Cambridge IGCSE Mathematics 0580 — 2017 May/June Paper 1 · Variant 3
0580/13/M/J/17 · 21 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 · Change $400 into euros (€) using the exchange rate $1 = €0.935
1 Change $400 into euros (€) using the exchange rate $1 = €0.935 . € ................................................ [1]
Mark scheme: Question Answer Marks Part marks 1 374 1
Q2 · B O C A A, B and C are points on the circumference of a circle, centre O
2 B O C A A, B and C are points on the circumference of a circle, centre O. Write down the mathematical name for (a) the line OA, ................................................... [1] (b) the line BC. ................................................... [1]
Mark scheme: 2(a) radius 1 2(b) chord 1
Q3 · Write 16% as (a) a decimal, ..................................................
3 Write 16% as (a) a decimal, ................................................... [1] (b) a fraction. ................................................... [1]
Mark scheme: 3(a) [0].16 1 3(b) 16 1 oe 100
Q4 · Green Lane School ends each day at 3.45 pm
4 Green Lane School ends each day at 3.45 pm. (a) Show this time on the clock. 12 11 1 10 2 9 3 8 4 7 5 6 [1] (b) Write 3.45 pm using the 24-hour clock. ................................................... [1]
Mark scheme: 4(a) Time correctly drawn on clock face 1 4(b) 15 45 1
Q5 · Write 5367 correct to the nearest hundred
5 (a) Write 5367 correct to the nearest hundred. ................................................... [1] (b) Write 42.3478 correct to 3 decimal places. ................................................... [1]
Mark scheme: 5(a) 5400 cao 1 5(b) 42.348 cao 1
Q6 · 25 students chose their favourite drink
6 25 students chose their favourite drink. The results are listed below. Tea Hot chocolate Coffee Milkshake Tea Hot chocolate Coffee Hot chocolate Hot chocolate Milkshake Lemonade Tea Milkshake Milkshake Lemonade Coffee Hot chocolate Lemonade Tea Tea Hot chocolate Lemonade Hot chocolate Lemonade Lemonade Complete the frequency table for the results. You may use the tally column to help you. Favourite drink Tally Frequency Tea Coffee Lemonade Milkshake Hot chocolate [2]
Mark scheme: 6 5, 3, 6, 4, 7 2 B1 for 3 correct If zero scored, SC1 for correct tally, or frequencies if frequency column incorrect
Q7 · Write down the next term in this sequence
7 (a) Write down the next term in this sequence. 24, 22, 18, 12, 4, … ................................................... [1] (b) The nth term of another sequence is 3n + 5. Write down the first three terms in this sequence. ................. , ................. , ................. [1]
Mark scheme: 7(a) −6 1 7(b) 8, 11, 14 1
Q8 · Find the value of (a) 173, ..................................................
8 Find the value of (a) 173, ................................................... [1] (b) 3 729 . ................................................... [1]
Mark scheme: 8(a) 4913 1 8(b) 9 1
Question 9
9 Factorise completely. 4x2 - 8xy ................................................... [2]
Mark scheme: 9 4 x ( x − 2 y ) final answer 2 2 M1 for 4 x − 2 xy or x ( 4 x − 8 y ) ( ) or 2 2 x 2 − 4 xy or 2x (2x – 4y) ( )
Q10 · Line l has the equation y = 4x - 6
10 Line l has the equation y = 4x - 6. (a) Write down the co-ordinates of the point where line l crosses the y-axis. ( ....................... , ......................) [1] (b) Write down the gradient of line l. ................................................... [1]
Mark scheme: 10(a) (0, −6) 1 10(b) 4 1
Q11 · Complete these calculations to make them correct
11 Complete these calculations to make them correct. 24 + 8 (a) = ............ 4 [1] (b) -18 ÷ ............ = 2 [1] 7 ............ 21 (c) # = 8 40 ............ [1]
Mark scheme: 11(a) 8 1 11(b) −9 1 11(c) 3 1 or equivalent fraction 5
Q12 · The three angles in a triangle are 5x°, 6x° and 7x°
12 The three angles in a triangle are 5x°, 6x° and 7x°. 7x° NOT TO SCALE 6x° 5x° (a) Find the value of x. x = ............................................ [2] (b) Work out the size of the largest angle in the triangle. ................................................... [1]
Mark scheme: 12(a) 10 2 180 M1 for 5 x + 6 x + 7 x = 180 oe or 5 + 6 + 7 or B1 for angles 50, 60 and 70 12(b) 70 1FT FT 7 × their (a) provided 0 < their answer < 180
Q13 · 13 (a) GH = c- 4 m Find (i) 5 GH , [1] f p (ii) HG
6 13 (a) GH = c- 4 m Find (i) 5 GH , [1] f p (ii) HG. [1] f p 6 2 8 (b) + = c 7 m c y m c 3 m Find the value of y. y = ............................................ [1]
