Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 Oct/Nov Paper 1 · Variant 2

This document consists of 12 printed pages. IB10 11_0581_12/FP © UCLES 2010 [Turn over *1387358591* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/12 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 0581/12/O/N/10 For Examiner's Use 1 x° 79° 57° NOT TO SCALE The diagram shows a quadrilateral. Work out the value of x. Answer x = [1] 2 Caroline changed £200 into New Zealand dollars (NZ$). The exchange rate was £1 = NZ$2.56 . How many New Zealand dollars did she receive? Answer NZ$ [1]

3 © UCLES 2010 0581/12/O/N/10 [Turn over For Examiner's Use 3 Francis recorded a temperature of −4°C on Sunday. By Monday it had gone down by 3°C. (a) Find the temperature on Monday. Answer(a) °C [1] (b) On Tuesday the temperature was −1°C. Find the change in temperature between Monday and Tuesday. Answer(b) °C [1] 4 The distance from the Sun to the planet Saturn is 1 429 400 000 kilometres. Write this distance in standard form, correct to 3 significant figures. Answer km [2] 5 A factory makes doors that are each 900 millimetres wide, correct to the nearest millimetre. Complete the statement about the width, w millimetres, of each door. Answer Y w I [2]

4 © UCLES 2010 0581/12/O/N/10 For Examiner's Use 6 NOT TO SCALE 6 cm 4 cm 15 cm A B C D E F The triangles ABC and DEF are similar. AB = 6 cm, BC = 4 cm and DE = 15 cm. Calculate EF. Answer EF = cm [2] 7 Maria puts $600 into a bank account for 3 years at a rate of 3.4% per year compound interest. Calculate how much will be in the account at the end of the 3 years. Answer $ [3]

5 © UCLES 2010 0581/12/O/N/10 [Turn over For Examiner's Use 8 (a) Factorise completely. 8pq + 12pr Answer(a) [2] (b) Use your answer to part (a) to make p the subject of the formula below. s = 8pq + 12pr Answer(b) p = [1] 9 North North 65° P Q NOT TO SCALE 840 m The diagram shows a straight road PQ. PQ = 840m and the bearing of Q from P is 065°. (a) Work out the bearing of P from Q. Answer(a) [1] (b) Calvin walks 7 4 of the distance from P to Q. How far is he from Q? Answer(b) m [2]

6 © UCLES 2010 0581/12/O/N/10 For Examiner's Use 10 The heights of 43 children are measured to the nearest centimetre. Braima draws a bar chart from this information. 16 14 12 10 8 6 4 2 0 120-129 130-139 140-149 150-159 160-169 170-179 180-189 Height (centimetres) Frequency A child is chosen at random. Write down, as a fraction, the probability that the child will be (a) in the group 140 – 149 cm, Answer(a) [1] (b) less than 160 cm, Answer(b) [1] (c) in the group 160 – 169 cm. Answer(c) [1]

7 © UCLES 2010 0581/12/O/N/10 [Turn over For Examiner's Use 11 O A D C B y° x° 55° NOT TO SCALE The diagram shows a circle, centre O, with diameter BC. AB is a tangent to the circle at B and angle BCD = 55°. A straight line from A meets the circle at D and C. Calculate the value of (a) x, Answer(a) x = [2] (b) y. Answer(b) y = [1] 12 (a) Write down the value of x when (i) 5x ÷ 52 = 54, Answer(a)(i) x = [1] (ii) 49 1 = 7 x. Answer(a)(ii) x = [1] (b) Write down the value of 3p0. Answer(b) [1]

8 © UCLES 2010 0581/12/O/N/10 For Examiner's Use 13 Dominic, Esther, Flora and Galena shared a pizza. (a) Dominic ate 5 1 of the pizza and Esther ate 7 2 of the pizza. Show that 35 18 of the pizza remained. Do not use your calculator and show all your working. Answer (a) [2] (b) Flora ate 3 2 of the pizza that remained. Find the fraction of the pizza that was left for Galena. Answer(b) [2] 14 4.95 86 0.53 7.8 9.6 × − × (a) (i) Rewrite this calculation with each number written correct to 1 significant figure. Answer(a)(i) [1] (ii) Work out the answer to your calculation in part(a)(i). Do not use a calculator and show all your working. Answer(a)(ii) [2] (b) Use your calculator to work out the correct answer to the original calculation. Answer(b) [1]

9 © UCLES 2010 0581/12/O/N/10 [Turn over For Examiner's Use 15 Some children took part in a sponsored swim to raise money for charity. The scatter diagram shows the results for 10 of the children. 0 100 90 80 70 60 50 40 30 20 10 50 100 150 200 250 300 350 400 450 500 550 600 G B F E J D C H A I Money raised ($) Distance (metres) (a) (i) How much further did A swim than J ? Answer(a)(i) m [1] (ii) How much more money did D raise than F ? Answer(a)(ii) $ [1] (b) The results for 2 more children are given in the table below. Child Distance (m) Money raised ($) K 125 35 L 475 80 Plot the results for K and L on the scatter diagram. [1] (c) What type of correlation does the scatter diagram show? Answer(c) [1]

