Cambridge IGCSE Mathematics - International 0607 — 2025 May/June Paper 2 · Variant 3
0607/23/M/J/25 · 23 questions · 75 marks · ≈84 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper12 pages
Mark scheme9 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Question 1
1 Work out. 2 - 5 # 3 + 7 ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 –6 1
Q2 · This is a list of numbers
2 This is a list of numbers. 20 21 22 23 24 25 26 27 From the list write down (a) the square number ................................................. [1] (b) the prime number ................................................. [1] (c) the triangle number. ................................................. [1]
Mark scheme: 2(a) 25 1 2(b) 23 1 2(c) 21 1
Question 3
3 Simplify. 2x - 3y - x - 2y ................................................. [2]
Mark scheme: 3 x − 5 y 2 B1 for x + ky or kx − 5 y , k not zero
Q4 · A regular polygon has 20 sides
4 A regular polygon has 20 sides. Work out the size of one interior angle of the polygon. ................................................. [3]
Mark scheme: 4 162 3 360 180(20 − 2) M2 for 180 − or 20 20 360 or M1 for or 180 (20 – 2) 20
Q5 · Ganpreet and Rahul share $240 in the ratio 7 : 5
5 Ganpreet and Rahul share $240 in the ratio 7 : 5. (a) Show that the value of Rahul’s share is $100. [1] (b) Ganpreet spends $x of her share. Rahul spends $x of his share. The ratio of their remaining money is Ganpreet : Rahul = 2 : 1. Find the value of x. x = ................................................ [3]
Mark scheme: 5(a) 240 240 1 5 or 5 7 + 5 12 5(b) 60 3 M2 for 140 – x = 2(100 – x) oe or M1 for 140 – x or 100 – x
Q6 · The cost of a bar of chocolate is $c
6 The cost of a bar of chocolate is $c. The cost of a packet of sweets is $p. The total cost of 5 bars of chocolate and 2 packets of sweets is $13. The total cost of 7 bars of chocolate and 4 packets of sweets is $20. By forming a pair of simultaneous equations, find the cost of one bar of chocolate and the cost of one packet of sweets. cost of one bar of chocolate = $ .................... cost of one packet of sweets = $ .................... [5]
Mark scheme: 6 5c + 2p = 13 2 B1 for each 7c + 4p = 20 [c = ] 2 3 M1 for correctly eliminating one variable [p = ] 1.5[0] A1 for 2 A1 for 1.5 If 0 scored, SC1 for answers that satisfy one of their equations
Q7 · Work out 5 ' 1
7 Work out 5 ' 1 . 3 5 Give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 7 1 3 16 5 80 24 3 cao M2 for or or better 3 3 8 15 15 16 8 5 or M1 for or or 3 5 8
Q8 · Y 6 5 4 3 2 T 1 P x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 1 (a) Translate…
8 y 6 5 4 3 2 T 1 P x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 1 (a) Translate triangle T by the vector e o. [2] - 4 (b) Describe fully the single transformation that maps triangle T onto triangle P. ..................................................................................................................................................... ..................................................................................................................................................... [3] 3
Mark scheme: 8(a) Image at (3, –3), (5, –3), (5, –2) 2 1 k B1 for translation or k −4 8(b) Enlargement 3 B1 for each [scale factor] –2 [centre] (1, 1)
Q9 · Find the value of 16 - 2
9 Find the value of 16 - 2 . ................................................. [2]
Mark scheme: 9 1 2 1 3 − 12 B1 for or 4 −or 4096 64 3 16 2
Q10 · D T NOT TO SCALE E x° C y° 105° z° U 70° B A A, B, C, D and E lie on the circle
10 D T NOT TO SCALE E x° C y° 105° z° U 70° B A A, B, C, D and E lie on the circle. TU is a tangent to the circle at C. Find the values of x, y and z. x = ................................................ y = ................................................ z = ................................................ [4]
Mark scheme: 10 [x = ] 70 4 B1 for x = 70 [y = ] 110 B1 for y = 110 [z = ] 35 B2 for z = 35 or M1 for angle CAB = 35 or angle CDB = 35
Question 11
11 (a) Simplify. 27 - 2 75 ................................................. [2] (b) Rationalise the denominator and simplify. 6 5 - 2 ................................................. [3]
Mark scheme: 11(a) − 7 3 2 M1 for 3 3 or 2 5 3 311(b) 2 5 + 2 2 or 2 5 + 2 6 5 + 2 ( ) ( ) M2 for 2 2 or better 5 − 2 ( ) ( ) 5 + 2 or M1 for × 5 + 2
Q12 · NOT TO SCALE 8 cm The diagram shows a sector of a circle with radius 8 cm
12 NOT TO SCALE 8 cm The diagram shows a sector of a circle with radius 8 cm. The area of the sector is 8r cm2. The perimeter of the sector is ( a + b r ) cm. Find the value of a and the value of b. a = ................................................ b = ................................................ [4]
Mark scheme: 12 [a = ] 16 1 [b = ] 2 nfww 3 [Angle of sector = x] 8π M2 for x = 360 or better π 8 2 x 2 or M1 for π 8 = 8π 360 their x M1 for 2 π 8 360 Max 2/3 if answer incorrect
