Cambridge IGCSE Mathematics 0580 — 2013 May/June Paper 2 · Variant 2
0580/22/M/J/13 · 4 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q18 · Solve 6x + 3 < x < 3x + 9 for integer values of x
18 Solve 6x + 3 < x < 3x + 9 for integer values of x. Answer ............................................... [4] _____________________________________________________________________________________
Mark scheme: 18 −1 −2 −3 −4 4 B3 for x < − 3 5 and x > −5.4 oe or B2 for x < − 3 5 or x > −5.4 oe or B1 for 5x < − 3 or − 9 < 2x oe Or mark on answer line −1 oe
Q19 · For Examiner′s Use D C A B Scale: 1 cm to 8 m The rectangle ABCD is a scale drawing of a…
19 For Examiner′s Use D C A B Scale: 1 cm to 8 m The rectangle ABCD is a scale drawing of a rectangular football pitch. The scale used is 1 centimetre to represent 8 metres. (a) Construct the locus of points 40 m from A and inside the rectangle. [2] (b) Using a straight edge and compasses only, construct the perpendicular bisector of DB. [2] (c) Shade the region on the football pitch which is more than 40 m from A and nearer to D than to B. [1] _____________________________________________________________________________________
Mark scheme: 19 (a) arc centre A radius 5 cm 2 B1 arc with centre A (b) ruled perpendicular bisector of DB with 2 2 B1 correct ruled line pairs of correct arcs B1 2 pairs of correct arcs (c) cao 1
Q20 · The heights, in metres, of 200 trees in a park are measured
20 The heights, in metres, of 200 trees in a park are measured. For Examiner′s Use Height (h m) 2 < h Ğ 6 6 < h Ğ 10 10 < h Ğ 13 13 < h Ğ 17 17 < h Ğ 19 19 < h Ğ 20 Frequency 23 47 45 38 32 15 (a) Find the interval which contains the median height. Answer(a) ............................................... [1] (b) Calculate an estimate of the mean height. Answer(b) ........................................... m [4] (c) Complete the cumulative frequency table for the information given in the table above. Height (h m) 2 < h Ğ 6 h Ğ 10 h Ğ 13 h Ğ 17 h Ğ 19 h Ğ 20 Cumulative 23 frequency [2] _____________________________________________________________________________________ Question 21 is printed on the next page.
Mark scheme: 20 (a) 10 < h ≤ 13 1 (b) 12.1[2] www 4 M1 for at least 5 correct mid-values seen M1 for ∑ fx where x is in the correct interval (c) 70, 115, 153, 185, 200 2 M1 for their ∑ fx ÷ 200 B1 for 3 or 4 correct
Q21 · 1 x Examiner′s , x ¸ 0 h(x) =21 f(x) = 5x + 4 g(x) = 2x c 2 m Use Find (a) fg(5)…
1 1 x Examiner′s , x ¸ 0 h(x) =21 f(x) = 5x + 4 g(x) = 2x c 2 m Use Find (a) fg(5) , Answer(a) ............................................... [2] (b) gg(x) in its simplest form, Answer(b) gg(x) = ............................................... [2] (c) f –1(x) , Answer(c) f –1(x) = ............................................... [2] (d) the value of x when h(x) = 8. Answer(d) x = ............................................... [2]
Mark scheme: 21 (a) 4.5 oe 2 B1 for [g(5)=] 0.1 oe 1 seen oe M1 for (b) x 2 2 1 ( 2 x ) x − 4 (c) oe 2 M1 for a correct first step 5 4 y e.g. y − 4 = 5x or = x + or 5 5 x = 5y + 4 (d) or − 3 2 M1 for 8 x 1 −x 3 or 2 = oe or 2 = 2 8
What was in this paper
The subtopics covered by these 4 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 2013 May/June, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.