Cambridge International Examinations

Cambridge International General Certificate of Secondary Education

* 4 2 1 2 2 9 3 3 0 7 *

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23

Paper 2 (Extended) May/June 2015
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.

This document consists of 12 printed pages.

DC (RW/SW) 99290/3
© UCLES 2015 [Turn over
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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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 3

Answer all the questions.

1 Round these numbers to 3 significant figures.

(a) 0.000 604 83

Answer(a) .................................................................. [1]

(b) 6 998 800

Answer(b) .................................................................. [1]

2 By rounding each number to 1 significant figure, estimate the value of

0.583 # 311.6 .
1.82 + 10.43
Show your working.

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

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3 a = 23 # 3 # 52 b = 22 # 32 # 76

(a) Find, giving each answer as the product of prime factors,

(i) the highest common factor (HCF) of a and b,

Answer(a)(i) .................................................................. [1]

(ii) b.

Answer(a)(ii) .................................................................. [1]

(b) ap is a cube number.

Find the smallest integer value of p.

Answer(b) .................................................................. [1]

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 5

3 cm
NOT TO
8 cm SCALE

5 cm

3 cm

The diagram shows a rectangle, two semicircles and two right-angled triangles.

(a) Find the total area of the shape.

Give your answer in the form a + br .

Answer(a) ...........................................................cm2 [3]

(b) Describe fully the symmetry of the shape.

Answer(b) .................................................................................................................................................

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

5 Solve.
5 ^x + 2h 1 2 ^4x - 7h

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

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6 François and George each ask a sample of students at their college how they travel to college.

These are their results.

Total number
Walk Cycle Bus Train Car
of students
François 7 3 4 1 5 20
George 46 24 44 11 25 150

(a) Explain why George’s results will give the better estimates of the probabilities of the different types of
travel.

Answer(a) ............................................................................................................................................. [1]

(b) A student is selected at random.

(i) Use George’s results to estimate the probability that the student cycles to college.

Answer(b)(i) .................................................................. [1]

(ii) There are 3000 students at the college.

Use George’s results to estimate the number of students who cycle to college.

Answer(b)(ii) .................................................................. [1]

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7
y

NOT TO
SCALE

0 x

The diagram shows the lines x =- 2 , y = 12 x + 1 and 3x + 4y = 20 .

(a) Use simultaneous equations to find the co-ordinates of the point A.

Answer(a) ( .................. , .................. ) [3]

(b) (i) P is a point in the region such that

x 1- 2 , y 2 12 x + 1 and 3x + 4y 1 20 .

On the diagram, mark and label a possible position of P. [1]

(ii) Q is a point in the region such that

x 2- 2 , y = 12 x + 1 and 3x + 4y 1 20 .

On the diagram, mark and label a possible position of Q. [1]

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8
C

B
NOT TO
SCALE

35°
A D

In the diagram, A, B, C, D and E are points on the circle.

AD is a diameter and angle CAD = 35° .

Find

(a) angle ACD,

Answer(a) .................................................................. [1]

(b) angle CBD,

Answer(b) .................................................................. [1]

(c) angle AEC.

Answer(c) .................................................................. [2]

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9 The sets P, Q and R are subsets of the universal set U.

• PkR ! Q
• Q is a subset of R
• QkP = Q

Complete the Venn diagram to show the sets P, Q, and R.

[3]

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10 (a) Factorise x 2 - 3x - 10 .

Answer(a) .................................................................. [2]

3
x
(b) Make x the subject of y = .
a

Answer(b) x = ........................................................... [2]

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1
11 (a) Find log 5 .
25

Answer(a) .................................................................. [1]

(b) Find x when

(i) log x - log 2 = log 6 ,

Answer(b)(i) .................................................................. [1]

1
(ii) log x 4 = .
2

Answer(b)(ii) .................................................................. [1]

Question 12 is printed on the next page.

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 12

12
y

NOT TO
SCALE

–3 0 2 x

(0, –12)

The diagram shows a sketch of the graph of y = ax 2 + bx + c .

The graph goes through the points ^- 3, 0h , ^0, -12h and ^2, 0h .

Find the values a, b and c.

Answer a = .....................................

b = .....................................

c = ...................................... [3]

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© UCLES 2015 0607/23/M/J/15