Cambridge IGCSE Mathematics 0580 — 2011 Oct/Nov Paper 1 · Variant 2

1 The temperature on Monday is 3 °C. For On Tuesday it is 5 °C lower. Examiner's Use Find the temperature on Tuesday. Answer °C [1]

Mark scheme: Qu. Answers Mark Part Marks 1 −2(°C) 1

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2 Joseph changed 120 New Zealand dollars (NZ$) into Australian dollars (A$) when the exchange rate was NZ$1 = A$0.796 . Calculate the exact amount he received. Answer A$ [1]

Mark scheme: 2 95.52 1 3

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3 A bus leaves a port every 15 minutes, starting at 09 00. The last bus leaves at 17 30. How many times does a bus leave the port during one day? Answer [2]

Mark scheme: 3 3 35 2 M1 for 4 × 8 + 3 or 4 × 8 4 1 525 510 or 4 × 8 + 1 or or + 1 2 15 15 SC1 for answer 34

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4 Write the following in order of size, starting with the smallest. 9 1 1.2 115% 1 8 6 Answer I I I [2]

Mark scheme: 4 9 1 2 M1 for all decimals (or %), allow 1 error or < 115% < 1 < 1.2 B1 for 3 in correct order 8 6 9 1 eg 115% < < 1 < 1.2 8 6 SC1 for reverse order

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5 Mortar is a mixture of cement, sand and lime in the ratio For Examiner's cement : sand : lime = 1 : 5 : 2. Use Calculate how much sand there is in a 12 kg bag of this mortar. Answer kg [2]

Mark scheme: 5 7.5 2 M1 for 12 × 5 ÷ (1 + 5 + 2) oe

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6 Find the cube root of 96. Give your answer correct to 2 decimal places. Answer [2]

Mark scheme: 6 4.58 cao 2 B1 for 4.6(0) or 4.57 or 4.579 or 4.578 or 4.5789 or 4.5788… SC1 for 4.583 only 8

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7 Write these numbers in standard form. (a) 734 000 000 Answer(a) [1] (b) 0.000587 Answer(b) [1]

Mark scheme: 7 (a) 7.34 × 108 1 (b) 5.87 × 10–4 1

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8 The population, P, of Brunei in 2008 was 400 000 correct to the nearest 1000. For Examiner's Complete the statement about the value of P. Use Answer Y P I [2]

Mark scheme: 8 399 500 (≤ P <) 400 500 1, 1 SC1 for both correct reverse order

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9 Use your calculator to find the value of (a) 30 × 2.52, Answer(a) [1] (b) 2.5 – 2. Answer(b) [1]

Mark scheme: 9 (a) 6.25 cao 1 (b) 0.16 cao 1

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10 For Examiner's Use 115° B E NOT TO SCALE y° x° A 20° D C In the diagram, AB is parallel to CDE. Find the value of (a) x, Answer(a) x = [1] (b) y. Answer(b) y = [2]

Mark scheme: 10 (a) (x =) 20 1 (b) (y =) 65 2 B1 for ABD = 65° or ADB = 95°

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11 NOT TO SCALE x° 75° 2x° 2x° (a) For the diagram above, write down an equation in x. Answer(a) [1] (b) Solve your equation. Answer(b) x = [2]

Mark scheme: 11 (a) x + 2x + 2x + 75 = 360 1 Allow 4x + x + 75 = 360 or 5x + 75 = 360 or 5x = 285 (b) (x =) 57 cao 2 M1 correct first step after 5x + 75 = 360 ie 5x = 360 − 75 or x + 15 = 72 If zero SC1 for correct solution to their linear equation seen in part (a) or in part (b) if (a) is blank IGCSE – October/November 2011 0580 12 1 6 4 3 13 25

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1 1 1 3 For 12 Jiwan incorrectly wrote 1 + + + = 1 . Examiner's 2 3 4 9 Use Show the correct working and write down the answer as a mixed number. Answer [3]

Mark scheme: 1 6 4 3 13 25 12 212 cao with correct working 3 M1 (1+) 12 + 12 + 12 oe A1 (1)12 or 12 oe

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13 Solve these simultaneous equations. 5x – 2y = 17 2x + y = 5 Answer x = y = [3]

Mark scheme: 13 (x =) 3 (y =) –1 www 3 M1 for consistent multiply and consistent add/ subtract as appropriate Allow computational but not method errors Likely 5x + 4x = 17 + 10 Other methods allowed A1 for correct x or y

