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CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22
Paper 2 Non-calculator (Extended) May/June 2025
1 hour 30 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.
● Calculators must not be used in this paper.
● You may use tracing paper.
● You must show all necessary working clearly. You will be given marks for correct methods even if your
answer is incorrect.
INFORMATION
● The total mark for this paper is 75.
● The number of marks for each question or part question is shown in brackets [ ].
This document has 12 pages.
DC (DE/CGW) 342615/3
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List of formulas
1
Area, A, of triangle, base b, height h. A = 2 bh
Area, A, of circle of radius r. A = rr 2
Circumference, C, of circle of radius r. C = 2rr
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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
Surface area, A, of sphere of radius r. A = 4r r 2
Volume, V, of prism, cross-sectional area A, length l. V = Al
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1
Volume, V, of pyramid, base area A, height h. V = 3 Ah
Volume, V, of cylinder of radius r, height h. V = rr 2 h
1
Volume, V, of cone of radius r, height h. V = 3 rr 2 h
4
Volume, V, of sphere of radius r. V = 3 rr 3
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-b ! b 2 - 4ac
For the equation ax 2 + bx + c = 0, where a ! 0, x= 2a
For the triangle shown,
a b c
= =
A sin A sin B sin C
a 2 = b 2 + c 2 - 2bc cos A
1
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c b Area = 2 ab sin C
B a C
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Calculators must not be used in this paper.
1 (a) Work out (0.02) 3 .
................................................. [1]
(b) Write your answer to part (a) in standard form.
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................................................. [1]
2 This is a list of numbers.
31 33 35 37 39 41
From this list, write down all the prime numbers.
................................................. [2]
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24
3 Write the fraction in its lowest terms.
64
................................................. [1]
4 Convert 250 cm 3 into m 3 .
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............................................ m 3 [1]
5 A quadrilateral has exactly one pair of parallel sides.
Write down the mathematical name of this quadrilateral.
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................................................. [1]
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6 (a) Share 120 in the ratio 2 : 3.
...................... , ...................... [2]
(b) Share Z in the ratio x : y.
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...................... , ...................... [2]
7 At a school, 50 students are asked their favourite car colour.
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The table shows the results.
Colour Red Blue White Silver Black
Frequency 7 x 15 16 x
(a) Find the value of x.
x = ................................................ [2]
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(b) Find the relative frequency of red.
................................................. [1]
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8 (a) Expand and simplify.
5 (2x - 1) - 3 (3 + 4x)
................................................. [2]
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(b) Factorise.
(i) 3y - y 2
................................................. [1]
(ii) 8ax - 3by + 2ay - 12bx
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................................................. [2]
(iii) 3x 2 + 5x - 12
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................................................. [2]
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9 The table shows the marks scored by each of 60 students in a science test.
Mark 0 1 2 3 4 5 6 7 8 9 10
Frequency 2 14 5 3 7 6 5 1 7 2 8
(a) Write down the mode.
................................................. [1]
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(b) Find the interquartile range.
................................................. [2]
10 Use set notation to describe each of the shaded regions.
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U U
A B P Q
.................................. .................................. [2]
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11 Simplify.
14
(5x) 3 ' b l
x
................................................. [2]
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12 In this question all lengths are in centimetres.
3x
NOT TO
SCALE
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3x
x
x
A solid is made by joining a cuboid to a pyramid.
The base of the cuboid is a square of side x.
The height of the cuboid is 3x.
The base of the pyramid is a square of side x.
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The height of the pyramid is 3x.
The total volume of the solid is 32 000 cm 3 .
Show that x = 20.
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[3]
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13
y cm
NOT TO
10 cm SCALE
x cm 13 cm
30°
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(a) Show that x = 5.
[2]
(b) Find the value of y.
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y = ................................................ [3]
14 Find the lowest common multiple (LCM) of these expressions.
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2x 3 y 4 3x 2 z 3 4y 2 z
................................................. [2]
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15 An unbiased die is numbered 2, 3, 4, 4, 5, 6.
Zaira rolls the die three times.
Find the probability that Zaira rolls an odd number two or more times.
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................................................. [4]
16 Find the next term and the nth term in each sequence.
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(a) 12, 14, 16, 18, 20, ....
next term = ................................................
nth term = ................................................ [3]
(b) 81, 27, 9, 3, 1, ....
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next term = ................................................
nth term = ................................................ [3]
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17
C
D
NOT TO
SCALE
A 116°
O P
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B
The diagram shows a circle, centre O.
AOBP is a straight line.
PC is a tangent to the circle.
Angle AOC = 116°.
Find
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(a) angle OAC
Angle OAC = ................................................ [1]
(b) angle ABC
Angle ABC = ................................................ [1]
(c) angle ADC
Angle ADC = ................................................ [1]
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(d) angle APC.
Angle APC = ................................................ [2]
18 Apples cost $2.50 per kilogram.
The total cost of x kg of apples and y kg of pears is $10 .
Find the cost of 1 kg of pears.
Give your answer in terms of x and y.
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$ ................................................. [3]
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1
19 f (x) = , x ! 0.8
5x - 4
(a) Find f (2) .
................................................. [1]
1
(b) Solve f (x) = .
11
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................................................. [2]
(c) Find f -1 (x) .
f -1 (x) = ................................................ [3]
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20 (a) Rationalise the denominator.
3- 2
3+ 2
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................................................. [3]
(b) Expand and simplify.
` x + 1 - xj` x + 1 + xj
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................................................. [2]
Question 21 is printed on the next page.
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21 Line L is perpendicular to the line with equation y = 2x + 1.
Line L passes through the point (3, 12).
(a) Find the equation of the line L.
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[3]
(b) The shortest distance from the point (3, 12) to the line y = 2x + 1 is k .
Find the value of k.
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k = ................................................ [5]
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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 Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
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