Cambridge IGCSE Mathematics 0580 — 2012 Oct/Nov Paper 3 · Variant 1

1 (a) (i) Write down two numbers that are multiples of 10. For Examiner's Use Answer(a)(i) and [1] (ii) Find the lowest common multiple of 10 and 15. Answer(a)(ii) [2] (b) 4 6 9 15 23 27 32 36 From the list above, write down (i) a factor of 18, Answer(b)(i) [1] (ii) a cube number, Answer(b)(ii) [1] (iii) a prime number. Answer(b)(iii) [1] (c) Give an example to show that each of these statements is not true. (i) All square numbers are even. Answer(c)(i) [1] (ii) When two prime numbers are added the answer is always even. Answer(c)(ii) [1] (d) Write the following in order of size, starting with the smallest. 25 80 4–2 169 Answer(d) I I I [2]

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) Any two multiples of 10 1 (ii) 30 2 B1 for any other common multiple of 10 and 15 ie 30k (b) (i) 6 or 9 or 6 and 9 cao 1 (ii) 27 cao 1 (iii) 23 cao 1 (c) (i) Example of odd square number 1 (ii) Example of odd sum of primes 1 (d) 4–2, 80, 169 , 25 2 B1 for only 1 out of order or for three seen correctly evaluated

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2 (a) Luka earns $475 each week. For Examiner's Use (i) He works for 38 hours each week. How much does he earn for each hour he works? Answer(a)(i) $ [1] (ii) Luka pays $175 in rent each week. Write the amount he pays in rent as a fraction of his weekly earnings. Give your answer in its lowest terms. Answer(a)(ii) [2] 7 (iii) He spends of his weekly earnings on bills. 20 How much money does he have left after paying rent and bills? Answer(a)(iii) $ [2] (b) Luka’s weekly earnings of $475 are increased by 6%. Calculate his new weekly earnings. Answer(b) $ [2] (c) Luka has saved $350. He invests this for 2 years at a rate of 4% per year compound interest. How much interest does he receive after 2 years? Answer(c) $ [3]

Mark scheme: 2 (a) (i) 12.5(0) 1 7 175 (ii) 2 B1 for oe seen 19 475 7 (iii) 133.75 2 M1 for × 475 20 (b) 503.5(0) 2 M1 for 106 ÷ 100 × 475 Or 475 + (6 ÷ 100 × 475) (c) 28.56 3 M1 for 350 × 1.042 oe dep M1 for ‘their 378.56’ – 350 Or M1 for (350 × 0.04) (imp by 14) and (350 + ‘their 14’) × 0.04 (imp by 14.56) dep M1 ‘their 14’ + ‘their 14.56’ IGCSE – October/November 2012 0580 31

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3 (a) Amir asked 15 friends how many hours they spent playing sport last weekend. For His results are shown in the table below. Examiner's Use Number of hours 0 1 2 3 4 5 Frequency 6 2 3 1 2 1 (i) Write down the mode. Answer(a)(i) hours [1] (ii) Find the median. Answer(a)(ii) hours [1] (iii) Calculate the mean. Answer(a)(iii) hours [3] (iv) On the grid, draw a bar chart to show the information given in the table. Frequency Number of hours [4] (b) Amir also asked these 15 friends which was their favourite sport. For His results are shown in the table below. Examiner's Use Football 4 Cricket 5 Basketball 2 Badminton 4 Amir picks one of these friends at random. Write down the probability that his friend’s favourite sport is (i) cricket, Answer(b)(i) [1] (ii) not football, Answer(b)(ii) [1] (iii) basketball or badminton. Answer(b)(iii) [1]

Mark scheme: 3 (a) (i) 0 1 (ii) 1 1 (iii) 1.6 3 M1 for (0 × 6) + 1 × 2 + 2 × 3 + 3 × 1 + 4 × 2 + 5 × 1 or better dep M1 for ‘their 24’ ÷ 15 (iv) Bar chart with 4 – horizontal axis correctly labelled B1 for horizontal axis labelled correctly – and vertical axis correctly scaled B1 for linear vertical scale to at least 5 – and bars of correct height and B2 for all bars correct height and equal width equal width, with equal or no gaps – and with equal gaps or no gaps Or B1 for unequal widths or at least four bars correct height and equal width 5 1 (b) (i) or 15 3 1 11 (ii) 1 15 6 2 (iii) or 1 15 5

