Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 May/June Paper 2 · Variant 1

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 fl uid. 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 specifi ed in the question, and if the answer is not exact, give the answer to three signifi cant fi gures. 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 70. MATHEMATICS 0581/21 Paper 2 (Extended) May/June 2013 1 hour 30 minutes Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certifi cate of Secondary Education This document consists of 12 printed pages. [Turn over IB13 06_0581_21/FP © UCLES 2013 *7019332774* www.XtremePapers.com

2 0581/21/M/J/13 © UCLES 2013 For Examiner′s Use 1 One January day in Munich, the temperature at noon was 3°C. At midnight the temperature was –8°C. Write down the difference between these two temperatures. Answer … °C [1] _____________________________________________________________________________________ 2 (a) Calculate 5.7 – 1.032 . Write down all the numbers displayed on your calculator. Answer(a) … [1] (b) Write your answer to part (a) correct to 3 decimal places. Answer(b) … [1] _____________________________________________________________________________________ 3 Pedro and Eva do their homework. Pedro takes 84 minutes to do his homework. The ratio Pedro’s time : Eva’s time = 7 : 6. Work out the number of minutes Eva takes to do her homework. Answer … min [2] _____________________________________________________________________________________ 4 50° a° 55° NOT TO SCALE Use the information in the diagram to fi nd the value of a. Answer a = … [2] _____________________________________________________________________________________

3 0581/21/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 5 Show that 1 2 1 ÷ 16 3 = 8. Do not use a calculator and show all the steps of your working. Answer [2] _____________________________________________________________________________________ 6 Factorise completely. 12xy – 3x2 Answer … [2] _____________________________________________________________________________________ 7 D N C A M B The diagram shows a square ABCD. M is the midpoint of AB and N is the midpoint of CD. (a) Complete the statement. The line MN is the locus of points inside the square which are … [1] (b) Shade the region inside the square containing points which are nearer to AB than to BC and nearer to A than to B. [1] _____________________________________________________________________________________

4 0581/21/M/J/13 © UCLES 2013 For Examiner′s Use 8 Solve the inequality. 3x – 1 Ğ 11x + 2 Answer … [2] _____________________________________________________________________________________ 9 An equilateral triangle has sides of length 16.1 cm, correct to the nearest millimetre. Find the lower and upper bounds of the perimeter of the triangle. Answer Lower bound = … cm Upper bound = … cm [2] _____________________________________________________________________________________ 10 Factorise completely. ap + bp – 2a – 2b Answer … [2] _____________________________________________________________________________________ 11 Write 12 1 x 3 27 ^ h in its simplest form. Answer … [2] _____________________________________________________________________________________

5 0581/21/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 12 3 5 1 2 F R 11 students are asked if they like rugby (R) and if they like football (F). The Venn diagram shows the results. (a) A student is chosen at random. What is the probability that the student likes rugby and football? Answer(a) … [1] (b) On the Venn diagram shade the region R' ∩ F' . [1] _____________________________________________________________________________________ 13 Martina changed 200 Swiss francs (CHF) into euros (€). The exchange rate was €1 = 1.14 CHF. Calculate how much Martina received. Give your answer correct to the nearest euro. Answer € … [3] _____________________________________________________________________________________ 14 Bruce invested $420 at a rate of 4% per year compound interest. Calculate the total amount Bruce has after 2 years. Give your answer correct to 2 decimal places. Answer $ … [3] _____________________________________________________________________________________

6 0581/21/M/J/13 © UCLES 2013 For Examiner′s Use 15 A sphere has a volume of 80 cm3. Calculate the radius of the sphere. [The volume, V, of a sphere with radius r is V = 3 4 πr 3 .] Answer … cm [3] _____________________________________________________________________________________ 16 A water pipe has a circular cross section of radius 0.75 cm. Water fl ows through the pipe at a rate of 16 cm/s. Calculate the time taken for 1 litre of water to fl ow through the pipe. Answer … s [3] _____________________________________________________________________________________

7 0581/21/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 17 Find the equation of the line passing through the points (0, –1) and (3, 5). Answer … [3] _____________________________________________________________________________________ 18 (a) Factorise x2 + x – 30. Answer(a) … [2] (b) Simplify 2 ( 5)( 4) x x x x 30 - + + - . Answer(b) … [1] _____________________________________________________________________________________

8 0581/21/M/J/13 © UCLES 2013 For Examiner′s Use 19 t varies inversely as the square root of u. t = 3 when u = 4. Find t when u = 49. Answer t = … [3] _____________________________________________________________________________________ 20 R Q S M r p O P NOT TO SCALE OPQR is a parallelogram, with O the origin. M is the midpoint of PQ. OM and RQ are extended to meet at S. = p and = r. (a) Find, in terms of p and r, in its simplest form, (i) , Answer(a)(i) = … [1] (ii) the position vector of S. Answer(a)(ii) … [1] (b) When = – 2 1 p + r , what can you write down about the position of T ? Answer(b) … [1] _____________________________________________________________________________________

9 0581/21/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 21 135° 12 cm 12 cm NOT TO SCALE The diagram shows a sector of a circle of radius 12 cm with an angle of 135°. Calculate the perimeter of the sector. Answer … cm [3] _____________________________________________________________________________________ 22 Write as a single fraction in its simplest form. 3 2 2 3 x x + + + Answer … [3] _____________________________________________________________________________________

