Cambridge IGCSE Mathematics 0580 — 2011 May/June Paper 1 · Variant 1
0580/11/M/J/11 · 19 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 scheme3 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · A concert hall has 1540 seats
1 A concert hall has 1540 seats. For Examiner's Calculate the number of people in the hall when 55% of the seats are occupied. Use Answer [1]
Mark scheme: Qu. Answers Mark Part Marks 1 847 1
Q2 · Write down in figures the number twenty thousand three hundred and seventy six
2 (a) Write down in figures the number twenty thousand three hundred and seventy six. Answer(a) [1] (b) Write your answer to part (a) correct to the nearest hundred. Answer(b) [1]
Mark scheme: 2 (a) 20 376 1 (b) 20 400 1ft Their (a) to nearest 100
Q3 · For an equilateral triangle, write down (a) the number of lines of symmetry, Answer(a)…
3 For an equilateral triangle, write down (a) the number of lines of symmetry, Answer(a) [1] (b) the order of rotational symmetry. Answer(b) [1]
Mark scheme: 3 (a) 3 1cao (b) 3 1
Q4 · A B Write down the geometrical name for (a) shape A, Answer(a) [1] (b) shape B
4 A B Write down the geometrical name for (a) shape A, Answer(a) [1] (b) shape B. Answer(b) [1]
Mark scheme: 4 (a) Trapezium 1 Do not allow Trapezoid (b) Parallelogram 1 600
Q5 · Mark and Naomi share $600 in the ratio Mark : Naomi = 5 : 1
5 Mark and Naomi share $600 in the ratio Mark : Naomi = 5 : 1. For Examiner's Calculate how much money Naomi receives. Use Answer $ [2]
Mark scheme: 5 100 2 M1 for 5+ 1 (×1) If zero, SC1 for answer of 500 2
Q6 · Calculate the area of a circle with radius 6.28 centimetres
6 Calculate the area of a circle with radius 6.28 centimetres. Answer cm2 [2]
Mark scheme: 6 124 or 123.8 2 M1 for π × 6.28 2 or 123.83 to 123.92 7.2 × 20000
Q7 · The scale on a map is 1 : 20 000
7 The scale on a map is 1 : 20 000. Calculate the actual distance between two points which are 2.7 cm apart on the map. Give your answer in kilometres. Answer km [2]
Mark scheme: 7.2 × 20000 7 0.54 2 M1 for oe 100000 or SC1 for figs 54 in answer
Q8 · Find m when 4m × 42 = 412
8 (a) Find m when 4m × 42 = 412. Answer(a) m = [1] (b) Find p when 6 p ÷ 67 = 62. Answer(b) p = [1]
Mark scheme: 8 (a) 10 1 (b) 9 1
Q9 · For Examiner's Use A B 2x° NOT TO SCALE C D x° 5x° AB is parallel to CD
9 For Examiner's Use A B 2x° NOT TO SCALE C D x° 5x° AB is parallel to CD. Calculate the value of x. Answer x = [3]
Mark scheme: 9 22.5 oe 3 B2 for 180 = 5x + 2x + x oe or better B1 for 2x or 6x marked in the correct place on the diagram
Q10 · Solve the simultaneous equations
10 Solve the simultaneous equations. 3x + y = 30 2x – 3y = 53 Answer x = y = [3]
Mark scheme: 10 x = 13 3 M1 for consistent multiplication and y = −9 addition/subtraction. A1 for x = 13 or A1 for y = –9 26 7 5 13 7 2 7 1 7 2
Q11 · Without using your calculator, and leaving your answer as a fraction, work out 1 7 2 –
11 Without using your calculator, and leaving your answer as a fraction, work out 1 7 2 – . 6 12 You must show all your working. Answer [3]
Mark scheme: 26 7 5 13 7 2 7 1 7 11 – or 2 – oe M2 M1 for − or − or − oe 12 12 12 6 12 212 12 6 12 7 19 112 or 12 oe A1
Q12 · Write 1738.279 correct to 1 decimal place
12 (a) Write 1738.279 correct to 1 decimal place. For Examiner's Use Answer(a) [1] (b) Write 28 700 in standard form. Answer(b) [1] (c) The mass of a ten-pin bowling ball is 7 kg to the nearest kilogram. Write down the lower bound of the mass of the ball. Answer(c) kg [1]
Mark scheme: 12 (a) 1738.3 1 (b) 2.87 × 10 4 1 (c) 6.5 1 IGCSE – May/June 2011 0580 11 2
Q13 · Paulo invests $3000 at a rate of 4% per year compound interest
13 Paulo invests $3000 at a rate of 4% per year compound interest. Calculate the total amount Paulo has after 2 years. Give your answer correct to the nearest dollar. Answer $ [3]
Mark scheme: 13 3245 3 M1 for 3000 × 1.04 2 A1 for 3244.8 If zero, SC2 for answer of 245 If zero, SC1 for their answer corrected to nearest dollar
Q14 · A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reach Paris
14 A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reach Paris. (a) Calculate the time the next day when the train arrives in Paris. Answer(a) [1] (b) The distance from Barcelona to Paris is 827 km. Calculate the average speed of the train in kilometres per hour. Answer(b) km/h [3]
