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

1 (a) Angelica goes to watch a football match. For She entered the stadium at 19 20 and left at 22 05. Examiner's Use Work out the number of hours and minutes she was in the stadium. Answer(a) hours minutes [1] (b) The number of people watching the football match was 25 926. Write 25 926 correct to the nearest thousand. Answer(b) [1] (c) The football club buys lemonade in 5 litre bottles. Work out the number of 250 millilitre drinks that can be poured from one bottle. Answer(c) [2] (d) The table shows the number of goals scored in each match by Mathsletico Rangers. Number of goals scored Number of matches 0 4 1 11 2 6 3 3 4 2 5 1 6 2 (i) Draw a bar chart to show this information. For Complete the scale on the frequency axis. Examiner's Use Frequency 0 1 2 3 4 5 6 Number of goals scored [3] (ii) Write down the mode. Answer(d)(ii) [1] (iii) Calculate the mean. Answer(d)(iii) [3]

Mark scheme: Qu. Part Answers Mark Part Marks 1 (a) 2 hours 45 minutes oe 1 (b) 26 000 1 (c) 20 2 M1 5 ÷ 0.25 or 5000 ÷ 250 (d) (i) fully correct bar chart 3 B1 correctly scaled frequency axis B2 correct height of bars ,width and spaces or B1 correct height of 5 or 6 bars or all bars correct height but unequal widths or gaps (ii) 1 1 (iii) 1.97 (1.9655….) 3 M1 attempt to multiply implied by 0, 11, 12, 9, 8, 5, 12 added implied by 57 M1 dep ft 57 ÷ their 29 or B2 1.96 or 2.103

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2 (a) The travel graph shows Helva’s journey from her home to the airport. For Examiner's Use 200 airport 180 160 140 120 Distance from home 100 (km) 80 60 40 20 home 0 08 00 10 00 12 00 14 00 16 00 Time (i) What happened at 09 30? Answer(a)(i) [1] (ii) Work out the time taken to travel from home to the airport. Give your answer in hours and minutes Answer(a)(ii) hours minutes [1] (iii) Calculate Helva’s average speed for the whole journey from home to the airport. Answer(a)(iii) km/h [2] (iv) Between which two times was Helva travelling fastest? Answer(a)(iv) and [1] (v) Helva’s husband left their home at 11 00 and travelled directly to the airport. He arrived at 15 30. Complete the travel graph for his journey. [1] (b) (i) Helva and her husband are flying from Finland to India. For Their plane takes off at 17 00 and arrives in India 7 hours 25 minutes later. Examiner's Use 1 The time in India is 3 hours ahead of the time in Finland. 2 What is the local time in India when the plane arrives? Answer(b)(i) [2] (ii) The temperature is O3°C in Finland and 23°C in India. Write down the difference between these two temperatures. Answer(b)(ii) °C [1] (c) Helva exchanged 7584 rupees for euros (€). The exchange rate was 1€ = 56 rupees. How many euros did Helva receive? Give your answer correct to 2 decimal places. Answer(c) € [2]

Mark scheme: 2 (a) (i) stopped 1 (ii) 5 hours 30 mins or 5 ½ hours 1 (iii) 32.72 – 32.73 or 32.7 2 ft M1 180 ÷ their (a)(ii) ft correct to 3 sig figs (iv) 10(00) and 12(00) 1 (v) Line or curve from 1100,0 to 1530,180 1 (b) (i) (0)355 or 3.55 am 2 B1 0025 or 2030 seen SC1 2055 as answer or 3.55 pm as answer (ii) 26° or –26° 1 (c) 135.43 cao 2 M1 135 or 135.4 or 7854 ÷ 56, implied by 135.(428…) IGCSE – October/November 2012 0580 33

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3 Mrs Ali sold her house for $600 000. For Examiner's Use 2 (a) She gives of the money to her son. 5 Work out how much her son receives. Answer(a)$ [1] (b) Mrs Ali gives $2400 to her grandchildren Elize, Sam and Juan in the ratio Elize : Sam : Juan = 8 : 3 : 5 . Calculate how much they each receive. Answer(b) Elize $ Sam $ Juan $ [3] (c) Mrs Ali invests $200 000 for 3 years at a rate of 4% per year compound interest. Calculate the total amount of money she will have at the end of the 3 years. Give your answer correct to the nearest dollar. Answer(c) $ [3] (d) Mrs Ali spends a total of $9000 on the following items. For Examiner's Use Amount spent ($) Angle in pie chart Holiday 4050 162° Television 90° Clothes 1800 72° Computer (i) Complete the table. [3] (ii) Complete the pie chart. Label each of your sectors. Holiday [2]

