# Cambridge International Examinations CAMBRIDGE INTERNATIONAL · PDF file...

date post

11-Jun-2020Category

## Documents

view

12download

0

Embed Size (px)

### Transcript of Cambridge International Examinations CAMBRIDGE INTERNATIONAL · PDF file...

IB16 06_0607_11/4RP © UCLES 2016 [Turn over

*7320481266*

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/11

45 minutes

Additional Materials: Geometrical Instruments

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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40.

2

Formula List

Area, A, of triangle, base b, height h. A = 1 2

bh

Area, A, of circle, radius r. A = πr2

Circumference, C, of circle, radius r. C = 2πr

Curved surface area, A, of cylinder of radius r, height h. A = 2πrh

Curved surface area, A, of cone of radius r, sloping edge l. A = πrl

Curved surface area, A, of sphere of radius r. A = 4πr2

Volume, V, of prism, cross-sectional area A, length l. V =Al

Volume, V, of pyramid, base area A, height h. V= 1 3

Ah

Volume, V, of cylinder of radius r, height h. V = πr2h

Volume, V, of cone of radius r, height h. V = 1 3

πr2h

Volume, V, of sphere of radius r. V = 4 3

πr3

3

Shade 3 2

of this shape.

[1]

2

Draw a sector inside this circle. Draw a chord inside this circle. [2] 3 Write down all the factors of 21. [2]

4

[1] 5 Complete the mapping diagram.

16

11

9

5

2

19

15

7

1

[1]

6 Jenny shares $40 between her two sons in the ratio 3:1. Work out how much each son receives.

$ and $ [2]

© UCLES 2016 0607/11/M/J/16 [Turn over

7 Tick the shapes that have both line symmetry and rotational symmetry.

Rectangle Kite Parallelogram

Rhombus Isosceles Triangle

[2]

8 The diagram shows a child’s solid building block in the shape of a cuboid 2 cm by 5 cm by 10 cm.

5 cm

10 cm

2 cm

Find the total surface area of the cuboid. cm2 [3]

6

9 Write down the next two terms in the sequence.

18, 18, 16, 12, 6, …

, [2]

10 The Venn diagram shows two sets A and B. U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A

U

B

4

(i) A = { } [1]

(ii) B′ = { } [1]

(iii) A ∩ B = { } [1] (b) What is the mathematical name given to the numbers in set A? [1]

(c) Circle the statements which are correct for this Venn diagram.

A ∪ B = U 7 ∉ A n(B) = 4 A ∩ B′ = {4} [2]

7

11 110° NOT TO

Find the value of r. r = [3]

12 A car travels 100 metres in 8 seconds. Find its speed in kilometres per hour. km/h [2]

13 Describe the single transformation that maps y = f(x) onto y = f(x) + 3.

[2]

.

He takes 50 shots at the target. How many times does he expect to hit the target? [1]

15 Write down all the integers that satisfy the following inequality.

–3 x < 2 [2]

Questions 16 and 17 are printed on the next page.

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. 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. © UCLES 2016 0607/11/M/J/16

16 (a) Factorise. (i) 3x + 6 [1]

(ii) p2 + pq [1]

(b) Expand the brackets and simplify. x – 3(2x – 7) [2]

17 Solve the following simultaneous equations. 2x + y = 8 3x + 2y = 12

x =

y = [3]

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

DC (LK/AR) 115879/3 © UCLES 2016 [Turn over

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

* 9 9 8 9 7 3 9 1 8 6 *

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2016 45 minutes Candidates answer on the Question Paper.

Additional Materials: Geometrical Instruments

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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES.

Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40.

2

For the equation ax bx c 0 2 + + = x a

b b ac 2

= - -

Curved surface area, A, of cylinder of radius r, height h. rA rh2=

Curved surface area, A, of cone of radius r, sloping edge l. rA rl=

Curved surface area, A, of sphere of radius r. rA r4 2=

Volume, V, of pyramid, base area A, height h. V Ah 3

1 =

Volume, V, of cylinder of radius r, height h. rV r h2=

Volume, V, of cone of radius r, height h. rV r h 3

1 2=

Volume, V, of sphere of radius r. rV r 3

4 3=

sinbc A 2

Answer all the questions.

4

4

1 -

[2]

2 (a) Shade two more squares so that this shape has exactly one line of symmetry.

