8 . Answer(a) x = [3]

(b) Make z the subject of za + b = 3 . Answer(b) z = [2]

(c) Find x when 2x3 = 54 . Answer(c) x = [2]

11


For

Examiner's

Use

(d) A rectangular field has a length of x metres. The width of the field is (2x – 5) metres. (i) Show that the perimeter of the field is (6x – 10) metres. Answer (d)(i) [2] (ii) The perimeter of the field is 50 metres. Find the length of the field. Answer(d)(ii) length =

m [2]

12

© UCLES 2011 0580/31/O/N/11

For

Examiner's

Use

8

A

B

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

The diagram shows two shapes A and B. (a) Describe fully the single transformation which maps A onto B. Answer(a) [2]

(b) On the grid, draw the line x = 2. [1] (c) On the grid, draw the image of shape A after the following transformations. (i) Reflection in the line x = 2. Label the image C. [1] (ii) Enlargement, scale factor 2, centre (0, 0). Label the image D. [2]

13


For

Examiner's

Use

9 (a) Factorise completely 3x2 + 12x. Answer(a) [2]

(b) Find the value of a3 + 3b2 when a = 2 and b = −2 . Answer(b) [2]

(c) Simplify 3x4 × 2x3. Answer(c) [2]

14

© UCLES 2011 0580/31/O/N/11

For

Examiner's

Use

10

2 m

5 m

10 m

x m

NOT TOSCALE

The diagram shows a ramp in the form of a triangular prism. The cross-section is a right-angled triangle of length 5 m and height 2 m. (a) Find the value of x. Give your answer correct to 1 decimal place. Answer(a) x = [3]

(b) Find the area of the cross-section. Answer(b) m2 [2]

(c) The ramp is 10 m long. Calculate the volume of the ramp. Answer(c) m3 [1]

15


For

Examiner's

Use

(d) Calculate the total surface area of all five faces of the ramp. Answer(d) m2 [3]

(e) Each face of the ramp is painted. Paint costs $2.25 per square metre. Calculate the total cost of the paint. Answer(e) $ [1]


16



© UCLES 2011 0580/31/O/N/11

For

Examiner's

Use

11

Diagram 1 Diagram 2 Diagram 3 The diagrams show a sequence of shapes. (a) On the grid, draw Diagram 4. [1] (b) Complete the table showing the number of lines in each diagram.

Diagram (n) Number of lines

1 6

2 11

3

4

5

[3] (c) Work out the number of lines in Diagram 8. Answer(c) [1]

(d) Write down an expression, in terms of n, for the number of lines in Diagram n. Answer(d) [2]

(e) Work out the number of lines in Diagram 100. Answer(e) [1]

(f) The number of lines in Diagram p is 66. Find the value of p. Answer(f) p = [2]



*4552761824*


MATHEMATICS 0580/32


2 hours

















2

© UCLES 2011 0580/32/O/N/11

For

Examiner's

Use

1 Mr and Mrs Sayed and their 3 children go on holiday. They travel to the airport by train. (a) The train departs at 16 20. (i) They leave home 45 minutes before the train departs. Find the time at which they leave home. Answer(a)(i) [1]

(ii) Write 16 20 using the 12-hour clock. Answer(a)(ii) [1]

(b) The train fare is $24 for an adult.

The train fare for a child is 3

2 of an adult fare.

Find (i) the fare for a child, Answer(b)(i) $ [1]

(ii) the total fare for Mr and Mrs Sayed and their 3 children. Answer(b)(ii) $ [2]

3


For

Examiner's

Use

2 Aminata buys a business costing $23 000. (a) She pays part of this cost with $12 000 of her own money. Calculate what percentage of the $23 000 this is. Answer(a) % [1]

(b) Aminata’s brother gives her 32% of the remaining $11 000. Show that $7 480 is still needed to buy the business. Answer(b)

[2] (c) Aminata borrows the $7 480 at a rate of 3.5 % per year compound interest. Calculate how much money she owes at the end of 3 years. Answer(c) $ [3]

(d) In the first year Aminata spent $11 000 on salaries, equipment and expenses.

5

2 of this money was spent on salaries, 0.45 of this money was spent on equipment and the

remainder was for expenses. Calculate how much of the $11 000 was spent on

(i) salaries, Answer(d)(i) $ [1]

(ii) equipment, Answer(d)(ii) $ [1]

(iii) expenses. Answer(d)(iii) $ [1]

(e) The three items in part (d) are in the ratio salaries : equipment : expenses = 0.4 : 0.45 : 0.15 . Write this ratio in its simplest form. Answer(e) : : [2]

4

© UCLES 2011 0580/32/O/N/11

For

Examiner's

Use

3 (a) r =

− 2

3 +

−

−

2

5

(i) Write down r as a single vector.

Answer(a)(i) r =

[1]

(ii) The point G(3, 2) is translated by the vector r to the point H. Find the co-ordinates of H. Answer(a)(ii) ( , ) [1]

(iii) Write down the vector of the translation that maps H onto G.

Answer(a)(iii)

[1]

5


For

Examiner's

Use

(b)

P

Q

y

x

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

0 1 2 3 4 5 6 7 8 9 10–1–2–3–4

The diagram shows two triangles P and Q. (i) Describe fully the single transformation which maps P onto Q. Answer(b)(i) [3]

(ii) On the grid, draw the reflection of P in the line x = 0. Label this image R. [2] (iii) On the grid, rotate P through 180° about (0, 0). Label this image S. [2] (iv) Describe fully the single transformation which maps triangle S onto triangle R. Answer(b)(iv) [2]

6

© UCLES 2011 0580/32/O/N/11

For

Examiner's

Use

4 (a) Expand and simplify 3(2x + y) + 5(x – y). Answer(a) [2]

(b) Expand x2(3x – 2y). Answer(b) [2]

(c) Factorise completely 4y2 – 10xy. Answer(c) [2]

(d) y = 3

42

x

(i) Find the value of y when x = O3 . Answer(d)(i) y = [2]

(ii) Make x the subject of the formula. Answer(d)(ii) x = [3]

7


For

Examiner's

Use

5 (a) An aeroplane takes off 140 metres before reaching the end of the runway. It climbs at an angle of 22° to the horizontal ground.

22°

h

140 m

NOT TOSCALE

Calculate the height of the aeroplane, h, when it is vertically above the end of the runway. Answer(a) h = m [2]

(b) After 3 hours 30 minutes the aeroplane has travelled 1850 km. Calculate the average speed of the aeroplane. Answer(b) km/h [2]

(c)

15 km

NOT TOSCALE

A B

C The aeroplane descends from A, at a height of 12 000 metres, to C, at a height of 8 300 metres. (i) Work out the vertical distance, BC, that the aeroplane descends. Answer(c)(i) m [1]

(ii) The distance AC is 15 kilometres. Calculate angle BAC. Answer(c)(ii) Angle BAC = [2]

8

© UCLES 2011 0580/32/O/N/11

For

Examiner's

Use

6

F

E

A

D

B

C24 cm

30 cm

16 cm

NOT TOSCALE

The diagram shows a wedge in the shape of a triangular prism. AB = 30 cm, AF = 16 cm and BC = 24 cm. Angle BAF = 90°. (a) Calculate (i) the area of triangle ABF, Answer(a)(i) cm2 [2]

(ii) the volume of the wedge. Answer(a)(ii) cm3 [1]

(b) (i) Calculate BF. Answer(b)(i) cm [2]

(ii)

1.6 cmNOT TOSCALE

A coin with diameter 1.6 cm is rolled down the sloping surface of the wedge. It travels in a straight line parallel to BF, starting on FE and ending on BC. Calculate the number of complete turns it makes. Answer(b)(ii) [3]

9


For

Examiner's

Use

(c) On the grid, complete the net of the wedge. The base and one of the triangles have been drawn for you. Each square on the grid represents a square of side 4 centimetres.

[3] (d) Calculate the surface area of the wedge. Answer(d) cm2 [3]

10

© UCLES 2011 0580/32/O/N/11

For

Examiner's

Use

7 (a) The table shows some values for y = x

18.

x O9 O6 O4 O3 O2 2 3 4 6 9

y O2 O4.5 O9 4.5 3


(ii) On the grid, draw the graph of y = x

18 for O9 Y x Y O2 and 2 Y x Y 9 .

y

x

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–9

0–1–2–3–4–5–6–7–8–9 4 5 6 7 8 9321

[4]

(iii) Use your graph to solve the equation x

18 = O5 .

Answer(a)(iii) x = [1]

11


For

Examiner's

Use

(b) (i) Complete the table of values for y = 2x + 3 .

x O4 O3 2 3

y O5 7

[2]

(ii) On the grid, draw the graph of y = 2x + 3 for O4 Y x Y 3 . [1] (iii) Find the co-ordinates of the points of intersection of the graphs of

y = x

18 and y = 2x + 3 .

Answer(b)(iii) ( , ) and ( , ) [2]

12

© UCLES 2011 0580/32/O/N/11

For

Examiner's

Use

8 The table shows the average temperature and rainfall each month at Wellington airport.


Temperature (°C)

18 18 17 14 12 10 9 10 11 13 15 16

Rainfall (mm)

67 48 76 87 99 113 111 106 82 81 74 74

(a) Complete the bar chart to show the temperature each month.

20

18

16

14

12

10

8

6

4

2

0Jan Feb Mar Apr May Jun Jul

Month

Aug Sep Oct Nov Dec

Temperature(°C)

[2] (b) For the rainfall calculate (i) the mean, Answer(b)(i) mm [2]

(ii) the median. Answer(b)(ii) mm [2]

13


For

Examiner's

Use

(c) In the scatter diagram the rainfall for January to April is plotted against temperature.

120

115

110

105

100

95

90

85

80

75

70

65

60

55

50

45

408 9 10 11 12 13 14 15 16 17 18 19 20

Temperature (°C)

Rainfall(mm)

(i) Complete the scatter diagram by plotting the values for the months May to December. [3] (ii) Draw the line of best fit on the scatter diagram. [1] (iii) What type of correlation does the scatter diagram show? Answer(c)(iii) [1]

14

© UCLES 2011 0580/32/O/N/11

For

Examiner's

Use

9 On the scale drawing opposite, point A is a port. B and C are two buoys in the sea and L is a lighthouse. The scale is 1 cm = 3 km. (a) A boat leaves port A and follows a straight line course that bisects angle BAC. Using a straight edge and compasses only, construct the bisector of angle BAC on the scale

drawing. [2] (b) When the boat reaches a point that is equidistant from B and from C, it changes course. It then follows a course that is equidistant from B and from C. (i) Using a straight edge and compasses only, construct the locus of points that are equidistant

from B and from C. Mark the point P where the boat changes course. [2] (ii) Measure the distance AP in centimetres. Answer(b)(ii) cm [1]

(iii) Work out the actual distance AP. Answer(b)(iii) km [1]

(iv) Measure the obtuse angle between the directions of the two courses. Answer(b)(iv) [1]

(c) Boats must be more than 9 kilometres from the lighthouse, L. (i) Construct the locus of points that are 9 kilometres from L. [2] (ii) Mark the point R where the course of the boat meets this locus. Work out the actual straight line distance, AR, in kilometres. Answer(c)(ii) km [1]

15


For

Examiner's

Use

A

B

C

L

Scale: 1 cm = 3 km


16



© UCLES 2011 0580/32/O/N/11

For

Examiner's

Use

10 (a) Write down the next term in each of the following sequences.

(i) 2, 9, 16, 23,

[1]

(ii) 75, 67, 59, 51,

[1]

(iii) 2, 5, 9, 14,

[1]

(iv) 2, 1,

2

1,

4

1,

[1]

(v) 2, 4, 8, 16,

[1]

(b) For the sequence in part (a)(i) write down (i) the 10th term, Answer(b)(i) [1]

(ii) the nth term. Answer(b)(ii) [2]

(c) The nth term of the sequence in part (a)(iii) is 2

32

nn +.

Calculate the 50th term of this sequence. Answer(c) [2]

(d) The nth term of the sequence in part (a)(v) is 2n. Calculate the 12th term of this sequence. Answer(d) [1]



*6881181028*


MATHEMATICS 0580/33


2 hours

















2

© UCLES 2011 0580/33/O/N/11

For

Examiner's

Use

1 Caroline goes to a shop. The shopping bill shows the items she buys.

Item Cost ($)

1 packet of cereal 1.20

3 bottles of water at $0.45 each 1.35

2 cartons of milk at $0.82 each

4 kg of rice at $0.90 per kg

0.7 kg of apples at $2.40 per kg

(a) Complete the shopping bill. [3] (b) (i) Calculate the total amount of money Caroline spends at the shop. Answer(b)(i) $ [1]

(ii) Caroline pays with a $10 note. Calculate how much change she receives. Answer(b)(ii) $ [1]

3


For

Examiner's

Use

(c) Caroline arrived at the shop at 09 48. She was in the shop for 18 minutes. She then took 5 minutes to walk to a café. She was in the café for 20 minutes. (i) At what time did Caroline leave the café? Answer(c)(i) [2]

(ii) Caroline then went to the library. She was in the library for 45 minutes. Work out the ratio time in the shop : time in the library. Give your answer in its simplest form. Answer(c)(ii) : [2]

(d) When Caroline left home she had $36.50. She returned home with $12.74. Calculate $12.74 as a percentage of $36.50. Answer(d) % [1]

4

© UCLES 2011 0580/33/O/N/11

For

Examiner's

Use

2 James takes 12 science tests during one school term. These are his marks.

18 11 20 15 15 12 15 9 11 15 14 13

(a) Find (i) the range, Answer(a)(i) [1]

(ii) the mode, Answer(a)(ii) [1]

(iii) the median, Answer(a)(iii) [2]

(iv) the mean. Answer(a)(iv) [2]

5


For

Examiner's

Use

(b) James sorts his marks into three levels. The levels are Satisfactory (less than 12), Good (12 to 16) and Excellent (more than 16). (i) Complete the frequency table to show this information.

Level Satisfactory Good Excellent

Frequency 7

[1] (ii) Complete the pie chart accurately and label each sector.

Good

[2] (c) What fraction of the marks were Satisfactory or Good? Give your answer in its lowest terms. Answer(c) [2]

6

© UCLES 2011 0580/33/O/N/11

For

Examiner's

Use

3

600

550

500

450

400

350

300

250

200

150

100

50

009 00 09 10 09 20 09 30 09 40

Time

09 50 10 00 10 10Bruce’s home

Park

Jason’s home

Distance fromBruce’s home(metres)

One morning, Bruce walked from his home to Jason’s home and the two boys walked to the park. The distance-time graph shows Bruce’s journey. (a) How many minutes was Bruce at Jason’s home? Answer(a) min [1]

(b) How far from the park were Bruce and Jason at 09 20? Answer(b) m [2]

(c) Work out the speed at which Bruce and Jason walked to the park. Give your answer in km/h. Answer(c) km/h [3]

(d) Bruce stayed at the park for 35 minutes. He then walked home at a speed of 60 metres per minute. Complete the graph to show Bruce’s time at the park and his journey home. [3]

7


For

Examiner's

Use

4 (a)

l

W

C

On the grid, (i) draw the reflection of W in the line l, [2] (ii) rotate W anticlockwise through 90°, about the point C. [2] (b)

y

x

3

2

1

–1

–2

–3

–4

0–1 1 2 3 4 5 6 7–2–3–4–5

PR

Q

(i) Describe fully the single transformation that maps P onto Q. Answer(b)(i) [2]

(ii) Describe fully the single transformation that maps P onto R. Answer(b)(ii) [3]

8

© UCLES 2011 0580/33/O/N/11

For

Examiner's

Use

5 (a)

A XB

CD

140°

52°

92° NOT TOSCALE

In the quadrilateral ABCD, angle BAD = 52°, angle ADC = 140° and angle DCB = 92°. AB is extended to X. (i) Calculate angle CBX. Answer(a)(i) Angle CBX = [2]

(ii) The line BY bisects angle CBX. Complete the statement.

The lines BY and AD are

because [2]

(b)

4x° x°O

T

U

PNOT TOSCALE

The diagram shows a circle, centre O. PT and PU are tangents to the circle at T and U. Angle TPU = x° and angle TOU = 4x°. Calculate the value of x. Answer(b) x = [3]

(c) The exterior angle of a regular polygon is 20°. Calculate the number of sides of the polygon. Answer(c) [2]

9


For

Examiner's

Use

6 (a) Complete the table for y = 4 + 2x O x2.

x –2 –1 0 1 2 3 4

y 1 5 1

[2]

(b) On the grid, draw the graph of y = 4 + 2x O x2 for –2 Y x Y 4 .

y

x

6

5

4

3

2

1

–1

–2

–3

–4

0–1–2 2 3 41

[4] (c) (i) Draw the line of symmetry of the graph. [1] (ii) Write down the equation of this line of symmetry. Answer(c)(ii) [1]

(d) Use your graph to solve the equation 4 + 2x O x2 = 0. Answer(d) x = or x = [2]

10

© UCLES 2011 0580/33/O/N/11

For

Examiner's

Use

7

8

7

6

5

4

3

2

1

03 3 1

2 4 4 12 5 5 1

2 6 6 12

Shoe size

Frequency

The bar chart shows the frequencies of the shoe sizes for a group of students. (a) Use the information in the bar chart to complete the frequency table.

Shoe size 3 32

1

4 42

1 5 5

2

1

6 62

1

Frequency 4 1

[2]

(b) How many students are in the group? Answer(b) [1]

(c) Calculate the mean shoe size. Answer(c) [3]

11


For

Examiner's

Use

8

A B

(a) Construct triangle ABC accurately, with AC = 10 cm and BC = 8 cm. The line AB has been drawn for you. [2] (b) (i) Using a straight edge and compasses only, construct the bisector of angle A. [2] (ii) The bisector of angle A meets BC at X. Measure the length of BX. Answer(b)(ii) BX = cm [1]

(c) (i) Using a straight edge and compasses only, construct the perpendicular bisector of AB. [2] (ii) The perpendicular bisector of AB meets AC at Y and AX at Z. Measure angle CYZ. Answer(c)(ii) Angle CYZ = [1]

(d) Shade the region inside triangle ABC which is

• nearer to AB than to AC and

• nearer to B than to A. [1]

12

© UCLES 2011 0580/33/O/N/11

For

Examiner's

Use

9 P

Q

R

12 cm

25 cm

5 cmNOT TOSCALE

The diagram shows a solid triangular prism of length 25 cm. The cross-section of the prism is triangle PQR. PQ = 5 cm, QR = 12 cm and angle PQR = 90°. (a) (i) Calculate the volume of the prism. Answer(a)(i) cm3 [3]

(ii) The prism is made from wood. The mass of 1 cm3 of the wood is 0.96 g. Calculate the mass of the prism. Give your answer in kilograms. Answer(a)(ii) kg [2]

13


For

Examiner's

Use

(b) (i) Show that PR = 13 cm. Answer(b)(i) [2] (ii) The prism is completely covered with plastic at a cost of $0.08 per square centimetre. By finding the total area of the two triangles and the three rectangles, calculate the total

cost of the plastic used. Answer(b)(ii) $ [4]

14

© UCLES 2011 0580/33/O/N/11

For

Examiner's

Use

10 (a) Tatiana goes for a walk. (i) She walks for 15 minutes at a speed of 80 metres per minute. Calculate the distance she walks. Answer(a)(i) m [1]

(ii) She then walks for a further p minutes at w metres per minute. Write down an expression, in terms of p and w, for the total distance Tatiana walks. Answer(a)(ii) m [1]

(iii) Write down an expression, in terms of p and w, for Tatiana’s average speed, in metres per

minute. Answer(a)(iii) m/min [2]

15


For

Examiner's

Use

(b) The volume, V, of a solid is given by the following formula.

V = 3b(t + 2

1

m)

(i) Find V when b = 4, t = 5 and m = 6 . Answer(b)(i) V = [2]

(ii) Find b when t =3, m = 2 and V = 84. Answer(b)(ii) b = [3]


16



© UCLES 2011 0580/33/O/N/11

For

Examiner's

Use

11 (a) Write down the next term in each of the following sequences.

(i) 8, 15, 22, 29, [1]

(ii) 3, 6, 12, 24, [1]

(iii) 1, 4, 9, 16, [1]

(iv) 0, 3, 8, 15, [1] (b) Write down an expression, in terms of n, for the nth term of (i) the sequence in part(a)(iii), Answer(b)(i) [1]

(ii) the sequence in part(a)(iv). Answer(b)(ii) [1]

(c) The nth term of a sequence is 7n –3 . (i) Write down the value of the 4th term. Answer(c)(i) [1]

(ii) Which term has a value of 592? Answer(c)(ii) [2]

(d) 1, 2, 2, 4, 8, 32, 256, …… Work out the next two terms of this sequence. Answer(d) , [2]



*0595577027*


MATHEMATICS 0580/11


1 hour


Additional Materials: Electronic Calculator Mathematical tables (optional) Geometrical Instruments Tracing paper (optional)















2

© UCLES 2010 0580/11/M/J/10

For

Examiner's

Use

1 A ferry to Crete leaves at 07 30. The journey takes 2 hours and 48 minutes. Work out the time when the ferry arrives in Crete. Answer [1]

2 (a) Write the following in order, starting with the smallest.

0.43 9

4 41%

Answer(a) < < [1]

(b) Only one of the following statements is correct.

sin 30° ≠ 0.5 42 > 16 0.3 < 3

1

Put a ring around the correct statement. [1]

3 In a group of 35 students, 14 go to school by bus. Write down the probability that a student, chosen at random, does not go to school by bus. Give your answer as a fraction in its lowest terms. Answer [2]

4 Write down the equation of the line, parallel to y = 4x + 1 , which passes through the point (0, −3). Answer [2]

3


For

Examiner's

Use

5 North

North107°

M

P

NOT TOSCALE

The bearing of P from M is 107°. Work out the bearing of M from P. Answer [2]

6 Martin recorded the outside temperature every three hours.

At 07 00 the temperature was − 2°C.

(a) This was 5°C higher than the temperature at 04 00. Write down the temperature at 04 00. Answer(a) °C [1]

(b) At 10 00 the temperature was 11°C. Write down the increase in temperature between 07 00 and 10 00. Answer(b) °C [1]

7 In a sale, the price of a car was reduced from $ 17 000 to $ 15 300. Calculate the reduction as a percentage of the original price. Answer % [2]

4

© UCLES 2010 0580/11/M/J/10

For

Examiner's

Use

8

2x – 7

x + 3x

NOT TOSCALE

The lengths, in centimetres, of the sides of a triangle are x , x + 3 and 2x − 7. The perimeter of the triangle is 52 cm. (a) Use this information to write down an equation in x. Answer(a) [1]

(b) Find the value of x. Answer(b) x = [2]

9 The area of a circle is 19.7 cm2. Calculate the radius of the circle. Answer cm [3]

10 Simplify

(a) 3 4

p p× ,

Answer(a) [1]

(b) 8 2

12 3q q÷ .

Answer(b) [2]

5


For

Examiner's

Use

11

160°160°

NOT TOSCALE

The diagram shows part of a regular polygon.

Each interior angle of the polygon is 160°. Calculate the number of sides of the polygon. Answer [3]

12 Write down the value of (a) 10-2, Answer(a) [1]

(b) 40, Answer(b) [1]

(c) 3343 .

Answer(c) [1]

13 Solve the simultaneous equations.

2x − y = 9

7x + 2y = 26 Answer x =

y = [3]

6

© UCLES 2010 0580/11/M/J/10

For

Examiner's

Use

14

O

C

A

B

S T

54°NOT TOSCALE

A, B and C lie on a circle, centre O. BC is a diameter and SCT is a tangent at C. Angle ACB = 54°. Find (a) angle BCT, Answer(a) Angle BCT = [1]

(b) angle COA, Answer(b) Angle COA = [1]

(c) angle CAB, Answer(c) Angle CAB = [1]

(d) angle ABC. Answer(d) Angle ABC = [1]

15

d =

− 5

3 e =

−

4

1 f =

7

0

Calculate (a) d – e,

Answer(a)

[2]

(b) 4f.

Answer(b)

[2]

7


For

Examiner's

Use

16 Complete the information about each shape.

Shape

Number of lines of symmetry

Order of rotational symmetry

[4]

17

3

2

1

0

City


Time (minutes)

Port0 15 30 45 60

(a) The travel graph shows the journey of a bus from a port to a city. Calculate the average speed of the bus (i) in kilometres per minute, Answer(a)(i) km/min [1]

(ii) in kilometres per hour. Answer(a)(ii) km/h [1]

(b) The bus waits in the city for 20 minutes and then returns to the port at an average speed of 12 km/h. Complete the travel graph. [2]

Questions 18 and 19 are printed on the next page.

8



© UCLES 2010 0580/11/M/J/10

For

Examiner's

Use

18 (a) Factorise 2

3 7y xy− .

Answer(a) [1]

(b) Expand the brackets and simplify completely.

( ) ( )4 5 2 6p p r r p r+ + +

Answer(b) [3]

19 Erica is tiling the floor of a rectangular room of length 3 metres and width 2.5 metres. She uses square tiles of side 25 centimetres. (a) Calculate (i) how many tiles will fit along the length of the room, Answer(a)(i) [1]

(ii) how many tiles she will need altogether. Answer(a)(ii) [2]

(b) Work out the area of one tile (i) in square centimetres, Answer(b)(i) cm2 [1]

(ii) in square metres. Answer(b)(ii) m2 [1]



*7313041459*


MATHEMATICS 0580/12


1 hour

















2

© UCLES 2010 0580/12/M/J/10

For

Examiner's

Use

1

157°

84° x°

NOT TOSCALE


Answer x = [1]

2 (a) Write down the smallest number which is a multiple of both 8 and 12. Answer(a) [1]

(b) Write down all the other multiples of both 8 and 12 which are less than 100. Answer(b) [1]

3 Factorise completely 6mp − 9pq. Answer [2]

3


For

Examiner's

Use

4 1 litre of apple juice is poured into 3 glasses.

The first glass contains 2

5 litre.

The second glass contains 1

4 litre.

What fraction of a litre does the third glass contain? Show all your working clearly. Answer [2]

5 A plane from Hong Kong to New Zealand leaves at 18 10 on Monday. The time in New Zealand is 4 hours ahead of the time in Hong Kong. (a) Write down the time in New Zealand when the plane leaves Hong Kong. Answer(a) [1]

(b) The plane arrives in New Zealand at 09 45 on Tuesday. How long, in hours and minutes, does the journey take? Answer(b) h min [1]

4

© UCLES 2010 0580/12/M/J/10

For

Examiner's

Use

6 Alphonse changed 400 Brazilian reals into South African Rand. The exchange rate was 1 Brazilian real = 4.76 South African Rand (R). How much did he receive? Answer R [2]

7 Joe measured the diameter of a tennis ball correct to the nearest millimetre. The upper bound of his measurement was 6.75 centimetres. Write down, in millimetres, the lower bound of his measurement. Answer mm [2]

8 Make p the subject of the formula m = p2 − 2. Answer p = [2]

5


For

Examiner's

Use

9

The positions of Perth (P), Darwin (D) and Hobart (H) are shown on the diagram. Measure accurately any angles you need and write down the bearing of (a) D from P, Answer(a) [1]

(b) P from H.

Answer(b) [1]

10 When c = 10 and d = −2, find the value of the following expressions. (a) c + 2d Answer(a) [1]

(b) 5c2 − cd

Answer(b) [2]

North

North

North

P

D

H

6

© UCLES 2010 0580/12/M/J/10

For

Examiner's

Use

11 Fifteen children ran a 60 metre race. In the scatter diagram below, the time taken is plotted against the age for each child.

18

17

16

15

14

13

12

11

10

9

87 8 9 10 11 12 13 14

Time(seconds)

Age (years) (a) Draw a line of best fit on the scatter diagram. [1] (b) What type of correlation does the scatter diagram show? Answer(b) [1]

(c) Describe how the times taken change with the ages of the children.

Answer (c)

[1]

7


For

Examiner's

Use

12 (a) 1

27= 3x .

Write down the value of x. Answer(a) x = [1]

(b) Simplify

(i) p7 × p

-2 ,

Answer(b)(i) [1]

(ii) m3 ÷ m

7.

Answer(b)(ii) [1]

13 (a) Work out 0.68 2.57 1.76

63

+ ×

.

Write down all the figures from your calculator display. Answer(a) [1]

(b) Write your answer to part (a) in standard form correct to 3 significant figures. Answer(b) [2]

14 Solve the simultaneous equations. 3x − 2y = 15 2x + y = 17 Answer x = y = [3]

8

© UCLES 2010 0580/12/M/J/10

For

Examiner's

Use

15 The diagram shows a prism. The lengths are in centimetres.

Part of an accurate net of the prism is drawn below. Complete the net.

[3]

1

2

1.5

2.5

4

8

3

NOT TOSCALE

9


For

Examiner's

Use

16 Daniel invested $2500 for 2 years at 5.5% per year compound interest. Calculate how much interest he received. Answer $ [3]

17

Write down the letter of the graph which is (a) y = x − 2, Answer(a) [1]

(b) x = − 2, Answer(b) [1]

(c) y = −2x + 4, Answer(c) [1]

(d) y = x2 − 4. Answer(d) [1]

y

x

6

–6

–3 30

A

y

x

6

–6

–3 30

B

y

x

6

–6

–3 30

C

y

x

6

–6

–3 30

E

y

x

6

–6

–3 30

F

y

x

6

–6

–3 30

G

y

x

6

–6

–3 30

D

10

© UCLES 2010 0580/12/M/J/10

For

Examiner's

Use

18 y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

0–1–2–3–4–5–6 5 64321

A

B

(a) Describe fully the single transformation which maps flag A onto flag B. Answer(a) [2]

(b) Draw, on the grid above, the image of flag A after rotation through 90° clockwise about the

origin. [2]

11


For

Examiner's

Use

19 The diagram shows a door, AEBCD, from a model of a house. ABCD is a rectangle and AEB is a semi-circle. AD = 14 cm and DC = 6 cm.

E

6 cm

14 cm

A B

D C

NOT TOSCALE

(a) Calculate the area of the door. Answer(a) cm2 [3]

(b) The door is 2 millimetres thick. Calculate, in cubic centimetres, the volume of the door. Answer(b) cm3 [2]


12



© UCLES 2010 0580/12/M/J/10

For

Examiner's

Use

20 A running track has a boundary that is always 40 metres from a straight line, AB. AB = 70 m. The scale drawing below shows the line AB. 1 centimetre represents 10 metres.

A B70 m

(a) Complete the scale drawing accurately to show the boundary of the running track. [2] (b) Calculate, in metres, the total length of the actual boundary. Answer(b) m [3]



*1727943591*


MATHEMATICS 0580/13


1 hour

















2

© UCLES 2010 0580/13/M/J/10

For

Examiner's

Use

1

45° 26°

x°NOT TOSCALE

Find the value of x. Answer x = [1]

2 A train to Paris leaves at 06 30. The journey takes 3 hours and 56 minutes. Work out the time when the train arrives in Paris. Answer [1]

3 Write down the factors of 48 which are between 10 and 40. Answer [2]

3


For

Examiner's

Use

4 I = K=

For each part, choose a symbol from those above to make a correct statement.

(a) 9

5

0.55 [1]

(b) 66%

3

2 [1]

5 In a sale, the price of a boat was reduced from $21 000 to $16 800. Calculate the reduction as a percentage of the original price. Answer % [2]

6 Write down the equation of the line, parallel to y = 3x + 5 , which passes through the point (0, −2). Answer [2]

4

© UCLES 2010 0580/13/M/J/10

For

Examiner's

Use

7 Mrs Duval makes one litre of ice cream.

She eats 1

8 litre and her children eat

3

5 litre.

Without using your calculator, find what fraction of a litre of ice cream is left. Show all your working clearly. Answer [2]

8 (a) Use your calculator to work out 27.4 × (3.28 + 1.6 × 9.8) . Write down all the figures from your calculator display. Answer(a) [1]

(b) Write your answer to part (a) correct to 3 significant figures. Answer(b) [1]

9 Calculate the area of a circle of radius 3.75 cm. Answer cm2 [2]

5


For

Examiner's

Use

10 (a)

Write down the order of rotational symmetry of the shape above. Answer(a) [1]

(b)

A M N O T X From the list, write down the letters which have only one line of symmetry. Answer(b) [2]

11 Simplify

(a) 53 −

×mm ,

Answer(a) [1]

(b) 28

315 kk ÷ .

Answer(b) [2]

6

© UCLES 2010 0580/13/M/J/10

For

Examiner's

Use

12

150° 150°

NOT TOSCALE

The diagram shows part of a regular polygon with each interior angle 150°. Calculate the number of sides of the polygon. Answer [3]

13 Expand the following expressions. (a) 5(3 – 4h) Answer(a) [1]

(b) )22

6(4 edd +

Answer(b) [2]

7


For

Examiner's

Use

14

4 cm

2.3 cm

1.75 cm NOT TOSCALE

The cuboid above has length 4 cm, width 2.3 cm and height 1.75 cm. Calculate the volume of the cuboid (a) in cubic centimetres, Answer(a) cm3 [2]

(b) in cubic millimetres. Answer(b) mm3 [1]

15 Simplify the following expressions. (a) 6r + 2s + s – 4r Answer(a) [1]

(b) 4f 2 – 3g + 4g – 9f

2

Answer(b) [2]

8

© UCLES 2010 0580/13/M/J/10

For

Examiner's

Use

16

4 cm

11 cm

NOT TOSCALE

A cylindrical can of beans has height 11 cm and radius 4 cm. A label covers the curved surface of the can completely. Calculate the area of the label. Answer cm2 [3]

17 Solve the simultaneous equations. 3x + y = 19 5x – y = 13 Answer x =

y = [3]

9


For

Examiner's

Use

18

P, Q and R lie on a circle, centre O.

PR is a diameter and angle OQR = 55°. Find (a) angle PQR, Answer(a) Angle PQR = [1]

(b) angle ROQ, Answer(b) Angle ROQ = [1]

(c) angle OPQ. Answer(c) Angle OPQ = [1]

19 f = 6

0

g = 3

6

−

h = 2

2−

Calculate (a) 3f,

Answer(a)

[2] (b) g – h.

Answer(b)

[2]

55°

R

O

P

Q

NOT TOSCALE

10

© UCLES 2010 0580/13/M/J/10

For

Examiner's

Use

20

100

90

80

70

60

50

40

30

20

10

00 1 2 3 4 5 6 7 8 9


Garage

Café

Factory

Time (hours) The travel graph shows part of the journey of a truck driver. The driver leaves a factory to deliver tyres to a garage. After unloading the tyres, the driver returns to the factory, but stops at a café for 1 hour. He then completes the journey at an average speed of 80 km/h. (a) Calculate the average speed of the truck on its journey from the factory to the garage. Answer(a) km/h [1]

(b) Write down the length of time the truck stays at the garage. Answer(b) hours [1]

(c) Complete the travel graph. [2]

11

© UCLES 2010 0580/13/M/J/10

For

Examiner's

Use

21

24°

9 cm16 cm

B

DA

C

NOT TOSCALE

The diagram shows a quadrilateral ABCD.

AB = 16 cm, BD = 9 cm and angle BDC = 24°.

Angle ADB = 90° = angle BCD. Calculate the length of (a) AD, Answer(a) AD = cm [3]

(b) CD. Answer(b) CD = cm [2]

12



0580/13/M/J/10

BLANK PAGE



*6596303759*


MATHEMATICS 0580/31


2 hours

















2

© UCLES 2010 0580/31/M/J/10

For

Examiner's

Use

1 The population of a village is 2250. (a) 32% of the population are children. Calculate the number of children in the village. Answer(a) [2]

(b) 360 people in the village are over the age of 60. (i) For these 360 people, the ratio of men to women is 2 : 7. Calculate how many men are over the age of 60. Answer(b)(i) [2]

(ii) Write 360 as a fraction of 2250 in its lowest terms. Answer(b)(ii) [2]

(c) The population of 2250 is expected to increase by 18% next year. Calculate the expected population next year. Answer(c) [3]

(d) Write the number 2250 in standard form. Answer(d) [1]

(e) Another village has a population of 1770, correct to the nearest ten. Write down the lower bound for the population of this village. Answer(e) [1]

3


For

Examiner's

Use

2

The diagram shows a block of stone in the shape of a prism of length 42 cm. The cross-section is a trapezium ABCD.

AB = 19 cm, AD = 10 cm, DC = 13 cm and angle ADC = 90°. (a) Calculate (i) the perimeter of the rectangular face ABFE, Answer(a)(i) cm [2]

(ii) the area of the cross-section ABCD, Answer(a)(ii) cm2 [3]

(iii) the volume of the block of stone. Answer(a)(iii) cm3 [2]

(b) The mass of 1 cubic centimetre of the stone is 4 grams. Calculate the mass of the block. Give your answer in kilograms.

Answer(b) kg [3]

A B

D C

E

H G

F

13 cm

19 cm

42 cm10 cm

NOT TOSCALE

4

© UCLES 2010 0580/31/M/J/10

For

Examiner's

Use

3 Twelve students each answer 30 questions in a quiz. The time taken and the number of correct answers for each student is given in the table.

Time taken in minutes

9 4 5 10 3 2 8 8 4 5 6 7

Number of correct answers

19 28 26 17 30 26 25 20 23 21 24 22

(a) Complete the scatter diagram below to show this information. The first six points have been plotted for you.

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

150 1 2 3 4 5 6

Time taken in minutes

7 8 9 10 11

Number ofcorrectanswers

[3]

5


For

Examiner's

Use

(b) What type of correlation does the scatter diagram show? Answer(b) [1]

(c) (i) Find the range of the time taken. Answer(c)(i) min [1]

(ii) Calculate the mean time taken. Answer(c)(ii) min [3]

(d) (i) Find the mode for the number of correct answers. Answer(d)(i) [1]

(ii) Find the median for the number of correct answers. Answer(d)(ii) [1]

(e) One of the 12 students is selected at random. Write down the probability that the student (i) took more than 8 minutes to answer the quiz, Answer(e)(i) [1]

(ii) took less than 5 minutes and had more than 24 correct answers. Answer(e)(ii) [2]

6

© UCLES 2010 0580/31/M/J/10

For

Examiner's

Use

4 A

NB C

29°

8.6 cm13.4 cm

NOT TOSCALE

In triangle ABC, AN = 8.6 cm and is perpendicular to BC.

Angle BAN = 29° and AC = 13.4 cm. (a) Use trigonometry to calculate (i) the length of BN, Answer(a)(i) BN = cm [3]

(ii) angle CAN. Answer(a)(ii) Angle CAN = [2]

(b) Calculate the length of NC. Answer(b) NC = cm [3]

7


For

Examiner's

Use

5

7

6

5

4

3

2

1

–1

–2

–3

–4

0–1–2–3–4–5–6–7 5 6 74321

y

x

A

B

C D

W

V U T

R

Q

P

S

(a) On the grid, draw the image of

(i) the flag ABCD after translation by

− 3

4, [2]

(ii) the flag ABCD after enlargement, scale factor 2, centre the origin, [2] (iii) the flag ABCD after reflection in the x-axis. [2] (b) Describe fully the single transformation which maps ABCD onto PQRS.

[2] (c) Describe fully the single transformation which maps ABCD onto TUVW.

[3]

8

© UCLES 2010 0580/31/M/J/10

For

Examiner's

Use

6 (a) Complete the table of values for the function x

y3

= , x ≠ 0.

x −3 −2.5 −2 −1.5 −1 −0.5 −0.3 0.3 0.5 1 1.5 2 2.5 3

y −1 −1.2 −2 −3 −6 3 2 1.5 1

[3]

(b) On the grid below, draw the graph of x

y3

= for −3 Y x Y −0.3 and 0.3 Y x Y 3.

[5]

y

x

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

0–1 1 2 3–2–3

9


For

Examiner's

Use

(c) Use your graph to solve the equation x

3 = 7.

Answer(c) x = [1]

(d) Complete the table of values for 13

2−=

xy .

x −3 0 3

y

[2]

(e) On the grid, draw the straight line 13

2−=

xy for −3 Y x Y 3. [2]

(f) Write down the co-ordinates of the points where the line 13

2−=

xy intersects

the graph of x

y3

= .

Answer(f) ( , ) and ( , ) [2]

7 4S a d= +

(a) Find S when a = 17 and d = − 5. Answer(a) S = [2]

(b) Find d when S = 37 and a = 5. Answer(b) d = [2]

(c) Make d the subject of the formula 4S a d= + .

Answer(c) d = [2]

10

© UCLES 2010 0580/31/M/J/10

For

Examiner's

Use

8 In this question give all your answers to 2 decimal places. (a) Ankuri lends her brother $275 for 4 years at a rate of 3.6% per year simple interest. Calculate the total amount her brother owes after 4 years. Answer(a) $ [3]

(b) Monesh invests $650 in a bank which pays 4% per year compound interest. Calculate the amount Monesh will have after 2 years. Answer(b) $ [3]

(c) Theresa and Ian have 400 euros (€) each. (i) Theresa changes her €400 for pounds (£) when the exchange rate is €1= £ 0.7857. Calculate the amount she receives. Answer(c)(i) £ [2]

(ii) Ian changes his €400 for dollars ($) when the exchange rate is $1= € 0.6374. Calculate the amount he receives. Answer(c)(ii) $ [3]

11


For

Examiner's

Use

9

Triangle ABC is drawn accurately. (a) Measure and write down (i) the length of AC, Answer(a)(i) AC = cm [1]

(ii) the size of angle CAB. Answer(a)(ii) Angle CAB = [1]

(b) Construct accurately the locus of all the points 7 cm from C. [2]

(c) The point X lies outside the triangle ABC, with CX = 7 cm and angle BCX= 67°. Draw accurately the line CX. [2]

(d) Draw the line BX. Measure and write down the length of this line.

Answer(d) BX = cm [1]

(e) Using a straight edge and compasses only, construct the locus of points equidistant from BC and from BX. [2]


C

A B

12

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2010 0580/31/M/J/10

For

Examiner's

Use

10

Look at the sequence of diagrams. (a) Diagram 2 has a height of 2. Write down the height of (i) Diagram 5, Answer(a)(i) [1]

(ii) Diagram 10, Answer(a)(ii) [1]

(iii) Diagram n. Answer(a)(iii) [1]

(b) Diagram 2 has a width of 3. Find the width of (i) Diagram 5, Answer(b)(i) [1]

(ii) Diagram 10, Answer(b)(ii) [1]

(iii) Diagram n. Answer(b)(iii) [2]

(c) There are 6 squares in Diagram 2 and 15 squares in Diagram 3. (i) Write down how many squares there are in Diagram 5. Answer(c)(i) [1]

(ii) Explain how this is found from the height and width of the diagram. Answer(c)(ii) [1]

(iii) Write down, in terms of n, how many squares there are in Diagram n. Answer(c)(iii) [1]




*4814804174*


MATHEMATICS 0580/32


2 hours

















2

© UCLES 2010 0580/32/M/J/10

For

Examiner's

Use

1 (a) (i) 1, 2 and 36 are factors of 36. Write down all the other factors of 36. Answer(a)(i) [2]

(ii) 1 and 2 are common factors of 36 and 90.

Write down two more common factors of 36 and 90. Answer(a)(ii) [2]

(b) Write down all the square numbers between 20 and 50.

Answer(b) [3]

(c) p and q are prime numbers.

p3 × q = 56

Find p and q. Answer(c) p =

q = [2]

3


For

Examiner's

Use

2 Francis earns $150 per week. He has $132 left after he pays his tax. (a) Calculate what percentage of his $150 he pays in tax. Answer(a) % [3]

(b) He divides the $132 between expenses, savings and family in the ratio

Expenses : Savings : Family = 15 : 7 : 11.

Calculate his expenses.

Answer(b) $ [3]

(c) His rent is $24 per week. What fraction of the $132 is this? Give your answer as a fraction in its simplest form. Answer(c) [2]

(d) His earnings of $150 per week increase by 8%. Calculate his new earnings. Answer(d) $ [2]

4

© UCLES 2010 0580/32/M/J/10

For

Examiner's

Use

3 Mrs Sesay leaves home by car at 13 30. After 15 minutes she stops at a shopping centre, 8 kilometres from home.

(a) Calculate the average speed for her journey. Give your answer in kilometres per hour.

Answer(a) km/h [2]

(b) She leaves the shopping centre half an hour later. She travels a further 12 kilometres at the speed of 36 km/h to Villeneuve.

