Cambridge IGCSE Mathematics 0580 — 2015 May/June Paper 1 · Variant 3
0580/13/M/J/15 · 20 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 paper8 pages
Mark scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · What is the value of the digit 7 in 43 782?
1 What is the value of the digit 7 in 43 782? Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: Question Answer Mark Part marks 1 700 1
Q2 · NOT TO 124° SCALE x° Find the value of x
2 NOT TO 124° SCALE x° Find the value of x. Answer x = ................................................ [1] __________________________________________________________________________________________
Mark scheme: 2 56 1 22 88
Q3 · Write 0.88 as a fraction in its simplest form
3 Write 0.88 as a fraction in its simplest form. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 22 88 3 cao 2 M1 for oe seen 25 100
Q4 · Ahmed and Babar share 240 g of sweets in the ratio 7 : 3
4 Ahmed and Babar share 240 g of sweets in the ratio 7 : 3. Calculate the amount Ahmed receives. Answer ............................................. g [2] __________________________________________________________________________________________
Mark scheme: 4 168 2 M1 for 240 ÷ (7 + 3) or better
Question 5
5 Factorise completely. 9x2 – 6x Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 5 3x(3x – 2) final answer 2 B1 for x(9x – 6) or 3(3x2 – 2x)
Q6 · The mass of a car is 1400 kg correct to the nearest hundred kilograms
6 The mass of a car is 1400 kg correct to the nearest hundred kilograms. Complete the statement about the mass, m kilograms, of the car. Answer .................. m < .................. [2] __________________________________________________________________________________________
Mark scheme: 6 1350 1450 1, 1 If zero, award SC1 for correct but reversed 2
Q7 · NOT TO SCALE 5 cm x° 2 cm Calculate the value of x
7 NOT TO SCALE 5 cm x° 2 cm Calculate the value of x. Answer x = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 2 7 66.4[2......] 2 M1 for cos [….=] oe 5
Question 8
8 (a) Work out. (–6) – (–8) Answer(a) ................................................ [1] (b) Write in the missing number. –3 × ........... = 18 [1] __________________________________________________________________________________________
Mark scheme: 8 (a) [+] 2 1 (b) −6 1
Q9 · Use your calculator to work out (a) 4.22 + 5.82 , Answer(a)…
9 Use your calculator to work out (a) 4.22 + 5.82 , Answer(a) ................................................ [1] (b) 3 42.875 . Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 9 (a) 7.16[1…] 1 (b) 3.5 oe 1
Q10 · Write 270 000 in standard form
10 (a) Write 270 000 in standard form. Answer(a) ................................................ [1] (b) Work out the mean of 6.4 × 107 and 8.5 × 108. Write your answer in standard form. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 10 (a) 2.7 × 105 1 (b) 4.57 × 108 2 M1 for (6.4 × 107 + 8.5 × 108) ÷ 2 or better If 0 scored SC1 for figs 457 or 9.14 × 108
Q11 · D NOT TO 102° E SCALE 82° x° 64° A B C The diagram shows an isosceles triangle ABE and a…
11 D NOT TO 102° E SCALE 82° x° 64° A B C The diagram shows an isosceles triangle ABE and a quadrilateral BCDE. ABC is a straight line. Calculate the value of x. Answer x = ................................................. [3] __________________________________________________________________________________________
Mark scheme: 11 44 www 3 M1 for angle [EBC =] 360 – (82 + 102 + 64) oe or better M1FT for angle ABE = 180 – ‘their EBC’
Q12 · On the shape, draw the lines of symmetry
12 (a) On the shape, draw the lines of symmetry. [2] (b) Write down the order of rotational symmetry of the shape. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 12 (a) correct horizontal and vertical lines only 2 B1 for one line only correct and no extras (b) 2 1
Q13 · James buys a drink for 2 euros (€)
13 James buys a drink for 2 euros (€). Work out the cost of the drink in pounds (£) when £1 = €1.252 . Give your answer correct to 2 decimal places. Answer £ ................................................ [3] __________________________________________________________________________________________