[1]

(b) Shade two more triangles so that this shape has rotational symmetry of order 3.

[1]

4

0607/21/M/J/16© UCLES 2016

. .

.

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

4 a 2 3 7 5 2 3 # #= b 2 3 5

3 4 # #=

Leaving your answer as the product of prime factors, find

(a) b2,

(b) the highest common factor (HCF) ofa and b, .

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

(c) the lowest common multiple (LCM) of aand b.

[2]

5

0607/21/M/J/16© UCLES 2016 [Turn over

5 Luis has a large jar containing red, yellow, green and blue beads. He takes a bead at random from the jar, notes its colour and replaces it. He repeats this 200 times.

The table shows his results.

Colour Red Yellow Green Blue

Number of beads 26 72 64 38

Relative frequency

(a) Complete the table to show the relative frequencies. [2]

(b) (i) There are 5000 beads in the jar altogether.

Estimate the number of green beads in the jar.

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

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

0607/21/M/J/16© UCLES 2016

7 U = {Integers from 1 to 18} F = {Factors of 12} M = {Multiples of 3} E = {Even numbers}

(a) Complete the Venn diagram by putting the numbers 2, 3, 4, 8, 12, 15 and 18 in the correct subsets.

F 1

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

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

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

7

9

C

D

A

B

A, B, C and D are points on the circle centre O. Angle BOD = 130°.

(a) Find angle DCB.

[2]

12

q

r

b

a

p

Write the vectors p, q and r in terms of a and b .

p =

q = ................................................

13

30 60–30–60 90 120 150 180 210 240 270 300 330

2

–2

y

x° 0

The graph of y=asin (x + b)° is shown in the diagram. Find the value of a and the value of b.

a = ................................................

NOT TO SCALE

The diagram shows a sketch of the graph of y=ax2+bx O is the point (0, 0), Pis the point (4, 0) andQ is the point (8, 96).

Find the value of a and the value of b.

a = ................................................

0607/21/M/J/16© UCLES 2016

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.

bLank page

* 0 0 1 1 9 8 9 2 0 8 *

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31

1 hour 45 minutes

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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES.

Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For r, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 96.

2

Formula List

Area, A, of triangle, base b, height h. A = bh 2

1

Area, A, of circle, radius r. A = rr2

Circumference, C, of circle, radius r. C = 2rr

Curved surface area, A, of cylinder of radius r, height h. A = 2rrh

Curved surface area, A, of cone of radius r, sloping edge l. A = rrl

Curved surface area, A, of sphere of radius r. A = 4rr2

Volume, V, of prism, cross-sectional area A, length l. V = Al

Volume, V, of pyramid, base area A, height h. V= Ah 3

1

Volume, V, of cylinder of radius r, height h. V = rr2h

Volume, V, of cone of radius r, height h. V = r h 3

1 2r

Volume, V, of sphere of radius r. V = r 3

4 3r

Answer all the questions.

1 (a) Write 356.31

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

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

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

(b) (i) Calculate . .16 8 9 61 2 - .

Write down all the figures shown on your calculator, giving your answer as a decimal.

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

(ii) Myrto estimates that the answer to part (b)(i) is 300.

(a) Find the difference between Myrto’s estimate and your answer to part (b)(i).

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

(b) Write this difference as a percentage of your answer to part (b)(i).

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

4

(i) as a power of 4,

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

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

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

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

5

0607/31/M/J/16© UCLES 2016 [Turn over

3 Tingwei buys 2 kg of cheese. The cheese costs $13.50 for one kilogram.

(a) Work out how much Tingwei pays for the 2 kg of cheese.

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

(b) He uses all the cheese to make 200 cheese balls.

Find the mass, in grams, of one cheese ball.

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

(c) (i) He sells all these cheese balls at a school fair for $0.25 each.

Work out how much money he received.

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

Work out how much money goes to the school charity.

$ ................................................................. [1] (d) The school fair makes a total profit of $460.

Write the profit that Tingwei made as a fraction of $460. Give your answer in its simplest form.

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

6

0607/31/M/J/16© UCLES 2016

4 The number of strawberries in each of 20 boxes is listed below.

32 28 27 32 33 28 34 28 29 29

28 28 33 31 33 33 30 29 29 26

(a) Complete the frequency table.

