Cambridge International Examinations Cambridge ... · MATHEMATICS 0580/11 Paper 1 (Core) May/June...

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Cambridge International ExaminationsCambridge International General Certificate of Secondary Education

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MATHEMATICS 0580/11Paper 1 (Core) May/June 2017 1 hourCandidates 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.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 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 r, 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.

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0580/11/M/J/17© UCLES 2017

1 Write, in figures, the number seventy thousand and twenty.

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

2 Write, as a decimal, the value of 5-3.

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

3 The thickness of one sheet of paper is 8 # 10-3 cm.

Work out the thickness of 250 sheets of paper.

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

4 Simplify. (x2)5

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

5

A

B

opposite congruent reflected translated

Choose the mathematical word from the list to complete this statement.

Pentagon A is ............................................................ to pentagon B. [1]

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6 31 33 35 37 39

From the list, write down a prime number.

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

7 Write 23.4571 correct to

(a) 4 significant figures,

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

(b) the nearest 10.

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

8 Factorise completely. 12n2 - 4mn

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

9 Find the highest common factor (HCF) of 126 and 150.

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

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0580/11/M/J/17© UCLES 2017

10 The table shows the temperatures in five places at 10 am one day in January.

Place Temperature (°C)

Helsinki -7

Chicago -10

London 3

Moscow -4

Bangkok 26

(a) Which place was the coldest?

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

(b) At 2 pm the temperature in Helsinki had increased by 4 °C.

Write down the temperature in Helsinki at 2 pm.

.........................................°C [1]

11 Expand the brackets and simplify.( ) ( )x y x y7 2 3 14+ - -

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

12 The mass, m kilograms, of an elephant is 3570 kg, correct to the nearest 5 kg.

Complete this statement about the value of m.

..................... G m 1 ..................... [2]

5


13 a

51=

-c m b

34=

-

-c m

Write a + 2b as a single vector.

f p [2]

14 Manuel changes 5000 Mexican Pesos to dollars. He receives $336.

Complete this statement about the exchange rate. Give your answer correct to 2 decimal places.

$1 = ................................. Mexican Pesos [2]

15 Maria asks 50 students in her school when their birthday is. She records the information in the table.

Jan to Mar Apr to Jun Jul to Sep Oct to Dec

Number of birthdays 9 21 14 6

(a) Find the relative frequency of a student having a birthday in April, May or June.

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

(b) There are 750 students in the school.

Estimate the number of students who have a birthday in April, May or June.

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

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16 Work out 6512

2

3 .

Write your answer as a fraction in its lowest terms.

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

17 A r4 2r=

Make r the subject of this formula.

r = ....................................... [2]

18 (a) Work out. 3 2 4#+ -

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

(b) In each of these, insert one pair of brackets to make the statement correct.

(i) 3 # 5 + 2 + 2 = 23 [1]

(ii) 12 ÷ 4 + 2 = 2 [1]

7


19 Without using a calculator, work out 1 32

75

+ .

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

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

20 Solve the simultaneous equations. You must show all your working.

14x yx y

5 2 247 4

- =

+ = -

x = .......................................

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

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21 A cuboid has length 6 cm, width 5 cm and height 3 cm.

On the 1 cm2 grid, complete the net of the cuboid. The base is drawn for you.

[3]

9


22 Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test.

025

30

35

40

Mark

45

50

1 2 3 4 5Time (hours)

6 7 8 9 10

(a) The data for two more students is shown in the table.

Time (hours) 4.5 6.5

Mark 33 35

Plot these two points on the scatter diagram. [1]

(b) What type of correlation is shown on the scatter diagram?

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

(c) Draw a line of best fit on the scatter diagram. [1]

(d) Another student spent 5.5 hours revising.

Estimate a mark for this student.

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

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23

B

A

C

The diagram shows the positions of three points, A, B and C.

(a) Using a ruler and compasses only, construct

(i) the perpendicular bisector of the line AB, [2]

(ii) the locus of all points that are 3 cm from C. [2]

(b) Shade the region that is

• closer to A than to B

and

• less than 3 cm from C. [1]

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24 The diagram shows a notice board.