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4 (a) For C Examiner's Use 70° NOT TO SCALE D 40° B E A In the diagram, ACE is a triangle. B is a point on AC and D is a point on CE. AE is parallel to BD, angle ACE = 70° and angle CBD = 40°. (i) Find angle BDC. Answer(a)(i) Angle BDC = [1] (ii) Write down the mathematical name of triangle BCD. Answer(a)(ii) [1] (iii) Find angle CAE. Give a reason for your answer. Answer(a)(iii) Angle CAE = because [2] (iv) Complete the following statement. Triangle ACE and triangle BCD are [1] (b) For Examiner's Use A NOT TO SCALE O C 55° B In the diagram, A and B lie on a circle, centre O. AC and BC are tangents to the circle and angle ACB = 55°. (i) Work out reflex angle ACB. Answer(b)(i) Reflex angle ACB = [1] (ii) Give a reason why angle OAC = angle OBC = 90°. Answer(b)(ii) [1] (iii) Work out angle AOB. Answer(b)(iii) Angle AOB = [1] (iv) Write down the mathematical name of quadrilateral OACB. Answer(b)(iv) [1]

Mark scheme: 4 (a) (i) 70° 1 (ii) isosceles 1 (iii) 40° 1 Corresponding (to angle CBD) 1 dep on 40° (accept longer reasons) (iv) similar 1 (b) (i) 305° 1 (ii) (Angle between) tangent (and) 1 radius (iii) 125° or 235° 1 (iv) kite 1 IGCSE – October/November 2012 0580 31 2 2 2

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5 For B 20 m C Examiner's Use NOT TO SCALE 15 m A 32 m D The diagram shows a plot of land, ABCD, in the shape of a trapezium. (a) Show that CD = 19.2 m, correct to 1 decimal place. Answer(a) [2] (b) A fence is built around the perimeter of the plot of land. The cost of the fence is $35 for each metre. Calculate the total cost of the fence. Answer(b) $ [2] (c) Calculate the area of the plot of land. Give your answer in square metres. Answer(c) m2 [2] (d) A house is built on the plot of land. For The area of the plot is divided in the ratio house : grounds = 3 : 7 . Examiner's Use Calculate the area of the grounds. Answer(d) m2 [2] (e) (i) In the space below, make a scale drawing of the plot of land. Use a scale of 1 centimetre to represent 4 metres. The side AB has been drawn for you. B A [2] (ii) Measure angle ADC. Answer(e)(ii) Angle ADC = [1] (iii) Use your diagram to find the actual length BD in metres. Answer(e)(iii) BD = m [1]

Mark scheme: 5 (a) (CD2 =) (32 – 20)2 + 152 oe M1 (CD =) 369 = 19.20 to 19.21 A1 A0 for 19.2 alone. 2 M1 for 20 + 15 + 32 + 19.2(1) [implied by (b) 3017 86.2(1)] Or M1 for (20 × 35) + (15 × 35) + (32 × 35) + (19.2(1) × 35) 2 M1 for (20 + 32) × 15 ÷ 2 oe (c) 390 2ft M1 for ‘their (c)’ × 7 ÷ 10 (d) 273 2 B1 for C or D correctly positioned (e) (i) trapezium constructed BC = 5 cm, AD = 8 cm Both 90o to AB 1ft (ii) 49 – 53° 1ft (iii) 34.4 – 36.4 m

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6 For Examiner's Use Diagram 1 Diagram 2 Diagram 3 Diagram 4 A sequence of diagrams is made from black counters and white counters. The first four diagrams in the sequence are shown. (a) Complete the table. Diagram 1 2 3 4 5 Number of black counters 1 4 Number of white counters 1 4 [4] (b) Complete the statement. The numbers of black counters are all numbers. [1] (c) How many white counters are needed for (i) Diagram 8, Answer(c)(i) [1] (ii) Diagram n? Answer(c)(ii) [2] (d) Diagram p contains 58 white counters. For Examiner's Use (i) Find the value of p. Answer(d)(i) p = [2] (ii) Find the number of black counters in Diagram p. Answer(d)(ii) [1]

Mark scheme: 6 (a) 9 16 25 2 B1 for 2 correct 7 10 13 2 B1 for 2 correct, or difference of 3 between diagrams 4 and 5 (b) square 1 (c) (i) 22 1 (ii) 3n – 2 oe final answer 2 B1 for 3n ± j seen Or kn – 2, where k ≠ 0 (d) (i) 20 2 ft M1 for ‘their (c)(ii)’ = 58 or better, seen (ii) 400 1ft ‘their (d)(i)’2 (must be evaluated) IGCSE – October/November 2012 0580 31

