Cambridge IGCSE Mathematics 0580 — 2010 May/June Paper 1 · Variant 2

1 Examiner's Use 157° NOT TO SCALE x° 84° Find the value of x. Answer x = [1]

Mark scheme: Qu. Answers Mark Part Marks 1 119 1

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2 (a) Write down the smallest number which is a multiple of both 8 and 12. Answer(a) [1] (b) Write down all the other multiples of both 8 and 12 which are less than 100. Answer(b) [1]

Mark scheme: 2 (a) 24 1 (b) (24), 48, 72, 96 1 SC1 for ans (48), 96 if their (a) is 48.

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3 Factorise completely 6mp − 9pq. Answer [2]

Mark scheme: 3 3p(2m − 3q) final answer 2 W1 for 3(2mp − 3pq) or p(6m − 9q) or 3p(am ± bq) where a and b are integers. 7 2 × 4 5 × 1 8 5

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4 1 litre of apple juice is poured into 3 glasses. Examiner's Use 2 The first glass contains litre. 5 1 The second glass contains litre. 4 What fraction of a litre does the third glass contain? Show all your working clearly. Answer [2]

Mark scheme: 7 2 × 4 5 × 1 8 5 4 or equivalent fraction isw www 2 M1 for + or + or 0.4 + 0.25 20 4 × 5 4 × 5 20 20 8 5 or 1− − or 1 − 0.4 − 0.25 or 40 + 25 20 20 or 400 + 250 or 1000 − 400 − 250 seen 7 If M0 then SC1 for with no, incomplete or 20 wrong working. Condone if followed by 0.35 or 35%

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5 A plane from Hong Kong to New Zealand leaves at 18 10 on Monday. The time in New Zealand is 4 hours ahead of the time in Hong Kong. (a) Write down the time in New Zealand when the plane leaves Hong Kong. Answer(a) [1] (b) The plane arrives in New Zealand at 09 45 on Tuesday. How long, in hours and minutes, does the journey take? Answer(b) h min [1]

Mark scheme: 5 (a) 22 10, 22:10, 22.10, 10 10pm 1 (b) 11(h) 35(min) 1ft Follow through time period from their (a) to 09 45

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6 Alphonse changed 400 Brazilian reals into South African Rand. Examiner's The exchange rate was 1 Brazilian real = 4.76 South African Rand (R). Use How much did he receive? Answer R [2]

Mark scheme: 6 1904 2 M1 for 400 × 4.76

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7 Joe measured the diameter of a tennis ball correct to the nearest millimetre. The upper bound of his measurement was 6.75 centimetres. Write down, in millimetres, the lower bound of his measurement. Answer mm [2]

Mark scheme: 7 66.5 2 W1 for figs 665 cao or SC1 answer of 66.5 < LB < 67.5

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8 Make p the subject of the formula m = p2 − 2. Answer p = [2]

Mark scheme: 8 (±)√(m + 2) final answer 2 W1 for p2 = m + 2 or ft square root after incorrect first step(s). SC1 answer of (±)√m + 2

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North9 Examiner's Use D North North P H The positions of Perth (P), Darwin (D) and Hobart (H) are shown on the diagram. Measure accurately any angles you need and write down the bearing of (a) D from P, Answer(a) [1] (b) P from H. Answer(b) [1]

Mark scheme: 9 (a) (0)34 to (0)36 1 (b) 286 to 289 1

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10 When c = 10 and d = −2, find the value of the following expressions. (a) c + 2d Answer(a) [1] (b) 5c2 − cd Answer(b) [2]

Mark scheme: 10 (a) 6 1 (b) 520 2 M1 for 5 × 102 − 10 × −2, or better If zero, SC1 for answer of 480 or 2520

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11 Fifteen children ran a 60 metre race. Examiner's In the scatter diagram below, the time taken is plotted against the age for each child. Use 18 17 16 15 14 Time (seconds) 13 12 11 10 9 8 7 8 9 10 11 12 13 14 Age (years) (a) Draw a line of best fit on the scatter diagram. [1] (b) What type of correlation does the scatter diagram show? Answer(b) [1] (c) Describe how the times taken change with the ages of the children. Answer (c) [1]

Mark scheme: 11 (a) Line of fit by eye 1 (b) Negative 1 (c) Older children run faster 1

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1 Examiner's 12 (a) = 3x . Use 27 Write down the value of x. Answer(a) x = [1] (b) Simplify (i) p7 × p-2 , Answer(b)(i) [1] (ii) m3 ÷ m7. Answer(b)(ii) [1]

