Cambridge IGCSE Mathematics 0580 — 2011 Oct/Nov Paper 3 · Variant 2

1 Mr and Mrs Sayed and their 3 children go on holiday. For They travel to the airport by train. Examiner's Use (a) The train departs at 16 20. (i) They leave home 45 minutes before the train departs. Find the time at which they leave home. Answer(a)(i) [1] (ii) Write 16 20 using the 12-hour clock. Answer(a)(ii) [1] (b) The train fare is $24 for an adult. 2 The train fare for a child is of an adult fare. 3 Find (i) the fare for a child, Answer(b)(i) $ [1] (ii) the total fare for Mr and Mrs Sayed and their 3 children. Answer(b)(ii) $ [2]

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 15 35 1 Accept 3.35 pm Condone 1535 pm (ii) (0)4 20 pm cao 1 (b) (i) 16(.00) 1 (ii) 96(.00) 2 M1 for 2 × 24 + 3 × their (b)(i) seen or implied

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2 Aminata buys a business costing $23 000. For Examiner's (a) She pays part of this cost with $12 000 of her own money. Use Calculate what percentage of the $23 000 this is. Answer(a) % [1] (b) Aminata’s brother gives her 32% of the remaining $11 000. Show that $7 480 is still needed to buy the business. Answer(b) [2] (c) Aminata borrows the $7 480 at a rate of 3.5 % per year compound interest. Calculate how much money she owes at the end of 3 years. Answer(c) $ [3] (d) In the first year Aminata spent $11 000 on salaries, equipment and expenses. 2 of this money was spent on salaries, 0.45 of this money was spent on equipment and the 5 remainder was for expenses. Calculate how much of the $11 000 was spent on (i) salaries, Answer(d)(i) $ [1] (ii) equipment, Answer(d)(ii) $ [1] (iii) expenses. Answer(d)(iii) $ [1] (e) The three items in part (d) are in the ratio salaries : equipment : expenses = 0.4 : 0.45 : 0.15 . Write this ratio in its simplest form. Answer(e) : : [2]

Mark scheme: 2 (a) 52.2(%) or 52.17… 1 (b) 11000 − (32 ÷ 100 × 11000) M1 or (68 ÷ 100 × 11000) (=) 7480 E1 Must see this for the second mark. (c) 8293 or 8290 or 8293.2 3 Either M1 for 7480 × 1.0352 oe or 8293.21 as final answer or M1 for 7480 × 1.035 = 7741.8 and their 7741.8 × 1.035 (M1 implied by 8012.76...) Then M1 dep for completion of method for the third year If zero SC1 for answer 813.(2…) (d) (i) 4 400 1 (ii) 4 950 1 (iii) 1 650 1ft 11 000 − their (d)(i) − their (d)(ii) (e) 8 : 9 : 3 cao 2 B1 for 40 : 45 : 15 oe seen or correct non-integer ratio IGCSE – October/November 2011 0580 32 ( ) (i) ( ) −2 

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 3   − 5  For3 (a) r =   +   Examiner's  −2   − 2  Use (i) Write down r as a single vector.     Answer(a)(i) r =   [1]     (ii) The point G(3, 2) is translated by the vector r to the point H. Find the co-ordinates of H. Answer(a)(ii) ( , ) [1] (iii) Write down the vector of the translation that maps H onto G.     Answer(a)(iii)   [1]     (b) For y Examiner's Use 10 9 8 7 6 5 Q 4 3 2 P 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 –3 –4 The diagram shows two triangles P and Q. (i) Describe fully the single transformation which maps P onto Q. Answer(b)(i) [3] (ii) On the grid, draw the reflection of P in the line x = 0. Label this image R. [2] (iii) On the grid, rotate P through 180° about (0, 0). Label this image S. [2] (iv) Describe fully the single transformation which maps triangle S onto triangle R. Answer(b)(iv) [2]

Mark scheme:   3 (a) (i) (r =)   1  −4  (ii) (1, −2) 1ft (3 + their −2, 2 + their −4)  2  (iii)   1ft Inverse of their (a)(i)  4  (b) (i) Enlargement 1 All independent (Scale Factor) 3 1 (Centre) (0, 0) 1 (ii) Reflection in x = 0 drawn 2 SC1 Reflection in y = 0 (iii) Rotation 180° about (0, 0) 2 SC1 180° rotation about any other point drawn (iv) Reflection 1ft Strict follow through x axis or y = 0 1ft Independent marks

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4 (a) Expand and simplify 3(2x + y) + 5(x – y). For Examiner's Use Answer(a) [2] (b) Expand x2(3x – 2y). Answer(b) [2] (c) Factorise completely 4y2 – 10xy. Answer(c) [2] 4 x 2 (d) y = 3 (i) Find the value of y when x = O3 . Answer(d)(i) y = [2] (ii) Make x the subject of the formula. Answer(d)(ii) x = [3]

