Cambridge IGCSE Mathematics 0580 — 2019 May/June Paper 1 · Variant 3
0580/13/M/J/19 · 25 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 3.058 correct to 3 significant figures
1 Write 3.058 correct to 3 significant figures. .................................................... [1]
Mark scheme: Question Answer Marks Partial Marks 1 3.06 cao 1
Q2 · Write 0.45 as a fraction in its simplest form
2 Write 0.45 as a fraction in its simplest form. .................................................... [1]
Mark scheme: 2 9 1 20
Q3 · Factorise 2x 2 - x
3 Factorise 2x 2 - x . .................................................... [1]
Mark scheme: 3 x(2x – 1) 1
Q4 · Find the co-ordinates of the point where the line y = 3x - 8 crosses the y-axis
4 Find the co-ordinates of the point where the line y = 3x - 8 crosses the y-axis. ( ....................... , ........................) [1]
Mark scheme: 4 (0, −8) 1
Q5 · Giulio’s reaction times are measured in two games
5 Giulio’s reaction times are measured in two games. In the first game his reaction time is 13 of a second. In the second game his reaction time is 18 of a second. Find the difference between the two reaction times. .................................................. s [1]
Mark scheme: 5 5 1 or 0.208 or 0.2083… 24
Q6 · The probability that Alex wins a prize is 0.27
6 The probability that Alex wins a prize is 0.27 . Find the probability that Alex does not win a prize. .................................................... [1]
Mark scheme: 6 0.73 oe 1
Q7 · The table shows the different methods of travel for 20 people going to work
7 The table shows the different methods of travel for 20 people going to work. Method of travel Frequency Car 10 Walk 5 Bike 3 Bus 2 Which type of average, mean, median or mode, can be used for this information? ................................................... [1]
Mark scheme: 7 Mode 1
Question 8
8 Calculate. (a) - 12 ' - 2 .................................................... [1] (b) 3 2 3 + 2 .................................................... [1]
Mark scheme: 8(a) 6 1 8(b) 2.15 or 2.154.... 1
Question 9
9 Simplify. 4x - 12y + 10x + 25y .................................................... [2]
Mark scheme: 9 14x + 13y final answer 2 B1 for 14x or 13y as answers If 0 scored, SC1 for correct answer seen then spoilt
Q10 · Here is a list of numbers
10 Here is a list of numbers. 21 23 13 31 121 51 0.7 From this list, write down (a) a prime number, .................................................... [1] (b) an irrational number. .................................................... [1]
Mark scheme: 10(a) 31 or 121 1 10(b) 13 1
Q11 · 1 11 p = q = e0o e6o Work out 2p + 3q
5 1 11 p = q = e0o e6o Work out 2p + 3q . [2] f p
Mark scheme: 11 13 2 10 3 13 n B1 for or or or 18 0 18 m 18
Q12 · Write down the type of correlation you would expect for the following
12 Write down the type of correlation you would expect for the following. (a) The average speed of a train and the time taken for a journey. .................................................... [1] (b) The distance travelled by a car and the amount of fuel used. .................................................... [1]
Mark scheme: 12(a) Negative 1 12(b) Positive 1
Q13 · The scale drawing shows a rock, R
13 The scale drawing shows a rock, R. The scale is 1 centimetre represents 30 metres. A lighthouse, L, is 210 m from R, on a bearing of 125°. On the diagram, mark the position of L. North R Scale : 1 cm to 30 m [2]
Mark scheme: 13 L correctly marked 2 B1 for 6.8 cm to 7.2 cm B1 for 123˚ to 127˚
Q14 · Rearrange 2 (w + h ) = P to make w the subject
14 Rearrange 2 (w + h ) = P to make w the subject. w = .................................................... [2]
Mark scheme: 14 P P − 2 h 2 P [w =] – h or final M1 for w + h = or 2w + 2h = P 2 2 2 answer
Q15 · Genaro measures the length, l cm, of his desk as 120 cm, correct to the nearest centimetre
15 Genaro measures the length, l cm, of his desk as 120 cm, correct to the nearest centimetre. Complete the statement about the value of l. ............................ G l 1 ............................ [2]
Mark scheme: 15 119.5 120.5 2 B1 for each If 0 scored, SC1 for both correct but reversed
Question 16
16 Solve. 7x - 5 = 16 x = .................................................... [2]
Mark scheme: 16 3 2 5 16 M1 for 7x = 16 + 5 or x − = or better 7 7
Q17 · 717 Without using a calculator, work out #
12 717 Without using a calculator, work out # . 35 9 You must show all your working and give your answer as a fraction in its simplest form. .................................................... [2]
