Notesale: Turn your study into money

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education

*6816953946*

0607/04

CAMBRIDGE INTERNATIONAL MATHEMATICS

May/June 2009

Paper 4 (Extended)

2 hours 15 minutes
Candidates answer on the Question Paper
Additional Materials:

Geometrical Instruments
Graphics Calculator

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

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

DO NOT WRITE IN ANY BARCODES
...

Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate
...

For π, use your calculator value
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The number of marks is given in brackets [ ] at the end of each question or part question
...

For Examiner's Use

This document consists of 23 printed pages and 1 blank page
...


A = 2πrh

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


A = 4πr2

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


V = πr2h

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


V=

A

1
3

Ah

1
3
4
3

πr2h

πr3

a
b
c
=
=
sin A sin B sin C

b

c

a2 = b2 + c2 – 2bc cos A

B

© UCLES 2009

a

C

Area =

0607/04/M/J/09

1
2

bc sin A

3
Answer all the questions
...


[2]
(b) Katharine spends $60
...

Find the amount Katharine has after 3 years
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He invests the remaining $60 for 3 years at 4% compound interest per year
...

Give your answer correct to 2 decimal places
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For
Examiner's
Use

Shoe size

35

36

37

38

39

40

Frequency

2

7

6

4

3

2

Find
(a) the mean,
Answer (a)

[1]

Answer (b)

[1]

Answer (c)

[1]

Answer (d)

[1]

Answer (e)

[1]

(b) the median,

(c) the mode,

(d) the lower quartile,

(e) the inter-quartile range
...


Answer (a)

[2]

(b) Solve the equation
2x2 + 2x − 5 = 0
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Answer (b) x =

© UCLES 2009

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or

[4]

5
(c) y varies as the square root of w
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Find the value of y when w = 36
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[1]

(b)

A

B

C
Shade (A ∩ B) ∪ C on the diagram
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6 students have fair hair
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8 students do not have fair hair and do not have long hair
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(i) y = x4 O 4x3

[2]

(ii) y = 40 O 17x

[2]

(b) Solve the equation x4 O 4x3 = 0
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,

) [2]

or

[2]

(d) Solve the equation x4 − 4x3 = 40 O 17x
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hours at 4 km/h
...


Answer (a)

km/h [3]

(b) Basil runs 10 kilometres at an average speed of 12
...

(i) Find the time, in minutes, Basil takes
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6 km/h is 5% faster than his speed in a previous run
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Answer (b)(ii)

© UCLES 2009

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km/h [2]

[Turn over

8
7

(a)

For
Examiner's
Use

y
2
1
...
5

–2

–1
...
5 0

x
0
...
5

2

–0
...
5
–2

The graph shows

y = f(x), where f(x) = 2x O 1
...


Answer (a)(i) f −1(x) =
(ii) Sketch the graph of y = f −1(x) on the diagram above
...
5
1
0
...
5

–1

–0
...
5

1

1
...
5
–1
–1
...

(i) Find the inverse function, g−1(x)
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[1]
[2]

(iii) Describe fully the single transformation which maps the graph of y = g(x) onto the graph of
y = g−1 (x)
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PA = 3 km, AB = 7 km and BP = 5 km
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11
(b) The bearing of A from P is 220°
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9

y

–2

0

3

x

f(x) = x3 − x2 − 7x − 1
For the domain −2 Y x Y 3
(a) sketch the graph of y = f(x),

[2]

(b) find the range of the function f(x)
...

The table shows the results
...

What is the probability that the team
(i) wins,

Answer (a)(i)

[1]

Answer (a)(ii)

[1]

Answer (a)(iii)

[1]

(ii) draws,

(iii) loses?

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13
(b) The football team plays two more games
...

First game

Second game
W
D

W

L
W
D

D

L
W
D

L

L

Using the probabilities you have worked out in part (a) for both of these games,
find the probability that the team
(i) wins both games,

Answer (b)(i)

[2]

Answer (b)(ii)

[2]

Answer (b)(iii)

[2]

(ii) wins one game and draws the other,

(iii) does not lose both games
...
5 cm

6 cm

Q

3 cm
X

T

In the diagram, XY and TU are parallel
...

(a) Complete the statement
...
”

“Triangle XQY is

[1]

(b) YQ = 2
...

(i) Calculate the length of QT
...
8 cm2
...


Answer (b)(ii)

cm2 [2]

Answer (b)(iii)

[3]

(iii) Angle XYQ = 26
...

Use the sine rule to calculate angle QXY
...

OKL and CPQ are identical sectors of radius 12 cm and angle 30°
...

Calculate

(a) the length of the arc KL,

Answer (a)

cm [2]

Answer (b)

cm2 [2]

(b) the area of the sector OKL,

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17
(c) the volume of the slice of cake,

For
Examiner's
Use

Answer (c)

cm3 [2]

Answer (d)

cm2 [4]

(d) the total surface area of the slice of cake
...

Player

Fred

Greg

Andy

Bill

Chris

Dave

Ed

Hans

Ian

Jim

Height (h)

185

190

183

186

165

185

175

170

190

170

Points (p)

50

59

52

53

47

55

50

51

63

52

(a) On the grid below, draw a scatter diagram to show the information in the table
...


Answer (b)

© UCLES 2009

[1]

0607/04/M/J/09

For
Examiner's
Use

19
(c) Find

For
Examiner's
Use

(i) the mean height,

Answer (c)(i)

cm [1]

(ii) the mean number of points scored
...


Answer (d)(i) p =
(ii) Draw the line of regression accurately on the grid
...


Answer (d)(iii)

© UCLES 2009

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[1]

[Turn over

20
14

For
Examiner's
Use

y
10
9
8
7
6
5
4
3
2
1
0

x
1

2

3

4

5

6

7

8

9

10

(a) On the grid above draw the following lines
...


(d) (x, y) lies in the region T
...

What is the greatest number of red pencils you can buy for 360 cents?

Answer (a)(i)

For
Examiner's
Use

[1]

(ii) Blue pencils cost x cents each
...


Answer (a)(ii)

[1]

(iii) Yellow pencils cost (x + 8) cents each
...


Answer (a)(iii)

[1]

(b) The number of blue pencils in part (a)(ii) is 16 more than the number of yellow pencils in part
(a)(iii)
...


[4]

© UCLES 2009

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23
(ii) Factorise
...


[2]

x2 + 8x − 180 = 0

Answer (b)(iii) x=

or

[1]

(iv) Write down the cost of a blue pencil
...
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 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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