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7 (a) The cost, $C, of hiring a meeting room for n people is calculated using the formula For Examiner's Use C = 80 + 5n. (i) Calculate C when n = 12. Answer(a)(i) [2] (ii) Maria pays $230 to hire the meeting room. Work out the number of people at the meeting. Answer(a)(ii) [2] (iii) Make n the subject of the formula C = 80 + 5n. Answer(a)(iii) n = [2] (b) Expand and simplify 2(3x + 4) – 3(2 – x) . Answer(b) [2] (c) Solve the simultaneous equations. 3x + y = 13 2x + 3y = 18 Answer(c) x = y = [3]

Mark scheme: 7 (a) (i) 140 2 M1 for 80 + 5 × 12 or better (ii) 30 2 M1 for (230 – 80) ÷ 5 or 150 seen C − 80 C 80 −C (iii) or − 16 or 2 M1 for C – 80 = 5n 5 5 − 5 C 80 5n final answer Or M1 for = + or better 5 5 5 (b) 9x + 2 final answer 2 M1 for 9x + k or mx + 2 or 6x + 8 or – 6 + 3x or 9x + 2 spoilt (c) x = 3, y = 4 3 M1 for correct method to eliminate one variable A1 x = 3 A1 y = 4

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8 (a) A water tank in the shape of a cuboid measures 55 cm by 40 cm by 75 cm. For Examiner's Use (i) Find the volume of the tank. Answer(a)(i) cm3 [2] (ii) Write down the volume of the tank in litres. Answer(a)(ii) litres [1] (b) Another water tank contains 260 litres. (i) The tank is emptied at a rate of 25 litres per minute. Work out the time taken to completely empty the tank. Give your answer in minutes and seconds. Answer(b)(i) minutes seconds [2] (ii) 260 litres is given correct to the nearest 10 litres. Write down the lower bound of this amount. Answer(b)(ii) litres [1] (c) A different tank is in the shape of a cube. It has a volume of 27 000 cm3. Find the height of this tank. Answer(c) cm [2]

Mark scheme: 8 (a) (i) 165 000 2 M1 for figs 165 or 55 × 40 × 75 seen (ii) 165 1ft ‘their (a)(i)’ ÷ 1000 (b) (i) 10 minutes 24 seconds 2 M1 for 260 ÷ 25 or 10.4 seen or 624 seen (ii) 255 1 3 27000 (c) 30 2 M1 for

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9 (a) Complete the table of values for y = 8 + 3x – x2. For Examiner's Use x –3 –2 –1 0 1 2 3 4 5 6 y –10 8 10 10 –10 [3] (b) On the grid, draw the graph of y = 8 + 3x – x2 for –3 Y x Y 6 . y 12 10 8 6 4 2 x –3 –2 –1 0 1 2 3 4 5 6 –2 –4 –6 –8 –10 [4] (c) Write down the equation of the line of symmetry of the graph. Answer(c) [1] (d) (i) On the grid, draw the graph of y = 6 . [1] (ii) Use your graphs to solve the equation 8 + 3x – x2 = 6 . Answer(d)(ii) x = or x = [2]

Mark scheme: 9 (a) y-values –2, 4, 8, 4, –2 3 B2 for 3 or 4 correct B1 for 2 correct (b) 10 correctly plotted points 3ft B2ft for 8 or 9 points B1ft for 6 or 7 points Smooth curve through 10 correct 1 Curve must pass above y = 10 points and correct shape. (c) x = 1.5 oe 1 (d) (i) Line y = 6 drawn 1 (ii) x = 3.5 to 3.7 1ft Ft their curve and their line drawn x = – 0.7 to – 0.5 1ft IGCSE – October/November 2012 0580 31

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10 For y Examiner's Use 8 7 6 5 C 4 3 A 2 B 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 –7 –8 Shapes A, B and C are shown on the grid. (a) Describe fully the single transformation which maps (i) shape A onto shape B, Answer(a)(i) [3] (ii) shape A onto shape C. Answer(a)(ii) [3] (b) On the grid, draw the image of shape A after  3  (i) translation by the vector   , [2]  −4  (ii) reflection in the line y = –1. [2]

Mark scheme: 10 (a) (i) Rotation, 3 B1 for each 90° anticlockwise oe, (centre) (0, 0), origin, O (ii) Enlargement, 3 B1 for each (scale factor) 2, (centre) (–1, 1) (b) (i) correct translation 2 B1 for 3 right or 4 down (ii) correct reflection 2 B1 for reflection in any line parallel to x-axis or for correct reflection in x = –1

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