Cambridge IGCSE™

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

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/43

Paper 4 (Extended) May/June 2020

2 hours 15 minutes

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a graphic display calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly and you will be given marks for correct methods, including
sketches, even if your answer is incorrect.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
● For r, use your calculator value.

INFORMATION
● The total mark for this paper is 120.
● The number of marks for each question or part question is shown in brackets [ ].

This document has 20 pages. Blank pages are indicated.

DC (ST/JG) 182698/2
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Formula List

- b ! b 2 - 4ac
For the equation ax 2 + bx + c = 0 x=
2a

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 = 4rr 2

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

Volume, V, of cylinder of radius r, height h. V = rr 2 h

1
Volume, V, of cone of radius r, height h. V = rr 2 h
3

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

A a b c
= =
sin A sin B sin C

b a 2 = b 2 + c 2 - 2bc cos A
c

1
Area = bc sin A
2

B a C

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Answer all the questions.

1 For each sequence, write down the next two terms and find an expression for the nth term.

(a) 15, 11, 7, 3, - 1, ...

Next two terms ....................... , .......................

nth term ................................................. [3]

(b) 1, 2, 4, 8, 16, ...

Next two terms ....................... , .......................

nth term ................................................. [3]

(c) 4, 10, 18, 28, 40, ...

Next two terms ....................... , .......................

nth term ................................................. [3]

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2 10 students take a language examination.

The examination consists of two parts, a speaking test and a writing test.
Both tests are marked out of 100.

The marks for the students in each of the tests is shown in the table.

Speaking mark (x) 86 62 53 34 76 95 30 70 88 72

Writing mark (y) 73 48 44 12 62 66 26 44 90 75

(a) Complete the scatter diagram to show these results.

The first five points have been plotted for you.

100

90

80

70

60
Writing
mark 50

40

30

20

10

0 x
0 10 20 30 40 50 60 70 80 90 100
Speaking mark
[2]

(b) What type of correlation is shown in your scatter diagram?

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

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(c) (i) Calculate the equation of the regression line in the form y = mx + c .

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

(ii) Use this equation to estimate a mark in the writing test for a student who scored 48 in the
speaking test.

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

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3 (a) Riaz invests $5000 at a rate of 2.5% per year simple interest.

(i) Calculate the value of the investment at the end of 4 years.

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

(ii) Calculate the number of complete years it will take for the value of the investment to be
$6500.

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

(b) Yasmin invests $5000 at a rate of 2% per year compound interest.

(i) Calculate the value of Yasmin’s investment at the end of 4 years.

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

(ii) Calculate the number of complete years it will take for the value of Yasmin’s investment to
first be worth more than $6500.

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

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4
y
30

0 x
–3 5

– 40

f (x) = x 3 - 4x 2 - 3x + 18

(a) On the diagram, sketch the graph of y = f (x) for - 3 G x G 5. [2]

(b) Solve the equation f (x) = 10 .

x = ..................... , or x = ..................... , or x = ..................... [3]

(c) Write down the coordinates of

(i) the local maximum,

(.................... , ....................) [2]

(ii) the local minimum.

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

(d) f (x) = k has only 1 solution.

Find the ranges of values of k .

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

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5 (a) (i) A reflection in the line y = 3 maps triangle A onto triangle B.

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

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

............................................................................................................................................. [1]
5
(ii) A translation using the vector e o maps triangle C onto triangle D.
-4
Describe fully the single transformation that maps triangle D onto triangle C.

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

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

(iii) An enlargement, centre (2, - 1) , scale factor 3, maps triangle G onto triangle H.

Describe fully the single transformation that maps triangle H onto triangle G.

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

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

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(b)
y
6

3
D A
2

– 11 – 10 – 9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 x
–1

–2

–3

–4

(i) Rotate triangle A through 90° anticlockwise, centre (-1, 0).

