Cambridge IGCSE Mathematics - International 0607 — 2018 May/June Paper 2 · Variant 2
0607/22/M/J/18 · 18 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 · A quadrilateral has exactly one pair of parallel sides
1 A quadrilateral has exactly one pair of parallel sides. Write down the mathematical name for this quadrilateral. .................................................... [1]
Mark scheme: Question Answer Marks Partial Marks 1 trapezium 1
Q2 · NOT TO SCALE x° 41° 76° A B AB is a straight line
2 NOT TO SCALE x° 41° 76° A B AB is a straight line. Find the value of x. x = .................................................... [1]
Mark scheme: 2 63 1
Q3 · A bag contains 2 blue balls, 3 red balls and 5 green balls only
3 A bag contains 2 blue balls, 3 red balls and 5 green balls only. One ball is chosen at random. Find the probability that this ball is red. .................................................... [1]
Mark scheme: 3 0.3 oe 1
Q4 · Write down a prime number between 60 and 70
4 Write down a prime number between 60 and 70. .................................................... [1]
Mark scheme: 4 61 or 67 1
Question 5
5 Solve. 7x + 9 = 5x + 17 x = .................................................... [2]
Mark scheme: 5 4 2 M1 for correctly moving at least one term
Q6 · Write 36 as a product of prime factors
6 Write 36 as a product of prime factors. .................................................... [2]
Mark scheme: 6 2 × 2 × 3 × 3 or 2 2 × 32 2 M1 for 2 and 3 as factors
Question 7
7 Solve. 3x + 7 1 1 .................................................... [2]
Mark scheme: 7 x < − 2 2 M1 for 3 x < 1 − 7
Q8 · Point A has co-ordinates (2, 12)
8 Point A has co-ordinates (2, 12). Point B has co-ordinates (4, 2). Find the co-ordinates of the midpoint of AB. ( ....................... , .......................) [2]
Mark scheme: 8 (3, 7) 2 B1 for each 9 41 11 66 25 6 − 10 or M2 for − or 3 oe 3 15 215 15 15 15 or M1 for denominator of 15k
Question 9
9 Work out. 2 2 4 - 1 5 3 .................................................... [3]
Mark scheme: Question Answer Marks Partial Marks 1 trapezium 1 2 63 1 3 0.3 oe 1 4 61 or 67 1 5 4 2 M1 for correctly moving at least one term 6 2 × 2 × 3 × 3 or 2 2 × 32 2 M1 for 2 and 3 as factors 7 x < − 2 2 M1 for 3 x < 1 − 7 8 (3, 7) 2 B1 for each 9 41 11 66 25 6 − 10 or M2 for − or 3 oe 3 15 215 15 15 15 or M1 for denominator of 15k
Q10 · 100 80 60 Cumulative frequency 40 20 0 x 0 10 20 30 40 50 Use the cumulative frequency…
10 100 80 60 Cumulative frequency 40 20 0 x 0 10 20 30 40 50 Use the cumulative frequency curve to estimate the inter-quartile range. .................................................... [2]
Mark scheme: 10 19 2 B1 for 15 or 34
Q11 · Here are the first four terms of a sequence
11 Here are the first four terms of a sequence. 13 9 5 1 (a) Write down the next term. .................................................... [1] (b) Find an expression, in terms of n, for the nth term. .................................................... [2]
Mark scheme: 11(a) –3 1 11(b) 17 – 4n oe 2 B1 for 17 – kn, k ≠ 0 or k – 4n
Question 12
12 Simplify. 75 - 12 + 27 .................................................... [2]
Mark scheme: 12 6 3 2 M1 for 5 3 or 2 3 or 3 3
Q13 · Shade the given sets in each of these diagrams
13 Shade the given sets in each of these diagrams. U U A B A B A' B (A' B')' [2]
Mark scheme: 13 2 B1 for each
Q14 · Point A has co-ordinates (2, 3)
14 Point A has co-ordinates (2, 3). Point B has co-ordinates (4, 11). Find the equation of the line AB. Give your answer in the form y = mx + c . y = .................................................... [3]
Mark scheme: 14 4x – 5 3 11 − 3 M1 for oe 4 − 2 M1 for correct substitution of their ‘m’ and a point
Q15 · Expand the brackets and simplify
15 Expand the brackets and simplify. 3x - 5y 5x - 3y ` `j j .................................................... [3]
Mark scheme: 15 15 x 2 − 34 xy + 15 y 2 final answer 3 M2 for 15 x 2 − 9 xy − 25 xy + 15 y 2 or M1 for 3 correct terms
Q16 · A factory makes soft centre chocolates and hard centre chocolates only
16 A factory makes soft centre chocolates and hard centre chocolates only. The probability that a chocolate chosen at random has a hard centre is 0.6 . Three chocolates are chosen at random. Find the probability they are all soft centre chocolates. .................................................... [3] Questions 17 and 18 are printed on the next page.
Mark scheme: 16 [0].064 3 M2 for 0.4 3 or M1 for 0.4 soi If 0 scored SC1 for answer 0.216
Question 17
17 Factorise. 4x 2 - 4xy - 3y 2 .................................................... [3]
Mark scheme: 17 (2 x − 3 y )(2 x + y ) final answer 3 M2 for (ax + by)(cx + dy) where ac = 4 and bd = –3 or M1 for ac = 4 or bd = –3 OR M2 for 2 x (2 x − 3 y ) + y (2 x − 3 y ) or 2 x (2 x + y ) − 3 y (2 x + y ) or M1 for 4 x 2 − 6 xy + 2 xy − 3 y 2 oe
Q18 · Write as a single fraction in its simplest form
18 Write as a single fraction in its simplest form. n + 1 n - 1 - n - 1 n + 1 .................................................... [4]
Mark scheme: 18 4 n 4 n 4 M1 for common denominator ( n − 1)( n + 1) or or final n 2 − 1 ( n − 1)( n + 1) n 2 − 1 answer M2 for ( n 2 + 2 n + 1) − ( n 2 − 2 n + 1) or better or M1 for ( n + 1) 2 or ( n − 1) 2 oe
What was in this paper
The subtopics covered by these 18 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 2018 May/June, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.