Cambridge IGCSE Mathematics 0580 — 2019 May/June Paper 1 · Variant 1
0580/11/M/J/19 · 22 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 scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write as a decimal
31 Write as a decimal. 4 ............................................ [1]
Mark scheme: Question Answer Marks Partial Marks 1 [0].75 1
Q2 · Work out $1.20 as a percentage of $16
2 Work out $1.20 as a percentage of $16. .........................................% [1]
Mark scheme: 2 7.5 oe 1
Q3 · Factorise 5y - 6py
3 Factorise 5y - 6py. ............................................ [1]
Mark scheme: 3 y (5 – 6p) final answer 1
Q4 · A bag contains green balls and red balls only
4 A bag contains green balls and red balls only. A ball is taken at random from the bag. The probability of taking a green ball is 0.38 . Write down the probability of taking (a) a red ball, ............................................ [1] (b) a blue ball. ............................................ [1]
Mark scheme: 4(a) [0].62 oe 1 4(b) 0 1
Q5 · On Monday the temperature at midday is 4 °C and the temperature at midnight is -3 °C
5 (a) On Monday the temperature at midday is 4 °C and the temperature at midnight is -3 °C. Work out the difference between these two temperatures. ........................................°C [1] (b) On Wednesday the temperature at midday is -1 °C. By 7 pm the temperature has fallen by 4 °C. Work out the temperature at 7 pm. ........................................°C [1]
Mark scheme: 5(a) 7 1 5(b) −5 1
Q6 · The volume of a cuboid is 180 cm3
6 The volume of a cuboid is 180 cm3. The base is a square of side length 6 cm. Calculate the height of this cuboid. ....................................... cm [2]
Mark scheme: 6 5 2 M1 for 180 ÷ 62 oe
Q7 · Write the following numbers in standard form
7 Write the following numbers in standard form. (a) 640 000 ............................................ [1] (b) 0.0006 ............................................ [1]
Mark scheme: 7(a) 6.4 × 105 1 7(b) 6 × 10-4 1
Question 8
8 Work out. 4 1 (a) - e-2o e5o [1] f p 3 (b) 6 e0o [1] f p
Mark scheme: 8(a) 3 1 −7 8(b) 18 1 0
Q9 · Asif and Ben share $2100 in the ratio Asif : Ben = 3 : 7
9 Asif and Ben share $2100 in the ratio Asif : Ben = 3 : 7. Work out how much Asif receives. $ ......................................... [2]
Mark scheme: 9 630 2 M1 for 2100 ÷ (3 + 7) [× 3] soi 210
Q10 · The length of a truck, L metres, is 8.2 m, correct to 1 decimal place
10 The length of a truck, L metres, is 8.2 m, correct to 1 decimal place. Complete this statement about the value of L. ..................... G L 1 ..................... [2]
Mark scheme: 10 8.15 8.25 2 B1 for each If 0 scored, SC1 for both correct but reversed
Question 11
11 Simplify. (a) t21 ÷ t7 ............................................ [1] (b) (u5)5 ............................................ [1]
Mark scheme: 11(a) t14 final answer 1 11(b) u25 final answer 1
Q12 · NOT TO SCALE 12 cm x cm 35° The diagram shows a right-angled triangle
12 NOT TO SCALE 12 cm x cm 35° The diagram shows a right-angled triangle. Calculate the value of x. x = ..................................... [2]
Mark scheme: 12 6.88 or 6.882 to 6.883 2 x M1 for sin 35 [ = ] oe or better 12
Q13 · 6 + 9.6213 p = 5.9 - 4.3 (a) By writing each number correct to 1 significant figure, work…
1.6 + 9.6213 p = 5.9 - 4.3 (a) By writing each number correct to 1 significant figure, work out an estimate for p. You must show all your working. ............................................ [2] (b) Calculate the exact value of p. ............................................ [1]
Mark scheme: 13(a) 2 + 10 2 M1 6 − 4 51 A1 13(b) 58.6 1
Q14 · 27 28 29 30 31 32 33 From the list of numbers, write down (a) a multiple of 7…
14 27 28 29 30 31 32 33 From the list of numbers, write down (a) a multiple of 7, ............................................ [1] (b) a cube number, ............................................ [1] (c) a prime number. ............................................ [1]
Mark scheme: 14(a) 28 1 14(b) 27 1 14(c) 29 or 31 1
Q15 · 215 Without using a calculator, work out +
5 215 Without using a calculator, work out + . 6 3 You must show all your working and give your answer as a mixed number in its simplest form. ............................................ [3]
Mark scheme: 15 5 4 M1 2 correct fractions with a suitable common + oe denominator 6k 6 6 1 A2 9 1 cao A1 for oe 2 6
Q16 · These are the first four terms of a sequence