(i) Write down the time when she leaves the shopping centre. Answer(b)(i) [1]

(ii) Calculate the time, in minutes, that she takes to travel from the shopping centre to

Villeneuve. Answer(b)(ii) min [2]

(iii) On the grid opposite, complete the travel graph showing her journey. [2] (c) Her son, Braima, also leaves home at 13 30 and cycles the 20 kilometres to Villeneuve. He cycles at a speed of 15 km/h. (i) Calculate how long his journey takes. Give your answer in hours and minutes. Answer(c)(i) h min [2]

(ii) Show his journey on the grid. [1] (iii) How many minutes after his mother does Braima arrive at Villeneuve? Answer(c)(iii) min [1]

5


For

Examiner's

Use

20

18

16

14

12

10

8

6

4

2

013 30 13 45 14 00 14 15 14 30 14 45 15 00

Villeneuve

Shoppingcentre

Home

Distancefrom home(km)

Time

6

© UCLES 2010 0580/32/M/J/10

For

Examiner's

Use

4

9

8

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7 8

Frequency

Number of goals per game Karen keeps a record of how many goals United score in each of 40 games. She draws a bar chart to show this information.

(a) Use the information in the bar chart to complete the frequency table below.

Number of goals per game 0 1 2 3 4 5 6 7 8

Frequency 0 2 1

Frequency × Number of goals 0 14 8

[2] (b) (i) How many goals did United score in the 40 games? Answer(b)(i) [1]

(ii) Calculate the mean number of goals scored per game. Answer(b)(ii) [2]

7


For

Examiner's

Use

(iii) Find the median. Answer(b)(iii) [2]

(iv) Write down the mode. Answer(b)(iv) [1]

(c) United won 23 games and lost 12 games. The other games ended in a draw. (i) How many games ended in a draw? Answer(c)(i) [1]

(ii) Complete the pie chart accurately to represent these results. Label the sectors.

[2] (d) If one game from the 40 is chosen at random, use the information in part (c) to find the

probability that United

(i) won, Answer(d)(i) [1]

(ii) did not draw. Answer(d)(ii) [1]

Won

8

© UCLES 2010 0580/32/M/J/10

For

Examiner's

Use

5 D C

A B140°

(x + 2) cm

x cm

NOT TOSCALEh cm

In the parallelogram ABCD, AB = (x + 2) cm, BC = x cm and angle ABC = 140°.

(a) When x = 10,

(i) use trigonometry to calculate the height, h cm, of the parallelogram, Answer(a)(i) h = [2]

(ii) calculate the area of the parallelogram. Answer(a)(ii) cm2 [1]

(b) For a different value of x, the perimeter of the parallelogram is 38 cm. Write down an equation in x and solve it. Answer(b) x =

[3]

9


For

Examiner's

Use

6 (a)

In the diagram, ABD is a straight line and angle ABC = 135°. (i) Find the size of angle CBD. Answer(a)(i) Angle CBD = [1]

(ii) A regular polygon has interior angles of 135°. Find the number of sides of the polygon. Answer(a)(ii) [2]

(iii) Write down the name of the polygon in part (a)(ii).

Answer(a)(iii) [1]

(b)

A, B, C, and D lie on a circle. AC is a diameter. FCG is a tangent to the circle at C. DE is parallel to CG. Find the values of x, y and z. Answer(b) x =

y =

z = [5]

64°

y°

x°

z°

F

C

G

B A

D

E

NOT TOSCALE

135°A B D

CNOT TOSCALE

10

© UCLES 2010 0580/32/M/J/10

For

Examiner's

Use

7 An area of land ABCDEF is in the shape of a hexagon. Part of a scale drawing of the land is shown on the opposite page. A pond, P, is inside the hexagon. On the plan, 1 centimetre represents 20 metres. Parts (a), (b), (c) and (f) must be completed using a ruler and compasses only.

All construction arcs must be clearly shown.

(a) On the land, AF = 80 m and EF = 100 m. On the scale drawing, find the point F, by construction. Draw the lines AF and EF. [2] (b) On the scale drawing, construct the perpendicular bisector of CD. Label the point M where the bisector crosses CD. [2] (c) On the scale drawing, construct the bisector of angle BCD. [2]

(d) The bisectors from part (b) and part (c) meet at L.

(i) Measure and write down the length of LM in centimetres. Answer(d)(i) cm [1]

(ii) Find the distance between L and M on the land. Give your answer in metres. Answer(d)(ii) m [1]

(e) Triangle CML is a field for sheep. Calculate the area of this field. Answer(e) m2 [2]

(f) There is also a field for cows inside the hexagon. This field is the region nearer to D than to C and less than 120 m from D. By constructing a suitable locus on the scale drawing, find and label this region R. [2]

11


For

Examiner's

Use

A

B

C D

EP

12

© UCLES 2010 0580/32/M/J/10

For

Examiner's

Use

8 (a) Complete the table for the function 18

y

x

= , (x ≠ 0).

x −18 −9 −6 −3 −2 −1 1 2 3 6 9 18

y −6 −9 −18 18 9 6

[3]

(b) On the grid below, draw the graph of 18

y

x

= for −18 Y x Y −1 and 1 Y x Y 18.

y

x

20

16

12

8

4

–4

–8

–12

–16

–20

4 8 12 16 20–20 –16 –12 –8 –4 0

[4]

(c) Write down the order of rotational symmetry of the graph. Answer(c) [1]

13


For

Examiner's

Use

(d) (i) On the grid, draw the graph of y = x. [1]

(ii) Write down the co-ordinates of the points of intersection of y = x and 18

y

x

= .

Answer(d)(ii) ( , ) and ( , ) [2]

(e) On the grid, draw the reflection of y = x in the y-axis. [1]

9 (a) Simplify the following expressions.

(i) 5k + 3p – 2 + p – 2k – 5 Answer(a)(i) [2]

(ii) 5y2 – 4x + 5x – 7y2

Answer(a)(ii) [2]

(b) Expand the following expressions.

(i) 3 ( 4 + 7g ) Answer(b)(i) [1]

(ii) 5m ( 5m2 – t2 )

Answer(b)(ii) [2]

14

© UCLES 2010 0580/32/M/J/10

For

Examiner's

Use

10 Three bolts at A, B and C join the rods AB, BC and CA to form the right-angled triangle, ABC. Angle ABC = 90°, AB = 8 cm and BC = 5 cm.

A B

C

8 cm

5 cmNOT TOSCALE

(a) Calculate

(i) the length of the rod AC,

Answer(a)(i) AC = cm [2] (ii) angle CAB.

Answer(a)(ii) Angle CAB = [2]

(b) Another right-angled triangle, ADE, is formed by adding rods to triangle ABC.

AC is extended to E and AB is extended to D, with more bolts at D and E. Rods AB and BD are the same length.

A B D

E

C NOT TOSCALE

(i) Complete the following statement.

Triangle ADE is to triangle ABC. [1]

(ii) Describe clearly the single transformation which maps triangle ABC onto triangle ADE.

Answer(b)(ii) [3]

15

© UCLES 2010 0580/32/M/J/10

For

Examiner's

Use


(c) The pattern of diagrams shown above is continued by adding more rods and bolts.

Complete the table below.

Diagram 1 2 3 4 5

Number of bolts 3 5 7

[2] (d) How many bolts are required for (i) Diagram 10, Answer(d)(i) [1]

(ii) Diagram n?

Answer(d)(ii) [2]

(e) The number of bolts in Diagram n is 47. Find the value of n. Answer(e) n =

[2]

16



0580/32/M/J/10

BLANK PAGE



*7186308287*


MATHEMATICS 0580/33


2 hours

















2

© UCLES 2010 0580/33/M/J/10

For

Examiner's

Use

1 A bookshop sold a total of 2750 books in January. (a) The ratio hardback books sold : paperback books sold was 4 : 7. Calculate how many paperback books were sold. Answer(a) [2]

(b) 24% of the 2750 books sold were non-fiction. Calculate how many non-fiction books were sold. Answer(b) [2]

(c) 330 cookery books were sold. Write 330 as a fraction of 2750 in its lowest terms. Answer(c) [2]

(d) In February, the bookshop sold 14% more than the 2750 books sold in January. Calculate the number of books sold in February. Answer(d) [3]

(e) The total value of the books sold in January was $9480 correct to the nearest 10 dollars. Write down the lower bound for this amount. Answer(e) $ [1]

(f) 35000 books were sold in a year. Write this number in standard form. Answer(f) [1]

3


For

Examiner's

Use

2 (a) Write down (i) five numbers which are multiples of 7, Answer(a)(i) , , , , [2]

(ii) two common multiples of 4 and 7. Answer(a)(ii) and [2]

(b) 10 12 13 16 17 23 25 39 From the list above, write down (i) a square number that is also an odd number, Answer(b)(i) [1]

(ii) a prime number that is one more than a square number. Answer(b)(ii) [1]

(c) n is an integer and n3 is between 60 and 70. Find the value of n. Answer(c) n = [1]

(d) k and m are prime numbers.

k2 + m = 23 Find k and m. Answer(d) k =

m = [2]

4

© UCLES 2010 0580/33/M/J/10

For

Examiner's

Use

3 (a) Complete the table of values for y = 5 + x – x2.

x −3 −2 −1 0 1 2 3

y −7 −1 5 3

[3]

(b) On the grid below draw the graph of y = 5 + x – x2 for –3 Y x Y 3.

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

0 1–1–2–3 2 3

y

x

[4] (c) Use your graph to solve the equation 5 + x – x2 = 2. Answer(c) x = or x = [2]

5


For

Examiner's

Use

(d) (i) Complete the table of values for y = 2x – 1.

x −3 0 3

y

[2]

(ii) On the grid, draw the straight line y = 2x – 1 for –3 Y x Y 3. [2] (iii) Write down the gradient of y = 2x – 1. Answer(d)(iii) [1]

(e) Write down the co-ordinates of the points where the line y = 2x – 1 intersects the graph of

y = 5 + x – x2. Answer(e) ( , ) and ( , ) [2]

4 (a) Solve the equation.

3(x + 1) + 5(x – 3) = 48 Answer(a) x = [3]

(b) Make f the subject of the formula g = 7f − 5. Answer(b) f = [2]

(c) Factorise completely 6xy − 10yz. Answer(c) [2]

6

© UCLES 2010 0580/33/M/J/10

For

Examiner's

Use

5

Triangles DAB and DCB form a kite ABCD.

Angle DAB = angle DCB = 90°. AD = DC = x cm and AB = BC = (x + 3) cm. (a) Complete the following statement. Triangle ADB is to triangle CDB. [1]

(b) When x = 8, calculate angle DBC. Answer(b) Angle DBC = [2]

(c) When x = 5, calculate (i) the area of triangle BCD, Answer(c)(i) cm2 [2]

(ii) the area of the kite ABCD. Answer(c)(ii) cm2 [1]

(d) For a different value of x, the perimeter of the kite is 62 cm. Write down and solve an equation to find this value of x. Answer(d) x = [3]

A C

D

B

x cmx cm

(x + 3) cm (x + 3) cm

NOT TOSCALE

7


For

Examiner's

Use

6 In triangle ABC, BC = 9 cm and AC = 11 cm. The side AB has been drawn for you.

A B (a) Using ruler and compasses only, complete the triangle ABC. [2] (b) Measure and write down the size of angle CAB. Answer(b) Angle CAB = [1]

(c) For the constructions below, use a straight edge and compasses only.

Leave in all your construction arcs.

(i) Construct the bisector of angle ABC. Label the point P where the bisector crosses AC. [2]

(ii) Construct the locus of points which are equidistant from A and from C. Label the point Q where the locus crosses AC. [2] (d) (i) Write down the length of PQ in centimetres.

Answer(d)(i) cm [1]

(ii) Shade the region inside the triangle which is nearer to AB than to BC and nearer to C than to A. [1]

(e) Triangle ABC is a scale drawing. The 9 cm line, BC, represents a wall 45 metres long. The scale of the drawing is 1 : n. Find the value of n.

Answer(e) n = [2]

8

© UCLES 2010 0580/33/M/J/10

For

Examiner's

Use

7 (a) The first four terms of a sequence are given below. 5 9 13 17 Write down (i) the next term, Answer(a)(i) [1]

(ii) the 8th term, Answer(a)(ii) [1]

(iii) an expression, in terms of n, for the nth term of the sequence. Answer(a)(iii) [2]

(b) The first four terms of a different sequence are given below. 4 10 18 28 (i) Find the next term. Answer(b)(i) [1]

(ii) The nth term of this sequence is n(n + p) where p is an integer. Find the value of p. Answer(b)(ii) p = [2]

(iii) Find the 100th term of this sequence. Answer(b)(iii) [1]

9


For

Examiner's

Use

8 Tom has 50 model cars. He has 10 blue cars and 19 red cars. He has no yellow cars. (a) Tom chooses a car at random. Write down the probability that it is (i) red, Answer(a)(i) [1]

(ii) red or blue, Answer(a)(ii) [1]

(iii) not blue, Answer(a)(iii) [1]

(iv) yellow. Answer(a)(iv) [1]

(b) The probability that a car is damaged is 1. How many cars are damaged? Answer(b) [1]

10

© UCLES 2010 0580/33/M/J/10

For

Examiner's

Use

9 The table below shows the number of visitors to a museum each day during one week.

Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday

Number of visitors

64 34 75 77 85 96 38

(a) Work out the mean number of visitors per day during this week.

Answer(a) [2] (b) Find the range. Answer(b) [1]

(c) On the grid below, draw a bar chart to show the information given in the table. Use a vertical scale of 1 cm to represent 10 visitors.

[5]

11


For

Examiner's

Use

10 In this question give all your answers correct to 2 decimal places. (a) A bank has an exchange rate of $1= € 0.6513. (i) Jonathan changes $500 into euros (€). Calculate the amount Jonathan receives. Answer(a)(i) € [2]

(ii) Arika changes €300 into dollars. Calculate the amount Arika receives. Answer(a)(ii) $ [3]

(b) Dania borrows $325 for 2 years at a rate of 3.8% per year simple interest. Calculate the total amount Dania owes after 2 years.

Answer(b) $ [3] (c) Lee borrows $550 for 2 years at a rate of 6% per year compound interest. Calculate the total amount Lee owes after 2 years. Answer(c) $ [3]


12



© UCLES 2010 0580/33/M/J/10

For

Examiner's

Use

11

Shapes A, B and C are shown on the grid. (a) Describe fully the single transformation which maps (i) shape A onto shape B,

Answer(a)(i) [2] (ii) shape A onto shape C.

Answer(a)(ii) [3] (b) On the grid draw the image of shape A after

(i) a translation by the vector 6

4

, [2]

(ii) an enlargement, scale factor 2, centre the origin. [2]

A

B

C

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

0 21 3 5–2 –1–3–5 –4–6–7–8 4 6

y

x



*5927902494*


MATHEMATICS 0580/11


1 hour

















2

© UCLES 2010 0580/11/O/N/10

For

Examiner's

Use

1 On Monday the temperature was − 3°C.

On Tuesday the temperature fell by 5°C. Write down the temperature on Tuesday. Answer °C [1]

2 Write 0.00387 in standard form. Answer [1]

3

The diagram is an accurate net for a solid shape. Write down the geometrical name for this solid shape. Answer [1]

4 On a map, a straight section of a canal is 3.5 cm long. The scale of the map is 1 cm to 5 km. Calculate the actual length of this straight section. Answer km [1]

3


For

Examiner's

Use

5 Sophie invests $450 at a rate of 1.5% per year simple interest. Calculate the interest she earns after 8 years. Answer $ [2]

6

A B


point A and from point B. Show clearly all your construction arcs. [2]

4

© UCLES 2010 0580/11/O/N/10

For

Examiner's

Use

7 A box is 12 cm high, correct to the nearest centimetre. Complete the statement about the height, h cm, of the box. Answer Y=h I [2]

8 The metal used to make a coin is a mixture of steel and copper. The ratio mass of steel : mass of copper is 108 : 7. The coin has a total mass of 230 milligrams. Calculate the mass of copper in this coin. Answer milligrams [2]

9

F

GH 6.3 m53°

NOT TOSCALE

Calculate the length FG. Answer m [2]

5


For

Examiner's

Use

10 Use your calculator to find the value of 25.63 .

Write down your answer (a) as it appears on your calculator, Answer(a) [1]

(b) correct to 4 significant figures. Answer(b) [1]

11 (a)

The diagram shows a rhombus. Draw all the lines of symmetry. [2] (b)

Shade two squares in the diagram above so that the figure has one line of symmetry and

no rotational symmetry. [1]

12 Solve the simultaneous equations.

183 =+ yx

3424 =− yx

Answer x =

y = [3]

6

© UCLES 2010 0580/11/O/N/10

For

Examiner's

Use

13 y

x

5

4

3

2

1

–1

–2

0–1–2–3–4 4321

P

Q

The points P ( 3 , 1 ) and Q (−1 , −1) are marked on the grid.

(a) Write down the vector .

Answer(a) =

[1]

(b) R and S are two more points.

PR =

−

1

2 and PS = 3 PR .

(i) Write down the vector PS .

Answer(b)(i) PS =

[1]

(ii) Mark the point S on the grid. [1]

7


For

Examiner's

Use

14 Simplify the following. (a) 80 Answer(a) [1]

(b) (x5)2 Answer(b) [1]

(c) p–3 ÷ p4 Answer(c) [1]

15 A tourist changes $900 to euros (€) when the exchange rate is €1 = $1.356. Calculate the amount he receives. Give your answer correct to 2 decimal places. Answer € [3]

8

© UCLES 2010 0580/11/O/N/10

For

Examiner's

Use

16 (a) Write down all the common factors of 30 and 42.

Answer(a) [2] (b) Write down the smallest number which is a multiple of both 12 and 18. Answer(b) [2]

17 Simon has ten cards, numbered 1 to 10. He chooses a card at random. Write down the probability that the number on the card is (a) 8, Answer(a) [1]

(b) 12, Answer(b) [1]

(c) an odd number, Answer(c) [1]

(d) not a multiple of 3. Answer(d) [1]

9


For

Examiner's

Use

18

35 cm

44 cm

NOT TOSCALE

A cylindrical tank, with radius 35 cm, is filled with water to a depth of 44 cm. (a) Calculate the area of the base of the tank. Answer(a) cm2 [2]

(b) Calculate the volume of water in the tank. Answer(b) cm3 [1]

(c) Change your answer to part (b) into litres. Answer(c) litres [1]

10

© UCLES 2010 0580/11/O/N/10

For

Examiner's

Use

19 In this question, you must show all the steps in your working. Without using a calculator, find the value of

(a) 5

42

3

11 ÷ ,

Answer(a) [3]

(b) 5

3

15

13+ .

Give your answer as a mixed number. Answer(b) [3]

11

© UCLES 2010 0580/11/O/N/10

For

Examiner's

Use

20

w° p° t°A

D C

B M

NOT TOSCALE

32°67°

The diagram shows a quadrilateral ABCD with DC parallel to AB.

(a) Write down the geometrical name for a quadrilateral with only one pair of parallel sides.

Answer(a) [1]

(b) ABM is a straight line and DC = AC.

Angle DCA = 32° and angle ACB = 67°.

Find the values of p, t and w, giving a reason for each answer.

Answer (b) p = because

[2]

t = because

[2]

w = because

[2]

12



© UCLES 2010 0580/11/O/N/10

BLANK PAGE



*2307185002*


MATHEMATICS 0580/12


1 hour

















2

© UCLES 2010 0580/12/O/N/10

For

Examiner's

Use

1

x° 79°

57°

NOT TOSCALE

The diagram shows a quadrilateral. Work out the value of x. Answer x = [1]

2 Caroline changed £200 into New Zealand dollars (NZ$). The exchange rate was £1 = NZ$2.56 . How many New Zealand dollars did she receive? Answer NZ$ [1]

3


For

Examiner's

Use

3 Francis recorded a temperature of −4°C on Sunday. By Monday it had gone down by 3°C. (a) Find the temperature on Monday. Answer(a) °C [1]

(b) On Tuesday the temperature was −1°C. Find the change in temperature between Monday and Tuesday. Answer(b) °C [1]

4 The distance from the Sun to the planet Saturn is 1 429 400 000 kilometres. Write this distance in standard form, correct to 3 significant figures. Answer km [2]

5 A factory makes doors that are each 900 millimetres wide, correct to the nearest millimetre.

Complete the statement about the width, w millimetres, of each door. Answer Y w I [2]

4

© UCLES 2010 0580/12/O/N/10

For

Examiner's

Use

6

NOT TOSCALE

6 cm

4 cm

15 cm

A

B

C

D

E

F

The triangles ABC and DEF are similar. AB = 6 cm, BC = 4 cm and DE = 15 cm. Calculate EF. Answer EF = cm [2]

7 Maria puts $600 into a bank account for 3 years at a rate of 3.4% per year compound interest. Calculate how much will be in the account at the end of the 3 years. Answer $ [3]

5


For

Examiner's

Use

8 (a) Factorise completely. 8pq + 12pr Answer(a) [2]

(b) Use your answer to part (a) to make p the subject of the formula below. s = 8pq + 12pr Answer(b) p = [1]

9

North

North

65°

P

Q NOT TOSCALE

840 m

The diagram shows a straight road PQ. PQ = 840m and the bearing of Q from P is 065°. (a) Work out the bearing of P from Q. Answer(a) [1]

(b) Calvin walks 7

4 of the distance from P to Q.

How far is he from Q? Answer(b) m [2]

6

© UCLES 2010 0580/12/O/N/10

For

Examiner's

Use

10 The heights of 43 children are measured to the nearest centimetre. Braima draws a bar chart from this information.

16

14

12

10

8

6

4

2

0120-129 130-139 140-149 150-159 160-169 170-179 180-189

Height (centimetres)

Frequency

A child is chosen at random. Write down, as a fraction, the probability that the child will be (a) in the group 140 – 149 cm, Answer(a) [1]

(b) less than 160 cm, Answer(b) [1]

(c) in the group 160 – 169 cm. Answer(c) [1]

7


For

Examiner's

Use

11

OA

DC

B

y°x°

55°NOT TOSCALE

The diagram shows a circle, centre O, with diameter BC. AB is a tangent to the circle at B and angle BCD = 55°. A straight line from A meets the circle at D and C. Calculate the value of (a) x, Answer(a) x = [2]


12 (a) Write down the value of x when

(i) 5x ÷ 52 = 54,

Answer(a)(i) x = [1]

(ii) 49

1 = 7

x.

Answer(a)(ii) x = [1]

(b) Write down the value of 3p0. Answer(b) [1]

8

© UCLES 2010 0580/12/O/N/10

For

Examiner's

Use

13 Dominic, Esther, Flora and Galena shared a pizza.

(a) Dominic ate 5

1 of the pizza and Esther ate

7

2 of the pizza.

Show that 35

18 of the pizza remained.

Do not use your calculator and show all your working. Answer (a)

[2]

(b) Flora ate 3

2 of the pizza that remained.

Find the fraction of the pizza that was left for Galena. Answer(b) [2]

14

4.95

860.537.89.6 ×−×

(a) (i) Rewrite this calculation with each number written correct to 1 significant figure.

Answer(a)(i) [1] (ii) Work out the answer to your calculation in part(a)(i). Do not use a calculator and show all your working. Answer(a)(ii) [2]

(b) Use your calculator to work out the correct answer to the original calculation. Answer(b) [1]

9


For

Examiner's

Use

15 Some children took part in a sponsored swim to raise money for charity. The scatter diagram shows the results for 10 of the children.

0

100

90

80

70

60

50

40

30

20

10

50 100 150 200 250 300 350 400 450 500 550 600

G B

F

E

J

D

C H

A

I

Moneyraised

($)

Distance (metres)

(a) (i) How much further did A swim than J ? Answer(a)(i) m [1]

(ii) How much more money did D raise than F ? Answer(a)(ii) $ [1]

(b) The results for 2 more children are given in the table below.

Child Distance (m) Money raised ($)

K 125 35

L 475 80

Plot the results for K and L on the scatter diagram. [1] (c) What type of correlation does the scatter diagram show? Answer(c) [1]

10

© UCLES 2010 0580/12/O/N/10

For

Examiner's

Use

16 Flags A and B are shown on the grid.

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

0–1–2–3–4–5–6 5 64321

A

B

(a) Describe fully the single transformation which maps flag A onto flag B.

Answer(a)

[3]

(b) On the grid, draw the translation of flag A by the vector

− 3

5. [2]

11


For

Examiner's

Use

17

AB =

− 3

3 AC =

−0

5

(a) Calculate AB + 3AC .

Answer(a)

[2]

(b) Write down .

Answer(b) =

[1]

(c) AC is drawn on the grid below.

AC

(i) On the grid, draw AB . [1]

(ii) Write down the obtuse angle between AB and AC .

Answer(c)(ii) [1]


12



© UCLES 2010 0580/12/O/N/10

For

Examiner's

Use

18

D C

A B

18 cm

NOT TOSCALE

The diagram shows a square ABCD. The length of the diagonal AC is 18 cm. (a) Calculate (i) the length of the side of the square, Answer(a)(i) cm [2]

(ii) the area of the square. Answer(a)(ii) cm2 [2]

(b) A, B, C and D lie on a circle with diameter AC. Calculate the area of this circle. Answer(b) cm2 [2]



*0472097942*


MATHEMATICS 0580/13


1 hour

















2

© UCLES 2010 0580/13/O/N/10

For

Examiner's

Use

1

Write down the name of the solid that can be made from the net shown in the diagram. Answer [1]

2 Write down all the square numbers which are factors of 100. Answer [2]

3



Answer(a) [1] (b) the order of rotational symmetry.

Answer(b) [1]

4 In a desert the temperature at noon was 38°C. At midnight the temperature was –3°C. (a) Find the change in temperature between noon and midnight. Answer(a) °C [1]

(b) At 02 00 the temperature was 4°C below the midnight temperature. Write down the temperature at 02 00. Answer(b) °C [1]

3


For

Examiner's

Use

5 Multiply out the brackets. x(2x + y) Answer [2]

6 Solve the equation.

43

12=

+x

Answer x = [2]

7 Work out 3 3

1007.2 − .

Give your answer correct to 3 decimal places. Answer [2]

8 Chris and Max share $45 in the ratio Chris:Max = 7 : 2 . Calculate how much Chris receives. Answer $ [2]

9 When Valentina was 10 years old, her mass was 32 kg. Two years later her mass had increased by 45%. Calculate Valentina’s mass when she was 12 years old. Answer kg [2]

4

© UCLES 2010 0580/13/O/N/10

For

Examiner's

Use

10 Change 18.75% into a fraction. Write your answer in its lowest terms. Answer [2]

11 Factorise completely. 3ac – 6ad Answer [2]

12 Simplify

3

2

11

−

.

Give your answer as a fraction. Answer [2]

13 Solve the simultaneous equations. 3x + y = 5 5x + y = 9 Answer x =

y = [2]

14 17 27 17 0.294 17

5

From the list of numbers, write down (a) a prime number, Answer(a) [1]

(b) an irrational number, Answer(b) [1]

(c) the smallest number. Answer(c) [1]

5


For

Examiner's

Use

15 Amiria invests $200 for 2 years at 3% per year compound interest. Calculate the total amount Amiria has at the end of the two years. Answer $ [3]

16

OT

A

U

C

BNOT TOSCALE

In the diagram, TAU is a tangent to the circle at A. AB is a diameter of the circle and AC = BC. Find (a) angle BCA, Answer(a) Angle BCA = [1]

(b) angle ABC, Answer(b) Angle ABC = [1]

(c) angle CAU. Answer(c) Angle CAU = [1]

6

© UCLES 2010 0580/13/O/N/10

For

Examiner's

Use

17 Insert brackets to make each statement correct. (a) 7 + 2 × 9 = 81 [1] (b) 36 ÷ 6 ÷ 2 = 12 [1] (c) 5 × 3 + 6 × 2 = 90 [1]

18

1 2 3 4 5 6 70

7

6

5

4

3

2

1

y

x

A

B

C

The diagram shows three points, A(1, 2), B(7, 5) and C(5, 7). (a) Write as column vectors

(i) AC ,

Answer(a)(i) AC =

[1]

(ii) CB .

Answer(a)(ii) CB =

[1]

(b) Use two of the symbols +, –, = in the spaces to make a correct statement. AC CB AB [1]

7


For

Examiner's

Use

19

0

2

6

y

x

The diagram shows a straight line passing through the points (0, 2) and (6, 0). Find the equation of this line in the form y = mx + c. Answer y = [3]

20

4 4 5 6 8

(a) The diagram shows 5 discs. One disc is chosen at random. (i) Which number is most likely to be chosen? Answer(a)(i) [1]

(ii) What is the probability that the number on the disc is even? Answer(a)(ii) [1]

(iii) What is the probability that the number on the disc is even and a factor of 20?

Answer(a)(iii) [1] (b) A disc is chosen at random from the discs with even numbers. What is the probability that the number on the disc is a factor of 20?

Answer(b) [1]

Questions 21 and 22 are printed on the next page

8



© UCLES 2010 0580/13/O/N/10

For

Examiner's

Use

21 0 0 0 1 2 2 4 4 5 9

The list shows the number of days absent in a school term for each of 10 students. Find the mode, the median and the mean for the number of days absent. Answer Mode =

Median =

Mean = [4]

22

08 00 08 05 08 10 08 15 08 20 08 25 08 30Time

Home

Shop

School


NOT TOSCALE

Rob walks to school each morning. One day, he leaves home at 08 00. He stops at a shop at 08 10 and stays there for 5 minutes. He then continues to school and arrives at 08 30. (a) Draw the travel graph for Rob’s journey from home to school. [3] (b) Rob’s average speed for the whole journey from home to school is 3.3 km/h. Calculate the distance from Rob’s home to school. Answer(b) km [2]



*1841370585*


MATHEMATICS 0580/31


2 hours

















2

© UCLES 2010 0580/31/O/N/10

For

Examiner's

Use

1 (a) Write down (i) a multiple of 7 between 80 and 90, Answer(a)(i) [1]

(ii) a prime number between 30 and 40, Answer(a)(ii) [1]

(iii) a square number between 120 and 130, Answer(a)(iii) [1]

(iv) a cube number between 100 and 200. Answer(a)(iv) [1]

(b) Write the following numbers in order, starting with the smallest.

0.31 5

9 55%

Answer(b) I I [2]

3


For

Examiner's

Use

2

O

S

R

P

T36°

NOT TOSCALE

The points P, R and S lie on a circle, centre O. ROT is a straight line and TS is a tangent to the circle at S.

Angle STO = 36°. (a) Write down the size of angle TSO, giving a reason for your answer.

Answer(a) Angle TSO = because

[2]

(b) (i) Calculate the size of angle TOS. Answer(b)(i) Angle TOS = [1]

(ii) Show that angle OPR = 63°. Answer(b)(ii) [2] (c) (i) Write down the size of angle PRS. Answer(c)(i) Angle PRS = [1]

(ii) Calculate the size of angle PSR. Answer(c)(ii) Angle PSR = [1]

4

© UCLES 2010 0580/31/O/N/10

For

Examiner's

Use

3

Month Total rainfall (mm) Average daily sunshine (hours)

January 79 6

February 84 7

March 62 4.5

April 46 1.5

May 53 3.5

June 54 1.5

The table shows some data about rainfall and sunshine. (a) For the rainfall, calculate (i) the mean, Answer(a)(i) mm [2]

(ii) the range. Answer(a)(ii) mm [1]

(b) For the sunshine, find (i) the mode, Answer(b)(i) h [1]

(ii) the median. Answer(b)(ii) h [2]

(c) Dinesh draws a pie chart to display the rainfall data. Calculate the sector angle for February. Answer(c) [2]

5


For

Examiner's

Use

(d) Amalia draws a pictogram to display the sunshine data for January and February.

January

February

March

(i) Complete the key for the pictogram.

[1] (ii) Complete the pictogram for March. [1] (e) Priya draws a scatter diagram to find the correlation between rainfall and sunshine for January

to June.

(i) Complete the scatter diagram below. January and February are plotted for you.

90

80

70

60

50

400 1 2 3

Average daily sunshine (hours)

4 5 6 7

Totalrainfall(mm)

[2]

(ii) What type of correlation does the scatter diagram show?

Answer(e)(ii) [1]

represents

6

© UCLES 2010 0580/31/O/N/10

For

Examiner's

Use

4 D C

BA

M LX

7 cm

7 cm

NOT TOSCALE

In the diagram, ABCD is a square of side 7 cm. BLC and DMA are equilateral triangles. (a) Find the perimeter of the shape ABLCDM. Answer(a) cm [1]

(b) (i) Write down the size of angle CBL. Answer(b)(i) Angle CBL = [1]

(ii) Calculate the length of LX. Answer(b)(ii) LX = cm [2]

(c) (i) Calculate the area of triangle BLC. Answer(c)(i) cm2 [2]

(ii) Calculate the area of the shape ABLCDM. Answer(c)(ii) cm2 [2]

7


For

Examiner's

Use

5 A shopkeeper buys cheese for $3.75 per kilogram and sells it for $5.10 per kilogram. (a) Calculate his percentage profit. Answer(a) % [3]

(b) Mrs Garcia buys cheese from the shopkeeper. Calculate the number of grams of cheese she can buy for $2.04 . Answer(b) g [2]

(c) The shopkeeper sells 7 kg of cheese and has 3 kg left. (i) He reduces his selling price of $5.10 per kilogram by 70%. Calculate the reduced price. Answer(c)(i) $ [2]

(ii) He sells the 3kg of cheese at the reduced price. Calculate the total amount of money he receives by selling all the cheese. Answer(c)(ii) $ [2]

8

© UCLES 2010 0580/31/O/N/10

For

Examiner's

Use

6 (a) Complete the table of values for 4

y

x

= , x ≠ 0 .

x −4 −3 −2 −1 − 0.5 0.5 1 2 3 4

y −1.3 −2 −8 8 4 2

[2]


y

x

= , for – 4 Y x Y – 0.5 and 0.5 Y x Y 4.

y

x–1–2–3–4 43210

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8 [4]

9


For

Examiner's

Use

(c) Complete the following statement.

The point (−2.5,

) lies on the graph of 4

y

x

= . [1]

(d) (i) On the grid, draw the line y = 5. [1]

(ii) Use your graphs to solve the equation 4

5x

= .

Answer(d)(ii) x = [1]

(e) (i) On the grid, draw the straight line joining the points (− 0.5 , − 8 ) and ( 2 , 2 ). [2] (ii) Find the gradient of this line. Answer(e)(ii) [1]

(iii) Write down the equation of this line in the form y = mx + c. Answer(e)(iii) y = [2]

10

© UCLES 2010 0580/31/O/N/10

For

Examiner's

Use

7 (a) Solve the equation. 4x + 3 = 2 + 6x

Answer(a) x = [2]

(b) Simplify.

7(3x – 4y) – 3(5x + 2y) Answer(b) [2]

(c) Factorise completely.

6g2 – 3g3 Answer(c) [2]

11


For

Examiner's

Use

8

PQ

R

y

x

6

5

4

3

2

1

–1

–2

–3

–4

–5

0–1–2–3–4–5–6–7 5 6 7432

Shapes P, Q, and R are shown on the grid. (a) On the grid, draw the image of shape P after

(i) a rotation through 180° about the origin, [2] (ii) a reflection in the line y = 3, [2]

(iii) a translation by the vector 5

3

−

. [2]

(b) Describe fully the single transformation which maps (i) shape P onto shape Q,

Answer(b)(i) [2]

(ii) shape P onto shape R .

Answer(b)(ii) [3]

12

© UCLES 2010 0580/31/O/N/10

For

Examiner's

Use

9

L M

R

210 km

325 km

North

NOT TOSCALE

The diagram shows three islands, L, M and R. L is due west of M and R is due south of M. LM = 210 km and LR = 325 km. (a) Calculate the distance RM. Answer(a) RM = km [3]

(b) (i) Use trigonometry to calculate angle LRM. Answer(b)(i) Angle LRM = [2]

(ii) Find the bearing of L from R. Answer(b)(ii) [2]

13


For

Examiner's

Use

(c) (i) A ferry travels directly from M to L. It leaves M at 06 15 and arrives at L at 13 45. Calculate the average speed of the ferry in kilometres per hour. Answer(c)(i) km/h [2]

(ii) The ferry then travels the 325 km from L to R at an average speed of 37 km/h. Calculate the time taken. Give your answer in hours and minutes, to the nearest minute. Answer(c)(ii) h min [3]

(iii) The ferry leaves L at 14 00. Use your answer to part (c)(ii) to find the time it arrives at R. Answer(c)(iii) [1]

14

© UCLES 2010 0580/31/O/N/10

For

Examiner's

Use

10

Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Each of the diagrams above shows one small shaded square and a number of small unshaded squares. The diagrams form a sequence. (a) Complete Diagram 5. [1] (b) Complete the table.

Diagram 1 2 3 4 5 50 n

Total number of small squares

1 4 9 16

Number of small shaded squares

1 1 1 1

Number of small unshaded squares

0 3 8 15

[7] (c) Diagram p has 9999 small unshaded squares. Find p. Answer(c) p = [1]

15

© UCLES 2010 0580/31/O/N/10

For

Examiner's

Use

11 Roberto earns a total of $p per week. He works for t hours each week and is paid a fixed amount per hour. He also receives a bonus of $k every week. The formula for p is

p = 8t + k. (a) Write down how much Roberto is paid per hour. Answer(a) $ [1]

(b) (i) Find how much Roberto earns in a week when he works for 40 hours and his bonus is $35. Answer(b)(i) $ [2]

(ii) Find how many hours Roberto works in a week when he earns $288 and his bonus is $24. Answer(b)(ii) h [3]

(c) Make t the subject of the formula. Answer(c) t = [2]

16



© UCLES 2010 0580/31/O/N/10

BLANK PAGE



*5557490338*


MATHEMATICS 0580/32


2 hours

















2

© UCLES 2010 0580/32/O/N/10

For

Examiner's

Use

1 A drink consists of water and fruit juice.

(a) 24% of the drink is water.

Show that there is a total of 760 cm3 of fruit juice in one litre of the drink.

Answer(a)

[2]

(b) What fraction of one litre of the drink is fruit juice?

Give your answer in its simplest form.

Answer(b) [2]

(c) The 760 cm3 of fruit juice in one litre of the drink is made from apple, mango and peach in the

following ratio.

Apple : Mango : Peach = 6 : 15 : 17

Calculate the amount of apple juice.

Answer(c) cm3 [2]

(d) A shopkeeper buys bottles of the drink for 65 cents each.

He sells them for 80 cents each.

Calculate the percentage profit he makes on each bottle he sells.

Answer(d) % [3]

3


For

Examiner's

Use

2 (a) (i) f × g = 90

f and g are both integers greater than 1.

Write down one possible pair of values of f and g.

Answer(a)(i) f = and g = [1]

(ii) Find all the prime factors of 90.

Answer(a)(ii) [3]

(b) Six number cards are shown below.

0 4 9 5 1 8

One or more of the cards are chosen to make different numbers.

For example 5 9 makes the number 59.

Choosing a card or cards, write down

(i) a 2-digit odd number less than 40,

Answer(b)(i) [1]

(ii) the largest 3-digit even number,

Answer(b)(ii) [1]

(iii) a 2-digit square number greater than 50,

Answer(b)(iii) [1]

(iv) a cube number,

Answer(b)(iv) [1]

(v) a 2-digit multiple of 13,

Answer(b)(v) [1]

(vi) the cube root of 64,

Answer(b)(vi) [1]

(vii) a prime number between 100 and 120.

Answer(b)(vii) [1]

4

© UCLES 2010 0580/32/O/N/10

For

Examiner's

Use

3 Kim left school at 15 30 to walk home.

On the way home he remembered he had left a book at school.

He ran back to school and arrived at 16 04.

The travel graph shows his journey.

4

3.5

3

2.5

2

1.5

1

0.5

015 30 15 40 15 50 16 00 16 10 16 20 16 30 16 40 16 50 17 00

Time

Distance(km)

School

Home

(a) Use the graph to answer the following questions.

(i) At what time did Kim start to run back to school?

Answer(a)(i) [1]

(ii) How far was he from school at this time?


(iii) How many minutes did he take to run back to school?

Answer(a)(iii) min [1]

(iv) What was his speed, in kilometres per hour, on his journey back to school?

Answer(a)(iv) km/h [3]

5


For

Examiner's

Use

(b) Kim spent 6 minutes at school collecting his book.

He then walked home at a speed of 6 km/h.

(i) Complete the travel graph. [3]

(ii) At what time did Kim arrive home?

Answer(b)(ii) [1]

(c) Kim’s sister, Julie, left the school at 15 48.

She walked at a steady speed, without stopping, and arrived home 46 minutes later.

(i) On the grid, draw the travel graph of Julie’s journey home from school. [2]

(ii) Complete the sentence.

arrived home first by minutes. [1]

6

© UCLES 2010 0580/32/O/N/10

For

Examiner's

Use

4 An accurate scale drawing of three sides of a garden, AB, BC, and CD is shown on the opposite page.

A is due north of B and C is due east of B.

(a) A vegetable area is to be constructed in the garden.

Parts (i) and (iii) must be completed using a straight edge and compasses only.

On the scale drawing

(i) construct the perpendicular bisector of BC, [2]

(ii) mark the point S at the midpoint of BC, [1]

(iii) construct the bisector of angle ABC, [2]

(iv) mark the point R where this line crosses the perpendicular bisector of BC, [1]

(v) mark the point Q on BA where BQ = SR, [1]

(vi) draw the vegetable area, quadrilateral BQRS. [1]

(b) On the scale drawing, 1 centimetre represents 6 metres.

Calculate the vegetable area in square metres.

Answer(b) m2 [3]

(c) A tree, T, is on a bearing of 070° from A and 345° from C.

On the scale drawing, mark the position of T. [2]

(d) Draw accurately the locus of points which are 24 metres from the tree, T. [2]

7


For

Examiner's

Use

North

North

C

D

B

A

Scale: 1 cm = 6 m

8

© UCLES 2010 0580/32/O/N/10

For

Examiner's

Use

5 y

x

12

10

8

6

4

2

–2

–4

–6

–8

–10

–12

0–2–4–6–8–10–12 10 128642

B

A

A graph is drawn on the grid.

Points A and B are marked on the curves.

(a) (i) Write down the co-ordinates of the points A and B.

Answer(a)(i) A( , ) and B( , ) [2]

(ii) The equation of the graph is xy = n.

Write down the value of n.

Answer(a)(ii) n = [1]

9


For

Examiner's

Use

(b) (i) Write down the order of rotational symmetry of the graph.

Answer(b)(i) [1]

(ii) On the grid, draw the lines of symmetry of the graph. [2]

(iii) Write down the equation of each line of symmetry.

Answer(b)(iii) and [2]

(c) (i) One line of symmetry crosses both curves.

Write down the x co-ordinates of the points where this line meets each curve.

Give your answers to 1 decimal place.

Answer(c)(i) x = and x = [2]

(ii) On the grid, draw the line which passes through the point (0, 4) and is parallel to the line of

symmetry in part (c)(i). [1]

(iii) Write down the equation of this line in the form y = mx + c.

Answer(c)(iii) y = [2]

10

© UCLES 2010 0580/32/O/N/10

For

Examiner's

Use

6 (a) The formula for finding the interior angle of a regular polygon with n sides is given below.

Interior angle = 180( 2)n

n

−

(i) Find the size of the interior angle of a regular polygon with 9 sides.

Answer(a)(i) [2]

(ii) Multiply out the brackets.

180(n – 2)

Answer(a)(ii) [1]

(iii) A regular polygon has an interior angle of 156°.

How many sides does this polygon have?

Answer(a)(iii) [3]


3x + 5y = 9

x + 2y = 4

Answer(b) x =

y = [3]

11


For

Examiner's

Use

7 C

D

A B50 cm

85 cm

65 cm

NOT TOSCALE

The diagram represents the cross-section of a storage box.

AB = 50 cm, AD = 65 cm and BC = 85 cm.

AD is parallel to BC.

(a) Write down the geometrical name of the quadrilateral ABCD.

Answer(a) [1]

(b) Calculate angle DCB.

Answer(b) Angle DCB = [3]

(c) Calculate the area of the cross-section ABCD.

Answer(c) cm2 [2]

(d) The storage box is 96 cm long.

Calculate the volume of the box.

Write down the units of your answer.