74 cm

NOT TOSCALE

The board is in the shape of a semicircle joined to a square with side 74 cm.

(a) Calculate

(i) the perimeter of the board,

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

(ii) the area of the board.

.......................................cm2 [3]

(b) The board is a prism that is 5 cm thick.

Calculate the volume of the board.

.......................................cm3 [1]

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0580/11/M/J/17© UCLES 2017

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.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series.

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.

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MATHEMATICS 0580/21Paper 2 (Extended) May/June 2017 1 hour 30 minutesCandidates answer on the Question Paper.Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional)





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1 Simplify. (x2)5

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

2 The thickness of one sheet of paper is 8 # 10-3 cm.

Work out the thickness of 250 sheets of paper.

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

3 Write 23.4571 correct to

(a) 4 significant figures,

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

(b) the nearest 10.

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

4 The table shows the temperatures in five places at 10 am one day in January.

Place Temperature (°C)

Helsinki -7

Chicago -10

London 3

Moscow -4

Bangkok 26

(a) Which place was the coldest?

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

(b) At 2 pm the temperature in Helsinki had increased by 4 °C.

Write down the temperature in Helsinki at 2 pm.

.........................................°C [1]

3


5 Factorise completely. 12n2 - 4mn

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

6 (a) 2 161r =

Find the value of r.

r = ....................................... [1] (b) 3 3t 5=

Find the value of t.

t = ........................................ [1]

7 Without using a calculator, work out 1 32

75

+ .

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

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

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8 Simon has two boxes of cards. In one box, each card has one shape drawn on it that is either a triangle or a square. In the other box, each card is coloured either red or blue. Simon picks a card from each box at random. The probability of picking a triangle card is t. The probability of picking a red card is r.

Complete the table for the cards that Simon picks, writing each probability in terms of r and t.

Event Probability

Triangle and red

Square and red (1 - t) r

Triangle and blue

Square and blue

[3]

9 h is directly proportional to the square root of p. h = 5.4 when p = 1.44 . Find h when p = 2.89 .

h = ....................................... [3]

5


10

1

–1

0

1

2

3

4

5

y

x2 3 4 5 6

By shading the unwanted regions of the grid, find and label the region R that satisfies the following four inequalities.

y G 2 y H 1 y G 2x - 1 y G 5 - x [3]

11 The two barrels in the diagram are mathematically similar.

h cm90 cm

NOT TOSCALE

The smaller barrel has a height of h cm and a capacity of 100 litres. The larger barrel has a height of 90 cm and a capacity of 160 litres.

Work out the value of h.

h = ....................................... [3]

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12 A line has gradient 5. M and N are two points on this line. M is the point (x, 8) and N is the point (k, 23). Find an expression for x in terms of k.

x = ....................................... [3]

13 A

E

H

D

B

C

G

F13 cm

NOT TOSCALE

5 cm

4 cm

The diagram shows a cuboid ABCDEFGH. AE = 5 cm, EH = 4 cm and AG = 13 cm.

Calculate the angle between the line AG and the base EFGH of the cuboid.

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

7


14 The diagram shows a regular octagon joined to an equilateral triangle.

NOT TOSCALE

x°

Work out the value of x.

x = ....................................... [3]

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15 The diagram shows information about the first 100 seconds of a car journey.

100

2

0

4

6

8

10

12

14

16

Speed(m/s)

18

20 30 40 50Time (s)

60 70 80 90 100

(a) Calculate the acceleration during the first 20 seconds of the journey.

......................................m/s2 [1]

(b) Work out the total distance travelled by the car in the 100 seconds.

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

9


16 Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test.

025

30

35

40

Mark

45

50

1 2 3 4 5Time (hours)

6 7 8 9 10

(a) The data for two more students is shown in the table.

Time (hours) 4.5 6.5

Mark 33 35

Plot these two points on the scatter diagram. [1] (b) What type of correlation is shown on the scatter diagram?

.............................................. [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) Another student spent 5.5 hours revising.

Estimate a mark for this student.

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

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17 (a) In this Venn diagram, shade the region F G, l.