16 These are the first four terms of a sequence. 5 8 11 14 (a) Write down the next term. ............................................ [1] (b) Find an expression, in terms of n, for the nth term. ............................................ [2]
Mark scheme: 16(a) 17 1 16(b) 3n + 2 oe final answer 2 B1 for 3n + k or cn + 2, c≠ 0
Q17 · Q B 75° NOT TO 18 cm 75° SCALE 6 cm 65° 40° 65° 40° A C P R 27 cm (a) Explain why…
17 Q B 75° NOT TO 18 cm 75° SCALE 6 cm 65° 40° 65° 40° A C P R 27 cm (a) Explain why triangle ABC and triangle PQR are similar. ............................................................................................................................................................ ............................................................................................................................................................ [1] (b) Find AC. AC = ............................. cm [2]
Mark scheme: 17(a) angle A = angle P, 1 accept any two of these angle B = angle Q, or any other correct reason angle C = angle R 17(b) 9 2 M1 for 27 ÷ 3 18 6 18 27 or B1 for or or or 6 18 27 18 1 2 or for [sf=] 3 or or or 1.5 oe 3 3
Q18 · A car travels at a constant speed of 20 m/s
18 A car travels at a constant speed of 20 m/s. Work out the time it takes for the car to travel 10 km. Give your answer in minutes and seconds. ..................... minutes ..................... seconds [3]
Mark scheme: 18 8 [min] 20 [sec] 3 10 M1 for [× 1000] soi 0.5 or 500 20 A1 for 500 [sec] or 8.33…[min] B1 for correctly converting their answer in seconds providing their answer is > 60 or decimal minutes to minutes and seconds
Q19 · On each shape, draw all the lines of symmetry
19 (a) On each shape, draw all the lines of symmetry. (i) [1] (ii) [2] (b) Write down the name of a quadrilateral that has • rotational symmetry of order 2 and • exactly two lines of symmetry. ............................................ [1]
Mark scheme: 19(a)(i) 2 correct lines of symmetry only 1 19(a)(ii) 4 correct lines of symmetry only 2 B1 for only 2 or 3 correct lines of symmetry 19(b) Rectangle or rhombus 1
Q20 · Change 3670 centimetres to metres
20 (a) Change 3670 centimetres to metres. .........................................m [1] (b) The scale drawing shows the positions of town S and town T. The scale is 1 centimetre represents 15 kilometres. North S North T Scale: 1 cm to 15 km (i) Find the actual distance between these two towns. .......................................km [2] (ii) Measure the bearing of town T from town S. ............................................ [1]
Mark scheme: 20(a) 36.7[0] 1 20(b)(i) 117 2 B1 for 7.8 20(b)(ii) 137 1
Q21 · The travel graph shows Michael’s journey from his home to the beach
21 The travel graph shows Michael’s journey from his home to the beach. Beach 12 10 8 Distance (km) 6 4 2 Home 0 08 00 08 30 09 00 09 30 10 00 10 30 11 00 Time (a) At what time did he start his journey? ............................................ [1] (b) On the journey he stopped for a rest. (i) Find the distance he was from home when he stopped for a rest. .......................................km [1] (ii) For how many minutes did he stop? ......................................min [1] (c) Explain how the graph shows that Michael travelled faster before he stopped than after he stopped. ............................................................................................................................................................ [1]
Mark scheme: 21(a) [0]8 10 1 21(b)(i) 8 1 21(b)(ii) 30 1 21(c) Line is steeper 1 accept any correct reason
Q22 · The diagram shows a point P and a line L
22 The diagram shows a point P and a line L. y 4 L 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x P – 1 – 2 – 3 – 4 (a) Write down the co-ordinates of point P. (.................... , ....................) [1] (b) Find the gradient of line L. ............................................ [2] (c) Write down the equation of line L in the form y = mx + c. y = ...................................... [2]
Mark scheme: 22(a) −3, −1 1 22(b) 1.5 oe 2 6 M1 for rise ÷ run e.g. 4 22(c) [y =] 1.5x − 1 oe 2 B1 for jx – 1 j ≠ 0 or 1.5x + k or their(b)x + k
What was in this paper
The subtopics covered by these 22 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Algebraic manipulation1Estimation1Gradient of linear graphs1Indices I1Introduction to probability1Limits of accuracy1Percentages1Rates1Ratio and proportion1Right-angled triangles1Scale drawings1Sequences1Similarity1Standard form1Surface area and volume1Symmetry1The four operations1Time1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2019 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.