Cambridge IGCSE Mathematics 0580 — 2013 Oct/Nov Paper 1 · Variant 2

1 Put one pair of brackets into this equation to make it correct. For Examiner′s Use 3 + 5 × 4 – 2 = 13 [1] _____________________________________________________________________________________

Mark scheme: Qu. Answer Mark Part Marks 1 3 + 5 × (4 – 2) 1 2 

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3 - 1 2 p = q = - 2 4 e o e o Work out p + q. Answer [1] f p _____________________________________________________________________________________

Mark scheme:  2  2   1 2  

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3 Zingon make light bulbs. 1 The probability that a Zingon light bulb is faulty is . 20 Gina tests 240 of these light bulbs. How many of them would she expect to be faulty? Answer ............................................... [1] _____________________________________________________________________________________

Mark scheme: 3 12 final answer 1

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4 The pictogram shows information about the numbers of different drinks sold in a café in one hour. Coffee Tea Hot chocolate Juice Key: represents 4 cups (a) In this hour, 14 cups of hot chocolate were sold. Complete the pictogram using this information. [1] (b) How many more cups of coffee than cups of tea were sold? Answer(b) ............................................... [1] _____________________________________________________________________________________

Mark scheme: 4 (a) 3.5 symbols in hot chocolate row 1 (b) 7 1 5 √

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5 Write the following in order of size, smallest fi rst. For Examiner′s Use 1 19% .0038 sin 11.4° 0.7195 5 Answer ......................... < ......................... < ......................... < ......................... < ......................... [2] _____________________________________________________________________________________

Mark scheme: 5 19% 0.7195 √0.038 sin 11.4 1/5 2 B1 for decimals [0.19], [0.2], 0.194…, 0.197…, 0.192… seen Or for four in correct order

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6 Use a calculator to work out the following. (a) 3 (– 4 × 62 – 5) Answer(a) ............................................... [1] (b) 3 × tan 30° + 2 × sin 45° Answer(b) ............................................... [1] _____________________________________________________________________________________

Mark scheme: 6 (a) −447 1 (b) 2 1

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7 Find the circumference of a circle of radius 2.5 cm. Answer ......................................... cm [2] _____________________________________________________________________________________

Mark scheme: 7 15.7 or 15.70 to 15.71 2 M1 for 2 × π × 2.5 8

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8 Bruce plays a game of golf. His scores for each of the 18 holes are shown below. 2 3 4 5 4 6 2 3 4 4 5 3 4 3 5 4 4 4 The information is to be shown in a pie chart. Calculate the sector angle for the score of 4. Answer ............................................... [2] _____________________________________________________________________________________

Mark scheme: 8 8 160 2 M1 for × 360 18

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9 (a) Add one line to the diagram so that it has two lines of symmetry. For Examiner′s Use [1] (b) Add two lines to the diagram so that it has rotational symmetry of order 2. [1] _____________________________________________________________________________________

Mark scheme: 9 (a) 1 (b) or or 1 Many other answers 2 2

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10 B NOT TO SCALE 4.6 cm A C 7.2 cm Calculate AB. Answer ......................................... cm [2] _____________________________________________________________________________________

Mark scheme: 10 8.54[4....] 2 M1 for 7.22 + 4.62 or better

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11 The table shows how the dollar to euro conversion rate changed during one day. For Examiner′s Use Time 10 00 11 00 12 00 13 00 14 00 15 00 16 00 $1 €1.3311 €1.3362 €1.3207 €1.3199 €1.3200 €1.3352 €1.3401 Khalil changed $500 into euros (€). How many more euros did Khalil receive if he changed his money at the highest rate compared to the lowest rate? Answer € ................................................ [3] _____________________________________________________________________________________

Mark scheme: 11 10.1[0] Final answer 3 M1 for 1.3199 and 1.3401 seen and M1 for 500 × 1.3199 or 500 × 1.3401 or for 500 × (their highest – their lowest) oe

More questions on Ratio and proportion

12 Pam wins the student of the year award in New Zealand. She sends three photographs of the award ceremony by post to her relatives. ● one of size 13 cm by 23 cm to her uncle in Australia ● one of size 15 cm by 23 cm to her sister in China ● one of size 23 cm by 35 cm to her mother in the UK Maximum lengths Australia Rest of the world 13 cm by 23.5 cm $1.90 $2.50 15.5 cm by 23.5 cm $2.40 $2.90 23 cm by 32.5 cm $2.80 $3.40 26 cm by 38.5 cm $3.60 $5.20 The cost of postage is shown in the table above. Use this information to calculate the total cost. Answer $ ................................................ [3] _____________________________________________________________________________________

Mark scheme: 12 10[.00] 3 M2 for 1.90 and 2.90 and 5.20 only or M1 for two of 1.90, 2.90, 5.20 in a list of three or two values from the table .340 + .5 20 or SC1 for 1.90, 2.90, 4.30 [from ] 2 IGCSE – October/November 2013 0580 12

