Cambridge IGCSE Mathematics 0580 — 2017 May/June Paper 1 · Variant 1
0580/11/M/J/17 · 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write, in figures, the number seventy thousand and twenty
1 Write, in figures, the number seventy thousand and twenty. .............................................. [1]
Mark scheme: Question Answer Marks Part marks 1 70 020 cao 1
Q2 · Write, as a decimal, the value of 5-3
2 Write, as a decimal, the value of 5-3. .............................................. [1]
Mark scheme: 2 [0].008 1
Q3 · The thickness of one sheet of paper is 8 # 10-3 cm
3 The thickness of one sheet of paper is 8 # 10-3 cm. Work out the thickness of 250 sheets of paper. ........................................ cm [1]
Mark scheme: 3 2 1
Question 4
4 Simplify. (x2) 5 .............................................. [1]
Mark scheme: 4 x10 1
Q5 · A B opposite congruent reflected translated Choose the mathematical word from the list to…
5 A B opposite congruent reflected translated Choose the mathematical word from the list to complete this statement. Pentagon A is ............................................................ to pentagon B. [1]
Mark scheme: 5 Congruent 1
Q6 · 31 33 35 37 39 From the list, write down a prime number
6 31 33 35 37 39 From the list, write down a prime number. .............................................. [1]
Mark scheme: 6 31 or 37 1
Q7 · Write 23.4571 correct to (a) 4 significant figures…
7 Write 23.4571 correct to (a) 4 significant figures, .............................................. [1] (b) the nearest 10. .............................................. [1]
Mark scheme: 7(a) 23.46 cao 1 7(b) 20 cao 1
Question 8
8 Factorise completely. 12n2 - 4mn .............................................. [2]
Mark scheme: 8 4n(3n – m) final answer 2 B1 for 4(3n2 – mn) or n(12n – 4m) or 2n(6n − 2m) or 2(6n2 – 2mn)
Q9 · Find the highest common factor (HCF) of 126 and 150
9 Find the highest common factor (HCF) of 126 and 150. .............................................. [2]
Mark scheme: 9 6 2 B1 for answer 2 or 3 or 2 × 3 or M1 for prime factors of 126 and 150 seen
Q10 · The table shows the temperatures in five places at 10 am one day in January
10 The table shows the temperatures in five places at 10 am one day in January. Place Temperature (°C) Helsinki -7 Chicago -10 London 3 Moscow -4 Bangkok 26 (a) Which place was the coldest? .............................................. [1] (b) At 2 pm the temperature in Helsinki had increased by 4 °C. Write down the temperature in Helsinki at 2 pm. .........................................°C [1]
Mark scheme: 10(a) Chicago 1 10(b) −3 1
Q11 · Expand the brackets and simplify
11 Expand the brackets and simplify. 7 (2x + 3y ) - x (14 - y) .............................................. [2]
Mark scheme: 11 21y + xy or y(21 + x) 2 B1 for 14x + 21y or −14x + xy final answer or answer of ky + xy
Q12 · The mass, m kilograms, of an elephant is 3570 kg, correct to the nearest 5 kg
12 The mass, m kilograms, of an elephant is 3570 kg, correct to the nearest 5 kg. Complete this statement about the value of m. ..................... G m 1 ..................... [2]
Mark scheme: 12 3567.5 1 3572.5 1 SC1 for both correct but reversed
Q13 · 5 - 3 a = b = c- 1m c- 4m Write a + 2b as a single vector
13 5 - 3 a = b = c- 1m c- 4m Write a + 2b as a single vector. [2] f p
Mark scheme: 13 −1 2 −6 k B1 for seen or answer or −9 −8 −9 −1 k
Q14 · Manuel changes 5000 Mexican Pesos to dollars
14 Manuel changes 5000 Mexican Pesos to dollars. He receives $336. Complete this statement about the exchange rate. Give your answer correct to 2 decimal places. $1 = ................................. Mexican Pesos [2]
Mark scheme: 14 14.88 2 M1 for 5000 ÷ 336 or B1 for 14.881 or 14.880[9...] or 14.9
Q15 · Maria asks 50 students in her school when their birthday is
15 Maria asks 50 students in her school when their birthday is. She records the information in the table. Jan to Mar Apr to Jun Jul to Sep Oct to Dec Number of birthdays 9 21 14 6 (a) Find the relative frequency of a student having a birthday in April, May or June. .............................................. [1] (b) There are 750 students in the school. Estimate the number of students who have a birthday in April, May or June. .............................................. [1]
Mark scheme: 15(a) 21 1 oe 50 15(b) 315 1FT FT their (a) × 750 provided 0 < their (a) < 1
Q16 · 512 16 Work out 2