Answer(d) [2]

96 cm

12

© UCLES 2010 0580/32/O/N/10

For

Examiner's

Use

8 (a) The results of 24 games of hockey played by a school team in one year are shown in the pie

chart below.

Won

Drawn

Lost

(i) Show that the school team won 10 games during the year.

Answer(a)(i)

[2]

(ii) Find how many games were lost and how many games were drawn.

Answer(a)(ii) Lost

Drawn [3]

13


For

Examiner's

Use

(b) The number of goals scored by the hockey team in each of the 24 games are shown below.

0 2 1 1 0 3 2 5

3 0 2 3 2 1 4 0

2 1 2 1 0 1 4 1

(i) Complete the frequency table below. You may use the tally column to help you.

Number of goals per game Tally Number of games

0

1

2

3

4

5

[2]


Answer(b)(ii) [1]

(iii) Find the median.

Answer(b)(iii) [2]

(iv) Calculate the mean number of goals per game.

Answer(b)(iv) [3]

14

© UCLES 2010 0580/32/O/N/10

For

Examiner's

Use

9 B D

EA

C

2.7 cm 2.7

cm NOT TOSCALE

(a) In the diagram above, AB and ED are vertical.

The diagram is symmetrical about a line through C parallel to AB.

Angle BCD = 90° and BC = CD = 2.7 cm.

(i) Calculate BD.

Answer(a)(i) BD = cm [2]

(ii) Complete the statement.

Triangle BCD is right-angled and [1]

(iii) Find the size of angle ABC.

Answer(a)(iii) Angle ABC = [1]

15

© UCLES 2010 0580/32/O/N/10

For

Examiner's

Use


(b) The pattern of diagrams above is continued by adding more lines and dots.

(i) On the grid, draw diagram 4. [1]

(ii) Complete the table below.

Diagram 1 2 3 4 5

Number of lines 4 7

[2]

(c) How many lines will there be in

(i) Diagram 9,

Answer(c)(i) [1]

(ii) Diagram n?

Answer(c)(ii) [2]

(d) The number of lines in Diagram r is 76.

Find the value of r.

Answer(d) r = [2]

(e) Write down an expression, in terms of n, for the number of dots in Diagram n.

Answer(e) [1]

16



© UCLES 2010 0580/32/O/N/10

BLANK PAGE



*8229900006*


MATHEMATICS 0580/33


2 hours

















2

© UCLES 2010 0580/33/O/N/10

For

Examiner's

Use

1

10

9

8

7

6

5

4

3

2

1

00 1 2 3

Number of children4 5 6

Frequency

The number of children in each of 40 families was recorded. The bar chart shows the results. (a) Complete the frequency table.

Number of children 0 1 2 3 4 5 6

Frequency 4 6

[3] (b) Find (i) the mode, Answer(b)(i) [1]

(ii) the median,

Answer(b)(ii) [2]

3


For

Examiner's

Use

(iii) the mean. Answer(b)(iii) [3]

(c) A pie chart showing the information has been started. (i) Calculate the angles of the sectors for 3 and 4 children. Answer(c)(i) , [3]

(ii) Complete the pie chart accurately.

2 children

1 child

0 children

6 children

5 children

[1]

4

© UCLES 2010 0580/33/O/N/10

For

Examiner's

Use

2 Eduardo lives in Argentina and travels to Uruguay for a holiday. (a) His flight from Buenos Aires to Montevideo takes 55 minutes. The plane departs at 17 35. (i) Write down the arrival time. Answer(a)(i) [1]

(ii) The distance between Buenos Aires and Montevideo is 230 km. Calculate the average speed of the plane. Answer(a)(ii) km/h [3]

(b) At the airport, Eduardo changed some Argentine pesos (ARS). He received 9121 Uruguay pesos (UYU). (i) The exchange rate was ARS 1 = UYU 6.515. Calculate how many Argentine pesos Eduardo changed. Answer(b)(i) ARS [2]

(ii) Eduardo spent 1890 Uruguay pesos on meals. Calculate this as a percentage of the UYU 9121. Answer(b)(ii) % [1]

(iii) At the end of his holiday, Eduardo has UYU 610 remaining. He changes this into Argentine pesos when the exchange rate is UYU 1 = ARS 0.149. Calculate how much Eduardo receives in Argentine pesos. Give your answer to the nearest whole number. Answer(b)(iii) ARS [2]

5


For

Examiner's

Use

3

G H

F I

y

x

12

11

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

0–1 1 2 3 4 5 6 7 8 9 10–2–3–4–5

(a) Describe fully the single transformation that maps

(i) flag F onto flag G,

Answer(a)(i) [2] (ii) flag F onto flag H,

Answer(a)(ii) [2] (iii) flag F onto flag I.

Answer(a)(iii) [3]

(b) On the grid, draw

(i) the reflection of flag F in the y-axis, [2]

(ii) the enlargement of flag F, centre (0, 0) and scale factor 4. [2]

6

© UCLES 2010 0580/33/O/N/10

For

Examiner's

Use

4 North

200 m

75 mNOT TOSCALE

B

North

NorthC

A

Dariella walks 200 m from A to B. She then turns through 90° and walks 75 m from B to C. (a) Calculate (i) the distance AC, Answer(a)(i) m [2]

(ii) angle CAB. Answer(a)(ii) Angle CAB = [2]

(b) The bearing of B from A is 065°. Find the bearing of (i) C from A, Answer(b)(i) [1]

(ii) A from C, Answer(b)(ii) [1]

(iii) C from B. Answer(b)(iii) [2]

7


For

Examiner's

Use

5 C

D

A

B

The diagram shows a quadrilateral ABCD. (a) Using a straight edge and compasses only, construct (i) the perpendicular bisector of AB, [2] (ii) the bisector of angle ADC. [2] (b) Draw accurately the locus of points, inside the quadrilateral, that are 2 cm from BC. [2] (c) Shade the region, inside the quadrilateral, which is nearer to B than to A and nearer to DC than to DA and more than 2 cm from BC. [1]

8

© UCLES 2010 0580/33/O/N/10

For

Examiner's

Use

6

6 cm

12 cm

20 cm

8 cmD

A B

C

NOT TOSCALE

The diagram shows a prism of length 20 cm. The cross-section of the prism is a trapezium, ABCD, with AB parallel to DC. AB = 12 cm, DC = 8 cm and the perpendicular distance between AB and DC is 6 cm. (a) Calculate (i) the area of the trapezium ABCD, Answer(a)(i) cm2 [2]

(ii) the volume of the prism. Answer(a)(ii) cm3 [1]

9


For

Examiner's

Use

(b) The prism is solid and made of brass. (i) One cubic centimetre of brass has a mass of 8.5 grams. Calculate the mass of the prism. Give your answer in kilograms. Answer(b)(i) kg [2]

(ii) Brass costs $2.26 for one kilogram. How much will the brass cost to make this prism? Give your answer correct to 2 decimal places. Answer(b)(ii) $ [2]

10

© UCLES 2010 0580/33/O/N/10

For

Examiner's

Use

7 Alex has d dollars to spend. He buys a book which costs $9 less than 2 times d. (a) Write down an algebraic expression, in terms of d, for the cost of the book. Answer(a) $ [2]

(b) The actual cost of the book is $7.80. Find the value of d. Answer(b) d = [2]

(c) How much does Alex have left after buying the book? Answer(c) $ [1]

11


For

Examiner's

Use

8 The area, A, of a sector of a circle of radius r is given by the formula below.

A = 5

π2

r

(a) Calculate the area when the radius is 7.5 cm. Answer(a) cm2 [2]

(b) Make r the subject of the formula. Answer(b) r = [3]

(c) Calculate r when A = 4.8 cm2. Answer(c) r = cm [2]

12

© UCLES 2010 0580/33/O/N/10

For

Examiner's

Use

9 (a) (i) Complete the table for y = 12 – x2.

x 0 1 2 3 4

y 12 11 – 4

[2]

(ii) On the grid, draw the graph of y = 12 – x2 for 0 Y x Y 4. y

x

12

11

10

9

8

7

6

5

4

3

2

1

0

–1

–2

–3

–4

1 2 3 4 5 6 7 8

[3] (iii) Use your graph to solve the equation 12 – x2 = 0. Answer (a)(iii) x = [1]

13


For

Examiner's

Use

(b) (i) Complete the table for y = 12

,x

x ≠ 0 .

x 1 2 3 4 5 6 7 8

y 12 6 4 2.4 1.7

[3]

(ii) On the grid opposite, draw the graph of y = 12

x

for 1 Y x Y 8. [3]

(c) Write down the co-ordinates of the points of intersection of the two graphs. Answer(c) ( , ) , ( , ) [2]

14

© UCLES 2010 0580/33/O/N/10

For

Examiner's

Use

10 F E

A B

D

C

G

H

NOT TOSCALE

ABCDEFGH is a regular octagon. (a) Show that angle BCD = 135°. Answer (a)

[2] (b) Find (i) angle DEB, Answer(b)(i) Angle DEB = [1]

(ii) angle FEB. Answer(b)(ii) Angle FEB = [1]

15


For

Examiner's

Use

(c)

F E

A B

D

QR

PS

C

G

H

NOT TOSCALE

The sides of the octagon are extended to form the square PQRS. The length of each side of the octagon is 12 cm and the length of BP is 8.485 cm. Calculate the area of (i) triangle BPC, Answer(c)(i) cm2 [2]

(ii) the octagon ABCDEFGH. Answer(c)(ii) cm2 [3]


16



© UCLES 2010 0580/33/O/N/10

For

Examiner's

Use

11 (a) (i)

0, 1, 1, 2, 3, 5, 8, …. This sequence has the rule:

After the first two terms, any term is the sum of the two previous terms.

The first two terms are 0 and 1, the 3rd term is 0 + 1 = 1, the 4th term is 1 + 1 = 2, the 5th term is 1 + 2 = 3 and so on. Show that the 8th term is 13. Answer(a)(i) [1]

(ii) Each of the following sequences have the same rule as part (a)(i). For each sequence write down the missing terms.

2, 5, 7, , [1]

4, 3, 7, , [1]

5, 2, ,

[1]

0, , 3,

[1]

1, , , 9, [1]

, , 5, 7 [1]

(b) For the following sequences find the next term and the n th term.

(i) 1, 3, 5, 7, 9, n th term = [3]

(ii) 1, 4, 9, 16, 25, n th term = [2]

(iii) 1, 1

2,

3

1,

4

1,

5

1,

n th term =

[2]

Location Entry Codes As part of CIE’s continual commitment to maintaining best practice in assessment, CIE uses different variants of some question papers for our most popular assessments with large and widespread candidature. The question papers are closely related and the relationships between them have been thoroughly established using our assessment expertise. All versions of the paper give assessment of equal standard. The content assessed by the examination papers and the type of questions is unchanged. This change means that for this component there are now two variant Question Papers, Mark Schemes and Principal Examiner’s Reports where previously there was only one. For any individual country, it is intended that only one variant is used. This document contains both variants which will give all Centres access to even more past examination material than is usually the case. The diagram shows the relationship between the Question Papers, Mark Schemes and Principal Examiners’ Reports that are available. Question Paper

Mark Scheme Principal Examiner’s Report

Introduction

Introduction Introduction

First variant Question Paper

First variant Mark Scheme First variant Principal Examiner’s Report

Second variant Question Paper

Second variant Mark Scheme

Second variant Principal Examiner’s Report

Who can I contact for further information on these changes? Please direct any questions about this to CIE’s Customer Services team at: [email protected] The titles for the variant items should correspond with the table above, so that at the top of the first page of the relevant part of the document and on the header, it has the words:

• First variant Question Paper / Mark Scheme / Principal Examiner’s Report

or

• Second variant Question Paper / Mark Scheme / Principal Examiner’s Report

as appropriate.



*5862600330*


MATHEMATICS 0580/11, 0581/11


1 hour

















2

© UCLES 2009 0580/11/M/J/09

For

Examiner's

Use

1 [ < > = Y

Choose one of the above symbols to make a correct statement in the answer space.

Answer 0.4

4

9 [1]

2 (a) Calculate 0.0763

1.85 + 4.7×8.

Answer(a) [1]

(b) Write 0.0763 in standard form.

Answer(b) [1]

3 How many glasses, each holding 200 cm3, can be filled completely from a full 4.5 litre bottle of

water?

Answer [2]

3


For

Examiner's

Use

4 In the diagram AB is parallel to CD.

Calculate the value of a.

A

B

C

D a°

5a°

NOT TO SCALE

Answer a = [2]

5 Hakim and Bashira measure their heights.

Hakim’s height is 157 cm and Bashira’s height is 163 cm, both correct to the nearest centimetre.

Find the greatest possible difference between their heights.

Answer cm [2]

6 (a) Write down the gradient of the line y = 3x – 4.

Answer(a) [1]

(b) Write down the equation of a line through (0, 0) parallel to y = 3x – 4.

Answer(b) [1]

4

© UCLES 2009 0580/11/M/J/09

For

Examiner's

Use

7 A and B are two points marked on a map.

By measuring a suitable angle, find the bearing of A from B.

North

A

B

North

Answer [2]

8 Town E is 13 kilometres due east of D.

Town F is due south of E, and DF = 16 kilometres.

Calculate the distance from E to F.

D E

F

13 km

16 km

NorthNOT TOSCALE

Answer km [2]

5


For

Examiner's

Use

9 In 2007 Klaus paid 350 euros (€) for a flight from Berlin to Nairobi.

The return flight from Nairobi to Berlin cost him 30 700 Kenyan Shillings (KES).

The exchange rate at the time of the return flight was €1 = 79.6 KES.

Calculate the difference, in euros, between the costs of the two flights.


Answer € [2]

10 (a) Expand and simplify 5(3c – 4d) – 8c.

Answer(a) [2]

(b) Factorise pq – q2.

Answer(b) [1]

11 (a) Find the lowest common multiple of 7 and 9.

Answer(a) [1]

(b) Without using a calculator, work out 8 5_

9 7, leaving your answer as a fraction.

You must show all your working.

Answer(b) [2]

6

© UCLES 2009 0580/11/M/J/09

For

Examiner's

Use

12 z = 2x – y

(a) Find z when x = –3 and y = 7.

Answer(a) z = [1]

(b) Make x the subject of the formula.

Answer(b) x = [2]

13 The diagram shows an accurate drawing of a triangular field.

1 centimetre represents 15 metres.

Florentina walks along a straight path from A to the side BC.

The path is always the same distance from AB and AC.

C

A B

(a) Using a straight edge and compasses only, construct the line of the path.

You must show your construction arcs clearly. [2]

(b) The path meets BC at D.

How far, in metres, is Florentina from B when she reaches D?

Answer(b) m [1]

7


For

Examiner's

Use

14 x is an integer between 60 and 90.

Write down the value of x when it is

(a) an odd square number,

Answer(a) x = [1]

(b) 43,

Answer(b) x = [1]

(c) a multiple of 29,

Answer(c) x = [1]

(d) a prime factor of 146.

Answer(d) x = [1]

15 Simplify

(a) 3p × 5p3,

Answer(a) [2]

(b) 24q2 ÷ 8q –3.

Answer(b) [2]

8

© UCLES 2009 0580/11/M/J/09

For

Examiner's

Use

16 The diagram shows a square tile of side 10 centimetres with 4 identical quarter circles shaded.

10 cm

10 cm

Calculate the area of the unshaded region.

Answer cm2 [4]

9


For

Examiner's

Use

17

A

B

C

y

x

10

8

6

4

2

0 2 4 6 8 10

Points A, B and C are shown on the grid.

(a) Plot the point D on the grid above so that ABCD is a rhombus. [1]

(b) Write BD as a column vector.

Answer(b) BD =

[2]

(c) M is the mid-point of AC.


Answer(c) =

[1]

10

© UCLES 2009 0580/11/M/J/09

For

Examiner's

Use

18 The plan of a rectangular garden with 4 triangular flowerbeds is shown in the diagram.

(a) Write down the name of the special triangles that are

(i) shaded,

Answer(a)(i) [1]

(ii) unshaded.

Answer(a)(ii) [1]

(b) State the order of rotational symmetry of the plan.

Answer(b) [1]

(c) Draw the lines of symmetry on the plan. [2]

11

© UCLES 2009 0580/11/M/J/09

For

Examiner's

Use

19 A school has 350 students.

(a) On the school sports day 96% of the students were present.

Calculate how many students were absent.

Answer(a) [2]

(b) The table shows the number of students attending school in one week.

Monday Tuesday Wednesday Thursday Friday

334 329 348 341 323

For these values,


Answer(b)(i) [2]

(ii) find the median,

Answer(b)(ii) [1]

(iii) find the range.

Answer(b)(iii) [1]

12



0580/11/M/J/09

BLANK PAGE


IB09 06_0580_12/RP © UCLES 2009 [Turn over

*4608374430*


MATHEMATICS 0580/12, 0581/12


1 hour

















2

© UCLES 2009 0580/12/M/J/09

For

Examiner's

Use

For

Examiner's

Use

1 [ < > = Y

Choose one of the above symbols to make a correct statement in the answer space.

Answer

7

9 0.7 [1]

2 (a) Calculate 0.0584

1.65 + 5.2×7.

Answer(a) [1]

(b) Write 0.0584 in standard form.

Answer(b) [1]

3 How many glasses, each holding 200 cm3, can be filled completely from a full 3.5 litre bottle of

water?

Answer [2]

3


For

Examiner's

Use

For

Examiner's

Use

4 In the diagram AB is parallel to CD.

Calculate the value of a.

A

B

C

D a°

5a°

NOT TO SCALE

Answer a = [2]

5 Hakim and Bashira measure their heights.

Hakim’s height is 159 cm and Bashira’s height is 167 cm, both correct to the nearest centimetre.

Find the greatest possible difference between their heights.

Answer cm [2]

6 (a) Write down the gradient of the line y = 3x – 4.

Answer(a) [1]

(b) Write down the equation of a line through (0, 0) parallel to y = 3x – 4.

Answer(b) [1]

4

© UCLES 2009 0580/12/M/J/09

For

Examiner's

Use

7 A and B are two points marked on a map.

By measuring a suitable angle, find the bearing of A from B.

North

A

B

North

Answer [2]

8 Town E is 14 kilometres due east of D.

Town F is due south of E, and DF = 17 kilometres.

Calculate the distance from E to F.

D E

F

14 km

17 km

NorthNOT TOSCALE

Answer km [2]

5


For

Examiner's

Use

9 In 2007 Klaus paid 350 euros (€) for a flight from Berlin to Nairobi.

The return flight from Nairobi to Berlin cost him 30 700 Kenyan Shillings (KES).

The exchange rate at the time of the return flight was €1 = 79.6 KES.

Calculate the difference, in euros, between the costs of the two flights.


Answer € [2]

10 (a) Expand and simplify 4(5c – 3d) – 7c.

Answer(a) [2]

(b) Factorise m2 – mn.

Answer(b) [1]

11 (a) Find the lowest common multiple of 7 and 9.

Answer(a) [1]

(b) Without using a calculator, work out 8 5_

9 7, leaving your answer as a fraction.

You must show all your working.

Answer(b) [2]

6

© UCLES 2009 0580/12/M/J/09

For

Examiner's

Use

12 z = 2x – y

(a) Find z when x = –3 and y = 7.

Answer(a) z = [1]

(b) Make x the subject of the formula.

Answer(b) x = [2]

13 The diagram shows an accurate drawing of a triangular field.

1 centimetre represents 15 metres.

Florentina walks along a straight path from A to the side BC.

The path is always the same distance from AB and AC.

C

A B

(a) Using a straight edge and compasses only, construct the line of the path.

You must show your construction arcs clearly. [2]

(b) The path meets BC at D.

How far, in metres, is Florentina from B when she reaches D?

Answer(b) m [1]

7


For

Examiner's

Use

14 x is an integer between 60 and 90.

Write down the value of x when it is

(a) an odd square number,

Answer(a) x = [1]

(b) 43,

Answer(b) x = [1]

(c) a multiple of 29,

Answer(c) x = [1]

(d) a prime factor of 146.

Answer(d) x = [1]

15 Simplify

(a) 4d × 6d 4,

Answer(a) [2]

(b) 28t3 ÷ 7t –4.

Answer(b) [2]

8

© UCLES 2009 0580/12/M/J/09

For

Examiner's

Use

16 The diagram shows a square tile of side 10 centimetres with 4 identical quarter circles shaded.

10 cm

10 cm

Calculate the area of the unshaded region.

Answer cm2 [4]

9


For

Examiner's

Use

17

A

B

C

y

x

10

8

6

4

2

0 2 4 6 8 10

Points A, B and C are shown on the grid.

(a) Plot the point D on the grid above so that ABCD is a rhombus. [1]

(b) Write BD as a column vector.

Answer(b) BD =

[2]

(c) M is the mid-point of AC.


Answer(c) =

[1]

10

© UCLES 2009 0580/12/M/J/09

For

Examiner's

Use

18 The plan of a rectangular garden with 4 triangular flowerbeds is shown in the diagram.

(a) Write down the name of the special triangles that are

(i) shaded,

Answer(a)(i) [1]

(ii) unshaded.

Answer(a)(ii) [1]

(b) State the order of rotational symmetry of the plan.

Answer(b) [1]

(c) Draw the lines of symmetry on the plan. [2]

11

© UCLES 2009 0580/12/M/J/09

For

Examiner's

Use

19 A school has 360 students.

(a) On the school sports day 95% of the students were present.

Calculate how many students were absent.

Answer(a) [2]

(b) The table shows the number of students attending school in one week.

Monday Tuesday Wednesday Thursday Friday

334 329 348 341 323

For these values,


Answer(b)(i) [2]

(ii) find the median,

Answer(b)(ii) [1]

(iii) find the range.

Answer(b)(iii) [1]

12



0580/12/M/J/09

BLANK PAGE



*6159588306*

For Examiner's Use


MATHEMATICS 0580/03, 0581/03


2 hours






You may use a soft pencil for any diagrams or graphs.


DO NOT WRITE ON ANY BARCODES.









2

© UCLES 2009 0580/03/M/J/09

For

Examiner's

Use

1 (a) Roberto owns 6000 square metres of land. He divides it between himself and his two children, Stefano and Tania, in the ratio Roberto : Stefano : Tania = 7 : 5 : 3. (i) Show that Roberto now has 2800 square metres of land. Answer(a)(i) [2] (ii) Calculate the area of land that Stefano and Tania each have. Answer(a)(ii) Stefano m2

Tania m2 [2]

(b) Roberto receives a rent of $1.40 per month for each square metre of his land. (i) Calculate the rent he receives in one year from his 2800 square metres of land. Answer(b)(i) $ [2]

(ii) Roberto uses 3

5 of this amount to buy more land.

Calculate the amount that he uses to buy more land. Answer(b)(ii) $ [2]

3


For

Examiner's

Use

(c) Stefano builds a house on his land. He borrows $5000 from a bank at 8% per year simple interest. Find the total amount of interest he will have paid at the end of 3 years. Answer(c) $ [2]

(d) Tania sells her land for $12 000.

She invests the money for 3 years at 6% per year compound interest. Calculate the total amount of money she will have at the end of the 3 years. Give your answer to the nearest dollar. Answer(d) $ [4]

4

© UCLES 2009 0580/03/M/J/09

For

Examiner's

Use

2 The diagram represents a fairground wheel with centre O, and diameter 30 metres. Point D is vertically below point A, and the line EDB is horizontal. ED = 20 metres.

O

C

A

BDE

NOT TOSCALE

30 m

20 m (a) A seat starts at B and travels one-third of the circumference to A. Explain why angle AOB equals 120°. Answer(a)

[1] (b) Find the value, in degrees, of (i) angle ABO, Answer(b)(i) Angle ABO = [1]

(ii) angle BAC, Answer(b)(ii) Angle BAC = [1]

(iii) angle ABD. Answer(b)(iii) Angle ABD = [1]

5


For

Examiner's

Use

(c) (i) Use trigonometry in triangle ABC to calculate the distance AB. Answer(c)(i) AB = m [2]

(ii) Show that AD = 22.5 metres. Answer(c)(ii) [2] (d) Eshe holds her camera at E and takes a photograph of her friend in the seat at A. Calculate angle AED. Answer(d) [2]

6

© UCLES 2009 0580/03/M/J/09

For

Examiner's

Use

3 All the times given in this question are the local time in Paris.

Pierre left Paris at 08 00 to go to his office in London. He travelled 30 kilometres to the airport. He arrived at 08 30 and his plane left one hour later. It flew 350 kilometres to London airport and landed at 10 15. Pierre left London airport at 10 50 and he arrived at his office in London 40 minutes later. (a) On the grid below, complete the travel graph.

400

300

200

100

Distancetravelled

(km)

Londonoffice

Paris08 00 08 30 09 00 09 30 10 00 10 30 11 00 11 30

Time [4]

7


For

Examiner's

Use

(b) (i) How long is the flight from Paris to London? Give your answer in hours. Answer(b)(i) h [1]

(ii) Calculate the average speed of the flight, in kilometres/hour. Answer(b)(ii) km/h [2]

(c) Pierre’s colleague, Annette, travelled from Paris to London by train.

She left at 09 50 and arrived at the London office at 12 45. Calculate the difference in the times taken by Pierre and Annette for the whole journey. Give your answer in minutes. Answer(c) min [3]

8

© UCLES 2009 0580/03/M/J/09

For

Examiner's

Use

4 (a) Garcia and Elena are each given x dollars.

(i) Elena spends 4 dollars. Write down an expression in terms of x for the number of dollars she has now. Answer(a)(i) $ [1]

(ii) Garcia doubles his money by working and then is given another 5 dollars. Write down an expression in terms of x for the number of dollars he has now. Answer(a)(ii) $ [1]

(iii) Garcia now has three times as much money as Elena. Write down an equation in x to show this. Answer(a)(iii) [1]

(iv) Solve the equation to find the value of x. Answer(a)(iv) x = [3]

(b) Solve the simultaneous equations

3x – 2y = 3, x + 4y = 8.

Answer(b) x =

y = [3]

9


For

Examiner's

Use

5

10

8

6

4

2

–2

–4

–6

–8

–10

0–2–4–6–8–10 108642

y

x

A B

(a) Two different single transformations can map shape A onto shape B. Describe each transformation fully.

Answer(a)

or [4] (b) Reflect shape A in the x axis. Draw the image and label it C. [2] (c) Rotate shape B through 90° clockwise about the origin. Draw the image and label it D. [2] (d) Describe fully the single transformation which maps shape C onto shape B.

Answer(d) [3]

(e) Draw the enlargement of shape A, centre (– 4, 8), with scale factor 1

2.

Label the image E. [2]

10

© UCLES 2009 0580/03/M/J/09

For

Examiner's

Use

6 (a) Write down the name of a polygon with 8 sides. Answer(a) [1]

(b) Find the size of the interior angle of a regular polygon with 8 sides. Answer(b) [2]

(c) A regular 8-sided polygon, centre O, and side 8 cm, is shown below. M is the mid-point of the side AB.

O

A M8 cm

B

F E

C

D

H

G

NOT TOSCALE

(i) Show that OM = 9.66 cm correct to 3 significant figures. Answer (c)(i) [3]

11


For

Examiner's

Use

(ii) Calculate the area of the triangle AOB. Answer(c)(ii) cm2 [2]

(iii) Calculate the area of the polygon. Answer(c)(iii) cm2 [1]

(d) The polygon forms the cross-section of a box. The box is a prism of height 12 cm.

Calculate the volume of the box. Answer(d) cm3 [1]

(e) The box contains 200 toffees in the shape of cuboids, 3 cm by 2 cm by 2 cm. Calculate (i) the total volume of the 200 toffees, Answer(e)(i) cm3 [2]

(ii) the percentage of the volume of the box not filled by the toffees. Answer(e)(ii) % [3]

12

© UCLES 2009 0580/03/M/J/09

For

Examiner's

Use

7 y = 9x – x2. (a) Complete the table of values for this equation.

x 0 1 2 3 4 5 6 7 8 9

y 8 20 20 8 0

[3]

(b) On the grid below, draw the graph of y = 9x – x2 for 0 Y x Y 9.

22

20

18

16

14

12

10

8

6

4

2

1 2 3 4 5 6 7 8 9

y

x0

[4]

13


For

Examiner's

Use

(c) Write down the values of x and y at the highest point of the curve. Answer(c) x =

y = [2]

(d) (i) On the grid, draw the line y = 6 for 0 Y x Y 9. [1] (ii) Use this line to find the solutions of the equation

9x – x2 = 6. Give your answers correct to one decimal place. Answer(d)(ii) x = or x = [2]

14

© UCLES 2009 0580/03/M/J/09

For

Examiner's

Use

8 The table below shows the age and price of 20 used cars in a showroom.

Age (years) 6 5 4 5 4 5 1 6 3 8

Price ($) 1800 7600 9500 2500 4100 3100 5600 4700 4800 7900

Age (years) 1 2 9 10 3 7 1 8 2 3

Price ($) 6500 7000 1000 3800 1900 5200 3400 2100 4300 8200

(a) Use this information to complete the following table.

Age of cars (years) Number of cars Angle in a pie chart

1 to 3 8 144°

4 to 6 7

7 or more

[3] (b) (i) Complete the frequency table for the price, $x, of the cars.

Price ($) 0 Y x < 2000 2000 Y x < 4000 4000 Y x < 6000 6000 Y x < 8000 8000 Y x < 10 000

Frequency

[2] (ii) Draw a histogram to show this information.

6

5

4

3

2

1

0 2000 4000 6000 8000 10 000

Price of car ($)

Frequency

[2]

15


For

Examiner's

Use

(c) (i) On the grid below complete the scatter diagram showing the age and price of each car. The first 10 points from the original table have been plotted.

0 1 2 3 4 5 Age of car (years)

6 7 8 9 10

10 000

9000

8000

7000

6000

5000

4000

3000

2000

1000

Price of car ($)

[3] (ii) What correlation is there between the price of a car and its age?

Answer(c)(ii) [1] (iii) A car is chosen at random. Using your scatter diagram, find the probability that the car is more than 4 years old and

the price is more than $5000. Answer(c)(iii) [2]

Question 9 is on the next page

16



© UCLES 2009 0580/03/M/J/09

For

Examiner's

Use

9 (a) The first four terms of a sequence are 12, 7, 2, –3. (i) Write down the next two terms of the sequence. Answer(a)(i) and [2]

(ii) State the rule for finding the next term of the sequence. Answer(a)(ii) [1]

(iii) Write down an expression for the nth term of this sequence. Answer(a)(iii) [2]

(b) The first four terms of another sequence are −3, 2, 7, 12. Write down an expression for the nth term of this sequence. Answer(b) [2]

(c) Add together the expressions for the nth terms of both sequences. Write your answer as simply as possible. Answer(c) [1]



*0999494023*

For Examiner's Use


MATHEMATICS 0580/11


1 hour
















2

© UCLES 2009 0580/11/O/N/09

For

Examiner's

Use

1 Insert one pair of brackets to make the following equation correct.

2 × 8 − 5 − 4 = 15

[1]

2 Write the following numbers in order starting with the smallest.

2

7 0.283 28 %

Answer < < [1]

3 Find the volume of a cube with sides of 2.3 cm.

Answer cm3 [1]

4

North

North

72°A

B

NOT TOSCALE

The diagram shows the position of two airports, A and B.

The bearing of B from A is 072°.

Work out the bearing of A from B.

Answer [2]

3


For

Examiner's

Use

5 The number of spectators, N, at a football match is 16 000, correct to the nearest thousand.

Complete the statement for N in the answer space.

Answer Y N < [2]

6 Work out the value of 3

3 1

4 7×1 .

Show all your working and leave your answer as a fraction.

Answer [2]

7 A

B C


AB and from BC.

Show clearly all your construction arcs. [2]

4

© UCLES 2009 0580/11/O/N/09

For

Examiner's

Use

8 4 8 25 5

2 0.3333

From the list above, write down

(a) a prime number,

Answer(a) [1]

(b) an irrational number.

Answer(b) [1]

9 A train sets off at 11 53 on a journey to Mumbai.

The journey takes 2 hours 30 minutes.

(a) Write down the time when the train arrives in Mumbai.

Answer(a) [1]

(b) The distance to Mumbai is 235 kilometres.

Calculate the average speed of the train.

Answer(b) km/h [2]

5


For

Examiner's

Use

10 Solve the simultaneous equations

5x − y = 15,

7x − 5y = 3.

Answer x =

y = [3]

11

15

10

5

0 5 10 15 20 25Kilometres

Miles

Distance can be measured in miles or kilometres. 24 kilometres is approximately equal to 15 miles.

(a) Draw a straight line on the grid to show the conversion between kilometres and miles. [2]

(b) Use your graph to estimate the number of kilometres equal to 12 miles.

Answer (b) km [1]

6

© UCLES 2009 0580/11/O/N/09

For

Examiner's

Use

12

4 cm

7 cm

NOT TOSCALE

The diagram shows a triangular prism of length 7 cm.

The cross-section is an equilateral triangle of side 4 cm.

Complete an accurate net of the prism.

One rectangular face has been drawn for you.

[3]

7


For

Examiner's

Use

13

–3 –2 –1

–1

–2

–3

–4

3

4

5

2

1

10 2 3 4 5

y

x

F

G

The points F and G are shown on the grid.

(a) Write down the co-ordinates of the point F.

Answer(a)( , ) [1]


Answer(b) = ( ) [1]

(c) GH =

_2

_7

. Mark and label the point H on the grid. [1]

8

© UCLES 2009 0580/11/O/N/09

For

Examiner's

Use

14 (a) Find the value of p when p3 = −27.

Answer(a) p = [1]

(b) Find the value of q when q

−1 = 1

6.

Answer(b) q = [1]

(c) Simplify 8s

2 ÷ 2s

−1.

Answer(c) [2]

15 J = 3

md

(a) Find the value of d when J = 35 and m = 7.

Answer(a) d = [2]


Answer(b) d = [2]

9


For

Examiner's

Use

16 As the earth rotates, a point on the equator moves round at a speed of 1669.8 kilometres/hour.

(a) Write down this number in standard form, correct to 3 significant figures.

Answer(a) [2]

(b) Change 1669.8 kilometres/hour into metres/second.

Answer(b) m/s [2]

17 (a) Factorise 5x2 + 4xy.

Answer (a) [1]

(b) Simplify completely 7(2x + y) − 3(3x − 2y).

Answer (b) [3]

10

© UCLES 2009 0580/11/O/N/09

For

Examiner's

Use

18

T

P

W

Q R

S

38° 105°

NOT TOSCALE

The lines PS and QT intersect at W.

PQR is a straight line.

Angle SPR = 38° and angle TQR = 105°.

Write down the size of the following angles.

In each case give a reason for your answer.

(a) Angle PQW = because

[2]

(b) Angle PWQ = because

[2]

(c) Angle TWS = because

[2]

11

© UCLES 2009 0580/11/O/N/09

For

Examiner's

Use

19

Silver

RedYellow

Other

The accurate pie chart shows information about the colours of 240 cars in a car park.

(a) The sector angle for silver cars is 90°.

Calculate the number of silver cars in the car park.

Answer(a) [1]

(b) There are 36 yellow cars in the car park.

Showing all your working, calculate the sector angle for yellow cars.

Answer(b) [2]

(c) (i) Measure and write down the sector angle for red cars.

Answer(c)(i) [1]

(ii) Calculate the percentage of red cars in the car park.

Answer(c)(ii) % [2]

12



0580/11/O/N/09

BLANK PAGE



*9591019568*

For Examiner's Use


MATHEMATICS 0580/12


1 hour
















2

© UCLES 2009 0580/12/O/N/09

For

Examiner's

Use

For

Examiner's

Use

1 Insert one pair of brackets to make the following equation correct.

2 × 8 − 5 − 4 = 15

[1]

2 Write the following numbers in order starting with the smallest.

2

7 0.283 28 %

Answer < < [1]

3 Find the volume of a cube with sides of 3.8 cm.

Answer cm3 [1]

4

North

North

72°A

B

NOT TOSCALE

The diagram shows the position of two airports, A and B.

The bearing of B from A is 072°.

Work out the bearing of A from B.

Answer [2]

3


For

Examiner's

Use

For

Examiner's

Use

5 The number of spectators, N, at a football match is 16 000, correct to the nearest thousand.

Complete the inequality for N in the answer space.

Answer Y N < [2]

6 Work out the value of 2

2 1

3 11

×1 .

Show all your working and leave your answer as a fraction.

Answer [2]

7 A

B C


AB and from BC.

Show clearly all your construction arcs. [2]

4

© UCLES 2009 0580/12/O/N/09

For

Examiner's

Use

8 4 8 25 5

2 0.3333

From the list above, write down

(a) a prime number,

Answer(a) [1]

(b) an irrational number.

Answer(b) [1]

9 A train sets off at 10 48 on a journey to Mumbai.

The journey takes 4 hours 30 minutes.

(a) Write down the time when the train arrives in Mumbai.

Answer(a) [1]

(b) The distance to Mumbai is 441 kilometres.

Calculate the average speed of the train.

Answer(b) km/h [2]

5


For

Examiner's

Use

For

Examiner's

Use


5x − 3y = 3,

6x − y = 14.

Answer x =

y = [3]

11

15

10

5

0 5 10 15 20 25Kilometres

Miles

Distance can be measured in miles or kilometres. 24 kilometres is approximately equal to 15 miles.

(a) Draw a straight line on the grid to show the conversion between kilometres and miles. [2]

(b) Use your graph to estimate the number of kilometres equal to 7 miles.

Answer (b) km [1]

6

© UCLES 2009 0580/12/O/N/09

For

Examiner's

Use

12

4 cm

7 cm

NOT TOSCALE

The diagram shows a triangular prism of length 7 cm.

The cross-section is an equilateral triangle of side 4 cm.

Complete an accurate net of the prism.

One rectangular face has been drawn for you.

[3]

7


For

Examiner's

Use

For

Examiner's

Use

13

–3 –2 –1

–1

–2

–3

–4

3

4

5

2

1

10 2 3 4 5

y

x

F

G

The points F and G are shown on the grid.

(a) Write down the co-ordinates of the point F.

Answer(a)( , ) [1]


Answer(b) = ( ) [1]

(c) =

_5

_3

. Mark and label the point H on the grid. [1]

8

© UCLES 2009 0580/12/O/N/09

For

Examiner's

Use

14 (a) Find the value of p when p3 = −27.

Answer(a) p = [1]

(b) Find the value of q when q

−1 = 1

6.

Answer(b) q = [1]

(c) Simplify 8s

2 ÷ 2s

−1.

Answer(c) [2]

15 J = 3

md

(a) Find the value of d when J = 32 and m = 8.

Answer(a) d = [2]


Answer(b) d = [2]

9


For

Examiner's

Use

For

Examiner's

Use

16 As the earth rotates, a point on the equator moves round at a speed of 1669.8 kilometres/hour.

(a) Write down this number in standard form, correct to 3 significant figures.

Answer(a) [2]

(b) Change 1669.8 kilometres/hour into metres/second.

Answer(b) m/s [2]

17 (a) Factorise 3mp + 7p2.

Answer (a) [1]

(b) Simplify completely 8(3m + p) − 5(2m − 3p).

Answer (b) [3]

10

© UCLES 2009 0580/12/O/N/09

For

Examiner's

Use

18

T

P

W

Q R

S

38° 105°

NOT TOSCALE

The lines PS and QT intersect at W.

PQR is a straight line.

Angle SPR = 38° and angle TQR = 105°.

Write down the size of the following angles.

In each case give a reason for your answer.

(a) Angle PQW = because

[2]

(b) Angle PWQ = because

[2]

(c) Angle TWS = because

[2]

11

© UCLES 2009 0580/12/O/N/09

For

Examiner's

Use

For

Examiner's

Use

19

Silver

RedYellow

Other

The accurate pie chart shows information about the colours of 240 cars in a car park.

(a) The sector angle for silver cars is 90°.

Calculate the number of silver cars in the car park.

Answer(a) [1]

(b) There are 36 yellow cars in the car park.

Showing all your working, calculate the sector angle for yellow cars.

Answer(b) [2]

(c) (i) Measure and write down the sector angle for red cars.

Answer(c)(i) [1]

(ii) Calculate the percentage of red cars in the car park.

Answer(c)(ii) % [2]

12



0580/12/O/N/09

BLANK PAGE



*7953581407*


MATHEMATICS 0580/03


2 hours
















2

© UCLES 2009 0580/03/O/N/09

For

Examiner's

Use

1

Jonah uses a fair five-sided spinner in a game. (a) What is the probability that the spinner lands on (i) 3, Answer(a)(i) [1]

(ii) an even number, Answer(a)(ii) [1]

(iii) a number greater than 5? Answer(a)(iii) [1]

(b) Jonah spins the spinner 25 times and records the results in a frequency table.

Number that the spinner lands on

Frequency

1 8

2 4

3 5

4

5 2

(i) Fill in the missing number. [1] (ii) Write down the mode. Answer(b)(ii) [1]

3


For

Examiner's

Use

(iii) Calculate the mean. Answer(b)(iii) [3]

(iv) On the grid, draw a bar chart to show these results.

10

8

6

4

2

0

Number that the spinner lands on

Frequency

1 2 3 4 5

[3]

4

© UCLES 2009 0580/03/O/N/09

For

Examiner's

Use

2

The diagram shows a circular pool, of radius 2.5 metres, surrounded by a path 0.8 metres wide. (a) Calculate (i) the perimeter of the pool,

Answer(a)(i) m [2]

(ii) the area of the pool, Answer(a)(ii) m2 [2]

(iii) the area of the path. Answer(a)(iii) m2 [2]

(b) The water in the pool has a depth of 0.4 metres. Calculate the volume of water in the pool. Give your answer in litres. [1 cubic metre = 1000 litres.] Answer(b) litres [2]

(c) When the pool is emptied for cleaning, the water flows out at a rate of 250 litres each minute. Calculate how long it takes to empty the pool. Give your answer to the nearest minute. Answer(c) min [3]

2.5 m 0.80.8 m0.8 m

pathpathpath

pool

NOT TOSCALE

5


For

Examiner's

Use

3 (a) Bruce mixes blue and yellow paint to make green paint. He uses blue and yellow paint in the ratio blue : yellow = 7 : 3. (i) He makes 15 litres of green paint. How many litres of yellow paint does he use? Answer(a)(i) litres [2]

(ii) He buys the yellow paint in tins. Each tin contains 2 litres of paint. Write down the number of tins of yellow paint he buys. Answer(a)(ii) [1]

(b) Tins of red paint cost $9.25 each. In a sale, the shop reduces the price by 12%. (i) Calculate the sale price. Answer(b)(i) $ [3]

(ii) Bruce buys 4 tins of red paint in the sale. How much does he pay? Answer(b)(ii) $ [1]

(iii) Before the sale, he bought 5 tins at $9.25 each. Calculate how much he paid for these 5 tins. Answer(b)(iii) $ [1]

(iv) Use parts (b)(ii) and (b) (iii) to find the average (mean) price he paid for a tin of red paint. Answer(b)(iv) $ [3]

6

© UCLES 2009 0580/03/O/N/09

For

Examiner's

Use

4 A

C

BND

35°

7 cm 7 cm

6 cm

NOT TOSCALE

The diagram shows a kite ABCD, with AB = AD and DC = BC. The diagonals AC and BD intersect at right angles at N. AN = 6 cm and NB = ND = 7 cm. Angle BCN = 35°. (a) (i) What is the mathematical name for triangle BCD? Answer(a)(i) [1]


Triangle BNC is congruent to triangle [1]

(iii) Write down the size of angle DCB. Answer(a)(iii) Angle DCB = [1]

7


For

Examiner's

Use

(b) (i) Use trigonometry to calculate the size of angle NAB. Answer(b)(i) Angle NAB = [2]

(ii) Calculate the length of AB. Answer(b)(ii) AB = cm [2]

(c) Use trigonometry to calculate the length of BC. Answer(c) BC = cm [3]

(d) Calculate the perimeter of the kite. Answer(d) cm [2]

8

© UCLES 2009 0580/03/O/N/09

For

Examiner's

Use

5 (a) Complete the table of values for y = x2 + 4x − 3.

x −5 −4 −3 −2 −1 0 1

y −3 −7 −6 −3

[3]

(b) On the grid below draw the graph of y = x2 + 4x − 3 for −5 Y x Y 1.

y

x

3

–1–1

1

2

–2

–3

–4

–5

–6

–7

–8

0–2–3–4–5 1

[4]

(c) (i) Write down the co-ordinates of the lowest point of the graph. Answer(c)(i) ( , ) [1]

(ii) Write down the solutions of the equation x2 + 4x − 3 = 0. Answer(c)(ii) x = or x = [2]

9


For

Examiner's

Use

(d) (i) Mark the point (−2, 1) on the grid and label it A. [1]

(ii) Draw the straight line joining A to the point where the graph of y = x2 + 4x − 3 cuts the y-axis. [1]

(iii) Find the gradient of your line. Answer(d)(iii) [2]

(iv) Write down the equation of your line in the form y = mx + c. Answer(d)(iv) y = [2]

6 Ravinder scores x marks in a test. (a) Manpreet scores 4 more marks than Ravinder. Write down Manpreet’s mark in terms of x. Answer(a) [1]

(b) Tamsin scores 3 times as many marks as Ravinder. Write down Tamsin’s mark in terms of x. Answer(b) [1]

(c) (i) Write down and simplify the total of the three marks in terms of x. Answer(c)(i) [2]

(ii) The mean of these marks is 28. Show that 5x + 4 = 84.

