Cambridge IGCSE Mathematics 0580 — 2013 May/June Paper 1 · Variant 3

1 The table shows the distances by road, in kilometres, between some towns in New Zealand. For Examiner′s Use Auckland 126 Hamilton New Napier 300 426 Plymouth 415 242 368 Rotorua 319 229 109 235 Wellington 460 356 332 531 657 Write down the distance between Rotorua and Hamilton. Answer ......................................... km [1] _____________________________________________________________________________________

Mark scheme: Question Answers Mark Part Marks 1 109 1

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2 Find the value of 1.473. Give your answer correct to 3 decimal places. Answer ............................................... [2] _____________________________________________________________________________________

Mark scheme: 2 3.177 2 B1 for 3.176[5] or 3.17 or 3.18

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3 The time in Lisbon is the same as the time in Funchal. A plane left Lisbon at 08 30 and arrived in Funchal at 10 20. It then left Funchal at 12 55 and returned to Lisbon. The return journey took 15 minutes more. What time did the plane arrive in Lisbon? Answer ............................................... [2] _____________________________________________________________________________________

Mark scheme: 3 1500 or 3 pm 2 B1 for 1h50 or 2h[0]5 or SC1 for 1255 + their 1h 50 + 15mins correctly evaluated 4 30 k oe www 2 M1 for 30 seen or seen 300 300

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5 Solve the equation 3x – 5 = 16 . Answer x = ............................................... [2] _____________________________________________________________________________________

Mark scheme: 5 [x =] 7 2 M1 for correct first step 5 16 3x = 16 + 5 or x − = 3 3

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6 A television screen size, S cm, is 80 cm correct to the nearest centimetre. Complete the statement for S in the answer space. Answer ......................... Y S I ......................... [2] _____________________________________________________________________________________

Mark scheme: 6 79.5 [≤ S <] 80.5 1, 1 SC1 answers reversed

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7 Sheila can pay her hotel bill in Euros (€) or Pounds (£). For Examiner′s The bill was €425 or £365 when the exchange rate was £1 = €1.14 . Use In which currency was the bill cheaper? Show all your working. Answer ............................................... [2] _____________________________________________________________________________________

Mark scheme: 7 £ or pound[s] M1 for 425 ÷ 1.14 or 365 × 1.14 working must be shown 2

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8 Without using a calculator, show that 3 5 3 ÷ 2 14 = 1 53 . You must show each step of your working. Answer [2] _____________________________________________________________________________________

Mark scheme: 8 18 9 M1 and seen 5 4 18 9 72 24 8 3 × or or and oe seen A1 Not essential to see 1 5 5 4 45 15 5

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9 Factorise completely. 6xy2 – 8y Answer ............................................... [2] _____________________________________________________________________________________

Mark scheme: 9 2y (3xy − 4) 2 B1 for 2 (3xy 2 − 4y) or y (6xy − 8)

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10 Use a calculator to fi nd For Examiner′s Use 5 (a) 5 24 , Answer(a) ............................................... [1] cos 40° (b) . 7 Answer(b) ............................................... [1] _____________________________________________________________________________________

Mark scheme: 10 (a) [ ± ] 2.28 or 2.282 to 2.2822 1 (b) 0.109 or 0.1094 [3 …] 1

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11 B NOT TO O SCALE A 87° 63° 81° C D (a) Calculate the size of angle AOB. Answer(a) Angle AOB = ............................................... [1] (b) What type of angle is angle AOB? Answer(b) ............................................... [1] _____________________________________________________________________________________

Mark scheme: 11 (a) 129 1 (b) Obtuse 1 IGCSE – May/June 2013 0580 13

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12 For Examiner′s y Use 6 P 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 Q –3 –4 The points P and Q are marked on the grid. (a) Work out the vector . Answer(a) = [1] f p - 8 (b) = - 1 e o Find the co-ordinates of the point R. Answer(b) (................ , ................) [1] _____________________________________________________________________________________

Mark scheme: 12 (a)  9  [PQ =]   1  −7  (b) (−1 , −3) 1

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13 Huy borrowed $4500 from a bank at a rate of 5% per year compound interest. He paid back the money and interest at the end of 2 years. How much interest did he pay? Answer $ ............................................... [3] _____________________________________________________________________________________

Mark scheme: 13 ( $ ) 461.25 cao 3 M1 for 4 500 × 1.05 2 oe A1 for 4961.25 A1ft their amount − 4500 OR M2for 4500×0.05+(4500×1.05)×1.05 or M1 for 4500 × 0.05 + 4500

