Cambridge IGCSE Mathematics - International 0607 — 2017 May/June Paper 2 · Variant 3
0607/23/M/J/17 · 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Work out 2 14
1 Work out 2 14 . .................................................... [2]
Mark scheme: Question Answer Marks Part Marks 1 1.5 oe 2 9 M1 for 4
Q2 · Change to a percentage
2 Change to a percentage. 25 ............................................... % [1]
Mark scheme: 2 28 1
Q3 · X = 5 Write down the two possible values of x
3 x = 5 Write down the two possible values of x. x = .......................... or x = .......................... [1]
Mark scheme: 3 – 5 and 5 1
Q4 · These are the first four terms of a sequence
4 These are the first four terms of a sequence. 15 11 7 3 Find (a) the next term, .................................................... [1] (b) the nth term. .................................................... [2]
Mark scheme: 4(a) – 1 1 4(b) – 4n + 19 oe 2 B1 for – 4n + k or pn + 19, p ≠ 0
Question 5
5 Expand. x 3 (x 2 + 3) .................................................... [2] 7
Mark scheme: 5 x 5 + 3 x 3 final answer 2 B1 for x 5 + kx n or kx n + 3 x 3 , k ≠ 0
Question 6
6 Work out # . 8 # 1022 Give your answer in standard form. .................................................... [2]
Mark scheme: 6 5 × 10−16 2 B1 for correct value, not in standard form, seen
Q7 · V = u + at Rearrange the formula to write t in terms of a, u and v
7 v = u + at Rearrange the formula to write t in terms of a, u and v. t = ................................................... [2]
Mark scheme: 7 v − u 2 M1 for correct rearrangement for at or t oe final answer M1 for correct division by a a
Question 8
8 Simplify. (a) 8y 8 ' 2y 2 .................................................... [2] (b) 2w 2 5 ^ h .................................................... [2]
Mark scheme: 8(a) 4y 6 2 B1 for ky 6 or 4 ky 8(b) 32w10 2 B1 for kw10 or 32 wk
Q9 · D C p° 75° NOT TO SCALE B E q° A A, B, C, D and E lie on the circle
9 D C p° 75° NOT TO SCALE B E q° A A, B, C, D and E lie on the circle. Angle BCE = 75˚. Find the value of p and the value of q. p = ........................................................ q = ................................................... [2]
Mark scheme: 9 [p =] 75 2 B1 for each [q=]105
Q10 · Y = x + 1 and y = 2 - x Find the value of x
10 y = x + 1 and y = 2 - x Find the value of x. x = ................................................... [2]
Mark scheme: 10 0.5 oe 2 M1 for x + 1 = 2 – x or for correctly eliminating x
Q11 · Each diagram shows the graph of y = f(x)
11 Each diagram shows the graph of y = f(x). On each diagram, sketch the function indicated. y y x x 0 0 y = f(x) – 2 y = – f(x) [2]
Mark scheme: 11 Correct sketches 2 B1 for each
Q12 · 2 Find the value of 16 3
412 Find the value of 16 3. .................................................... [1]
Mark scheme: 12 8 1
Question 13
13 (a) Simplify. (4 - 3)(4 + 3 ) .................................................... [2] (b) Rationalise the denominator. 5 7 .................................................... [1]
Mark scheme: 13(a) 13 2 2 2 M1 for 4 − 3 or better ( ) or for three of the terms of 16 + 4 3 − 4 3 − 3 correct 13(b) 5 7 1 7
Question 14
14 Factorise. (a) p 2 - p - 30 .................................................... [2] (b) x (u - v) - y (v - u) .................................................... [2]
Mark scheme: 14(a) ( p − 6)( p + 5) 2 B1 for ( p + a )( p + b ) where ab = – 30 or a + b = – 1 or p ( p + 5) − 6( p + 5) or p ( p − 6) + 5( p − 6) 14(b) (u − v )( x + y ) 2 M1 for x (u − v ) + y (u − v ) or u ( x + y ) − v ( x + y )
Q15 · Y \ x3 When x = 2, y = 2
15 y \ x3 When x = 2, y = 2. Find y when x = 10. y = ................................................... [3]
Mark scheme: 15 16 3 k oe M1 for y = 3 oe 1000 x M1 for substituting x = 2 and y = 2 in their equation to find k
Q16 · F(x) = 6cos(6x) Find the amplitude and the period of f(x)
16 f(x) = 6cos(6x) Find the amplitude and the period of f(x). Amplitude = ........................................................ Period = ................................................... [2] Questions 17 and 18 are printed on the next page.
Mark scheme: 16 [amplitude = ] 6 2 B1 for each [period = ] 60 If 0 scored, SC1 if answers reversed
Q17 · C 60° NOT TO SCALE 5 cm 8 cm A B Find AB
17 C 60° NOT TO SCALE 5 cm 8 cm A B Find AB. AB = ............................................ cm [3]
Mark scheme: 17 7 3 B1 for cos60 = 0.5 M1 for 52 + 82 −×2 5 × 8 × cos60
Q18 · F ()x = 10 x Find f - 1 ()x
18 f ()x = 10 x Find f - 1 ()x . f - 1 ()x = .................................................. [1]
Mark scheme: 18 logx 1
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 2017 May/June, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.