Cambridge IGCSE Mathematics - International 0607 — 2021 May/June Paper 2 · Variant 3
0607/23/M/J/21 · 20 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 · Write 84% as a fraction in its lowest terms
1 Write 84% as a fraction in its lowest terms. .................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 21 1 cao 25
Q2 · Work out ( 1 - 0.8) 2
2 Work out ( 1 - 0.8) 2 . .................................................. [1]
Mark scheme: 2 0.04 1
Q3 · Find the value of x 2 - x when x = -3
3 Find the value of x 2 - x when x = -3. .................................................. [1]
Mark scheme: 3 12 1
Q4 · A quadrilateral has all sides equal and exactly two lines of symmetry
4 A quadrilateral has all sides equal and exactly two lines of symmetry. Write down the mathematical name of this quadrilateral. .................................................. [1]
Mark scheme: 4 Rhombus 1
Q5 · NOT TO SCALE x° 50° 60° Find the value of x
5 NOT TO SCALE x° 50° 60° Find the value of x. x = ................................................. [1]
Mark scheme: 5 160 1
Q6 · On the Venn diagram, shade A , B
6 On the Venn diagram, shade A , B . U A B [1]
Mark scheme: 6 1
Q7 · Find the size of one interior angle of a regular polygon with 20 sides
7 Find the size of one interior angle of a regular polygon with 20 sides. .................................................. [3]
Mark scheme: 7 162 3 360 180(20 − 2) M2 for 180 − or 20 20 360 or M1 for or 180(20 – 2) oe 20
Q8 · Find the value of - 4 + 4
8 Find the value of - 4 + 4 . .................................................. [1]
Mark scheme: 8 8 1
Q9 · A van has length 9 m
9 A van has length 9 m. It takes 1 second for the van to completely pass a gate of length 1 m. Find the speed of the van. Give your answer in km/h. ........................................ km/h [2]
Mark scheme: 9 36 2 M1 for (9 + 1) × 60 × 60 ÷ 1000 oe If 0 scored, SC1 for answer 32.4
Q10 · The faces of a die are numbered 1, 1, 2, 3, 3 and 4
10 The faces of a die are numbered 1, 1, 2, 3, 3 and 4. When it is rolled it is equally likely to show any face. The die is rolled twice. Find the probability that it shows an odd number both times. .................................................. [2]
Mark scheme: 10 4 16 2 4 4 or oe M1 for × oe 9 36 6 6
Q11 · Here are the first five terms of a sequence
11 Here are the first five terms of a sequence. 1 1 4 16 64 4 (a) Find the next term. .................................................. [1] (b) Find the nth term. .................................................. [2]
Mark scheme: 11(a) 256 1 11(b) 4 n − 2 oe 2 M1 for 4 n + k , k ≠0 or 2 2 n + k , k ≠0
Question 12
12 Factorise. 1+ a - c - ac .................................................. [2]
Mark scheme: 12 (1 + a )(1 − c ) 2 M1 for 1 + a − c (1 + a ) or 1 − c + a (1 − c )
Q13 · A P NOT TO SCALE 9 cm 8 cm B C Q R 10 cm 6 cm The diagram shows two similar triangles…
13 A P NOT TO SCALE 9 cm 8 cm B C Q R 10 cm 6 cm The diagram shows two similar triangles, ABC and PQR. (a) Find the length of PR. PR = ............................................ cm [2] (b) The triangles are the cross-sections of mathematically similar prisms. The volume of the larger prism is 500 cm3. Find the volume of the smaller prism. ........................................... cm3 [2]
Mark scheme: 13(a) 4.8 2 10 8 M1 for = oe 6 PR 13(b) 108 2 3 3 6 10 M1 for or oe seen 10 6
Q14 · A = P ( 1 + x) 3 Rearrange the formula to write x in terms of A and P
14 A = P ( 1 + x) 3 Rearrange the formula to write x in terms of A and P. x = ................................................. [3]
Mark scheme: 14 A 3 M1 for correct division by P 3 − 1 final answer M1 for correct cube root P M1 for correct subtraction of 1 Maximum mark of M2 if answer incorrect
Q15 · NOT TO S R SCALE Q A 70°70° B T Points Q, R, S and T lie on the circle
15 NOT TO S R SCALE Q A 70°70° B T Points Q, R, S and T lie on the circle. AB is a tangent to the circle at T. Angle RTB = 70˚. Find angle RQT. Angle RQT = ................................................. [2]
Mark scheme: 15 110 2 B1 for angle RST = 70 or angle RTA = 110
Q16 · P varies inversely as the square root of q
16 p varies inversely as the square root of q. When q = 9, p = 12. Find p when q = 16. p = ................................................. [3]
Mark scheme: 16 9 3 36 B2 for p = oe q 12 × 9 or = p or better 16 k or M1 for p = oe q or 12 × 9 = p × 16
Q17 · Simplify by rationalising the denominator
17 Simplify by rationalising the denominator. 3 2 2 - 1 .................................................. [2] Questions 18, 19 and 20 are printed on the next page.
Mark scheme: 17 3(2 2 + 1) 6 2 + 3 2 2 2 + 1 or M1 for × 7 7 2 2 + 1
Q18 · Y NOT TO 4 SCALE 0 2 x The diagram shows the graph of y = ax + b , where a 2 0
18 y NOT TO 4 SCALE 0 2 x The diagram shows the graph of y = ax + b , where a 2 0 . Find the value of a and the value of b. a = ................................................. b = ................................................. [2]
Mark scheme: 18 [a =] 2 2 B1 for each [b =] –4
Q19 · Write as a single fraction in its simplest form
19 Write as a single fraction in its simplest form. 3 - 2 x - 2 .................................................. [2]
Mark scheme: 19 7 − 2 x 2 B1 for 3 – 2( x − 2) final answer x − 2
Q20 · 2 log p = 3 log x - log y Find p in terms of x and y
20 2 log p = 3 log x - log y Find p in terms of x and y. p = ................................................. [3]
Mark scheme: 20 3 M1 for log p 2 or log x 3 3x oe final answer y M1 for correct use of u log u − log v = log v
What was in this paper
The subtopics covered by these 20 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Angles2Algebraic fractions1Circle theorems I1Fractions, decimals and percentages1Geometrical terms1Graphs of functions1Introduction to algebra1Probability of combined events1Proportion1Rates1Sequences1Sets1Similarity1Surds1The four operations1The logarithmic function1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2021 May/June, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.