Label the image B. [2]
1
(ii) Enlarge triangle A with scale factor - , centre (1, 3).
2
Label the image C. [2]

(iii) Describe fully the single transformation that maps triangle A onto triangle D.

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

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

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6 The cumulative frequency graph shows the heights, in centimetres, of 120 plants in location A.

120

110

100

90

80

70
Cumulative
frequency 60

50

40

30

20

10

0
0 10 20 30 40 50 60 70 80 90 100
Height (cm)

(a) Use the graph to estimate

(i) the median,

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

(ii) the interquartile range,

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

(iii) the number of plants over 80 cm in height.

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

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(b) The table gives some information about 120 similar plants in location B.

Minimum height Lower quartile Median Interquartile range Range

(cm) (cm) (cm) (cm) (cm)
10 34 50 28 90

(i) On the grid opposite, draw the cumulative frequency curve for the heights of the plants in
location B. [3]

(ii) Use the curves to estimate how many more plants had heights of over 70 cm in location A
than in location B.

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

(iii) The heights of the plants in location A are more consistent than the heights of the plants in
location B.

By comparing the shapes of the curves, explain how you know this is true.

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

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

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7 The diagram shows a radio in the shape of a prism.

This diagram shows the base of the radio.

F E

D
G

B C

H I

ABC is an equilateral triangle.

The circles have their centres at A, B and C and each has a radius of 5 cm.
DE, FG and HI are tangents to the circles.

(a) Show that AB = 8.66 cm, correct to 3 significant figures.

[3]

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(b) Calculate the area of the base of the radio.

.......................................... cm 2 [4]

(c) The height of the radio is 12 cm.

Calculate the volume of the radio.

.......................................... cm 3 [1]

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8 The number of people living in each house in a street of 100 houses is recorded.
The results are shown in the table.

Number of people Frequency

1 5
2 16
3 28
4 32
5 17
6 2

(a) Find

(i) the range,

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

(ii) the median,

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

(iii) the mean.

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

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(b) Two of the houses are selected at random.

Find the probability that

(i) both had exactly one person living in them,

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

(ii) one had exactly 2 people living in it and the other had exactly 3 people living in it,

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

(iii) at least one house had fewer than 5 people living in it.

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

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9
y
A NOT TO
SCALE

O x

A is the point (-2, 6), B is the point (3, 2) and C is the point (3, -4).

(a) Write down the equation of BC.

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

(b) Find the coordinates of the point M, the mid-point of AC.

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

(c) The quadrilateral ABCD has rotational symmetry of order 2 about the point M.

Find the coordinates of the point D.

(.................... , ....................) [2]

(d) Find the equation of the perpendicular bisector of AC.

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

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10 In this question, all lengths are in centimetres.

NOT TO
SCALE

2x + 4 2x + 1

30°
4x 4x + 5

The areas of the two triangles are equal.

(a) Show that 8x 2 + 18x - 5 = 0 .

[5]

(b) Solve 8x 2 + 18x - 5 = 0 .

You must show all your working.

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

(c) Find the area of each of the triangles.

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

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11
North

A NOT TO
SCALE
110°
80 km
120 km

North
B

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

(a) Calculate BC.

BC = ........................................... km [3]

(b) Use the sine rule to calculate angle ABC.

Angle ABC = ................................................. [3]

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(c) The bearing of C from A is 130°.

Find the bearing of B from C.

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

(d) A ship leaves B at 13 50 and sails in a straight line towards C.

Its constant speed is 37 km/h.

Find the time when it is at its closest point to A.

Give your answer correct to the nearest minute.

.................................................. [5]

Question 12 is printed on the next page.

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12 f (x) = 2x + 3 g (x) = 5 - 3x

(a) Find f (4) .

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

(b) Solve f (x) - g (x) = 5.

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

(c) Find g -1 (x) .

g -1 (x) = ................................................. [2]

(d) Find and simplify f (g (x)) .

.................................................. [2]
2 3
(e) Simplify + .
f (x) g (x)

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

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
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

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

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