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

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

Mark scheme: Qu. Answers Mark Part Marks 33 1 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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2 Factorise completely ax + bx + ay + by. Answer [2]

Mark scheme: 2 (a + b)(x + y) 2 M1 x(a + b) + y(a + b) or M1 a(x + y) + b(x + y)

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

Mark scheme: 3 (a) 6.25 cao 1 (b) 0.16 cao 1

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4 The cost of making a chair is $28 correct to the nearest dollar. Calculate the lower and upper bounds for the cost of making 450 chairs. Answer lower bound $ upper bound $ [2]

Mark scheme: 4 12375 cao 2 B1, B1 12825 cao If no marks scored give M1 for 27.5 and 28.5 seen 1 6 4 3 13 25

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1 1 1 3 For 5 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 5 212 cao with correct working 3 M1 (1+) 12 + 12 + 12 oe A1 (1)12 or 12 oe 2

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6 The force, F, between two magnets varies inversely as the square of the distance, d, between them. F = 150 when d = 2. Calculate F when d = 4. Answer F = [3]

Mark scheme: 6 37.5 3 M1 F = k/d 2 A1 k = 600

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 0 2   a   8  For 7     =   Examiner's _  3 4   b   25  Use Find the value of a and the value of b. Answer a = b = [3]

Mark scheme: 7 a = –3 3 M1 –3a + 4b = 25 b = 4 B1 one correct

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8 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: 8 11.3 3 M2 22 × 1.852 × 1000/3600 oe or M1 22 × figs 1852 or 22 × 1000/3600 ( ) ( )

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9 A sequence is given by u1 = 1 , u2 = 3 , u3 = 5 , u4 = 7 , … For Examiner's Use (a) Find a formula for un , the nth term. Answer(a) un = [2] (b) Find u29 . Answer(b) u29 = [1]

Mark scheme: 9 (a) (2 n − )1 2 M1 (2 n + k ) or 2n – 1 (b) 57 or 7.55 1ft From their (a) 2 2

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10 Write as a single fraction in its simplest form. 3 1 O x + 10 x + 4 Answer [3]

Mark scheme: 10 2 x + 2 3 B1 common denominator (x + 10)(x + 4) oe seen oe ( x + 10 )( x + 4 ) B1 3(x + 4) – (x + 10) seen oe 3 3

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11 Find the values of m and n. For Examiner's (a) 2m = 0.125 Use Answer(a) m = [2] (b) 24n × 22n = 512 Answer(b) n = [2]

Mark scheme: 11 (a) –3 2 M1 1/23 or 2–3 (b) 1.5 2 M1 26n or 6n = 9

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12 40 30 Small car Speed 20 (m / s) Large car 10 0 1 2 3 4 5 6 7 8 9 10 Time (seconds) A small car accelerates from 0 m/s to 40 m/s in 6 seconds and then travels at this constant speed. A large car accelerates from 0 m/s to 40 m/s in 10 seconds. Calculate how much further the small car travels in the first 10 seconds. Answer m [4]

Mark scheme: 12 80 www 4 M1 attempting area under the graph M1 large or small car area found correctly Dep M1 correct final area statement

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13 For North Examiner's T Use B NOT TO SCALE 76° A C O P AOC is a diameter of the circle, centre O. AT is a straight line that cuts the circle at B. PT is the tangent to the circle at C. Angle COB = 76°. (a) Calculate angle ATC. Answer(a) Angle ATC = [2] (b) T is due north of C. Calculate the bearing of B from C. Answer(b) [2]

Mark scheme: 13 (a) 52 2 M1 OAB or OBA = 38 or OCT = 90 (b) 322 2 M1 BCT = 38 or BCO = 52 IGCSE – October/November 2011 0580 22

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14 For y Examiner's Use 7 6 5 R 4 3 2 1 x 0 1 2 3 4 5 6 7 The region R is bounded by three lines. Write down the three inequalities which define the region R. Answer [4]

Mark scheme: 14 y ≤ 5 4 B1 each inequality but accept any of the four x ≥ 2 inequality symbols y ≥ x Final B1 all 3 symbols correct

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15 For y Examiner's Use 6 5 B 4 3 2 A 1 x 0 1 2 3 4 5 6 The points A(1, 2) and B(5, 5) are shown on the diagram . (a) Work out the co-ordinates of the midpoint of AB. Answer(a) ( , ) [1] (b) Write down the column vector .     Answer(b) =   [1]     (c) Using a straight edge and compasses only, draw the locus of points which are equidistant from A and from B. [2]

Mark scheme: 15 (a) (3, 3½) 1  4  (b)   1  3  (c) Correct perpendicular bisector with 2 B1 line through (3, 3½) perp to AB arcs B1 two sets of correct arcs

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16 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: 16 (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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17 For a Examiner's O A Use c M C B 4a O is the origin, = a, = c and = 4a. M is the midpoint of AB. (a) Find, in terms of a and c, in their simplest form (i) the vector , Answer(a)(i) = [2] (ii) the position vector of M. Answer(a)(ii) [2] (b) Mark the point D on the diagram where = 3a + c. [2]

Mark scheme: 17 (a) (i) 3a + c 2 B1 AO + OC + CB or –a + c + 4a 1 1 1 (ii) 2 a + c oe 2 M1 a + their (a)(i) 2 2 2 (b) D marked ¾ way along CB 2 B1 D on CB 5

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1 18 w = LC (a) Find w when L = 8 × 10 O3 and C = 2 × 10 O9. Give your answer in standard form. Answer(a) w = [3] (b) Rearrange the formula to make C the subject. Answer(b) C = [3] Question 19 is printed on the next page.

Mark scheme: 18 (a) 2.5 × 105 3 B2 250000 oe or M1 correct part value seen (b) C = 1/(Lw2) 3 M1 each correct move

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19 For y Examiner's Use 6 5 C 4 A 3 2 1 B x 0 1 2 3 4 5 6 7 A(1, 3), B(4, 1) and C(6, 4) are shown on the diagram. (a) Using a straight edge and compasses only, construct the angle bisector of angle ABC. [2] (b) Work out the equation of the line BC. Answer(b) [3] (c) ABC forms a right-angled isosceles triangle of area 6.5 cm2. Calculate the length of AB. Answer(c) AB = cm [2]

Mark scheme: 19 (a) correct bisector (through 3½, 3½) 2 B1 correct line B1 correct arcs 1 1 (b) y = 1 x – 5 oe 3 B2 y = 1 x + k or y = kx – 5 k any number 2 2 1 or B1 1 x + k or kx – 5 2 1 If O scored allow one each for m = 1 or c = –5 2 clearly identified in working 1 2 2 (c) 3.61 2 M1 × L × L = 6.5 or M1 (3 + 2 ) 2

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