Cambridge IGCSE Mathematics - International 0607 — 2022 Oct/Nov Paper 2 · Variant 3
0607/23/O/N/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
Q1 · 125° m° NOT TO k° SCALE The diagram shows a straight line intersecting two parallel lines
1 125° m° NOT TO k° SCALE The diagram shows a straight line intersecting two parallel lines. Find the value of k and the value of m. k = ................................................ m = ................................................ [2]
Mark scheme: Question Answer Marks Partial Marks 1 [k =] 125 2 B1 for each [m =] 55
Question 2
2 Solve the equation. 2q - 7 = 2 - 7q q = ................................................ [2]
Mark scheme: 2 1 2 M1 for 2q + 7q = 2 + 7 oe
Q3 · 1 m 2 = 10n cm 2 Find the value of n
3 1 m 2 = 10n cm 2 Find the value of n. n = ................................................ [1]
Mark scheme: 3 4 1
Q4 · Work out 1 -
4 Work out 1 - . 3 6 ................................................. [2]
Mark scheme: 4 3 2 M1 for correct working with common oe denominator or better 6
Q5 · An unbiased six-sided die is numbered 1, 2, 3, 4, 5, 6
5 An unbiased six-sided die is numbered 1, 2, 3, 4, 5, 6. The die is rolled. Find the probability that it shows (a) 6, ................................................. [1] (b) a number greater than 6. ................................................. [1]
Mark scheme: 5(a) 1 1 6 5(b) 0 1
Q6 · A cone has base radius 5 cm and height cm
6 A cone has base radius 5 cm and height cm . 4 A hemisphere has radius r cm. The volume of the hemisphere is equal to the volume of the cone. Find the value of r. r = ................................................ [3]
Mark scheme: 6 1 3 125 3 2 oe M2 for r3 = or better 2 12 2 1 4 3 1 2 5 or M1 for r and 5 2 3 3 4
Question 7
7 Simplify. 30t 30 ' 5t 5 ................................................. [2]
Mark scheme: 7 6t 25 2 B1 for kt 25 or 6kt
Q8 · 12 cm NOT TO SCALE 18 cm The diagram shows two triangles formed by two parallel lines and…
8 12 cm NOT TO SCALE 18 cm The diagram shows two triangles formed by two parallel lines and two intersecting lines. (a) Use one of these words to complete the statement. alternate congruent similar cyclic parallel The triangles are ................................................ [1] (b) The area of the smaller triangle is 24 cm 2. Calculate the area of the larger triangle. ......................................... cm2 [2]
Mark scheme: 8(a) similar 1 8(b) 54 2 2 2 18 12 M1 for oe or oe 12 18
Q9 · U P Q b a c i e d f g h j U = {a, b, c, d, e, f, g, h, i, j} Complete each statement
9 U P Q b a c i e d f g h j U = {a, b, c, d, e, f, g, h, i, j} Complete each statement. (a) ( P , Q ) l = {..........................................................} [1] (b) {a, e} = P....... Q [1] (c) n ( P l , Q ) = ................ [1]
Mark scheme: 9(a) f, g, h, j 1 9(b) 1 9(c) 7 1
Q10 · Rearrange the formula to write x in terms of a and y
10 Rearrange the formula to write x in terms of a and y. y = x 2 + 2a 2 x = ................................................ [3]
Mark scheme: 10 2 2 3 M1 for correct squaring [+] y − 2 a final answer M1 for correct rearranging for x term M1 for correct square root Max 2 marks if answer incorrect
Q11 · C NOT TO SCALE B 55° X E 25° 40° D A Y A, B, C and D are four points on a circle
11 C NOT TO SCALE B 55° X E 25° 40° D A Y A, B, C and D are four points on a circle. AC and BD meet at E. XAY is a tangent to the circle at A. Find (a) angle CDB, Angle CDB = ................................................ [1] (b) angle ACB, Angle ACB = ................................................ [1] (c) angle DCE, Angle DCE = ................................................ [1] (d) angle YAD. Angle YAD = ................................................ [1]
Mark scheme: 11(a) 25 1 11(b) 40 1 11(c) 60 1 11(d) 60 1 FT their (c)
Q12 · Simplify ( 3 # 10 85) # ( 7 # 10 15 )
12 Simplify ( 3 # 10 85) # ( 7 # 10 15 ) . Give your answer in standard form. ................................................. [2]
Mark scheme: 12 2.1 10101 cao 2 B1 for 21 10100
Question 13
13 Factorise. (a) 49 - 16u 2 ................................................. [1] (b) 1 + 4xy - 2x - 2y ................................................. [2]
Mark scheme: 13(a) ( 7 + 4u )( 7 − 4u ) final answer 1 13(b) (1 − 2 x )(1 − 2 y ) final answer 2 M1 for 1 − 2 y − 2 x (1 − 2 y ) or 1 − 2 x − 2 y (1 − 2 x)
Question 14
14 Rationalise the denominator. 5 3 - 2 ................................................. [2]
Mark scheme: 14 5 3 + 2 2 3 + 2 ( ) M1 for 3 + 2
Q15 · Log y = log h + log p - log x Find y in terms of h, p and x
15 log y = log h + log p - log x Find y in terms of h, p and x. y = ................................................ [1] Questions 16 and 17 are printed on the next page.
Mark scheme: 15 hp 1 final answer x
Q16 · = 32x16 8 4 Find the value of x
3 = 32x16 8 4 Find the value of x. x = ................................................ [2]
Mark scheme: 16 4 2 M1 for 16 or 24 or 25x seen oe 5
Question 17
17 Simplify. 4 - 3x 2 - x - 2 Write your answer as a single fraction in its simplest form. ................................................. [3]
Mark scheme: 17 5 x − 8 3 B1for common denominator x – 2 final answer M1 for 2(x – 2) – (4 – 3x) or better x − 2 seen
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 Oct/Nov, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.