Mark scheme: 13 1.60 cao 3 B2 for 1.597… or 1.6 or M1 for 2 ÷ 1.252 15 135
Question 14
5 7 . ÷14 Without using a calculator, work out 1 8 9 Show all your working and give your answer as a fraction in its lowest terms. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 15 135 14 B1 or 8 72 15 9 135 40 their × oe M1 or ÷ or equivalent division with 8 5 72 72 fractions with common denominators 27 3 or 3 cao A1 8 8
Question 15
15 Solve the equation. 3(x + 4) = 2(4x – 1) Answer x = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 15 2.8 oe 3 M2 for 12 + 2 = 8x – 3x or better or M1 for 3x + 12 or 8x – 2
Q16 · In a sale, the cost of a coat is reduced from $85 to $67.50
16 In a sale, the cost of a coat is reduced from $85 to $67.50 . Calculate the percentage reduction in the cost of the coat. Answer ............................................ % [3] __________________________________________________________________________________________
Mark scheme: 16 20.6 or 20.58 to 20.59 3 85 − 675. 67 5. M2 for × 100 or − 1 × 100 85 85 85 − 67 5. 675. or M1 for or × 100 85 85 675. − 85 If zero scored SC1 for × 100 85
Q17 · Y 6 A 5 4 B 3 2 1 x 0 1 2 3 4 5 6 7 8 (a) Write down the co-ordinates of A
17 y 6 A 5 4 B 3 2 1 x 0 1 2 3 4 5 6 7 8 (a) Write down the co-ordinates of A. Answer(a) (...................... , ......................) [1] (b) Write down the vector . Answer(b) = [1] f p (c) Work out. + 6 5 e- 4 2 o e o Answer(c) [1] f p (d) Work out. - 3 6 e 7 o Answer(d) [1] f p __________________________________________________________________________________________
Mark scheme: 17 (a) 1, 5 1 5 (b) 1 −2 6 (c) 1 −1 − 18 (d) 1 42
Q18 · 4 + 7.3 .18 (a) Calculate 19.56 - 3.51 Give your answer correct to 2 significant figures
6.4 + 7.3 .18 (a) Calculate 19.56 - 3.51 Give your answer correct to 2 significant figures. Answer(a) ................................................ [2] (b) Write the following numbers in order of size, smallest first. 5 57% 0.5077 0.507 9 Answer(b) ..................... < ..................... < ..................... < ..................... [2] __________________________________________________________________________________________
Mark scheme: 18 (a) [0].85 final answer 2 B1 for 0.853[5…] or 13.7 and 16.05 seen 5 (b) 0.507 0.5077 57% 2 M1 for 3 in the correct order 9 or B1 for [0].57 and [0].55… or 0.56
Q19 · Write down the prime number between 62 and 70
19 (a) Write down the prime number between 62 and 70. Answer(a) ................................................ [1] (b) Write 54 as the product of its prime factors. Answer(b) ................................................ [2] (c) Find the highest common factor (HCF) of 54 and 90. Answer(c) ................................................ [2] __________________________________________________________________________________________ Question 20 is printed on the next page.
Mark scheme: 19 (a) 67 1 (b) 2 × 33 oe 2 B1 for a correct factor tree or 2,3,3,3 identified (c) 18 cao 2 B1 for final answer of 2, 3, 6 or 9
Q20 · A cylinder has diameter 12 cm and length 18 cm
20 (a) A cylinder has diameter 12 cm and length 18 cm. NOT TO SCALE 12 cm 18 cm Calculate the volume of the cylinder. Answer(a) ......................................... cm3 [2] (b) NOT TO SCALE 14 cm 8 cm 20 cm (i) Calculate the surface area of this cuboid. Answer(b)(i) ......................................... cm2 [3] (ii) Write your answer to part (b)(i) in square millimetres. Answer(b)(ii) ........................................ mm2 [1]
Mark scheme: 20 (a) 2040 or 2036 or 2035.7 to 2036.1 2 M1 for π × 62 × 18 If zero, SC1 for answer of 8140 (after use of diameter) (b)(i) 1104 3 M2 for 2×(20×14 + 20×8 + 8×14) oe or M1 for 20×14 + 20×8 + 8×14 (b)(ii) their (b)(i) × 100 1FT
What was in this paper
The subtopics covered by these 20 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 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.