Mark scheme: 3 (a) 240000 1 (b) 1200, 450, 750 3 SC2 for all three correct in wrong order seen SC1 for 2400 ÷ 16 implied by 150 (c) 224973 3 M2 224972.8 or 200000 × 1.043 or 224793.0(0) if M0 M1 200000 × 1.042 or 216320 SC1 for their answer correctly rounded to nearest dollar (d) (i) 2250 1,1,1 If first B0,B0 then SC1 for adding to 3150 900 36 (ii) 2 correct sectors 1 correct labels 1 Must only be 4 sectors in total

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4 (a) Solve the following equations. For Examiner's (i) 6x O 2 = 2x + 8 Use Answer(a)(i) x = [2] (ii) 4(2y O 3) = 24 Answer(a)(ii) y = [3] (b) Solve the simultaneous equations. 5x + 9y = O21 12x O 2y = 44 Answer(b) x = y = [4]

Mark scheme: 4 (a) (i) 2.5 or 5/2 or 2 ½ 2 M1 6x − 2x = 8 + 2 or better (ii) 4.5 or 9/2 or 4 ½ 3 M1 8y − 12 or 2y − 3 = 6 M1 8y = 36 ft or 2y=9 ft their first step (b) (x =) 3, (y =) −4 4 M1 coefficient of x or y the same dep M1 for addition or subtraction A1 for 1 correct answer (their first answer)

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5 For y Examiner's Use 8 7 6 5 4 3 A 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 B –3 –4 –5 –6 (a) What special type of quadrilateral is shape A? Answer(a) [1] (b) Describe fully the single transformation which maps shape A onto shape B. Answer(b) [3] (c) On the grid (i) reflect shape A in the y-axis and label the image C, [2]  − 6  (ii) translate shape A by   and label the image D, [2]  − 4  (iii) enlarge shape A by scale factor 2, with centre (0, 0) and label the image E. [2]

Mark scheme: 5 (a) Parallelogram 1 (b) Rotation, 90° clockwise, about origin 1,1,1 (c) (i) Correct reflection 2 B1 reflection in the x axis (ii) Correct translation 2 B1 for translation –6,k or k,–4 (iii) Correct enlargement 2 B1 Correct size, wrong position

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6 (a) These are the first four terms of a sequence. For Examiner's Use 19 15 11 7 (i) Write down the next two terms of this sequence. Answer(a)(i) and [2] (ii) Write down the rule for finding the next term of this sequence. Answer(a)(ii) [1] (iii) Find an expression for the nth term of this sequence. Answer(a)(iii) [2] (b) The nth term of another sequence is 2n + 6 . Write down the first three terms of this sequence. Answer(b) , , [2] (c) The first three diagrams of a different sequence are shown below. Diagram 1 Diagram 2 Diagram 3 Complete the table. Diagram 1 2 3 8 n Number of lines 6 9 12 [3]

Mark scheme: 6 (a) (i) 3 − 1 1,1 If B0 award B1 if term 2 − term 1 = − 4 (ii) subtract 4 1 Accept minus 4, take away 4 (iii) − 4n + 23 oe final answer 2 M1 −4n+ k or jn+23 ( j ≠ 0) as answer (b) 8, 10, 12 2 M1 2 correct terms SC1 for 6, 8, 10 (c) 27, 3n+ 3 oe final answer 3 B1 27 B1 3n + k or jn + 3 ( j ≠ 0) IGCSE – October/November 2012 0580 33

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7 For H Examiner's Use NOT TO SCALE F C K G A B 117° D E I J The points F, G, H and I lie on a circle, centre C. FG is a diameter and DE is a tangent to the circle at I. DE is parallel to AB and angle GKI = 117°. Complete the following statements. (a) Angle FKI = because [2] (b) Angle FHG = because [2] (c) Angle EIJ = because [2] (d) Angle CIE = because [2]

