Cambridge IGCSE Mathematics 0580 — 2018 May/June Paper 1 · Variant 3
0580/13/M/J/18 · 24 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 75% as a fraction in its simplest form
1 Write 75% as a fraction in its simplest form. ................................................... [1]
Mark scheme: Question Answer Marks Partial Marks 1 3 1 4
Question 2
2 Factorise. w + w3 ................................................... [1]
Mark scheme: 2 w(1 + w2) final answer 1
Q3 · Liz takes 65 seconds to run 400 m
3 Liz takes 65 seconds to run 400 m. Calculate her average speed. ............................................ m/s [1]
Mark scheme: 3 2 1 6.15 or 6.153 to 6.154 or 6 13
Question 4
4 Calculate. 182 0.5 + 1.75 ................................................... [1]
Mark scheme: 4 12 1
Q5 · Work out the value of 4 - 2
5 Work out the value of 4 - 2 . ................................................... [1]
Mark scheme: 5 1 1 [0].0625 or 16
Q6 · Write down the mathematical name of the type of angle marked
6 (a) Write down the mathematical name of the type of angle marked. ................................................... [1] (b) A and B are points on the circumference of a circle, centre O. O B A Write down the mathematical name of the line AB. ................................................... [1]
Mark scheme: 6(a) acute 1 6(b) diameter 1
Q7 · Write these numbers in order, starting with the smallest
7 Write these numbers in order, starting with the smallest. 4 1 26% 0.24 15 4 ..................... 1 ..................... 1 ..................... 1 ..................... [2] smallest
Mark scheme: 7 1 4 2 B1 for three in the correct order or [0].24 26[%] M1 for .266/.27 .26 .25 seen 4 15
Q8 · Complete the list of factors of 36
8 Complete the list of factors of 36. 1, 2, .................................................................................................................. , 36 [2]
Mark scheme: 8 3, 4, 6, 9, 12, 18 2 B1 for list with one or two errors or omissions or for a complete list of products
Q9 · Increase $22 by 15%
9 Increase $22 by 15%. $ ................................................. [2]
Mark scheme: 9 25.3[0] 2 15 M1 for 22 × oe or better 100
Q10 · Write 209 802 correct to the nearest thousand
10 (a) Write 209 802 correct to the nearest thousand. ................................................... [1] (b) Write 4123 correct to 3 significant figures. ................................................... [1]
Mark scheme: 10(a) 210 000 cao 1 10(b) 4120 cao 1
Q11 · Jez and Soraya share $2500 in the ratio Jez : Soraya = 7 : 3
11 Jez and Soraya share $2500 in the ratio Jez : Soraya = 7 : 3. Work out how much Soraya receives. $ ................................................. [2]
Mark scheme: 11 750 2 M1 for 2500 ÷ (7 + 3) [× 3]
Q12 · The probability that Kim wins a game is 0.72
12 The probability that Kim wins a game is 0.72 . In one year Kim will play 225 games. Work out an estimate of the number of games Kim will win. ................................................... [2]
Mark scheme: 12 162 2 M1 for 225 × 0.72 oe
Q13 · Write .482 # 10 -3 as an ordinary number
13 (a) Write .482 # 10 -3 as an ordinary number. ................................................... [1] (b) Write 52 million in standard form. ................................................... [1]
Mark scheme: 13(a) [0].004 82 cao 1 13(b) 5.2 × 107 1
Question 14
14 Solve. 1 - p = 4 3 p = ............................................ [2]
Mark scheme: 14 – 11 2 M1 for 1 − p = 3 × 4 or better p 1 or − = 4 − or better 3 3
Q15 · The mass, m kilograms, of a package is 6.2 kg, correct to 1 decimal place
15 The mass, m kilograms, of a package is 6.2 kg, correct to 1 decimal place. Complete the statement about the value of m. ..................... G m 1 ..................... [2]
Mark scheme: 15 6.15 6.25 2 B1 for each or SC1 both correct but reversed
Q16 · NOT TO 16 cm x cm SCALE 35° The diagram shows a right-angled triangle
16 NOT TO 16 cm x cm SCALE 35° The diagram shows a right-angled triangle. Calculate the value of x. x = ............................................ [2]
Mark scheme: 16 9.18 or 9.177… 2 x M1 for sin 35 = or better 16
Q17 · The diagram shows a cuboid
