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

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 0581/22 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_22/FP © UCLES 2013 *1313574368* www.XtremePapers.com

2 0581/22/M/J/13 © UCLES 2013 For Examiner′s Use 1 Shade the required region on each Venn diagram. A B A' ∪ B A B A' ∩ B' [2] _____________________________________________________________________________________ 2 Factorise completely. kp + 3k + mp + 3m Answer … [2] _____________________________________________________________________________________ 3 The fi rst fi ve terms of a sequence are shown below. 13 9 5 1 –3 Find the nth term of this sequence. Answer … [2] _____________________________________________________________________________________

3 0581/22/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 4 Calculate (4.3 × 108 ) + (2.5 × 107 ) . Give your answer in standard form. Answer … [2] _____________________________________________________________________________________ 5 A B C 8 cm NOT TO SCALE Triangle ABC has a height of 8 cm and an area of 42 cm². Calculate the length of BC. Answer BC = … cm [2] _____________________________________________________________________________________

4 0581/22/M/J/13 © UCLES 2013 For Examiner′s Use 6 George and his friend Jane buy copies of the same book on the internet. George pays $16.95 and Jane pays £11.99 on a day when the exchange rate is $1 = £0.626. Calculate, in dollars, how much more Jane pays. Answer $ … [2] _____________________________________________________________________________________ 7 (a) Use your calculator to work out 65 – 1.72 . Write down all the numbers displayed on your calculator. Answer(a) … [1] (b) Write your answer to part (a) correct to 2 signifi cant fi gures. Answer(b) … [1] _____________________________________________________________________________________ 8 Joe measures the side of a square correct to 1 decimal place. He calculates the upper bound for the area of the square as 37.8225 cm2. Work out Joe’s measurement for the side of the square. Answer … cm [2] _____________________________________________________________________________________

5 0581/22/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 9 A car, 4.4 metres long, has a fuel tank which holds 65 litres of fuel when full. The fuel tank of a mathematically similar model of the car holds 0.05 litres of fuel when full. Calculate the length of the model car in centimetres. Answer … cm [3] _____________________________________________________________________________________ 10 85° 58° 19° B C A E D N NOT TO SCALE A, B, C, D and E are points on a circle. Angle ABD = 58°, angle BAE = 85° and angle BDC = 19°. BD and CA intersect at N. Calculate (a) angle BDE, Answer(a) Angle BDE = … [1] (b) angle AND. Answer(b) Angle AND = … [2] _____________________________________________________________________________________

6 0581/22/M/J/13 © UCLES 2013 For Examiner′s Use 11 Without using a calculator, work out 7 6 ÷ 1 3 2 . Write down all the steps in your working. Answer … [3] _____________________________________________________________________________________ 12 Solve the equation. 5(2y – 17) = 60 Answer y = … [3] _____________________________________________________________________________________ 13 Carol invests $6250 at a rate of 2% per year compound interest. Calculate the total amount Carol has after 3 years. Answer $ … [3] _____________________________________________________________________________________

7 0581/22/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 14 y is inversely proportional to x3. y = 5 when x = 2. Find y when x = 4. Answer y = … [3] _____________________________________________________________________________________ 15 Use the quadratic equation formula to solve 2x2 + 7x – 3 = 0 . Show all your working and give your answers correct to 2 decimal places. Answer x = … or x = … [4] _____________________________________________________________________________________

8 0581/22/M/J/13 © UCLES 2013 For Examiner′s Use 16 40 0 3 22 Time (minutes) 26 Speed (km/h) NOT TO SCALE The diagram shows the speed-time graph of a train journey between two stations. The train accelerates for 3 minutes, travels at a constant maximum speed of 40 km/h, then takes 4 minutes to slow to a stop. Calculate the distance in kilometres between the two stations. Answer … km [4] _____________________________________________________________________________________

9 0581/22/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 17 The owner of a small café records the average air temperature and the number of hot drinks he sells each day for a week. Air temperature (°C) 18 23 19 23 24 25 20 Number of hot drinks sold 12 8 13 10 9 7 12 (a) On the grid, draw a scatter diagram to show this information. 14 13 12 11 10 9 8 7 6 0 17 18 19 20 21 22 23 24 25 26 Air temperature (°C) Number of hot drinks sold [2] (b) What type of correlation does your scatter diagram show? Answer(b) … [1] (c) Draw a line of best fi t on the grid. [1] _____________________________________________________________________________________ 18 Solve 6x + 3 < x < 3x + 9 for integer values of x. Answer … [4] _____________________________________________________________________________________

10 0581/22/M/J/13 © UCLES 2013 For Examiner′s Use 19 D A C B Scale: 1 cm to 8 m The rectangle ABCD is a scale drawing of a rectangular football pitch. The scale used is 1 centimetre to represent 8 metres. (a) Construct the locus of points 40 m from A and inside the rectangle. [2] (b) Using a straight edge and compasses only, construct the perpendicular bisector of DB. [2] (c) Shade the region on the football pitch which is more than 40 m from A and nearer to D than to B. [1] _____________________________________________________________________________________