Mark scheme: 12 (a) −3 1 (b) (i) p5 1 1 (ii) m–4 or 4 1 m IGCSE – May/June 2010 0580 12

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0.68 + 2.57 × 1.76 13 (a) Work out . 63 Write down all the figures from your calculator display. Answer(a) [1] (b) Write your answer to part (a) in standard form correct to 3 significant figures. Answer(b) [2]

Mark scheme: 13 (a) 0.08259(.….) 1 (b) 8.26 × 10–2 2ft W1 for their figs 826, i.e. to 3 sig figs (a) must have a minimum of 4 figures in order to qualify for this mark. or W1 ind for their (a) in standard form.

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14 Solve the simultaneous equations. 3x − 2y = 15 2x + y = 17 Answer x = y = [3]

Mark scheme: 14 (x) = 7, (y) = 3, www 3 M1 for multiplying and subtracting or adding as appropriate. (allow errors in arithmetic operations) or any other correct methods A1 for one correct variable.

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15 The diagram shows a prism. Examiner's The lengths are in centimetres. Use 2.5 NOT TO SCALE 1 3 8 2 4 Part of an accurate net of the prism is drawn below. Complete the net. [3]

Mark scheme: 15 Rectangle width 1.5 cm. 1 in a correct place Rectangle width 1 cm. 1 in a correct place Accurately drawn cross-section piece 1 in a correct place

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16 Daniel invested $2500 for 2 years at 5.5% per year compound interest. Examiner's Use Calculate how much interest he received. Answer $ [3]

Mark scheme: 16 ($)282.56(…) 3 M1 for 2500 × 1.0552 oe 2782(. ...) and M1 dep for subtracting 2500

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y y y y17 6 6 6 6 x x x x –3 0 3 –3 0 3 –3 0 3 –3 0 3 –6 –6 –6 –6 A B C D y y y 6 6 6 x x x –3 0 3 –3 0 3 –3 0 3 –6 –6 –6 E F G Write down the letter of the graph which is (a) y = x − 2, Answer(a) [1] (b) x = − 2, Answer(b) [1] (c) y = −2x + 4, Answer(c) [1] (d) y = x2 − 4. Answer(d) [1]

Mark scheme: 17 (a) D 1 (b) E 1 (c) G 1 (d) F 1 7 

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18 Examiner's y Use 6 5 A 4 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 B –2 –3 –4 –5 –6 (a) Describe fully the single transformation which maps flag A onto flag B. Answer(a) [2] (b) Draw, on the grid above, the image of flag A after rotation through 90° clockwise about the origin. [2]

Mark scheme: 18 (a) Translation  7  2 W1 cao for translation (allow poor spelling)  −6  or W1 independent for correct vector alone. (b) Correct rotation 2 W1 for (2, 4) missed but other points correct (4, 4), (5, 4), (5, 2) and (2, 4) or SC1 for 90 anti-clockwise rotation or SC1 correct rotation, any other centre

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19 The diagram shows a door, AEBCD, from a model of a house. Examiner's Use ABCD is a rectangle and AEB is a semi-circle. AD = 14 cm and DC = 6 cm. E A B NOT TO SCALE 14 cm D 6 cm C (a) Calculate the area of the door. Answer(a) cm2 [3] (b) The door is 2 millimetres thick. Calculate, in cubic centimetres, the volume of the door. Answer(b) cm3 [2] Question 20 is printed on the next page.

Mark scheme: 19 (a) 98.1 or 3 M1 for 14 × 6 (+……) 98.13 to 98.14 M1 ind for π × 32 ÷ 2 (b) 19.6 or 2ft M1 for their (a) × figs 2 19.62 to 19.63 Figs 196…. implies M1

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20 A running track has a boundary that is always 40 metres from a straight line, AB. Examiner's AB = 70 m. Use The scale drawing below shows the line AB. 1 centimetre represents 10 metres. A 70 m B (a) Complete the scale drawing accurately to show the boundary of the running track. [2] (b) Calculate, in metres, the total length of the actual boundary. Answer(b) m [3]

Mark scheme: 20 (a) Two parallel straight lines 2 W1 for 2 correct lines or 2 semicircles. 7 cm long and 4 cm from AB and two semicircular ends 4 cm from A and from B. (b) 391 or 3 M1 for 2 × 70 soi 391.3 to 391.4 cao and M1 ind for 2 × π × 40 SC2 for answer of 39.1 or 39.13 to 39.14

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