Cambridge IGCSE Mathematics (with coursework) 0581 — 2011 Oct/Nov Paper 1 · Variant 3

This document consists of 12 printed pages. IB11 11_0581_13/FP © UCLES 2011 [Turn over *3964003232* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/13 Paper 1 (Core) October/November 2011 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 2011 0581/13/O/N/11 For Examiner's Use 1 During April the probability that it will rain on any one day is 6 5 . On how many of the 30 days in April would it be expected to rain? Answer [1] 2 (a) Write, in figures, the number one hundred and five thousand and two. Answer(a) [1] (b) Write your answer to part (a) correct to the nearest ten thousand. Answer(b) [1] 3 Simplify the expression. 7x + 11y + x – 6y Answer [2] 4 Insert one pair of brackets into each calculation to make the answer correct. (a) 7 × 6 – 3 + 5 = 26 [1] (b) 8 – 6 × 4 – 1 = –10 [1]

3 © UCLES 2011 0581/13/O/N/11 [Turn over For Examiner's Use 5 Write the following in order of size, starting with the smallest. 0.525 21 11 211 111 52.4% Answer I I I [2] 6 Thomas fills glasses from a jug containing 2.4 litres of water. Each glass holds 30 centilitres. How many glasses can Thomas fill? Answer [2] 7 Martha divides $240 between spending and saving in the ratio spending : saving = 7 : 8 . Calculate the amount Martha has for spending. Answer $ [2]

4 © UCLES 2011 0581/13/O/N/11 For Examiner's Use 8 210 211 212 213 214 215 216 From the list of numbers, find (a) a prime number, Answer(a) [1] (b) a cube number. Answer(b) [1] 9 Calculate the selling price of a bicycle bought for $120 and sold at a profit of 15%. Answer $ [2] 10 Solve the simultaneous equations. x + 5y = 22 x + 3y = 12 Answer x = y = [2]

5 © UCLES 2011 0581/13/O/N/11 [Turn over For Examiner's Use 11 Solve the equation. 2 3 2 − x = 2 Answer x = [2] 12 The population of a city is 128 000, correct to the nearest thousand. (a) Write 128 000 in standard form. Answer(a) [1] (b) Write down the upper bound of the population. Answer(b) [1] 13 Pedro invested $800 at a rate of 5% per year compound interest. Calculate the total amount he has after 2 years. Answer $ [2]

6 © UCLES 2011 0581/13/O/N/11 For Examiner's Use 14 Factorise completely. 5g2h + 10hj Answer [2] 15 For her holiday, Dina changed 500 Swiss francs (CHF) into pounds (£). The rate was £1 = CHF 1.6734 . Calculate how much Dina received in pounds. Give your answer correct to 2 decimal places. Answer £ [2] 16 Simplify 4x4 × 5x5. Answer [2]

7 © UCLES 2011 0581/13/O/N/11 [Turn over For Examiner's Use 17 The scale of a map is 1 : 500 000. On the map the centres of two cities are 26 cm apart. Calculate the actual distance, in kilometres, between the centres of the two cities. Answer km [2] 18 Show that 3 –2 + 2 –2 = 36 13 . Write down all the steps of your working. Answer [2]

8 © UCLES 2011 0581/13/O/N/11 For Examiner's Use 19 In Vienna, the mid-day temperatures, in °C, are recorded during a week in December. This information is shown below. –2 2 1 –3 –1 –2 0 Calculate (a) the difference between the highest temperature and the lowest temperature, Answer(a) °C [1] (b) the mean temperature. Answer(b) °C [2] 20 2.5 m 8 m 8 m NOT TO SCALE The diagram shows a circular pool of radius 2.5 m. A square piece of land surrounds the pool. Each side of the square is 8 m long. Calculate the shaded area of the land that surrounds the pool. Answer m2 [3]

9 © UCLES 2011 0581/13/O/N/11 [Turn over For Examiner's Use 21 40° 58° A B C D NOT TO SCALE In the quadrilateral ABCD, AB = AD and CB = CD. Angle BAD = 40° and angle CBD = 58°. (a) Calculate (i) angle ABD, Answer(a)(i) Angle ABD = [1] (ii) angle BCD. Answer(a)(ii) Angle BCD = [1] (b) Write down the mathematical name for the quadrilateral ABCD. Answer(b) [1]

