Cambridge IGCSE Mathematics 0580 — 2012 May/June Paper 3 · Variant 3

1 (a) The minimum temperatures at Beijing Airport, for five days, are given in this table. For Examiner's Use Day Monday Tuesday Wednesday Thursday Friday Temperature (°C) –3 5 –1 2 –4 (i) Write down the lowest temperature. Answer(a)(i) °C [1] (ii) Write these temperatures in order, starting with the lowest. Answer(a)(ii) < < < < [1] (iii) What is the difference between the temperatures on Monday and Tuesday? Answer(a)(iii) °C [1] (b) The table shows part of the timetable for flights from Beijing to Hong Kong. Beijing 07 45 08 00 09 30 Hong Kong 11 20 11 40 13 05 (i) At what time does the first plane after midday arrive in Hong Kong? Answer(b)(i) [1] (ii) How long, in hours and minutes, does the 07 45 flight from Beijing to Hong Kong take? Answer(b)(ii) h min [1] (c) A plane travels 1708 km in 3.5 hours. Work out the average speed of the plane. Give the units of your answer. Answer(c) [2]

Mark scheme: Qu. Answers Mark Part Mark 1 (a) (i) –4 1 (ii) –4 –3 –1 2 5 1 (iii) 8 1 allow –8 (b) (i) 1305 1 (ii) 3 (h) 35 (m) cao 1 (c) 488 1 km/h 1

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2 (a) Find all the factors of 28 . For Examiner's Use Answer(a) [2] (b) Write down a multiple of 8 that is greater than 20 . Answer(b) [1] (c) Work out 183 . Answer(c) [1] (d) p and q are prime numbers. p3 × q2 = 200 Find the values of p and q. Answer(d) p = q = [2] (e) A town has two bus companies. Buses from Western Travel stop at the Town Hall every 8 minutes. Buses from Eastern Travel stop at the Town Hall every 14 minutes. (i) Write down the lowest common multiple of 8 and 14 . Answer(e)(i) [2] (ii) A bus from each company stops at the Town Hall at 08 00. When is the next time that a bus from each company stop together at the Town Hall? Answer(e)(ii) [1] (iii) The cost of an adult ticket on Western Travel is $a and the cost of a child’s ticket is $c. One day 84 adult tickets and 36 child tickets are sold. Write an expression, in terms of a and c, for the total cost of these tickets. Answer(e)(iii) $ [2]

Mark scheme: 2 (a) 1, 2, 4, 7, 14, 28 2 1 for four or five correct or 1 × 28 and 2 × 14 and 4 × 7 (b) 24 1 (c) 5832 1 (d) (p =) 2 1 (q =) 5 1 (e) (i) 56 2 M1 for a method to achieve this such as prime factors, 8 = 23 and 14 = 2 × 7 or another multiple of 56, or two trials (ii) 08 56 1ft accept 8 56 (am) (iii) 84a + 36c final answer 2 B1 for either 84a or 36c IGCSE – May/June 2012 0580 33

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3 Here is a scale drawing of a shop floor, EFGH. For The scale is 1 centimetre represents 2 metres. Examiner's Use F G H Scale: 1 cm to 2 m E (a) What is the mathematical name of the shape EFGH? Answer(a) [1] (b) What type of angle is angle EFG? Answer(b) [1] (c) Find the actual length, in metres, of the side EH. Answer(c) m [2] (d) Measure angle FEH. Answer(d) Angle FEH = [1] (e) Complete this part using ruler and compasses only. All construction arcs must be clearly shown. A table is placed • nearer to E than to H and • less than 14 m from H. By constructing two loci on the scale drawing, find and label the region R, where the table is placed. [5] (f) The shop sells shoes which are packed in boxes. Each box is a cuboid 33.2 cm long, 16.8 cm wide and 11 cm high. Calculate the volume of one of these shoe boxes. Answer(f) cm3 [2]

Mark scheme: 3 (a) quadrilateral 1 (b) obtuse 1 (c) 23.6–24.4 2 M1 for 11.8 – 12.2 (d) 31–35 1 (e) construction of perpendicular 5 B1 for two pairs of arcs, same radius, centres E bisector of EH and H part circle centre H radius 7 cm B1 for bisector within 2mm of correct one, ± 2° of indication of region correct angle B1 for part circle centre H B1 for radius 7 cm B1ft for an indication of the region, ft dependent on at least B2 from above (f) 6135.36 or 6135.4 or 6135 or 6140 2 M1 for 33.2 × 16.8 × 11

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4 (a) In a café the price of an adult’s meal is $24 and the price of a child’s meal is $16. For A 12% service charge is added to the costs of the meals. Examiner's Use Calculate the total cost of meals for 2 adults and 3 children. Answer(a) $ [3] (b) On a Saturday night the adult meal price of $24 is increased by 20%. Calculate the increased price of this meal. Answer(b) $ [2] (c) The price of a large cup of coffee increases from $3.00 to $3.42 . Calculate the percentage increase in the price. Answer(c) % [3]