Answer (c)(ii) [1] (iii) Solve the equation 5x + 4 = 84. Answer(c)(iii) x = [2]

(d) What mark did Tamsin score? Answer(d) [1]

(e) Dinesh scored 63 marks out of 75. Work out the mark Dinesh scored as a percentage. Answer(e) % [2]

10

© UCLES 2009 0580/03/O/N/09

For

Examiner's

Use

7

Peter makes square tiles, like the one shown above. (a) Write down the order of rotational symmetry of the tile. Answer(a) [1]

(b) On the diagram, draw all the lines of symmetry of the tile. [2] (c) Charles orders 2800 tiles from Peter at 1.75 euros (€) each. He pays Peter €2300 now. Calculate the amount he still has to pay. Answer(c) € [3]

(d) Peter changes the €2300 into dollars ($) when the exchange rate is €1 = $1.348. Calculate how many dollars Peter receives. Give your answer correct to 2 decimal places. Answer(d) $ [2]

(e) Peter borrows $5000 from a bank at a rate of 9.2% per year compound interest. Calculate the amount he owes after 2 years. Give your answer correct to 2 decimal places. Answer(e) $ [3]

11


For

Examiner's

Use

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

0–1–2–3–4–5–6–7–8–9 987654321

y

x

(a) On the grid,

(i) translate Х by the vector ( )_72

, [2]

(ii) rotate Υ through 90° anticlockwise about the origin. [2] (b) (i) On the grid, reflect Ζ in the x-axis. This is the image Ζ1 . [2] (ii) On the grid, reflect the image Ζ1 in the line x = 4. This is the image Ζ2 . [2] (iii) Describe a single transformation which maps the image Ζ2 onto the original Ζ. Answer(b)(iii) [2]


12



© UCLES 2009 0580/03/O/N/09

For

Examiner's

Use

9

Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 The diagrams show a pattern of lines and dots. (a) Complete the table below.

Diagram number 1 2 3 4 5

Number of lines 1 3 7

Number of dots 1 3 6

[4] (b) Work out the number of lines and the number of dots in Diagram 7.

Answer(b) Number of lines = , Number of dots = [2]

(c) The number of dots in Diagram n is 1

2

n(n + 1).

(i) Use this formula to check your result for Diagram 5. You must show your working.

Answer (c)(i) [2] (ii) How many dots are there in Diagram 20? Answer(c)(ii) [2]

(d) The number of lines in Diagram n is n2 + kn + 1. Use the information about Diagram 3 from the table to calculate the value of k. Answer(d) k = [2]



Introduction









or


as appropriate.



*9048474401*

For Examiner's Use


MATHEMATICS 0580/11, 0581/11


1 hour

















2

© UCLES 2008 0580/11/M/J/08

For

Examiner's

Use

1 Work out the value of 11 4 7

3

+ ×

.

Answer [1]

2 A train leaves Paris at 10 56 and arrives in Marseille at 13 12. How long does the journey take? Give your answer in hours and minutes. Answer h min [1]

3

200

190

180

The diagram above shows part of a thermometer which measures the temperature in ºC inside an

oven. What is the temperature in the oven? Answer °C [1]

3


For

Examiner's

Use

4 When Jon opened a packet containing 30 biscuits, he found that 3 biscuits were broken. What percentage of the biscuits were broken? Answer % [1]

5 Write the following in order, starting with the smallest.

0.35 33% 3

1

Answer < < [1]

6 In May, the average temperature in Kiev was 12 ºC. In February, the average temperature was 26 ºC lower than in May. What was the average temperature in February? Answer °C [1]


4

© UCLES 2008 0580/11/M/J/08

For

Examiner's

Use

8

For the diagram above, write down (a) the number of lines of symmetry, Answer(a) [1]


9 Rehana pays $284 in tax.

This is 29

of the money she earns.

How much does Rehana earn? Answer $ [2]

10 The height, h metres, of a telegraph pole is 12 metres correct to the nearest metre. Complete the statement about the value of h. Answer Y h I [2]

11 A packet of sweets costs $2.45. Felipe and his brother share the cost in the ratio 4 : 3. How much does Felipe pay? Answer $ [2]

5


For

Examiner's

Use

12 (a) There are 11 boys and 13 girls in a choir. The teacher chooses one choir member at random. What is the probability that this is a girl? Write your answer as a fraction. Answer(a) [1]

(b) The probability that Carla arrives at school before 08 00 is 20

9.

What is the probability that Carla does not arrive before 08 00? Write your answer as a fraction. Answer(b) [1]

13

6 cm

h cm

5 cm

8 cm

NOT TOSCALE

A model ship is flying two flags. The first is a rectangle 5 centimetres by 6 centimetres. The second is an isosceles triangle with base 8 centimetres and height h centimetres. The flags are equal in area. Find the value of h. Answer h = [2]

6

© UCLES 2008 0580/11/M/J/08

For

Examiner's

Use

14 Find the circumference of a circle of radius 5.7 cm. Write down your answer (a) exactly as it appears on your calculator, Answer(a) cm [1]

(b) correct to the nearest centimetre. Answer(b) cm [1]

15

7654321–1–2–3

6

5

4

3

2

1

–1

0

y

x

On the grid, draw the reflection of the parallelogram in the line x = 3. [2]

7


For

Examiner's

Use

16

NOT TOSCALE

2.4 m

3.9 m

A

B C

ABC is a right-angled triangle. AB = 3.9 m and BC = 2.4 m. Calculate the length of AC. Answer AC = m [2]

17 A shop sells batteries at 68 cents each, or $2.15 for a pack of four. How much will Daniel save if he buys two packs of four instead of 8 single batteries? Answer $ [2]

18 Factorise completely 6x − 9x2y. Answer [2]

8

© UCLES 2008 0580/11/M/J/08

For

Examiner's

Use

19 (a) When x = −3 and y = 4, find the value of (i) x3, Answer(a)(i) [1]

(ii) xy2. Answer(a)(ii) [1]

(b) Simplify 1

2

z

z

−

−

.

Answer(b) [1]

20 4 14 36 64 81 100 From the list above, write down (a) a prime number, Answer(a) [1]

(b) a factor of 27, Answer(b) [1]

(c) a multiple of 4, Answer(c) [1]

(d) an irrational number. Answer(d) [1]

9


For

Examiner's

Use

21

Diagram 1 Diagram 2 Diagram 3 Diagram 4 Look at the sequence of diagrams above. The number of dots in each diagram is given in the table below.

Diagram number 1 2 3 4

Number of dots 13 16 19 22

Find the number of dots in (a) Diagram 5, Answer(a) [1]

(b) Diagram 11, Answer(b) [1]

(c) Diagram n. Answer(c) [2]

10

© UCLES 2008 0580/11/M/J/08

For

Examiner's

Use

22

D

C 34

B 24

A 010 22 270

Time (minutes)


NOT TOSCALE

The diagram shows the graph of Rachel’s journey on a motorway. Starting at A, she drove 24 kilometres to B at a constant speed. Between B and C she had to drive slowly through road works. At C she drove a further distance to D at her original speed. (a) For how many minutes was she driving through the road works? Answer(a) min [1]

(b) At what speed did she drive through the road works? Give your answer in

(i) kilometres / minute, Answer(b)(i) km/min [1]

(ii) kilometres / hour. Answer(b)(ii) km/h [1]

(c) What is the total distance from A to D? Answer(c) km [2]

11


For

Examiner's

Use

23 Nicolas needs to borrow $4000 for 3 years. The bank offers him a choice:

Offer A Offer B

Interest Rate 8.5% per year Interest Rate 8% per year

Pay the interest at the end of Pay all the interest at the end of

each year three years

Nicolas recognises that offer A is simple interest and offer B is compound interest. (a) If he takes offer A, what is the total amount of interest he will pay? Answer(a) $ [2]

(b) If he takes offer B, how much interest will he pay?

Give your answer correct to 2 decimal places. Answer(b) $ [3]

12



0580/11/M/J/08

For

Examiner's

Use

24 a = 3_2

and b = _1

2

(a) Work out (i) a + 3b,

Answer(a)(i)

[2]

(ii) b – a.

Answer(a)(ii)

[2]

(b) PQ = 2b.

The point P is marked on the grid below.

Draw the vector PQ on the grid.

–3 –2 –1 1 2 3 4 5 60

7

6

5

4

3

2

1

–1

–2

P

y

x

[2]

2

© UCLES 2008 0580/12/M/J/08

For

Examiner's

Use

1 Work out the value of 12 3 11

5

+ ×

.

Answer [1]

2 A train leaves Paris at 9 52 and arrives in Marseille at 13 21. How long does the journey take? Give your answer in hours and minutes. Answer h min [1]

3

200

190

180

The diagram above shows part of a thermometer which measures the temperature in ºC inside an

oven. What is the temperature in the oven? Answer °C [1]

3


For

Examiner's

Use

4 When Jon opened a packet containing 40 biscuits, he found that 8 biscuits were broken. What percentage of the biscuits were broken? Answer % [1]

5 Write the following in order, starting with the smallest.

0.35 33% 3

1

Answer < < [1]

6 In May, the average temperature in Kiev was 13 ºC. In February, the average temperature was 22 ºC lower than in May. What was the average temperature in February? Answer °C [1]


4

© UCLES 2008 0580/12/M/J/08

For

Examiner's

Use

8

For the diagram above, write down (a) the number of lines of symmetry, Answer(a) [1]


9 Rehana pays $276 in tax.

This is 3

11 of the money she earns.

How much does Rehana earn? Answer $ [2]

10 The height, h metres, of a telegraph pole is 12 metres correct to the nearest metre. Complete the statement about the value of h. Answer Y h I [2]

11 A packet of sweets costs $2.25. Felipe and his brother share the cost in the ratio 5 : 4. How much does Felipe pay? Answer $ [2]

5


For

Examiner's

Use

12 (a) There are 12 boys and 17 girls in a choir. The teacher chooses one choir member at random. What is the probability that this is a girl? Write your answer as a fraction. Answer(a) [1]

(b) The probability that Carla arrives at school before 08 00 is 7

20.

What is the probability that Carla does not arrive before 08 00? Write your answer as a fraction. Answer(b) [1]

13

9 cm

h cm

6 cm

8 cm

NOT TOSCALE

A model ship is flying two flags. The first is a rectangle 6 centimetres by 9 centimetres. The second is an isosceles triangle with base 8 centimetres and height h centimetres. The flags are equal in area. Find the value of h. Answer h = [2]

6

© UCLES 2008 0580/12/M/J/08

For

Examiner's

Use

14 Find the circumference of a circle of radius 5.2 cm. Write down your answer (a) exactly as it appears on your calculator, Answer(a) cm [1]

(b) correct to the nearest centimetre. Answer(b) cm [1]

15

7654321–1–2–3

6

5

4

3

2

1

–1

0

y

x

On the grid, draw the reflection of the parallelogram in the line x = 3. [2]

7


For

Examiner's

Use

16

NOT TOSCALE

1.5 m

4.2 m

A

B C

ABC is a right-angled triangle. AB = 4.2 m and BC = 1.5 m. Calculate the length of AC. Answer AC = m [2]

17 A shop sells batteries at 68 cents each, or $2.15 for a pack of four. How much will Daniel save if he buys two packs of four instead of 8 single batteries? Answer $ [2]

18 Factorise completely 6x − 9x2y. Answer [2]

8

© UCLES 2008 0580/12/M/J/08

For

Examiner's

Use

19 (a) When x = −4 and y = 6, find the value of (i) x3, Answer(a)(i) [1]

(ii) xy2. Answer(a)(ii) [1]

(b) Simplify 1

2

z

z

−

−

.

Answer(b) [1]

20 4 14 36 64 81 100 From the list above, write down (a) a prime number, Answer(a) [1]

(b) a factor of 27, Answer(b) [1]

(c) a multiple of 4, Answer(c) [1]

(d) an irrational number. Answer(d) [1]

9


For

Examiner's

Use

21

Diagram 1 Diagram 2 Diagram 3 Diagram 4 Look at the sequence of diagrams above. The number of dots in each diagram is given in the table below.

Diagram number 1 2 3 4

Number of dots 13 16 19 22

Find the number of dots in (a) Diagram 5, Answer(a) [1]

(b) Diagram 11, Answer(b) [1]

(c) Diagram n. Answer(c) [2]

10

© UCLES 2008 0580/12/M/J/08

For

Examiner's

Use

22

D

C 34

B 24

A 010 22 270

Time (minutes)


NOT TOSCALE

The diagram shows the graph of Rachel’s journey on a motorway. Starting at A, she drove 24 kilometres to B at a constant speed. Between B and C she had to drive slowly through road works. At C she drove a further distance to D at her original speed. (a) For how many minutes was she driving through the road works? Answer(a) min [1]

(b) At what speed did she drive through the road works? Give your answer in

(i) kilometres / minute, Answer(b)(i) km/min [1]

(ii) kilometres / hour. Answer(b)(ii) km/h [1]

(c) What is the total distance from A to D? Answer(c) km [2]

11


For

Examiner's

Use

23 Nicolas needs to borrow $6000 for 3 years. The bank offers him a choice:

Offer A Offer B

Interest Rate 7.4% per year Interest Rate 7% per year

Pay the interest at the end of Pay all the interest at the end of

each year three years

Nicolas recognises that offer A is simple interest and offer B is compound interest. (a) If he takes offer A, what is the total amount of interest he will pay? Answer(a) $ [2]

(b) If he takes offer B, how much interest will he pay?

Give your answer correct to 2 decimal places. Answer(b) $ [3]

12



© UCLES 2008 0580/12/M/J/08

For

Examiner's

Use

24 a = 3_2

and b = _1

2

(a) Work out (i) a + 3b,

Answer(a)(i)

[2]

(ii) b – a.

Answer(a)(ii)

[2]

(b) PQ = 2b.

The point P is marked on the grid below.

Draw the vector PQ on the grid.

–3 –2 –1 1 2 3 4 5 60

7

6

5

4

3

2

1

–1

–2

P

y

x

[2]



*7626748314*

For Examiner's Use


MATHEMATICS 0580/03, 0581/03


2 hours

















2

© UCLES 2008 0580/03/M/J/08

For

Examiner's

Use

1 Alphonse, his wife and child fly from Madrid to the Olympic Games in Beijing.

The adult plane fare is 450 euros.

The child fare is 68% of the adult fare.

(a) Show that the total plane fare for the family is 1206 euros. Show all your working clearly.

Answer (a)

[3]

(b) The ratio of the money spent on plane fares : accommodation : tickets = 6 : 5 : 3.

Calculate the total cost.

Answer(b) euros [3]

(c) Alphonse changes 500 euros into Chinese Yuan at a rate of 1 euro = 9.91 Chinese Yuan.

How many Chinese Yuan does he receive?

Answer(c) Yuan [2]

(d) Their plane leaves Madrid at 05 45. The journey takes 11 hours 35 minutes.

Beijing time is 6 hours ahead of Madrid time.

Find the time in Beijing when they arrive.

Answer(d) [2]

3


For

Examiner's

Use

2

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–6 –5 –4 –3 –2 –1 1 2 3 4 5 60

A

B

CD

E

y

x

Describe fully the single transformation which maps

(a) A onto B,

Answer(a) [3]

(b) C onto D,

Answer(b) [2]

(c) A onto C,

Answer(c) [3]

(d) C onto E.

Answer(d) [3]

4

© UCLES 2008 0580/03/M/J/08

For

Examiner's

Use

3 Marie counts the number of people in each of 60 cars one morning.

(a) She records the first 40 results as shown below.

Number of people in a car

1

2

3

4

5

6

Tally Number of cars

The remaining 20 results are

2, 2, 5, 2, 2, 4, 2, 6, 5, 3, 4, 5, 4, 6, 2, 5, 3, 2, 1, 6.

(i) Use these results to complete the frequency table above. [2]

(ii) On the grid below, draw a bar chart to show the information for the 60 cars.

1 2 3 4 5 6

Number of people in a car

20

18

16

14

12

10

8

6

4

2

0

Numberof cars

[1]

5


For

Examiner's

Use

(iii) Write down the mode.

Answer(a)(iii) [1]

(iv) Find the median.

Answer(a)(iv) [1]

(v) Work out the mean.

Answer(a)(v) [3]

(b) Manuel uses Marie’s results to draw a pie chart.

Work out the sector angle for the number of cars with 5 people.

Answer(b) [2]

6

© UCLES 2008 0580/03/M/J/08

For

Examiner's

Use

4 (a) Solve the equations

(i) 3x − 4 = 14,


(ii) +1

= 25

y,


(iii) 3(2z − 7) − 2(z − 3) = −9.

Answer(a)(iii) z = [3]

(b) Donna sent p postcards and q letters to her friends.

(i) The total number of postcards and letters she sent was 12.

Write down an equation in p and q.

Answer(b)(i) [1]

(ii) A stamp for a postcard costs 25 cents and a stamp for a letter costs 40 cents.

She spent 375 cents on stamps altogether.

Write down another equation in p and q.

Answer(b)(ii) [1]

(iii) Solve these equations to find the values of p and q.

Answer(b)(iii) p = and q = [3]

7


For

Examiner's

Use

5 (a) (i) Calculate the area of a circle with radius 3.7 centimetres.

Answer(a)(i) cm2 [2]

(ii) A can of tomatoes is a cylinder with radius 3.7 centimetres and height h centimetres.

The volume of the cylinder is 430 cubic centimetres.

Calculate h.

Answer(a)(ii) h = [2]

2 cans

2 cans

3 cans

NOT TOSCALE

(b) Twelve cans fit exactly inside a box 3 cans long, 2 cans wide and 2 cans high.

(i) Write down the length, width and height of the box.

Answer(b)(i) length = cm

width = cm

height = cm [3]

(ii) Calculate the volume of the box.

Answer(b)(ii) cm3 [2]

(iii) Calculate the percentage of the volume of the box occupied by the cans.

Answer(b)(iii) % [3]

8

© UCLES 2008 0580/03/M/J/08

For

Examiner's

Use

6

63°100°

z°

y°x°P

T

S R

Q

NOT TOSCALE

(a) In the diagram PQ is parallel to SR, and QR is parallel to PT.

PQ = QR, angle PRS = 63° and angle RST = 100°.

Find the value of

(i) x,


(ii) y,


(iii) z.

Answer(a)(iii) z = [2]

(b) The shape of a flower bed is a regular octagon, ABCDEFGH, with sides of 4 metres.

(i) Show that the interior angle of a regular octagon is 135°.

Answer(b)(i)

[2]

9


For

Examiner's

Use

(ii) Use a ruler and protractor to complete an accurate scale drawing of the flower bed.

Use a scale of 1 centimetre to represent 1 metre.

The line AB and the centre O are already shown.

A B4 m

O

[2]

(iii) Measure and write down the distance from the centre, O, to the mid-point of AB.

Answer(b)(iii) cm [1]

(iv) Calculate the area of triangle OAB in the scale drawing.

Answer(b)(iv) cm2 [2]

(v) Calculate the actual area of the flower bed.

Answer(b)(v) m2 [1]

10

© UCLES 2008 0580/03/M/J/08

For

Examiner's

Use

7

98°

Q R

S

P13.5 km

10.3 km

7.2 km

NOT TOSCALE

North

P, Q, R and S are ferry ports on a wide river, as shown in the diagram above.

A ferry sails from P, stopping at Q, R and S before returning to P.

(a) Q is 7.2 kilometres due south of P and R is 10.3 kilometres due east of Q.

(i) Show by calculation that angle QPR = 55°.

Answer(a)(i)

[2]

(ii) Write down the bearing of R from P.

Answer(a)(ii) [1]

(b) The bearing of S from P is 098° and SP = 13.5 km.

(i) Explain why angle RPS = 27°.

Answer (b)(i)

[1]

(ii) Angle PRS = 90°. Calculate the distance RS.

Answer(b)(ii)RS = km [2]

11


For

Examiner's

Use

(iii) Find the total distance the ferry sails.

Answer(b)(iii) km [1]

(c) The total sailing time for the ferry is 4 hours 30 minutes.

Calculate the average sailing speed, in kilometres per hour, for the whole journey.

Answer(c) km/h [2]

12

© UCLES 2008 0580/03/M/J/08

For

Examiner's

Use

8 (a) The width of a rectangle is x centimetres.

The length of the rectangle is 3 centimetres more than the width.

Write down an expression, in terms of x, for

(i) the length of the rectangle,

Answer(a)(i) cm [1]

(ii) the area of the rectangle.

Answer(a)(ii) cm2 [1]

(iii) The area of the rectangle is 7 square centimetres.

Show that x2 + 3x − 7 = 0.

Answer (a)(iii)

[1]

(b) (i) Complete the tables of values for the equation y = x2 + 3x − 7.

x −5 −4 −3 −2 −1 0 1 2

y 3 −7 −9 −7 3

[3]

13


For

Examiner's

Use

(ii) On the grid below, draw the graph of y = x2 + 3x − 7 for −5 Y x Y 2. y

x–5 21–4 –3 –2 –1 0

4

2

–2

–4

–6

–8

–10

A

[4]

(c) (i) Use your graph to find the solutions to the equation x2 + 3x − 7 = 0.

Answer(c)(i) x = or x = [2]

(ii) Find the length of the rectangle in part (a).

Answer(c)(ii) cm [1]

(d) The point A(1, −1) is marked on the grid.

(i) Draw a straight line through A with a gradient of 2. [1]

(ii) Write down the equation of this line in the form y = mx + c.

Answer(d)(ii) y = [2]

14

© UCLES 2008 0580/03/M/J/08

For

Examiner's

Use

9 In this question, all construction arcs must be shown clearly.

Jalal buys an area of land on which to build a school.

The land, ABCDE, is in the shape of a polygon with 5 sides.

(a) Write down the mathematical name of this polygon.

Answer(a) [1]

(b) Jalal starts to make an accurate plan of the land, as shown below.

He uses a scale of 1 centimetre to represent 10 metres.

A

B C

D

45 m

70 m

m

(i) The actual lengths of AB and BC are written on the plan.

Write the actual length of CD on the plan. [1]

(ii) Use compasses to find the point E such that AE = 64 m and DE = 58 m.

Draw the lines AE and DE. [2]

15

© UCLES 2008 0580/03/M/J/08

For

Examiner's

Use

(c) The land is to be divided into distinct regions.

Construct, using a straight edge and compasses only,

(i) the perpendicular bisector of BC, [2]

(ii) the bisector of angle ABC. [2]

(d) The music department building will be nearer to B than to C and nearer to BC than to BA.

Write a letter M on the plan where the music department could be. [1]

(e) The school gate, PQ, will be 8 metres wide.

It will lie along AB so that AP = QB.

Mark P and Q accurately on the plan. [2]

16



0580/03/M/J/08



Introduction









or


as appropriate.



*7272401607*

For Examiner's Use


MATHEMATICS 0580/11, 0581/11


1 hour

















2

© UCLES 2008 0580/01/O/N/08

For

Examiner's

Use

1 Write down a multiple of 4 and 14 which is less than 30. Answer [1]

2

Write down the order of rotational symmetry of the diagram above. Answer [1]

3 On 1st August the level of water in a lake was −15 metres. A month later the level was 2 metres higher. Write down the new level of water. Answer m [1]

4 The area of a square is 42.25 cm2. Work out the length of one side of the square. Answer cm [1]

5 Expand the brackets and simplify 5x − 6(3x − 2). Answer [2]

5

0

–5

–10

–15

3


For

Examiner's

Use

6 The scale on a map is 1:250 000. A road is 4.6 centimetres long on the map. Calculate the actual length of the road in kilometres. Answer km [2]

7 > = < Choose one of the symbols above to complete each of the following statements.

(a) 74%

5

7

[1]

(b)

_3

1

2

8 [1]

8 Juanita changed $20 into euros when the exchange rate was €1=$1.2685. How many euros did she receive? Give your answer correct to 2 decimal places. Answer € [2]

9 Solve the equation 5x + 2 = 53. Answer x = [2]

10 The length of the River Nile is 6700 kilometres, correct to the nearest hundred kilometres. Complete the statement about the length, L kilometres, of the River Nile. Answer Y L I [2]

4

© UCLES 2008 0580/01/O/N/08

For

Examiner's

Use

11

City centre 11 15 12 30 13 10 13 40

Heatherton 11 25 12 40 13 20 13 50

Rykneld 11 29 12 44 13 24 13 54

The table above is part of a bus timetable. (a) The 11 15 bus left the City centre on time and arrived at Rykneld 2 minutes early. How many minutes did it take to reach Rykneld? Answer(a) min [1]

(b) Paulo walked to the bus stop at Heatherton and arrived at 12 56. The next bus arrived on time. How many minutes did Paulo wait for the bus? Answer(b) min [1]

12 The line with equation y = 2x − k passes through the point (4 , 0). Work out the value of k. Answer k = [2]

13 Write 0.00578 (a) in standard form, Answer(a) [1]

(b) correct to 2 significant figures, Answer(b) [1]

(c) correct to 2 decimal places. Answer(c) [1]

5


For

Examiner's

Use

14 Without using your calculator, work out 5 3 ÷ 3

8 4.

Give your answer as a fraction in its lowest terms. You must show all your working. Answer

[3]

15

y

x

B

–4 –3 –2 –1 0

–1

–2

–3

3

2

1

1 2 3 4

l

(a) Mark clearly on the diagram the point with co-ordinates (3, 2) and label it A. [1] (b) Write down the co-ordinates of the point B. Answer(b) ( , ) [1]

(c) Find the gradient of the line l. Answer(c) [1]

6

© UCLES 2008 0580/01/O/N/08

For

Examiner's

Use

16 Simplify

(a)

0

1

p

,

Answer(a) [1] (b) q4 × q7, Answer(b) [1]

(c) ( )_32r .

Answer(c) [1]

17

A

B

C

168°

78°

North

North

North

NOT TOSCALE

The diagram shows the route of a fishing boat.

The boat sails from A to B on a bearing 168° and then from B to C on a bearing 078°. AB = BC.

(a) Show that angle ABC = 90°.

Answer(a) [1] (b) Work out the bearing of C from A. Answer(b) [2]

7


For

Examiner's

Use

18 (a) Calculate the volume of a cylinder of radius 50 cm and height 138 cm. Answer(a) cm3 [2]

(b) Write your answer to part (a) in cubic metres. Answer(b) m3 [1]

19

10 cm

14 cm

22 cm

6 cm

NOT TOSCALE



8

© UCLES 2008 0580/01/O/N/08

For

Examiner's

Use

20 (a) 85% of the seeds in a packet will produce red flowers. One seed is chosen at random. What is the probability that it will not produce a red flower? Answer(a) [1]

(b) A box of 15 pencils contains 5 red, 4 yellow and 6 blue pencils. One pencil is chosen at random from the box. Find the probability that it is (i) yellow, Answer(b)(i) [1]

(ii) yellow or blue, Answer(b)(ii) [1]

(iii) green. Answer(b)(iii) [1]

21

D

B

A

C

E

68°

NOT TOSCALE

12 cm

8 cm

10 cm

In the diagram BC is parallel to DE. (a) Complete the following statement.

Triangle ABC is to triangle ADE. [1] (b) AB = 12 cm, BC = 8 cm and DE = 10 cm. Calculate the length of AD. Answer(b) cm [2]

(c) Angle ABC = 68°. Calculate the size of the reflex angle at D. Answer(c) [2]

9

© UCLES 2008 0580/01/O/N/08

For

Examiner's

Use

22 A travel brochure contains 24 pictures from different countries. The table shows how many pictures there are from each country.

Country Number of pictures Angle in a pie chart

Argentina 6 90°

South Africa 10 150°

Australia 3

New Zealand

(a) Complete the table. [3] (b) Complete the pie chart accurately and label the sectors for South Africa, Australia and New

Zealand.

Argentina

[2]

10

0580/01/O/N/08

BLANK PAGE

11

0580/01/O/N/08

BLANK PAGE

12



0580/01/O/N/08

BLANK PAGE



*9940372872*

For Examiner's Use


MATHEMATICS 0580/12, 0581/12


1 hour












If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place





2

© UCLES 2008 0580/12/O/N/08

For

Examiner's

Use

1 Write down a multiple of 9 and 12 which is less than 40. Answer [1]

2

Write down the order of rotational symmetry of the diagram above. Answer [1]

3 On 1st August the level of water in a lake was −15 metres. A month later the level was 2 metres higher. Write down the new level of water. Answer m [1]

4 The area of a square is 54.76 cm2. Work out the length of one side of the square. Answer cm [1]

5 Expand the brackets and simplify 3x − 5(4x − 2). Answer [2]

5

0

–5

–10

–15

3


For

Examiner's

Use

6 The scale on a map is 1:250 000. A road is 3.8 centimetres long on the map. Calculate the actual length of the road in kilometres. Answer km [2]

7 > = < Choose one of the symbols above to complete each of the following statements.

(a) 74%

5

7

[1]

(b)

_3

1

2

8 [1]

8 Juanita changed $30 into euros when the exchange rate was €1=$1.2685. How many euros did she receive? Give your answer correct to 2 decimal places. Answer € [2]

9 Solve the equation 5x + 1 = 54. Answer x = [2]

10 The length of the River Nile is 6700 kilometres, correct to the nearest hundred kilometres. Complete the statement about the length, L kilometres, of the River Nile. Answer Y L I [2]

4

© UCLES 2008 0580/12/O/N/08

For

Examiner's

Use

11

City centre 11 15 12 30 13 10 13 40

Heatherton 11 25 12 40 13 20 13 50

Rykneld 11 29 12 44 13 24 13 54

The table above is part of a bus timetable. (a) The 11 15 bus left the City centre on time and arrived at Rykneld 2 minutes early. How many minutes did it take to reach Rykneld? Answer(a) min [1]

(b) Paulo walked to the bus stop at Heatherton and arrived at 12 56. The next bus arrived on time. How many minutes did Paulo wait for the bus? Answer(b) min [1]

12 The line with equation y = 2x − k passes through the point (4 , 0). Work out the value of k. Answer k = [2]

13 Write 0.00656 (a) in standard form, Answer(a) [1]

(b) correct to 2 significant figures, Answer(b) [1]

(c) correct to 2 decimal places. Answer(c) [1]

5


For

Examiner's

Use

14 Without using your calculator, work out 4 2÷ 6

9 3.

Give your answer as a fraction in its lowest terms. You must show all your working. Answer

[3]

15

y

x

B

–4 –3 –2 –1 0

–1

–2

–3

3

2

1

1 2 3 4

l

(a) Mark clearly on the diagram the point with co-ordinates (3, 2) and label it A. [1] (b) Write down the co-ordinates of the point B. Answer(b) ( , ) [1]

(c) Find the gradient of the line l. Answer(c) [1]

6

© UCLES 2008 0580/12/O/N/08

For

Examiner's

Use

16 Simplify

(a)

0

1

p

,

Answer(a) [1] (b) q3 × q5, Answer(b) [1]

(c) ( )_24

r .

Answer(c) [1]

17

A

B

C

168°

78°

North

North

North

NOT TOSCALE

The diagram shows the route of a fishing boat.

The boat sails from A to B on a bearing 168° and then from B to C on a bearing 078°. AB = BC.

(a) Show that angle ABC = 90°.

Answer(a) [1] (b) Work out the bearing of C from A. Answer(b) [2]

7


For

Examiner's

Use

18 (a) Calculate the volume of a cylinder of radius 60 cm and height 129 cm. Answer(a) cm3 [2]

(b) Write your answer to part (a) in cubic metres. Answer(b) m3 [1]

19

10 cm

14 cm

22 cm

6 cm

NOT TOSCALE



8

© UCLES 2008 0580/12/O/N/08

For

Examiner's

Use

20 (a) 85% of the seeds in a packet will produce red flowers. One seed is chosen at random. What is the probability that it will not produce a red flower? Answer(a) [1]

(b) A box of 15 pencils contains 5 red, 4 yellow and 6 blue pencils. One pencil is chosen at random from the box. Find the probability that it is (i) yellow, Answer(b)(i) [1]

(ii) yellow or blue, Answer(b)(ii) [1]

(iii) green. Answer(b)(iii) [1]

21

D

B

A

C

E

63°

NOT TOSCALE

15 cm

9 cm

12 cm

In the diagram BC is parallel to DE. (a) Complete the following statement.

Triangle ABC is to triangle ADE. [1] (b) AB = 15 cm, BC = 9 cm and DE = 12 cm. Calculate the length of AD. Answer(b) cm [2]

(c) Angle ABC = 63°. Calculate the size of the reflex angle at D. Answer(c) [2]

9

© UCLES 2008 0580/12/O/N/08

For

Examiner's

Use

22 A travel brochure contains 24 pictures from different countries. The table shows how many pictures there are from each country.

Country Number of pictures Angle in a pie chart

Argentina 6 90°

South Africa 10 150°

Australia 3

New Zealand

(a) Complete the table. [3] (b) Complete the pie chart accurately and label the sectors for South Africa, Australia and New

Zealand.

Argentina

[2]

10

0580/12/O/N/08

BLANK PAGE

11

0580/12/O/N/08

BLANK PAGE

12



0580/12/O/N/08

BLANK PAGE



*9276915310*

For Examiner's Use


MATHEMATICS 0580/03, 0581/03


2 hours
















2

© UCLES 2008 0580/03/O/N/08

For

Examiner's

Use

1 Aida, Bernado and Cristiano need $30 000 to start a business.

(a) (i) They borrow 25

of this amount.

Show that they still need $18 000. Answer (a)(i) [1]

(ii) They provide the $18 000 themselves in the ratio Aida : Bernado : Christiano = 5 : 4 : 3. Calculate the amount each of them provides. Answer(a)(ii)Aida $

Bernado $

Cristiano $ [3]

(b) (i) Office equipment costs 35 % of the $30 000. Calculate the cost of the equipment. Answer(b)(i)$ [2]

(ii) Office expenses cost another $6500. Write this as a fraction of $30 000. Give your answer in its lowest terms. Answer(b)(ii) [2]

(iii) How much remains of the $30 000 now? Answer(b)(iii)$ [1]

(c) They invest $12 500. After one year this has increased to $15 500. Calculate this percentage increase. Answer(c) % [3]

3


For

Examiner's

Use

2

NOT TOSCALE

E D

F

C

B

18°25°

12 m

55m

A

ABCD represents a building with a vertical flagpole, AF, on the roof. The points E, D and C are on level ground. EA = 55 metres. The angle of elevation of A from E is 18° and the angle of elevation of F from E is 25°. (a) Calculate (i) ED, Answer(a)(i) m [2]

(ii) FD, Answer(a)(ii) m [2]

(iii) DA. Answer(a)(iii) m [2]

(b) Show that AF = 7.4 metres, correct to 1 decimal place. Answer(b)

[1] (c) The width, AB, of the building is 12 metres. The top of the flagpole is attached to the point B by a rope. Calculate

(i) the length of the rope, FB,

Answer(c)(i) m [2] (ii) the angle of elevation of F from B. Answer(c)(ii) [2]

4

© UCLES 2008 0580/03/O/N/08

For

Examiner's

Use

3 The table below shows the average daily sunshine, s, and the total monthly rainfall, r, for a city during one year.

Month Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

s (hours) 6 7 7 9 10 12 12 12 9 8 6 5

r (mm) 70 52 72 41 20 6 1 4 16 52 65 67

(a) For s, find (i) the mode Answer(a)(i) hours [1]

(ii) the range, Answer(a)(ii) hours [1]

(iii) the median. Answer(a)(iii) hours [2]

(b) On the grid below, plot the 10 points for March to December to complete the scatter diagram.

70

60

50

40

30

20

10

05 6 7 8 9 10 11 12

Average Daily Sunshine (hours)

TotalMonthlyRainfall(mm)

s

r

[3]

5


For

Examiner's

Use

(c) (i) Calculate the mean of s.

Answer(c)(i) hours [2]

(ii) The mean of r is 38.8 millimetres. On the grid, plot the point representing these means. Label this point M. [1] (d) (i) Draw a line of best fit on the grid. [1] (ii) What type of correlation does your scatter diagram show? Answer(d)(ii) [1]

4

68°

AE

B

D

C

G

NOT TOSCALE

EG is a diameter of the circle through E,C and G. The tangent AEB is parallel to CD and angle AEC = 68°. Calculate the size of the following angles and give a reason for each answer.

(a) Angle CEG = because

[2]

(b) Angle ECG = because

[2]

(c) Angle CGE = because

[2]

(d) Angle ECD = because

[2]

6

© UCLES 2008 0580/03/O/N/08

For

Examiner's

Use

5 Aminata and her brother live 18 kilometres from a shopping centre.

(a) Aminata leaves home at 09 00 and runs 3 kilometres to a bus stop. She arrives there at 09 30.

Write down her average speed, in kilometres per hour. Answer(a) km / h [1]

(b) She waits 15 minutes for the bus. The bus travels the remaining 15 kilometres to the shopping centre at an average speed of

20 km / h.

(i) At what time does she arrive at the shopping centre? Answer(b)(i) [2]

(ii) On the grid below, complete the travel graph showing her journey to the shopping centre.

20

18

16

14

12

10

8

6

4

2

009 00 10 00 11 00 12 00 13 00

Time

Home

Shopping Centre

Distancefrom home(km)

[2]

7


For

Examiner's

Use

(c) Her brother leaves home at 11 15. He travels to the shopping centre by car at an average speed of 54 km / h. (i) Work out how long, in minutes, he takes to travel to the shopping centre. Answer(c)(i) minutes [1]

(ii) Show his journey on the grid. [1] (d) Aminata and her brother leave the shopping centre at 12 00. They travel home by car and arrive at 12 45. (i) Show their journey home on the grid. [1] (ii) Calculate the average speed of their journey home. Answer(d)(ii) km / h [2]

6 (a) 2y = 75 − 7x (i) Find y when x = 7. Answer(a)(i) y = [2]

(ii) Find x when y = 6. Answer(a)(ii) x = [2]

(b) Make x the subject of the equation 2y = 75 − 7x. Answer(b) x = [2]

(c) Solve these simultaneous equations.

4x − y = 45 7x + 2y = 75

Answer(c) x =

y = [3]

8

© UCLES 2008 0580/03/O/N/08

For

Examiner's

Use

7 (a) Complete the table of values for the equation y = x2 + x − 3.

x −4 −3 −2 −1 0 1 2 3

y 9 −1 −3 −1 9

[3] (b) On the grid, draw the graph of y = x2 + x − 3.

y

x

10

9

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–4 –3 –2 –1 0 1 2 3

[4]

(c) Write down the coordinates of the lowest point of the curve. Answer(c) ( , ) [2]

(d) (i) Draw the line of symmetry of the graph. [1] (ii) Write down the equation of the line of symmetry. Answer(d)(ii) [1]

9


For

Examiner's

Use

8

A

y

x

C

B

6

5

4

3

2

1

–1

–2

–3

–4

–5

–4–5–6 –3 –2 –1 0 1 2 3 4 5 6

Triangle ABC is drawn on the grid. (a) (i) Write down the coordinates of A. Answer(a)(i) ( , ) [1]

(ii) Write AB and BC as column vectors.

Answer(a)(ii) AB =

BC =

[2]

(b) Translate triangle ABC by the vector 4

_3

. Label the image T. [2]

(c) AP = 2AB and AQ = 2AC .

(i) Plot the points P and Q on the grid. [2] (ii) Describe fully the single transformation which maps triangle ABC onto triangle APQ.

Answer(c)(ii)

[3]

(d) Rotate triangle ABC through 180° about the midpoint of the side AB. Label the image R. [2]

10

© UCLES 2008 0580/03/O/N/08

For

Examiner's

Use

9 The quadrilateral ABCD is a scale drawing of a park. Angle ABC = 90° and 1 centimetre represents 10 metres.

A

B C

D

(a) Write down (i) the actual length, in metres, of the side CD, Answer(a)(i) m [1]

(ii) the size of angle BAD. Answer(a)(ii) [1]

(b) Two straight paths cross the park.

One path is the same distance from AB as from BC.

The other path is the same distance from A as from D. (i) Using a straight edge and compasses only, construct the lines which show each path. [4] (ii) Tennis courts in the park are situated in a region closer to AB than to BC and closer to A

than to D. Label this region T. [1] (c) Keith cycles past the park, so that he is always 30 metres outside the boundary ABC. Construct the locus of points which shows this part of his route. [2]

11

© UCLES 2008 0580/03/O/N/08

For

Examiner's

Use

10 The first three diagrams in a sequence are shown below. Each diagram has one more trapezium added on the right.

Diagram 1 Diagram 2 Diagram 3 (a) Complete the table which shows the number of lines and dots in each diagram.

Diagram 1 2 3 4

Number of lines 4 7

Number of dots 4 6

[2] (b) Find the number of lines and dots in Diagram 10. Answer(b) lines and dots [2]

(c) For Diagram n, write down in terms of n, the number of (i) lines, Answer(c)(i) [2]

(ii) dots. Answer(c)(ii) [2]

(d) Find the difference, in terms of n, between your answers to parts (c)(i) and (c)(ii). Simplify your answer. Answer(d) [2]

12



0580/03/O/N/08

BLANK PAGE

Location Entry Codes

From the June 2007 session, as part of CIE’s continual commitment to maintaining best practice in assessment, CIE has begun to use different variants of some question papers for our most popular assessments with extremely large and widespread candidature, The question papers are closely related and the relationships between them have been thoroughly established using our assessment expertise. All versions of the paper give assessment of equal standard. The content assessed by the examination papers and the type of questions are unchanged. This change means that for this component there are now two variant Question Papers, Mark Schemes and Principal Examiner’s Reports where previously there was only one. For any individual country, it is intended that only one variant is used. This document contains both variants which will give all Centres access to even more past examination material than is usually the case. The diagram shows the relationship between the Question Papers, Mark Schemes and Principal Examiner’s Reports.

Question Paper Mark Scheme Principal Examiner’s Report

Introduction Introduction Introduction

First variant Question Paper First variant Mark Scheme First variant Principal Examiner’s Report

Second variant Question Paper Second variant Mark Scheme Second variant Principal Examiner’s Report

Who can I contact for further information on these changes? Please direct any questions about this to CIE’s Customer Services team at: [email protected]



*9556778355*

For Examiner's Use

P


MATHEMATICS 0580/01, 0581/01


1 hour

















wyliet

First Variant QP

2

© UCLES 2007 0580/01/J/07

For

Examiner's

Use 1 Work out the value of

_9 3×7

3×2.

Answer [1]

2 Write the following in order, with the smallest first.

3

5 0.58 62%

Answer < < [1]

3 Jamal arrived at work at 09 20 and left at 17 15. How long, in hours and minutes, did he spend at work? Answer h min [1]

4

NOT TOSCALE

150 cm A piece of wood is 150 centimetres long.

It has to be cut into equal lengths of 64

1 centimetres.

How many of these lengths can be cut from this piece of wood? Answer [1]

wyliet

First Variant QP

3

© UCLES 2007 0580/01/J/07 [Turn over

For

Examiner's

Use

5 Daniel plots a scatter diagram of speed against time taken. As the time taken increases, speed decreases. Which one of the following types of correlation will his scatter graph show?

Positive Negative Zero Answer [1]

6 The average temperatures in Moscow for each month are shown in the table below.


Temperature °C −10.2 −8.9 −4.0 4.5 12.2 16.3 18.5 16.6 10.9 4.3 −2.0 −7.5

(a) Which month has the lowest average temperature? Answer(a) [1]

(b) Find the difference between the average temperatures in July and December.