Mark scheme: 13(a)(i) 30 1 −20 13(a)(ii) −6 1 4 13(b) − 4 1
Q14 · These are the weights, in kilograms, of 10 babies
14 These are the weights, in kilograms, of 10 babies. 3.7 2.7 3.5 3.8 3.1 3.0 3.8 2.8 4.1 3.7 (a) Find the range. .............................................. kg [1] (b) Calculate the mean. .............................................. kg [2]
Mark scheme: 14(a) 1.4 1 14(b) 3.42 2 M1 for (sum of the 10 numbers) ÷ 10
Q15 · Write down a prime number between 80 and 90
15 (a) Write down a prime number between 80 and 90. ................................................... [1] (b) Find the lowest common multiple (LCM) of 21 and 30. ................................................... [2]
Mark scheme: 15(a) 83 or 89 1 15(b) 210 2 M1 for 210 × k or for 3,7 and 2,3,5 seen or for a list of at least 4 correct multiples of both 21 and 30 or 2 × 3 × 5 × 7 as answer
Q16 · 5x ÷ 25 = 56 Find the value of x
16 (a) 5x ÷ 25 = 56 Find the value of x. x = ............................................ [1] (b) Solve the simultaneous equations. You must show all your working. 2x + 3y = 16 - 2x + 5y = 24 x = ............................................ y = ............................................ [2]
Mark scheme: 16(a) 8 1 16(b) [x = ] 0.5 1 [y = ] 5 1 If zero scored, SC1 for correct substitution and evaluation to find the other variable
Q17 · $600 is invested for 3 years at a rate of 2.5% per year compound interest
17 $600 is invested for 3 years at a rate of 2.5% per year compound interest. Calculate the total value of the investment at the end of the 3 years. $ ................................................ [3]
Mark scheme: 17 646 or 646.1[3…] 3 M2 for 600 × 1.0253 oe or M1 for 600 × 1.0252 oe If zero scored, SC2 for 46.1 or 46.1[3…]
Q18 · 3 218 Without using your calculator, work out - - 12 c 4 3 m
11 3 218 Without using your calculator, work out - - 12 c 4 3 m. You must show all your working and give your answer as a fraction in its simplest form. ................................................... [4]
Mark scheme: 18 common denominator 12 B1 accept k × 12 throughout 9 8 M1 9 k 8 k one correct from or oe accept or 12 12 12 k 12 k 5 A2 10 k cao A1 for or10 6 12 12 k
Q19 · A café owner records the number of hours of sunshine and the number of ice-creams sold…
19 A café owner records the number of hours of sunshine and the number of ice-creams sold for 10 days. The results are shown in the table. Day 1 2 3 4 5 6 7 8 9 10 Hours of 12 0 3 6.5 6 4.5 4 8 10 5 sunshine Number of 150 5 35 86 72 56 38 120 127 74 ice-creams sold 160 140 120 100 Number of ice-creams 80 sold 60 40 20 0 2 4 6 8 10 12 14 16 Hours of sunshine (a) Complete the scatter diagram. The first 8 points have been plotted for you. [1] (b) What type of correlation is shown on the scatter diagram? ................................................... [1] (c) On the scatter diagram, draw a line of best fit. [1] (d) The weather forecast predicts 7 hours of sunshine for tomorrow. Use your line of best fit to estimate the number of ice-creams that will be sold tomorrow. ................................................... [1]
Mark scheme: 19(a) 2 points correctly plotted 1 19(b) positive 1 19(c) ruled line of best fit 1 19(d) 80 to 92 1
Q20 · A NOT TO 6.3 m 6.3 m SCALE B C Calculate the length BC
20 (a) A NOT TO 6.3 m 6.3 m SCALE B C Calculate the length BC. BC = .................................... m [2] (b) D NOT TO 223 cm SCALE 52 cm F E Calculate angle DFE. Angle DFE = ............................ [2]
Mark scheme: 20(a) 8.91 2 M1 for [ BC2 =] 6.32 + 6.32 or 6.3 ÷ sin 45 or 6.3 ÷ cos 45 20(b) 13.5 or 13.48… 2 52 M1 for sin [=] 223
Question 21
21 Simplify. (a) 6w0 ................................................... [1] (b) 5x3 − 3x3 ................................................... [1] (c) 3y6 # 5y-2 ................................................... [2]
Mark scheme: 21(a) 6 1 21(b) 2x 3 final answer 1 21(c) 15y 4 final answer 2 B1 for 15 ky or ky 4 as final answer (k ≠ 0)
What was in this paper
The subtopics covered by these 21 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Algebraic manipulation1Angles1Averages and range1Classifying statistical data1Equations1Equations of linear graphs1Geometrical terms1Indices II1Limits of accuracy1Percentages1Powers and roots1Pythagoras’ theorem1Ratio and proportion1Scatter diagrams1Sequences1The four operations1Time1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2017 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.