Mark scheme: 14 (a) (0)8(.)01(am) 1 Not 8.01 pm (b) 78.4 or 78.38 to 78.39 3 M2 for 827 ÷ 10.55 or M1 for figs 827 ÷ their time
Q15 · The table shows part of a railway timetable
15 (a) The table shows part of a railway timetable. For Examiner's Use arrival time 12 58 13 56 14 54 15 52 Peartree Station departure time 13 07 14 05 15 03 16 01 (i) Each train waits the same number of minutes at Peartree Station. Write down how many minutes each train waits. Answer(a)(i) min [1] (ii) Janine is at Peartree Station at 3 pm. At what time does the next train depart? Answer(a)(ii) [1] (b) The average temperature each month in Moscow and Helsinki is recorded. The table shows this information from January to June. January February March April May June Temperature in −16 −14 −8 1 8 11 Moscow (°C) Temperature in −9 −10 −7 −1 4 10 Helsinki (°C) (i) Find the difference in temperature between Moscow and Helsinki in January. Answer(b)(i) °C [1] (ii) Find the increase in temperature in Helsinki from March to June. Answer(b)(ii) °C [1]
Mark scheme: 15 (a) (i) 9 1 (ii) 15 03, 3.03pm 1 (b) (i) 7 or −7 1 (ii) 17 1
Q16 · For Examiner's Use NOT TO Red SCALE Blue 96° 120° 60° Yellow Green In a survey a number…
16 For Examiner's Use NOT TO Red SCALE Blue 96° 120° 60° Yellow Green In a survey a number of people chose their favourite colour. The results are shown in the pie chart. (a) Calculate the size of the sector angle for green. Answer(a) [1] (b) The number of people who chose red is 16. Calculate the number who chose yellow. Answer(b) [1] (c) Calculate the total number of people in the survey. Answer(c) [1] (d) Write down the fraction who chose red. Answer(d) [1]
Mark scheme: 16 (a) 84° 1 Check diagram (b) 10 1 (c) 60 1ft ft their (b) × 6 where (b) is an integer 96 16 16 (d) or 1ft ft oe where (c) is an integer 360 60 their (c) ( ) 6
Q17 · For y Examiner's Use 4 3 2 B 1 x –3 –2 –1 0 1 2 3 4 5 6 7 A –1 –2 –3 (a) Write down the…
17 For y Examiner's Use 4 3 2 B 1 x –3 –2 –1 0 1 2 3 4 5 6 7 A –1 –2 –3 (a) Write down the vector . Answer(a) [1] − 3 (b) = 1 Mark the point C on the grid. [1] (c) Work out − 3 7 (i) + , 1 −4 Answer(c)(i) [1] − 3 (ii) 4 × . 1 Answer(c)(ii) [1]
Mark scheme: 17 (a) 1 2 (b) C marked at (1, 2) 1 4 (c) 1 −3 − 12 (d) 1 4
Q18 · For C Examiner's Use NOT TO SCALE O B 24° T A A, B and C are points on a circle, centre O
18 For C Examiner's Use NOT TO SCALE O B 24° T A A, B and C are points on a circle, centre O. TA is a tangent to the circle at A and OBT is a straight line. AC is a diameter and angle OTA = 24°. Calculate (a) angle AOT, Answer(a) Angle AOT = [2] (b) angle BOC, Answer(b) Angle BOC = [1] (c) angle OCB. Answer(c) Angle OCB = [1]
Mark scheme: 18 (a) 66° 2 M1 for 90° clearly identified as A (b) 114° 1ft 180 − their (a) 180 − their (b) their (a) (c) 33° 1ft or 2 2
Q19 · Piet, Rob and Sam collect model aeroplanes
19 Piet, Rob and Sam collect model aeroplanes. For Piet has x aeroplanes. Examiner's Rob has 7 more aeroplanes than Piet. Use Sam has three times as many aeroplanes as Piet. (a) Write down an expression, in terms of x, for (i) the number of aeroplanes Rob has, Answer(a)(i) [1] (ii) the number of aeroplanes Sam has. Answer(a)(ii) [1] (b) The total number of aeroplanes is 32. (i) Use the information in part (a) to write down an equation in x. Answer(b)(i) [1] (ii) Solve your equation. Answer(b)(ii) x = [2] (c) Write down the number of aeroplanes Rob has. Answer(c) [1]
Mark scheme: 19 (a) (i) x + 7 1 (ii) 3x 1 (b) (i) x+their (a)(i)+their (a)(ii)=32 1ft ft dependent on 2 algebraic expressions in (a) or better (ii) (x =) 5 2ft M1 for 5x = 32 − 7 oe ft their (b)(i) with M1 for ax = b and A1 if answer is an integer. (c) 12 1ft ft their (b)(ii) substituted into their (a)(i) or their (b)(ii) + 7 evaluated correctly
What was in this paper
The subtopics covered by these 19 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Angles1Area and perimeter1Equations1Fractions, decimals and percentages1Geometrical terms1Indices I1Introduction to algebra1Limits of accuracy1Rates1Ratio and proportion1Right-angled triangles1Scale drawings1Statistical charts and diagrams1Symmetry1Time1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2011 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.