Cambridge IGCSE Mathematics - International 0607 — 2010 Oct/Nov Paper 3 · Variant 1

This document consists of 14 printed pages and 2 blank pages. IB10 11_0607_03/3RP © UCLES 2010 [Turn over *9269295756* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/03 Paper 3 (Core) October/November 2010 1 hour 45 minutes Candidates answer on the Question Paper Additional Materials: Geometrical Instruments Graphics Calculator READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, highlighters, glue or correction fluid. You may use a pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For π, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 96. www.XtremePapers.com

2 © UCLES 2010 0607/03/O/N/10 Formula List Area, A, of triangle, base b, height h. A = 1 2 bh Area, A, of circle, radius r. A = πr2 Circumference, C, of circle, radius r. C = 2πr Curved surface area, A, of cylinder of radius r, height h. A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l. A = πrl Curved surface area, A, of sphere of radius r. A = 4πr2 Volume, V, of prism, cross-sectional area A, length l. V =Al Volume, V, of pyramid, base area A, height h. V= 1 3 Ah Volume, V, of cylinder of radius r, height h. V = πr2h Volume, V, of cone of radius r, height h. V = 1 3 πr2h Volume, V, of sphere of radius r. V = 4 3 πr3

3 © UCLES 2010 0607/03/O/N/10 [Turn over For Examiner's Use Answer all the questions. 1 In 2008 the population of a city was 276 000. (a) Write 276 000 in standard form. Answer(a) [1] (b) 197 400 of the population were male. Calculate the number of males in the population. Answer(b) [2] (c) A year later the population of 276 000 had increased by 4 %. (i) Calculate the new population. Answer(c)(i) [2] (ii) Write your answer to part (c)(i) correct to the nearest ten thousand. Answer(c)(ii) [1]

4 © UCLES 2010 0607/03/O/N/10 For Examiner's Use 2 20 students answered questions in a quiz. The number of correct answers for each student is shown in the table. 25 21 24 25 29 18 24 30 25 25 29 17 15 15 19 25 23 21 16 19 (a) (i) Complete the stem-and-leaf plot to show this information. The numbers in the first row of the table above have been plotted. Stem Leaf 1 8 2 5 1 4 5 9 4 5 5 3 0 Key 1 | 8 = 18 [2] (ii) Complete the ordered stem-and-leaf plot. Stem Leaf 1 2 3 Key 1 | 8 = 18 [1] (iii) Use your stem-and-leaf plot in part(a)(ii) to find the median. Answer(a)(iii) [1]

5 © UCLES 2010 0607/03/O/N/10 [Turn over For Examiner's Use (b) Complete the bar chart, which has already been started for you. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 6 5 4 3 2 1 0 Number of students Number of correct answers [3] (c) Calculate the percentage of students who scored 29 correct answers. Answer(c) % [2]

6 © UCLES 2010 0607/03/O/N/10 For Examiner's Use 3 y x 8 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –8 0 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 T V (a) On the grid, (i) draw the translation of triangle T by 4 2    , [2] (ii) draw the reflection of triangle T in the y-axis, [2] (iii) draw the rotation of triangle T about (0, 0) through 180°. [2] (b) Describe fully the single transformation that maps triangle T onto triangle V. [3]

7 © UCLES 2010 0607/03/O/N/10 [Turn over For Examiner's Use 4 Farah takes 19 minutes to walk from home to school. The distance from her home to school is 850 metres. (a) She leaves home at 07 51. At what time does she arrive at school? Answer(a) [1] (b) Calculate her average speed in (i) metres per minute, Answer(b)(i) m/min [2] (ii) kilometres per hour. Answer(b)(ii) km/h [2] (c) Each day, in a week of 5 school days, Farah walks to and from school. Calculate the total distance Farah walks. Give your answer in kilometres. Answer(c) km [2]

8 © UCLES 2010 0607/03/O/N/10 For Examiner's Use 5 0 9 –1 – 4 4 y x f(x) = x2 g(x) = (x – 1)2 (a) Sketch the graphs of y = f(x) and y = g(x) on the axes above. [4] (b) Describe fully the single transformation that maps the graph of y = f(x) onto the graph of y = g(x). [2] (c) The graph of y = h(x) is a translation of the graph of y = f(x) by the vector 0 3    . Write down h(x) in terms of x. Answer(c) h(x) = [2]

9 © UCLES 2010 0607/03/O/N/10 [Turn over For Examiner's Use 6 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 y x (a) (i) On the grid, draw accurately the line y = 1 2 x + 2, for 0 Y x Y 8. [2] (ii) P is the point where the line cuts the y-axis. Q is the point on the line where x = 6. Mark the points P and Q on the grid. [2] (b) Mark the point R (6, 2) on the grid and draw the triangle QPR. [1] (c) Use trigonometry to calculate angle QPR. Give your answer correct to 1 decimal place. Answer(c) Angle QPR = [3]

