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Title: International Mathematics 2009 past paper
Description: International Mathematics s09 qp 4
Description: International Mathematics s09 qp 4
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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
...
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
...
He invests the remaining $60 for 3 years at 4% compound interest per year
...
Give your answer correct to 2 decimal places
...
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
...
Answer (b) x =
© UCLES 2009
0607/04/M/J/09
or
[4]
5
(c) y varies as the square root of w
...
Find the value of y when w = 36
...
[1]
(b)
A
B
C
Shade (A ∩ B) ∪ C on the diagram
...
6 students have fair hair
...
8 students do not have fair hair and do not have long hair
...
(i) y = x4 O 4x3
[2]
(ii) y = 40 O 17x
[2]
(b) Solve the equation x4 O 4x3 = 0
...
,
) [2]
or
[2]
(d) Solve the equation x4 − 4x3 = 40 O 17x
...
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
...
6 km/h is 5% faster than his speed in a previous run
...
Answer (b)(ii)
© UCLES 2009
0607/04/M/J/09
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)
...
[1]
[2]
(iii) Describe fully the single transformation which maps the graph of y = g(x) onto the graph of
y = g−1 (x)
...
PA = 3 km, AB = 7 km and BP = 5 km
...
© UCLES 2009
0607/04/M/J/09
11
(b) The bearing of A from P is 220°
...
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?
© UCLES 2009
0607/04/M/J/09
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,
© UCLES 2009
0607/04/M/J/09
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
0607/04/M/J/09
[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
0607/04/M/J/09
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
Title: International Mathematics 2009 past paper
Description: International Mathematics s09 qp 4
Description: International Mathematics s09 qp 4