Cambridge IGCSE Mathematics - International 0607 — 2022 May/June Paper 2 · Variant 1
0607/21/M/J/22 · 15 questions · 40 marks · ≈45 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 paper8 pages
Mark scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · On the number line, show the inequality - 2 G x 1 3
1 On the number line, show the inequality - 2 G x 1 3 . x – 4 – 3 – 2 – 1 0 1 2 3 4 [2]
Mark scheme: Question Answer Marks Partial Marks 1 2 B1 for either correct line or correct ends –2 3 Two lines scores max of 1 mark
Q3 · 21 24 25 27 29 39 48 From the list of numbers, write down (a) the prime number…
3 21 24 25 27 29 39 48 From the list of numbers, write down (a) the prime number, ................................................. [1] (b) the cube number. ................................................. [1]
Mark scheme: 3(a) 29 only 1 3(b) 27 only 1
Q4 · Factorise x 3 - 2x
4 Factorise x 3 - 2x . ................................................. [1]
Mark scheme: 4 x ( x 2 2) final answer 1
Q5 · Write 7.297 84 correct to 3 significant figures
5 (a) Write 7.297 84 correct to 3 significant figures. ................................................. [1] (b) Write 0.000 003 06 in standard form. ................................................. [1]
Mark scheme: 5(a) 7.30 cao 1 5(b) 6 1 3.06× 10 final answer cao
Question 6
6 Solve. (a) 4x = 28 x = ................................................ [1] (b) 3 ( a - 6) = 24 a = ................................................ [2]
Mark scheme: 6(a) 7 1 6(b) 14 2 M1 for a 6 24 3 or 3a 18 24
Q7 · Karen has 3 blue hats, 5 red hats and 2 white hats
7 Karen has 3 blue hats, 5 red hats and 2 white hats. She also has 4 blue scarves, 3 red scarves and 1 white scarf. (a) Karen takes a hat at random and replaces it. Find the probability that it is white. ................................................. [1] (b) Karen takes a hat and a scarf at random. Find the probability that both the hat and the scarf are blue. ................................................. [2]
Mark scheme: 7(a) 2 1 oe 10 7(b) 12 2 3 4 oe M1 for only 80 10 8
Q8 · Find the value of 49 1
28 Find the value of 49 1. ................................................. [1]
Mark scheme: 8 7 1
Q9 · Write 90 as the product of its prime factors
9 Write 90 as the product of its prime factors. ................................................. [2]
Mark scheme: 9 2 × 3 × 3 × 5 or 2 × 32 × 5 final answer 2 M1 for 2, 3 and 5 seen as factors
Q10 · Find the magnitude of the vector
10 Find the magnitude of the vector . 6 Give your answer in simplest surd form. ................................................. [2]
Mark scheme: 10 2 10 2 M1 for 6 2 2 2 or 40
Q11 · Shade P , Q
11 (a) Shade P , Q . U P Q [1] (b) Describe the shaded area using set notation. U R S ................................................. [1] (c) The Venn diagram shows the number of elements in each subset. U A B 5 3 6 2 7 1 C 4 2 Find n (( B l + C) + A ) . ................................................. [1]
Mark scheme: 11(a) 1 P Q 11(b) R′ ∩ S oe 1 11(c) 7 only 1
Q12 · B A 32° NOT TO SCALE C D A, B, C, and D are points on a circle
12 (a) B A 32° NOT TO SCALE C D A, B, C, and D are points on a circle. Angle DAC = 32° . BC = DC. Find angle BCD. Angle BCD = ................................................ [2] (b) B D NOT TO O SCALE C 42° A E A, B and C are points on the circle centre O. ECD is a tangent to the circle at C. Angle ACE = 42° . Find angle AOC. Angle AOC = ................................................ [2]
Mark scheme: 12(a) 116 2 B1 for angle DBC = 32⁰ allow angle BDC = 32⁰ 12(b) 84 2 B1 for angle ABC = 42⁰ soi or for angle OCA = 48⁰ soi
Question 13
13 (a) Simplify fully. 75 - 48 + 12 ................................................. [2] (b) Rationalise the denominator, giving your answer in its simplest form. 1 3 + 5 ................................................. [2]
Mark scheme: 13(a) 3 3 final answer 2 M1 for either 5 3 or 2 3 13(b) 3 5 5 3 2 3 5 or oe final answer M1 for oe 22 22 3 5 Must be convinced that 3 5 and NOT 3 5
Q14 · X 2 - 14 x + c = ( x + d ) 2 Find the value of c and the value of d
14 x 2 - 14 x + c = ( x + d ) 2 Find the value of c and the value of d. c = ................................................ d = ................................................ [3] Questions 15 and 16 are printed on the next page.
Mark scheme: 14 [c =] 49 3 2 M1 for correct expansion of x d [d =]−7 M1 for equating their coefficients (dependent on a three term expression) OR B2 for d = −7 only or B1 for 2d = [±] 14 soi If 0 scored SC1 for c = (their d)2
Question 15
15 (a) Factorise fully. 6x 2 - 7x - 3 ................................................. [2] (b) Solve. 6x 2 - 7x - 3 1 0 ................................................. [3]
Mark scheme: 15(a) (2 x 3)(3 x 1) final answer 2 M1 for ( ax b )( cx d ) where ac= 6 AND bd = –3 or ad bc 7 or for 2 x (3 x 1) 3(3 x 1) or for 3 x (2 x 3) (2 x 3) 15(b) 1 3 3 FT their factors from (a) x final answer 3 2 or 1 3 ‘ x AND x ’ final answer 1 3 3 2 B2 for ‘ x [or] x ’ 3 2 (must include the word AND) 1 3 or B1 for x or B1 for x 3 2 1 or B1 for x AND x 3 soi 3 2
Question 16
16 Solve. 2 log 3 - log 2 = logp p = ................................................. [2]
Mark scheme: 16 9 2 M1 for correct use of one rule of logs 4.5 or oe 2 9 2 E.g. log log4.5 , or 2log3 log3 2
What was in this paper
The subtopics covered by these 15 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
What you needed in this session
Cambridge’s own grade thresholds for 2022 May/June, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.