Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 Oct/Nov Paper 1 · Variant 3

This document consists of 8 printed pages. IB10 11_0581_13/FP © UCLES 2010 [Turn over *9917595614* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/13 Paper 1 (Core) October/November 2010 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional) 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. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 56. www.XtremePapers.com

2 © UCLES 2010 0581/13/O/N/10 For Examiner's Use 1 Write down the name of the solid that can be made from the net shown in the diagram. Answer [1] 2 Write down all the square numbers which are factors of 100. Answer [2] 3 For the diagram, write down (a) the number of lines of symmetry, Answer(a) [1] (b) the order of rotational symmetry. Answer(b) [1] 4 In a desert the temperature at noon was 38°C. At midnight the temperature was –3°C. (a) Find the change in temperature between noon and midnight. Answer(a) °C [1] (b) At 02 00 the temperature was 4°C below the midnight temperature. Write down the temperature at 02 00. Answer(b) °C [1]

3 © UCLES 2010 0581/13/O/N/10 [Turn over For Examiner's Use 5 Multiply out the brackets. x(2x + y) Answer [2] 6 Solve the equation. 4 3 1 2 = + x Answer x = [2] 7 Work out 3 3 100 7.2 − . Give your answer correct to 3 decimal places. Answer [2] 8 Chris and Max share $45 in the ratio Chris:Max = 7 : 2 . Calculate how much Chris receives. Answer $ [2] 9 When Valentina was 10 years old, her mass was 32 kg. Two years later her mass had increased by 45%. Calculate Valentina’s mass when she was 12 years old. Answer kg [2]

4 © UCLES 2010 0581/13/O/N/10 For Examiner's Use 10 Change 18.75% into a fraction. Write your answer in its lowest terms. Answer [2] 11 Factorise completely. 3ac – 6ad Answer [2] 12 Simplify 3 2 1 1 −     . Give your answer as a fraction. Answer [2] 13 Solve the simultaneous equations. 3x + y = 5 5x + y = 9 Answer x = y = [2] 14 17 27 17 0.294 17 5 From the list of numbers, write down (a) a prime number, Answer(a) [1] (b) an irrational number, Answer(b) [1] (c) the smallest number. Answer(c) [1]

5 © UCLES 2010 0581/13/O/N/10 [Turn over For Examiner's Use 15 Amiria invests $200 for 2 years at 3% per year compound interest. Calculate the total amount Amiria has at the end of the two years. Answer $ [3] 16 O T A U C B NOT TO SCALE In the diagram, TAU is a tangent to the circle at A. AB is a diameter of the circle and AC = BC. Find (a) angle BCA, Answer(a) Angle BCA = [1] (b) angle ABC, Answer(b) Angle ABC = [1] (c) angle CAU. Answer(c) Angle CAU = [1]

6 © UCLES 2010 0581/13/O/N/10 For Examiner's Use 17 Insert brackets to make each statement correct. (a) 7 + 2 × 9 = 81 [1] (b) 36 ÷ 6 ÷ 2 = 12 [1] (c) 5 × 3 + 6 × 2 = 90 [1] 18 1 2 3 4 5 6 7 0 7 6 5 4 3 2 1 y x A B C The diagram shows three points, A(1, 2), B(7, 5) and C(5, 7). (a) Write as column vectors (i) AC, Answer(a)(i) AC =           [1] (ii) CB. Answer(a)(ii) CB =           [1] (b) Use two of the symbols +, –, = in the spaces to make a correct statement. AC CB AB [1]

7 © UCLES 2010 0581/13/O/N/10 [Turn over For Examiner's Use 19 0 2 6 y x The diagram shows a straight line passing through the points (0, 2) and (6, 0). Find the equation of this line in the form y = mx + c. Answer y = [3] 20 4 4 5 6 8 (a) The diagram shows 5 discs. One disc is chosen at random. (i) Which number is most likely to be chosen? Answer(a)(i) [1] (ii) What is the probability that the number on the disc is even? Answer(a)(ii) [1] (iii) What is the probability that the number on the disc is even and a factor of 20? Answer(a)(iii) [1] (b) A disc is chosen at random from the discs with even numbers. What is the probability that the number on the disc is a factor of 20? Answer(b) [1] Questions 21 and 22 are printed on the next page