Answer(b) °C [1]

7

145°

North

P

L

NOT TOSCALE

North

The bearing of a lighthouse, L, from a port, P, is 145°. Find the bearing of P from L. Answer [2]

wyliet

First Variant QP

4

© UCLES 2007 0580/01/J/07

For

Examiner's

Use

8 The points A and B are marked on the diagram.

y

x–4 –3 –2 –1 1 2 3 40

4

3

2

1

–1

–2

–3

–4

A

B

(a) Write AB as a column vector.

Answer(a) AB =

[1]

(b) BC = 3

2

−

−

.

Write down the co-ordinates of C. Answer(b) ( , ) [1]

9 Expand the brackets and simplify

3x2 – x(x−3y). Answer [2]

wyliet

First Variant QP

5

© UCLES 2007 0580/01/J/07 [Turn over

For

Examiner's

Use

10

NOT TOSCALE

25°

130°

A B

E F

C D

In the diagram, AB, CD and EF are parallel lines. Angle ABC = 25° and angle CEF = 130°. Calculate angle BCE. Answer Angle BCE = [2]

11 The net of a solid is drawn accurately below.

Write down the special name for (a) the triangles shown on the net, Answer(a) [1]

(b) the solid. Answer(b) [1]

wyliet

First Variant QP

6

© UCLES 2007 0580/01/J/07

For

Examiner's

Use

12 Write down the equation of the straight line through (0, −1) which is parallel to y = 3x + 5. Answer y = [2]

13 (a) 4p × 45 = 415. Find the value of p.

Answer(a) p = [1]

(b) 27 ÷ 2q = 24. Find the value of q.

Answer(b) q = [1]

(c) 5r = 1

25. Find the value of r.

Answer(c) r = [1]

14 (a) Alex changed $250 into euros (€) when the rate was €1 = $1.19886. How many euros did he receive? Answer(a) € [2]

(b) Write 1.19886 correct to 3 significant figures. Answer(b) [1]

wyliet

First Variant QP

7

© UCLES 2007 0580/01/J/07 [Turn over

For

Examiner's

Use

15 The diagram shows a regular hexagon and a square.

x°y°

NOT TOSCALE

Calculate the values of x and y. Answer x =

y = [3]

16 Aminata bought 20 metres of cloth at a cost of $80. She sold 15 metres of the cloth at $5.40 per metre and 5 metres at $3 per metre. (a) Calculate the profit she made. Answer(a) $ [2]

(b) Calculate this profit as a percentage of the original cost. Answer(b) % [1]

wyliet

First Variant QP

8

© UCLES 2007 0580/01/J/07

For

Examiner's

Use

17 (a) The surface area of the earth is approximately 510 000 000 square kilometres. Write this number in standard form. Answer(a) km2 [2]

(b) 29.4% of the surface area of the earth is land.

Calculate the area of land. Answer(b) km2 [2]

18

O N

M

1200 m

900 mNOT TOSCALE

A hot air balloon, M, is 900 metres vertically above a point N on the ground. A boy stands at a point O, 1200 metres horizontally from N. (a) Calculate the distance, OM, of the boy from the balloon. Answer(a) OM = m [2]

(b) Calculate angle MON. Answer(b) Angle MON = [2]

wyliet

First Variant QP

9

© UCLES 2007 0580/01/J/07 [Turn over

For

Examiner's

Use

19 In triangle ABC, AB = 110 mm, AC = 65 mm and BC = 88 mm. (a) Calculate the perimeter of the triangle ABC. Answer(a) mm [1]

(b) Construct the triangle ABC, leaving in your construction arcs.

The side AB is drawn for you.

A 110 mm B [2]

(c) The side AB is 110 mm, correct to the nearest millimetre. Write down the shortest possible length of AB. Answer(c) mm [1]

wyliet

First Variant QP

10

© UCLES 2007 0580/01/J/07

For

Examiner's

Use

20 15 students estimated the area of the rectangle shown below.

Their estimates, in square centimetres, were

45 44 50 50 48

24 50 46 43 50

48 20 45 49 47

(a) Work out (i) the mode, Answer(a)(i) cm2 [1]

(ii) the mean, Answer(a)(ii) cm2 [2]

(iii) the median. Answer(a)(iii) cm2 [2]

(b) Explain why the mean is not a suitable average to represent this data. Answer(b) [1]

wyliet

First Variant QP

11

© UCLES 2007 0580/01/J/07

For

Examiner's

Use

21

1400

1200

1000

800

600

400

200

0 50 100 150 200

Time (seconds)

250 300 350 400Home

Work

Distance(metres)

AB

CD

AB

CD

E

The graph shows the distance travelled by a cyclist on a journey from Home to Work.

(a) The cyclist stopped twice at traffic lights. For how many seconds did the cyclist wait altogether? Answer(a) s [2]

(b) For which part of the journey did the cyclist travel fastest? Answer(b) [1]

(c) (i) How far did the cyclist travel from Home to Work? Answer(c)(i) m [1]

(ii) Calculate the cyclist’s average speed for the whole journey. Answer(c)(ii) m/s [3]

wyliet

First Variant QP


IB07 06_0580_01_TZ/RP © UCLES 2007 [Turn over

*0089378030*

For Examiner's Use

Q


MATHEMATICS 0580/01, 0581/01


1 hour

















wyliet

Second Variant QP

2

© UCLES 2007 0580/01/M/J/07

For

Examiner's

Use 1 Work out the value of 6-3×12

3×2.

Answer [1]

2 Write the following in order, with the smallest first.

4

5 0.79 81%

Answer < < [1]

3 Jamal arrived at work at 09 40 and left at 17 25. How long, in hours and minutes, did he spend at work? Answer h min [1]

4

NOT TOSCALE

150 cm A piece of wood is 150 centimetres long.

It has to be cut into equal lengths of 64

1 centimetres.

How many of these lengths can be cut from this piece of wood? Answer [1]

wyliet

Second Variant QP

3


For

Examiner's

Use

5 Daniel plots a scatter diagram of speed against time taken. As the time taken increases, speed decreases. Which one of the following types of correlation will his scatter graph show?

Positive Negative Zero Answer [1]

6 The average temperatures in Moscow for each month are shown in the table below.


Temperature °C −10.2 −8.9 −4.0 4.5 12.2 16.3 18.5 16.6 10.9 4.3 −2.0 −7.5

(a) Which month has the lowest average temperature? Answer(a) [1]

(b) Find the difference between the average temperatures in February and October. Answer(b) °C [1]

7

125°

North

P

L

NOT TOSCALE

North

The bearing of a lighthouse, L, from a port, P, is 125°. Find the bearing of P from L. Answer [2]

wyliet

Second Variant QP

4

© UCLES 2007 0580/01/M/J/07

For

Examiner's

Use

8 The points A and B are marked on the diagram.

y

x–4 –3 –2 –1 1 2 3 40

4

3

2

1

–1

–2

–3

–4

A

B

(a) Write AB as a column vector.

Answer(a) AB =

[1]

(b) BC =

_3

_2

.

Write down the co-ordinates of C. Answer(b) ( , ) [1]

9 Expand the brackets and simplify

4x2 – x(x −2y). Answer [2]

wyliet

Second Variant QP

5


For

Examiner's

Use

10

NOT TOSCALE

35°

135°

A B

E F

C D

In the diagram, AB, CD and EF are parallel lines. Angle ABC = 35° and angle CEF = 135°. Calculate angle BCE. Answer Angle BCE = [2]

11 The net of a solid is drawn accurately below.

Write down the special name for (a) the triangles shown on the net, Answer(a) [1]

(b) the solid. Answer(b) [1]

wyliet

Second Variant QP

6

© UCLES 2007 0580/01/M/J/07

For

Examiner's

Use

12 Write down the equation of the straight line through (0, −3) which is parallel to y = 2x + 3. Answer y = [2]

13 (a) 3p × 35 = 314. Find the value of p. Answer(a) p = [1]

(b) 28 ÷ 2q = 23. Find the value of q. Answer(b) q = [1]

(c) 6

r = 1

36. Find the value of r.

Answer(c) r = [1]

14 (a) Alex changed $270 into euros (€) when the rate was €1 = $1.19886. How many euros did he receive? Answer(a) € [2]

(b) Write 1.19886 correct to 3 significant figures. Answer(b) [1]

wyliet

Second Variant QP

7


For

Examiner's

Use

15 The diagram shows a regular hexagon and a square.

x°y°

NOT TOSCALE

Calculate the values of x and y. Answer x =

y = [3]

16 Aminata bought 20 metres of cloth at a cost of $90. She sold 15 metres of the cloth at $5.80 per metre and 5 metres at $3 per metre. (a) Calculate the profit she made. Answer (a)$ [2]

(b) Calculate this profit as a percentage of her original cost. Answer (b) % [1]

wyliet

Second Variant QP

8

© UCLES 2007 0580/01/M/J/07

For

Examiner's

Use

17 (a) The surface area of the earth is approximately 510 000 000 square kilometres. Write this number in standard form. Answer(a) km2 [2]

(b) 29.4% of the surface area of the earth is land.

Calculate the area of land. Answer(b) km2 [2]

18

A C

B

1100 m

800 m

NOT TOSCALE

A hot air balloon, B, is 800 metres vertically above a point C on the ground. A girl stands at a point A, 1100 metres horizontally from C. (a) Calculate the distance, AB, of the girl from the balloon. Answer(a) AB = m [2]

(b) Calculate the angle BAC. Answer(b) Angle BAC = [2]

wyliet

Second Variant QP

9


For

Examiner's

Use

19 In triangle LMN, LM = 120 mm, LN = 70 mm and MN = 86 mm. (a) Calculate the perimeter of the triangle LMN. Answer(a) mm [1]

(b) Construct the triangle LMN, leaving in your construction arcs. The side LM is drawn for you.

L 120 mm M [2] (c) The side LM is 120 mm, correct to the nearest millimetre. Write down the shortest possible length of LM. Answer(c) mm [1]

wyliet

Second Variant QP

10

© UCLES 2007 0580/01/M/J/07

For

Examiner's

Use

20 15 students estimated the area of the rectangle shown below.

Their estimates, in square centimetres were

45 44 50 50 51

21 50 46 43 50

48 22 45 49 48

(a) Work out (i) the mode, Answer(a)(i) cm2 [1]

(ii) the mean, Answer(a)(ii) cm2 [2]

(iii) the median. Answer(a)(iii) cm2 [2]

(b) Explain why the mean is not a suitable average to represent this data. Answer(b) [1]

wyliet

Second Variant QP

11

© UCLES 2007 0580/01/M/J/07

For

Examiner's

Use

21

1400

1200

1000

800

600

400

200

0 50 100 150 200

Time (seconds)

250 300 350 400Home

Work

Distance(metres)

AB

CD

AB

CD

E

The graph shows the distance travelled by a cyclist on a journey from Home to Work. (a) The cyclist stopped twice at traffic lights. For how many seconds did the cyclist wait altogether? Answer (a) s [2]

(b) For which part of the journey did the cyclist travel fastest? Answer (b) [1]

(c) (i) How far did the cyclist travel from Home to Work? Answer (c)(i) m [1]

(ii) Calculate the cyclist’s average speed for the whole journey. Answer(c)(ii) m/s [3]

wyliet

Second Variant QP



*9910953725*

For Examiner's Use


MATHEMATICS 0580/03, 0581/03


2 hours


Additional Materials: Electronic calculator Mathematical tables (optional) Geometrical instruments Tracing paper (optional)















2

© UCLES 2007 0580/03/J/07

For

Examiner's

Use

1 (a) Find the value of (i) 50, Answer(a)(i) [1]

(ii) the square root of 64, Answer(a)(ii) [1]

(iii) the cube root of 64, Answer(a)(iii) [1]

(iv) the integer closest in value to (1.8)3. Answer(a)(iv) [1]

(b) Write down (i) a common factor of 15 and 27, which is greater than 1, Answer(b)(i) [1]

(ii) a common multiple of 10 and 12. Answer(b)(ii) [1]

(c) (i) Two of the factors of 2007 are square numbers. One of these is 1. Find the other square number. Answer(c)(i) [1]

(ii) Write down the two factors of 2007 which are prime. Answer(c)(ii) and [2]

3

© UCLES 2007 0580/03/J/07 [Turn over

For

Examiner's

Use

2 Marguerite earns $336 per month. She divides her earnings between bills, food, savings and personal spending.

(a) Her bills take 27

of her earnings.

Show that $240 is left for her other items. Answer(a) [2] (b) She divides the $240 between food, savings and personal spending in the ratio 5 : 3 : 4. Calculate how much she spends on food. Answer(b) $ [2]

(c) She saves the same amount each month. Show that she saves $720 in one year. Answer(c) [2] (d) She invests the $720 in a bank which pays 6% per year compound interest. How much will this be worth after 2 years? Answer(d) $ [3]

4

© UCLES 2007 0580/03/J/07

For

Examiner's

Use

3 (a) Kinetic energy, E, is related to mass, m, and velocity, v, by the formula

E = 12

mv2.

(i) Calculate E when m = 5 and v = 12. Answer(a)(i) E= [2]

(ii) Calculate v when m = 8 and E = 225. Answer(a)(ii) v = [2]

(iii) Make m the subject of the formula. Answer(a)(iii) m = [2]

(b) Factorise completely xy2 – x2y. Answer(b) [2]

(c) Solve the equation 3(x – 5) + 2(14 – 3x) = 7. Answer(c) x = [3]

(d) Solve the simultaneous equations

4x + y = 13, 2x + 3y = 9.

Answer(d) x = y = [3]

5

© UCLES 2007 0580/03/J/07 [Turn over

For

Examiner's

Use

4 (a) The table shows corresponding values of x and y for the function

y =x

60 (x ≠ 0).

x −6 −5 −4 −3 −2 −1 1 2 3 4 5 6

y −12 −15 −30 60 12 10

[2] (i) Fill in the missing values of y in the table above. (ii) Plot the points on the grid below and draw the graph for −6 x −1 and 1 x 6.

y

x

60

50

40

30

20

10

–10

–20

–30

–40

–50

–60

–6 –5 –4 –3 –2 –1 10 2 3 4 5 6

[4] (b) Write down the order of rotational symmetry of the graph. Answer(b) [1]

(c) Draw the lines of symmetry of the graph on the grid. [2] (d) One line of symmetry intersects the graph at two points. (i) Write down the co-ordinates of these two points. Answer(d)(i) ( , ) and ( , ) [2]

(ii) Write down the equation of this line of symmetry. Answer(d)(ii) [1]

(e) Find the gradient of the other line of symmetry. Answer(e) [1]

6

© UCLES 2007 0580/03/J/07

For

Examiner's

Use

5 A bag contains 24 discs. 10 discs are red, 9 discs are green and 5 discs are yellow. (a) The number of discs of each colour can be shown by three sectors on a pie chart. The sector angle for the red discs is 150°. Work out the sector angle for (i) the green discs, Answer(a)(i) [1]

(ii) the yellow discs. Answer(a)(ii) [1]

(iii) Complete the pie chart below and label the sectors.

[2]

7

© UCLES 2007 0580/03/J/07 [Turn over

For

Examiner's

Use

(b) A disc is chosen at random. Find, as a fraction, the probability of each of the following events. (i) Event A: the disc is red. Answer(b)(i) [1]

(ii) Event B: the disc is red or yellow. Answer(b)(ii) [1]

(iii) Event C: the disc is not yellow. Answer(b)(iii) [1]

(c)

Impossible

Probability Scale

Certain

........... ...........(c)(i) (c)(ii)

The diagram shows a horizontal probability scale. Write on the dotted lines in the diagram, the probability of (i) an impossible event, [1]

(ii) a certain event. [1]

(d) Using the notation, A, B and C, mark the positions of your three answers in part (b) on the Probability Scale diagram in part (c). [3]

8

© UCLES 2007 0580/03/J/07

For

Examiner's

Use

6

56°

D C

A B

E

O

NOT TOSCALE

6 m 6 m

ABCED is the cross-section of a tunnel. ABCD is a rectangle and DEC is a semi-circle. O is the mid-point of AB. OD = OC = 6 m and angle DOC = 56°. (a) (i) Show that angle COB = 62°.

Answer(a)(i) [1] (ii) Calculate the length of OB. Answer(a)(ii) OB = m [2]

(iii) Write down the width of the tunnel, AB. Answer(a)(iii) AB= m [1]

(iv) Calculate the length of BC. Answer(a)(iv) BC = m [2]

9

© UCLES 2007 0580/03/J/07 [Turn over

For

Examiner's

Use

(b) Calculate the area of (i) the rectangle ABCD, Answer(b)(i) m2 [2]

(ii) the semi-circle DEC, Answer(b)(ii) m2 [2]

(iii) the cross-section of the tunnel. Answer(b)(iii) m2 [1]

(c) The tunnel is 500 metres long. (i) Calculate the volume of the tunnel. Answer(c)(i) m3 [2]

(ii) A car travels through the tunnel at a constant speed of 60 kilometres per hour. How many seconds does it take to go through the tunnel? Answer(c)(ii) s [3]

10

© UCLES 2007 0580/03/J/07

For

Examiner's

Use

7

A B

CD

A B

CD

O

l

A quadrilateral ABCD, a line l and a point O are shown on the grid above. (a) Write down the mathematical name for the quadrilateral ABCD. Answer(a) [1]

(b) On the grid above, draw the images of the quadrilateral ABCD under the following transformations.

(i) Translation by the vector 9

3

−

. Label this image P. [2]

(ii) Reflection in the line l. Label this image Q. [2] (iii) Rotation, centre A, through 90° anti-clockwise. Label this image R. [2] (iv) Enlargement, centre O and scale factor 3. Label this image S. [3]

11

© UCLES 2007 0580/03/J/07 [Turn over

For

Examiner's

Use

8

O

P

A

B

R

The diagram shows a circular garden, centre O. A straight path AB touches the circle at P. (a) (i) Draw on the diagram the diameter PQ and label the point Q. [1] (ii) Without measuring, write down the size of angle APQ. Answer(a)(ii) Angle APQ= [1]

(iii) The point R is marked on the circumference of the circle. Draw the lines PR and QR. [1] (iv) Write down the reason why the angle PRQ is 90°.

Answer(a)(iv) [1] (b) Showing all your construction lines, use a straight edge and compasses only to construct (i) the perpendicular bisector of QR, [2] (ii) the bisector of angle PRQ. [2]

(c) Shade the region of the garden between PQ and QR which is closer to R than to Q and closer to RQ than to RP. [2]

Question 9 is on the next page.

12



© UCLES 2007 0580/03/J/07

For

Examiner's

Use

9 In the pattern below each diagram shows a letter E formed by joining dots.


(a) Draw the next letter E in the pattern. [1] (b) Complete the table showing the number of dots in each letter E.

Diagram 1 2 3 4 5

Dots 8 15

[3] (c) How many dots make up the letter E in (i) Diagram 10, Answer(c)(i) [2]

(ii) Diagram n? Answer(c)(ii) [2]

(d) The letter E in Diagram n has 113 dots.

Write down an equation in n and use it to find the value of n. Answer(d) n = [3]

Location Entry Codes

As part of CIE’s continual commitment to maintaining best practice in assessment, CIE has begun to use different variants of some question papers for our most popular assessments with extremely large and widespread candidature, The question papers are closely related and the relationships between them have been thoroughly established using our assessment expertise. All versions of the paper give assessment of equal standard. The content assessed by the examination papers and the type of questions are unchanged. This change means that for this component there are now two variant Question Papers, Mark Schemes and Principal Examiner’s Reports where previously there was only one. For any individual country, it is intended that only one variant is used. This document contains both variants which will give all Centres access to even more past examination material than is usually the case. The diagram shows the relationship between the Question Papers, Mark Schemes and Principal Examiner’s Reports.

Question Paper Mark Scheme Principal Examiner’s Report

Introduction Introduction Introduction

First variant Question Paper First variant Mark Scheme First variant Principal Examiner’s Report

Second variant Question Paper Second variant Mark Scheme Second variant Principal Examiner’s Report

Who can I contact for further information on these changes? Please direct any questions about this to CIE’s Customer Services team at: [email protected]



*7675095749*

For Examiner's Use

P


MATHEMATICS 0580/01, 0581/01


1 hour

















wyliet

First Variant QP

2

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

1 On a winter’s day in Vienna the maximum temperature was –2°C. The minimum temperature was 11°C lower than this. Write down the minimum temperature. Answer °C [1]

2 Chris and Roberto share $35 in the ratio 5:2. Calculate how much Roberto receives. Answer $ [2]

3 Solve the equation 1 – 2x = x + 4. Answer x = [2]

4 In 2005, a toy cost 52.50 reals in Brazil. In Argentina, 1 peso = 0.875 reals. Work out the cost of the toy in pesos. Answer pesos [2]

wyliet

First Variant QP

3


For

Examiner's

Use

5 Factorise completely 4xy – 2x. Answer [2]

6

NOT TO

SCALE

pº

30 m

25 m

The height of a tree is 25 metres. The shadow of the tree has a length of 30 metres. Calculate the size of the angle marked p° in the diagram. Answer p = [2]

7 The distance, d kilometres, between Windhoek and Cape Town is 1300 km, correct to the nearest 100 kilometres.

Complete the statement about the value of d. Answer d < [2]

wyliet

First Variant QP

4

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

8 (a)

Draw all the lines of symmetry on the shape above. [1] (b) A quadrilateral has rotational symmetry of order 2 and no lines of symmetry. Write down the geometrical name of this shape. Answer(b) [1]

9 (a) Write in the missing number. 18

...

6

5=

[1] (b) Without using your calculator and writing down all your working, show that

18

7

6

5

9

21 =− .

Answer(b)

[2]

wyliet

First Variant QP

5


For

Examiner's

Use

10 Each interior angle of a regular polygon is 150°. (a) Work out the size of each exterior angle. Answer(a) [1]

(b) Work out the number of sides of this polygon. Answer(b) [2]

11

A

B

North

NOT TO

SCALE

140º

50 km

A ship travels 50 kilometres from A to B on a bearing of 140°, as shown in the diagram. Calculate how far south B is from A. Answer km [3]

wyliet

First Variant QP

6

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

12 y

x

l

0

3

1

NOT TO

SCALE

A straight line, l, crosses the x-axis at (1, 0) and the y-axis at (0, 3). (a) Find the gradient of the line l. Answer(a) [1]

(b) Write down the equation of the line l, in the form y = mx + c. Answer(b) y = [2]

13 A school has 240 students. (a) There are 131 girls. What percentage of the students are girls? Answer(a) [2]

(b) One day 6.25% of the 240 students are absent. Work out the number of students who are absent. Answer(b) [2]

wyliet

First Variant QP

7


For

Examiner's

Use

14 (a) Calculate the circumference of a circle of diameter 8 cm. Answer(a) cm [2]

(b)

Q

BA

NOT TO

SCALE

29º

AQB is a semi-circle. Angle QAB = 29°. Work out the size of angle ABQ. Answer(b) Angle ABQ = [2]

15 Simplify (a) a0, Answer(a) [1]

(b) ( )2

3x

Answer(b) [1]

(c) -2

3 x

.

Answer(c) [2]

wyliet

First Variant QP

8

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

16 (a) (i) Write 17 598 correct to 2 significant figures. Answer(a)(i) [1]

(ii) Write your answer to part (a)(i) in standard form. Answer(a)(ii) [1]

(b) Write 5.649 × 10-2 as a decimal, correct to 3 decimal places. Answer(b) [2]

17 (a) Alex invests $200 for 2 years at 4.05% per year simple interest. Calculate how much interest Alex receives. Answer(a) $ [2]

(b) Bobbie invests $200 for 2 years at 4% per year compound interest. Calculate how much interest Bobbie receives. Give your answer to 2 decimal places. Answer(b) $ [2]

wyliet

First Variant QP

9


For

Examiner's

Use

18 y

x

5

4

3

2

1

–1

–2

–3

–4

–5

–4 –3 –2 –1 10 2 3 4 5 6

K

(a) KL =

−

3

3. The point K is marked on the diagram.

(i) Draw KL on the diagram. [1]

(ii) Write down the co-ordinates of the point L. Answer(a)(ii) ( , ) [1]

(b) P is the point (−3, −3).

PR= 2

1

and PS = 2PR .

Find the co-ordinates of S. Answer(b) ( , ) [2]


wyliet

First Variant QP

10

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

19

1200

900

600

300

0

1500

08 00 08 2008 10 08 30

Time

Distance

(metres)

School

Home

The travel graph shows Maria’s walk to school one Monday morning.

(a) Calculate her speed during the first 20 minutes

(i) in metres / minute,

Answer(a)(i) m / min [1]

(ii) in kilometres / hour.

Answer(a)(ii) km / h [2]

(b) Calculate the average speed of her walk from home to school in kilometres / hour.

Answer(b) km / h [2]

wyliet

First Variant QP


IB07 11_0580_01_TZ/2RP © UCLES 2007 [Turn over

*5528231567*

For Examiner's Use


MATHEMATICS 0580/01, 0581/01


1 hour








DO NOT WRITE IN ANY BARCODES









Q

wyliet

Second Variant QP

2

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

1 On a winter’s day in Lesotho the maximum temperature was –3 °C. The minimum temperature was 9 °C lower than this. Write down the minimum temperature. Answer °C [1]

2 Paulo and Maria share $45 in the ratio 4:5. Calculate how much Maria receives. Answer $ [2]

3 Solve the equation 2 – 3x = x + 10. Answer x = [2]

4 In 2006, a toy cost 70.80 reals in Brazil. In Argentina, 1 peso = 0.885 reals. Work out the cost of the toy in pesos. Answer pesos [2]

wyliet

Second Variant QP

3


For

Examiner's

Use

5 Factorise completely 2pq – 4q. Answer [2]

6

NOT TO

SCALE

pº

32 m

22 m

The height of a tree is 22 metres. The shadow of the tree has a length of 32 metres. Calculate the value of the angle marked p° in the diagram. Answer p = [2]

7 The distance, d kilometres, between Auckland and Tokyo is 8800 km, correct to the nearest 100 kilometres.

Complete the statement about the value of d. Answer d < [2]

wyliet

Second Variant QP

4

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

8 (a)

Draw all the lines of symmetry on the shape above. [1] (b) A quadrilateral has rotational symmetry of order 2 and no lines of symmetry. Write down the geometrical name of this shape. Answer(b) [1]

9 (a) Write in the missing number. =

5 ...

8 24

[1] (b) Without using your calculator and writing down all your working, show that

5 5 191 =12 8 24

_ .

Answer(b)

[2]

wyliet

Second Variant QP

5


For

Examiner's

Use

10 Each interior angle of a regular polygon is 160°. (a) Work out the size of each exterior angle. Answer(a) [1]

(b) Work out the number of sides of this polygon. Answer(b) [2]

11

A

B

North

NOT TO

SCALE

150º

40 km

A ship travels 40 kilometres from A to B on a bearing of 150°, as shown in the diagram. Calculate how far south B is from A. Answer km [3]

wyliet

Second Variant QP

6

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

12 y

x

l

0

4

2

NOT TO

SCALE

A straight line, l, crosses the x-axis at (2, 0) and the y-axis at (0, 4). (a) Work out the gradient of the line l. Answer(a) [1]

(b) Write down the equation of the line l, in the form y = mx + c. Answer(b) y = [2]

13 A school has 320 students. (a) There are 153 girls. What percentage of the students are girls? Answer(a) [2]

(b) One day 3.75% of the 320 students are absent. Work out the number of students absent. Answer(b) [2]

wyliet

Second Variant QP

7


For

Examiner's

Use

14 (a) Calculate the circumference of a circle of diameter 13 cm. Answer(a) cm [2]

(b)

Q

BA

NOT TO

SCALE

33º

AQB is a semi-circle. Angle QAB = 33°. Work out the value of angle ABQ. Answer(b) Angle ABQ = [2]

15 Simplify (a) t0, Answer(a) [1]

(b) ( )42

y

Answer(b) [1]

(c) 2-

5

p

.

Answer(c) [2]

wyliet

Second Variant QP

8

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

16 (a) (i) Write 15 583 correct to 2 significant figures. Answer(a)(i) [1]

(ii) Write your answer to part (a)(i) in standard form. Answer(a)(ii) [1]

(b) Write 3.718 × 10-3 as a decimal, correct to 4 decimal places. Answer(b) [2]

17 (a) Abdul invests $400 for 2 years at 6.05% per year simple interest. Calculate how much interest Abdul receives. Answer(a) $ [2]

(b) Samia invests $400 for 2 years at 6% per year compound interest. Calculate how much interest Samia receives. Give your answer to 2 decimal places. Answer(b) $ [2]

wyliet

Second Variant QP

9


For

Examiner's

Use

18

y

x

5

4

3

2

1

–1

–2

–3

–4

–5

–4 –3 –2 –1 10 2 3 4 5 6

K

(a) KL =

_2

5

. The point K is marked on the diagram.

(i) Draw KL on the diagram. [1]

(ii) Write down the co-ordinates of the point L. Answer(a)(ii) ( , ) [1]

(b) P is the point (−4, −4).

PR= 3

2

and PS = 2PR .

Find the co-ordinates of S. Answer(b) ( , ) [2]

Question 19 is printed on the next page

wyliet

Second Variant QP

10

© UCLES 2007 0580/01/O/N/07

For

Examiner's

Use

19

1200

1400

600

800

1000

200

400

0

1600

08 00 08 2008 10 08 30

Time

Distance

(metres)

School

Home

The travel graph shows Cecilia’s walk to school one Monday morning.

(a) Calculate her speed during the first 20 minutes

(i) in metres / minute,

Answer(a)(i) m / min [1]

(ii) in kilometres / hour.

Answer(a)(ii) km / h [2]

(b) Calculate the average speed of her walk from home to school in kilometres / hour.

Answer(b) km / h [2]

wyliet

Second Variant QP

11

0580/01/O/N/07

BLANK PAGE

wyliet

Second Variant QP

12



0580/01/O/N/07

BLANK PAGE

wyliet

Second Variant QP



*6355629826*

For Examiner's Use


MATHEMATICS 0580/03, 0581/03


2 hours











If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place





2

© UCLES 2007 0580/03/O/N/07

For

Examiner's

Use

1 Margarita keeps a record of all her marks for science experiments, as shown in the table below.

Mark 5 6 7 8 9 10

Frequency 1 5 10 9 7 3

(a) (i) How many science experiments did Margarita do? Answer(a)(i) [1]

(ii) Write down the mode. Answer(a)(ii) [1]

(iii) Find the median. Answer(a)(iii) [1]

(iv) Calculate the mean. Answer(a)(iv) [3]

(b) Margarita draws a pie chart to show this information. The sectors for her marks of 5, 6, 7 and 8 have already been drawn.

5

6

7

8

(i) Calculate the angle of the sector for her mark of 9. Answer(b)(i) [2]

(ii) Complete the pie chart accurately. [1]

3


For

Examiner's

Use

2

y

x0–1–2–3–4–5–6–7

–1

–2

–3

–4

–5

–6

–7

1

2

3

4

5

6

7

1 2 3 4 5 6 7

T

(a) Draw the image of triangle T after translation by the vector_6

3

. Label it A. [2]

(b) Draw the image of triangle T after reflection in the line y = −1. Label it B. [2] (c) Draw the image of triangle T after rotation through 180° about the point (0, 0). Label it C. [2] (d) Draw the image of triangle T after enlargement, centre (0, 0), scale factor 2. Label it D. [2] (e) Describe clearly the single transformation which maps triangle D onto triangle T. Answer(e) [3]

4

© UCLES 2007 0580/03/O/N/07

For

Examiner's

Use

3 (a) Complete the table for the function 36=y

x, (x ≠ 0).

x −6 −5 −4 −3 −2 −1 1 2 3 4 5 6

y −7.2 −9 −18 18 9 7.2

[3]

(b) On the grid below, draw the graph of 36=y

x for −6 x −1 and 1 x 6.

y

x0–1–2–3–4–5–6 1 2 3 4 5 6

40

30

20

10

–10

–20

–30

–40 [4] (c) Use your graph to find x when y = 21. Answer(c) x = [1]

5


For

Examiner's

Use

(d) Complete the table for the function y = x2.

x −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

y 25 16 4 1 1 4 16 25

[2] (e) On the same grid, draw the graph of y = x2 for −6 x 6. [4]

(f) Write down the co-ordinates of the point of intersection of the graphs of 36=y

x and y = x2.

Answer(f)( , ) [1]

4

2rr

The area of the shape is given by the formula 25π

= .2

rA

(a) Calculate the area when r = 3 cm. Answer(a) A = cm2 [2]

(b) Calculate the value of r when A = 200 cm2. Answer(b) r = cm [3]

(c) Make r the subject of the formula. Answer(c) [3]

6

© UCLES 2007 0580/03/O/N/07

For

Examiner's

Use

5 (a) –4 –16 0.12 7 144 7 2

32

From this list of numbers, write down (i) the smallest number, Answer(a)(i) [1]

(ii) a natural number, Answer(a)(ii) [1]


(iv) an irrational number. Answer(a)(iv) [1]

(b) Write down 40 as a product of prime numbers. (1 is not a prime number.)

Answer(b) 40 = [2]

(c) Three pairs of prime numbers have a sum of 40. One pair is 3 and 37. Find the other two pairs.

Answer(c) and and [2]

7


For

Examiner's

Use

6 (a) Pencils cost 5 cents each and erasers cost 4 cents each.

(i) Work out the total cost of 10 pencils and 7 erasers. Answer(a)(i) cents [1]

(ii) Write down, in terms of p and e, the total cost of p pencils and e erasers. Answer(a)(ii) cents [1]

(b) The cost of a pen is x cents and the cost of a ruler is y cents. 2 pens and 3 rulers have a total cost of 57 cents. 5 pens and 1 ruler have a total cost of 58 cents. (i) Write down two equations in x and y. Answer(b)(i)

[2]

(ii) Find the value of x and the value of y. Answer(b)(ii) x =

y = [4]

8

© UCLES 2007 0580/03/O/N/07

For

Examiner's

Use

7

A

CB D3 cm

3 cm3 cm

8 cm

A

CB 3 cm

3 cm3 cm

NOT TO

SCALE

Diagram 1 Diagram 2 A physics teacher uses a set of identical triangular glass prisms in a lesson. Diagram 1 shows one of the prisms. Diagram 2 shows the cross-section of one prism. The triangle ABC is equilateral, with sides of length 3 cm and height AD. (a) (i) Calculate the length of AD. Answer(a)(i) cm [2]

(ii) Calculate the area of triangle ABC. Answer(a)(ii) cm2 [2]

(iii) The length of the prism is 8 cm. Calculate the volume of the prism. Answer(a)(iii) cm3 [2]

9


For

Examiner's

Use

(b) After the lesson, the glass prisms are put into a box, which is also a triangular prism. The cross-section is an equilateral triangle, with sides of length 9 cm. The length of the box is 16 cm.

16 cm9 cm

9 cm9 cm

NOT TO

SCALE

(i) Work out the largest number of glass prisms that can fit into the box. Answer(b)(i) [2]

(ii) Sketch a net of the box. (Accurate construction is not required.) [1] (iii) Calculate the surface area of the box. Answer(b)(iii) cm2 [6]

(iv) The box was made out of plastic, which cost 6 cents per square centimetre. To make the box, 540 cm2 of plastic was bought. Calculate the total cost of the plastic, giving your answer in dollars. Answer(b)(iv) $ [2]

10

© UCLES 2007 0580/03/O/N/07

For

Examiner's

Use

8 Carlos is in a class of 12 students. He compares the results of the students in a mathematics test with their results in a history test. The table shows these results.

Student A B C D E F G H I J K L

Mathematics mark 17 8 11 15 14 19 9 12 19 18 13 15

History mark 10 13 10 8 11 7 14 11 10 11 11 10

(a) A student is chosen at random. What is the probability that the student scored more than 10 marks (i) in mathematics, Answer(a)(i) [1]

(ii) in mathematics and in history, Answer(a)(ii) [1]

(iii) in at least one subject? Answer(a)(iii) [1]

(b) The mean mathematics mark is 14.2. Calculate the mean history mark. Answer(b) [2]

(c)

Mathematics mark

History

mark

15

14

13

12

11

10

9

8

7

7 8 9 10 11 12 13 14 15 16 17 18 19 200

(i) On the grid, plot the points to show the results of the 12 students. [3] (ii) Draw a line of best fit. [1]

(iii) What type of correlation does this show?

Answer(c)(iii) [1]

11


For

Examiner's

Use

9

Q

TP

The scale drawing shows a map of a town. The positions of the town hall, T, and two post offices, P and Q, are marked. On the scale drawing, 1 centimetre represents 200 metres. (a) A new post office in the town is to be built so that it is 800 m from T and equidistant from P and from Q. (i) On the scale drawing, draw the locus of points which are 800 m from T. [1] (ii) On the scale drawing, using a straight edge and compasses only, construct the locus of points which are equidistant from P and from Q. [2] (iii) Label the position of the new post office R. [1] (iv) Find the actual distance between post offices P and R. Answer(a)(iv) m [2]

(b) On the scale drawing, draw straight lines to make triangle PQT. Using a straight edge and compasses only, construct the locus of points which are equidistant from PT and from QT. [2]

(c) On the scale drawing, shade the region inside triangle PQT, where points are nearer to Q than to P and nearer to PT than to QT. [2]


12



© UCLES 2007 0580/03/O/N/07

For

Examiner's

Use

10

Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Look at the sequence of five diagrams above. Diagram 1 has 2 dots and 1 line. Diagram 2 has 6 dots and 7 lines. The numbers of dots and lines in each of the diagrams are shown in the table below.

Diagram number 1 2 3 4 5 6 7

Number of dots 2 6 12 20 30

Number of lines 1 7 17 31 49

(a) Fill in the empty spaces in the table for Diagrams 6 and 7. [4]

(b) How many dots are there in Diagram n? Answer(b) [2]

(c) The number of lines in Diagram n is 2n2 – 1. Which diagram has 287 lines? Answer(c) [2]


IB06 06_0580_01/3RP

UCLES 2006

[Turn over

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS

International General Certificate of Secondary Education

MATHEMATICS

Paper 1 (Core) 0580/01 0581/01

Candidates answer on the Question Paper. Additional Materials: Electronic calculator

Geometrical instruments May/June 2006

Mathematical tables (optional)

Tracing paper (optional) 1hour

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in.




DO NOT WRITE IN THE BARCODE.

DO NOT WRITE IN THE GREY AREAS BETWEEN THE PAGES.




The total number of marks for this paper is 56.


If the degree of accuracy is not specified in the question, and if the answer is

not exact, give the answer to three significant figures. Give answers in

degrees to one decimal place.


Candidate

Name

Centre

Number

Candidate

Number

*051001*

For Examiner's Use

2

© UCLES 2006 0580/01 0581/01

For

Examiner's

Use

1 The temperature at noon at an Antarctic weather centre was –15 °C.

At midnight it had fallen by 12 °C. What was the temperature at midnight?

Answer oC [1]

2 0.09 90% 1000

9 9% 0.9

100

9 900%

Write down the three numbers from the list above which have the same value.

Answer [1]

3 Write down the number of square centimetres in one square metre.

Answer [1]

4 (a) Write down a number, other than 1, which is a factor of both 14 and 35.

Answer(a) [1] (b) Write down a number which is a multiple of both 14 and 35.

Answer(b) [1]

5

l m

l m

l mNOT TO

SCALE

A cube of side l metres has a volume of 20 cubic metres. Calculate the value of l.

Answer l = [2]

3

© UCLES 2006 0580/01 0581/01 [Turn over

For

Examiner's

Use

6 (a) Work out

7.528

0.063 12.48

+

×

.

Write down all the figures on your calculator display.

Answer(a) [1] (b) Write your answer to part (a) correct to 2 significant figures.

Answer(b) [1]

7 The population of a city is 350 000 correct to the nearest ten thousand. Complete the statement about the limits of the population.

population < Answer [2]

8 Factorise completely 2x2 – 6xy.

Answer [2]

9 (a) A bowl of fruit contains 3 apples, 4 bananas, 2 pears and 1 orange. Aminata chooses one piece of fruit at random. What is the probability that she chooses (i) a banana,

Answer(a)(i) [1] (ii) a mango?

Answer(a)(ii) [1]

(b) The probability that it will rain in Switzerland on 1st September is 12

5.

State the probability that it will not rain in Switzerland on 1st September.

Answer(b) [1]

10 Simplify

(a) p2 × p3, Answer(a) [1]

(b) q3 ÷ q−4, Answer(b) [1]

(c) (r2)3. Answer(c) [1]

4

© UCLES 2006 0580/01 0581/01

For

Examiner's

Use

11 Rodriguez puts $500 into a bank account. The bank pays 5% compound interest per year. (a) How much is the interest after one year?

Answer(a) $ [1] (b) Work out the total amount he has in his bank account after two years.

Answer(b) $ [2]

12 (a) Draw all the lines of symmetry on the following shapes. (Shape B is a regular polygon.)

Shape A Shape B

[2] (b) Write down the order of rotational symmetry of shape A.

Answer(b) [1]


3x − y = 18, 2x + y = 7.

Answer x =

y = [3]

14 (a) Pierre arrives at school at 08 40 and leaves at 15 30. How long, in hours and minutes, is he in school?

h Answer(a) min [1]

(b) Each day, Pierre gets up at 07 00 and goes to bed at 22 00. What percentage of each day is he in bed?

Answer(b) % [2]

5

© UCLES 2006 0580/01 0581/01 [Turn over

For

Examiner's

Use

15 =

−

4

1 and = 3 .


Answer(a) =

[1]

(b) Make two statements about the relationship between the lines AB and CD.

Statement 1

Statement 2 [2]

16 Yousef asked 24 students to choose their favourite sport. He recorded the information in the table below so that he could draw a pie chart. (a) Complete the table.

Sport Volleyball Football Hockey Cricket

Number of students 6 9 7 2

Angle on pie chart 90o 135o

[2] (b) Complete the pie chart accurately to show this data.

Volleyball

Football

[1] (c) Which is the modal sport?

Answer(c) [1]

6

© UCLES 2006 0580/01 0581/01

For

Examiner's

Use

17

NOT TO

SCALE

90 m (a) The diagram shows the plan for a new soccer field. The length of the pitch is 90 metres. The ratio length : width is 5 : 3. Calculate the width of the pitch.

Answer(a) m [2] (b) The centre circle has a circumference of 57.5 metres. Calculate the radius.

Answer(b) m [2]

7

© UCLES 2006 0580/01 0581/01 [Turn over

For

Examiner's

Use

18

3 cm

2 cm

4 cm

NOT TO

SCALE

The solid shown is a cuboid with length 4 cm, width 2 cm and height 3 cm. (a) Draw an accurate net of the cuboid on the grid below.

[2] (b) Using your net, calculate the total surface area of the cuboid.

Answer(b) cm2 [2]

8

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every

reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included,

the publisher will be pleased to make amends at the earliest possible opportunity.

University of Cambridge International Examinations is part of the University of Cambridge Local Examinations Syndicate (UCLES), which is itself a

department of the University of Cambridge.

0580/01 0581/01

For

Examiner's

Use

19 Joseph, Maria and Rebecca each win a prize. Their total prize money is $30.

Joseph wins 12

7 of the $30.

Maria wins 30% of the $30. Rebecca wins the rest of the $30. Calculate the amount each receives.

Answer Joseph $ [2]

Maria $ [2]

Rebecca $ [1]

20 There are 565 sheets of paper in a book. (a) How many sheets of paper are there in 2000 of these books? Give your answer in standard form.

Answer(a) [2] (b) A pile of 565 sheets of paper is 25 millimetres high. Calculate the thickness of 1 sheet of paper. Give your answer in standard form.

Answer(b) mm [3]


IB06 06_0580_03/4RP

UCLES 2006

[Turn over



MATHEMATICS

Paper 3 (Core) 0580/03 0581/03




Tracing paper (optional) 2 hours













not exact, give the answer to three significant figures. Given answers

in degrees to one decimal place.


Candidate

Name

Centre

Number

Candidate

Number

*058001*

For Examiner's Use

2

© UCLES 2006 0580/03 0581/03 Jun 2006

For

Examiner's

Use

1

x

y

0 108642–2–4–6

6

4

2

–2

–4

–6

B

T

A

The shapes T, A and B are drawn on the grid above. (a) In each case describe fully the single transformation which maps (i) T onto A,

Answer(a)(i) [3] (ii) T onto B.