�F G

[1] (b) = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {x: x is an odd number} B = {x: x is a square number} C = {x: x is a multiple of 3}

(i) Write all the elements of in the Venn diagram below.

�

A B

C

[2] (ii) Another number is included in the set . This number is in the region A B C+ +l .

Write down a possible value for this number.

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

11


18 The diagram shows a parallelogram OCEG.

Bb

a

C D E

F

NOT TOSCALE

GA

H

O

O is the origin, OA a= and OB b= . BHF and AHD are straight lines parallel to the sides of the parallelogram.

OG OA3= and OC OB2= .

(a) Write the vector HE in terms of a and b.

HE = .................................. [1] (b) Complete this statement.

a + 2b is the position vector of point ......................... [1] (c) Write down two vectors that can be written as 3a - b.

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

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19 ABCD is a rhombus with side length 10 cm.

D 40°

10 cm

B

NOT TOSCALE

A

C

Angle ADC = 40°. DAC is a sector of a circle with centre D. BAC is a sector of a circle with centre B.

Calculate the shaded area.

...................................... cm2 [4]

13


20 The diagram shows a fair spinner.

1

3

34

6

Anna spins it twice and adds the scores. (a) Complete the table for the total scores.

Score on first spin

1 3 3 4 6

Score on second spin

1 2 4 4 5 7

3 4 6 6 7 9

3 4 6 6 7 9

4

6

[1] (b) Write down the most likely total score.

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

(c) Find the probability that Anna scores (i) a total less than 6,

.............................................. [2] (ii) a total of 3.

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

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21 (a)

A

B

C

D

X35°

NOT TOSCALE

v°

u°

A, B, C and D are points on the circle. AD is parallel to BC. The chords AC and BD intersect at X.

Find the value of u and the value of v.

u = .......................................

v = ....................................... [3] (b)

FG

H

NOT TOSCALE

O210°

p°

F, G and H are points on the circle, centre O.

Find the value of p.

p = ....................................... [2]

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22 Write as a single fraction in its simplest form.

(a) xx x

93

2

2

-

-

.............................................. [3] (b) x x4

32 5

2-

++

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

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MATHEMATICS 0580/31Paper 3 (Core) May/June 2017 2 hoursCandidates answer on the Question Paper.Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional)





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0580/31/M/J/17© UCLES 2017

1 Camilla joins a soccer club. The total cost of joining is made up of membership, kit and travel.

(a) The ratio membership : kit : travel = 3 : 5 : 6. The cost of membership is $78.

(i) Show that the total cost of joining is $364.

[1]

(ii) Calculate the cost of the kit and the cost of the travel.

Kit = $ ................................................

Travel = $ ................................................ [3]

(b) Camilla’s father pays 1310 of the $364.

Camilla pays the rest.

Calculate how much she pays.

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

(c) Camilla’s brother joins the soccer club. He receives a 12% discount on the $364 because he is younger than Camilla.

Calculate the total cost of joining for him.

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

3


(d) During the year, Camilla’s team played 24 matches. The table gives some information about the results of these matches.

Played Won Drawn Lost

24 W 6 L

(i) Write down an equation, in terms of W and L, for the number of matches played.

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

(ii) Points are given when a team wins or draws a match.

The points are Match won 3 points Match drawn 1 point Match lost 0 points.

The team has a total of 54 points.

Write down an equation, in terms of W, for the total points given.

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

(iii) Work out the value of W and the value of L.

W = ................................................

L = ................................................ [3]

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0580/31/M/J/17© UCLES 2017

2

–10 –8 –6 –4 –2 0 2 4 6 8 10

–10

–8

–6

–4

–2

2

4

6

8

10

A

B

x

y

(a) Write down the mathematical name of the shaded polygon.

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

5


(b) Describe fully the single transformation that maps the shaded polygon onto polygon A.

..............................................................................................................................................................

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

(c) Describe fully the single transformation that maps the shaded polygon onto polygon B.

..............................................................................................................................................................

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

(d) On the grid, draw the reflection of the shaded polygon in the line x = 2. [2]

(e) On the grid, draw the rotation of the shaded polygon through 90° anti-clockwise about the origin. [2]

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3 Francis asks 30 families how many children they have. The table shows the results.