Question 13
13 Work out. 4.9 # 10 199 + 4. 9 # 10 197 ................................................. [2]
Mark scheme: 13 4.949 × 10199 2 B1 for answer figs 4949 or for 0.049 × 10199 or 490 × 10197 seen
Q14 · F ( x) = cos x , 0° G x G 360° (a) Write down the exact value of (i) f ( 0 )…
14 f ( x) = cos x , 0° G x G 360° (a) Write down the exact value of (i) f ( 0 ) ................................................. [1] (ii) f ( 30 ) . ................................................. [1] (b) y 1 0 x 360° -1 On the diagram, sketch the graph of y = f ( x) for 0° G x G 360° . [2] (c) Write down the amplitude of f ( )x . ................................................. [1]
Mark scheme: 14(a)(i) 1 1 14(a)(ii) 3 1 2 14(b) Correct sketch 2 B1 for correct shape but wrong amplitude or period 14(c) 1 1
Q15 · Y 2 k # y 3 = y Find the value of k
15 y 2 k # y 3 = y Find the value of k. k = ................................................ [2]
Mark scheme: 15 –2 2 M1 for 2k + 3 = –1 oe or better
Q16 · Rearrange 4y - 3x = 1 - py to write y in terms of p and x
16 Rearrange 4y - 3x = 1 - py to write y in terms of p and x. y = ................................................ [2]
Mark scheme: 16 1 + 3 x 2 M1 for isolating terms in y oe final answer 4 + p M1 for factorising 2 terms in y and dividing to final answer Max M1 if answer incorrect
Q17 · Y NOT TO SCALE 0 x -1 (1, -2) The diagram shows a sketch of the graph of y = x 2 + ax + b
17 y NOT TO SCALE 0 x -1 (1, -2) The diagram shows a sketch of the graph of y = x 2 + ax + b . The point (1, –2) is a minimum. Find the value of a and the value of b. a = ................................................ b = ................................................ [3]
Mark scheme: 17 [a ] = –2 3 2 M2 for ( x − 1) − 2 [b ] = –1 or M1 for ( x − 1) 2 + k OR M2 for b = –1 and 1 + a + b = –2 or better or M1 for b = –1 or 1 + a + b = –2 or better
Question 18
18 Solve. 3 ( 2x + 1 ) 2 5 - 4 x ................................................. [3]
Mark scheme: 18 1 3 B1 for 6x + 3 x > oe final answer M1 for collecting terms 5 e.g. 6x + 4x > 5 – 3
Question 19
19 Solve. Give each answer as an exact value. (a) 2 x = 5 x = ................................................ [1] (b) 2 logy = 1 y = ................................................ [1]
Mark scheme: 19(a) log5 1 or log 2 5 log2 19(b) 1 1 10 or 10 2
Q20 · These are the first 5 terms of a sequence
20 These are the first 5 terms of a sequence. 3 6 12 24 48 (a) Find the next term of the sequence. ................................................. [1] (b) Find the nth term of the sequence. ................................................. [2]
Mark scheme: 20(a) 96 1 20(b) 3 2 n −1 oe final answer 2 B1 for 2k oe
Q21 · F NOT TO SCALE D C E 12 cm 3 cm A 4 cm B The diagram shows a triangular prism
21 F NOT TO SCALE D C E 12 cm 3 cm A 4 cm B The diagram shows a triangular prism. The cross-section is a right-angled triangle EAB. AE = 3 cm, AB = 4 cm and BC = 12 cm. (a) Work out the length of BF. BF = ........................................... cm [3] (b) Find the sine of the angle between BF and the base ABCD. ................................................. [1]
Mark scheme: 21(a) 13 3 M2 for 32 + 4 2 + 12 2 oe or M1 for 32 + 42 or 12 2 + 32 or 42 + 122 21(b) 3 1 13
Q22 · Write as a single fraction in its simplest form
22 Write as a single fraction in its simplest form. 3 2 - x - 2 ................................................. [2] Question 23 is printed on the next page.
Mark scheme: 22 2 x − 7 7 − 2 x 2 B1 for 2(x – 2) – 3 or better seen or final answer x − 2 2 − x
Q23 · Bag A Bag B Bag A contains 4 white balls and 3 black balls
23 Bag A Bag B Bag A contains 4 white balls and 3 black balls. Bag B contains 5 white balls and 4 black balls. (a) Ranjit picks a ball at random from Bag A and replaces it. Ranjit also picks a ball at random from Bag B and replaces it. Find the probability that the two balls are the same colour. ................................................. [3] (b) Leyla picks a ball at random from Bag A. She places it into Bag B. She then picks a ball at random from Bag B. Find the probability that the ball she picks from Bag B is black. ................................................. [3]
Mark scheme: 23(a) 32 3 3 4 4 5 M2 for + 63 7 9 7 9 3 4 4 5 or M1 for or 7 9 7 9 23(b) 31 3 3 5 4 4 M2 for + 70 7 10 7 10 3 5 4 4 or M1 for or 7 10 7 10
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2The four operations2Algebraic fractions1Algebraic manipulation1Algebraic manipulation1Angles1Circle theorems II1Circles, arcs and sectors1Finding a quadratic function using1Indices I1Indices II1Inequalities1Probability of combined events1Pythagoras’ theorem1Sequences1Standard form1Surds1The logarithmic function1Transformations1Trigonometric functions1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2025 May/June, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.