Answer(a)(ii) [3]

(b) Draw on the grid the rotation of T by 90° anticlockwise about (0,0). Label your answer R. [2] (c) Draw on the grid the reflection of T in the line y = –2. Label your answer M. [2]

3

© UCLES 2006 0580/03 0581/03 Jun 2006 [Turn over

For

Examiner's

Use

2 A candle, made from wax, is in the shape of a cylinder. The radius is 1.5 centimetres and the height is 20 centimetres. (a) Calculate, correct to the nearest cubic centimetre, the volume of wax in the candle.

[The volume of a cylinder, radius r, height h, is hr2π .]

Answer(a) cm3 [2] (b) The candle burns 0.8 cm3 of wax every minute. How long, in hours and minutes, will it last? Write your answer correct to the nearest minute.

h Answer(b) min [3]

(c) The candles are stored in boxes which measure x cm by 24 cm by 20 cm. Each box contains 96 candles. Calculate the minimum value of x.

Answer(c) x = [2] (d) A shopkeeper pays $25 for one box of 96 candles. He sells all the candles for 35 cents each. (i) How much profit does he make?

Answer(d)(i) $ [2] (ii) Calculate his profit as a percentage of the cost price.

Answer(d)(ii) % [3]

20 cm

1.5 cm

NOT TO

SCALE

20 cm

24 cm

x cm

NOT TO

SCALE

4

© UCLES 2006 0580/03 0581/03 Jun 2006

For

Examiner's

Use

3 (a) Simplify the expression 5p – 2q – (p + q).

Answer(a) [2] (b) Solve the equation 3(2x – 5) = 27.

Answer(b) x = [3] (c) A kite has sides of length j cm and k cm. (i) Write down an expression in terms of j and k for the perimeter of the kite.

Answer(c)(i) cm [1]

(ii) The perimeter of the kite is 72 centimetres. Write down an equation in j and k.

Answer(c)(ii) [1] (iii) If k = 2j, find the value of k.

Answer(c)(iii) k = [2]

(d) (i) Use the formula w =r

ts − to find the value of w when

6

5=s ,

3

2=t and

2

1

=r .

Show all your working clearly.

Answer(d)(i) [3] (ii) Rearrange the formula in part (d)(i) to find s in terms of w, r and t.

Answer(d)(ii) s = [2]

j cm k cm

NOT TOSCALE

5


For

Examiner's

Use

4

Diagram 1 Diagram 3 Diagram 4Diagram 2 The diagrams show a sequence of regular hexagons. Sticks of equal length are used to make the hexagons. (a) Complete the table for the number of sticks in each diagram.

Diagram 1 2 3 4 5

Sticks 6 11 [3]

(b) How many sticks are there in the 20th diagram?

Answer(b) [2] (c) How many sticks are there in the nth diagram?

Answer(c) [2] (d) How many hexagons are there in a diagram which has 186 sticks?

Answer(d) [2]

6

© UCLES 2006 0580/03 0581/03 Jun 2006

For

Examiner's

Use

5 A train leaves Madrid at 07 00 and travels to Cordoba, a distance of 340 kilometres. The distance-time graph shows the journey.

07 00 08 00 09 00 10 00Madrid

Cordoba

Seville

400

300

200

100

Time

DistancefromMadrid(kilometres)

(a) Find the average speed of the train from Madrid to Cordoba, in kilometres per hour.

Answer(a) km/h [2] (b) The train stops for 12 minutes at Cordoba. It then continues its journey at the same average speed to Seville. (i) Complete the graph to show its journey. [2]

(ii) At what time does it arrive in Seville?

Answer(b)(ii) [1] (c) Another train leaves Seville at 07 30 and travels, without stopping, to Madrid. This train arrives in Madrid at 09 45. (i) Draw a line on the grid to show this journey. [2] (ii) How far from Madrid are the two trains when they pass each other?

Answer(c)(ii) km [1] (iii) Calculate the average speed of the train from Seville to Madrid, in kilometres per hour.

Answer(c)(iii) km/h [2]

7


For

Examiner's

Use

6 Ahmed selected a sample of 10 students from his school and measured their hand spans and heights. The results are shown in the table below.

Hand span (cm) 15 18.5 22.5 26 19 23 17.5 25 20.5 22

Height (cm) 154 156 164 178 162 170 154 168 168 160

He calculated the mean hand span to be 20.9 cm and the range of the hand spans to be 11 cm. (a) Calculate (i) the mean height,

Answer(a)(i) Mean = cm [2] (ii) the range of the heights.

Answer(a)(ii) Range = cm [2] (b) In order to compare the two measures, he used a scatter diagram. The first three points are plotted on the grid.

150

152

154

156

158

160

162

164

166

168

170

172

174

176

178

180

14 16 18 20 22 24 26

Height

(cm)

Hand span (cm) (i) Complete the scatter diagram by plotting the remaining 7 points. [2] (ii) Draw the line of best fit on the grid. [1] (iii) Use the line of best fit to estimate the height of a student with hand span 21 cm.

Answer(b)(iii) cm [1] (iv) Which one of the following words describes the correlation?

Positive Negative Zero

Answer(b)(iv) [1] (v) What does this indicate about the relationship between hand span and height?

Answer(b)(v) [1]

8

© UCLES 2006 0580/03 0581/03 Jun 2006

For

Examiner's

Use

7 (a) The equation of a straight line is y = mx + c.

Which letter in this equation represents the gradient?

Answer(a) [1] (b)

12

10

8

6

4

2

–2

–4

4321–1–2–3–4 0

y

x

Write down the equation of the line shown on the grid above.

Answer(b) [2] (c) Complete the table of values for y = 12 – x2.

x – 4 – 3 – 2 – 1 0 1 2 3 4

y – 4 3 11 11 8 – 4

[3] (d) On the grid above, draw the graph of y = 12 – x2. [3] (e) Write down the coordinates of the points of intersection of the straight line with your curve.

, ) and ( , ) [2] Answer(e) (

9


For

Examiner's

Use

8 (a) ABCDE is a regular polygon with centre O.

A

B

C

DE

ONOT TO

SCALE

(i) What is the special name for the polygon?

Answer(a)(i) [1] (ii) Calculate angle EOD.

Answer(a)(ii) Angle EOD = [2] (iii) Calculate angle AED.

Answer(a)(iii) Angle AED = [2] (b) In the diagram below, AB and CD are straight lines which intersect at M. LMN and PQRS are parallel straight lines.

Angle QMR = 35° and angle BMN = 64°.

64o

35o

xo

yo zoP Q R S

L N

D B

A C

NOT TO

SCALE

M

Find the values of x, y and z.

Answer(b) x = [1]

y = [2]

z = [2]

10

© UCLES 2006 0580/03 0581/03 Jun 2006

For

Examiner's

Use

9 A farmer owns a triangular field ABC. A scale diagram of this field is drawn below. 1 centimetre represents 10 metres.

A B

C

(a) (i) Complete the following statement.

The side of the field, AC, is metres long. [1] (ii) Measure, in degrees, the angle ACB.

Answer(a)(ii) Angle ACB = [1] In the following parts, leave in all your construction lines.

(b) The farmer divides the field with a fence from A to the side BC. Each point on the fence is the same distance from AB as from AC. (i) Using a straight edge and compasses only, construct the line representing the fence. [2] (ii) Write down the length of this fence, in metres.

Answer(b)(ii) m [1] (c) He puts another fence along the perpendicular bisector of the side AC. Using a straight edge and compasses only, construct the line representing this fence. [2] (d) He decides to keep goats in the region of the field which is closer to AC than to AB and closer

to A than to C. Label the region G in the field where he can keep goats. [2]

11

© UCLES 2006 0580/03 0581/03 Jun 2006

For

Examiner's

Use

10 Bashira lives in town A and works in town B, which is 13 kilometres from A on a bearing of 040°. She drives from home to work and then drives to visit her mother who lives in town C.

Town C is 17 kilometres from B on a bearing of 130° from B.

40o

qopo

130o

13 km

17 km

A

B

C

North

North

North

NOT TO

SCALE

(a) By writing down the values of p and q, show that angle ABC = 90o.

and q = Answer(a) p = [1]

(b) Use trigonometry to calculate the size of angle ACB.

Answer(b) Angle ACB = [2] (c) Calculate the distance CA.

Answer(c) CA = km [2] (d) Calculate the area of the triangle ABC.

Answer(d) km2 [2] (e) Work out the bearing of A from C.

Answer(e) [2]

12






0580/03 0581/03 Jun 2006

BLANK PAGE


IB06 11_0580_01/3RP

UCLES 2006

[Turn over



MATHEMATICS

Paper 1 (Core) 0580/01 0581/01


Geometrical instruments October/November 2006




Write in dark blue or black pen in the spaces provided on the Question Paper.














Candidate

Name

Centre

Number

Candidate

Number

For Examiner's Use

*058001*

2

© UCLES 2006 0580/01/N/06

For

Examiner's

Use

1 At noon one day the temperature is −9.5 °C. By midnight the temperature has fallen by 3.6 °C. What is the temperature at midnight?

Answer °C [1]

2 Insert brackets to make the following statement correct. 2 × 3 – 4 + 5 = 3 [1]

3 Which word describes the correlation in the scatter graph below?

positive negative none

Answer [1]

4 The nth term of a sequence is given by n2+2. Work out the 4th term.

Answer [1]

5 $1 = 0.78 euros

Use this exchange rate to change $15.50 into euros.

Answer euros [1]

3

© UCLES 2006 0580/01/N/06 [Turn Over

For

Examiner's

Use

6 Factorise completely 2a2b − 6a.

Answer [2]

7 (a) Change 56.1 metres into kilometres.

Answer(a) km [1] (b) Change 15.3 metres into millimetres.

Answer(b) mm [1]

8 Simplify 3x2y × x4y2.

Answer [2]

9 Work out 433 , giving (a) your full calculator display,

Answer(a) [1] (b) your answer correct to the nearest thousand.

Answer(b) [1]

10 Write these fractions in order with the smallest first.

33 2 6

50 3 10

< < Answer [2]

4

© UCLES 2006 0580/01/N/06

For

Examiner's

Use

11 Solve the equation 5x − 2 = 10x − 8.

Answer x = [2]

12 Only two of the following five statements are correct. A 0.07077 0.07707 B 0.07077 ≠ 0.07707 C 0.07077 = 0.07707 D 0.07077 < 0.07707 E 0.07077 > 0.07707 Write down the letters which correspond to the two correct statements.

and Answer [2]

13 Work out 2.6 × 10−3 + 9.1 × 10−4. Write your answer in standard form.

Answer [2]

14 The length of a mirror is 15.6 centimetres correct to the nearest millimetre. Complete the statement below about the length of the mirror.

Answer cm length < cm [2]

15 A truck uses 2.5 litres of fuel to travel 8 kilometres. (a) How far will the truck travel on 1 litre of fuel?

Answer(a) km [1] (b) How far will the truck travel on 120 litres of fuel?

Answer(b) km [1]

5

© UCLES 2006 0580/01/N/06 [Turn Over

For

Examiner's

Use

16 Write down the value of x when

(a) x

2 = 8,

Answer(a) x= [1]

(b) x

3 = 81

1.

Answer(b) x= [1]

17 The surface area of a sphere with radius r is A = 4πr2. (a) Calculate the surface area of a sphere with a radius of 5 centimetres.

Answer(a) cm2 [1]

(b) Make r the subject of the formula A = 4πr2.

Answer(b) r = [2]

18

10 00 11 0 0 12 00 13 00 14 00 15 00

Time of day

100

80

60

40

20

Distance

from A(km)

A

B

(a) Carla drives from town A to a supermarket. At 11 00 she continues her journey to town B, driving at 80 km/h. The first part of the journey is shown on the grid above. (i) How many minutes is Carla at the supermarket?

Answer(a) (i) min [1] (ii) Draw the rest of her journey to town B on the grid. [1] (b) Carla spends 1 hour in town B and then drives back to town A, at a constant speed, arriving

at 14 30. Show this information on the grid. [2]

6

© UCLES 2006 0580/01/N/06

For

Examiner's

Use

19 A shopkeeper buys some ready-made meals from a supplier. (a) Complete the bill shown below.

Meal Cost of one meal Number of meals Total cost

Chicken curry $3.48 15 $

Pizza $2.99 28 $

[1] (b) He sells all 15 Chicken curry meals for $4.00 each. Work out the total profit on these meals.

Answer(b) $ [1] (c) He sells 15 Pizzas for $3.55 each but is unable to sell the rest. Calculate his loss on the Pizzas as a percentage of the total cost of the Pizzas.

Answer(c) % [2]

20 (a) Draw the lines of symmetry on the two letters below.

[2] (b) Write down the order of rotational symmetry for each of the figures below.

Order Order [2]

7

© UCLES 2006 0580/01/N/06 [Turn Over

For

Examiner's

Use

21 Write the following as single vectors.

(a)

−

−+

1

3

0

1

3

2

Answer(a)

[2]

(b) 6

− 4

5

Answer(b)

[2]

22

( )13224.8

1613.5

÷−

+

(a) Rewrite this calculation with each number rounded to 1 significant figure. Answer(a)

[2] (b) Use your answer to part (a) to estimate the answer to the calculation. Show your working and write your answer correct to 1 significant figure.

Answer(b) [1] (c) Use your calculator to find the answer to the original calculation correct to 3 significant figures.

Answer(c) [2]

8






© UCLES 2006 0580/01/N/06

For

Examiner's

Use

23 The diagram shows a six-sided spinner.

6

3

1

2

5

4

(a) Amy spins a biased spinner and the probability she gets a two is .

36

5

Find the probability she (i) does not get a two,

Answer(a) (i) [1] (ii) gets a seven,

Answer(a) (ii) [1] (iii) gets a number on the spinner less than 7.

Answer(a) (iii) [1] (b) Joel spins his blue spinner 99 times and gets a two 17 times. Write down the relative frequency of getting a two with Joel’s spinner.

Answer(b) [1]

(c) The relative frequency of getting a two with Piero’s spinner is 102

21.

Which of the three spinners, Amy’s, Joel’s or Piero’s, is most likely to give a two?

Answer(c) [1]


IB06 11_0580_03/3RP

UCLES 2006

[Turn over



MATHEMATICS

Paper 3 (Core) 0580/03 0581/03




















Candidate

Name

Centre

Number

Candidate

Number

For Examiner's Use

*058003*

2

© UCLES 2006 0580/03/N/06

For

Examiner's

Use

1 (a)

3

2 2 3 3.14 35 10 24 37 45 88

From the list of numbers above choose one that is

(i) an irrational number, Answer(a) (i) [1]

(ii) the cube root of 27, Answer(a) (ii) [1]

(iii) a multiple of 9, Answer(a) (iii) [1]

(iv) a prime number, Answer(a) (iv) [1]

(v) a factor of 44, Answer(a) (v) [1]

(vi) the product of 6 and 4. Answer(a) (vi) [1]

(b) The diagram below shows a sequence of patterns made with small triangular tiles.

Pattern

number1 2 3 4

(i) Draw the next pattern in the sequence. [1]

(ii) Complete the table below.

Pattern number 1 2 3 4 5 6

Number of tiles 1 4 9

[2]

(iii) How many tiles will be in the 100th pattern?

Answer(b) (iii) [1]

(iv) How many tiles will be in the nth pattern?

Answer(b) (iv) [1]

(v) What is the special name given to the numbers in the second row of the table?

Answer(b) (v) [1]

3

© UCLES 2006 0580/03/N/06 [Turn Over

For

Examiner's

Use

2 (a) Complete the table for the equation y = − x2 + x + 2.

x −3 −2 −1 0 1 2 3 4

y −10 0 2 2 0

[3]

(b) On the grid below draw the graph of y = − x2 + x + 2. y

x3 2 1 43210

2

1

1

2

3

4

5

6

7

8

9

10

3

[4]

(c) On the grid, draw the line of symmetry of your graph. [1]

(d) Use your graph to find the maximum value of y.

Answer(d) y = [1]

(e) Draw the line y = 1 on the grid. [1]

(f) Write down the two values of x for which − x2 + x + 2 = 1.

or x = Answer(f) x = [2]

4

© UCLES 2006 0580/03/N/06

For

Examiner's

Use

3 (a) (i) Calculate the interior angle of a regular heptagon (seven-sided polygon).

Write down all the figures on your calculator display.

Answer(a) (i) [2]

(ii) Round your answer to part (a)(i) to 1 decimal place.

Answer(a) (ii) [1]

(b)

80º 95º

xº

3yº

NOT TO

SCALE

The diagram shows four angles around a point.

(i) Write down an equation in x and y.

Answer(b) (i) [1]

(ii) Simplify your equation.

Answer(b) (ii) [1]

(iii) Find y when x = 65.

Answer(b) (iii) y = [2]

5

© UCLES 2006 0580/03/N/06 [Turn Over

For

Examiner's

Use

(c) (i)

aº

2bº70º

B

A

C

NOT TO

SCALE

Explain why a + 2b = 110 in the triangle above.

Answer(c) (i) [1]

(ii)

NOT TO

SCALE

bº aº

Explain why a + b = 90 in the semi-circle above.

Answer(c) (ii) [1]

(iii) Solve the equations

a + 2b = 110,

a + b = 90.

Answer(c) (iii) a =

b = [2]

(iv) Work out the size of angle ABC in the triangle in part (c)(i).

Answer(c) (iv) Angle ABC = [1]

6

© UCLES 2006 0580/03/N/06

For

Examiner's

Use

4

3 2 1 2 3 4 5 6 7 84

y

x0

5

4

3

2

1

1

2

3

4

A

B

C

1

5


(i) triangle A onto triangle B,

Answer(a) (i) [3]

(ii) triangle A onto triangle C.

Answer(a) (ii) [2]

(b) On the grid above draw

(i) the translation of A by the vector

− 3

2, [2]

(ii) the rotation of B through 180° about the point (−1, −2). [2]

7

© UCLES 2006 0580/03/N/06 [Turn Over

For

Examiner's

Use

5 A B

D C18 cm

10 cm

X

55º

NOT TO

SCALE

The diagram shows a rectangular tile ABCD which has a shaded triangle DXB.

DC = 18 centimetres, BC = 10 centimetres and angle ADX = 55°.

(a) Calculate the area of triangle BDC.

Answer(a) cm2 [2]

(b) Calculate the length of AX.

Answer(b) cm [2]

(c) Calculate the shaded area.

Answer(c) cm2 [3]

(d) Calculate the length of BD.

Answer(d) cm [2]

8

© UCLES 2006 0580/03/N/06

For

Examiner's

Use

6

Part of the wall

brick face

20 cm

10 cmNOT TO

SCALE

(a) A builder estimates the number of bricks in a wall by dividing the area of the wall by the

area of the face of a brick.

A brick wall is 10 metres long and 1.5 metres high.

Each brick is 20 centimetres long and 10 centimetres high.

Calculate how many bricks the builder estimates are in the wall.

Show all your working.

Answer(a) bricks [3]

(b) Another wall will need 720 bricks.

The builder adds an extra 5% to this number to allow for mistakes.

(i) Calculate how many bricks the builder needs to buy.

Answer(b) (i) bricks [2]

(ii) Bricks are sold in packs of 100 which can not be split.

How many packs should the builder buy?

Answer(b) (ii) packs [1]

(c) The builder mixes sand and cement in the ratio 5:2 to make mortar.

He wants 14 buckets of mortar.

(i) How many buckets of sand and how many buckets of cement does he need?

buckets of sand and buckets of cement. Answer(c) (i) He needs [2]

(ii) One bag of cement fills 3.5 buckets.

How many bags of cement must the builder buy?

Answer(c) (ii) bags [1]

9

© UCLES 2006 0580/03/N/06 [Turn Over

For

Examiner's

Use

7

3 2 1 1 2 3 4 5 6 7 8

y

x0

A B6

5

4

3

2

1

1

2

3

4

Two straight lines labelled A and B are shown on the grid above.

(a) Find the gradient of line A.

Answer(a) [2]

(b) The equation of line B can be written as y = mx + c.

Find the values of m and c.

Answer(b) m =

c = [2]

(c) (i) On the diagram draw the line which is parallel to B and passes through the point (1,−1).

[1]

(ii) Write down the equation of this line.

Answer(c) (ii) [2]

10

© UCLES 2006 0580/03/N/06

For

Examiner's

Use

8 (a) Naomi records the sizes of the 34 pairs of shoes that her shop sells in one day.

4 10 5 6 4 8 6 4 7 3 9 7 4

7 3 5 4 6 5 10 7 5 5 6 4 7

7 6 6 5 5 3 5 6

(i) Using the list above complete the frequency table.

Shoe size 3 4 5 6 7 8 9 10

Frequency

[3]

(ii) Calculate the mean of these shoe sizes.

Answer(a) (ii) [3]

(iii) Find the range of these sizes.

Answer(a) (iii) [1]

(iv) Find the mode of these sizes.

Answer(a) (iv) [1]

(v) Work out the median shoe size.

Answer(a) (v) [2]

(vi) Calculate the percentage of all the pairs of shoes that are size 7.

Answer(a) (vi) %. [2]

(vii) Naomi orders 306 pairs of shoes to sell in her shop.

Estimate how many of these pairs of shoes should be size 7.

Answer(a) (vii) [2]

11

© UCLES 2006 0580/03/N/06 [Turn Over

For

Examiner's

Use

(b) Findlay draws a bar chart to show how many pairs of shoes he has sold in his shop in one week.

Shoe size

Frequency

3

5

10

15

4 5 6 7 8 9 10

(i) Use the information in the bar chart to complete the frequency table below.

Shoe size 3 and 4 5 and 6 7 and 8 9 and 10

Frequency

[2]

(ii) Which is the modal class in the frequency table?

Answer(b) (ii) [1]

12

© UCLES 2006 0580/03/N/06

For

Examiner's

Use

9 The sketch shows the positions of three islands A, B and C.

B is 150 kilometres due West of A.

C is 110 kilometres due North of A.

C

AB 150 km

110 kmNOT TO

SCALE

North

(a) Using a scale of 1 centimetre to represent 20 kilometres draw accurately the triangle ABC.

A is marked for you.

A

[3]

(b) A boat sets out from B to sail directly to C.

(i) Use your protractor to find the three-figure bearing of B from C.

Answer(b) (i) [2]

13

© UCLES 2006 0580/03/N/06

For

Examiner's

Use

(ii) Measure BC on your diagram and hence find the distance in kilometres of B from C.

Answer(b) (ii) km [2]

(iii) The boat sails at 20 knots.

[1 knot is 1.85 kilometres per hour.]

How long will the boat take for the first 100 kilometres of the journey?

Give your answer in hours and minutes, to the nearest minute.

hours Answer(b) (iii) min [4]

(iv) The boat takes 45 minutes for the next 18 kilometres.

Calculate this speed in kilometres per hour.

Answer(b) (iv) km/h [2]

(v) A radio beacon at A has a range of 100 kilometres.

On your diagram in part (a) draw accurately the locus of points that are 100 kilometres

from A.

[2]

(vi) For how many kilometres is the boat within range of the beacon?

Answer(b) (vi) km [2]

14

0580/03/N/06

BLANK PAGE

15

0580/03/N/06

BLANK PAGE

16


University of Cambridge International Examinations is part of the University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

0580/03/N/06

BLANK PAGE


IB05 06_0580_01/4RP

UCLES 2005

[Turn over



MATHEMATICS

Paper 1 (Core) 0580/01 0581/01




















Candidate

Name

Centre

Number

Candidate

Number

For Examiner's Use

*058001*

2

© UCLES 2005 0580/01, 0581/01 Jun 05

For

Examiner's

Use

1 The diameter of the sun is 1 392 530 kilometres. Write this value correct to 4 significant figures.

Answer km [1]

2 A bag of 30 sweets contains 8 chocolates, 13 nougats and 9 toffees. A sweet is selected at random. What is the probability that it is a toffee?

Answer [1]

3 Anne took a test in chemistry. She scored 20 marks out of 50. Work out her percentage mark.

Answer % [1]

4 Write, in its simplest form, the ratio

3.5 kilograms : 800 grams.

: Answer [2]

5 Work out 4-3 as a fraction.

Answer [2]

6 2, 3, 5, 9, 12, 15 From the set of numbers above, write down (a) a multiple of 6,

Answer (a) [1] (b) a prime factor of 27.

Answer (b) [1]

3

© UCLES 2005 0580/01, 0581/01 Jun 05 [Turn over

For

Examiner's

Use

7 Alphonse spends $28 on food.

This amount is 9

4 of his allowance.

Calculate his allowance.

Answer $ [2]

8 When x = –3 find the value of

x3+ 2x2.

Answer [2]

9 At the market, Fernando weighs his fruit to the nearest 10 grams. He weighs a mango as 260 grams. Complete the statement in the answer space.

g weight of mango < Answer g [2]

10

16o

12 m

h m

NOT TO

SCALE

A ramp from a car park to a shopping centre slopes upward at an angle of 16° to the horizontal. The length of the ramp is 12 metres. Calculate the difference in height, h metres, between the car park and the shopping centre.

Answer m [2]

4

© UCLES 2005 0580/01, 0581/01 Jun 05

For

Examiner's

Use

11 Yasmeen is setting up a business. She borrows $5000 from a loan company. The loan company charges 6% per year simple interest. How much interest will Yasmeen pay after 3 years?

Answer $ [2]

12 Make s the subject of the formula

p = st – q.

Answer s = [2]

13

A

B

C

D

E

35o

NOT TO

SCALE

In the diagram BC is parallel to DE. ABD and ACE are straight lines. (a) Choose one of the following words to complete the statement in the answer space. congruent equilateral isosceles similar

Answer (a) Triangle ABC and triangle ADE are [1]

(b) Angle BDE = 35°. Calculate the size of angle DBC.

Answer (b) Angle DBC = [1]

5


For

Examiner's

Use

14

30 mm

2 mmNOT TO

SCALE

An old Greek coin is a cylinder with a diameter of 30 millimetres and a thickness of 2 millimetres. Calculate, in cubic millimetres, the volume of the coin.

[The volume of a cylinder, radius r, height h, is πr2h.]

Answer mm3 [2]

15 (a) Write down a common multiple of 6 and 8.

Answer (a) [1] (b) Work out

8

3

6

5− .

Give your answer as a fraction in its lowest terms. You must show all your working.

Answer (b) [2]

16 Look at the sequence of numbers 7, 11, 15, 19, ………. (a) Write down the next number in the sequence.

Answer (a) [1] (b) Find the 10th number in the sequence.

Answer (b) [1] (c) Write an expression, in terms of n, for the nth number in the sequence.

Answer (c) [1]

6

© UCLES 2005 0580/01, 0581/01 Jun 05

For

Examiner's

Use

17 (a) Expand the bracket and simplify the expression

7x + 5 – 3(x – 4).

Answer (a) [2]

(b) Factorise 5x2 – 7x.

Answer (b) [1]

18 Camilla has $5 to spend in the market.

She buys 1 kilograms of bananas priced at 80 cents per kilogram and 3 yams priced at 45 cents each.

How much money does she have left?

Answer $ [3]

19 8.95 − 3.05 × 1.97

2.92 (a) (i) Write the above expression with each number rounded to one significant figure.

Answer (a)(i) [1] (ii) Use your answer to find an estimate for the value of the expression.

Answer (a)(ii) [1] (b) Use your calculator to work out the value of the original expression. Give your answer correct to 2 decimal places.

Answer (b) [1]

2

1

7


For

Examiner's

Use

20

Country Area (km2)

Brazil 8.51 x 106

Panama 7.71 x 104

Guyana 2.15 x 105

Colombia 1.14 x 106

The table above gives the areas of four South American countries, correct to 3 significant figures. (a) List the countries in order of area, smallest to largest.

< Guyana < < Answer (a) [1]

(b) Use a whole number to complete the statement in the answer space.

Answer (b) The area of Colombia is approximately times the area of Guyana. [2]

21

SALE

All items

35% Reduction

Abdul bought a spade in this sale. Its original price was $16. (a) How much did Abdul save?

Answer (a) $ [2] (b) The next day, all items were sold at half the original price. How much more would Abdul have saved if he had waited until the next day to buy the spade?

Answer (b) $ [1]

8

© UCLES 2005 0580/01, 0581/01 Jun 05

For

Examiner's

Use

22

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

7 30 8 00 8 30 9 00

School

Friend's House

Home

DISTANCE

FROM

HOME (km)

TIME (am) Ricardo rode to his friend’s house. He waited for his friend to get ready. Then they cycled together to school. Ricardo’s journey is shown on the grid. (a) Work out the speed at which Ricardo cycled to his friend’s house.

Answer (a) km/h [2] (b) How long did he wait for his friend?

Answer (b) min [1]

9

© UCLES 2005 0580/01, 0581/01 Jun 05

For

Examiner's

Use

(c) Ricardo’s brother left home at 8 00 am. He cycled directly to school at a constant speed of 15 kilometres per hour. Draw his journey on the grid opposite. [1] (d) How many minutes earlier than Ricardo did his brother arrive at school?

Answer (d) min [1]

23

A B

E

D

C

O

25o

NOT TO

SCALE

In the diagram, DE is a diameter of the circle, centre O. AEB is the tangent at the point E. The line DCB cuts the circle at C.

Angle DEC = 25°. (a) Write down the size of angle DCE.

Answer (a) Angle DCE = [1] (b) Calculate the size of angle CDE.

Answer (b) Angle CDE = [2] (c) Calculate the size of angle DBE.

Answer (c) Angle DBE = [2]

10

0580/01, 0581/01 Jun 05

BLANK PAGE

11

0580/01, 0581/01 Jun 05

BLANK PAGE

12



0580/01, 0581/01 Jun 05

BLANK PAGE


IB05 06_0580_03/5RP

UCLES 2005

[Turn over



MATHEMATICS

Paper 3 (Core) 0580/03 0581/03




















Candidate

Name

Centre

Number

Candidate

Number

For Examiner's Use

*058003*

2

© UCLES 2005 0580/03, 0581/03 Jun 05

For

Examiner's

Use

1 Juana is travelling by plane from Spain to England.

(a) Her case weighs 17.2 kilograms.

The maximum weight allowed is 20 kilograms.

By how much is the weight of her case below the maximum allowed?

Answer (a) kg [1]

(b) She changes 150 euros (€) into pounds (£).

The exchange rate is €1 = £0.71.

Calculate how much she receives.

Answer (b) £ [1]

(c) She travels from her home to the airport by train.

She catches a train at 09 55 and the journey takes 45 minutes.

(i) Write down the time she arrives at the airport.

Answer (c)(i) [1]

(ii) She has to wait until 12 10 to get on her plane.

Work out how long she has to wait.

h Answer (c)(ii) min [1]

(d) The plane takes off at 12 40 Spanish time, which is 11 40 English time.

The flight takes 2 hours.

What is the time in England when she arrives?

Answer (d) [1]

(e) The plane has seats for 420 passengers.

15% of the seats are empty.

How many passengers are on the plane?

Answer (e) [3]

4

1

3


For

Examiner's

Use

2 (a) Complete the table of values for y = 1 + 2x – x2.

x 3− 2− 1− 0 1 2 3 4 5

y 14− 7− 1 2− 14−

[3]

(b) Draw the graph of y = 1 + 2x – x2 on the grid below.

y

x

4

2

–2

–4

–6

–8

–10

–12

–14

0 1 5432–3 –2 –1

[4]

(c) Use your graph to find the solutions to the equation 1 + 2x – x2 = 0.

Answer (c) x =

or x = [2]

(d) (i) On the grid, draw the line of symmetry of the graph. [1]

(ii) Write down the equation of this line of symmetry.

Answer(d)(ii) [1]

4

© UCLES 2005 0580/03, 0581/03 Jun 05

For

Examiner's

Use

3

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

Minimum

temperature oC

4 6 0 −2 −4 2

Maximum

temperature oC

8 10 5 7 2 7

The table shows the minimum and maximum temperatures on six days of a week.

(a) (i) On Sunday the minimum temperature was 5 °C lower than on Saturday.

The maximum temperature was 2 °C higher than on Saturday.

Use this information to complete the table. [2]

(ii) Find the difference between the minimum and maximum temperatures on Thursday.

Answer(a)(ii) oC [1]

(b) Use the table to complete the graphs below for all seven days.

TemperatureoC

10

8

6

4

2

0

–2

–4

–6

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

Minimum

temperature

Maximum

temperature

[2]

5


For

Examiner's

Use

(c) Use your graphs to find

(i) on how many days the temperature fell below −1 °C,

Answer(c)(i) [1]

(ii) which day had the largest difference between minimum and maximum temperatures.

Answer(c)(ii) [1]

(d) The formula for changing degrees Celsius (C) to degrees Fahrenheit (F) is

325

9+=

CF .

Use the formula to change 6 degrees Celsius to degrees Fahrenheit.


Answer(d) [2]

6

© UCLES 2005 0580/03, 0581/03 Jun 05

For

Examiner's

Use

4

0–5 –4 –3 –2 –1

4

3

2

1

–1

–2

–3

–4

1 2 3 4 5 6

A

C

D

B

y

x

(a) A translation is given by 3

6 +

4

3

−

−

.

(i) Write this translation as a single column vector.

Answer(a)(i) [2]

(ii) On the grid, draw the translation of triangle A using this vector. [2]

(b) Another translation is given by –2 1

1

−

(i) Write this translation as a single column vector.

Answer(b)(i) [2]

(ii) On the grid, draw the translation of triangle B using this vector. [2]

(c) Describe fully the single transformation that maps shape C onto shape D.

Answer(c)

[3]

7


For

Examiner's

Use

(d)

y

xO

The triangle in the diagram above is isosceles.

(i) How many lines of symmetry does this triangle have?

Answer(d)(i) [1]

(ii) Write down the order of rotational symmetry of this triangle.

Answer(d)(ii) [1]

(iii) On the grid above, draw the rotation of this triangle about O through 180o. [2]

(iv) Describe fully another single transformation that maps this triangle onto your answer for

part (d)(iii).

Answer(d)(iv)

[2]

8

© UCLES 2005 0580/03, 0581/03 Jun 05

For

Examiner's

Use

5

6

3

51

42

(a) Asif tests a six-sided spinner.

The results of 60 spins are shown below.

3 3 6 5 6 1 2 6 5 2

3 4 4 4 3 4 6 5 2 1

6 3 6 4 1 5 3 6 2 6

6 6 3 6 1 6 6 5 1 6

1 6 2 5 3 6 4 2 3 5

1 4 4 1 5 4 6 6 2 3

(i) Use these results to complete the frequency table.

Number Frequency

1

2

3

4

5

6

[3]


Answer(a)(ii) [1]

(iii) Find the median.

Answer(a)(iii) [2]

9


For

Examiner's

Use

(iv) Calculate the mean.

Give your answer correct to one decimal place.

Answer(a)(iv) [3]

(b) Asif tests a different six-sided spinner.

He draws a bar chart to show the results.

14

12

10

8

6

4

2

01 2 3 4 5 6

Number

Frequency

(i) How many times did he spin this spinner?

Answer(b)(i) [2]

(ii) Calculate the mean score for this spinner.

Answer(b)(ii) [3]

10

© UCLES 2005 0580/03, 0581/03 Jun 05

For

Examiner's

Use

6 (a)

x cm

2x cm

NOT TO

SCALE

The perimeter of the rectangle in the diagram above is 36 centimetres.

(i) Find the value of x.


(ii) Using this value of x, calculate the area of the rectangle.

Answer(a)(ii) cm2 [2]

(b)

4z + 2

10z – 1

y + 33yNOT TO

SCALE

The diagram above shows another rectangle.

(i) In this rectangle 3y = y + 3.

Solve the equation to find y.

Answer(b)(i) y = [2]

(ii) Write down an equation in z.

Answer(b)(ii) [1]

(iii) Solve the equation in part (b)(ii) to find z.

Answer(b)(iii) z = [3]

11


For

Examiner's

Use

(c)

17

3

4a+b

a–b NOT TO

SCALE

The diagram above shows another rectangle.

(i) Write down two equations in a and b.

Answer(c)(i)

[2]

(ii) Solve these two equations simultaneously to find a and b.

Answer(c)(ii) a =

b = [3]

12

© UCLES 2005 0580/03, 0581/03 Jun 05

For

Examiner's

Use

7

North

North

14 km

A

B

C

R

Land

Sea

At midday, a ship is somewhere along the line from A to C.

(a) By measuring an angle, write down the three figure bearing of the ship from A.

Answer(a) [2]

(b) The coastguard at B sees the ship on a bearing of 350o.

(i) On the diagram draw accurately the line showing a bearing of 350o from B. [1]

(ii) On the diagram mark the position of the ship, S. [1]

(c) (i) Measure the length, in centimetres, of the line AB on the diagram.

Answer(c)(i) cm [1]

(ii) The distance from A to B is 14 kilometres.

Calculate the scale of the drawing.

Give your answer in the form 1:n.

Answer(c)(ii) 1: [2]

13


For

Examiner's

Use

(d) The ship is sailing straight for the rocks, R.

There is a lighthouse at A.

The range of the light from the lighthouse is 10 kilometres.

(i) Using your scale, draw the locus of points that are 10 kilometres from A. [2]

(ii) Draw the line SR on the diagram.

How far is the ship from the rocks when the light from the lighthouse is first seen on the

ship?

Answer(d)(ii) km [2]

(e) If the ship does not alter course it will hit the rocks at 12 40.

A lifeboat sets off from the coastguard station, B, at 12 00 and sails straight towards the rocks.

(i) Measure and calculate the distance, in kilometres, from the coastguard station, B, to the

rocks, R.

Answer(e)(i) km [2]

(ii) Calculate the speed, in kilometres per hour, at which the lifeboat must sail to reach the

rocks by 12 40.

Answer(e)(ii) km/h [3]

(iii) A knot is 1 nautical mile per hour.

One nautical mile is equal to 1.85 kilometres.

Calculate the speed found in part (e)(ii) in knots.

Answer(e)(iii) knots [2]

14

© UCLES 2005 0580/03, 0581/03 Jun 05

For

Examiner's

Use

8

A

A

B

B

C

C

NOT TO

SCALE

NOT TO

SCALE

4 cm

6 cm

8 cm

The diagram above shows a cuboid and its net.

(a) Calculate the total surface area of the cuboid.

Answer(a) cm2 [3]

15

© UCLES 2005 0580/03, 0581/03 Jun 05

For

Examiner's

Use

(b) Calculate the volume of the cuboid.

Answer(b) cm3 [2]

(c) An ant walks directly from A to C on the surface of the cuboid.

(i) Draw a straight line on the net to show this route. [1]

(ii) Calculate the length of the ant’s journey.

Answer(c)(ii) cm [3]

(iii) Calculate the size of angle CAB on the net.

Answer(c)(iii) Angle CAB = [3]

16



0580/03, 0581/03 Jun 05

BLANK PAGE


IB05 11_0580_01/5RP

UCLES 2005

[Turn over



MATHEMATICS

Paper 1 (Core) 0580/01 0581/01




















Candidate

Name

Centre

Number

Candidate

Number

*051001*

For Examiner's Use

2

© UCLES 2005 0580/01, 0581/01 Nov 2005

For

Examiner's

Use

1 The distance from Buenos Aires to Wellington is approximately 10 100 kilometres. Write this number in standard form.

Answer km [1]

2 Factorise 3xy – 2x.

Answer [1]

3 The highest mountain in Argentina is Aconcagua. Its height is 6960 metres, correct to the nearest twenty metres. Write down the smallest possible height of Aconcagua.

Answer m [1]

4 Which one of the numbers below is not a rational number?

7 2

3 5 –1 1

2 81

Answer [1]

5 Solve the equation 5x – 7 = 8.

Answer x = [2]

6 A bottle of lemonade contains 2

11 litres.

A glass holds 8

1 litre.

How many glasses can be filled from one bottle of lemonade?

Answer [2]

3

© UCLES 2005 0580/01, 0581/01 Nov 2005 [Turn over

For

Examiner's

Use

7 The table below shows the average monthly temperatures (°C) in the Islas Orcadas, Argentina.

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

1 1 0.5 –1 –5 –8 –9 –8 –5 –3 –1 0.5

(a) Work out the difference between the highest and the lowest average monthly temperature.

Answer(a) °C [1]

(b) The highest recorded temperature for July is x °C.

This is 21 °C above the average for July shown in the table. Work out the value of x.

Answer(b) x = [1]

8 The formula for the perimeter, P, of a rectangle with length a and width b is P = 2a + 2b. Make a the subject of the formula.

Answer a = [2]

9 0.072 72% 0.702 10

7

100

7 7.2%

From the values listed above, write down (a) the smallest,

Answer(a) [1] (b) the largest,

Answer(b) [1] (c) the two which are equal. Answer(c) and [1]

4

© UCLES 2005 0580/01, 0581/01 Nov 2005

For

Examiner's

Use

10 An integer n is such that 60 n 70. Write down a value of n which is (a) a prime number,

Answer(a) [1] (b) a multiple of 9,

Answer(b) [1] (c) a square number.

Answer(c) [1]

11

p =

− 3

2 and q =

1

3.

(a) Write p + q as a column vector.

Answer (a) p + q =

[2]

(b) The point O is marked on the grid below.

Draw the vector where = p.

1 2 3–3 –2 –1

3

2

1

–1

–2

–3

O

y

x

[1]

5


For

Examiner's

Use

12

S

T

1.2 km

21o

NOT TO

SCALE

The diagram shows a path, ST, up a hill.

The path is 1.2 kilometres long and slopes at an angle of 21° to the horizontal. Calculate the height of the hill, showing all your working. Give your answer in metres.

Answer m [3]

13 The population of Latvia in 1989 was 2 700 000. In 1994 it was 2 500 000. Calculate the percentage decrease in the population between 1989 and 1994.

Answer % [3]

14 = < > Choose one of the symbols given above to complete each of the following statements. When x = 6 and y = –7, then

(a) x y [1]

(b) x² y² [1]

(c) y - x x - y [1]

6

© UCLES 2005 0580/01, 0581/01 Nov 2005

For

Examiner's

Use

15 (a) Write 0.48 correct to 1 significant figure.

Answer(a) [1] (b) (i) Find an approximate answer for the sum

9.87 – 5.79 × 0.48 by rounding each number to 1 significant figure. Show your working.

Answer(b)(i) [1] (ii) Use your calculator to find the exact answer for the sum in part (b) (i). Write down all the figures on your calculator.

Answer(b)(ii) [1]

16 Simplify the following expressions.

(a) 9r – 4s – 6r + s

Answer(a) [1]

(b) q4 ÷ q3

Answer(b) [1]

(c) p6 × p−2

Answer(c) [1]

17 Three friends, Cleopatra, Dalila and Ebony go shopping. The money they each have is in the ratio Cleopatra : Dalila : Ebony = 5 : 7 : 8. Cleopatra has $15. (a) How many dollars do they have in total?

Answer(a) [2] (b) Dalila spends $12 on a hat. How many dollars does she have left?

Answer(b) [1]

7


For

Examiner's

Use

18 A 400 metre running track has two straight sections, each of length 120 metres, and two semicircular ends.

120 m

NOT TOSCALE

d

(a) Calculate the total length of the curved sections of the track.

Answer(a) m [1] (b) Calculate d, the distance between the parallel straight sections of the track.

Answer(b) d = m [2]

19 Joseph buys 45 kilograms of potatoes from a supplier for $0.65 per kilogram. (a) How much does he pay for the potatoes?

Answer(a) $ [1] (b) He then puts the potatoes into bags which each hold 2.5 kilograms. How many bags can he fill with the potatoes?

Answer(b) bags [1] (c) At the market he sells the bags of potatoes for $2.20 per bag. Calculate the smallest number of complete bags he needs to sell in order to make a profit.

Answer(c) bags [2]

8

© UCLES 2005 0580/01, 0581/01 Nov 2005

For

Examiner's

Use

20

$900

Lorenzo saves money for a motorbike. The marked price of the motorbike is $900. He pays a deposit of 35% of the marked price. (a) Calculate his deposit.

Answer(a) $ [2] (b) He then makes 12 monthly payments of $60 each. How much more than the $900 marked price does he pay altogether?

Answer(b) $ [3]

9

© UCLES 2005 0580/01, 0581/01 Nov 2005

For

Examiner's

Use

21 The graph below shows the amount a plumber charges for up to 6 hours work.

01 2 3

Time (hours)

4 5 6

120

100

80

60

40

20

Charge ($)

(a) How much does he charge for 32

1 hours work?

Answer(a) $ [1] (b) The plumber charged $50. How many hours did he work?