17 The diagram shows a cuboid. NOT TO 8 cm SCALE 4 cm 10 cm Work out the surface area of this cuboid. ............................................cm2 [3]
Mark scheme: 17 304 3 M2 for [2 ×]( (10 × 4) + (10 × 8) + (4 × 8)) or M1 for one of 10 × 4 or 10 × 8 or 4 × 8
Q18 · 118 Without using a calculator, work out ' 1
2 118 Without using a calculator, work out ' 1 . 3 5 You must show all your working and give your answer as a fraction in its simplest form. ................................................... [3]
Mark scheme: 18 6 B1 18 accept equivalent fractions e.g. 5 15 2 5 M1 10 18 × their or ÷ oe 3 6 15 15 5 A1 cao 9
Question 19
19 (a) Work out. 5 2 (i) + c- 1m c 6 m [1] f p - 5 (ii) 4 c 2m [1] f p (b) y 4 3 P 2 1 x 0 –4 –3 –2 –1 1 2 3 4 –1 –2 –3 –4 4 P is the point (-1, 2) and PQ = c- 3m. Find the co-ordinates of Q. (................ , ................) [1]
Mark scheme: 19(a)(i) 7 1 5 19(a)(ii) − 20 1 8 19(b) 3, −1 1
Q20 · Line L has the equation y = 5x + 12
20 (a) Line L has the equation y = 5x + 12 . Write down the gradient of line L. ................................................... [1] (b) Another line, M, has the equation y = 8x + 3 . Write down the equation of the line parallel to line M that passes through the point (0, 6). ................................................... [2]
Mark scheme: 20(a) 5 1 20(b) y = 8x + 6 2 M1 for y = 8x + k, k ≠ 3 or 6 or y = mx + 6, m ≠ 0 or 8 or for answer of 8x + 6
Q21 · Change 568 000 cm into metres
21 (a) Change 568 000 cm into metres. ............................................... m [1] (b) The scale drawing shows the positions of two towns, A and B. The scale is 1 centimetre represents 5 kilometres. North B North A Scale : 1 cm to 5 km (i) Measure the bearing of town B from town A. ................................................... [1] (ii) Find the actual distance, in kilometres, from town A to town B. ............................................. km [2]
Mark scheme: 21(a) 5680 1 21(b)(i) [0]68 1 21(b)(ii) 46 2 B1 for 9.2 [cm]
Q22 · Work out the area of each shape
22 Work out the area of each shape. (a) 8.4 cm NOT TO SCALE 3.5 cm ............................................cm2 [2] (b) 18 cm NOT TO SCALE 12 cm 10 cm ............................................cm2 [2]
Mark scheme: 22(a) 29.4 2 M1 for 8.4 × 3.5 22(b) 168 2 M1 for 12 × (10 +18) ÷ 2 oe
Q23 · Solve the simultaneous equations
23 Solve the simultaneous equations. You must show all your working. 3x - 2y = 23 2x + 5y = 9 x = ............................................ y = ............................................ [4] Question 24 is printed on the next page.
Mark scheme: 23 correctly multiplying both equations to M1 reach the same coefficient for one variable correctly adding or subtracting the M1 equations [x =] 7 A1 [y =] −1 A1 If zero scored then SC1 for both answers correct and no supporting working or for two answers that satisfy one of the original equations
Q24 · ABCD is a quadrilateral
24 ABCD is a quadrilateral. A D B C (a) Using a straight edge and compasses only, construct the perpendicular bisector of BC. Show all your construction arcs. [2] (b) Using a straight edge and compasses only, construct the bisector of angle BCD. Show all your construction arcs. [2] (c) Shade the region inside ABCD that is • nearer to B than to C and • nearer to CD than to BC. [1]
Mark scheme: 24(a) correct perpendicular bisector with 2 B1 for correct perpendicular bisector correct arcs without any arcs or with incorrect arcs 24(b) correct angle bisector with correct arcs 2 B1 for correct angle bisector without any arcs or with incorrect arcs 24(c) correct region shaded 1 Dep on B1, B1
What was in this paper
The subtopics covered by these 24 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Equations2Fractions, decimals and percentages2Limits of accuracy2Algebraic manipulation1Angles1Equations of linear graphs1Geometrical constructions1Introduction to probability1Ordering1Percentages1Powers and roots1Rates1Ratio and proportion1Right-angled triangles1Scale drawings1Standard form1The four operations1Types of number1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2018 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.