8 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. © UCLES 2010 0581/13/O/N/10 For Examiner's Use 21 0 0 0 1 2 2 4 4 5 9 The list shows the number of days absent in a school term for each of 10 students. Find the mode, the median and the mean for the number of days absent. Answer Mode = Median = Mean = [4] 22 08 00 08 05 08 10 08 15 08 20 08 25 08 30 Time Home Shop School Distance (kilometres) NOT TO SCALE Rob walks to school each morning. One day, he leaves home at 08 00. He stops at a shop at 08 10 and stays there for 5 minutes. He then continues to school and arrives at 08 30. (a) Draw the travel graph for Rob’s journey from home to school. [3] (b) Rob’s average speed for the whole journey from home to school is 3.3 km/h. Calculate the distance from Rob’s home to school. Answer(b) km [2]

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 0581 MATHEMATICS 0581/13 Paper 1 (Core), maximum raw mark 56 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 0581 13 © UCLES 2010 Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working Qu. Answers Mark Part Marks 1 Pyramid 1 2 1, 4, 25, 100 2 B1 for any two and none incorrect. −1 each incorrect 3 (a) 2 (b) 2 1 1 4 (a) 41 or −41 (b) −7 1 1 5 2x2 + xy final answer 2 B1 for 2x2 or xy seen in working 6 5.5 2 M1 for 2x + 1 = 3 × 4 or better or 3 2x = 4 − 3 1 7 6.489 2 B1 for 6.5 or 6.49 or 6.4891…. 8 35 2 M1 for 45 ÷ (7 + 2) SC1 for answer = 10 9 46.4 2 M1 for 32 × 1.45 oe or B1 for answer of 14.4 10 16 3 2 B1 for 10000 1875 or any equivalent fraction. 11 3a(c − 2d) 2 B1 for a(3c − 6d) or 3(ac − 2ad) or 3a(jc − kd) where j and k are non-zero. 12 27 8 2 M1 for 1 ÷ (1 2 1 )3 oe or SC1 for 8 27 13 (x =) 2, (y =) −1 2 M1 for correct method for eliminating one variable. Subtract or multiply by 3 and 5, then subtract

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 13 © UCLES 2010 14 (a) 17 (b) √17 or 4.12(….) (c) 0.294 1 1 1 15 212.18 final answer cao 3 M2 for 200 × 1.032 oe or M1 for (200 × 1.03) × 0.03 oe 16 (a) 90 1 (b) 45 1ft ft 2 1 (180 − their (a)) (c) 45 1ft ft 90 − their (b) 17 (a) (7 + 2) × 9 (b) 36 ÷ (6 ÷ 2) = 12 (c) 5 × (3 + 6) × 2 = 90 1 1 1 18 (a) (i)     5 4 1 (ii)     −2 2 1 (b) (AC) + (CB) = (AB) 1 19 (y =) −3 1 x + 2 cao 3 B1 for gradient of ± 3 1 oe (Allow ±0.33 or better) B1 ind for mx + 2 where m ≠ 0. 20 (a) (i) 4 1 (ii) 5 4 oe 1 (iii) 5 2 oe 1 (b) 4 2 oe 1 21 (Mode =) 0 (Median =) 2 (Mean =) 2.7 1 1 2 M1 (0 + 0 + 0) + 1 + 2 + 2 + 4 + 4 + 5 + 9

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 13 © UCLES 2010 22 (a) Lines connecting (08 00, home) to (08 10, shop) (their 08 10, shop) to (their 08 15, shop) (their 08 15, shop) to (08 30, school) (b) 1.65 3 2 B1 home to shop B1ft horizontal and 5 minute period B1ft for line to 08 30 and school M1 for use of speed × time SC1 for 1.375 or 1.376 to 1.38