10 © UCLES 2010 0607/03/O/N/10 For Examiner's Use 7 D E A C B X NOT TO SCALE 108° The diagram shows a five-sided polygon ABCDE, with the side AB extended to X. (a) Write down the geometrical name of the polygon ABCDE. Answer(a) [1] (b) AE is parallel to BC and angle EAB = 108°. Write down the size of angle CBX. Answer(b) [1] (c) Calculate the sum of the five interior angles of the polygon ABCDE. Answer(c) [2] (d) The angles BCD, CDE and DEA are equal. Calculate the size of one of these angles. Answer(d) [2] (e) (i) On the diagram, extend the sides CD and AE until they meet at F. [1] (ii) Write down the special name of the quadrilateral ABCF. Answer(e)(ii) [1] (iii) Calculate the size of angle DFE. Answer(e)(iii) [2] (iv) Write down the special name of the triangle DEF. Answer(e)(iv) [1]

11 © UCLES 2010 0607/03/O/N/10 [Turn over For Examiner's Use 8 U P Q g c d b e f a The Venn diagram shows a universal set, U = {a, b, c, d, e, f, g}, and the sets P and Q. (a) Complete the following statements. (i) P = { } [1] (ii) = { b, c, d, g } [1] (iii) P∩Q = { } [1] (iv) n(P∪Q) = [1] (b) On the Venn diagram, shade the region P ∩Q′. [1] (c) An element is chosen at random from U. (i) Write down the probability that the element is e. Answer(c)(i) [1] (ii) Write down the probability that the element is h. Answer(c)(ii) [1] (d) An element is chosen at random from set P. Write down the probability that the element is e. Answer(d) [1] (e) 70 students are asked to choose a letter at random from U. How many students would you expect to choose a letter from set P? Answer(e) [2]

12 © UCLES 2010 0607/03/O/N/10 For Examiner's Use 9 Fahran counted the number of steps it took each student to walk across the sports hall. The results for the 100 students are shown in the table. Number of steps 18 19 20 21 22 23 24 Frequency 3 7 9 11 20 31 19 (a) Calculate the fraction of students who took 22 steps. Give your answer in its lowest terms. Answer(a) [2] (b) Find (i) the range, Answer(b)(i) [1] (ii) the mean, Answer(b)(ii) [1] (iii) the median, Answer(b)(iii) [1] (iv) the mode. Answer(b)(iv) [1] (c) Fahran planned to draw a pie chart to show his results. Calculate the sector angle for the number of students who took 23 steps. Do not draw the pie chart. Answer(c) [2]

13 © UCLES 2010 0607/03/O/N/10 [Turn over For Examiner's Use 10 (a) 1 hectare (ha) = 10 000 m2 Calculate the number of hectares in 1 km2. Answer(a) [1] (b) E D A B C 0.4 km 0.8 km 1.2 km 0.3 km NOT TO SCALE The diagram shows a field ABCDE. Calculate the area of the field (i) in km2, Answer(b)(i) km2 [3] (ii) in hectares. Answer(b)(ii) ha [1] (c) (i) There is a fence around the field ABCDE. Calculate the length of the fence. Answer(c)(i) km [4] (ii) The cost of the fence is $450 per kilometre. Calculate the total cost of the fence. Answer(c)(ii) $ [1]

14 © UCLES 2010 0607/03/O/N/10 For Examiner's Use 11 4 –4 –3 6 0 y x f(x) = 2 x x − , x ≠ 2 (a) On the diagram, sketch the graph of y = 2 x x − . [3] (b) The graph has two asymptotes. Write down the equation of each asymptote. Answer(b) [2] (c) Write down the range of f(x). Answer(c) [2] (d) (i) On the same diagram, sketch the graph of y = 2 x . [1] (ii) Solve the equation 2 x x − = 2 x . Answer(d)(ii) x = or x = [2]

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2010 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/03 Paper 3 (Core), maximum raw mark 96 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes must be read in conjunction with the question papers and the report on the examination. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2010 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