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14 For Examiner′s 4 cm Use NOT TO SCALE 5 cm 10 cm 18 cm The shaded shape has rotational symmetry of order 2. Work out the shaded area. Answer ........................................ cm2 [3] _____________________________________________________________________________________

Mark scheme: 14 260 3 M2 for [2 × ] (4 × 10 + 18 × 5) oe or M1 for a correct area statement

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15 (a) 5x × 53 = 510 Find the value of x. Answer(a) x = ............................................... [1] (b) Simplify. 12h3 ÷ 4h–2 Answer(b) ............................................... [2] _____________________________________________________________________________________

Mark scheme: 15 (a) [x =] 7 1 (b) 3h 5 2 B1 for 3h n (n ≠ 0) or kh 5

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16 Calculate, giving your answers in standard form, (a) 2 × (5.5 × 104) , Answer(a) ............................................... [2] (b) (5.5 × 104) – (5 × 104) . Answer(b) ............................................... [2] _____________________________________________________________________________________

Mark scheme: 16 (a) 1.1 × 10 5 2 B1 for 110 000 oe e.g.11 × 10 4 (b) 3 2 4 5 × 10 B1 for 5000 oe e.g.0.5 × 10

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17 For Examiner′s F Use NOT TO SCALE C D E 6 cm A 4 cm B The diagram shows a triangular prism. Triangle ABC is equilateral. AB = 4 cm and BE = 6 cm. (a) Write down the size of angle ABC. Answer(a) Angle ABC = ............................................... [1] (b) On the 1 cm2 grid, draw an accurate net of the prism. The line BE has been drawn for you. B E [3] _____________________________________________________________________________________

Mark scheme: 17 (a) 60 1 (b) Correct net 3 B1 for 3 rectangles and a triangle to the right and left of rectangles. B1 for 3 accurate (6 by 4) rectangles joined. B1 for 2 equilateral triangles joined in correct positions

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18 On the fi rst day of each month, a café owner records the midday temperature (°C) and the number of For Examiner′s hot meals sold. Use Month J F M A M J J A S O N D Temperature (°C) 2 4 9 15 21 24 28 27 23 18 10 5 Number of hot meals 38 35 36 24 15 10 4 5 12 20 18 32 (a) Complete the scatter diagram. The results for January to June have been plotted for you. 40 35 30 25 Number of 20 hot meals 15 10 5 0 5 10 15 20 25 30 Temperature (°C) [2] (b) On the grid, draw the line of best fi t. [1] (c) What type of correlation does this scatter diagram show? Answer(c) ............................................... [1] _____________________________________________________________________________________

Mark scheme: 18 (a) 6 points correctly plotted 2 B1 for 4 or 5 correct (b) Correct ruled line of best fit. 1 (c) Negative 1

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19 For Examiner′s y Use 8 7 6 5 4 A 3 2 1 x 0 1 2 3 4 The point A (1, 3.5) is plotted on the grid. (a) Plot the point B (3, 6.5) and draw the straight line through A and B. [1] (b) (i) Find the gradient of the line in part (a). Answer(b)(i) ............................................... [2] (ii) Write down the equation of the line in the form y = mx + c. Answer(b)(ii) y = ............................................... [2] (c) On the grid, draw a line through the point (2, 5) that is perpendicular to the line in part (a). [1] _____________________________________________________________________________________

Mark scheme: 19 (a) B (3 , 6.5) plotted and a ruled line A to B 1 Rise (b) (i) 1.5 oe 2ft M1 for applied to their line Run (ii) (y = ) 1.5 x + 2 2ft B1 for their (b) (i) x + a ( a ≠ 2) or b x + their 2 (b ≠ 0 or 1.5) (c) Ruled Line perpendicular to their line 1ft (±2º) and through the point (2 , 5) IGCSE – May/June 2013 0580 13

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20 For Examiner′s B Use NOT TO SCALE 17 cm C 6 cm A In the diagram, AB is a diameter of the circle and C is a point on the circumference. AB = 17 cm and AC = 6 cm. (a) Calculate the area of the circle. Answer(a) ........................................ cm2 [2] (b) (i) Explain why angle ACB = 90°. Answer(b)(i) ...................................................................................................................... [1] (ii) Calculate BC. Answer(b)(ii) BC = ......................................... cm [3] _____________________________________________________________________________________

Mark scheme: 20 (a) 226.98 to 227.01 2 M1 for π × (17 ÷ 2) 2 (b) (i) Angle or triangle [in a] semi-circle 1 (ii) 15.9 or 15.90 to 15.91 3 2 2 M2 for 17 − 6 or or 253 2 2 2 M1 for 17 = BC + 6 or better.

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