Mark scheme: 17 84 4 7 12 1 4 1 M1 Accept any correct cancelling or × or × or × 315 35 3 5 9 5 3 4 A1 cao 15
Q18 · Q 7.7 cm B C R NOT TO SCALE 5.5 cm P A a cm D 9.8 cm S Shape ABCD is similar to shape PQRS
18 Q 7.7 cm B C R NOT TO SCALE 5.5 cm P A a cm D 9.8 cm S Shape ABCD is similar to shape PQRS. Work out the value of a. a = .................................................... [2]
Mark scheme: 18 7 2 5.5 7.7 9.8 7.7 M1 for or or or oe 7.7 5.5 7.7 9.8
Q19 · Harry invests $800 for 2 years at a rate of 3% per year compound interest
19 Harry invests $800 for 2 years at a rate of 3% per year compound interest. Calculate the amount of interest he receives at the end of the 2 years. $ ................................................. [3]
Mark scheme: 19 48.72 3 2 3 M1 for 800 1 + oe 100 A1 for 848.72
Q20 · Solve the simultaneous equations
20 Solve the simultaneous equations. You must show all your working. 5x - 2y = 26 7x + 6y = 10 x = .................................................... y = .................................................... [3]
Mark scheme: 20 For correct method to equate M1 coefficients and eliminate one variable [x =] 4 A2 A1 for each [y =] −3 If 0 scored, SC1 for 2 values satisfying one of the original equations SC1 if no working shown, but 2 correct answers given
Q21 · Write down the next term in each sequence
21 (a) Write down the next term in each sequence. (i) 12, 7, 2, -3, -8, ............... [1] (ii) 4, 7, 13, 25, 49, ............... [1] (b) Find an expression, in terms of n, for the nth term of this sequence. 5, 8, 11, 14, … .................................................... [2]
Mark scheme: 21(a)(i) −13 1 21(a)(ii) 97 1 21(b) 3n + 2 oe final answer 2 B1 for 3n + j or kn + 2 k ≠ 0
Q22 · A closed box in the shape of a cuboid has length 5 cm, width 4 cm and height 2 cm
22 A closed box in the shape of a cuboid has length 5 cm, width 4 cm and height 2 cm. (a) Calculate the volume of the box. ............................................. cm3 [2] (b) On the 1 cm2 grid, complete the net of this box. [2]
Mark scheme: 22(a) 40 2 M1 for 5 × 4 × 2 22(b) 4 correct rectangles only, added in 2 B1 for 2 correct rectangles in correct correct positions positions
Q23 · K J NOT TO E D SCALE O A C F B H G The diagram shows two regular pentagons
23 K J NOT TO E D SCALE O A C F B H G The diagram shows two regular pentagons. Pentagon FGHJK is an enlargement of pentagon ABCDE, centre O. Find angle AEK. Angle AEK = .................................................... [4]
Mark scheme: 23 126 4 360 − 180 – ( 360 ÷ 5 ) M3 for or 2 360 − 180 × ( 5 − 2 ) ÷ 5 2 180 × ( 5 − 2 ) 360 or M2 for or 180 – 5 5 360 or M1 for 180 × (5 – 2) or 5
Q24 · D NOT TO SCALE 15 m 38° A B 10.7 m C A vertical flagpole, BD, stands on horizontal ground…
24 D NOT TO SCALE 15 m 38° A B 10.7 m C A vertical flagpole, BD, stands on horizontal ground and is held by two ropes, AD and CD. AD = 15m , BC = 10.7m and angle DAB = 38 ° . (a) Using trigonometry, calculate BD. BD = ................................................. m [2] (b) Calculate CD. CD = ................................................. m [2]
Mark scheme: 24(a) 9.23 or 9.234 to 9.235 2 BD M1 for sin38 = or better 15 24(b) 14.1 or 14.13...... 2 FT their (a) M1 ( their (a))2 + 10.72
Q25 · Jason spends 480 minutes at school each day
25 Jason spends 480 minutes at school each day. The pie chart shows the time he spends in three of his lessons. Maths 45° English Science (a) Measure the sector angle for science. .................................................... [1] (b) Work out the time, in minutes, Jason spends in English. .............................................. min [2] (c) Jason spends 100 minutes in geography and the rest of the day is free time. Complete the pie chart. [2]
Mark scheme: 25(a) 84˚ 1 25(b) 60 2 45 M1 for × 480 oe 360 25(c) [Geography] sector 75˚ 2 100 100 M1 for × 360 oe or × 45 480 their (b)
What was in this paper
The subtopics covered by these 25 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Equations2Fractions, decimals and percentages2Limits of accuracy2The four operations2Angles1Averages and range1Equations of linear graphs1Introduction to probability1Percentages1Right-angled triangles1Scale drawings1Scatter diagrams1Sequences1Similarity1Statistical charts and diagrams1Surface area and volume1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2019 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.