Cambridge IGCSE Mathematics 0580 — 2015 May/June Paper 2 · Variant 1
0580/21/M/J/15 · 3 questions · 70 marks · ≈79 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 paper12 pages
Mark scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q21 · NOT TO SCALE 9 cm 4 cm The diagram shows a toy
21 NOT TO SCALE 9 cm 4 cm The diagram shows a toy. The shape of the toy is a cone, with radius 4 cm and height 9 cm, on top of a hemisphere with radius 4 cm. Calculate the volume of the toy. Give your answer correct to the nearest cubic centimetre. [The volume, V, of a cone with radius r and height h is V = 13 πr 2h.] [The volume, V, of a sphere with radius r is V = 43 πr 3.] Answer ......................................... cm3 [4] __________________________________________________________________________________________
Mark scheme: 21 285 cao 4 M1 for 13 × π × 4 2 × 9 , 48π 1 4 3 128 π M1 for × × π × 4 , 2 3 3 272 π A1 for 284.8 to 284.9, 3 If A0 then B1 for their final answer rounded correctly to nearest whole number from their more accurate answer dependent on at least M1 22 17
Q22 · 7 - 2 1 22 (a) Calculate - 1 4 4 2 f fp p
3 7 - 2 1 22 (a) Calculate - 1 4 4 2 f fp p. Answer(a) [2] f p 5 3 (b) Calculate the inverse of 6 4 f p. Answer(b) [2] f p __________________________________________________________________________________________ Question 23 is printed on the next page.
Mark scheme: 22 17 for a 2 × 2 matrix with 2 correct elements22 (a) 2 M1 18 7 1 4 − 3 1 a b 4 − 3 (b) 2 M1 for soi or k c d 2 2 − 6 5 − 6 5 or det = 2 soi
Q23 · F(x) = 5 – 3x (a) Find f(6)
23 f(x) = 5 – 3x (a) Find f(6). Answer(a) ................................................ [1] (b) Find f(x + 2). Answer(b) ................................................ [1] (c) Find ff(x), in its simplest form. Answer(c) ................................................ [2] (d) Find f –1(x), the inverse of f(x). Answer(d) f –1(x) = ................................................ [2]
Mark scheme: 23 (a) −13 1 (b) −3x − 1 or 5 − 3( x + 2 ) 1 (c) 9x − 10 cao 2 M1 for 5 − 3( 5 − 3x) 5 − x (d) final answer oe 2 M1 for correct first step e.g. 3 y 5 y + 3 x = 5 or = − x or y − 5 = − 3 x or 3 3 better or for interchanging x and y, e.g. x = 5 − 3 y , this does not need to be the first step
What was in this paper
The subtopics covered by these 3 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 2015 May/June, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.