Mark scheme: 4 (a) 11x − 2y final answer 2 B1 for 6x + 3y or 5x − 5y or 11x or −2y in working (b) 3x3 − 2x2 y final answer 2 B1 for 3x3 ± jx2y or kx3 − 2x2y (c) 2y(2y − 5x) final answer 2 B1 for y(4y − 10x) or 2(2y2 − 5xy) or SC1 for 2y(2y + 5x) or SC1 for 2y(2y − 5x) in working but then spoilt 4 × ( −3) 2 (d) (i) 12 2 M1 for or better in working. 3 3y (ii) (x) = final answer oe 3 Maximum of M2 from 4 M1 for × by 3 M1 for ÷ by 4 M1 for square root h

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5 (a) An aeroplane takes off 140 metres before reaching the end of the runway. For It climbs at an angle of 22° to the horizontal ground. Examiner's Use NOT TO SCALE h 22° 140 m Calculate the height of the aeroplane, h, when it is vertically above the end of the runway. Answer(a) h = m [2] (b) After 3 hours 30 minutes the aeroplane has travelled 1850 km. Calculate the average speed of the aeroplane. Answer(b) km/h [2] (c) A B NOT TO SCALE 15 km C The aeroplane descends from A, at a height of 12 000 metres, to C, at a height of 8 300 metres. (i) Work out the vertical distance, BC, that the aeroplane descends. Answer(c)(i) m [1] (ii) The distance AC is 15 kilometres. Calculate angle BAC. Answer(c)(ii) Angle BAC = [2]

Mark scheme: h 5 (a) 56.6 or 56.56… 2 M1 for tan 22 =140 or better 140 or M1 for tan(90–22) = or better h (1850) (b) 529 (km/h) or 528.6 or 528.57… 2 M1 for or better. 5.3 (c) (i) 3700(m) 1 their (c)(i) (ii) 14.3 or 14.2(8…) 2ft M1 for sin (BAC) = 15000 IGCSE – October/November 2011 0580 32

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6 For E NOT TO Examiner's SCALE Use F 16 cm D C 24 cm A 30 cm B The diagram shows a wedge in the shape of a triangular prism. AB = 30 cm, AF = 16 cm and BC = 24 cm. Angle BAF = 90°. (a) Calculate (i) the area of triangle ABF, Answer(a)(i) cm2 [2] (ii) the volume of the wedge. Answer(a)(ii) cm3 [1] (b) (i) Calculate BF. Answer(b)(i) cm [2] (ii) 1.6 cm NOT TO SCALE A coin with diameter 1.6 cm is rolled down the sloping surface of the wedge. It travels in a straight line parallel to BF, starting on FE and ending on BC. Calculate the number of complete turns it makes. Answer(b)(ii) [3] (c) On the grid, complete the net of the wedge. For The base and one of the triangles have been drawn for you. Examiner's Use Each square on the grid represents a square of side 4 centimetres. [3] (d) Calculate the surface area of the wedge. Answer(d) cm2 [3]

Mark scheme: 6 (a) (i) 240 2 M1 for 0.5 × 30 × 16 (ii) 5760 1ft ft is (a)(i) × 24 (b) (i) 34 2 M1 for (FB 2) = 16 2 + 30 2 (ii) 6 3 M1 for (circumference) = 1.6 × π M1 dep their (b)(i) ÷ their 1.6π (6.76 implies M1, M1) If 0 scored either SC1 for their (b)(i) ÷ 3.2 × π and then SC1 for truncating correctly If M1 or still 0 scored then SC1 for truncating correctly any number with at least 1 decimal place (c) 6 by 4 rectangle above 1 6 by their 8.5 rectangle below 1ft ft (b)(i) ÷ 4 Correct triangle on AB 1 1 1 (d) 2400 3cao M2 for × 30 × 16 + × 30 × 16 + 16 × 24 + 2 2 30 × 24 + their 34 × 24 (M1 for any 3 areas) If 0, SC2 for 150 or SC1 for 120 (3 rectangles) or SC1 for 30 (2 triangles)

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18 For 7 (a) The table shows some values for y = . Examiner's x Use x O9 O6 O4 O3 O2 2 3 4 6 9 y O2 O4.5 O9 4.5 3 (i) Complete the table. [2] 18 (ii) On the grid, draw the graph of y = for O9 Y x Y O2 and 2 Y x Y 9 . x y 9 8 7 6 5 4 3 2 1 x –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 –5 –6 –7 –8 –9 [4] 18 (iii) Use your graph to solve the equation = O5 . x Answer(a)(iii) x = [1] (b) (i) Complete the table of values for y = 2x + 3 . For Examiner's Use x O4 O3 2 3 y O5 7 [2] (ii) On the grid, draw the graph of y = 2x + 3 for O4 Y x Y 3 . [1] (iii) Find the co-ordinates of the points of intersection of the graphs of 18 y = and y = 2x + 3 . x Answer(b)(iii) ( , ) and ( , ) [2]