Mark scheme: 4 (a) 107.52 3 M1 2×24 + 3×16 or 96 M1 for their 96 × 1.12 oe (b) 28.8(0) 2 M1 for 24 × 1.2(0) oe (c) 14 3 B1 for 42(c) or ($ 0).42 42 .042 M1 for their oe (× 100) or (× 100) 300 3 .342 342 alt. method : M1 (× 100) or (× 100) 3 300 M1 their 114 – 100

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5 (a) Draw all the lines of symmetry on this rectangle. For Examiner's Use [2] (b) Shade one square so that the shaded shape has rotational symmetry of order 2. [1] (c) On the grid below, draw an enlargement of the triangle with a scale factor of 2. [2] (d) For y Examiner's Use 6 5 4 3 A 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 D –3 –4 P –5 –6 (i) Write down the co-ordinates of the point P. Answer(d)(i) ( , ) [1] (ii) Reflect triangle A in the y-axis. Label the image B. [1]  1  (iii) Translate triangle A by the vector   .  −3  Label the image C. [2] (iv) Describe the single transformation that maps triangle A onto triangle D. Answer(d)(iv) [3]

Mark scheme: 5 (a) two correct ruled lines 1,1 SC1 correct but freehand or fully correct with one extra line (b) correct square shaded 1 (c) correct enlargement 2 1 for a correct side (d) (i) 1, –5 1 (ii) correct reflection 1 (iii) correct translation 2 B1 for either direction e.g. 1 to the right or 3 down SC1 for complete correct 3 left and 1 up triangle (iv) rotation, (centre) (0,0) 3 1 for rotation, 1 for (centre) (0,0), 1 for angle 180 angle 180 IGCSE – May/June 2012 0580 33

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6 James and Wei have a car. For Each year James drives 3 600 km and Wei drives 4 800 km. Examiner's Use (a) Write 3 600 : 4 800 as a ratio in its simplest form. Answer(a) : [1] (b) A garage charges $420 to service the car. James and Wei share the $420 in the ratio James : Wei = 2 : 3 . Find the amount that James pays. Answer(b) $ [2] (c) On a 268 km journey the car uses 22.8 litres of fuel. By writing these numbers to 1 significant figure, estimate the distance travelled using one litre of fuel. Show all your working. Answer(c) km [2] (d) On another journey the car uses 46.3 litres of fuel. Fuel costs $1.48 per litre. Work out the cost of the fuel for this journey. Answer(d) $ [2] (e) The table shows some information about the car. For Examiner's Use Fuel tank capacity 64 litres (to the nearest litre) Width 1810 mm (to 3 significant figures) (i) Write down the upper bound of the fuel tank capacity. Answer(e)(i) litres [1] (ii) Write down the minimum width of the car. Answer(e)(ii) mm [1]

Mark scheme: 6 (a) 3 : 4 cao 1 (b) 168 2 M1 420 ÷ (2 + 3) or 84 seen (c) 300 ÷ 20 = 15 2 250 / 260 / 270 / 300 if 0 scored SC1 for 20 / 23 / 25 or 15 ww (d) 68.5(2) 2 M1 for 46.3 × 1.48, 68.53 or 68.524 (e) (i) 64.5 1 (ii) 1805 1

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7 The table shows the marks for ten students in their Chemistry papers for Unit A and Unit B. For Examiner's Use Unit A 32 78 45 63 36 73 58 41 68 54 Unit B 43 81 49 58 40 74 60 50 72 59 (a) On the grid, complete the scatter diagram for these results. The first six points have been plotted for you. 90 80 70 Unit B 60 50 40 30 30 40 50 60 70 80 90 Unit A [2] (b) What type of correlation does the scatter diagram show? Answer(b) [1] (c) (i) Calculate the mean of the marks for Unit A. For Examiner's Use Answer(c)(i) [2] (ii) Work out the range of the marks for Unit A. Answer(c)(ii) [1] (iii) The mean for Unit B is 58.6 . Which unit did the students find more difficult? Give a reason for your answer. Answer(c)(iii) Unit because [1] (d) (i) Draw a line of best fit on the grid. [1] (ii) Lee scored 48 on Unit A but she was absent for Unit B. Use your line of best fit to estimate her score on Unit B. Answer(d)(ii) [1] (e) Find how many students scored more than 65 marks on both units. Answer(e) [1]