11 0581/22/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 20 The heights, in metres, of 200 trees in a park are measured. Height (h m) 2 < h Ğ 6 6 < h Ğ 10 10 < h Ğ 13 13 < h Ğ 17 17 < h Ğ 19 19 < h Ğ 20 Frequency 23 47 45 38 32 15 (a) Find the interval which contains the median height. Answer(a) … [1] (b) Calculate an estimate of the mean height. Answer(b) … m [4] (c) Complete the cumulative frequency table for the information given in the table above. Height (h m) 2 < h Ğ 6 h Ğ 10 h Ğ 13 h Ğ 17 h Ğ 19 h Ğ 20 Cumulative frequency 23 [2] _____________________________________________________________________________________ Question 21 is printed on the next page.

12 0581/22/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 21 f(x) = 5x + 4 g(x) = x 2 1 , x ¸ 0 h(x) = x 2 1 c m Find (a) fg(5) , Answer(a) … [2] (b) gg(x) in its simplest form, Answer(b) gg(x) = … [2] (c) f –1(x) , Answer(c) f –1(x) = … [2] (d) the value of x when h(x) = 8. Answer(d) x = … [2]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0581 MATHEMATICS 0581/22 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 22 © Cambridge International Examinations 2013 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 1 1 2 (p + 3)(k + m) 2 B1 for k(p + 3) + m(p + 3) or p(k + m) + 3(k + m) 3 17 − 4n 2 B1 for ± 4n seen 4 4.55 × 108 2 B1 for figs 455 seen 5 10.5 www 2 M1 for 42 = 2 1 × BC × 8 or better 6 2.2[0...] 2 M1 for 11.99 ÷ 0.626 soi by 19.2 or 19.15... 7 (a) (b) 5.17225... 5.2 1 1FT FT their (a) 8 6.1 final answer 2 M1 for [√37.8225=] 6.15 9 40.3 or 40.31 to 40.32 3 M2 for 3 65 05 .0 4.4 × soi or M1 for 3 65 05 .0 soi or 3 05 .0 65 soi 10 (a) (b) 95 77 1 2 B1 for [angle] ACD = 58° or [angle] BAC = 19° or [angle] ANB = 103° or [angle] CAE = 66° A B A B

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 22 © Cambridge International Examinations 2013 Qu Answers Mark Part Marks 11 with 2 correct steps seen k k 35 18 3 B1 for k k 3 5 and M1 for
 × their 3 5 12 14.5 oe 3 M2 for complete correct method or M1 for one correct step 13 6632.55 cao final answer 3 M2 for 6250 ×
1    oe or M1 for 6250 ×
1    oe SC2 for answer 382.55 final answer 14 0.625 oe 3 M1 for 3 x k y = A1 for k = 40 15 2 2 )3 )( 2 ( 4 7 7 2 × − − ± − 0.39, −3.89 cao B2 B1,B1 B1 for ) 3 )( 2 ( 4 72 − − or better seen B1 for p = −7 and r = 2 × 2 or better as long as in the form r q p + or r q p − After B0B0 for the two answers, SC1 for 0.4 or 0.386[0009...] and −3.9 or −3.886[0009...] or SC1 for −0.39 and 3.89 16 15 4 M2 for ( ) 19 26 40 2 1 + × × oe or M1 for one valid area calculation Indep M1 for ÷ 60 SC3 for answer 900 17 (a) (b) (c) 7 correct plots Negative ruled line of best fit within tolerance 2 1 1 P1 for 5 or 6 correct

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 22 © Cambridge International Examinations 2013 Qu Answers Mark Part Marks 18 −1 −2 −3 −4 4 B3 for 5 3 − < x and 5.4 − > x oe or B2 for 5 3 − < x or 5.4 − > x oe or B1 for 5x < − 3 or − 9 < 2x oe Or mark on answer line −1 oe 19 (a) (b) (c) arc centre A radius 5 cm ruled perpendicular bisector of DB with 2 pairs of correct arcs cao 2 2 1 B1 arc with centre A B1 correct ruled line B1 2 pairs of correct arcs 20 (a) (b) (c) 10 < h ≤ 13 12.1[2] www 70, 115, 153, 185, 200 1 4 2 M1 for at least 5 correct mid-values seen M1 for fx ∑ where x is in the correct interval M1 for their fx ∑ ÷ 200 B1 for 3 or 4 correct 21 (a) (b) (c) (d) 4.5 oe x 5 4 − x oe − 3 2 2 2 2 B1 for [g(5)=] 0.1 oe M1 for ( ) x 2 1 2 1 seen oe M1 for a correct first step e.g. y − 4 = 5x or 5 4 5 + = x y or x = 5y + 4 M1 for

   8 or

  

  or 8 1 2 = x oe or 3 2 2 = −x