Answer(b) hours [1] (c) Another plumber charges $16 per hour. (i) Draw a line on the grid above to show his charges. Start your line at (0,0). [2] (ii) Write down the number of hours for which the two plumbers charge the same amount.

Answer(c)(ii) hours [1]

10

0580/01, 0581/01 Nov 2005

BLANK PAGE

11

0580/01, 0581/01 Nov 2005

BLANK PAGE

12






0580/01, 0581/01 Nov 2005

BLANK PAGE


IB05 11_0580_03/7RP

© UCLES 2005

[Turn over



MATHEMATICS

Paper 3 (Core) 0580/03 0581/03




















Candidate

Name

Centre

Number

Candidate

Number

*058001*

For Examiner's Use

2

© UCLES 2005 0580/03, 0581/03 Nov 2005

For

Examiner's

Use

1 (a) Draw accurately the reflection of the letter E in the mirror line m.

m [2]

(b) Each diagram below shows a shaded letter and its image.

In each case describe fully the single transformation which maps the shaded figure onto its image.

Mark and label any points you need in your descriptions.

(i)

Answer(b)(i) [3]

(ii)

Answer(b)(ii) [3]

(iii) y

x–6 –4 –2 2 4 60

4

2

–2

–4

Answer(b)(iii) [3]

3


For

Examiner's

Use

2 In the diagram below ABD is a straight line.

AB = 4 m and AC = 6 m. Angle BAC = 90°.

A DB

C

4 m

6 m

NOT TO

SCALE

(a) (i) Use trigonometry to calculate angle ABC.

Answer(a)(i) Angle ABC= [2]

(ii) Find angle CBD.

Answer(a)(ii) Angle CBD= [1]

(b) Calculate the length of BC.

Answer(b) BC = m [2]

(c) Work out the perimeter and area of triangle ABC.

Give the correct units for each.

Area = Answer (c) Perimeter = [3]

4

© UCLES 2005 0580/03, 0581/03 Nov 2005

For

Examiner's

Use

3 (a) (i) Complete the table of values for 322

−−= xxy .

x −3 −2 −1 0 1 2 3 4 5

y 12 0 −4 −3 0 5

[3]

(ii) Draw the graph of 322

−−= xxy on the grid below.

–3 –2 –1 1 5432

12

10

8

6

4

2

–2

–4

0

y

x

[4]

(iii) Use your graph to find the solutions to 1322

−=−− xx .

Give your answers to 1 decimal place.

or x = Answer(a)(iii) x = [2]

(b) (i) Complete the table of values for the equation x

y2

= .

x 0.25 0.5 1 2 3 4 5

y 4 1 0.7 0.5 0.4

[1]

(ii) On the same grid draw the graph of x

y2

= for 0.25 x 5. [3]

(iii) Write down the x co-ordinate of the point of intersection of your two graphs.

Answer(b)(iii) x = [1]

5


For

Examiner's

Use

4 Jane records the number of telephone calls she receives each day for two weeks.

5 6 10 0 15 6 12 2 13 16 0 16 6 10

(a) Calculate the mean.

Answer(a) [3]

(b) Find the median.

Answer(b) [2]

(c) Write down the mode.

Answer(c) [1]

(d) Complete the frequency table below.

Number of calls 0 − 4 5 − 9 10 − 14 15 − 19

Frequency

[2]

(e) Find the probability that Jane receives

(i) ten or more calls,

Answer(e)(i) [1]

(ii) less than five calls.

Answer(e)(ii) [1]

(f) Estimate the number of days in the next six weeks that Jane can expect to receive 10 − 14 calls.

Answer(f) days [2]

6

© UCLES 2005 0580/03, 0581/03 Nov 2005

For

Examiner's

Use

5 North

5 km

6 km

NOT TOSCALE

A

B

C

110o

In triangle ABC, AB = 5 km, AC = 6 km and angle BAC = 110º.

The bearing of C from A is 100°.

(a) Make a scale drawing of the triangle ABC.

Use a scale of 1 centimetre to represent 1 kilometre.

Start at the point A marked below, where a North line has been drawn.

A

North

[4]

7


For

Examiner's

Use

(b) Measure and write down

(i) angle ABC,

Answer(b)(i) Angle ABC = [1]

(ii) the bearing of B from C.

Answer(b)(ii) [1]

(c) Find the distance in kilometres between B and C.

Answer(c) km [1]

(d) A well is 4 kilometres from A and 5 kilometres from C.

(i) Use your compasses to find two possible positions for the well.

Label the two positions P and Q. [3]

(ii) The well is less than 6 kilometres from B.

Use a measurement from your drawing to complete the following statement.

and is Answer(d)(ii) The well is at position kilometres from B.[2]

8

© UCLES 2005 0580/03, 0581/03 Nov 2005

For

Examiner's

Use

6 The diagram shows a swimming pool with cross-section ABCDE.

The pool is 6 metres long and 3 metres wide.

AB = 2 m, ED = 1 m and BC = 3.6 m.

1 m

2 m

3 m

6 m

3.6 m

A

B C

D

E

NOT TOSCALE

(a) (i) Calculate the area of the cross-section ABCDE.

Show your working.

Answer(a)(i) m2 [4]

(ii) Calculate the volume of the water in the pool when it is full.

Give your answer in litres.

[1 cubic metre is 1000 litres.]

Answer(a)(ii) litres [2]

(iii) One litre of water evaporates every hour for each square metre of the water surface.

How many litres of water will evaporate in 2 hours?

Answer(a)(iii) litres [2]

9


For

Examiner's

Use

(b) Another pool holds 61 500 litres of water.

Jon uses a hosepipe to fill this pool.

Water flows through the hosepipe at 1000 litres per hour.

(i) Calculate how long it takes to fill the pool.

Give your answer in hours and minutes.

hours Answer(b)(i) minutes [2]

(ii) Change 61 500 litres to gallons.

[4.55 litres = 1 gallon.]

Answer(b)(ii) gallons [1]

(iii) Every 10 000 gallons of water needs 2.5 litres of purifier.

How many litres of purifier does Jon use for this pool?

Answer(b)(iii) litres [2]

(iv) The purifier is sold in 1 litre bottles.

How many bottles of purifier must Jon buy for this pool?

Answer(b)(iv) [1]

10

© UCLES 2005 0580/03, 0581/03 Nov 2005

For

Examiner's

Use

7 (a)

y

x

3

2

1

–1

–2

–3

–4

–5

–3 –2 –1 543210

The simultaneous equations 2x − y = 3 and x + y = 2 can be solved graphically.

(i) Which of these equations is shown by the line on the grid above?

Answer(a)(i) [1]

(ii) Find the gradient of the line on the grid.

Answer(a)(ii) [2]

(iii) Complete the table below for the other equation.

x −1 0 1 2 3

y

[2]

(iv) Draw this line on the grid above. [1]

(v) Use your graphs to write down the solution to the two equations.

Give your values correct to 1 decimal place.

Answer(a)(v) x =

y = [3]

11


For

Examiner's

Use

(b) Use algebra to solve the following simultaneous equations exactly.


2x − y = 3,

x + y = 2.

Answer(b) x =

y = [4]

8 The diagram below shows a sequence of patterns made from dots and lines.

1 dot 3 dots2 dots 4 dots

(a) Draw the next pattern in the sequence in the space above. [1]

(b) Complete the table for the numbers of dots and lines.

Dots 1 2 3 4 5 6

Lines 4 7 10

[2]

(c) How many lines are in the pattern with 99 dots?

Answer(c) [2]

(d) How many lines are in the pattern with n dots?

Answer(d) [2]

(e) Complete the following statement.

There are 85 lines in the pattern with dots. [2]

12






© UCLES 2005 0580/03, 0581/03 Nov 2005

For

Examiner's

Use

9 (a) Calculate the size of one exterior angle of a regular heptagon (seven-sided polygon).

Give your answer correct to 1 decimal place.

Answer(a) [3]

(b)

ro

qo130o po

F B C G

tosoAD E

NOT TOSCALE

In the diagram above, DAE and FBCG are parallel lines.

AC = BC and angle FBA = 130°.

(i) What is the special name given to triangle ABC?

Answer(b)(i) [1]

(ii) Work out the values of p, q, r, s and t.

Answer (b)(ii) p = q = r = s = t = [5]

(c)

J, K and L lie on a circle centre O.

KOL is a straight line and angle JKL = 65°.

Find the value of y.

Answer(c) y = [2]

65o

yo

J

K

L

ONOT TOSCALE

Centre Number Candidate Number Name

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSInternational General Certificate of Secondary Education

MATHEMATICS 0580/01

0581/01Paper 1 (Core)

May/June 2004

Candidates answer on the Question Paper. 1 hour

Additional Materials: Electronic calculator

Geometrical instruments


Tracing paper (optional)











If the degree of accuracy is not specified in the question, and if the answer is not exact, give theanswer to three significant figures. Give answers in degrees to one decimal place.


For Examiner’s Use


IB04 06_0580_01/4RP

� UCLES 2004 [Turn over

If you have been given a label, look at thedetails. If any details are incorrect ormissing, please fill in your correct details inthe space given at the top of this page.

Stick your personal label here, if provided.

2

0580/1, 0581/1 Jun/04

For

Examiner's

Use1 Work out 43 – 52.

Answer [1]

2 The Dead Sea shore is 395 metres below sea level.Hebron is 447 metres above sea level.Find the difference in height.

Answer [1]

3 Write as a fraction in its lowest terms

(a) 75%,

Answer (a) [1]

(b) 0.07.

Answer (b) [1]

4 Look at the numbers

21, 35, 49, 31, 24.

From this list write down

(a) a square number,

Answer (a) [1]

(b) a prime number.

Answer (b) [1]

5

NOT TO

SCALE

A model of a car has a scale of 1:25.The model is 18 cm long.Calculate, in metres, the actual length of the car.

Answer m [2]

3

0580/1, 0581/1 Jun/04 [Turn over

For

Examiner's

Use

6 Without using a calculator, work out 2

1

4

12 � as a single fraction.


Answer [2]

7 Sergio’s height is 142 cm, to the nearest centimetre.Complete the statement about the limits of his height.

Answer cm height < cm [2]

8 Factorise completely xzxy 64 � .

Answer [2]

9 Alix changed a traveller’s cheque for 200 euros (€) into dollars ($) when she visited the USA.The exchange rate was 1 dollar = 1.05 euros.How many dollars did she receive?

Answer $ [2]

10

For the shape shown, write down


Answer (a) [1]


Answer (b) [1]

4

0580/1, 0581/1 Jun/04

For

Examiner's

Use11

O

P Q35o

NOT TO

SCALE

PQ is a chord of a circle, centre O. Angle OPQ = 35o.Calculate angle POQ.

Answer Angle POQ = [2]

12 (a)8

1

2

1��

�

��

� x

Write down the value of x.

Answer (a) x = [1]

(b) 17 �y

Write down the value of y.

Answer (b) y = [1]

13 39218 �

(a) (i) Write both numbers in the calculation above correct to one significant figure.

�Answer (a)(i) [1]

(ii) Use your answer to part (i) to estimate the value of the calculation.

Answer (a)(ii) [1]

(b) Use your calculator to find the value of the calculation correct to two significant figures.

Answer (b) [1]

5

0580/1, 0581/1 Jun/04 [Turn over

For

Examiner's

Use14 Shampoo is sold in two sizes, A and B.

1.5 litres $2.30800 millilitres $1.30

1.5

litres

800

millilitres

NOT TO

SCALE

A B

A contains 800 ml and costs $ 1.30.B contains 1.5 litres and costs $ 2.30.Which is the better value for money?Show your working clearly.

Answer [3]

15

A B

C

32o

5 m NOT TO

SCALE

In the right-angled triangle ABC, AC = 5 metres and angle CAB = 32o.Calculate the length of BC.

Answer BC = m [3]

6

0580/1, 0581/1 Jun/04

For

Examiner's

Use16 bcay ��

(a) Find the value of y when a = 3� , b = 2 and c = 8.

Answer (a) y = [2]

(b) Make c the subject of the formula.

Answer (b) c = [2]

17 In a school, the number of students taking part in various sports is shown in the table below.

Sport Number of students

Basketball 40

Soccer 55

Tennis 35

Volleyball 70

Draw a bar chart below to show this data.Show your scale on the vertical axis and label the bars.

Answer

Sport

Number of

students

[4]

7

0580/1, 0581/1 Jun/04 [Turn over

For

Examiner's

Use18 Carlos buys a box of 50 oranges for $ 8.

He sells all the oranges in the market for 25 cents each.

(a) Calculate the profit he makes.

Answer (a) $ [2]

(b) Calculate the percentage profit he makes on the cost price.

Answer (b) % [2]

19

30 cm

80 cmNOT TO

SCALE

The diagram shows a cylindrical tank.The radius is 30 cm and the height is 80 cm.

(a) Calculate the area of the base of the tank.

Answer (a) cm2 [2]

(b) Calculate the volume of the tank in litres.

Answer (b) litres [2]

8

0580/1, 0581/1 Jun/04

For

Examiner's

Use20 Solve the equations

(a) 3154 ��x ,

Answer (a) x = [2]

(b) 36)5(4 ��y .

Answer (b) y = [2]

21

The time in Dubai is 3 hours ahead of Birmingham.

(a) If it is 21 15 on Sunday in Birmingham, what time on Monday is it in Dubai?

Answer (a) [1]

(b) An aircraft leaves Birmingham at 21 15 on Sunday and arrives in Dubai on Monday at 07 45local time.

(i) How long did the journey take?

hAnswer (b)(i) min [1]

(ii) The distance from Birmingham to Dubai is 5620 km. Calculate the average speed of theaircraft.

Answer (b)(ii) km/h [3]


UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSInternational General Certificate of Secondary Education

MATHEMATICS 0580/03

0581/03Paper 3 (Core) May/June 2004

Candidates answer on the Question Paper. 2 hours






Write your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen in the spaces provided on the Question Paper.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid.

Answer all questions.If working is needed for any question it must be shown below that question.The number of marks is given in brackets [ ] at the end of each question or part question.The total of the marks for this paper is 104.Electronic calculators should be used.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answerto three significant figures. Give answers in degrees to one decimal place.For π , use either your calculator value or 3.142.

FOR EXAMINER’S USE


IB04 06_0580_03/6RP

� UCLES 2004 [Turn over

If you have been given a label, look atthe details. If any details are incorrect ormissing, please fill in your correct detailsin the space given at the top of this page.

Stick you personal label here, if provided.

2

© UCLES 2004 0580/3, 0581/3 Jun/04

For

Examiner's

Use1 (a) The list shows marks in an examination taken by a class of 10 students.

65, 51, 35, 34, 12, 51, 50, 75, 48, 39

(i) Write down the mode.

Answer(a)(i) [1]

(ii) Work out the median.

Answer(a)(ii) [2]

(iii) Calculate the mean.

Answer(a)(iii) [2]

(b) Grades were awarded for the examination.The table below shows the number of students in the whole school getting each grade.

Grade Number ofstudents

Angle on a piechart

A 5

B 15

C 40

D 20

E 10

Totals 90

(i) Complete the table above by calculating the angles required to draw a pie chart. [2]

(ii) Using the circle at the top of the opposite page, draw an accurate pie chart to show the datain the table.Label the sectors A, B, C, D and E.

3

© UCLES 2004 0580/3, 0581/3 Jun/04 [Turn over

For

Examiner's

Use

[3]

(iii) What is the probability that a student chosen at random from the group taking theexamination was awarded

(a) grade C,

Answer(b)(iii)(a) [1]

(b) grade D or grade E?

Answer(b)(iii)(b) [2]

4

© UCLES 2004 0580/3, 0581/3 Jun/04

For

Examiner's

Use2

3 m

2 m

3 m

NOT TO

SCALE

The diagram shows a shelter that Vudnella will build for her goats.The shelter will stand on level ground with four identical vertical posts at the corners. Three wallswill be made by attaching thin rectangular pieces of wood to the posts. The front will be left open.The shelter will have a thin square roof, 3 metres by 3 metres. The shelter will be 2 metres high.

(a) Calculate the area of the roof.

Answer(a) m2 [1]

(b) (i) Calculate the area of one wall.

Answer(b)(i) m2 [1]

(ii) Write down the total area of the three walls.

Answer(b)(ii) m2 [1]

(c) The three walls will be made up from thin rectangular pieces of wood.Each piece of wood is 3 metres long and 20 centimetres wide.You may ignore the thickness of the wood.

(i) Calculate the area, in square metres, of one of the pieces of wood.

Answer(c)(i) m2 [2]

(ii) Calculate the total number of pieces of wood she will need to build the three walls of theshelter.

Answer(c)(ii) [2]

5


For

Examiner's

Use(d) The four corner posts are each 2 metres high and 10 centimetres by 10 centimetres in cross-

section.Calculate the volume, in cubic metres, of one post.

Answer(d) m3 [2]

(e) To build the shelter, she will also need 1.5 kilograms of nails.Complete the table below.

Item Total cost of item

Posts at $1.20 each $……………………

Rectangular pieces of wood at $0.30 each $……………………

Roof material at $1.60 per m2 $……………………

Nails at $1.40 per kg $……………………

Total cost of shelter $……………………

[5]

6

© UCLES 2004 0580/3, 0581/3 Jun/04

For

Examiner's

Use

3 (a) Complete the table below for2

8 xy �� .

x -3.5 -3 -2.5 -2 -1.5 -1 0 1 1.5 2 2.5 3 3.5

y -4.25 -1 1.75 4 5.75 7 5.75 1.75 -4.25

[3]


8 xy �� for 5.3� x 3.5.

11

10

9

8

7

6

5

4

3

2

1

_1

_2

_3

_4

_5

y

x0_

4_

3_

2_

1 1 2 3 4

[4]

7


For

Examiner's

Use

(c) Using the graph, write down the values of x for which 082

�� x .

andAnswer(c) x = [2]

(d) Complete the table below for 52 �� xy .

x 3� 0 3

y 11

[2]

(e) On the grid on the opposite page, draw the line 52 �� xy for 3� x 3. [2]

(f) Find the gradient of the line 52 �� xy .

Answer(f) [2]

(g) Using your graphs, write down the x coordinates of the intersections of the graphs of 2

8 xy ��

and 52 �� xy .

andAnswer(g) x = [2]

8

© UCLES 2004 0580/3, 0581/3 Jun/04

For

Examiner's

Use4 In this question the diagrams are not to scale.

(a) Calculate the value of s.

80o

110o so

50o

Answer(a) s = [1]

(b) Calculate the value of t.

75o

75o

t o

2t o

Answer(b) t = [2]

(c) (i)

50o

2yox

o

x + 2y =Complete the equation [2]

9


For

Examiner's

Use(ii)

160o

xo y

o

100o

x + y =Complete the equation [2]

(iii) Solve the simultaneous equations given by your answers to parts (c)(i) and (c)(ii) to findthe values of x and y.

, y =Answer(c)(iii) x = [3]

10

© UCLES 2004 0580/3, 0581/3 Jun/04

For

Examiner's

Use5 (a) Change 200 metres to kilometres.

Answer(a) km [1]

(b)

In the diagram, Q and S lie on a circle,radius 7.8 kilometres, centre C.CQ is extended by 200 metres to P.PS is a tangent to the circle at S.

(i) Why is angle PSC a right angle?

Answer(b)(i) [1]

(ii) Write down the length of PC in kilometres.

Answer(b)(ii) km [1]

(iii) Calculate the length of PS in kilometres.

Answer(b)(iii) km [3]

(iv) Calculate the area of triangle PSC.Give your answer correct to 2 significant figures.

Answer(b)(iv) km2 [3]

C

S

Q

P

200 m

7.8 km

NOT TO

SCALE

11


For

Examiner's

Use6

y

x0

8

7

6

5

4

3

2

1

_1

_2

_3

_4

_5

_6

87654321_1

_3

_4

_5

_6

_7

_8

_2

A

C

D

E F

B


(i) shape A onto shape B,

Answer(a)(i) [3]

(ii) shape C onto shape D.

Answer(a)(ii)

[3]

(b) On the grid above, draw

(i) the reflection of shape E in the y-axis, [2]

(ii) the enlargement of shape F, with scale factor 2 and centre (0, 0). [2]

12

© UCLES 2004 0580/3, 0581/3 Jun/04

For

Examiner's

Use7 (a) (i) What is the special name given to a five-sided polygon?

Answer(a)(i) [1]

(ii) Calculate the total sum of the interior angles of a regular five-sided polygon.

Answer(a)(ii) [2]

(iii) Calculate the size of one interior angle of a regular five-sided polygon.

Answer(a)(iii) [1]

(b)

North

North

North

A

B

C

70o

xo

yo

160o

100 km

120 km

NOT TO

SCALE

A ship sails 100 kilometres from A on a bearing of 070o to B.It then sails 120 kilometres on a bearing of 160o to C.

(i) Show that x + y = 90o.

Answer(b)(i)

[2]

(ii) Use trigonometry to calculate the size of angle BAC.

Answer(b)(ii) [2]

13


For

Examiner's

Use(iii) Find the three-figure bearing of C from A.

Answer(b)(iii) [1]

(iv) Find the three-figure bearing of A from C.

Answer(b)(iv) [1]

14

© UCLES 2004 0580/3, 0581/3 Jun/04

For

Examiner's

Use8

A

B

C

ROAD

The map shows three towns, A, B and C and a road.

(a) (i) Measure and write down the distance, in centimetres, from A to B.

Answer(a)(i) cm [1]

(ii) The towns A and B are 60 kilometres apart.The map is drawn to scale.Complete the statement in the answer space.

Answer(a)(ii) 1 cm represents km [2]

(iii) Find the actual distance, in kilometres, from town A to town C.

Answer(a)(iii) km [1]

(b) An airport is to be built 10 kilometres from the road.On the map, draw accurately the locus of the points that are 10 kilometres from the road. [2]

(c) The airport must be the same distance from A as it is from B.Using compasses and a straight edge only, draw the locus of the points that are equidistant fromA and B. [2]

(d) The airport must be not more than 40 kilometres from C.Draw the locus of points that are 40 kilometres from C. [2]

(e) Mark and label L, the position for the airport. [1]

15

© UCLES 2004 0580/3, 0581/3 Jun/04

For

Examiner's

Use9 (a) Look at the sequence of dots and squares below.

Number of dots

Number of squares

4

1

6

2

8

3

10

4

Find the number of dots when there are

(i) 5 squares,

Answer(a)(i) [1]

(ii) 9 squares,

Answer(a)(ii) [1]

(iii) n squares.

Answer(a)(iii) [2]

(b) Another sequence of dots and squares is shown below.

DiagramNumber of dotsNumber of squares

141

284

3129

41616

(i) For diagram 5, find

(a) the number of dots,

Answer(b)(i)(a) [1]

(b) the number of squares.

Answer(b)(i)(b) [1]

(ii) Find the number of dots in the diagram that has 144 squares.

Answer(b)(ii) [2]

(iii) Find the number of squares in the diagram that has 40 dots.

Answer(b)(iii) [2]

16

Every reasonable effort has been made to trace all copyright holders. The publishers would be pleased to hear from anyone whose rights we have unwittingly infringed.

University of Cambridge International Examinations is part of the University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the

University of Cambridge.

0580/3, 0581/3 Jun/04

BLANK PAGE


IB04 11_0580_01/3RP

© UCLES 2004

[Turn over



MATHEMATICS

Paper 1 (Core) 0580/01 0581/01

















not exact, give the answer to three significant figures. Given answers in



Candidate

Name

Centre

Number

Candidate

Number

*051001*

For Examiner's Use

2

© UCLES 2004 0580/01/O/N/04

For

Examiner's

Use

1 At a weather centre the temperature at midnight was −21

oC.

By noon the next day it had risen to −4

oC. By how many degrees had the temperature risen?

Answer oC [1]

2 Place brackets in the following calculation to make it a correct statement.

6039510 =+×− [1]

3 Write 9

5 as a decimal, correct to two decimal places.

Answer [2]

4 When x = 5 find the value of (a) 4x

2,

Answer(a) [1] (b) (4x)2.

Answer(b) [1]

5 Antonia is making a cake. She uses currants, raisins and sultanas in the ratio

currants : raisins : sultanas = 4 : 3 : 5. The total mass of the three ingredients is 3.6 kilograms. Calculate the mass of sultanas.

Answer kg [2]

3


For

Examiner's

Use

6 Write as a 3-figure bearing the direction

(a) West,

Answer(a) [1]

(b) North-East.

Answer(b) [1]

7 Reflex Right Acute Obtuse Use one of the above terms to describe each of the angles given. (a) 100o

Answer(a) [1] (b) 200o

Answer(b) [1]

8

a =

4

3 and b =

2

1–

Work out a – 2b.

Answer [2]

9

5

3 ÷

10

7 =

7

6

Show how this calculation is done without using a calculator. Write down the working. Answer

[2]

4

© UCLES 2004 0580/01/O/N/04

For

Examiner's

Use

10 Simplify the following expressions. (a) a

2 × a5

Answer(a) [1] (b) b

4 ÷ b3

Answer(b) [1]

11 = < >

Use one of the above symbols to complete each of the statements in the answer spaces.

23 Answer(a) 32 [1]

9 % Answer(b) 0.09 [1]

12 Write down the order of rotational symmetry of each of the following shapes.

(a)

Equilateral Triangle

Answer(a) [1]

(b)

Rhombus

Answer(b) [1]

5


For

Examiner's

Use

13

The diagram shows a pyramid with a square base. All the sloping edges are the same length. In the space below sketch a net of the pyramid. [2]

14 Bernard is buying a radio priced at $19.60. The shopkeeper gives him a 15% discount. Calculate how much Bernard pays.

Answer $ [3]

6

© UCLES 2004 0580/01/O/N/04

For

Examiner's

Use

15

350 cm

350 cm

200 cmNOT TO

SCALE

A large tank, in the shape of a cuboid, has a square base of side 350 cm and height 200 cm. The tank is filled with water. Find, in litres, the volume of water it holds when full.

Answer litres [3]

16

NOT TO SCALE

8 cm

6 cm

The measurements shown are correct to the nearest centimetre. (a) Write down the least possible measurement of (i) the base of the right-angled triangle,

base = Answer(a)(i) cm [1]

(ii) the height of the right-angled triangle.

height = Answer(a)(ii) cm [1]

(b) Use your answers to part (a) to calculate the least possible area of the triangle.

area = Answer(b) cm2 [1]

7


For

Examiner's

Use

17 Ferdinand’s electricity meter is read every three months. The reading on 1st April was 70683 units and on 1st July it was 71701 units. (a) How many units of electricity did he use in those three months?

Answer(a) units [1] (b) Electricity costs 8.78 cents per unit. Calculate his bill for those three months. Give your answer in dollars, correct to the nearest cent.

Answer(b) $ [2]

18 (a) List all the factors of 30.

Answer(a) [2] (b) Write down the prime factors of 30. (1 is not a prime number.)

Answer(b) [1]

8

© UCLES 2004 0580/01/O/N/04

For

Examiner's

Use

19 In New Zealand, a bus leaves New Plymouth at 8.10 am and arrives in Wellington at 2.55 pm. (a) How long, in hours and minutes, does the journey take?

h Answer(a) min [1]

(b) The distance from New Plymouth to Wellington is 355 kilometres. Calculate, in kilometres per hour, the average speed for the journey.

Answer(b) km/h [3]

20 Aminata has a bag containing 35 beads. The beads are either blue, yellow or red. One bead is chosen at random.

The probability of choosing a blue bead is 7

2 and the probability of choosing a yellow bead is

5

3.

Calculate (a) the number of blue beads in the bag,

Answer(a) [2] (b) the probability of choosing a red bead.

Answer(b) [2]

9

© UCLES 2004 0580/01/O/N/04

For

Examiner's

Use

21 Calculate, giving your answer in standard form,

(a) (1.5 × 103) + (8.4 × 102),

Answer(a) [2]

(b) (1.5 × 103) × (8.4 × 102).

Answer(b) [2]

22

OA B

NOT TO SCALE

The diagram shows half of a circle, centre O. (a) What is the special name of the line AB?

Answer(a) [1] (b) AB = 12 cm. (i) Calculate the perimeter of the shape.

Answer(b)(i) cm [2] (ii) Calculate the area of the shape.

Answer(b)(ii) cm2 [2]

10

0580/01/O/N/04

BLANK PAGE

11

0580/01/O/N/04

BLANK PAGE

12

Every reasonable effort has been made to trace all copyright holders where the publishers (i.e. UCLES) are aware that third-party material has been reproduced. The

publishers would be pleased to hear from anyone whose rights they have unwittingly infringed.



0580/01/O/N/04

BLANK PAGE


IB04 11_0580_03/4RP

© UCLES 2004

[Turn over



MATHEMATICS

Paper 3 (Core) 0580/03 0581/03




















Candidate

Name

Centre

Number

Candidate

Number

*058001*

For Examiner's Use

2

© UCLES 2004 0580/03/O/N/04

For

Examiner's

Use

1 (a) Two friends, Hatab and Yasin, went on a cycle ride. Part of the distance-time graph for their journey is shown below.

10 00

18

16

14

12

10

8

6

4

2

0

11 00 12 00 13 00 14 00 15 00

Hatab

and Yasin

Yasin

Hatab

Time of day

Distance

from home

(km)

For the first part of the journey they cycled at the same speed. (i) Find their speed for the first part of the journey.

Answer(a)(i) km/h [1] (ii) At 11 00 they stopped for half an hour. Show this on the graph. [1] (iii) They continued on their ride and at 12 45 they were 16 kilometres from home. Show this part of the journey on the graph. [1] (iv) They stopped again and then had a race going home. (a) For how long did they stop?

Answer(a)(iv)(a) min [1] (b) Who won the race?

Answer(a)(iv)(b) [1] (v) What was the total length of their journey?

Answer(a)(v) km [1]

3


For

Examiner's

Use

(b) On a certain day the conversion rate between dollars ($) and Indian rupees was

$1 = 45 rupees. (i) How many rupees were equivalent to $10?

Answer(b)(i) rupees [1] (ii) Use this information to draw a conversion graph on the axes below.

500

400

300

200

100

0 1 2 3 4 5 6 7 8 9 10 11

Dollars ($)

Rupees

[2] (iii) Use your graph to find (a) how many rupees were equivalent to $6.80,

Answer(b)(iii)(a) rupees [1] (b) how many dollars were equivalent to 480 rupees.

Answer(b)(iii)(b) $ [1]

4

© UCLES 2004 0580/03/O/N/04

For

Examiner's

Use

2

0 1_1

_2

_3

_4

_5

_6

_7 2 3 4 5 6 7 x

y

A

B

C

D

6

5

4

3

2

1

_1

_2

_3

_4

_5

_6

(a) Describe fully the single transformation that maps triangle A onto triangle B.

Answer(a)

[3]

(b) Describe fully the single transformation that maps triangle A onto triangle C.

Answer(b)

[3]

(c) Find the centre and the scale factor of the enlargement that maps triangle A onto triangle D.

( , ) scale factor Answer(c) centre [2]

(d) On the grid

(i) draw the image of triangle A under a reflection in the line x = −1, [2]

(ii) draw the image of triangle B under a rotation of 180° about (−4, −3). [2]

5


For

Examiner's

Use

3

40o

A

ECD

B

6 cm

2 cm

10 cm

NOT TO SCALE

On the above diagram, AB = 2 cm, BD = 6 cm, AE = 10 cm, angle BCD = 40° and angle BDE = 90°. (a) Write down the length of AD.

Answer(a) AD = cm [1] (b) Calculate the length of DE.

Answer(b) DE = cm [2] (c) Calculate the size of angle AED.

Answer(c) angle AED = [2] (d) Calculate the length of CD.

Answer(d) CD = cm [3] (e) Find the length of CE.

Answer(e) CE = cm [1]

6

© UCLES 2004 0580/03/O/N/04

For

Examiner's

Use

4 (a)

A

B C

5 cm 6 cm

4 cm

NOT TO SCALE

(i) In the space below, using a ruler and compasses only, construct the above triangle

accurately. [3] (ii) Using the triangle you have drawn, measure and write down the size of angle ACB.

Answer(a)(ii) angle ACB = [1]

7


For

Examiner's

Use

(b) In the diagram below two points, P and Q, are joined by a straight line.

P Q

(i) On the diagram draw the locus of all the points that are 4 centimetres from the line PQ. [3] (ii) On the same diagram, using a straight edge and compasses only, construct the locus of the

points that are equidistant from P and Q. Show all your construction lines. [2] (iii) Shade the region which contains the points that are closer to P than to Q and are less than

4 centimetres from the line PQ. [2]

8

© UCLES 2004 0580/03/O/N/04

For

Examiner's

Use

5 (a)

80o

yo

140o

A

C

BD

NOT TO SCALE

In the diagram above AB=BC and AD=DC. (i) What is the special name of the quadrilateral ABCD?

Answer(a)(i) [1]

(ii) On the diagram draw the line of symmetry. [1] (iii) Calculate the value of y.

Answer(a)(iii) y = [2] (b)

N

M

L

K

O

40o

ro

po

qo

NOT TO SCALE

In the diagram above, the points K,L,M and N lie on the circle centre O. KN is parallel to LM. Find the values of p,q and r.

p = , q = , r = [3] Answer(b)

9


For

Examiner's

Use

(c)

xo

NOT TO SCALE

The diagram above shows a regular seven-sided polygon.

Each of the interior angles measures x°. One of the angles is marked in the diagram. Calculate the value of x, giving your answer correct to 1 decimal place. Show all your working.

Answer(c) x = [4]

10

© UCLES 2004 0580/03/O/N/04

For

Examiner's

Use

6 (a) Complete the table below for y = x2 − 2x.

x −2 −1 0 1 2 3 4

y 8 −1 3 8

[3]

(b) On the grid below, draw the graph of y = x2 − 2x for −2 x 4.

421_

1 0

8

7

6

5

4

3

2

1

_1

_2

y

3_

2_

3_

4x

y = 2

[4]

(c) The line y = 2 is drawn on the diagram.

Use your graph to find the values of x that solve the equation x2 − 2x = 2.

x = or x = Answer(c) [2]

(d) Complete the table below for y = 4 − x.

x −4 0 4

y 8

[2]

(e) On the grid above, draw the line y = 4 − x for −4 x 4. [1]

(f) Write down the x coordinates of the points of intersection of the graphs of y = x2 − 2x and

y = 4 − x.

x = or x = Answer(f) [2]

11


For

Examiner's

Use

7 (a) Rajeesh thought of a number.

He multiplied this number by 2.

He then added 10.

The answer was 42.

(i) What was the number Rajeesh first thought of?

Answer(a)(i) [1]

(ii) Simon thought of a number x.

He multiplied this number by 3 and then added 8.

Write down an expression in x for his answer.

Answer(a)(ii) [2]

(b) Simplify − 8a + 7b − a − 2b.

Answer(b) [2]

(c) Factorise fully 6a − 9a2

.

Answer(c) [2]

(d) Make t the subject of the formula

v = u + at.

Answer(d) t= [2]

(e) Solve the simultaneous equations

8x + 2y = 13,

3x + y = 4.

x = , y = Answer(e) [4]

12

© UCLES 2004 0580/03/O/N/04

For

Examiner's

Use

8 (a) The list shows the rainfall in millimetres in Prestbury for the 12 months of 2002.

61 146 22 54 67 94 141 22 37 167 87 170

(i) Write down the mode.

Answer(a)(i) mm [1]

(ii) Find the median.

Answer(a)(ii) mm [2]

(iii) Calculate the mean.

Answer(a)(iii) mm [2]

(b) During the years 1996 - 2000 the total rainfall in Prestbury was 5400 millimetres.

The pie chart shows how this was spread over the five years.

1996

1997

1998

1999

2000

13


For

Examiner's

Use

(i) Measure the angles of the sectors for 1998, 1999 and 2000.

Write your answers in the table below. [3]

(ii) Work out the annual rainfall, in millimetres, for each of the years 1998, 1999 and 2000.

Write your answers in the table below. [3]

Answers (b)(i) and (ii)

Year Angle (degrees) Rainfall (mm)

1996 54 810

1997 60 900

1998

1999

2000

Total 360 5400

(iii) What do you notice about the trend in the rainfall from 1996 to 2000?

Answer(b)(iii)

[1]

14

© UCLES 2004 0580/03/O/N/04

For

Examiner's

Use

9 (a) A pattern of numbers is shown below.

26

1

2

3

4

5

6

17

.....

10

18

.....

5

11

19

.....

2

6

12

20

.....

1

3

7

13

21

.....

4

8

14

22

.....

9

15

23

.....

16

24

.....

25

..... .....

row

(i) On the diagram complete row 6. [1]

(ii) The last numbers in each row form a sequence.

1, 4, 9, 16, 25, ……………

(a) What is the special name given to these numbers?

Answer(a)(ii)(a) [1]

(b) Write down the last number in the 10th row.

Answer(a)(ii)(b) [1]

(c) Write down an expression for the last number in the nth row.

Answer(a)(ii)(c) [1]

(iii) The numbers in the middle column of the pattern form a sequence.

1, 3, 7, 13, 21, 31, …………..

(a) Write down the next number in this sequence.

Answer(a)(iii)(a) [1]

(b) The expression for the nth number in this sequence is n2 − n + 1.

Work out the 30th number.

Answer(a)(iii)(b) [2]

15

© UCLES 2004 0580/03/O/N/04

For

Examiner's

Use

(b) Another pattern of numbers is shown below.

row

1 1 2 3 4 5 6 7 8 9 10

2 11 12 13 14 15 16 17 18 19 20

3 21 22 23 24 25 26 27 28 29 30

4 31 32 33 34 35 36 37 38 39 40

(i) What is the last number in the 10th row?

Answer(b)(i) [1]

(ii) Find an expression for the last number in the nth row.

Answer(b)(ii) [1]

(iii) What is the first number in the 10th row?

Answer(b)(iii) [1]

(iv) Find an expression for the first number in the nth row.

Answer(b)(iv) [1]

16

Every reasonable effort has been made to trace all copyright holders where the publishers (i.e. UCLES) are aware that third-party material has been reproduced. The

publishers would be pleased to hear from anyone whose rights they have unwittingly infringed.



0580/03/O/N/04

BLANK PAGE


CAMBRIDGE INTERNATIONAL EXAMINATIONS


MATHEMATICS

0580/01

0581/01

Paper 1May/June 2003

1 hour
















If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer

to three significant figures. Give answers in degrees to one decimal place.




� CIE 2003 [Turn over

If you have been given a label, look at the

details. If any details are incorrect or

missing, please fill in your correct details in

the space given at the top of this page.


2

0580/1, 0581/1 Jun 03

For

Examiner's

Use

1 Work out33

9.21.7 � , giving

(a) your full calculator display,

Answer (a).……………….………

(b) your answer to 2 decimal places.

Answer (b).……………….………

[1]

[1]

2 The diagram shows how the water level of a river went down during a drought.

2

1

0

-1

-2

-3

-4

2

1

0

-1

-2

-3

-4

The measurements are in metres.

(a) By how many metres did the water level go down?

Answer (a).……………….………m

(b) A heavy rainfall followed the drought and the water level went up by 1.6 metres.

What was the water level after the rainfall?

Answer (b).……………….………m

[1]

[1]

3 (a) Write in order of size, smallest first

0.68,

��

��

, 67%.

Answer (a) ………………. � ……………… � .……………….……

(b) Convert 0.68 into a fraction in its lowest terms.

Answer (b).……………….………

[1]

[1]

3

0580/1, 0581/1 Jun 03 [Turn over

For

Examiner's

Use

4 Mahesh and Jayraj share $72 in the ratio 7:5.

How much does Mahesh receive?

Answer $.……………….……… [2]

5 The population of a city is 550 000.

It is expected that this population will increase by 42% by the year 2008.

Calculate the expected population in 2008.

Answer .……………….……… [2]

6 Areeg goes to a bank to change $100 into riyals.

The bank takes $2.40 and then changes the rest of the money at a rate of $1 = 3.75 riyals.

How much does Areeg receive in riyals?

Answer .……………….………riyals [2]

7 Write down the value of � �2�

�

�

� as a fraction.

Answer .……………….……… [2]

8 (a) vuvy 34 �� .

Find the value of y when 3��u and 2�v .

Answer (a) y = .……………….………

(b) Factorise vuv 34 � .

Answer (b) …………………….………

[1]

[1]

4

0580/1, 0581/1 Jun 03

For

Examiner's

Use

9 Solve the equation

�� 4x )2(3 x� .

Answer x = .……………….……… [3]

10 There are approximately 500 000 grains of wheat in a 2 kilogram bag.

(a) Calculate the mass of one grain in grams.

Answer (a) .……………….………g

(b) Write your answer to part (a) in standard form.

Answer (b) .……………….………g

[2]

[1]

11 Solve the simultaneous equations 723 �� ba ,

52 �� ba .

Answer a = .……………….………

b = .……………….……… [3]

5

0580/1, 0581/1 Jun 03 [Turn over

For

Examiner's

Use

12 The diagram shows a pole of length l centimetres.

lcm

(a) Hassan says that l = 88.2.

Round this to the nearest whole number.

Answer (a) l = .……………….………

(b) In fact the pole has a length 86 cm, to the nearest centimetre.

Complete the statement about l.

Answer (b) ……………... l � …….………

[1]

[2]

13 On a journey a bus takes 35 minutes to travel the first 10 kilometres.

It then travels a further 20 kilometres in the next 40 minutes.

(a) The bus started the journey at 18 50.

At what time did it complete the journey?

Answer (a).…………………………………

(b) Calculate the average speed of the whole journey in

(i) kilometres/minute,

Answer (b)(i).……………….………km/min

(ii) kilometres/hour.

Answer (b)(ii).……………….……..…km/h

[1]

[2]

[1]

6

0580/1, 0581/1 Jun 03

For

Examiner's

Use

14 Show all your working for the following calculations.

The answers are given so it is only your working that will be given marks.

(a)�

��

�

�

�

�� ,

Answer (a)

(b)10

12

4

31

5

11 �� .

Answer (b)

[2]

[2]

15 The diagram shows a square of side 8 cm and four congruent triangles of height 7 cm.

7cm

8cm

(a) Calculate

(i) the area of one triangle,

Answer (a)(i) .…….………….…cm2

(ii) the area of the whole shape.

Answer (a)(ii) .……………….…cm2

(b) The shape is the net of a solid.

Write down the special name for this solid.

Answer (b) ………………….………

[2]

[2]

[1]

7

0580/1, 0581/1 Jun 03 [Turn over

For

Examiner's

Use

16 In the diagram AB is the diameter of a circle, centre O. The length of AB is 12 cm.

40O

12cm

O

A P

B

(a) Write down the size of angle APB.

Answer (a) Angle APB = .……………….………

(b) Angle PAB = 40°.

Calculate the length of PB.

Answer (b) PB = ……….………………….…cm

(c) Calculate the area of the circle.

Answer (c) .……………….…………………cm2

[1]

[2]

[2]

NOT TO

SCALE

8

0580/1, 0581/1 Jun 03

For

Examiner's

Use

17

P

RQ 4.8km

8.3km

North

A straight road between P and Q is shown in the diagram.

R is the point south of P and east of Q.

PR = 8.3 km and QR = 4.8 km.

Calculate

(a) the length of the road PQ,

Answer (a) .……………….…...km

(b) the bearing of Q from P.

Answer (b) .……………….………

[2]

[3]

NOT TO

SCALE

9

0580/1, 0581/1 Jun 03

For

Examiner's

Use

18

120O

35O

5.5cm

16.6cm

8.3cmA B

X

C D

In the diagram the lines AB and CD are parallel.

The lines AD and BC intersect at X.

Angle XDC = 35° and angle CXD = 120°.

(a) (i) Write down the size of angle BAX.

Answer(a)(i) Angle BAX = …….………….

(ii) Write down the size of angle ABX.

Answer(a)(ii) Angle ABX = ………….…....

(b) Complete the statement

Triangle AXB is ……………………………… to triangle DXC.

(c) AB = 8.3 cm, BX = 5.5 cm and CD = 16.6 cm.

Calculate the length of CX.

Answer (c) .……………….……….…cm

[1]

[1]

[1]

[2]

NOT TO

SCALE

10

0580/1, 0581/1 Jun 03

BLANK PAGE

11

0580/1, 0581/1 Jun 03

BLANK PAGE

12

0580/1, 0581/1 Jun 03

BLANK PAGE




MATHEMATICS

0580/03

0581/03

Paper 3May/June 2003

2 hours
























missing, please fill in your correct details

in the space given at the top of this page.


