Cambridge IGCSE Mathematics - International 0607 — 2022 Oct/Nov Paper 2 · Variant 2
0607/22/O/N/22 · 14 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 · These are the scores of 10 students in a test
1 These are the scores of 10 students in a test. 7 15 9 4 16 6 8 11 12 10 Find (a) the median, ................................................. [2] (b) the mean. ................................................. [2]
Mark scheme: Question Answer Marks Partial Marks 1(a) 9.5 2 M1 for 4, 6, 7, 8, 9, 10, 11, 12, 15, 16 Ordered as far as 10 forwards or 9 backwards 1(b) 9.8 2 M1 for (7 + 15 + 16 + 4 ...) ÷ 10
Q2 · A regular polygon has 24 sides
2 A regular polygon has 24 sides. Find the size of each interior angle of the polygon. ................................................. [3]
Mark scheme: 2 165 3 360 (24 − 2)180 M2 for 180 – or 24 24 360 or M1 for or (24 – 2) × 180 24
Q3 · P = 2a + b 2 - 3c Find P when a = 5 , b =- 4 and c =- 3
3 P = 2a + b 2 - 3c Find P when a = 5 , b =- 4 and c =- 3 . P = ................................................ [2]
Mark scheme: 3 35 2 B1 for two of 10, +16 or +9
Q4 · You are given that 7 = 2.65 and 70 = 8.37 , each correct to 2 decimal places
4 You are given that 7 = 2.65 and 70 = 8.37 , each correct to 2 decimal places. Use this information to find the value of (a) 700, ................................................. [1] (b) 280. ................................................. [1]
Mark scheme: 4(a) 26.5 1 4(b) 16.74 or 16.7 1
Q5 · A biased 5-sided spinner is spun 200 times
5 A biased 5-sided spinner is spun 200 times. The results are shown in the table. Number 1 2 3 4 5 Frequency 24 48 63 38 27 (a) Find the relative frequency of the spinner landing on 2. ................................................. [1] (b) The spinner is spun 1000 times. Find the expected number of times that the spinner lands on 2. ................................................. [1]
Mark scheme: 5(a) 48 1 oe 200 5(b) 240 1
Q6 · Solve 2x + 6 2 5x - 10
6 Solve 2x + 6 2 5x - 10 . ................................................. [2]
Mark scheme: 6 16 1 2 16 x < or x < final answer B1 for x * where * is =, >, ⩽ or ⩾ 3 53 3 OR M1 for 6 + 10 > 5x – 2x oe
Q7 · Describe fully the inverse of each transformation
7 Describe fully the inverse of each transformation. - 2 (a) Translation by e 5o. ..................................................................................................................................................... [2] (b) Enlargement with centre (2, 3) and scale factor 2. ..................................................................................................................................................... ..................................................................................................................................................... [2]
Mark scheme: 7(a) Translation 2 B1 for each 2 −5 7(b) Enlargement or reduction 1 and centre (2, 3) 1 1 Scale factor 2
Q8 · Find the value of 125 - 3
8 Find the value of 125 - 3. ................................................. [1]
Mark scheme: 8 1 1 or 0.2 5
Q9 · Y is inversely proportional to x3
9 y is inversely proportional to x3. When x = 5, y = 2 . Find y when x = 10 . y = ................................................ [3]
Mark scheme: 9 1 3 k oe M1 for y = oe 4 x 3 A1 for k = 250 OR 10 3 M2 for 2 ÷ oe 5 1 y 10 3 or M1 for = oe 2 1 53
Q10 · 60° NOT TO 2 3cm SCALE x cm Find the value of x
10 60° NOT TO 2 3cm SCALE x cm Find the value of x. x = ................................................ [3]
Mark scheme: 10 6 3 x M1 for tan 60 = 2 3 B1 for tan 60 = 3
Question 11
11 Simplify. ax 2 + 5ax + bx + 5b x 2 - 25 ................................................. [3]
Mark scheme: 11 ax + b 3 B1 for (ax + b)(x + 5) final answer B1 for (x + 5)(x – 5) x − 5
Q12 · F ( x) = 11 x + 2 g ( x) = sin x° (a) Find f -1 ( x)
12 f ( x) = 11 x + 2 g ( x) = sin x° (a) Find f -1 ( x) . f -1 ( x) = ................................................ [2] (b) Find g ( f ( 8)) . ................................................. [2]
Mark scheme: 12(a) x − 2 2 y 2 oe final answer M1 for y – 2 = 11x or = x + 11 11 11 or x = 11y +2 12(b) 1 2 M1 for sin (11x + 2) soi or B1 for 90
Q13 · B A NOT TO SCALE C Q 55° D P A, B, C and D are points on the circle
13 B A NOT TO SCALE C Q 55° D P A, B, C and D are points on the circle. PQ is a tangent to the circle at D. Angle BDQ = 55° . Complete these statements giving a reason for each answer. (a) Angle BAD = ....................... because ........................................................................................ ..................................................................................................................................................... [2] (b) Angle BCD = ...................... because ......................................................................................... ..................................................................................................................................................... [2]
Mark scheme: 13(a) 55 2 B1 for each Alternate Segment 13(b) 125 2 FT 180 – their 55 Opposite angles in cyclic quadrilateral B1 for each
Q14 · 4 log y + 3 log x = 2 Find y in terms of x
14 4 log y + 3 log x = 2 Find y in terms of x. ................................................. [3]
Mark scheme: 14 100 3 M1 for one correct use of nloga = logan y = [ ] 4 3 or log(a × b) = loga + logb x a or log = loga – logb b B1 for 100
What was in this paper
The subtopics covered by these 14 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 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.