Mark scheme: 7 (a) four points correctly plotted 2 M1 for three points correctly plotted (b) positive 1 ignore extras like ‘strong’ (c) (i) 54.8 2 M1 for their sum (548) ÷ 10 (ii) 46 1 (iii) A and it has a lower mean 1ft allow any correct reason using appropriate information from the table and ft their mean (d) (i) correct ruled line 1 at A = 40 allow 44–48 at A = 70 allow 70–78 (ii) correct reading from their line 1ft read from their ruled line (e) 3 1ft

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8 (a) Complete the table of values for y = x2 – 2x + 5 . For Examiner's Use x –3 –2 –1 0 1 2 3 4 5 y 20 8 8 20 [3] (b) On the grid, draw the graph of y = x2 – 2x + 5 for −3 Y x Y 5 . y 22 20 18 16 14 12 10 8 6 4 2 x –4 –3 –2 –1 0 1 2 3 4 5 6 [4] (c) (i) On the grid, draw the line of symmetry of the graph. [1] (ii) Write down the equation of the line of symmetry. Answer(c)(ii) [1] (d) (i) On the grid, draw the line y = 12 . [1] For Examiner's (ii) Use your graph to solve the equation x2 – 2x + 5 = 12 . Use Answer(d)(ii) x = or x = [2] (e) The equation of a straight line is y = 6 – 3x . (i) Write down the gradient of this line. Answer(e)(i) [1] (ii) Write down the co-ordinates of the point where this line crosses the y-axis. Answer(e)(ii) ( , ) [1] (iii) Write down the equation of a line parallel to y = 6 – 3x . Answer(e)(iii) [1] (f) Simplify 3(2x + 1) O=2(6 – 3x) . Answer(f) [2]

Mark scheme: 8 (a) (20) 13 (8) 5 4 5 (8) 13 (20) 3 B2 for 4 correct B1 for 2 or 3 correct or a correct substitution seen (b) correctly plotting 9 points and 4 P3 for correctly plotting 9 points, P2 for correctly connecting with a smooth curved line plotting 7 or 8 points and P1 for 5 or 6 points C1 for a smooth curve (c) (i) correct line of symmetry cao 1 (ii) x = 1 1ft ft their line (d) (i) correct line 1 (ii) –1.9 to –1.7 and 3.7 to 3.9 1ft,1ft SC1 for correct co-ordinates (e) (i) –3 cao 1 (ii) (0,6) cao 1 (iii) y = c – 3x 1 c can be any number except 6 (f) 12x – 9 or 3(4x – 3) 2 B1 for 6x + 3, –12 + 6x, 12x or –9 IGCSE – May/June 2012 0580 33

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9 The diagram shows a regular hexagon inside a circle, centre O and radius 8 cm. For Each vertex of the hexagon is on the circumference of the circle. Examiner's A and B are two vertices of the hexagon and M is the midpoint of AB. Use NOT TO SCALE O 8 cm A M B (a) Calculate (i) angle AOB, Answer(a)(i) Angle AOB = [1] (ii) angle AOM. Answer(a)(ii) Angle AOM = [1] (b) Write down the length AB. Answer(b) AB = cm [1] (c) Show that the length of OM = 6.93 cm, correct to 3 significant figures. Answer(c) [2] (d) Calculate the area of triangle AOB. For Examiner's Use Answer(d) cm2 [2] (e) Calculate the shaded area. Answer(e) cm2 [4] Question 10 is printed on the next page.

Mark scheme: 9 (a) (i) 60 1 (ii) 30 1ft ft their (i) ÷ 2 (b) 8 (cm) 1 x (c) cos 30 = or 82 = x2 + 42 M1ft ft their angle AOM or AB 8 6.928..... A1 (d) 27.7(2) cao 2 1 M1 × their (b) × 6.93 soi 2 (e) 34.7–34.9 4 M1 (circle) = π × 82 soi M1 (hexagon) = 6 × their (d) soi M1dep their circle – their hexagon

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10 The Patterns shown below form a sequence. For Examiner's Pattern 1 has 6 dots and 6 lines. Use Pattern 2 has 10 dots and 11 lines. Pattern 1 Pattern 2 Pattern 3 Pattern 4 (a) On the grid, draw Pattern 4. [1] (b) (i) Find the number of dots in Pattern 5. Answer(b)(i) [1] (ii) Explain how you worked out your answer in part (b)(i). Answer(b)(ii) [1] (c) Write down an expression, in terms of n, for the number of dots in Pattern n. Answer(c) [2] (d) The number of dots in Pattern n is 62 . Find n. Answer(d) n = [2]

Mark scheme: 10 (a) correct pattern 1 (b) (i) 22 1 (ii) add 4 1 must have 4 with a direction, accept plus 4 (c) 4n + 2 or 4(n – 1) + 6 oe 2 B1 for 4n + j or kn + 2 (k ≠ 0) seen (d) 15 cao 2 M1 their (c) = 62 or multiple additions or subtractions

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