Mark scheme: 7 (a) 63 1 (Angles on a straight) line (add to) 180 1 (b) 90 1 (Angle in a) semi circle 1 (c) 117 1 Corresponding (angles) 1 (d) 90 1 Tangent and radius 1

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8 For D Examiner's Use NOT TO SCALE 42° E C F H 8.5 m 6 m G 2 m A 12 m B The diagram shows a house, built on level ground. ABCE is a rectangle with AB = 12 m and BC = 8.5 m. CDE is an isosceles triangle. (a) Use trigonometry to calculate DF. Answer(a) DF = m [2] (b) Calculate the area of triangle CDE. Answer(b) m2 [2] (c) A ladder, GH, of length 6 m, leans against the house wall. The foot of the ladder is 2 m from this wall. Calculate AH. Answer(c) AH = m [3] (d) This diagram shows the plan of the driveway to the house. For Examiner's Use HOUSE 12 m NOT TO SCALE 18 m 3 m 14 m Work out the perimeter of the driveway. Answer(d) m [2] (e) The driveway is made from concrete. The concrete is 15 cm thick. Calculate the volume of concrete used for the driveway. Give your answer in cubic metres. Answer(e) m3 [4]

Mark scheme: 8 (a) 5.4(0) 2 M1 tan 42 = DF/6 or better (b) 32.4 2ft M1 12 × their 5.4 ft 2 (c) 5.66 3 M2 6 2 − 2 2 or better (accept √32 or 5.65) or M1 62 − 22 or better (accept 32 ) (d) 64 2 M1 12 + 18 + 14 + 3 + 2 + 15 (e) 33.3 cao 4 M1 (12 × 18) + (their (2) × 3) oe and A1 222 and M1 their 222 ft × 0.15

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9 (a) Complete the table of values for y = x2 + 2x O=4 . For Examiner's Use x O4 O3 O2 O1 0 1 2 3 y 4 O4 O4 11 [3] (b) On the grid, draw the graph of y = x2 + 2x O=4 for O4 Y x Y 3 . y 12 11 10 9 8 7 6 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 –1 –2 –3 –4 –5 –6 [4] (c) (i) Draw the line of symmetry on the graph. [1] For Examiner's Use (ii) Write down the equation of this line of symmetry. Answer(c)(ii) [1] (d) Use your graph to solve the equation x2 + 2x O=4 = 3 Answer(d) x = or x = [2] Question 10 is printed on the next page.

Mark scheme: 9 (a) −1, −5, −1, 4 3 B2 3 correct B1 2 correct (b) 8 correct points plotted 3ft B2ft 6 or 7 points plotted ft B1ft 4 or 5 points plotted ft Smooth curve through 8 correct points 1 and correct shape (c) (i) x = − 1 drawn 1 (ii) x = − 1 oe cao 1 (d) 1.8 to 1.9 and –3.8 to – 3.9 2 ft B1 B1 IGCSE – October/November 2012 0580 33

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10 (a) The diagram shows the positions of three towns A, B and C. For The scale is 1 cm represents 2 km. Examiner's Use North North C A North B Scale: 1 cm = 2 km (i) Find the distance in kilometres from A to B. Answer(a)(i) km [2] (ii) Town D is 9 km from A on a bearing of 135°. Mark the position of town D on the diagram. [2] (iii) Measure the bearing of A from C. Answer(a)(iii) [1] (b) The population of town C is 324 100. (i) Write this number in standard form. Answer(b)(i) [1] (ii) The population of town D is 7.64 × 104. Which town, C or D, has the larger population and by how much? Give your answer in standard form. Answer(b)(ii) Town by [3]

Mark scheme: 10 (a) (i) 14.8 to 15.2 2 M1 7.4 to 7.6 (ii) D correctly marked 133 –137° and 2 B1 for correct bearing or distance. 4.3 −4.7 cm from A (iii) 260 to 264° 1 (b) (i) 3.24 (1) × 105 1 (ii) C by 2.477 × 105 3 SC2 for C by figs 2477 or figs 248 or 2.48 × 105 M1 324100 – 76400 or their (b) − 7.64 × 104 evaluated

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