Number of strawberries 26 27 28 29 30 31 32 33 34

Frequency 1 1 1

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

(c) One of these boxes of strawberries is chosen at random.

Find the probability that it contains

(i) exactly 33 strawberries,

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

7

5 (a) A B C D5 2 2

1= - -

(i) Find the value of A when B = 2, C = 3 and D = 6.

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

(ii) Find the value of B when A = 12, C = 1 and D = 4.

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

(b) Find the value of 7p − 4q when p = −3 and q = –2.

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

(c) Rearrange 2y = 3x − 9 to make x the subject.

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

(d) The mass of 1 pomegranate and 2 kiwi fruit is 480 g. The mass of 1 pomegranate and 6 kiwi fruit is 840 g.

Find the mass of 1 pomegranate and the mass of 1 kiwi fruit. Show all your working.

1 pomegranate = ............................. g

8

0607/31/M/J/16© UCLES 2016

6 30 people were asked where they were going on holiday. The results are to be shown in a pie chart.

Country India Spain South Africa United States Australia

Number of people 5 12 3 6 4

Sector angle 60° 48°

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

Australia India

7 (a)

SCALE

DG

H

AFB and CGD are parallel lines. EFGH is a straight line and angle AFE = 105°.

Find

r°

s°

p°

70°

q°

AOB and COD are diameters of a circle, centre O. The lines AD and CB are parallel and angle CAB = 70°.

Find the values of p, q, r and s.

p = ................................

q = ................................

r = ................................

C SB

The diagram shows four straight cycle tracks HB, HC, BC and CS. BC = CS and HC = 2.5 km. Angle HBC = 90° and angle BHC = 40°.

(a) Abimela cycles from home, H, to school, S, each day along cycle track HC and CS.

(i) Use trigonometry to find the distance BC.

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

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

(b) One day track HC is blocked and she has to cycle along tracks HB, BC and CS.

Find the distance HB.

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

(c) Find the extra distance that Abimela now has to cycle to school.

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

9

1

0

2

3

4

5

6

7

8

9

y

x

(a) On the grid, plot the points A(2, 3) and B(5, 7). Draw the line AB. [2]

(b) Write down the co-ordinates of the midpoint of AB.

( .................... , .................... ) [1]

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

(d) Find the equation of the line parallel to AB that passes through the point (0, 4).

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

12

NOT TO SCALE

The diagram shows 12 solid cylinders packed into a box. Each cylinder has radius 1 cm and length 15 cm.

(a) (i) Find the volume of one cylinder.

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

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

(b) The box measures 15 cm by 12 cm by 4 cm.

Find the volume of the box.

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

(c) Find the volume of the box not taken up by the cylinders.

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

(d) Write your answer to part (c) as a percentage of the total volume of the box.

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

13

11

2

2

−2

−4

−6

4

6

8

10

y

P

The diagram shows a pentagon, P.

(a) Draw the image of P after a reflection in the y-axis. Label this image Q. [1]

(b) Draw the image of P after a translation by the vector 2

6-

J

Label this image R. [2]

(c) Draw the image of P after an enlargement, scale factor 3, centre (0, 0). Label this image S. [2]

(d) Find the ratio

length of horizontal side of S : length of horizontal side of P.

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

Choose a word from the list to complete the statement.

P and S are ……………..……… shapes. [1]

14

0607/31/M/J/16© UCLES 2016

12 The masses of 200 meerkats are recorded in the frequency table.

Mass (x grams) Frequency

x200 3001 G 5

Total 200

.................... x1 G .................... [1]

(b) (i) Show that the midpoint of the first group is 250.

[1]

(ii) Find an estimate of the mean mass of these 200 meerkats.

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

Mass (x grams) Cumulative frequency

x 300G 5

(d) Complete the cumulative frequency curve.

20

600 700 800 900 1000

40

60

80

0

100

120

(i) the median,

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

(iii) the number of meerkats with a mass of more than 850 g.

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

16

0607/31/M/J/16© UCLES 2016

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.

13

( )f x x x 22= +

(a) On the diagram, sketch the graph of y = f(x) from x = −3 to x = 3. [4]

(b) Write down the equation of the vertical asymptote for this graph.

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

( .................... , .................... ) [1]

(d) Write down the number of solutions of y = f(x) when y = 6.

