Cambridge IGCSE Mathematics 0580 — 2012 May/June Paper 1 · Variant 1
0580/11/M/J/12 · 18 questions · 56 marks · ≈63 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
Q1 · Kyle scores 84 marks out of 96 in an examination
1 Kyle scores 84 marks out of 96 in an examination. For Examiner's Work out his percentage mark. Use Answer % [1]
Mark scheme: Qu Answers Mark Part marks 1 87.5 1
Q2 · The lengths of each side of this triangle are the same
2 The lengths of each side of this triangle are the same. (a) Write down the mathematical name for this triangle. Answer(a) [1] (b) Write down the number of lines of symmetry for the triangle. Answer(b) [1]
Mark scheme: 2 (a) Equilateral 1 (b) 3 1
Q3 · Work out the number of minutes from 18 27 on Tuesday to 03 19 on Wednesday
3 Work out the number of minutes from 18 27 on Tuesday to 03 19 on Wednesday. Answer min [2]
Mark scheme: 3 532 2 M1 for 5(h)33(min) + 3(h)19(min)
Q4 · Gregor changes $700 into euros (€) when the rate is €1 = $1.4131
4 Gregor changes $700 into euros (€) when the rate is €1 = $1.4131 . For Examiner's Calculate the amount he receives. Use Answer € [2]
Mark scheme: 4 495.36 2 M1 for 700 ÷ 1.4131
Q5 · W = 3a – 5b Calculate w when a = 2 and b = –3
5 w = 3a – 5b Calculate w when a = 2 and b = –3. Answer w = [2]
Mark scheme: 5 21 2 M1 for 2 × 3 – 5 × (–3) or better or B1 for 6 and –15 i.e. both terms evaluated
Q6 · One bracelet costs 85 cents and one necklace costs $7.50
6 One bracelet costs 85 cents and one necklace costs $7.50 . Write down an expression, in dollars, for the total cost of b bracelets and n necklaces. Answer $ [2]
Mark scheme: 6 0.85b + 7.5n 2 B1 for 0.85b OR 7.5n seen 85 n + 750 n OR final answer 100
Q7 · A quadrilateral has four sides of equal length and two pairs of equal angles
7 (a) A quadrilateral has four sides of equal length and two pairs of equal angles. For Examiner's Write down the mathematical name for this quadrilateral. Use Answer(a) [1] (b) 92° NOT TO SCALE 74° 63° Three of the angles in a quadrilateral are 63°, 74° and 92°. Work out the size of the fourth angle. Answer(b) [1]
Mark scheme: 7 (a) Rhombus 1 (b) 131° 1 2 7
Q8 · Solve the equation 4x – 2 = 7
8 Solve the equation 4x – 2 = 7 . Answer x = [2]
Mark scheme: 2 7 8 2.25 oe 2 M1 4x = 7 + 2 OR x – = or better 4 4
Q9 · The temperature at the top of a mountain is –12°C
9 The temperature at the top of a mountain is –12°C. The temperature at the bottom of the mountain is 18°C. (a) Work out the difference in these temperatures. Answer(a) °C [1] (b) 18°C is given correct to the nearest degree. Write down the upper bound for this temperature. Answer(b) °C [1]
Mark scheme: 9 (a) 30 1 (b) 18.5 1 x
Q10 · For Examiner's NOT TO Use 29 cm SCALE x cm 53.2° Calculate the value of x
10 For Examiner's NOT TO Use 29 cm SCALE x cm 53.2° Calculate the value of x. Answer x = [2]
Mark scheme: x 10 23.2 2 M1 for sin 53.2 = implicit form or better 29
Q11 · Write down all the factors of 15
11 (a) Write down all the factors of 15. Answer(a) [1] (b) Factorise completely. 15p2 + 24pt Answer(b) [2]
Mark scheme: 11 (a) 1, 3, 5, 15 1 (b) 3p(5p + 8t) final answer 2 B1 for answer of 3(5p2 + 8pt) or p(15p + 24t) or SC1 for correct answer seen in working IGCSE – May/June 2012 0580 11
Q12 · Triangle ABC has sides AB = 40 m, BC = 25 m and AC = 35 m
12 Triangle ABC has sides AB = 40 m, BC = 25 m and AC = 35 m. Using a scale of 1 cm to represent 5 m, construct triangle ABC. The construction must be completed using a ruler and compasses only. All construction arcs must be clearly shown. Answer A B [3]
Mark scheme: 12 Triangle drawn correctly 3 M1 for one side drawn to correct length with ruler and arcs and M1 for clear method of crossing arcs even if wrong scale or inaccurate 750 × 5 × 2 5
Q13 · For 13 Shania invests $750 at a rate of 2 2 % per year simple interest
1 For 13 Shania invests $750 at a rate of 2 2 % per year simple interest. Examiner's Use Calculate the total amount Shania has after 5 years. Answer $ [3]
Mark scheme: 750 × 5 × 5.2 13 843.75 3 M2 for + 750 oe 100 750 × 5 × 5.2 or M1 for oe 100 or SC2 for answer 93.75 55 27 25 27
Q14 · 9 14 Without using your calculator, work out 1 +
5 9 14 Without using your calculator, work out 1 + . 6 10 You must show your working and give your answer as a mixed number in its simplest form. Answer [3]
Mark scheme: 55 27 25 27 14 + oe or )1( + oe M1 for denominator of 30k 30 30 30 30 82 52 oe or )1( oe M1 for denominator of 30k dependent on previous M1 30 30 11 2 M2 must be scored A1 If M0 scored then SC1 for common denominator of 15 30k seen
Q15 · Find the value of x
15 (a) Find the value of x. For Examiner's Use NOT TO x° SCALE 51° Answer(a) x = [1] (b) EF is a diameter of the circle. Find the value of y. y° E 63° NOT TO SCALE F Answer(b) y = [1] (c) Find the value of z in this isosceles triangle. NOT TO 48° SCALE z° Answer(c) z = [1]
Mark scheme: 15 (a) 51° 1 (b) 90° 1 (c) 66° 1
Q16 · Solve the simultaneous equations
16 Solve the simultaneous equations. For 3x + 5y = 24 Examiner's x + 7y = 56 Use Answer x = y = [3]
Mark scheme: 16 x = −7 3 M1 for consistent multiplication and addition/ y = 9 subtraction as appropriate. Allow computational errors A1 for x= –7 or y = 9
Q17 · For y Examiner's Use 7 6 5 4 3 A 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 B –4 (a) Write…
17 For y Examiner's Use 7 6 5 4 3 A 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 B –4 (a) Write down the co-ordinates of point A. Answer(a) ( , ) [1] (b) Write as a column vector. Answer(b) = [1] 2 (c) = 3 Write down the co-ordinates of C. Answer(c) ( , ) [1]
Mark scheme: 17 (a) (–1, 2) 1 4 (b) 1 −5 (c) 1 (1, 5)
Q21 · For 13 17 13 17 19 13 31 21 29 Examiner'sUse (a) For the numbers above, find (i) the…
21 For 13 17 13 17 19 13 31 21 29 Examiner'sUse (a) For the numbers above, find (i) the range, Answer(a)(i) [1] (ii) the median. Answer(a)(ii) [2] (b) Write down the only number in the list which is not a prime number. Answer(b) [1]
Mark scheme: (b) 21 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 2012 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.