Cambridge IGCSE Mathematics - International 0607 — 2022 May/June Paper 2 · Variant 2
0607/22/M/J/22 · 17 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
Question 1
1 Work out. ( 0. 03) 2 ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 0.0009 1
Q2 · Write the fraction in its lowest terms
2 (a) Write the fraction in its lowest terms. 40 ................................................. [1] (b) Work out. 2 2 + 3 9 ................................................. [2]
Mark scheme: 2(a) 3 1 final answer 8 2(b) 8 2 M1 for both fractions correct with same common denominator 9
Question 3
3 Solve the equation. x - 11 =- 4 x = ................................................ [1]
Mark scheme: 3 7 1
Q4 · Change 600 cm 3 into m3
4 Change 600 cm 3 into m3. ............................................ m3 [1] 1
Mark scheme: 4 0.0006 1
Question 5
5 Work out 643 . ................................................. [1]
Mark scheme: 5 4 only 1
Q6 · A NOT TO 63° SCALE D 75° E B C AB is parallel to CD
6 A NOT TO 63° SCALE D 75° E B C AB is parallel to CD. Find angle ACD. Angle ACD = ................................................ [1]
Mark scheme: 6 63 1
Q7 · Kendra jogs 7 km in 45 minutes
7 Kendra jogs 7 km in 45 minutes. She then runs at 12 km/h for 30 minutes. Find her average speed in km/h for the whole journey. ......................................... km/h [3]
Mark scheme: 7 156 3 30 10.4 or oe (7 12 ) 15 60 (7 6) M2 for 60 or oe 45 30 0.75 0.5 or M1 for (their total dist) / (their total time)
Q8 · The mean of eight numbers is 25
8 The mean of eight numbers is 25. When two extra numbers are included the mean of the ten numbers is 24. Find the mean of the two extra numbers. ................................................. [2]
Mark scheme: 8 20 2 M1 for 10 24 or 8 25
Q9 · Solve the simultaneous equations
9 Solve the simultaneous equations. 5x + 2y =- 12 3x - y =- 5 x = ................................................ y = ................................................ [3]
Mark scheme: 9 Correct method to eliminate one M1 If 0 scored, SC1 for answers that satisfy one variable equation [ x ] 2 A1 [ y ] 1 A1
Q10 · A is the point (–1, 13) and B is the point (3, 1)
10 A is the point (–1, 13) and B is the point (3, 1). Find the equation of the line AB, giving your answer in the form y = mx + c . y = ................................................ [3]
Mark scheme: 10 [ y ] 3 x 10 3 13 1 M1 for [Grad ] 1 3 oe M1 for subst their grad and A or B correctly into y mx c. or M1 for y 1 their ( 3) ( x 3) or y 13 their ( 3) ( x 1)
Question 11
11 Solve. 6x 2 - 5x - 6 = 0 x = ........................... or x = ........................... [3]
Mark scheme: 11 2 3 3 M2 for (3 x 2)(2 x 3) , 3 2 or M1 for ( ax b )( cx d ) with two of ac 6, bd 6, ad bc 5 OR M2 for correct use of formula or M1 for one error in substituting into formula
Q12 · The lengths of the sides of a triangle are 3 cm, 4 cm and 5 cm
12 The lengths of the sides of a triangle are 3 cm, 4 cm and 5 cm. Find the sine of the smallest angle. ................................................. [1]
Mark scheme: 12 3 1 oe 5
Q13 · John goes to a shop that sells newspapers and magazines only
13 John goes to a shop that sells newspapers and magazines only. (a) Complete the table of probabilities of John buying something at the shop. Buys a newspaper Does not buy a newspaper Total Buys a magazine 0.40 Does not buy a magazine 0.25 Total 0.55 1.00 [2] (b) Find the probability that John buys a magazine but not a newspaper. ................................................. [1]
Mark scheme: 13(a) 2 B1 for at least 2 correct N not N Total M 0.3 0.1 not M 0.35 0.6 Total 0.45 13(b) 1 1 FT their table 0.1 or 10
Q14 · F ( )x = 2x + 3 Find the values of x when f ( )x = 15
14 f ( )x = 2x + 3 Find the values of x when f ( )x = 15 . ................................................. [2]
Mark scheme: 14 [ x ] 6, [ x ] 9 2 B1 for each
Q15 · A bag has 5 black counters, 4 white counters and 1 red counter
15 A bag has 5 black counters, 4 white counters and 1 red counter. One counter is chosen at random and is replaced. A second counter is then chosen at random. Find the probability that the two counters chosen are different colours. ................................................. [4]
Mark scheme: 15 29 58 4 5 5 4 6 1 9 or or 0.58 oe M3 for oe 50 100 10 10 10 10 10 10 or M2 for any 2 correct 5 5 4 6 1 9 or M1 for or or 10 10 10 10 10 10 OR 5 4 5 1 1 4 M3 for 2 oe 10 10 10 10 10 10 or M2 for any 2 correct 5 4 5 1 1 4 or M1 for or or 10 10 10 10 10 10 OR 5 5 4 4 1 1 M3 for 1 10 10 10 10 10 10 5 5 4 4 1 1 or M2 for and and 10 10 10 10 10 10 5 5 4 4 1 1 or M1 for or or 10 10 10 10 10 10
Question 16
16 Solve. 2 log x = 1 + log 9 - log 8 + 2 log 3 x = ................................................ [3] Question 17 is printed on the next page.
Mark scheme: 16 5 3 B1 for 1 log10 M1 for one correct use of log laws eg log a log b log ab log a b b log a
Q17 · Expand the brackets and simplify
17 (a) Expand the brackets and simplify. a + b a - b ` `j j ................................................. [2] (b) Rationalise the denominator. 1 7 + 6 ................................................. [1] (c) Work out the value of 1 1 1 1 1 + + + + . 9 + 8 8 + 7 7 + 6 6 + 5 5 + 4 ................................................. [2]
Mark scheme: 17(a) a b 2 M1 for a a a b b a b b oe 17(b) 7 6 1 17(c) 1 2 M1 for at least 3 of 9 8 8 7....... 4 or B1 for 9 4
What was in this paper
The subtopics covered by these 17 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 2. A higher threshold means an easier paper — the bar moves with how the cohort did.