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

* 8 3 9 8 4 2 2 7 1 6 *

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/41

2 hours 15 minutes

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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES.

Answer all the questions. Unless instructed otherwise, give your answers exactly…

*7320481266*

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/11

45 minutes

Additional Materials: Geometrical Instruments

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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40.

2

Formula List

Area, A, of triangle, base b, height h. A = 1 2

bh

Area, A, of circle, radius r. A = πr2

Circumference, C, of circle, radius r. C = 2πr

Curved surface area, A, of cylinder of radius r, height h. A = 2πrh

Curved surface area, A, of cone of radius r, sloping edge l. A = πrl

Curved surface area, A, of sphere of radius r. A = 4πr2

Volume, V, of prism, cross-sectional area A, length l. V =Al

Volume, V, of pyramid, base area A, height h. V= 1 3

Ah

Volume, V, of cylinder of radius r, height h. V = πr2h

Volume, V, of cone of radius r, height h. V = 1 3

πr2h

Volume, V, of sphere of radius r. V = 4 3

πr3

3

Shade 3 2

of this shape.

[1]

2

Draw a sector inside this circle. Draw a chord inside this circle. [2] 3 Write down all the factors of 21. [2]

4

[1] 5 Complete the mapping diagram.

16

11

9

5

2

19

15

7

1

[1]

6 Jenny shares $40 between her two sons in the ratio 3:1. Work out how much each son receives.

$ and $ [2]

© UCLES 2016 0607/11/M/J/16 [Turn over

7 Tick the shapes that have both line symmetry and rotational symmetry.

Rectangle Kite Parallelogram

Rhombus Isosceles Triangle

[2]

8 The diagram shows a child’s solid building block in the shape of a cuboid 2 cm by 5 cm by 10 cm.

5 cm

10 cm

2 cm

Find the total surface area of the cuboid. cm2 [3]

6

9 Write down the next two terms in the sequence.

18, 18, 16, 12, 6, …

, [2]

10 The Venn diagram shows two sets A and B. U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A

U

B

4

(i) A = { } [1]

(ii) B′ = { } [1]

(iii) A ∩ B = { } [1] (b) What is the mathematical name given to the numbers in set A? [1]

(c) Circle the statements which are correct for this Venn diagram.

A ∪ B = U 7 ∉ A n(B) = 4 A ∩ B′ = {4} [2]

7

11 110° NOT TO

Find the value of r. r = [3]

12 A car travels 100 metres in 8 seconds. Find its speed in kilometres per hour. km/h [2]

13 Describe the single transformation that maps y = f(x) onto y = f(x) + 3.

[2]

.

He takes 50 shots at the target. How many times does he expect to hit the target? [1]

15 Write down all the integers that satisfy the following inequality.

–3 x < 2 [2]

Questions 16 and 17 are printed on the next page.

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. 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. © UCLES 2016 0607/11/M/J/16

16 (a) Factorise. (i) 3x + 6 [1]

(ii) p2 + pq [1]

(b) Expand the brackets and simplify. x – 3(2x – 7) [2]

17 Solve the following simultaneous equations. 2x + y = 8 3x + 2y = 12

x =

y = [3]

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

DC (LK/AR) 115879/3 © UCLES 2016 [Turn over

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

* 9 9 8 9 7 3 9 1 8 6 *

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2016 45 minutes Candidates answer on the Question Paper.

Additional Materials: Geometrical Instruments

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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES.

Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40.

2

For the equation ax bx c 0 2 + + = x a

b b ac 2

= - -

Curved surface area, A, of cylinder of radius r, height h. rA rh2=

Curved surface area, A, of cone of radius r, sloping edge l. rA rl=

Curved surface area, A, of sphere of radius r. rA r4 2=

Volume, V, of pyramid, base area A, height h. V Ah 3

1 =

Volume, V, of cylinder of radius r, height h. rV r h2=

Volume, V, of cone of radius r, height h. rV r h 3

1 2=

Volume, V, of sphere of radius r. rV r 3

4 3=

sinbc A 2

Answer all the questions.

4

4

1 -

[2]

2 (a) Shade two more squares so that this shape has exactly one line of symmetry.

[1]

(b) Shade two more triangles so that this shape has rotational symmetry of order 3.

[1]

4

0607/21/M/J/16© UCLES 2016

. .

