Cambridge IGCSE Mathematics 0580 — 2004 Oct/Nov Paper 1 · Variant 1

1 At a weather centre the temperature at midnight was −21 oC. For By noon the next day it had risen to −4 oC. Examiner's By how many degrees had the temperature risen? Use Answer oC [1]

Mark scheme: 1 17 1 Not -17

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2 Place brackets in the following calculation to make it a correct statement. 10 − 5 × 9 + 3 = 60 [1]

Mark scheme: 2 (10 - 5) x (9 + 3) 1 Ignore omission of final bracket only

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3 Write 5 as a decimal, correct to two decimal places. 9 Answer [2]

Mark scheme: 3 0.56 2 B1 for 5 ÷ 9 or digits 55 (….) or digits 56 Common answer for B1 is 0.55

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4 When x = 5 find the value of (a) 4x2, Answer(a) [1] (b) (4x)2. Answer(b) [1]

Mark scheme: 4 (a) 100 1 (b) 400 1

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5 Antonia is making a cake. She uses currants, raisins and sultanas in the ratio currants : raisins : sultanas = 4 : 3 : 5. The total mass of the three ingredients is 3.6 kilograms. Calculate the mass of sultanas. Answer kg [2]

Mark scheme: 5 1.5 (0...) 2 5 M1 for x 3.6 ( 4 + 3 + 5 ) SC1 for 1.2 or 0.9 (ie. Wrong ingredient)

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6 Write as a 3-figure bearing the direction For Examiner's (a) West, Use Answer(a) [1] (b) North-East. Answer(b) [1]

Mark scheme: 6 (a) 270 1 (b) (0)45 1

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7 Reflex Right Acute Obtuse Use one of the above terms to describe each of the angles given. (a) 100o Answer(a) [1] (b) 200o Answer(b) [1]

Mark scheme: 7 Obtuse 1 Reflex 1

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8  3   – 1 a =   and b =    4   2  Work out a – 2b.       Answer [2]

Mark scheme: 8  5  1 + 1 One mark each component. If   only number 5 in bracket allow   0 1 mark. − 2   2  If 0 scored SC1 for   or    4   −4   0  seen, or    5  Ignore a line between Components

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9 3 7 6 ÷ = 5 10 7 Show how this calculation is done without using a calculator. Write down the working. Answer [2]

Mark scheme: 9 3 10 M1 Only acceptable method. x 5 7 30 6 = or 35 7 E1 3 × 2 6 = 1 × 7 7 IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 1

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10 Simplify the following expressions. For Examiner's (a) a2 × a5 Use Answer(a) [1] (b) b4 ÷ b3 Answer(b) [1]

Mark scheme: 10 (a) a7 1 (b) b 1 Allow b1

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11 = < > Use one of the above symbols to complete each of the statements in the answer spaces. Answer(a) 23 32 [1] Answer(b) 9 % 0.09 [1]

Mark scheme: 11 (a) < 1 (b) = 1

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12 Write down the order of rotational symmetry of each of the following shapes. (a) Equilateral Triangle Answer(a) [1] (b) Rhombus Answer(b) [1]

Mark scheme: 12 (a) 3 1 Ignore any added words (b) 2 1

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13 For Examiner's Use The diagram shows a pyramid with a square base. All the sloping edges are the same length. In the space below sketch a net of the pyramid. [2]

Mark scheme: 13 Net of the pyramid. A 2 1 for a square square with 4 equal 1 for all 4 triangles, isosceles or isosceles triangles equilateral. correctly positioned. Reasonable accuracy by eye. Ignore any tabs shown.

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14 Bernard is buying a radio priced at $19.60. The shopkeeper gives him a 15% discount. Calculate how much Bernard pays. Answer $ [3]

Mark scheme: 14 16.66 cao 3 M1 for 0.15 x 19.60 (implied by 2.94 seen) M1 for 19.60 – his 2.94 (allow if 2.94 is rounded to 2.90, method only) or M2 for 0.85 x 19.60 [allow for (1 – 0.15) x 19.60] Answer 1666 2 marks, 1670 1 mark ww. 16.7(0) implies M2

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15 For Examiner's Use NOT TO 200 cm SCALE 350 cm 350 cm A large tank, in the shape of a cuboid, has a square base of side 350 cm and height 200 cm. The tank is filled with water. Find, in litres, the volume of water it holds when full. Answer litres [3]

Mark scheme: 15 24500 3 M1 for 350 x 350 x 200 or 3.5 x 3.5 x 2 soi A1 for 24500000 or 24.5 seen B1 for his ‘volume’ correctly converted to litres.