3 512 16 Work out 2 . 6 Write your answer as a fraction in its lowest terms. .............................................. [2]
Mark scheme: 16 2 2 8 4 B1 for or 9 36 18
Q17 · A = 4 rr 2 Make r the subject of this formula
17 A = 4 rr 2 Make r the subject of this formula. r = ....................................... [2]
Mark scheme: 17 A 1 A 2 A or oe M1 for r2 = or 2r π = A 4π 2 π 4π A A or 4r2 = or πr2 = π 4
Question 18
18 (a) Work out. 3 + 2 # - 4 .............................................. [1] (b) In each of these, insert one pair of brackets to make the statement correct. (i) 3 # 5 + 2 + 2 = 23 [1] (ii) 12 ÷ 4 + 2 = 2 [1]
Mark scheme: 18(a) –5 1 18(b)(i) 3 × (5 + 2) + 2 = 23 1 18(b)(ii) 12 ÷ (4 + 2) = 2 1
Q19 · 519 Without using a calculator, work out 1 +
2 519 Without using a calculator, work out 1 + . 3 7 Write down all the steps of your working and give your answer as a mixed number in its simplest form. .............................................. [3]
Mark scheme: 19 14 ( or 35 ) 15 M1 14 k ( or 35k ) 15k + accept + 21 21 21k 21k 8 A2 50 8 29 29 2 cao or A1 for or 1 or or 1 21 21 21 21 21
Q20 · Solve the simultaneous equations
20 Solve the simultaneous equations. You must show all your working. 5x - 2y = 24 7x + 4y = -14 x = ....................................... y = ....................................... [3]
Mark scheme: 20 Correctly eliminating one variable M1 [x =] 2 A1 [y =] −7 A1 If zero scored, SC1 for 2 values satisfying one of the original equations SC1 for both correct but no working
Q21 · A cuboid has length 6 cm, width 5 cm and height 3 cm
21 A cuboid has length 6 cm, width 5 cm and height 3 cm. On the 1 cm2 grid, complete the net of the cuboid. The base is drawn for you. [3]
Mark scheme: 21 Complete correct ruled net 3 B2 for 4 correct rectangles in correct places or B1 for 2 correct side rectangles in correct places
Q22 · Six students revise for a test
22 Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test. 50 45 40 Mark 35 30 25 0 1 2 3 4 5 6 7 8 9 10 Time (hours) (a) The data for two more students is shown in the table. Time (hours) 4.5 6.5 Mark 33 35 Plot these two points on the scatter diagram. [1] (b) What type of correlation is shown on the scatter diagram? .............................................. [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) Another student spent 5.5 hours revising. Estimate a mark for this student. .............................................. [1]
Mark scheme: 22(a) Points plotted at 1 (4.5, 33) and (6.5, 35) 22(b) Positive 1 22(c) Correct ruled line 1 22(d) 33.5 to 37.5 1FT FT from their line provided positive gradient
Q23 · B C A The diagram shows the positions of three points, A, B and C
23 B C A The diagram shows the positions of three points, A, B and C. (a) Using a ruler and compasses only, construct (i) the perpendicular bisector of the line AB, [2] (ii) the locus of all points that are 3 cm from C. [2] (b) Shade the region that is • closer to A than to B and • less than 3 cm from C. [1]
Mark scheme: 23(a)(i) Correct ruled bisector of AB with 2 pairs of arcs 2 B1 for correct bisector with no or incorrect arcs or 2 pairs of correct arcs 23(a)(ii) Complete circle, 2 B1 for an arc of correct radius or a circle radius 3 cm, centre C of incorrect radius 23(b) Correct region shaded 1 dep on at least B1 in both parts
Q24 · The diagram shows a notice board
24 The diagram shows a notice board. NOT TO SCALE 74 cm The board is in the shape of a semicircle joined to a square with side 74 cm. (a) Calculate (i) the perimeter of the board, ........................................ cm [3] (ii) the area of the board. .......................................cm2 [3] (b) The board is a prism that is 5 cm thick. Calculate the volume of the board. .......................................cm3 [1]
Mark scheme: 24(a)(i) 338 or 338.3 nfww 3 M1 for 3 × 74 or 338.2 to 338.26 and M1 for 74 × π ÷ 2 24(a)(ii) 7630 nfww 3 M1 for 742 or 7626 to 7627 π× 37 2 and M1 for 2 24(b) 38100 nfww 1FT FT their (a)(ii) × 5 or 38200 or 38150 or 38130 to 38140
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.
3Types of number3Limits of accuracy2Powers and roots2Ratio and proportion2Area and perimeter1Compound shapes and parts of shapes1Equations1Fractions, decimals and percentages1Geometrical constructions1Indices I1Introduction to probability1Ordering1Scatter diagrams1The four operations1Transformations1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2017 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.