Cambridge IGCSE Mathematics - International 0607 — 2022 May/June Paper 2 · Variant 3
0607/23/M/J/22 · 12 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. (a) 0.3 # 0.2 ................................................. [1] (b) 12 ' 0.4 ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 0.06 1 1(b) 30 1
Q2 · This is a list of 8 numbers
2 This is a list of 8 numbers. 11 7 8 13 7 14 15 5 (a) Find the median. ................................................. [2] (b) An extra number is added to the list. The mean of the nine numbers is 1 more than the mean of the eight numbers. Find the ninth number. ................................................. [3]
Mark scheme: 2(a) 9.5 oe 2 M1 for 5 7 7 8 11 ... or (8 + 11) ÷ 2 2(b) 19 3 M1 for attempt at mean (5 + 7 + 7 + 8 ..+ 15) / 8 M1 for 9 × (their 10 + 1)
Q3 · Show this inequality on the number line
3 Show this inequality on the number line. - 3 1 x G 4 x –6 –5 – 4 –3 –2 –1 0 1 2 3 4 5 6 [2]
Mark scheme: 3 2 –3 4 Correct line B1 for correct line or correct ends Correctly marked ends
Q4 · Express 175 as the product of its prime factors
4 (a) Express 175 as the product of its prime factors. ................................................. [2] (b) Kurt has two timers. One is set to ring every 175 minutes. The other is set to ring every 70 minutes. Both timers ring together at 09 15. Find the time when the timers next ring together. ................................................. [3]
Mark scheme: 4(a) 5 × 5 × 7 or 52 × 7 2 B1 for 5 and 7 identified as factors 4(b) 15 05 3 B2 for [LCM=] 350 or B1 for 2 × 5 × 7 or 10 25, 11 35, 12 45... or 70, 140, 210, 280, 350
Question 5
5 Expand. 3 ( 2x - 1) ................................................. [1]
Mark scheme: 5 6x – 3 final answer 1
Q6 · Find the exterior angle of a regular polygon with 15 sides
6 Find the exterior angle of a regular polygon with 15 sides. ................................................. [2]
Mark scheme: 6 24 2 M1 for 360 / 15 OR B1 for 156
Q7 · Eggs are graded into four sizes: extra large, large, medium and small
7 Eggs are graded into four sizes: extra large, large, medium and small. A farmer records the sizes of a sample of 100 eggs that she collects. The results are shown in the table. Size Extra large Large Medium Small Number of eggs 28 36 24 12 (a) Find the relative frequency for large eggs. ................................................. [1] (b) In one month, the farmer collects 2500 eggs. Calculate an estimate for the number of these eggs that are small. ................................................. [2]
Mark scheme: 7(a) 36 9 1 or oe 100 25 7(b) 300 2 2500 M1 for 12 oe 100
Question 8
8 Factorise fully. 2cx 2 - 2dx - cx + d ................................................. [2]
Mark scheme: 8 (cx – d)(2x – 1) final answer 2 B1 for 2 pairs factorised e.g. cx(2x – 1) – d(2x – 1) or 2x(cx – d) – (cx – d)
Q9 · E NOT TO SCALE D F C A B ABCD is a parallelogram
9 E NOT TO SCALE D F C A B ABCD is a parallelogram. EDA and EFB are straight lines. (a) Show that triangles EDF and BCF are similar. [2] (b) BC = 4 cm, DE = 5 cm and FB = 3 cm. Find EF. EF = ........................................... cm [2]
Mark scheme: 9(a) EFD = BFC (Vert) opposite s 2 B1 for 1 pair with reason or all 3 equal angle pairs EDF = BCF Alternate s identified DEF = CBF Alternate s OR Two of the above AND 3 angles are equal, triangles are similar 9(b) 3 2 EF 5 3 oe M1 for oe 4 3 4
Q10 · A is the point (-5, 7) and C is the point (1, -2)
10 A is the point (-5, 7) and C is the point (1, -2). (a) B is the mid-point of AC. Find the coordinates of B. (....................... , .......................) [2] (b) The line CD is perpendicular to the line AC. Find the equation of line CD. ................................................. [4]
Mark scheme: 10(a) (–2, 2.5) oe 2 B1 for each coordinate 10(b) 2 8 4 Equivalent 3 term equation. y x oe 3 3 2 7 M1 for gradient of BC = oe 1 ( 5) 3 M1 for gradient of CD = –1 ÷ (their ) 2 M1 for substituting (1, – 2) and their m into y = mx + c oe
Q11 · Y is inversely proportional to ( x + 2) 2
11 y is inversely proportional to ( x + 2) 2 . When x = 3, y = 2. (a) Find y in terms of x. y = ................................................ [2] (b) Find the positive value of x when y = 0.5 . x = ................................................ [2] Question 12 is printed on the next page.
Mark scheme: 11(a) 50 2 k M1 for y = ( x 2) 2 ( x 2) 2 11(b) 8 2 M1 for (x + 2)2 = their 50 ÷ 0.5
Q12 · A = b = - 10 2 Find the magnitude of the vector a - b
12 a = b = - 10 2 Find the magnitude of the vector a - b. Give your answer in its simplest surd form. ................................................. [4]
Mark scheme: 12 4 13 4 B3 for 208 OR 8 B1 for oe 12 M1 for (their 8)2 + (their(–12))2
What was in this paper
The subtopics covered by these 12 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 3. A higher threshold means an easier paper — the bar moves with how the cohort did.