Number of children in each family 0 1 2 3 4 5

Number of families 4 6 6 2 9 3

(a) (i) Write down the mode.

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

(ii) Find the median.

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

(iii) Calculate the mean.

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

(iv) Complete the bar chart, including the vertical scale.

Number offamilies

0 1 2 3

Number of children in each family

4 5

[3]

7


(b) Francis also recorded the age group and gender of the children aged 12 or less. The information is shown in the table.

Age 4 and younger Age 5 to 8 Age 9 to 12 Total

Male 9

Female 11 36

Total 30 20 75

Complete the table. [2]

(c) Francis displays the results for the totals of each age group on a pie chart. The sector angle for the group ‘Age 4 and younger’ is 120°.

Calculate the sector angle for

(i) age 5 to 8,

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

(ii) age 9 to 12.

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

(d) Complete the pie chart.

Age 4 and younger

[1]

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0580/31/M/J/17© UCLES 2017

4 (a)

49°A

O

D

NOT TOSCALE

C

B

5.4 cm

The diagram shows a circle, centre O, with points B and D on the circumference. The line AC touches the circle at B. OB is parallel to DC and angle OAB = 49°.

(i) Write down the mathematical name of the line OB.

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

(ii) Write down the reason why angle ABO is 90°.

......................................................................................................................................................

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

(iii) Find angle AOB.

Angle AOB = ................................................ [1]

(iv) Write down the reason why angle ADC = angle AOB.

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

(v) Complete the statement using a mathematical word.

Triangle AOB is ................................................................. to triangle ADC. [1]

9


(vi) AB = 5.4 cm

Calculate

(a) OB,

OB = ......................................... cm [2]

(b) OA,

OA = ......................................... cm [2]

(c) the area of triangle AOB.

.........................................cm2 [2]

(b) Here is a polygon with 7 sides.

Show that the sum of the interior angles of this polygon is 900°.

[1]

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0580/31/M/J/17© UCLES 2017

5 (a) Complete the table of values for y x x2 12= + - .

x -5 -4 -3 -2 -1 0 1 2 3

y 14 2 -1 -1 2

[3]

(b) On the grid, draw the graph of y x x2 12= + - for x5 3G G- .

–5 –4 –3 –2 –1 0 1 2 3–5 –4 –3 –2 –1 0 1 2 3

–4

–3

–2

–1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

y

x

[4]

11


(c) (i) On the grid, draw the line of symmetry. [1]

(ii) Write down the equation of the line of symmetry.

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

(d) (i) On the grid, plot the points ( , )5 7- and ( , )0 3- and join them with a straight line, L. [2]

(ii) Write down the x co-ordinate of each point where the line L crosses the graph of y x x2 12= + - .

x = ........................ and x = ........................ [2]

(iii) Work out the gradient of the line L.

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

12

0580/31/M/J/17© UCLES 2017

6 Eduardo goes to the Theatre. He leaves his house at twenty-five minutes to six in the evening.

(a) Write down this time using the 24-hour clock.

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

(b) He travels to the Theatre by bus. Part of the timetable is shown below.

Belmont Road 17 40 18 15 18 50

Railway Station 17 47 18 20 18 57

Leisure Centre 17 59 18 34 19 07

Theatre 18 05 18 40 19 12

Bus Station 18 16 18 48 19 22

It takes Eduardo 16 minutes to walk to the Railway Station from his house.

(i) Find the time he arrives at the Railway Station.

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

(ii) He gets on the next bus to the Theatre.

Find the time he arrives at the Theatre.

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

(iii) The 18 50 bus from Belmont Road takes the least time to travel to the Bus Station.

Work out how many minutes quicker this journey is than the journey on the 17 40 bus.

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

(iv) The distance from Belmont Road to the Bus Station is 8.5 km.

Calculate the average speed for the bus leaving Belmont Road at 17 40. Give your answer in kilometres per hour, correct to 1 decimal place.

