Cambridge IGCSE Mathematics 0580 — 2011 May/June Paper 1 · Variant 2

1 One square number between 50 and 100 is also a cube number. For Examiner's Write down this number. Use Answer [1]

Mark scheme: Qu. Answers Mark Part Marks 1 64 1cao

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2 x° NOT TO SCALE 52° A straight line intersects two parallel lines as shown in the diagram. Find the value of x. Answer x = [1]

Mark scheme: 2 52 1

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3 A letter is chosen at random from the following word. S T A T I S T I C S Write down the probability that the letter is (a) A or I , Answer(a) [1] (b) E. Answer(b) [1]

Mark scheme: 3 3 1 (a) or 0.3 or 30% 10 1 0 (b) 0 or or 0% 10

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4 Ingrid throws a javelin a distance of 58.3 metres, correct to 1 decimal place. Complete the statement about the distance, d metres, the javelin is thrown. Answer Y d I [2]

Mark scheme: 4 58.25 Y d < 58.35 1,1 SC1 for both correct values but reversed 14 16 14 7

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5 7 7 For 5 Show that 1 ÷ 1 = . Examiner's 9 9 8 Use Write down all the steps in your working. Answer [2]

Mark scheme: 14 16 14 7 5 Working must be shown. 2 M1 and M1 = oe 9 9 16 8 or visible cancelling 2 16

More questions on Fractions, decimals and percentages

3 2 6 I p I 5 3 Which of the following could be a value of p? 16 4 0.67 60% (0.8)2 27 9 Answer [2]

Mark scheme: 16 6 0.82 2 M1 conversion of (= 0.5(9..)) and 27 0.82 (= 0.64) to decimals seen 3 3

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7 Calculate 324 × 17. Give your answer in standard form, correct to 3 significant figures. Answer [2]

Mark scheme: 7 5.51 × 103 2 B1 for 5.508 × 103 or figs 551 or 5.5 × 103

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8 A meal on a boat costs 6 euros (€) or 11.5 Brunei dollars ($). For Examiner's In which currency does the meal cost less, on a day when the exchange rate is €1 = $1.9037? Use Write down all the steps in your working. Answer [2]

Mark scheme: 8 euros (with correct working) 2 M1 one of 6 × 1.9037 or 11.5 ÷ 1.9037 or (6)€ or 11.5 ÷ 6 seen 9 4 k 4x–24 or 24 2 B1 4xn B1 24 or kx–24 for any numerical k, n x x 2 2

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10 C NOT TO 9 cm SCALE B A 17 cm In the triangle ABC, AB = 17 cm, BC = 9 cm and angle ACB = 90°. Calculate AC. Answer AC = cm [3]

Mark scheme: 10 14.4(……) 3 M2 for (17 2 − 9 2 ) or M1 for 172 = x2 + 92 or better seen

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11 The table shows the opening and closing times of a café. For Examiner's Use Mon Tue Wed Thu Fri Sat Sun Opening time 0600 0600 0600 0600 0600 (a) 0800 Closing time 2200 2200 2200 2200 2200 2200 1300 (a) The café is open for a total of 100 hours each week. Work out the opening time on Saturday. Answer(a) [2] (b) The owner decides to close the café at a later time on Sunday. This increases the total number of hours the café is open by 4%. Work out the new closing time on Sunday. Answer(b) [1]

Mark scheme: 11 (a) (0)700 or 7 am 2 M1 100 – (5 × their(22 – 6) + their(13 – 8)) or better soi (b) 1700 or 5 pm 1 IGCSE – May/June 2011 0580 12

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 3 − 5  12 =   and =    −1  4  (a) Find . You may use the grid below to help if you wish.     Answer(a) =   [2]     (b) Work out .     Answer(b) =   [1]    

Mark scheme: 12 − 2  1,1 B1 for 1 correct component. (a)   SC1 for both correct but written as coordinates as  3  the answer.  2  1ft ft their (a) with signs reversed. (b)   Not a strict follow through.  −3 

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13 (a) Rewrite this calculation with all the numbers rounded to 1 significant figure. For Examiner's 77.8 Use 21.9 − 3.8 × 4.3 Answer(a) [1] (b) Use your answer to part (a) to work out an estimate for the calculation. Answer(b) [1] (c) Use your calculator to find the actual answer to the calculation in part (a). Give your answer correct to 1 decimal place. Answer(c) [2]

Mark scheme: 13 80 1 Condone either 78 for 80 or 22 for 20 but not (a) both. 20 − 4 × 4 (b) 20 1 SC1 for answer 13 if clearly from 78 ÷ (22 − 4 × 4) or 78 ÷ (22 − 16). (c) 14.0 2 B1 for 13.9(9……….) or 14 in working or in the answer.