Mark scheme: 7 (a) (i) −3, −6, 9, 6, 2 2 B1 for 4 correct (ii) Graph P3ft P2ft for 8 or 9 points correct P1ft for 6 or 7 points correct C1 Correct curve and not crossing axis (iii) −3.7 to −3.5 1ft ft their curve (b) (i) −3, 9 1, 1 (ii) Ruled continuous line y = 2x + 3 1 Line long enough to intersect both parts (iii) (2.2 to 2.5, 7.5 to 7.8) 1ft ft their line intersection with the curves (−4.0 to −3.7, −4.8 to −4.5) 1ft

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8 The table shows the average temperature and rainfall each month at Wellington airport. For Examiner's Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Use Temperature 18 18 17 14 12 10 9 10 11 13 15 16 (°C) Rainfall 67 48 76 87 99 113 111 106 82 81 74 74 (mm) (a) Complete the bar chart to show the temperature each month. 20 18 16 14 12 Temperature 10 (°C) 8 6 4 2 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month [2] (b) For the rainfall calculate (i) the mean, Answer(b)(i) mm [2] (ii) the median. Answer(b)(ii) mm [2] (c) In the scatter diagram the rainfall for January to April is plotted against temperature. For Examiner's Use 120 115 110 105 100 95 90 85 Rainfall 80 (mm) 75 70 65 60 55 50 45 40 8 9 10 11 12 13 14 15 16 17 18 19 20 Temperature (°C) (i) Complete the scatter diagram by plotting the values for the months May to December. [3] (ii) Draw the line of best fit on the scatter diagram. [1] (iii) What type of correlation does the scatter diagram show? Answer(c)(iii) [1]

Mark scheme: 8 (a) heights 11, 13, 15, 16 2 B1 for 3 correct (b) (i) 84.8(3…) 2 M1 addition of 12 rainfall values (ii) 81.5 2 Either M1 for evidence of ordering values or substantial part of list (at least first 7 or last 7) or M1 for answers of 81 and 82 (c) (i) 8 values correctly plotted P3 P2 for 6 or 7 correct P1 for 4 or 5 correct (ii) Line of best fit 1 Must be continuous and straight (iii) Negative 1 IGCSE – October/November 2011 0580 32

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9 On the scale drawing opposite, point A is a port. For B and C are two buoys in the sea and L is a lighthouse. Examiner's Use The scale is 1 cm = 3 km. (a) A boat leaves port A and follows a straight line course that bisects angle BAC. Using a straight edge and compasses only, construct the bisector of angle BAC on the scale drawing. [2] (b) When the boat reaches a point that is equidistant from B and from C, it changes course. It then follows a course that is equidistant from B and from C. (i) Using a straight edge and compasses only, construct the locus of points that are equidistant from B and from C. Mark the point P where the boat changes course. [2] (ii) Measure the distance AP in centimetres. Answer(b)(ii) cm [1] (iii) Work out the actual distance AP. Answer(b)(iii) km [1] (iv) Measure the obtuse angle between the directions of the two courses. Answer(b)(iv) [1] (c) Boats must be more than 9 kilometres from the lighthouse, L. (i) Construct the locus of points that are 9 kilometres from L. [2] (ii) Mark the point R where the course of the boat meets this locus. Work out the actual straight line distance, AR, in kilometres. Answer(c)(ii) km [1] For Examiner's Use L C B Scale: 1 cm = 3 km A Question 10 is printed on the next page.

Mark scheme: 9 (a) Bisector of angle BAC with correct 2 Either B1 correct without arcs arcs or B1 for 2 pairs of accurate arcs seen (b) (i) Bisector of BC with 2 pairs of 2 Either B1 correct without arcs correct arcs or B1 for 2 pairs of accurate arcs seen (ii) 10.8 to 11.2 (cm) cao 1 (iii) 32.4 to 33.6 1ft Their (b)(ii) × 3 (iv) 155° to 165° cao 1 (c) (i) Circle centre L, radius 3cm 2 B1 circle centre L, incorrect radius or SC1 for part circle with correct radius (ii) 41km to 44km cao 1

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10 (a) Write down the next term in each of the following sequences. For Examiner's Use (i) 2, 9, 16, 23, [1] (ii) 75, 67, 59, 51, [1] (iii) 2, 5, 9, 14, [1] 1 1 (iv) 2, 1, , , [1] 2 4 (v) 2, 4, 8, 16, [1] (b) For the sequence in part (a)(i) write down (i) the 10th term, Answer(b)(i) [1] (ii) the nth term. Answer(b)(ii) [2] n 2 + 3n (c) The nth term of the sequence in part (a)(iii) is . 2 Calculate the 50th term of this sequence. Answer(c) [2] (d) The nth term of the sequence in part (a)(v) is 2n. Calculate the 12th term of this sequence. Answer(d) [1]

Mark scheme: 10 (a) (i) 30 1 (ii) 43 1 (iii) 20 1 1 (iv) or 0.125 1 8 (v) 32 1 (a) (i) 65 1 (ii) 7n − 5 or equivalent 2 B1 for 7n seen 502 + 3 × 50 (c) 1325 2 B1 for or better seen 2 (d) 4096 1

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