Page 2 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0607 03 © UCLES 2010 1 (a) 2.76 × 105 B1 [1] (b) 135 930 (allow 135 900 and 136 000) B2 [2] If B0, M1 for 276000 ÷ 400 × 197 (c) (i) 287040 (allow 287000) B2 [2] If B0, M1 for 276000 × 1.04 oe SC1 for 11040 (ii) 290000 ft B1ft [1] ft their (i), if at least 6 figures [6] 2 (a) (i) 7, 5, 5, 9, 6, 9 9, 5, 3, 1 B1 B1 [2] (ii) 5, 5, 6, 7, 8, 9, 9 1, 1, 3, 4, 4, 5, 5, 5, 5, 5, 9, 9 0 B1 ft [1] (iii) 23.5 B1 ft [1] Correct or ft their (ii) (b) Columns for 23, 24, 25, 29 and 30 all correct B3 ft [3] B2 for 4 correct, B1 for 3 correct Correct or ft their (ii) (c) 10 ft B2 ft [2] ft their value in (a) (either (i) or (ii) if different) If B0, M1 for their frequency in (a) ÷ 20 × 100 [9] 3 (a) (i) Triangle with vertices (–4, 4), (0, 4), (–4, 6) B2 [2] If B0, SC1 for any translation (ii) Triangle with vertices (8, 2), (4, 2), (8, 4) B2 [2] If B0, SC1 for reflection in x-axis (iii) Triangle with vertices (8, –2), (4, –2), (8, –4) B2 [2] If B0, SC1 for any other rotation by 180° (b) Enlargement, (centre) (–8, 6) (scale factor) 3 B1, B1, B1 [3] Each B1 independent All 0 if combination of transformations [9] 4 (a) 08 10 B1 [1] Allow any reasonable form e.g. 8h 10 (b) (i) 44.7 (44.73 – 44.74) B2 [2] If B0, M1 for 850 ÷ 19 (ii) 2.68 (2.682 to 2.684….) ft B2 ft [2] ft their (i) × 60 ÷ 1000 If B0, M1 for their (i) × 60 ÷ 1000 (c) 8.5 B2 [2] SC1 for 4.25 or M1 for 10 × 850 (implied by 8500) [7] 5 (a) f(x) parabola shape, vertex (0, 0) g(x) parabola shape, vertex (1, 0) B1, B1 B1, B1 [4] (b) Translation     0 1 B1, B1 [2] Must be translation but vector can be described The two B1’s are independent (c) x2 + 3 B2 [2] B1 for f(x) + 3 [8]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0607 03 © UCLES 2010 6 (a) (i) Accurate graph ruled for full domain B2 [2] If B0, SC1 for correct short line or correct full domain but freehand or gradient 0.5 or y – intercept 2 (ii) Points (0, 2) and (6, 5) correctly plotted B1, B1 [2] ft if B2 or SC1 in (i) (b) (6, 2) plotted (condone absence of R) and triangle drawn B1 [1] Condone freehand and absence of labels (d) 26.6 B3 [3] If B0, M1 for tan = 6 3 oe, A1 for accurate answer to at least 2 dp (26.56 to 26.57 implies M1A1) [8] 7 (a) Pentagon B1 [1] (b) 108 B1 [1] (c) 540 B2 [2] If B0, M1 for (n – 2) × 180 oe seen or 540 seen (d) 120 B2 [2] If B0, M1 for their ((c) – 180) ÷ 3 (e) (i) CD and AE drawn and meeting B1 [1] Condone absence of label and accept freehand (ii) Trapezium B1 [1] (iii) 60 ft B2 ft [2] ft their 180 – 2 × (180 – their (d)) if positive If B0 M1 for 180 – 2 × (180 – their (d)) if positive (iv) Equilateral dep or ft B1 ft [1] Dependent on (iii) correct or if (d) incorrect ft is isosceles [11] 8 (a) (i) a, e, f B1 [1] (ii) = P′ B1 [1] (iii) {e, f} B1 [1] (iv) 6 B1 [1] (b) P but not Q shaded B1 [1] (c) (i) 7 1 oe B1 [1] (ii) 0 B1 [1] Allow zero or 7 0 (d) 3 1 oe B1 [1] (e) 30 B2 [2] If B0, M1 for 7 3 soi or 70 7 1 × (implied by 10) [10]

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0607 03 © UCLES 2010 9 (a) 5 1 B2 [2] If B0, allow B1 for any correct fraction (b) (i) 6 B1 [1] (ii) 22.07 (allow 22.1) B1 [1] (iii) 22.5 B1 [1] (iv) 23 B1 [1] (c) 111.6 (or 112) B2 [2] If B0, M1 for 31 ÷ 100 × 360 oe [8] 10 (a) 100 B1 [1] (b) (i) 0.9 B3 [3] If B0, M1 for 1.2 × 0.8, M1 for 0.5 × 0.4 × 0.3 (or 0.5 × 400 × 300), If collecting areas, M1 for a rectangle, M1 for a triangle or trapezium (ii) 90 ft B1 ft [1] ft their (i) × their (a) (c) (i) 3.8 B4 [4] If B0, M1 for 0.32 + 0.42 seen (or 3002 + 4002 ), A1 for 0.5 (or 500) M1 for adding 5 lengths in same units. If 0, SC1 for 4 or 3.3 (ii) 1710 ft B1 ft [1] ft their (i) × 450 [10] 11 (a) Rectangular hyperbola B3 [3] B1 for curve through origin B1 for two branches B1 for Roughly having asymptotes parallel to axes (b) x = 2, y = 1 B1, B1 [2] (c) y ∈R, y ≠1 B1, B1 [2] Independent. Can accept either answer in words. (d) (i) Line through origin sketched to meet hyperbola twice B1 [1] Can be freehand (ii) 0, 4 cao B1, B1 [2] [10]