....................................... km/h [4]

13


7 Here is a sequence of diagrams made using identical rectangles. A dot is shown at the junction of three lines. A cross is shown at the junction of two lines.

x

x

x

x

x

x

x

x

xx

x

x

x

x

x

x

x

x

x

xx x

x x

Diagram 1 Diagram 2 Diagram 3 Diagram 4

(a) Write down the order of rotational symmetry of Diagram 1.

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

(b) Complete Diagram 4 using dots and crosses. [1]

(c) Complete the table for Diagram 4 and Diagram 5.

Diagram 1 2 3 4 5

Number of dots 0 4 10

Number of crosses 4 6 8

[3]

(d) (i) Describe, in words, the rule for continuing the sequence for the number of dots.

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

(ii) The expression for the number of dots in Diagram n is n n 22 + - .

Find the number of dots in Diagram 12.

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

(e) (i) Write down an expression for the number of crosses in Diagram n.

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

(ii) Diagram n has 100 crosses.

Find the value of n.

n = ................................................ [2]

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8 The scale drawing shows the positions of Bogota (B) and Quito (Q). The scale is 1 centimetre represents 150 kilometres.

North

North

Scale: 1 cm to 150 km

B

Q

(a) (i) Measure the length of the line BQ.

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

(ii) Work out the actual distance from Bogota to Quito.

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

(iii) Measure the bearing of Quito from Bogota.

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

(b) A plane leaves Quito and flies straight to Manaus. Manaus is 2100 km on a bearing of 100° from Quito.

On the scale drawing, mark the position of Manaus (M). [3]

15


(c) The plane flies the 2100 km from Quito to Manaus at an average speed of 550 km/h.

Calculate the time taken for this flight

(i) in hours, correct to 3 significant figures,

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

(ii) in hours and minutes, correct to the nearest minute.

........................ h........................ min [1]

Question 9 is printed on the next page.

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9 Francesca owns a business. One year she has a total of $6000 to spend on rent, furniture and office equipment.

(a) (i) The rent is $400 per month.

Work out how much Francesca spends on rent in this year.

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

(ii) Desks cost $58.50 each and chairs cost $15 each. Francesca buys 2 desks and 5 chairs.

Work out how much Francesca spends on furniture.

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

(iii) Francesca also spends $800 on office equipment.

Work out how much remains of the $6000.

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

(iv) She spends this remaining amount on boxes of paper. Paper costs $4.95 per box.

Work out how many boxes she buys.

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

(b) Francesca needs to buy computer equipment. She borrows $2000 from a bank for 3 years at a rate of 5% per year compound interest.

Calculate the total amount she pays back at the end of the 3 years.

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

® IGCSE is a registered trademark.


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Cambridge International Examinations Cambridge International General Certificate of Secondary Education

MATHEMATICS 0580/11 Paper 1 (Core) May/June 2017

MARK SCHEME

Maximum Mark:56

Published

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0580/11 Cambridge IGCSE – Mark Scheme PUBLISHED

May/June 2017

© UCLES 2017 Page 2 of 4

Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied

Question Answer Marks Part marks

1 70 020 cao 1

2 [0].008 1

3 2 1

4 x10 1

5 Congruent 1

6 31 or 37 1

7(a) 23.46 cao 1

7(b) 20 cao 1

8 4n(3n – m) final answer 2 B1 for 4(3n2 – mn) or n(12n – 4m) or 2n(6n − 2m) or 2(6n2 – 2mn)