.

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

4 a 2 3 7 5 2 3 # #= b 2 3 5

3 4 # #=

Leaving your answer as the product of prime factors, find

(a) b2,

(b) the highest common factor (HCF) ofa and b, .

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

(c) the lowest common multiple (LCM) of aand b.

[2]

5

0607/21/M/J/16© UCLES 2016 [Turn over

5 Luis has a large jar containing red, yellow, green and blue beads. He takes a bead at random from the jar, notes its colour and replaces it. He repeats this 200 times.

The table shows his results.

Colour Red Yellow Green Blue

Number of beads 26 72 64 38

Relative frequency

(a) Complete the table to show the relative frequencies. [2]

(b) (i) There are 5000 beads in the jar altogether.

Estimate the number of green beads in the jar.

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

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

0607/21/M/J/16© UCLES 2016

7 U = {Integers from 1 to 18} F = {Factors of 12} M = {Multiples of 3} E = {Even numbers}

(a) Complete the Venn diagram by putting the numbers 2, 3, 4, 8, 12, 15 and 18 in the correct subsets.

F 1

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

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

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

7

9

C

D

A

B

A, B, C and D are points on the circle centre O. Angle BOD = 130°.

(a) Find angle DCB.

[2]

12

q

r

b

a

p

Write the vectors p, q and r in terms of a and b .

p =

q = ................................................

13

30 60–30–60 90 120 150 180 210 240 270 300 330

2

–2

y

x° 0

The graph of y=asin (x + b)° is shown in the diagram. Find the value of a and the value of b.

a = ................................................

NOT TO SCALE

The diagram shows a sketch of the graph of y=ax2+bx O is the point (0, 0), Pis the point (4, 0) andQ is the point (8, 96).

Find the value of a and the value of b.

a = ................................................

0607/21/M/J/16© UCLES 2016

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.

bLank page

* 0 0 1 1 9 8 9 2 0 8 *

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31

1 hour 45 minutes

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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES.

Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For r, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 96.

2

Formula List

Area, A, of triangle, base b, height h. A = bh 2

1

Area, A, of circle, radius r. A = rr2

Circumference, C, of circle, radius r. C = 2rr

Curved surface area, A, of cylinder of radius r, height h. A = 2rrh

Curved surface area, A, of cone of radius r, sloping edge l. A = rrl

Curved surface area, A, of sphere of radius r. A = 4rr2

Volume, V, of prism, cross-sectional area A, length l. V = Al

Volume, V, of pyramid, base area A, height h. V= Ah 3

1

Volume, V, of cylinder of radius r, height h. V = rr2h

Volume, V, of cone of radius r, height h. V = r h 3

1 2r

Volume, V, of sphere of radius r. V = r 3

4 3r

Answer all the questions.

1 (a) Write 356.31

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

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

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

(b) (i) Calculate . .16 8 9 61 2 - .

Write down all the figures shown on your calculator, giving your answer as a decimal.

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

(ii) Myrto estimates that the answer to part (b)(i) is 300.

(a) Find the difference between Myrto’s estimate and your answer to part (b)(i).

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

(b) Write this difference as a percentage of your answer to part (b)(i).

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

4

(i) as a power of 4,

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

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

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

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

5

0607/31/M/J/16© UCLES 2016 [Turn over

3 Tingwei buys 2 kg of cheese. The cheese costs $13.50 for one kilogram.

(a) Work out how much Tingwei pays for the 2 kg of cheese.

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

(b) He uses all the cheese to make 200 cheese balls.

Find the mass, in grams, of one cheese ball.

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

(c) (i) He sells all these cheese balls at a school fair for $0.25 each.

Work out how much money he received.

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

Work out how much money goes to the school charity.

$ ................................................................. [1] (d) The school fair makes a total profit of $460.

Write the profit that Tingwei made as a fraction of $460. Give your answer in its simplest form.

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

6

0607/31/M/J/16© UCLES 2016

4 The number of strawberries in each of 20 boxes is listed below.

32 28 27 32 33 28 34 28 29 29

28 28 33 31 33 33 30 29 29 26

(a) Complete the frequency table.

Number of strawberries 26 27 28 29 30 31 32 33 34

Frequency 1 1 1

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

(c) One of these boxes of strawberries is chosen at random.

