Cambridge IGCSE Mathematics 0580 — 2019 May/June Paper 1 · Variant 2
0580/12/M/J/19 · 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 30 682 in words
1 Write 30 682 in words. .................................................................................................................................................................... [1]
Mark scheme: Question Answer Marks Partial Marks 1 Thirty thousand six hundred [and] 1 eighty-two
Q2 · Change 4365 metres into centimetres
2 Change 4365 metres into centimetres. ......................................... cm [1]
Mark scheme: 2 436 500 1
Q3 · Insert one pair of brackets to make this statement correct
3 Insert one pair of brackets to make this statement correct. 4 # 6 - 2 + 1 = 17 [1]
Mark scheme: 3 4 × (6 – 2) + 1 = 17 1
Q4 · The probability that Tommy has his calculator for his mathematics lesson is 0.4
4 The probability that Tommy has his calculator for his mathematics lesson is 0.4 . There are 120 mathematics lessons in one year. Work out an estimate of the number of mathematics lessons in one year that Tommy has his calculator. ............................................... [1]
Mark scheme: 4 48 1
Q5 · Subtract 123 from 1 million
5 (a) Subtract 123 from 1 million. ............................................... [1] (b) Subtract 9 from 2. ............................................... [1]
Mark scheme: 5(a) 999 877 1 5(b) −7 1
Question 6
6 Complete each statement. (a) A quadrilateral with only one pair of parallel sides is called a ............................................... . [1] (b) An angle greater than 90° but less than 180° is called ............................................... . [1]
Mark scheme: 6(a) Trapezium 1 6(b) Obtuse 1
Q7 · Shade five-eighths of this rectangle
7 (a) Shade five-eighths of this rectangle. [1] (b) Shade two more squares so that this grid has rotational symmetry of order 4. [1]
Mark scheme: 7(a) Any 15 blocks shaded 1 7(b) 2 correct squares shaded 1
Q8 · A d b c e X f g The diagram shows two parallel lines and a straight line crossing them
8 a d b c e X f g The diagram shows two parallel lines and a straight line crossing them. Write down, using letters from a to g, (a) the angle that is alternate to angle X, ............................................... [1] (b) the angle that is corresponding to angle X. ............................................... [1]
Mark scheme: 8(a) b 1 8(b) d 1
Q9 · 50 students each choose their favourite colour from a list of six colours
9 50 students each choose their favourite colour from a list of six colours. The results for the colours Red, Orange, Yellow, Green and Blue are shown in the tally chart. Complete the tally chart. Favourite colour Tally Red IIII IIII I Orange IIII IIII IIII Yellow IIII IIII Green IIII Blue III Purple [2]
Mark scheme: 9 2 B1 for 11, 14, 9, 5, 3 allow one error or omission or for 50 − 42 seen or for 8 purple
Q10 · Write 0.047 883 correct to 2 significant figures
10 (a) Write 0.047 883 correct to 2 significant figures. ............................................... [1] (b) Write 0.005 27 in standard form. ............................................... [1]
Mark scheme: 10(a) 0.048 cao 1 10(b) 5.27 × 10− 3 1
Q11 · Find the highest common factor (HCF) of 90 and 48
11 Find the highest common factor (HCF) of 90 and 48. ............................................... [2]
Mark scheme: 11 6 2 M1 for 2 × 32 × 5 or 24 × 3 or for 2 × 3 as final answer or B1 for 2 or 3 as final answer
Q12 · NOT TO SCALE 3.5 cm 8.4 cm Calculate the area of this triangle
12 NOT TO SCALE 3.5 cm 8.4 cm Calculate the area of this triangle. ........................................ cm2 [2]
Mark scheme: 12 14.7 2 1 M1 for × 8.4 × 3.5 oe 2
Q13 · X° NOT TO 23 m SCALE 6.2 m The diagram shows a right-angled triangle
13 x° NOT TO 23 m SCALE 6.2 m The diagram shows a right-angled triangle. Calculate the value of x. x = .............................................. [2]
Mark scheme: 13 74.4 or 74.36… 2 6.2 M1 for cos[x =] oe 23
Q14 · The diagram shows a solid cuboid made of identical cubes
14 (a) The diagram shows a solid cuboid made of identical cubes. NOT TO SCALE Work out the number of cubes in the cuboid. ............................................... [1] (b) The diagram shows the nets of two solids. Write down, under each net, the mathematical name for the solid. ................................................ ................................................ [2]
Mark scheme: 14(a) 160 1 14(b) Cone, [square based] pyramid 2 B1 for each
Q15 · A box contains 22 coloured pencils