9 6 2 B1 for answer 2 or 3 or 2 × 3 or M1 for prime factors of 126 and 150 seen

10(a) Chicago 1

10(b) −3 1

11 21y + xy or y(21 + x) final answer

2 B1 for 14x + 21y or −14x + xy or answer of ky + xy

12 3567.5 1

3572.5 1 SC1 for both correct but reversed

13 19−

−

2B1 for

68

− −

seen or answer 9k

− or

1k−

14 14.88 2 M1 for 5000 ÷ 336 or B1 for 14.881 or 14.880[9...] or 14.9


May/June 2017



15(a) 2150

oe 1

15(b) 315 1FT FT their (a) × 750 provided 0 < their (a) < 1

16 29

2

B1 for 836

or 418

17

4πA or 1

2 πA oe

2M1 for r2 =

4πA or 2r π = A

or 4r2 = πA or πr2 =

4A

18(a) –5 1

18(b)(i) 3 × (5 + 2) + 2 = 23 1

18(b)(ii) 12 ÷ (4 + 2) = 2 1

19 ( )14 or 35 1521 21

+ M1

accept ( )14 or 35 1521 21

k k kk k

+

8221

cao A2

or A1 for 50 21

or 1 821

or 2921

or 1 2921

20 Correctly eliminating one variable M1

[x =] 2 A1

[y =] −7 A1 If zero scored, SC1 for 2 values satisfying one of the original equations SC1 for both correct but no working

21 Complete correct ruled net 3 B2 for 4 correct rectangles in correct places or B1 for 2 correct side rectangles in correct places

22(a) Points plotted at (4.5, 33) and (6.5, 35)

1

22(b) Positive 1

22(c) Correct ruled line 1

22(d) 33.5 to 37.5 1FT FT from their line provided positive gradient


May/June 2017



23(a)(i) Correct ruled bisector of AB with 2 pairs of arcs 2 B1 for correct bisector with no or incorrect arcs or 2 pairs of correct arcs

23(a)(ii) Complete circle, radius 3 cm, centre C

2 B1 for an arc of correct radius or a circle of incorrect radius

23(b) Correct region shaded 1 dep on at least B1 in both parts

24(a)(i) 338 or 338.3 nfww or 338.2 to 338.26

3 M1 for 3 × 74 and M1 for 74 × π ÷ 2

24(a)(ii) 7630 nfww or 7626 to 7627

3 M1 for 742

and M1 for 237

2π×

24(b) 38100 nfww or 38200 or 38150 or 38130 to 38140

1FT FT their (a)(ii) × 5





MATHEMATICS 0580/21 Paper 2 (Extended) May/June 2017

MARK SCHEME

Maximum Mark: 70

Published



May/June 2017



Question Answer Mark Part marks

1 x10 1

2 2 1

3(a) 23.46 cao 1

3(b) 20 cao 1

4(a) Chicago 1

4(b) − 3 1

5 4n(3n – m) final answer 2 B1 for 4(3n2 – mn) or n(12n – 4m) or 2n(6n – 2m) or 2(6n2 – 2mn)

6(a) − 4 1

6(b) 15

or 0.2 1

7 ( )14 or 3521

+ 1521

M1

accept ( )14 or 3521

k kk

+ 1521

kk

2 8

21 cao

A2or A1 for 50

21 or 1 8

21 or 29

21 or 1 29

21

8 rt

(1 – t) r

(1 − r)t oe

(1 – r)(1 – t) oe

3

B1 for each

9 7.65 3 M1 for h = k p oe M1 for h = their k p

or M2 for 5.41.44

= 2.89h oe

0

©

Qu

1

1

1

0580/21

© UCLES 2017

estion

10 Co

11 76

12 k –

13 22

14 16

5(a) 0.8

5(b) 11

6(a) Po(6

orrect region

6.9 or 76.94 t

– 3 or 3 k− +

2.6 or 22.61 t

65

8 or 45

180

oints plotted .5, 35)

R

C

Answer

n identified

to 76.95

k

to 22.62

at (4.5, 33) a

R

Cambridge P

and

IGCSE – MPUBLISHED

Page 3 of 5

Mar

Mark SchemD

rk

3 SC1 fo

3M2 for

or M1

3

90h

3M1 for

M1 for

e.g. [x =

3M2 for

or M1

3M2 for

or M1

[exterio

1

3 M2 for(0.5 × or M1

1

e

P

or

r 90 ÷ 3160100

for 3160100

so

100160

= oe

r 5 = 23 8 k x−−

o

r 5(k – x) = 2

=] k − 23 85−

r sin [=] 513

o

for identifyin

r 3608

+ 3603

for [exterior

or angle of tr

r 16 × 20) + (0for part area

3 2

0

1

1 2

2

M

Part marks

or 90 × 31016

oi or 3100160

oe

23 – 8 or bett8

oe

ng angle AG

0 oe

r angle of oct

riangle =] 363

0.5 × 4 × 30)a

1

1 2

May/June 201

00

soi or

ter

GE

tagon =] 3608

603

oe

) + (80 × 12)

