Cambridge IGCSE Mathematics 0580 — 2010 May/June Paper 1 · Variant 3

1 Examiner's Use x° NOT TO SCALE 45° 26° Find the value of x. Answer x = [1]

Mark scheme: Qu. Answers Mark Part Marks 1 109 1

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2 A train to Paris leaves at 06 30. The journey takes 3 hours and 56 minutes. Work out the time when the train arrives in Paris. Answer [1]

Mark scheme: 2 10 26 (am), 10:26, 10.26 1

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3 Write down the factors of 48 which are between 10 and 40. Answer [2]

Mark scheme: 3 12, 16, 24 2 W1 for any 2 correct out of their 2 or 3 answers in the range or W1 for all 3 with other factors outside the range.

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4 I = K= Examiner's Use For each part, choose a symbol from those above to make a correct statement. 5 (a) 0.55 [1] 9 2 (b) 66% [1] 3

Mark scheme: 4 (a) > 1 (b) < 1 their ( 21000 − 16800) 4200

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5 In a sale, the price of a boat was reduced from $21 000 to $16 800. Calculate the reduction as a percentage of the original price. Answer % [2]

Mark scheme: their ( 21000 16800) 4200 5 20 2 M1 for or 21000 21000

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6 Write down the equation of the line, parallel to y = 3x + 5 , which passes through the point (0, −2). Answer [2]

Mark scheme: 6 y = 3x – 2 oe final answer 2 W1 for 3x + j, j ≠ 5 or W1 for kx − 2, k ≠ 0 11 3 × 8 5 × 1 5 24

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7 Mrs Duval makes one litre of ice cream. Examiner's 1 3 Use She eats litre and her children eat litre. 8 5 Without using your calculator, find what fraction of a litre of ice cream is left. Show all your working clearly. Answer [2]

Mark scheme: 11 3 × 8 5 × 1 5 24 7 or equivalent fraction isw www 2 M1 for + or + or 0.6 + 0.125 40 5 × 8 8 × 5 40 40 cao Condone if followed by 0.275 or 27.5% 5 24 or 1 − − or 1 − 0.6 − 0.125 or 600 + 125 40 40 or 60 + 12.5 or 1000 − 600 − 125 seen 11 If M0, then SC1 for with no, incomplete or 40 wrong working.

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8 (a) Use your calculator to work out 27.4 × (3.28 + 1.6 × 9.8) . Write down all the figures from your calculator display. Answer(a) [1] (b) Write your answer to part (a) correct to 3 significant figures. Answer(b) [1]

Mark scheme: 8 (a) 519.504 1 (b) 520 1ft Only ft if their (a) is 4 figs or more 2

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9 Calculate the area of a circle of radius 3.75 cm. Answer cm2 [2]

Mark scheme: 9 44.2 2 M1 for 3.752 × π or 44.15 to 44.19

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10 (a) Examiner's Use Write down the order of rotational symmetry of the shape above. Answer(a) [1] (b) A M N O T X From the list, write down the letters which have only one line of symmetry. Answer(b) [2]

Mark scheme: 10 (a) 2 1 (b) A M T 2 W1 for 4 letters listed, 3 of them correct or W1 for 2 and only 2 correct 2 1

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11 Simplify (a) m 3 × m −5 , Answer(a) [1] (b) 15 k 8 ÷ 3k 2 . Answer(b) [2]

Mark scheme: 1 11 (a) m–2, o.e. 1 m 2 (b) 5k6 2 W1 for 5kn (n ≠ 0) or mk6 (m ≠ 0).