2

0580/3, 0581/3 Jun 03

For

Examiner's

Use

1 Fifty students take part in a quiz.

The table shows the results.

(a) How many students had 6 correct answers?

Answer(a)……………….………

(b) How many students had less than 11 correct answers?

Answer(b)………………….....…

(c) Find

(i) the modal number of correct answers,

Answer(c)(i)…………………….

(ii) the median number of correct answers,

Answer(c)(ii)……………...…….

(iii) the mean number of correct answers.

Answer(c)(iii)……….…………..

(d) A bar chart is drawn to show the results.

The height of the bar for the number of students who had 5 correct answers is 2 cm.

What is the height of the bar for the number of students who had 9 correct

answers?

Answer(d)……….………...…cm

[1]

[1]

[1]

[2]

[3]

[2]

Number of correct answers 5 6 7 8 9 10 11 12

Number of students 4 7 8 7 10 6 5 3

3

0580/3, 0581/3 Jun 03 [Turn over

For

Examiner's

Use

(e) A pie chart is drawn to show the results.

What is the angle for the number of students who had 11 correct answers?

Answer(e)……………………….

(f) The students who had the most correct answers shared a top prize of $22.50.

How much did each of these students receive?

Answer(f) $……………………..

(g) Work out the percentage of students who had less than 7 correct answers.

Answer(g)………………….…%

(h) A student is chosen at random from the fifty students.

What is the probability that this student had

(i) exactly 10 correct answers,

Answer(h)(i)…………………….

(ii) at least 10 correct answers,

Answer(h)(ii)……………………

(iii) more than 1 correct answer?

Answer(h)(iii)…………………..

[2]

[2]

[2]

[1]

[1]

[1]

4

0580/3, 0581/3 Jun 03

For

Examiner's

Use

2 (a) Complete the table for the equationx

y

120

� .

(b) On the grid below, draw the curvex

y

120

� for 1 x 6.

1 2 3 4 5 60

20

40

60

80

100

120

x

y

(c) Use your graph to find x when y = 70.

Answer(c) x = ………………….

(d) Complete the table for the equation xy 20120 �� .

(e) On the same grid above, draw the graph of xy 20120 �� for 0 x 6.

[3]

[4]

[1]

[2]

[2]

x 1 1.5 2 3 4 5 6

y 80 60 40 30

x 0 2 4 6

y 80 40

5

0580/3, 0581/3 Jun 03 [Turn over

For

Examiner's

Use

(f) The graphs of

x

y

120

� and xy 20120 �� intersect at two points.

Write down the coordinates of these two points.

Answer(f) ( ….… , ….…) and (….… , ….…)

(g) Write down the gradient of the line xy 20120 �� .

Answer(g)………………………

[2]

[2]

6

0580/3, 0581/3 Jun 03

For

Examiner's

Use

3 (a) Bottles of water cost 25 cents each.

(i) Find the cost of 7 bottles in cents.

Answer(a)(i)……………...cents

(ii) Write down an expression in b for the cost of b bottles in cents.

Answer(a)(ii)……………...cents

(iii) Change your answer to part (i) into dollars.

Answer(a)(iii) $…...……………

(iv) Write down an expression in b for the cost of b bottles in dollars.

Answer(a)(iv) $…………………

(b) The total cost, T, of n bars of chocolate is given by ncT � .

(i) Write c in terms of T and n.

Answer(b)(i) c = …………………

(ii) What does c represent?

Answer(b)(ii) .……………………………………………………………………………

(c) The average cost of a book is $A.

(i) The total cost of 8 books is $36.

Find the value of A.

Answer(c)(i) A = .………………

(ii) One of the 8 books is removed.

The cost of this book is $6.60.

Find the new value of A.

Answer(c)(ii) A = ………………

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[2]

7

0580/3, 0581/3 Jun 03 [Turn over

For

Examiner's

Use

(iii) The total cost of x books is $y.

Write an expression for A in terms of x and y.

Answer(c)(iii) A = ………………

(iv) One of the x books is removed.

The cost of this book is $7.

Write a new expression for A in terms of x and y.

Answer(c)(iv) A = ………………

[1]

[2]

8

0580/3, 0581/3 Jun 03

For

Examiner's

Use

4

1 3 5 7 9 112 4 6 8 10 120

1

3

5

7

9

11

2

4

6

8

10

12

x

y

E

D

NM

F

G

L K

T

A

(a) Draw accurately the image of triangle T under the following transformations.

(i) Translate triangle T by the vector �

�

��

�

� � 3

4

. Label it P. [2]

(ii) Reflect triangle T in the line x = 8. Label it Q. [2]

(iii) Rotate triangle T about the point A through 90° anti-clockwise.

Label it R. [2]

(iv) Enlarge triangle T with centre of enlargement A and scale factor 2.

Label it S. [2]

9

0580/3, 0581/3 Jun 03 [Turn over

For

Examiner's

Use

(b) Describe fully the single transformation which maps

(i) triangle P onto triangle T,

Answer(b)(i)…………………………………………………………………………………. [2]

(ii) triangle S onto triangle T.

Answer(b)(ii)………………………………………………………………………………… [3]

(c) The rectangle DEFG is rotated onto the rectangle KLMN, with D mapped onto K.

Write down

(i) the angle of the rotation,

Answer(c)(i)…...…………………... [1]

(ii) the coordinates of the centre of the rotation.

Answer(c)(ii) (…..…….. , ....…..….) [2]

10

0580/3, 0581/3 Jun 03

For

Examiner's

Use

5

B

O A

The quarter-circle above has centre O and radius 7 cm.

(a) Using a straight edge and compasses only construct

(i) the perpendicular bisector of AO, [2]

(ii) the locus of points inside the quarter-circle which are 5 cm from O. [2]

(b) Shade the region, inside the quarter-circle, containing the points which are

more than 5 cm from O and nearer to A than O. [1]

(c) (i) The line OX bisects angle AOB and is 12 cm long.

Draw OX accurately. [2]

(ii) Draw accurately the tangent to the quarter-circle at A. [1]

(iii) This tangent meets the line OX at Y.

Measure the length of AY.

Answer(c)(iii) AY = …………..…….cm [1]

11

0580/3, 0581/3 Jun 03 [Turn over

For

Examiner's

Use

6

1cm

2.5 cm

9 cm

1.5 cm1.5 cm 1.5 cm

1 cm1cm

3cm

In the diagram above, all the angles are right angles.

(a) Show that the area of the shape is 13.5 cm2

.

Answer(a)

(b) The shape is the cross-section of a metal prism of length 2.8 metres.

Calculate the volume of the prism in cubic centimetres.

Answer(b)………………….cm3

(c) A metal cuboid is melted down so that prisms as described in part (b) can be made.

The cuboid measures 2 metres by 1.2 metres by 0.8 metres.

(i) Calculate the volume of the cuboid in cubic metres,

Answer(c)(i)……...…………..m3

(ii) Calculate the volume of the cuboid in cubic centimetres.

Answer(c)(ii)……..…………cm3

(iii) Calculate the number of prisms which can be made.

Answer(c)(iii)……...…………….

(d) Draw any lines of symmetry of the shape on the diagram above.

(e) Describe the rotational symmetry of the shape above.

Answer(e)………………………………………………………………………………..

[2]

[3]

[2]

[2]

[2]

[1]

[1]

12

0580/3, 0581/3 Jun 03

For

Examiner's

Use

7

4 8 12 162 6 10 14 18 200

20

40

60

10

30

50

70

80

90

Time (minutes)

Temperature

(OC)

The graph shows the temperature of a cup of tea cooling down in a room.

(a) What is the temperature of the tea after

(i) 0 minutes,

Answer(a)(i)……………………. [1]

(ii) 20 minutes?

Answer(a)(ii)...…………………. [1]

(b) After how many minutes is its temperature 30 °C?

Answer(b)……………………… [1]

(c) By how much has its temperature gone down between 4 minutes and 8 minutes?

Answer(c)……………………… [1]

(d) (i) Complete the table which shows falls in temperature.

[3]

(ii) What pattern do you notice about these falls in temperature?

Answer(d)(ii)…………………………………………………………………… [1]

Between0 and 4

minutes

4 and 8

minutes

8 and 12

minutes

12 and 16

minutes

Fall in temperature

13

0580/3, 0581/3 Jun 03

For

Examiner's

Use

(e) Estimate the room temperature.

Answer(e)…………………. °C [1]

8

Diagram 4Diagram 1

3 dots

1 triangle

Diagram 2

4 dots

3 triangles

Diagram 3

5 dots

6 triangles

Look at the diagrams above.

(a) Complete Diagram 4 to continue the pattern. [2]

(b) Complete the table below.

[3]

(c) Complete the table below.

[3]

(d) A line is now drawn inside each of the diagrams as shown below.

Diagram 1

2 triangles

Diagram 2

6 triangles

Diagram 3

How many triangles are there in Diagram 3?

Answer(d)………………………[2]

Diagram 1 2 3 4 5 n

Number of dots 3 4 5

Diagram 1 2 3 4 5 6 10

Number of triangles 1 3 6 10

14

0580/3, 0581/3 Jun 03

BLANK PAGE

15

0580/3, 0581/3 Jun 03

BLANK PAGE

16

0580/3, 0581/3 Jun 03

BLANK PAGE




MATHEMATICS

0580/01

0581/01

Paper 1October/November 2003

1 hour
















If the degree of accuracy is not specified in the question, and if the answer is not exact, give the

answer to three significant figures. Give answers in degrees to one decimal place.







missing, please fill in your correct details in

the space given at the top of this page.


2

0580/1, 0581/1/Nov 03

For

Examiner’s

Use

1 Write 0.4 kilograms in grams.

Answer….………….………grams [1]

2 The price of a book is $18. Sara is given a discount of 15%.

Work out this discount.

Answer $.……..….………….…… [2]

3

SUS A N

Susan writes the letters of her name on five cards.

One of the five cards is chosen at random.

Find the probability that the letter on the card is

(a) S, Answer (a).……………….………

(b) E. Answer (b).……………….………

[1]

[1]

4 A country has three political parties, the Reds, the Blues and the Greens.

The pie chart shows the proportion of the total vote that each party received in an election.

RED

BLUE GREEN

xo

144o

NOT TO

SCALE

(a) Find the value of x.

Answer (a) x =..………….………

(b) What percentage of the votes did the Red party receive?

Answer (b).…………….………%

[1]

[2]

3

0580/1, 0581/1/Nov 03 [Turn over

For

Examiner’s

Use

5

20

5 m

A

B

C

o

The diagram shows a right-angled triangle ABC with AB = 5 m and angle BAC = 20�.

Calculate the length BC.

Answer BC =.….………….………m [2]

6 Jeff takes 10 minutes to walk 1 kilometre. Find his average walking speed in kilometres per

hour.

Answer .……………….………km/h [2]

7 Find the size of one of the ten interior angles of a regular decagon.

Answer .…………………….……… [3]

8 The length of a road is 1300 metres, correct to the nearest 100 metres.

Complete the statement in the answer space.

Answer .……………….………m road length � .……………….……m [2]

4

0580/1, 0581/1/Nov 03

For

Examiner’s

Use

9 (a) Multiply out the brackets 5x (2x – 3y).

Answer (a).……………….………

(b) Factorise completely 6x2

+ 12x.

Answer (b).……………….………

[2]

[2]

10

65o

28o

xo

AB

C

D E

F

yo

zo

NOT TO

SCALE

The diagram shows the side view of the roof of a house. AB and DE are horizontal.

EF is vertical.

Find the value of

(a) x,

Answer (a) x =.……………….………

(b) y,

Answer (b) y =.……………….………

(c) z.

Answer (c) z =.……………….………

[1]

[1]

[1]

5

0580/1, 0581/1/Nov 03 [Turn over

For

Examiner’s

Use

11 In each of the shapes below draw one line which divides it into two congruent shapes.

[3]


3x – y = 0,

x + 2y = 28.

Answer x =.……………….…………

y =.………………….……… [3]

13 (a) Work out

2.7 � 8.3 � (12 – 2.7),

writing down

(i) your full calculator display,

Answer (a)(i) = .…………....….……

(ii) your answer to two decimal places.

Answer (a)(ii) = .…….…..….………

(b) Work out

3

116 �

�

��

�

�� .

Answer (b) = .……………….………

[1]

[1]

[2]

6

0580/1, 0581/1/Nov 03

For

Examiner’s

Use

14 The temperatures at sunrise in Berne on the seven days of one week were:

Sunday -1 �C

Monday -7 �C

Tuesday -6 �C

Wednesday 1 �C

Thursday 3 �C

Friday 0 �C

Saturday -4 �C

(a) List the days on which the temperature at sunrise was less than –3 �C.

Answer (a).…………………………..…………….……………….………

(b) Work out the mean (average) of the seven temperatures.

Answer (b)….……………….………�C

[1]

[3]

15 (a) Work out each of the following as a decimal.

(i) 28%

Answer (a)(i).………………….………

(ii)

1000

275

Answer (a)(ii).………..….…….………

(iii)

7

2

Answer (a)(iii)…………………………

(b) Write 28%,

1000

275

and

7

2

in order of the size, smallest first.

Answer (b)………�…….…�…………

[1]

[1]

[1]

[1]

7

0580/1, 0581/1/Nov 03 [Turn over

For

Examiner’s

Use

16

2 m

5 m

NOT TO

SCALE

A

B

xo

The diagram shows a ladder, AB, standing up against a palm tree. The ladder is 5 metres long and

its base is 2 metres from the tree.

(a) Calculate how high up the tree the ladder reaches.

Answer (a)…………………….……m

(b) The ladder makes an angle of x� with the ground. Calculate the value of x.

Answer (b) x =.……………….………

[2]

[2]

17 Write down the value of n in each of the following statements.

(a) 1500 = 1.5 � 10n

Answer (a) n =.……………….………

(b) 0.00015 = 1.5 � 10n

Answer (b) n =.……………….………

(c) 5n

= 1

Answer (c) n =.……………….………

(d)

36

1

= 6n

Answer (d) n =.……………….………

[1]

[1]

[1]

[1]

8

0580/1, 0581/1/Nov 03

For

Examiner’s

Use

18 The diagram below shows the graph of y = x2

– 3x + 1.

0

5

4

3

1

-1

-2

-1 1 2 3 4

2

y = x2

-3x + 1

x

y

(a) Use the graph to solve the equation

x2

– 3x + 1 = 0.

Answer (a) x =.…………or…….………

(b) (i) Complete the table for y = x + 1.

[2]

x -1 1 3

y 2 4 [1]

(ii) Draw the graph for y = x + 1 on the grid above.

(c) Write down the coordinates of the intersections of the two graphs.

Answer (c)(.…… , ……) (……. , ……)

[1]

[2]


MCS-UCH160-S40984/2© CIE 2003 [Turn over

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

MATHEMATICS 0580/030581/03

Paper 3October/November 2003

2 hoursCandidates answer on the Question Paper.Additional Materials: Electronic calculator

Geometrical instrumentsMathematical tables (optional)Tracing paper (optional)


Write your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen in the spaces provided on the Question Paper.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid.

Answer all questions.If working is needed for any question it must be shown below that question.The number of marks is given in brackets [ ] at the end of each question or part question.

The total of the marks for this paper is 104.Electronic calculators should be used.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer tothree significant figures. Answers in degrees should be given to one decimal place.For π, use either your calculator value or 3.142.



If you have been given a label, look at thedetails. If any details are incorrect ormissing, please fill in your correct detailsin the space given at the top of this page.

Stick your personal label here, ifprovided.

1 20 21 22 23 24 25 26 27 28 29 30

From the set of numbers above, write down

(a) a multiple of 8,Answer (a).......................................... [1]

(b) a square,Answer (b).......................................... [1]

(c) a cube,Answer (c).......................................... [1]

(d) two prime numbers,Answer (d) ......................................... [2]

(e) a factor of 156,Answer (e).......................................... [1]

(f) the square root of 784,Answer (f ) ..........................................[1]

(g) two numbers whose product is 567.Answer (g) ..........................................[1]

2 (a) Jorina recorded the temperature every hour during the school day.The graph shows the results.

(i) At what time was the highest temperature recorded?

Answer (a)(i)...................................... [1]

(ii) At what time was the temperature 21 °C?Answer (a)(ii)......................................[1]

(iii) Find the increase in temperature between 11 00 and 12 00.

Answer (a)(iii) ............................. °C�[2]0580/03/0581/03/O/N/03

2 ForExaminer’s

use

0

5

10

15

20

25

30

35

09 00 10 00 11 00 12 00 13 00 14 00 15 00 16 00

Temperature(°C)

Time

(b) The conversion rate between euros (e) and dollars ($) was e1 # $0.87.


[2]

(ii) Draw a graph on the grid below to convert between euros and dollars.

[2]

(iii) How many euros were equivalent to $8?

Answer (b)(iii)�e................................ [1]

(iv) How many euros were equivalent to $500?

Answer (b)(iv)�e ................................ [1]

0580/03/0581/03/O/N/03 [Turn over

3 ForExaminer’s

use

e 0 5 10

$ 0

0 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

dollars ($)

euros (e)

The diagram shows a rectangular tank of base 30 cm by 25 cm. It contains water to a depthof 8 cm.

(a) Calculate the volume of water in the tank.

Answer (a) ..................................cm�3�[2]

The diagram shows a cylinder of radius 10 cm and height 14 cm which is full of water.

(i) Calculate the volume of water in the cylinder.

Answer (b)(i) ............................. cm�3�[3]

(ii) All the water in the cylinder is poured into the rectangular tank. Find the totalvolume of water now in the tank.

Answer (b)(ii) ............................ cm�3�[1]

(iii) Calculate the new depth of water in the tank.

Answer (b)(iii)............................. cm�[3]

0580/03/0581/03/O/N/03

4 ForExaminer’s

use

NOT TOSCALE

25 cm

30 cm

8 cm

14 cm

10 cm

NOT TOSCALE

3

(b)

4 A dentist recorded the number of fillings that each of a group of 30 children had in theirteeth. The results were

2��4��0��5��1��1��3��2��6��0

2��2��3��2��1��4��3��0��1��6

1��4��1��6��5��1��0��3��4��2

(a) Complete this frequency table.

[2]

(b) What is the modal number of fillings?

Answer (b).......................................... [1]

(c) Find the median number of fillings.

Answer (c).......................................... [2]

(d) Work out the mean number of fillings.

Answer (d) ......................................... [2]

(e) One of these children is chosen at random.Find the probability that this child has

(i) exactly one filling,

Answer (e)(i) ...................................... [1]

(ii) more than three fillings.

Answer (e)(ii) ..................................... [1]

(f) These 30 children had been chosen from a larger group of 300 children. Estimate howmany in the larger group have no fillings in their teeth.

Answer (f ) ......................................... [1]

0580/03/0581/03/O/N/03 [Turn over

5 ForExaminer’s

use

Number of fillings Frequency

0

1

2

3

4

5

6

(a) Triangle ABD is translated onto triangle EGF by the vector .

Write down the value of x and the value of y.

Answer (a)�x #..................................

y #.................................. [2]

(b) Describe fully the single transformation which maps triangle ABD onto

(i) triangle CDB,

Answer (b)(i).....................................................................................................................

.................................................................................................................................... [3]

(ii) triangle HBF.

Answer (b)(ii) ...................................................................................................................

.................................................................................................................................... [3]

(c) (i) Work out the area of triangle ABD.

Answer (c)(i) ...................................... [1]

(ii) What is the ratio area of triangle ABD : area of triangle HBF?Give your answer in its lowest terms.

Answer (c)(ii)................. : ................. [2]

(d) Find the gradient of the line BF.

Answer (d) ......................................... [2]

�xy�

0580/03/0581/03/O/N/03

6 ForExaminer’s

use

0 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

A

B C

D

EF

G

H

x

y5

6 (a) The perimeter, P, of a triangle is given by the formula

(i) Find the value of P when x # 4.

Answer (a)(i)�P # .............................. [1]

(ii) Find the value of x when P # 39.

Answer (a)(ii)�x # .............................. [2]

(iii) Rearrange the formula to find x in terms of P.

Answer (a)(iii)�x #............................. [2]

(b) The perimeter of another triangle is (9x ! 4) centimetres.

Two sides of this triangle are of length 2x centimetres and (3x ! 1) centimetres.

(i) Find an expression, in terms of x, for the length of the third side.

Answer (b)(i) ............................... cm�[2]

(ii) The perimeter of this triangle is 49 cm. Find the length of each side.

Answer (b)(ii).................. cm, .................. cm, ...................cm�[3]

P = 6x + 3.

0580/03/0581/03/O/N/03 [Turn over

7 ForExaminer’s

use

The diagram shows the net of a solid.

(i) Work out the perimeter of the net.

Answer (a)(i) ............................... cm�[2]

(ii) Work out the area of the net.

Answer (a)(ii) .............................cm�2�[3]

(iii) Write down the mathematical name of the solid.

Answer (a)(iii).................................... [1]

(iv) Write down the surface area of the solid.

Answer (a)(iv) ............................cm�2�[1]

(v) Work out the volume of the solid.

Answer (a)(v) .............................cm�3�[2]

0580/03/0581/03/O/N/03

8 ForExaminer’s

use

2 cm

3 cm

4 cm

7 (a)

This is the net of a solid with edges of length p, q and r.

Find an expression for

(i) the surface area of the solid,

Answer (b)(i)...................................... [2]

(ii) the volume of the solid.

Answer (b)(ii)..................................... [2]

0580/03/0581/03/O/N/03 [Turn over

9 ForExaminer’s

use

p

q

r

(b)

8 (a) A mobile phone company changes its rental charge from $80 per year to $7.50 permonth.Work out the percentage increase.

Answer (a) .................................... %�[3]

(b) George’s phone card lasts for 300 minutes. He has used of this time.Work out how many minutes are left on his phone card.

Answer (b)........................... minutes�[3]

(i) On the diagram above, using a straight edge and compasses only, construct theloci which are

(1)�equidistant from A and from B, [2](2)�equidistant from CB and from CD. [2]

(ii) The diagram shows a field ABCD. The mobile phone company plans to put amast in the field. The mast must be

��nearer to B than to A��nearer to CD than to CB.

Shade the part of the diagram which shows where the mast should be put. [2]

�35 ��

0580/03/0581/03/O/N/03

10 ForExaminer’s

use

A

B

CD

(c)

The diagram, drawn to scale, shows the positions of Johannesburg (J), Cape Town (C�) andDurban (D).

(a) The distance from Johannesburg to Durban is 450 kilometres.On the diagram JD # 3 cm.

(i) How many kilometres are represented by 1 cm on the diagram?

Answer (a)(i)...................................... [1]

(ii) Work out the scale of the diagram as a ratio.

Answer (a)(ii)�1 : ........................... [2]

(b) Use the diagram to find

(i) the distance from Cape Town to Johannesburg,

Answer (b)(i)............................... km�[2]

(ii) the bearing of Johannesburg from Cape Town,

Answer (b)(ii)..................................... [1]

(iii) the bearing of Cape Town from Durban.

Answer (b)(iii).................................... [2]

0580/03/0581/03/O/N/03 [Turn over

11 ForExaminer’s

use

C

D

North

J

North

9

10 Look at this arrangement of numbers. It is known as Pascal’s Triangle.

Line Sum ofnumbers

1 1 1 2

2 1 2 1 4

3 1 3 3 1 8

4 1 4 6 4 1 16

5 1 5 10 10 5 1 32

6 __ __ __ __ __ __ __ __

7 __ __ __ __ __ __ __ __ __

(a) Complete lines 6 and 7 above. [5]

(b) (i) What is the sum of the numbers on the 9th line?

Answer (b)(i)...................................... [2]

(ii) What is the sum of the numbers on the nth line?

Answer (b)(ii)..................................... [2]

(c) The 12th line is given below. Fill in the blanks in the 11th line.

[2]

0580/03/0581/03/O/N/03

12 ForExaminer’s

use

11 1 11 55 �__ __ __ __ __ __ __ __ __

12 1��12 66 220 495 792 924 792 495 220 66 12 1

This question paper consists of 7 printed pages and 1 blank page.

SB (SC) S07105/4© CIE 2002 [Turn over



MATHEMATICS 0580/1, 0581/1PAPER 1

MAY/JUNE SESSION 20021 hour

Candidates answer on the question paper.Additional materials:

Electronic calculatorGeometrical instrumentsMathematical tables (optional)Tracing paper (optional)

TIME 1 hour

INSTRUCTIONS TO CANDIDATES

Write your name, Centre number and candidate number in the spaces at the top of this page.


Write your answers in the spaces provided on the question paper.


INFORMATION FOR CANDIDATES




If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answerto three significant figures. Give answers in degrees to one decimal place.


CandidateCentre Number Number

Candidate Name


UNIVERSITY of CAMBRIDGELocal Examinations Syndicate

2

0580/1, 0581/1 Jun02

1 Work out 7 – 2 x 4.

Answer ........................................................... [1]

2 Write as a decimal

(a) ,

Answer (a) ...................................................... [1]

(b) 127%.

Answer (b) ...................................................... [1]

3 Factorise completely 8y – 12ty.

Answer ........................................................... [2]

4 Put one of the symbols <, > or = in each part to make these two statements correct,

(a) ...................... 0.3 x 0.5, [1]

(b) 2.793 ............ 4.632. [1]

5 A spoon can hold 5 ml of medicine.

(a) Write 5 ml in litres.

Answer (a) ............................................. litres [1](b) Write your answer in standard form.

Answer (b) ............................................. litres [1]

6 Hassan picks 24 kg of fruit.He finds that 8% of the fruit is rotten.Work out the mass of fruit which is rotten.

Answer ....................................................... kg [2]

0 0225.

7––20

ForExaminer’s

Use

3

0580/1, 0581/1 Jun02 [Turn over

ForExaminer’s

Use

7 Work out 48 k10 ÷ 24k8 giving your answer in its simplest form.

Answer ........................................................... [2]

8 The population, P, of a city is 280 000, to the nearest ten thousand. Complete the statement about P.

Answer ...................... � P <......................... [2]

9 In June 2000, one euro (€) was worth 0.59 British pounds (£).Work out the value, in pounds, of a car which cost €12 800.Give your answer to the nearest hundred pounds.

Answer £......................................................... [3]

10 (a) Write down the name of the special quadrilateral which has rotational symmetry of order 2 butno lines of symmetry.

Answer (a) ...................................................... [1]

(b) On the grid, draw a quadrilateral which has exactly one line of symmetry but no rotationalsymmetry.Draw the line of symmetry on your diagram.

[2]

4

0580/1, 0581/1 Jun02

11

The diagram shows a triangular prism.AB = 5cm, BC = 6 cm and angle ABC = 90°. The prism has a length of 24 cm.Calculate the volume of the prism.

Answer ................................................... cm3 [3]

12

In the diagram, A is the point (1,1) and B is the point (4,3).

(a) Write →AB as a column vector.

Answer (a)→AB = � � [1]

(b) The point C is such that→BC = 2

→BA.

(i) Draw→BC on the diagram. [1]

(ii) Write down the coordinates of C.

Answer (b)(ii) � .................. , .................� [1]

1– 1– 2– 3 2 3 4 5 x

– 1

– 2

1

2

3

4

0

y

A

B

NOT TOSCALEA

CB24cm

5cm

6cm

ForExaminer’s

Use

5

0580/1, 0581/1 Jun02 [Turn over

13 Doreen cycles to her friend’s home.She leaves at 09 40 and arrives at 10 20.

(a) Write down the time taken

(i) in minutes,

Answer (a)(i) ..................................... minutes [1]

(ii) as a fraction of an hour in its lowest terms.

Answer (a)(ii) ....................................... hours [1]

(b) The distance Doreen cycles is 8.4km.Work out Doreen’s average speed in km/h.

Answer (b) ............................................. km/h [2]

14 (a) Six three-digit numbers can be made from the digits 1, 2 and 3 when each digit is used once.One number is 231.Write down all the other numbers.

Answer (a) 231, ………… , ………… , ………… , ………… , ………… . [2]

(b) One of the six numbers is picked from the above list at random.Write down the probability that it is

(i) even,

Answer (b)(i) .................................................. [1]

(ii) a multiple of 5.

Answer (b)(ii) ................................................. [1]

15 Solve the simultaneous equations 2c + 5d = 49,3c + d = 15.

Answer c = ...................................................... [4]

Answer d = ...................................................... [4]

ForExaminer’s

Use

6

0580/1, 0581/1 Jun02

16

A railway line, between stations A and B, is straight and has a length of 4800 m.The bearing of B from A is 200 °.The point P is due east of B and due south of A.

(a) Complete the sketch above to show triangle ABP. [1]

(b) Calculate the length of AP.

Answer (b) AP = ......................................... m [3]

17

In the diagram, AB is a diameter of the circle, centre O.DBC is a tangent at B.

(a) Write down the size of angle ABC.

Answer (a) Angle ABC = ................................ [1]

(b) The angles BAC and ACB are in the ratio 5:7.Work out the size of angle BAC.

Answer (b) Angle BAC = ................................ [3]

A

O

D B C

NOT TOSCALE

A

B

NOT TOSCALE

North

4800m

200°

ForExaminer’s

Use

7

0580/1, 0581/1 Jun02

18

(a) On the diagram draw accurately the locus of points inside the rectangle which are

(i) 6 cm from D, [1]

(ii) equidistant from AB and BC. [2]

(b) Shade the region inside the rectangle containing points which are more than 6 cm from Dand nearer to AB than to BC. [1]

19

The diagram shows a garden.It is made up of a square of side 16 m and four semicircles of radius 8 m.

Calculate (a) the perimeter of the garden,

Answer (a) ...................................................m [2]

(b) the area of the garden.

Answer (b) ..................................................m2 [3]

NOT TOSCALE

16m

16m

A B

CD

ForExaminer’s

Use

8

0580/1, 0581/1 Jun02

BLANK PAGE

This question paper consists of 7 printed pages and 1 blank page.

© CIE 2002 [Turn over

Centre Number

Candidate

Number

Candidate Name



MATHEMATICS

PAPER 1 OCTOBER/NOVEMBER SESSION 2002

1 hour

Candidates answer on the question paper.

Additional materials:

Electronic calculator




Time 1 hour












For �, use either your calculator value or 3.142.


2

0580/1/O/N/02

For

Examiner's

Use1 Work out $50 – $23.46.

Answer $.……………….………[1]

2 A train leaves Johannesburg at 09 45 and arrives in Pretoria at 10 32.

How many minutes does the journey take?

Answer.……………….………minutes [1]

3 Work out .

1337

1337

33

�

�

Answer.……………….……… [2]

4 Write 24% as a fraction in its lowest terms.

Answer.……………….………[2]

5 The integer n is such that –3 � n < 3.

List all the possible values of n.

Answer.……………….………[2]

6

NOT TO

SCALE

AB and AC are tangents to the circle,

centre O.

Angle BAC = 54�.

(a) Write down the size of angle

ABO.

Answer (a) Angle ABO =.……………….………

(b) Work out angle BOC.

Answer (b) Angle BOC =.……………….………

[1]

[1]

54�

B

A

C

O

3

0580/1/O/N/02 [Turn over

For

Examiner's

Use7 When Carla started work she was paid $80 each week.

After 3 months her pay was increased by 15%.

After the increase how much was she paid each week?

Answer $.……………….……… [2]

8 The population of Argentina is 3.164 � 107

. Its area is 2.8 � 106

square kilometres.

Work out the average number of people per square kilometre in Argentina.

Answer.……………….………people/km2 [2]

9 The diagram shows a flood-warning post in a river.

(a) Write down the water level shown in the diagram.

Answer (a).……………….………cm

(b) The water level rises by 1 metre.

What is the new level?

Answer (b).……………….………cm

[1]

[1]

+1m

+50cm

-50cm

-1m

0

4

0580/1/O/N/02

For

Examiner's

Use10 Complete this diagram accurately so that it has rotational symmetry of order 3 about the

point O.

[2]

11 An athlete’s time for a race was 43 .78 seconds.

(a) Write this time correct to

(i) one decimal place,

Answer (a) (i).……………….………seconds

(ii) one significant figure.

Answer (a) (ii).……………….………seconds

(b) Write 43.78 and your answers to (a) parts (i) and (ii) in order, largest first.

Answer (b) .……………….………>.……………….………>.……………….………

[1]

[1]

[1]

12

In triangle ABC, AB = AC.

(a) What is the special name of this triangle?

Answer (a).……………….………

(b) Angle BAC = 128�. Work out angle ABC.

Answer (b) Angle ABC =.……………….………

[1]

[2]

O

128�

A

CB

NOT TO

SCALE

5

0580/1/O/N/02 [Turn over

For

Examiner's

Use

13 T = 2 .n

(a) Find T when n = 25.

Answer (a) T =.……………….………

(b) Make n the subject of the formula.

Answer (b) n =.……………….………

[1]

[2]

14 Brussels is 220 km North and 139 km

East of Paris.

Calculate the bearing of Brussels from

Paris, to the nearest degree.

Answer.……………….……… [3]

15 (a) Write down the values of

20

= ……. , 21

= ……. , 22

= ……. , 23

= ……. , 24

= ……. [2]

(b) Change

49

5 to a decimal. Write down your full calculator display.

Answer (b)

49

5 =.……………….………

(c) What do you notice about your answers to parts (a) and (b)?

Answer (c) .……...……….……………………………………………………….……….

…………………………………………………………………………………………….

[1]

[1]

Paris

Brussels139 km

220 km

North

NOT TO

SCALE

6

0580/1/O/N/02

For

Examiner's

Use16 The diagram shows part of the

graph of y = 6 – x2

for –3 � x � 0.

Complete the graph

for – 4 � x � 4.

[4]

17 The frequency of radio waves (F) is connected to the wavelength (l) by the formula

l

000300

�F .

(a) Calculate the value of F when l = 1500.

Answer (a) F = .……………….………

(b) Calculate the value of l when F = 433, giving your answer to the nearest whole number.

Answer (b) l = .……………….………

[1]

[3]

18 Seven people were asked to guess the number of beans

in a jar. Their guesses were

194, 173, 170, 144, 182, 259, 159.

(a) Find the median.

Answer (a) ……………….………

(b) Work out the mean.

Answer (b) .……………….………

[2]

[2]

6

4

2

y=6 −x2

-2

-2 2 4-4

-4

-6

-8

-10

0x

y

7

0580/1/O/N/02

For

Examiner's

Use19 (a) Factorise 40a – 8b + 32c.

Answer (a) .……………….………

(b) Solve the equations

(i) x – 7 = 9,

Answer (b) (i) x = .……………….………

(ii) 2 (y + 1) = 3y – 5.

Answer (b) (ii) y = .……………….………

[2]

[1]

[2]

20

y

x

3

2

1

-1

-2-3 -1 1 2 3 4

-2

-3

0

(a) On the grid above, plot the points A (0,2), B (2,2), C (4,1) and D (–2, –1).

(b) Find the area of the quadrilateral ABCD.

Answer (b) .……………….………cm2

(c) The vector BC = �

�

��

�

�

y

x

.

Find the value of x and the value of y.

Answer (c) x =.……………….………

y =.……………….………

[1]

[2]

[2]

8

0580/1/O/N/02

BLANK PAGE

This question paper consists of 12 printed pages.

SJF2284/CG S14615/4© CIE 2002 [Turn over



MATHEMATICS 0580/3, 0581/3OCTOBER/NOVEMBER SESSION 2002

PAPER 3 2 hours

Candidates answer on the question paper.Additional materials:

Electronic calculatorGeometrical instrumentsMathematical tables (optional)Tracing paper (optional)

TIME 2 hours










If the degree of accuracy is not specified in the question, and if the answer is not exact, the answershould be given to three significant figures. Answers in degrees should be given to one decimal place.


CandidateCentre Number Number

Candidate Name


2

0580/3/O/N02

1 (a) A bottle of mass 480 grams contains 75 centilitres of water.

(i) Write 75 centilitres in millilitres.

Answer (a)(i) ……………..……… ml [1]

(ii) Write 75 centilitres in litres.

Answer (a)(ii) ……………………… l [1]

(iii) The mass of 480 grams is correct to the nearest 10 grams.

Complete the statement on the answer line.

Answer (a)(iii) ………… g � mass < ………… g [2]

(iv) Write 480 grams in kilograms.

Answer (a)(iv) …………………… kg [1]

(b) The diagrams below are accurate scale drawings of containers with water in them.

(i) The capacity of this cylindrical jar is 600 ml of water.

By measuring the height of the jar and the height of the water,find the amount of water in the jar.

Answer (b)(i) ……………….….… ml [2]

(ii) The capacity of this bucket is 7 litres.

Estimate the amount of water in the bucket.

Answer (b)(ii) ……………………… l [2]

ForExaminer’s

Use

3

0580/3/O/N02 [Turn over

2 (a) The results of the school’s senior football team during a year are recorded, using W for a win, Lfor a loss and D for a draw. They are:

L L W D L W L WL L D L L W W LW L L W D L L W

(i) Complete the table below to show these results.

Then display this information in the pie chart below.

[6]

(ii) The team play another match.

Based on the results above, what is the probability that they will win?

Answer (a)(ii) …………………… [1]

(b) The probability that the school’s junior team wins is 0.45 and the probability that it loses is 0.35.What is the probability of a draw?

Answer (b) ……………….……… [2]

ForExaminer’s

Use

W

Frequency Pie chart angle

L

D

TOTAL 360°

4

0580/3/O/N02

3

In triangle LMN, angle LNM = 90°, angle MLN = 28° and LM = 10 cm.

(a) Calculate

(i) MN,

Answer (a)(i) MN = …………………… cm [2]

(ii) LN,

Answer (a)(ii) LN = …………………… cm [2]

(iii) the area of triangle LMN.

Answer (a)(iii) ………...……………… cm2 [2]

(b) A circle is drawn with LM as diameter.

(i) Work out the area of the circle.

Answer (b)(i) …………………………. cm2 [2]

(ii) Showing all your working, find the area of triangle LMN as a percentage of the area of thecircle.

Answer (b)(ii) …………………………... % [2]

(iii) Explain why the point N is on the circle.

Answer (b)(iii) ................................................................................................................... [1]

ForExaminer’s

Use

28°L

10cm

N

M

NOT TO SCALE

5


ForExaminer’s

Use4

(a) Describe fully the transformation which maps

(i) shape L onto shape M,

Answer (a)(i) ..................................................................................................................... [2]

(ii) shape L onto shape N.

Answer (a)(ii) .................................................................................................................... [2]

(b) (i) Translate shape L using the vector . [2]

(ii) Enlarge shape L with centre of enlargement 0, scale factor . [2]1–2

–7–4

N

L

M

0

-1

-2

-3

-4

-5

-6

-7

1 2 3 4 5 6 7x

1

2

3

4

5

6

7

-1-2-3-4-5-6-7

y

6

0580/3/O/N02

ForExaminer’s

Use5 The cuboid shown in the diagram has EF = 4 cm, FG = 6 cm and AE = 3 cm.

(a) Calculate

(i) the volume of the cuboid,

Answer (a)(i) …………………… cm3 [2]

(ii) the surface area of the cuboid.

Answer (a)(ii) …………………… cm2 [3]

(b) The cuboid is divided into two equal triangular prisms. One of them is shown in the diagram.

(i) Write down the volume of the triangular prism.

Answer (b)(i) …………………… cm3 [1]

(ii) Work out the area of the rectangle AFGD.

Answer (b)(ii) …………………… cm2 [3]

A

NOT TO SCALE

H

D

G

E F

A B

E F4cm

6cm

D C

GH

NOT TO SCALE

3cm

7


ForExaminer’s

Use6 Ian and Joe start to dig a garden. They both dig at the same rate.

(a) When they are half-way through the job, what fraction of the garden has Ian dug?

Answer (a) …………….………… [2]

(b) Keith then arrives to help.All three dig at the same rate until the job is finished.

(i) What fraction of the garden did Ian dig after Keith arrived?

Answer (b)(i) ….………………… [2]

(ii) What fraction of the garden did Ian dig altogether?

Answer (b)(ii) …………………… [2]

(c) Ian and Joe started to dig at 09 00.Keith started to dig at 10 00.Each dug at the same rate throughout.At what time was the job finished?

Answer (c) ….…………………… [2]

8

0580/3/O/N02

7

The graph of 3x + 2y = 12 is drawn on the grid above.

(a) (i) Complete the table of values for y = 3x – 1.

[2]

(ii) On the grid above, draw the graph of y = 3x –1 for 0 � x � 2. [1]

(b) Use the graphs to find the solution of the simultaneous equations

3x + 2y = 12,y = 3x – 1.

Answer (b) x = ………… , y = ………… [2]

(c) Use algebra to find the exact solution of the simultaneous equations

3x + 2y = 12,y = 3x – 1.

Answer (c) x …………, y = ………… [4]

ForExaminer’s

Use

-2 0

-2

2

4

6

2 4

3x+2y=12

x

y

x 0 1

2

2

y

9


8

The diagram shows an island, drawn to a scale of 1cm to 30km.

(a) Find the distance in kilometres between points A and B.

Answer (a) AB = …………………… km [2]

(b) On the diagram draw the locus of points on the island which are

(i) 150 km from A, [1]

(ii) 150 km from B. [1]

Label the point T on the island where these two loci intersect. [1]

(c) A tower is built at T, to send television signals to the western part of the island. The maximumrange of its signals is 150 km.

Draw the locus of points 150 km from T. [1]

(d) A second tower is built, which can send television signals up to 120km, to reach the rest of theisland.

Use the points C, D and E to help you to find a suitable position for the second tower.

Label the position X.

Leave in any construction lines or arcs that you draw. [3]

ForExaminer’s

Use

A

North Scale: 1cm to 30km

B

C

ED

10

0580/3/O/N02

ForExaminer’s

Use9 Students try to find the best price at which to sell their school newspaper.

When the price was 10 cents, they sold 200 newspapers.

When the price was 60 cents, they sold only 75 newspapers.

They drew the graph below using this information.

(a) Use the graph to answer these questions.

(i) At what price will no-one buy the newspaper?

Answer (a)(i) …………………… cents [1]

(ii) 150 newspapers are sold. What was the price?

Answer (a)(ii) …………………… cents [1]

(iii) Complete the table below.

[6]

200

150

100

Number ofnewspapers

sold

Price (cents)

50

00 10 20 30 40 50 60 70 80 90

Price (cents)

10

20

30

40

50

60

70

80

90

Number of newspapers sold

200

175

75

Money received (cents)

2000

3500

4500

11


(b) Use the table in part (a)(iii) to answer these questions.

The total printing cost is $20.

(i) When the newspapers are sold at 20 cents each, calculate the profit in dollars.

Answer (b)(i) $ …………….…………… [2]

(ii) Estimate the price that will give the greatest profit.

Answer (b)(ii) ………………...………… [1]

10 A number that has only two different prime factors is called semi-prime.

For example, 77 is semi-prime since it has only two prime factors, 7 and 11.

[Remember that 1 is not prime.]

(a) Show that each of the three consecutive numbers 33, 34 and 35 is semi-prime.

Answer (a) .......................................................................................................................................

..........................................................................................................................................................

.................................................................................................................................................... [3]

(b) Find the smallest semi-prime number.

Answer (b) ……………………………… [2]

(c) Find two consecutive numbers between 10 and 20 which are semi-prime.

Answer (c) …………… and …………… [1]

(d) Find three consecutive numbers between 80 and 90 which are semi-prime.

Answer (d) …………… , …………… and …………… [3]

ForExaminer’s

Use

12

0580/3/O/N02

ForExaminer’s

Use11

The diagram shows wooden beams which support the roof of a house.

(a) Complete the table below.

[4]

(b) When L = 10, find the values of x, y and T.

Answer (b) x = ……………………………

y = ……………………………

T = ……………………………[3]

(c) Write down a formula for

(i) x in terms of L ,

Answer (c)(i) x = ………………………[1]

(ii) y in terms of L ,

Answer (c)(ii) y = …..………………… [1]

(iii) T in terms of L.

Answer (c)(iii) T = …………………… [2]

(d) When T = 83, find the value of L.

Answer (d) L = ……..………………… [1]

L metres

1m 1m 1m

1m 1m

2m 2m 2m 2m 2m 2m2m

Length of roof (L metres) 1

2

1

5

2

4

3

11

3 4 5

10

9

29

6

Number of 2 metre beams (x)

Number of 1 metre beams (y)

Total length of wood (T metres)

Igcse core papers 2002 2014

Education

Transcript of Igcse core papers 2002 2014