17

0 or

oe


May/June 2017



16(b) Positive 1

16(c) Correct ruled line 1

16(d) 33.5 to 37.5 1FT FT from their line providing positive gradient

17(a) 1

17(b)(i)

2 B1 for four out of the eight regions correct

17(b)(ii) Any even square number that is also a multiple of 3

1

18(a) 2a + b 1

18(b) D 1

18(c) CFuuur

and BGuuur

2 B1 for each

19 5.53 or 5.54 or 5.534 to 5.543… 4 M3 for

2 × {( 40360

× π × 102)– ( 12

× 102 × sin 40)}

or M2 for

12 ×

102 × sin 40 and [2 40] 360

× × π × 102

or M1 for

12 ×

102 × sin 40 or [2 ]× 40360

× π × 102

20(a) 5 7 7 8 10 7 9 9 10 12

1

20(b) 7 1

F G

A B

9 5 7 4

2 8 C

3 6

1


May/June 2017



20(c)(i) 725

or 0.28 or 28% 2FT

FT 725

their

B1 for 25k

If zero scored, then SC1 for 25

or 615

if no

values in the bottom two rows of the table.

20(c)(ii) 0 1FTFT 0

25their

21(a) [u =] 35 1

[v =] 110 2 B1 for ACB or ADB = 35

21(b) 75 2 B1 for 150

or M1 for 360 2102−

22(a) 3

xx +

final answer 3 B1 for x(x – 3)

B1 for (x – 3)(x + 3)

22(b) 8 7( 4)(2 5)

xx x

+− +

final answer 3 B1 for common denominator of (x − 4)(2x + 5)

oe M1 for 3(2x + 5) + 2(x − 4) oe with an attempt to expand the brackets





MATHEMATICS 0580/31 Paper 3 (Core) May/June 2017

MARK SCHEME

Maximum Mark: 104

Published



May/June 2017




1(a)(i) 78 ÷ 3 × (3 + 5 + 6) [= 364] 1

1(a)(ii) [kit] 130 [travel] 156

3 M1 for 364 ÷ (3 + 5 + 6) × 5 (or × 6 if travel first) or 78 ÷ 3 × 5 (or × 6 if travel first) A1 for one of kit or travel correct If zero scored, SC1 for kit + travel = 286

1(b) 84 2 M1 for 3 ÷ 13[ × 364] or 364 – (10 ÷ 13 × 364) or B1 for 280

1(c) 320.32 final answer 2 M1 for (100 – 12) ÷ 100 [× 364] or B1 for 43.68

1(d)(i) W + 6 + L = 24 oe 1

1(d)(ii) 3W + 6 = 54 isw 1

1(d)(iii) [W=] 16 2 M1 for 3W = 54 – 6 or W + 2 = 18 or better or correct first step from an equation in W only

[L=] 2 1FT FT is 18 – their W If zero scored, SC1 for both correct but reversed

2(a) Quadrilateral 1

2(b) Enlargement 1

[Scale factor] 3 1

[Centre] (–3, –1) 1

2(c) Translation 1

107

−

1

2(d) Vertices (6, 2), (7, −1), (8, −1), (9, 1)

2 B1 for a correct reflection in x = k or y = 2


May/June 2017



2(e) Vertices (−2, −2), (1, −3), (1, −4), (−1, −5)

2 B1 for a ‘correct’ 90° clockwise rotation about the origin If zero scored, SC1 for correct size and orientation but wrong position

3(a)(i) 4 1

3(a)(ii) 2 1

3(a)(iii) 2.5 3 M1 for [(0 × 4)+] (1 × 6) + (2 × 6) + (3 × 2) + (4 × 9) + (5 × 3) oe M1 dep their total ÷ 30 soi