Find the probability that it contains

(i) exactly 33 strawberries,

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

7

5 (a) A B C D5 2 2

1= - -

(i) Find the value of A when B = 2, C = 3 and D = 6.

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

(ii) Find the value of B when A = 12, C = 1 and D = 4.

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

(b) Find the value of 7p − 4q when p = −3 and q = –2.

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

(c) Rearrange 2y = 3x − 9 to make x the subject.

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

(d) The mass of 1 pomegranate and 2 kiwi fruit is 480 g. The mass of 1 pomegranate and 6 kiwi fruit is 840 g.

Find the mass of 1 pomegranate and the mass of 1 kiwi fruit. Show all your working.

1 pomegranate = ............................. g

8

0607/31/M/J/16© UCLES 2016

6 30 people were asked where they were going on holiday. The results are to be shown in a pie chart.

Country India Spain South Africa United States Australia

Number of people 5 12 3 6 4

Sector angle 60° 48°

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

Australia India

7 (a)

SCALE

DG

H

AFB and CGD are parallel lines. EFGH is a straight line and angle AFE = 105°.

Find

r°

s°

p°

70°

q°

AOB and COD are diameters of a circle, centre O. The lines AD and CB are parallel and angle CAB = 70°.

Find the values of p, q, r and s.

p = ................................

q = ................................

r = ................................

C SB

The diagram shows four straight cycle tracks HB, HC, BC and CS. BC = CS and HC = 2.5 km. Angle HBC = 90° and angle BHC = 40°.

(a) Abimela cycles from home, H, to school, S, each day along cycle track HC and CS.

(i) Use trigonometry to find the distance BC.

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

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

(b) One day track HC is blocked and she has to cycle along tracks HB, BC and CS.

Find the distance HB.

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

(c) Find the extra distance that Abimela now has to cycle to school.

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

9

1

0

2

3

4

5

6

7

8

9

y

x

(a) On the grid, plot the points A(2, 3) and B(5, 7). Draw the line AB. [2]

(b) Write down the co-ordinates of the midpoint of AB.

( .................... , .................... ) [1]

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

(d) Find the equation of the line parallel to AB that passes through the point (0, 4).

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

12

NOT TO SCALE

The diagram shows 12 solid cylinders packed into a box. Each cylinder has radius 1 cm and length 15 cm.

(a) (i) Find the volume of one cylinder.

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

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

(b) The box measures 15 cm by 12 cm by 4 cm.

Find the volume of the box.

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

(c) Find the volume of the box not taken up by the cylinders.

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

(d) Write your answer to part (c) as a percentage of the total volume of the box.

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

13

11

2

2

−2

−4

−6

4

6

8

10

y

P

The diagram shows a pentagon, P.

(a) Draw the image of P after a reflection in the y-axis. Label this image Q. [1]

(b) Draw the image of P after a translation by the vector 2

6-

J

Label this image R. [2]

(c) Draw the image of P after an enlargement, scale factor 3, centre (0, 0). Label this image S. [2]

(d) Find the ratio

length of horizontal side of S : length of horizontal side of P.

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

Choose a word from the list to complete the statement.

P and S are ……………..……… shapes. [1]

14

0607/31/M/J/16© UCLES 2016

12 The masses of 200 meerkats are recorded in the frequency table.

Mass (x grams) Frequency

x200 3001 G 5

Total 200

.................... x1 G .................... [1]

(b) (i) Show that the midpoint of the first group is 250.

[1]

(ii) Find an estimate of the mean mass of these 200 meerkats.

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

Mass (x grams) Cumulative frequency

x 300G 5

(d) Complete the cumulative frequency curve.

20

600 700 800 900 1000

40

60

80

0

100

120

(i) the median,

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

(iii) the number of meerkats with a mass of more than 850 g.

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

16

0607/31/M/J/16© UCLES 2016

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.

13

( )f x x x 22= +

(a) On the diagram, sketch the graph of y = f(x) from x = −3 to x = 3. [4]

(b) Write down the equation of the vertical asymptote for this graph.

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

( .................... , .................... ) [1]

(d) Write down the number of solutions of y = f(x) when y = 6.

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

* 8 3 9 8 4 2 2 7 1 6 *

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/41

2 hours 15 minutes

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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES.

Answer all the questions. Unless instructed otherwise, give your answers exactly…