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13 (a) Complete the following statement. For Examiner′s Use The two common factors of 15 and 20 are 1 and ......................... . [1] (b) Write down the next square number that is greater than 169. Answer(b) ............................................... [1] (c) Write down a prime number between 90 and 100. Answer(c) ............................................... [1] _____________________________________________________________________________________

Mark scheme: 13 (a) 5 cao 1 (b) 196 cao 1 (c) 97 cao 1

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14 The straight line, L, has the equation y = 5 – 2x . Write down (a) the co-ordinates of the point where the line crosses the y-axis, Answer(a) (....................... , .......................) [1] (b) the gradient of the line, Answer(b) ............................................... [1] (c) the equation of a line parallel to L. Give your answer in the form y = mx + c. Answer(c) y = ............................................... [1] _____________________________________________________________________________________

Mark scheme: 14 (a) (0, 5) 1 (b) –2 1 (c) y = –2x + k 1 k ≠ 5

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15 c = 10d + 3 For Examiner′s Use (a) Find the value of c when d = 2.3 . Answer(a) c = ............................................... [1] (b) Make d the subject of the formula. Answer(b) d = ............................................... [2] _____________________________________________________________________________________

Mark scheme: 15 (a) 26 1 c − 3 3 −c (b) or oe final answer 2 M1 for one correct step of a two step method. 10 − 10

More questions on Algebraic manipulation

16 NOT TO SCALE 10 cm 6 cm This shape is made from a rectangle and a semicircle. The rectangle measures 10 cm by 6 cm. Work out the area of the shape. Answer ........................................ cm2 [3] _____________________________________________________________________________________

Mark scheme: 16 74.1 or 74.137 to 74.140 3 M1 for 10 × 6 and M1 for 0.5 × π × 32

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17 Solve the simultaneous equations. For Examiner′s 2x + 5y = 26 Use 4x + 3y = 24 Answer x = ............................................... y = ............................................... [3] _____________________________________________________________________________________

Mark scheme: 17 [x =] 3, [y =] 4 3 M1 for correctly eliminating one variable A1 for [x =] 3 A1 for [y =] 4 If zero scored, SC1 for correct substitution and evaluation to find the other variable. 7

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18 Simplify the following. (a) x5 × x2 Answer(a) ............................................... [1] (b) 20y4 ÷ 4y–2 Answer(b) ............................................... [2] _____________________________________________________________________________________

Mark scheme: 18 (a) x7 1 (b) 5y6 2 B1 for 5ym or ky6 in answer m ≠ 0, k ≠ 0

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19 Mario says that 5 gallons = 22.5 litres. For Examiner′s Use (a) On the grid, draw a straight line to show the conversion rate that Mario uses. 25 20 15 Litres 10 5 0 1 2 3 4 5 Gallons [2] (b) Use your graph to fi nd (i) the number of litres equivalent to 4 gallons, Answer(b)(i) ...................................... litres [1] (ii) the number of gallons equivalent to 15 litres. Answer(b)(ii) .................................. gallons [1] _____________________________________________________________________________________

Mark scheme: 19 (a) Ruled line from (0, 0) to (5, 22.5) 2 B1 for (5, 22.5) or (0, 0) at the ends of the ruled line. (b) (i) 17.5 to 18.5 1FT FT their straight line (ii) 3.3 to 3.4 1FT FT their straight line

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20 For Examiner′s Use The diagram shows part of the net of a cuboid. It is drawn full size. (a) Complete the net of the cuboid. [2] (b) Work out the volume of the cuboid. Write down the units of your answer. Answer(b) ................................ .............. [3] _____________________________________________________________________________________

Mark scheme: 20 (a) Net completed 2 With one 2 by 5, one 3 by 5 and two 2 by 3 rectangles correctly positioned B1 for 2 correct rectangles correctly positioned (b) 30 2 M1 for 3 × 2 × 5 cm3 1 Independent mark

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21 Use a straight edge and compasses only for the constructions in parts (a) and (b). For Examiner′s Leave in all your construction arcs. Use B A C (a) Construct the bisector of angle ABC. [2] (b) Construct the perpendicular bisector of AB. [2] (c) Shade the region inside triangle ABC containing points that are ● less than 7 cm from C and ● closer to A than to B. [2] _____________________________________________________________________________________

Mark scheme: 21 (a) Angle bisector with correct arcs 2 B1 for correct line, with incorrect or no arcs or correct arcs with incorrect or no line (b) Perpendicular bisector with two 2 B1 for correct line, with incorrect or no arcs or correct pairs of arcs correct arcs with incorrect or no line (c) Arc centre C, radius 7cm 1 Correct region shaded 1FT FT their arc centre C

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