3(a)(iv) 4 bars correct height, correct width and correct gaps

2

B1 for 2 bars correct heights and widths, or 4 correct heights

Correct vertical scale shown 1

3(b) 6 values correctly placed

14 16 [9] 39 [11] 14 11 [36] 25 [30] [20] [75]

2 B1 for 3, 4 or 5 correctly placed

3(c)(i) 144 2 M1 for 30 ÷ 75 [× 360] oe

3(c)(ii) 96 1FT FT 240 – their (c)(i)

3(d) Correct line from centre to circumference, angles 144° and 96°

1FT FT their angles provided they sum to 240°

4(a)(i) Radius 1

4(a)(ii) [Angle between] tangent [and] radius

1

4(a)(iii) 41 1

4(a)(iv) Corresponding [angles] 1

4(a)(v) Similar 1

4(a)(vi)(a) 6.21 or 6.211 to 6.212 2M1 for tan 49 =

5.4OB or better

4(a)(vi)(b) 8.23 or 8.229 to 8.231 2FTM1 for cos 49 = 5.4

OAor better

or for 5.42 + their (vi)(a)2 or better

4(a)(vi)(c) 16.8 or 16.76 to 16.77 2FT M1 for their (vi)(a) × 5.4 ÷ 2

4(b) 5 × 180 1


May/June 2017



5(a) 7 –2 7 14

3 B2 for 3 correct B1 for 2 correct

5(b) Correct smooth curve 4 B3FT for 8 or 9 correct plots or B2FT for 6 or 7 correct plots or B1FT for 4 or 5 correct plots

5(c)(i) Ruled line, x = –1, drawn 1

5(c)(ii) x = –1 oe 1

5(d)(i) Ruled line L drawn, joining (–5, 7) and (0, −3)

2 B1 for one of the points correct and line drawn, or both points correct and no or wrong line.

5(d)(ii) −3.3 to −3.5, −0.5 to −0.7 2FT B1FT for one correct.

5(d)(iii) −2 2M1FT for their Rise

Runfrom part (d)(i) or their 2 1

2 1

y yx x

−−

If zero scored, SC1 for answer 2

6(a) 17 35 1

6(b)(i) 17 51 1FT B1 for their (a) + 16 minutes

6(b)(ii) 18 40 cao 1

6(b)(iii) 4 nfww 2 B1 for 36 minutes or 32 minutes

6(b)(iv) 14.2 cao 4 M2 for 8.5 ÷ their 36 × 60 soi or M1 for 8.5 ÷ their 36 or their 36 ÷ 60 soi or 8.5 ÷ time in mins × 60 A1 for 14.17 or 14.16 to 14.17 If A0 then SC1 for their answer ⩾ 2 decimal places rounded to 1 decimal place

7(a) 2 1

7(b) 3 dots correctly placed 4 crosses correctly placed

1

7(c) 18 28

1,1 If zero scored, SC1 for their 18 + 10

10 12

1

7(d)(i) Add two more each time oe 1

7(d)(ii) 154 2 M1 for 122 + 12 − 2

7(e)(i) 2n + 2 oe final answer 2 B1 for 2n + j or kn + 2 (k ≠ 0 or 1)


May/June 2017



7(e)(ii) 49 2 M1 for their (e)(i) = 100 provided (e)(i) is algebraic soi

8(a)(i) 4.4 1

8(a)(ii) 660 1FT their (a)(i) × 150

8(a)(iii) 220 1

8(b) 14 [cm] from Q 2 M1 for 2100 ÷ 150 soi

100° from Q 1

8(c)(i) 3.82 cao 2 M1 for 2100 ÷ 550

8(c)(ii) 3[h] 49[min] 1FT their time correctly converted

9(a)(i) 4800 1

9(a)(ii) 192 2 M1 for 2 × 58.5 + 5 × 15 or B1 for 117 or 75 seen

9(a)(iii) 208 2FT M1 for [6000 – ] (their (a)(i) + their (a)(ii) + 800) oe

9(a)(iv) 42 2FT M1 for their (a)(iii) ÷ 4.95

9(b) 2315.25 cao 3 M2 for 2000 × 1.053 oe or M1 for 2000 × 1.052 oe If zero scored, SC1 for 315.25

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