15 A box contains 22 coloured pencils. 6 pencils are pink, 9 pencils are blue and 7 pencils are yellow. (a) Write down the ratio pink pencils : not pink pencils. Give your answer in its simplest form. ...................... : ...................... [2] (b) A pencil is taken at random from the box. Write down the probability that this pencil is green. ............................................... [1]
Mark scheme: 15(a) 3 : 8 cao 2 B1 for 6 : 16 or 8 2 3 1: or 1:2 or 1:2.67 or :1 or 0.375:1 3 3 8 If 0 scored, SC1 for 8 : 3 15(b) 0 1
Question 16
16 (a) Expand. x 2 ( x - 7) ............................................... [2] (b) Factorise. y 2 + y ............................................... [1]
Mark scheme: 16(a) x3 – 7x2 final answer 2 B1 for x 3 − jx k j ≠ 0 or nx p − 7 x 2 n ≠ 0 as answers If 0 scored, SC1 for correct answer seen then spoilt 16(b) y(y + 1) final answer 1
Q17 · Show that there is not a square number between 50 and 60
17 (a) Show that there is not a square number between 50 and 60. [2] (b) Write down a prime number between 50 and 60. ............................................... [1]
Mark scheme: 17(a) 7 2 = 49 and 8 2 = 64 2 B1 for 7 2 = 49 or 8 2 = 64 or 49 and 64 or √49 = 7 and √64 = 8 or values of at least √50 (or √51) and√59 (or √60) without further comment 17(b) 53 or 59 1
Q18 · A machine always takes 5 minutes to paint an 80 metre white line on a road
18 A machine always takes 5 minutes to paint an 80 metre white line on a road. (a) Work out the number of metres painted in 45 minutes. ........................................... m [1] (b) Work out the number of minutes taken to paint a 2.8 km line. ........................................ min [2]
Mark scheme: 18(a) 720 1 18(b) 175 cao 2 2.8 × 1000[× 5] or 2.8 × 1000 × 45 M1 for 80 their (a) or B1 for figs 175
Question 19
19 Simplify. (a) 5m 2 # 2m 3 ............................................... [2] 3 (b) x 8 ` j ............................................... [1]
Mark scheme: 19(a) 10m 5 final answer 2 B1 for 10 m k or km 5 as final answer 19(b) x 24 final answer 1
Q20 · ' 7 .20 Without using a calculator, work out 2 14 3 You must show all your working and…
' 7 .20 Without using a calculator, work out 2 14 3 You must show all your working and give your answer as a mixed number in its simplest form. ............................................... [3]
Mark scheme: 20 9 7 63 12 M2 9 × or ÷ oe with common B1 for oe seen 4 3 28 28 4 denominator 9 7 or M1 for their × 4 3 1 A1 5 cao 4
Q21 · NOT TO SCALE 9 cm The diagram shows a semicircle with diameter 9 cm
21 NOT TO SCALE 9 cm The diagram shows a semicircle with diameter 9 cm. Calculate the total perimeter of this semicircle. ......................................... cm [3]
Mark scheme: 21 23.1 or 23.137 to 23.139 or 23.14 3 9π M2 for oe 2 or M1 for 9π oe
Q22 · Gerry and Alain run around a running track
22 Gerry and Alain run around a running track. To run around the track once • Gerry always takes 90 seconds • Alain always takes 105 seconds. They start together at the same point. After how many minutes are they next together at that point? ........................................ min [3]
Mark scheme: 22 10.5 oe isw 3 B2 for 630 or M1 for 630k or B1 for 3 correct multiples of each
Q23 · Rearrange this formula to make x the subject
23 Rearrange this formula to make x the subject. 5x 2 - 3y = 4y + 8 x = .............................................. [3]
Mark scheme: 23 7 y + 8 3 M1 for 5 x 2 = 4 y + 3 y + 8 or better x = oe final answer 5 2 their (4 y + 3 y ) + 8 M1 for x = or better 5 their (7 y ) + 8 M1 for x = 5 An incorrect final answer scores a maximum of 2
Q24 · B A C (a) (i) Using a straight edge and compasses only, construct the perpendicular…
24 B A C (a) (i) Using a straight edge and compasses only, construct the perpendicular bisector of AB. Show all your construction arcs. [2] (ii) Using a ruler and compasses only, construct the locus of points inside the triangle that are 4 cm from C. [1] (b) Shade the region inside the triangle that is • more than 4 cm from C and • closer to B than to A. [1]
Mark scheme: 24(a)(i) Ruled bisector of AB with 2 pairs of 2 M1 for 2 pairs of correct arcs correct arcs or B1 for correct ruled bisector with incomplete or no arcs 24(a)(ii) Arc centre C radius 4 cm 1 24(b) Closed region shaded 1
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.
3Area and perimeter2Fractions, decimals and percentages2The four operations2Algebraic manipulation1Angles1Classifying statistical data1Equations1Geometrical constructions1Geometrical terms1Indices I1Limits of accuracy1Percentages1Rates1Ratio and proportion1Right-angled triangles1Surface area and volume1Time1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2019 May/June, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.