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12 Examiner's Use NOT TO SCALE 150° 150° The diagram shows part of a regular polygon with each interior angle 150°. Calculate the number of sides of the polygon. Answer [3]

Mark scheme: 12 12 3 M1 for exterior angle 180 − 150 implied by 30 (could be on the diagram) and M1 dep for 360 ÷ their 30

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13 Expand the following expressions. (a) 5(3 – 4h) Answer(a) [1] (b) 4 d ( 6 d 2 + e 2 ) Answer(b) [2]

Mark scheme: 13 (a) 15 – 20h final answer 1 (b) 24d3 + 4de2 final answer 2 W1 for 24d3 or (+)4de2 seen

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14 Examiner's Use 1.75 cm NOT TO SCALE 2.3 cm 4 cm The cuboid above has length 4 cm, width 2.3 cm and height 1.75 cm. Calculate the volume of the cuboid (a) in cubic centimetres, Answer(a) cm3 [2] (b) in cubic millimetres. Answer(b) mm3 [1]

Mark scheme: 14 (a) 16.1 2 M1 for 4 × 2.3 × 1.75, or better (b) 16100 1ft 1000 × their (a) IGCSE – May/June 2010 0580 13

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15 Simplify the following expressions. (a) 6r + 2s + s – 4r Answer(a) [1] 2 2 (b) 4f – 3g + 4g – 9f Answer(b) [2]

Mark scheme: 15 (a) 2r + 3s final answer 1 (b) g – 5f 2 final answer 2 W1 for g or for – 5f 2 seen

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16 Examiner's Use NOT TO SCALE 11 cm 4 cm A cylindrical can of beans has height 11 cm and radius 4 cm. A label covers the curved surface of the can completely. Calculate the area of the label. Answer cm2 [3]

Mark scheme: 16 276 3 M2 for 2π × 4 × 11, or better, seen or 276.3 to 276.5 or M1 for 2π × 4 SC1 for 4 × π × 11 or 138…., seen

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17 Solve the simultaneous equations. 3x + y = 19 5x – y = 13 Answer x = y = [3]

Mark scheme: 17 (x =) 4 (y =) 7 www 3 M1 for adding or multiplying and subtracting (allow errors in arithmetic operations) or any other correct methods A1 for one correct variable.

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18 R Examiner's Use NOT TO SCALE O 55° Q P P, Q and R lie on a circle, centre O. PR is a diameter and angle OQR = 55°. Find (a) angle PQR, Answer(a) Angle PQR = [1] (b) angle ROQ, Answer(b) Angle ROQ = [1] (c) angle OPQ. Answer(c) Angle OPQ = [1]

Mark scheme: 18 (a) 90° 1 (b) 70° 1 (c) 35° 1ft ft their (b) ÷ 2 only 18 

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6  − 3   2  19 f =  g =   h =   0  6   −2  Calculate (a) 3f,           Answer(a)   [2] (b) g – h.           Answer(b)   [2]

Mark scheme:  18  19 (a)  0  1, 1 − 5  (b)  8  1, 1

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20 Examiner's Use 100 Garage 90 80 70 Distance (kilometres) 60 50 Café 40 30 20 10 Factory 0 0 1 2 3 4 5 6 7 8 9 Time (hours) The travel graph shows part of the journey of a truck driver. The driver leaves a factory to deliver tyres to a garage. After unloading the tyres, the driver returns to the factory, but stops at a café for 1 hour. He then completes the journey at an average speed of 80 km/h. (a) Calculate the average speed of the truck on its journey from the factory to the garage. Answer(a) km/h [1] (b) Write down the length of time the truck stays at the garage. Answer(b) hours [1] (c) Complete the travel graph. [2]

Mark scheme: 20 (a) 45 1 (b) 1.5 o.e. 1 Allow 1 h(our) 30(min) or 1:30 (c) horizontal line from 1 (5.5, 40) to (6.5, 40) diagonal line from their 1ft Independent (x, 40) to (x + ½ , 0) √ 2 2 √

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21 Examiner's B Use C 16 cm 9 cm NOT TO SCALE 24° A D The diagram shows a quadrilateral ABCD. AB = 16 cm, BD = 9 cm and angle BDC = 24°. Angle ADB = 90° = angle BCD. Calculate the length of (a) AD, Answer(a) AD = cm [3] (b) CD. Answer(b) CD = cm [2]

Mark scheme: 21 (a) 13.2 3 M2 for √(162 – 92) or √175 or 13.22 to 13.23 or M1 for 162 = x2 + 92 or better CD (b) 8.22 to 8.23 2 M1 for cos 24 = or better 9

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