Cambridge IGCSE Mathematics 0580 — 2012 May/June Paper 2 · Variant 2
0580/22/M/J/12 · 11 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 scheme3 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · The ferry from Helsinki to Travemunde leaves Helsinki at 17 30 on a Tuesday
1 The ferry from Helsinki to Travemunde leaves Helsinki at 17 30 on a Tuesday. For The journey takes 28 hours 45 minutes. Examiner's Use Work out the day and time that the ferry arrives in Travemunde. Answer Day Time [2]
Mark scheme: Qu Answers Mark Part marks 1 Wednesday 2 B1 22 15 or 10 15pm B1
Q2 · T R I G O N O M E T R Y From the above word, write down the letters which have (a)…
2 T R I G O N O M E T R Y From the above word, write down the letters which have (a) exactly two lines of symmetry, Answer(a) [1] (b) rotational symmetry of order 2. Answer(b) [1]
Mark scheme: 2 (a) I cao 1 (b) I N cao 1 x 5
Q3 · For this question, 1 < x < 2
3 For this question, 1 < x < 2 . Write the following in order of size, smallest first. 5 x 5x x O 5 x 5 Answer < < < [2]
Mark scheme: x 5 3 x – 5 5x 2 M1 evaluating all 4 expressions for one value in 5 x the range. (1 and 2 are out of range)
Q4 · 1 1 p 4 1 + + = 2 3 4 12 Work out the value of p
1 1 1 p 4 1 + + = 2 3 4 12 Work out the value of p. Show all your working. Answer p = [2]
Mark scheme: 4 25 (correct working essential) 2 M1 for 18 + 4 + 3 with denominator 12 must be soi (oe is possible) 4 4 k
Q5 · A lake has an area of 63 800 000 000 square metres
5 A lake has an area of 63 800 000 000 square metres. For Examiner's Write this area in square kilometres, correct to 2 significant figures. Use Answer km2 [2]
Mark scheme: 5 64000 or 6.4 × 104 2 SC1 for 63800 or 6.38 × 104 or figs 64 or 6.4 × 10k in answer space.
Q6 · X is a positive integer and 15x – 43 < 5x + 2
6 x is a positive integer and 15x – 43 < 5x + 2 . Work out the possible values of x. Answer [3]
Mark scheme: 6 1, 2, 3, 4 3 M1 10x < 45 A1 x < 4.5
Q7 · 8 cm NOT TO r SCALE 6 cm The perimeter of the rectangle is the same length as the…
7 8 cm NOT TO r SCALE 6 cm The perimeter of the rectangle is the same length as the circumference of the circle. Calculate the radius, r, of the circle. Answer r = cm [3]
Mark scheme: 7 4.46 or 4.456 to 4.459 cao 3 B1 for 28 seen their 28 M1ft for oe or better. 2π 2 3
Q8 · A car company sells a scale model of the size of one of its cars
8 A car company sells a scale model of the size of one of its cars. Examiner's 10 Use Complete the following table. Scale Model Real Car Area of windscreen (cm2) 135 Volume of storage space (cm3) 408 000 [3]
Mark scheme: 8 13500 408 3 M1 135 × 102 or 408000 ÷ 103 oe A1 A1
Q9 · P NOT TO SCALE 78.3° A B 58.4 m 170 m The line AB represents the glass walkway between…
9 P NOT TO SCALE 78.3° A B 58.4 m 170 m The line AB represents the glass walkway between the Petronas Towers in Kuala Lumpur. The walkway is 58.4 metres long and is 170 metres above the ground. The angle of elevation of the point P from A is 78.3°. Calculate the height of P above the ground. Answer m [3]
Mark scheme: 9 452 3 x SC2 282 in answer M1 tan 78.3 = space 584. M1 “282” + 170
Q10 · For Examiner's 500 Use 400 300 Speed (m / min) 200 100 0 10 20 30 40 50 60 Time (min) The…
10 For Examiner's 500 Use 400 300 Speed (m / min) 200 100 0 10 20 30 40 50 60 Time (min) The diagram shows the speed-time graph for a boat journey. (a) Work out the acceleration of the boat in metres / minute2. Answer(a) m / min 2 [1] (b) Calculate the total distance travelled by the boat. Give your answer in kilometres. Answer(b) km [2]
Mark scheme: 10 (a) 50 1 (b) 15 2 M1 finding area under graph SC1 15000 2
Q14 · Y 3 2 A B 1 x 0 1 2 3 4 5 6 7 8 (a) Describe fully the single transformation that maps…
14 y 3 2 A B 1 x 0 1 2 3 4 5 6 7 8 (a) Describe fully the single transformation that maps triangle A onto triangle B. Answer(a) [3] (b) Find the 2 × 2 matrix which represents this transformation. Answer(b) [2]
Mark scheme: (c) 14 to 14.5 1
What was in this paper
The subtopics covered by these 11 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 2012 May/June, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.