10 © UCLES 2011 0581/13/O/N/11 For Examiner's Use 22 (a) Calculate 3 28.6 700 . Answer(a) [1] (b) Work out (8 × 106)2, giving your answer in standard form. Answer(b) [2]

11 © UCLES 2011 0581/13/O/N/11 [Turn over For Examiner's Use 23 y x 3 2 1 –1 –2 –3 –4 –5 0 1 –1 –2 –3 –4 –5 2 3 4 5 A M The diagram shows two points A (–5, 2) and M (2, –3). (a) B is the point (5, –2). (i) On the grid, mark the point B. [1] (ii) Write as a column vector. Answer(a)(ii) =           [1] (b) M is the midpoint of the line BD. Find the co-ordinates of D. Answer(b) ( , ) [2] Question 24 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 2011 0581/13/O/N/11 For Examiner's Use 24 A B D C 13 cm 7 cm 12 cm NOT TO SCALE In triangle ABC, D is on AB so that angle ADC = angle BDC = 90°. AC = 13 cm, BC = 12 cm and CD = 7 cm. (a) Calculate the length of DB. Answer(a) DB = cm [3] (b) Use trigonometry to calculate angle CAD. Answer(b) Angle CAD = [2]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2011 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. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the October/November 2011 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 2011 0581 13 © University of Cambridge International Examinations 2011 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 25 1 2 (a) 105 002 1 (b) 110 000 1ft 3 8x + 5y cao 2 B1 8x or 5y in final answer 4 (a) 7 × (6 − 3) + 5 1 (b) 8 − 6 × (4 − 1) 1 5 21 11 , 52.4%, 0.525, 211 111 2 M1 for conversion to decimals or %, allow 1 error 0.5238…, 0.524, 0.525, 0.526 or B1 for 3 in correct order SC1 correct but reverse order 6 8 2 M1 for 240 or 0.3 seen or figs 24 ÷ figs 3 7 112 2 M1 for 240 ÷ (7 + 8) × 7 8 (a) 211 cao 1 (b) 216 cao 1 9 ($)138 2 M1 for 120 × 1.15 oe SC1 answer 18 10 (x =) −3 (y =) 5 2 M1 for correctly eliminating one variable 11 (x =) 3.5 2 M1 for 2x − 3 = 2 × 2 or better 2 2x = 2 + 2 3 12 (a) 1.28 × 105 1 (b) 128 500 1 13 882 2 M1 800 × 1.05 × 1.05 14 5h(g2 + 2j) 2 B1 for 5(g2h + 2hj) or for h(5g2 + 10j) 15 298.79 cao 2 M1 for 500 ÷ 1.6734 16 20x9 cao 2 B1 for kx9or 20xk 17 130 2 M1 for 26 × 500 000 or 1 cm represents 5 km oe

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 13 © University of Cambridge International Examinations 2011 18 9 1 , 4 1 M1 Both fractions seen       = + 4 1 9 1 36 4 + 36 9 = 36 13 E1 Both fractions over a common denominator and added to give 36 13 19 (a) 5 or −5 1 (b) −0.714 (−0.7143 to −0.7142) or −7 5 2 M1 for −2 + 2 + 1 − 3 − 1 − 2 and ÷ 7 20 44.4 (44.36 to 44.38) 3 www M2 for 8 × 8 − π × 2.52 or M1 for π × 2.52 21 (a) (i) 70 1 (ii) 64 1 (b) Kite 1 22 (a) 0.0299 or 0.02992… 1 (b) 6.4 × 1013 2 B1 for 64 × 1012 or 64 000 000 000 000 23 (a) (i) B at (5, −2) 1 (ii)       −4 10 1ft (b) (–1, –4) 2ft B1, B1 follow through their B plotted 24 (a) (DB =) 9.75 or 9.746 to 9.747 3 M2 for ( ) 2 2 7 12 − or M1 for 122 = 72+ x2 or better (b) (Angle CAD =) 32.6 or 32.57 to 32.58 2 M1 for sin 13 7