10 © UCLES 2010 0581/12/O/N/10 For Examiner's Use 16 Flags A and B are shown on the grid. y x 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 0 –1 –2 –3 –4 –5 –6 5 6 4 3 2 1 A B (a) Describe fully the single transformation which maps flag A onto flag B. Answer(a) [3] (b) On the grid, draw the translation of flag A by the vector       −3 5 . [2]

11 © UCLES 2010 0581/12/O/N/10 [Turn over For Examiner's Use 17 AB =       −3 3 AC =      − 0 5 (a) Calculate AB + 3AC. Answer(a)       [2] (b) Write down . Answer(b) =       [1] (c) AC is drawn on the grid below. A C (i) On the grid, draw AB . [1] (ii) Write down the obtuse angle between AB and AC. Answer(c)(ii) [1] Question 18 is printed on the next page.

12 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 0581/12/O/N/10 For Examiner's Use 18 D C A B 18 cm NOT TO SCALE The diagram shows a square ABCD. The length of the diagonal AC is 18 cm. (a) Calculate (i) the length of the side of the square, Answer(a)(i) cm [2] (ii) the area of the square. Answer(a)(ii) cm2 [2] (b) A, B, C and D lie on a circle with diameter AC. Calculate the area of this circle. Answer(b) cm2 [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 0581/12 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 12 © 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 1 134 1 2 512(.00) 1 3 (a) −7 (b) (+)6 1 1ft ft −1 − their (a) 4 1.43 × 109 final answer 2 B1 for answers of 1.43 × 10n (n ≠ 0) or figs 143 or 1.429(….) × 109 SC1 for answer of 1.42 × 109 or 1.4 × 109 5 899.5 Y w < 900.5 2 B1 for 1 correct or SC1 for correct but reversed. 6 10 www 2 M1 for 15 ÷ 6 soi or B1 for 4 6 = EF 15 oe or better 7 662.794 to 663.304…. final answer 3 M2 for 600 × 1.0343 or M1 for (600 + 0.034 × 600) × 0.034 or (600 × 1.034) × 0.034 and M1 dep correct method for the remaining time. 8 (a) 4p(2q + 3r) 2 B1 for p(8q + 12r) or 2p(4q + 6r) or 4p(aq + br) a, b integers or 4(2pq + 3pr) (b) (p =) ) 3 2 ( 4 r q s + oe 1ft ft if p is a common factor in (a) or in working in (b) 9 (a) 245 1 (b) 360 2 M1 for 7 3 × 840 or SC1 for answer 480

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 12 © UCLES 2010 10 (a) 43 15 cao final answer 1 If zero in (a) and (b) then SC1 if both (a) and (b) are correct decimals or percentages as answers. (Mark as 0 for (a) and SC1 for (b)) (b) 43 42 cao final answer 1 (c) 0 or 43 0 1 11 (a) (x=) 35 (b) (y=) 55 2 1ft B1 for angle BDC = 90 soi May be marked on the diagram ft 90 − their x 12 (a) (i) (x=) 6 (ii) (x=) −2 (b) 3 1 1 1 13 (a) Two stage proof 2 M1 for 7 5 5 2 7 1 × × + × or 7 5 5 2 7 5 7 1 × × + × × or alt 5 4 − 7 2 or 7 5 − 5 1 M1dep for 1− their 35 17 or 35 18 + 35 17 = 35 35 or alt 35 10 28− oe or 35 7 25− oe (b) 35 6 final answer 2 M1 for 3 1 × 35 18 oe If zero SC1 for answer of 35 12 14 (a) (i) 5 90 5.0 8 10 × − × 1 (ii) 7(.0) cao (b) 5.92 or 5.919(…..) 2 1 B1 for 80 (from 10 × 8) or 45 (from 0.5 × 90) or 5 (denominator) seen 15 (a) (i) 175 (ii) 70 (b) 2 points plotted correctly (±1mm). (c) Positive 1 1 1 1

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 12 © UCLES 2010 16 (a) Rotation or enlargement 180° (SF) −1 (about or centre) origin oe (b) Correct translation 5 right and 3 down 1 1 1 2 Two transformations named, zero for (a) Independent Independent B1 for 5 right or 3 down applied 17 (a)     − − 3 12 2 B1 for 1 component correct. (b)    − 3 3 1 (c) (i) Vector AB drawn (ii) 134° to 136° 1 1 Diagonal line, ignore working lines 18 (a) (i) 12.7 to 12.73 2 M1 for 18 x = sin45 or 18 x = cos45 or better (ii) 161 to 162.1 2ft M1 for method for squaring their (a)(i). (b) 254 to 255 2 M1 for π × 92