10 0581/21/M/J/13 © UCLES 2013 For Examiner′s Use 23 F D E B A C 6 cm 5 cm 12 cm NOT TO SCALE The diagram shows a triangular prism of length 12 cm. Triangle ABC is a cross section of the prism. Angle BAC = 90°, AC = 6 cm and AB = 5 cm. Calculate the angle between the line CE and the base ABED. Answer … [4] _____________________________________________________________________________________ 24 A = 1 3 2 4 e o B = 4 1 3 2 e o Find (a) AB, Answer(a) AB = [2] (b) B –1, the inverse of B. Answer(b) B –1 = [2] _____________________________________________________________________________________

11 0581/21/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 25 28 0 20 30 Time (seconds) Speed (m/s) NOT TO SCALE The diagram shows the speed-time graph of a car. It travels at 28 m/s for 20 seconds and then decelerates until it stops after a further 10 seconds. (a) Calculate the deceleration of the car. Answer(a) … m/s2 [1] (b) Calculate the distance travelled during the 30 seconds. Answer(b) … m [3] _____________________________________________________________________________________ Question 26 is printed on the next page.

12 0581/21/M/J/13 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 2013 For Examiner′s Use 26 D A C B 9 cm 15 cm 6 cm 4 cm NOT TO SCALE The diagram shows a solid prism of length 15 cm. The cross section of the prism is the trapezium ABCD. Angle DAB = angle CDA = 90°. AB = 9 cm, DC = 6 cm and AD = 4 cm. Calculate the total surface area of the prism. Answer … cm2 [5]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0581 MATHEMATICS 0581/21 Paper 2 (Extended), maximum raw mark 70 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 should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. www.XtremePapers.com

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 21 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 soi seen or implied Qu. Answers Mark Part Marks 1 11 or –11 1 2 (a) 1.32656... 1 (b) 1.327 1ft 3 72 2 M1 for 84 ÷ 7 4 105 2 M1 for 180 – 55 – 50 or B1 for 55 or 75 seen in the correct angle inside the triangle 5 correct working; e.g. 8 3 16 2 3 = × n n k k 2 M1 for and A1 for 8 3 16 = × n n 6 3x(4y – x) final answer 2 B1 for 3(4xy – x2) or x(12y – 3x) 7 (a) Equidistant from A and B (or C and D or AD and BC) 1 (b) 1 8 x ≥−3 8 oe 2 M1 for –3 ≤ 8x oe If 0 then SC1 for −3 8 with incorrect inequality. 9 48.15, 48.45 cao 2 B1 B1 If 0 then M1 for 16.0 and 16.15 soi 10 (a + b)(p – 2) 2 B1 p(a + b) – 2(a + b) or a(p – 2) + b(p – 2) 11 3x4 2 B1 for kx4 or 3xk k k 2 3 k k 2 3

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 21 12 (a) 3 11 1 (b) 1 13 175 cao final answer 3 B2 for 175.4 ... or M1 for 200 ÷ 1.14 14 454.27 cao final answer 3 M1 for 420 × (1+ 100 4 )2 oe and A1 for 454 or 454.2 to 454.3 or SC2 for answer 34.27 or SC1 for answer 34.2 to 34.3 15 2.67 or 2.672 to 2.67301 3 M2 for 3 3 4 ) π 80 ( ÷ oe or M1 for 80 ÷ 4 3π ( ) oe 16 35.4 or 35.36 to 35.37 3 M2 for 1000 ÷ (π × 0.752 ×16) oe or M1 for π × 0.752 ×16 oe or ) 75 .0 π ( 1000 2 × ÷ 17 y = 2x − 1 3 B2 for y = mx – 1 or y = 2x + c or 2x – 1 or B1 for gradient = 2, B1 for c = –1 or SC1 for 3 6 or ] 0 [3 1 5 − − − 18 (a) (x + 6)(x–5) 2 SC1 for (x + a)(x + b) where ab = –30 or a + b (b) x + 4 x + 6 final answer 1 19 6 7 or 0.857[1…] 3 M1 for t = k u oe A1 for k = 6 20 (a) (i) p + 1 2 r 1 (ii) 2p + r 1ft 2 × their (i) (b) Midpoint of RQ 1

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 21 21 52.3 or 52.27 to 52.28 3 SC2 for 28.3 or 28.7 to 28.8 If 0, M2 for 12 2 24 π 360 135 × + × × or M1 for 24 360 135 × ×π 22 ) 2 )( 3 ( 13 5 + + + x x x oe final answer 3 B1 for common denominator (x + 3)(x + 2) seen M1 for 2(x + 2) + 3(x + 3) soi 23 24.8 or 24.77 to 24.78 4 M1 for recognition of angle CEA M1 for 122 + 52 M1 for tan = AE their 6 oe 24 (a) 6 7 16 17     2 B1 for 1 correct row or 1 correct column (b) 1 5 2 −3 −1 4     2 B1 for k 2 −3 −1 4     or 1 5 a b c d     25 (a) 2.8 oe 1 (b) 700 3 M2 for ½(20 + 30) × 28 oe or M1 for a correct area statement 26 420 5 M1 for [CB =] 2 2 ) 6 9 ( 4 − + M1 for their CB from Pythagoras × 15 M1 for [2 ×] 4 ) 9 6 ( 2 1 × + M1 for 4 × 15, 9 × 15, 6 × 15 with intention to add