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14 A bag contains only red, yellow and blue counters. For Bashira picks a counter at random from the bag, records its colour, and puts it back in the bag. Examiner's She does this 60 times. Use (a) Complete the table for her results. Colour Frequency Relative frequency Red 19 Yellow Blue 28 [2] (b) Gita picks a counter at random from the same bag. Which colour counter is she most likely to pick? Answer(b) [1]

Mark scheme: 14 (a) 13 1 19 their 13 1ft All needed for the mark (Red) (Yellow) oe isw cancelling or decimals after correct fractions 60 60 seen 28 (Blue) oe 60 (b) Blue 1ft Strict ft their highest frequency

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15 A cruise ship travels at 22 knots. [1 knot is 1.852 kilometres per hour.] Convert this speed into metres per second. Answer m/s [3]

Mark scheme: 15 11.3 3 M2 22 × 1.852 × 1000/3600 oe or M1 22 × figs 1852 or 22 × 1000/3600

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16 (a) Write down a common multiple of 8 and 14. For Examiner's Use Answer(a) [1] (b) (i) Complete the list of factors of 81. 1, , , , 81 [2] (ii) Write down the prime factor of 81. Answer(b)(ii) [1]

Mark scheme: 16 (a) Any multiple of 56 1 (b) (i) 3, 9, 27 (in any order) 2 B1 for 2 correct (ii) 3 cao 1

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17 For y Examiner's B Use 6 5 4 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 A –3 –4 –5 –6 The diagram shows two straight lines, A and B, drawn on a grid. (a) Write down the equation of line A. Answer(a) [1] (b) The equation of line B is y = 3x – 1 . (i) Draw a line parallel to line B that passes through the point (0, 2). [1] (ii) Write down the equation of your line in the form y = mx + c. Answer(b)(ii) y = [2]

Mark scheme: 17 (a) y = −2 or y + 2 = 0 1 (b) (i) Ruled line parallel to B through 1 Must at least go through (−1, –1) (0, 2) (ii) (y =) 3x + 2 cao final answer 2 B1 3x + j j ≠ –1 or 2 or kx + 2 k ≠ 3 SC1 for 3x + 2 then spoiled by the final answer

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18 For O Examiner's Use NOT TO SCALE 75° A B (a) Triangle AOB is isosceles. OA = OB. Calculate angle AOB. Answer(a) Angle AOB = [1] (b) O NOT TO SCALE 75° A B AB is one side of a regular polygon with n sides. (i) Calculate n. Answer(b)(i) n = [2] (ii) Find the size of an interior angle of this polygon. Answer(b)(ii) [1]

Mark scheme: 18 (a) 30 1 (b) (i) 12 2ft M1 for 360 ÷ their (a) (Any answer for (a) for method) Only ft for A1 if 360 ÷ their (a) is an integer Other methods allowed if complete (ii) 150 cao 1

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19 (a) For y Examiner's Use 8 7 6 B C 5 4 3 A 2 1 x 0 1 2 3 4 5 6 7 8 Three vertices of the quadrilateral ABCD are shown in the diagram. (i) Write down the co-ordinates of the point B. Answer(a)(i) ( , ) [1] (ii) On the grid, plot and label the point D so that quadrilateral ABCD has rotational symmetry of order 2. [1] (iii) Draw the quadrilateral ABCD. Draw in all the lines of symmetry on your quadrilateral. [1] (b) Write down the mathematical names of these quadrilaterals. P Q Answer(b) P Q [2] Question 20 is printed on the next page.

Mark scheme: 19 (a) (i) (1, 5) 1 (ii) D at (5, 2) 1 (iii) Lines x = 3 and y = 3.5 only 1 Dep on (a)(ii) Extra line(s) zero drawn Lines should at least meet the sides (b) Kite Trapezium 1, 1 1 mark for each

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20 In a survey of 60 cars, the type of fuel that they use is recorded in the table below. For Examiner's Each car only uses one type of fuel. Use Petrol Diesel Liquid Hydrogen Electricity 40 12 2 6 (a) Write down the mode. Answer(a) [1] (b) Olav drew a pie chart to illustrate these figures. Calculate the angle of the sector for Diesel. Answer(b) [2] (c) Calculate the probability that a car chosen at random uses Electricity. Write your answer as a fraction in its simplest form. Answer(c) [2]

Mark scheme: 20 (a) Petrol cao 1 (b) 72 2 M1 for 360 × 12 ÷ 60 1 6 3 2 (c) 2 B1 or or or 0.1 or 10% 10 60 30 20

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