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16 NOT TO SCALE 6 cm 8 cm The measurements shown are correct to the nearest centimetre. (a) Write down the least possible measurement of (i) the base of the right-angled triangle, Answer(a)(i) base = cm [1] (ii) the height of the right-angled triangle. Answer(a)(ii) height = cm [1] (b) Use your answers to part (a) to calculate the least possible area of the triangle. Answer(b) area = cm2 [1]

Mark scheme: 16 (a) (i) (base) = 7.5 1 Allow 2 marks for correct (ii) (height) = 5.5 1 answers reversed. Allow 1 mark for one of the answers seen in either (i) or (ii). (b) 20.6 (25) or 20.62 1 A correct calculation of the or 20.6 (3) f.t. area using his values of base and height regardless of his values.

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17 Ferdinand’s electricity meter is read every three months. For The reading on 1st April was 70683 units and on 1st July it was 71701 units. Examiner's Use (a) How many units of electricity did he use in those three months? Answer(a) units [1] (b) Electricity costs 8.78 cents per unit. Calculate his bill for those three months. Give your answer in dollars, correct to the nearest cent. Answer(b) $ [2]

Mark scheme: 17 (a) 1018 1 (b) 89.38 final answer ft. 2 M1 for his (a) x 8.78 soi or SC1 for answer in cents. IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 1

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18 (a) List all the factors of 30. Answer(a) [2] (b) Write down the prime factors of 30. (1 is not a prime number.) Answer(b) [1]

Mark scheme: 18 (a) 1,2,3,5,6,10,15,30 cao 2 B1 for 4 correct factors, none or 1 x 30, 2 x 15, 3 x 10, incorrect. 5 x 6 cao (b) 2,3,5 or 2 x 3 x 5 1f.t. All the correct primes from his part (a), and at least one prime and no non-primes.

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19 In New Zealand, a bus leaves New Plymouth at 8.10 am and arrives in Wellington at 2.55 pm. For Examiner's (a) How long, in hours and minutes, does the journey take? Use Answer(a) h min [1] (b) The distance from New Plymouth to Wellington is 355 kilometres. Calculate, in kilometres per hour, the average speed for the journey. Answer(b) km/h [3]

Mark scheme: 19 (a) 6 (hours) 45 (minutes) 1 16 (b) rounds to 52.6 or 52 3f.t. 3 27 B1 for 6.75 or 6 oe used or 4 his time correctly converted to hours. M1 for 355 ÷ his time. (any form) (55.0…or 0.87….ww implies M1) A1 f.t. provided his (a) correctly converted to hours.

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20 Aminata has a bag containing 35 beads. The beads are either blue, yellow or red. One bead is chosen at random. 2 3 The probability of choosing a blue bead is and the probability of choosing a yellow bead is . 7 5 Calculate (a) the number of blue beads in the bag, Answer(a) [2] (b) the probability of choosing a red bead. Answer(b) [2]

Mark scheme: 20 (a) 10 2 2 M1 for x 35 7 2 4 2  3  (b) oe or 0.114 (...) + M1 for 1 -   soi or 35  7 5  or 11.4% 3 [35 - (his (a) + x 35] ÷ 35 5 0.11 or 11% seen imply M1

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21 Calculate, giving your answer in standard form, For Examiner's (a) (1.5 × 103) + (8.4 × 102), Use Answer(a) [2] (b) (1.5 × 103) × (8.4 × 102). Answer(b) [2]

Mark scheme: 21 (a) 2.34 x 103 2 SC1 for figs 234 seen or 2.3 x 103 SC1 for figs 126 seen or 1.3 x 106 (b) 1.26 x 106 2

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22 NOT TO SCALE A O B The diagram shows half of a circle, centre O. (a) What is the special name of the line AB? Answer(a) [1] (b) AB = 12 cm. (i) Calculate the perimeter of the shape. Answer(b)(i) cm [2] (ii) Calculate the area of the shape. Answer(b)(ii) cm2 [2]

Mark scheme: 22 (a) diameter 1 (b)(i) rounds to 30.8 or 30.9 2 M1 for 0.5 x π x 12 or 12 + π x 12 (implied by rounding to18.8 or (ii) rounds to 56.5 or 56.6 2 18.9 or 49.7 seen) M1 for using π x 62 (implied by 113 (. ) seen

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