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14 (a) Complete the list to show all the factors of 18. 1, 2, , , , 18 [2] (b) Write down the prime factors of 18. Answer(b) [1] (c) Write down all the multiples of 18 between 50 and 100. Answer(c) [1]

Mark scheme: 14 (a) (1, 2,) 3, 6, 9, (18) 2 B1 for 2 correct. (b) 2, 3 1 (c) 54, 72, 90 1cao

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15 (a) Expand the brackets and simplify. For 3(2x O 5y) O 4(x O y) Examiner'sUse Answer(a) [2] (b) Factorise completely. 6x2 O 9xy Answer(b) [2]

Mark scheme: 15 (a) 2x − 11y final answer 2 M1 for 6x − 15y or − 4x + 4y or better seen or B1 for 2x ± jy or kx − 11y. (b) 3x(2x − 3y) final answer 2 B1 for 3(2x2 − 3xy) or x(6x − 9y) or 3x(2x − by) or 3x(ax − 3y) (a, b ≠ 0) x

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16 D NOT TO SCALE 28.5 m 38° A B C 47.1 m A flagpole, BD, is attached to level horizontal ground by ropes, AD and CD. AD = 28.5 m, BC = 47.1 m and angle DAB = 38°. Calculate (a) BD, the height of the flagpole, Answer(a) BD = m [2] (b) angle BCD. Answer(b) Angle BCD = [2]

Mark scheme: x 16 (a) 17.5(………) 2 M1 for sin38 = or better 285. (b) 20.38 to 20.44 2ft M1 for tan (BCD =) their (a) ÷ 47.1

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17 (a) For C Examiner's Use A NOT TO SCALE B Points A, B and C lie on the circumference of the circle shown above. When angle BAC is 90° write down a statement about the line BC. Answer(a) [1] (b) NOT TO SCALE O 54° A D B C O is the centre of a circle and the line ABC is a tangent to the circle at B. D is a point on the circumference and angle BOD = 54°. Calculate angle DBC. Answer(b) Angle DBC = [3]

Mark scheme: 17 (a) Diameter 1 (b) 27 3 M1 for (180 − 54) ÷ 2 M1 ind for 90 − their angle OBD.

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18 For Examiner's Use C B A (a) On the diagram above, using a straight edge and compasses only, construct (i) the bisector of angle ABC, [2] (ii) the locus of points which are equidistant from A and from B. [2] (b) Shade the region inside the triangle which is nearer to A than to B and nearer to AB than to BC. [1]

Mark scheme: 18 (a) (i) 2 B1 correct line B1 2 sets of correct arcs (ii) 2 B1 correct line B1 two sets of correct arcs R (b) 1 correct region, shaded or shown by the letter R IGCSE – May/June 2011 0580 12

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19 (a) The travel graph on the opposite page shows Joel’s journey to his school. For He walks to the bus stop and waits for the bus, which takes him to the school. Examiner's Use (i) How long did Joel wait for the bus? Answer(a)(i) min [1] (ii) Find the distance from the bus stop to the school. Answer(a)(ii) km [1] (b) Joel’s sister, Samantha, leaves home 14 minutes later than Joel to cycle to the same school. She cycles at a constant speed and arrives at the school at 08 16. (i) On the grid, show her journey. [1] (ii) At what time did the bus pass Samantha? Answer(b)(ii) [1] (iii) How far from the school was she when the bus passed her? Answer(b)(iii) km [1] (iv) How many minutes after Joel did Samantha arrive at the school? Answer(b)(iv) min [1] 10 For Examiner's Use School 9 8 7 6 Distance 5 (km) 4 3 2 1 Home 0 07 00 07 10 07 20 07 30 07 40 07 50 08 00 08 10 08 20 Time

Mark scheme: 19 (a) (i) 8 (min) 1 (ii) 7.8 (km) 1 (b) (i) Ruled line from 1 Ignore line continued above school. (07 20, 0) to (08 16, 9.4) (ii) (0)7 38 to (0)7 40 1ft Follow through their graph (iii) 5.8 (km) to 6.4 (km) 1ft Follow through their graph. (iv) 17 to 19 (min) 1ft Follow through their graph

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