Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 Oct/Nov 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) October/November 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 11 printed pages and 1 blank page. [Turn over IB13 11_0581_21/FP © UCLES 2013 *7420664094* www.XtremePapers.com

2 0581/21/O/N/13 © UCLES 2013 For Examiner′s Use 1 Work out 72 cents as a percentage of 83 cents. Answer … % [1] _____________________________________________________________________________________ 2 Calculate . . . . 4 89 4 07 5 27 0 93 - - . Give your answer correct to 4 signifi cant fi gures. Answer … [2] _____________________________________________________________________________________ 3 55° p° NOT TO SCALE Find the value of p. Answer p = … [2] _____________________________________________________________________________________ 4 Calculate 17.5% of 44 kg. Answer … kg [2] _____________________________________________________________________________________

3 0581/21/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 5 Solve the equation. 5 – 2x = 3x – 19 Answer x = … [2] _____________________________________________________________________________________ 6 S P A C E S One of the 6 letters is taken at random. (a) Write down the probability that the letter is S. Answer(a) … [1] (b) The letter is replaced and again a letter is taken at random. This is repeated 600 times. How many times would you expect the letter to be S? Answer(b) … [1] _____________________________________________________________________________________ 7 The length, p cm, of a car is 440 cm, correct to the nearest 10 cm. Complete the statement about p. Answer … Ğ p < … [2] _____________________________________________________________________________________

4 0581/21/O/N/13 © UCLES 2013 For Examiner′s Use 8 Emily invests $x at a rate of 3% per year simple interest. After 5 years she has $20.10 interest. Find the value of x. Answer x = … [3] _____________________________________________________________________________________ 9 Find the nth term in each of the following sequences. (a) 3 1 , 4 2 , 5 3 , 6 4 , 7 5 , … Answer(a) … [1] (b) 0, 3, 8, 15, 24, … Answer(b) … [2] _____________________________________________________________________________________ 10 Make b the subject of the formula. 2 2 c a b + = Answer b = … [3] _____________________________________________________________________________________ 11 The volume of a child’s model plane is 1200 cm3. The volume of the full size plane is 4050 m3. Find the scale of the model in the form 1 : n. Answer 1 : … [3] _____________________________________________________________________________________

5 0581/21/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 12 A B C D 59° 28° 42° NOT TO SCALE A, B, C and D lie on the circle. Find (a) angle ADC, Answer(a) Angle ADC = … [1] (b) angle ADB. Answer(b) Angle ADB = … [2] _____________________________________________________________________________________ 13 (a) 3x = 5 3 4 Find the value of x. Answer(a) x = … [1] (b) Simplify 15 2 y 5 32 ^ h . Answer(b) … [2] _____________________________________________________________________________________

6 0581/21/O/N/13 © UCLES 2013 For Examiner′s Use 14 Write as a single fraction in its simplest form. 2 t t 3 1 + - - Answer … [3] _____________________________________________________________________________________ 15 Do not use a calculator in this question and show all the steps of your working. Give each answer as a fraction in its lowest terms. Work out. (a) 4 3 – 12 1 Answer(a) … [2] (b) 2 2 1 × 25 4 Answer(b) … [2] _____________________________________________________________________________________

7 0581/21/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 16 7 1 0 –1 8 x y A B NOT TO SCALE A is the point (–1, 1) and B is the point (8, 7). (a) Write as a column vector. Answer(a) = f p [1] (b) Find | |. Answer(b) | | = … [2] (c) = 2 . Write down the co-ordinates of C. Answer(c) (… , …) [1] _____________________________________________________________________________________ 17 Factorise completely. (a) a + b + at + bt Answer(a) … [2] (b) x2 – 2x – 24 Answer(b) … [2] _____________________________________________________________________________________

8 0581/21/O/N/13 © UCLES 2013 For Examiner′s Use 18 The diagram shows a solid hemisphere. The total surface area of this hemisphere is 243 π. The volume of the hemisphere is k π. Find the value of k. [The surface area, A, of a sphere with radius r is A = 4 πr2.] [The volume, V, of a sphere with radius r is V = 3 4 πr3.] Answer k = … [4] _____________________________________________________________________________________ 19 (a) Convert 144 km/h into metres per second. Answer(a) … m/s [2] (b) A train of length 120 m is travelling at 144 km/h. It passes under a bridge of width 20 m. Find the time taken for the whole train to pass under the bridge. Give your answer in seconds. Answer(b) … s [2] _____________________________________________________________________________________

9 0581/21/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 20 A B C (a) In this part, use a straight edge and compasses only and show your construction arcs. Construct accurately (i) the bisector of angle B, [2] (ii) the locus of points equidistant from B and from C. [2] (b) Shade the region inside triangle ABC containing the points which are nearer to BC than to BA and nearer to C than to B. [1] _____________________________________________________________________________________

10 0581/21/O/N/13 © UCLES 2013 For Examiner′s Use 21 A B X C D NOT TO SCALE ABCD is a kite. The diagonals AC and BD intersect at X. AC = 12 cm, BD = 20 cm and DX : XB = 3 : 2 . (a) Calculate angle ABC. Answer(a) Angle ABC = … [3] (b) Calculate the area of the kite. Answer(b) … cm2 [2] _____________________________________________________________________________________

11 0581/21/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 22 5 11 19 15 R T The Venn diagram shows the number of red cars and the number of two-door cars in a car park. There is a total of 50 cars in the car park. R = {red cars} and T = {two-door cars}. (a) A car is chosen at random. Write down the probability that (i) it is red and it is a two-door car, Answer(a)(i) … [1] (ii) it is not red and it is a two-door car. Answer(a)(ii) … [1] (b) A two-door car is chosen at random. Write down the probability that it is not red. Answer(b) … [1] (c) Two cars are chosen at random. Find the probability that they are both red. Answer(c) … [2] (d) On the Venn diagram, shade the region R ∪ T '. [1] _____________________________________________________________________________________

12 0581/21/O/N/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. BLANK PAGE © UCLES 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 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 October/November 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 – October/November 2013 0581 21 © 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 Qu. Answers Mark Part Marks 1 86.7 or 86.74 to 86.75 1 2 5.293 cao 2 B1 for 5.29 or 5.292 to 5.2927 3 125 2 B1 for 55 or 125 in any other correct position on diagram or M1 for 180–55 4 7.7 2 M1 for 44 × 100 5. 17 oe 5 4.8 oe 2 M1 for 5 + 19 = 3x + 2x oe or better or B1 for 24 – 2x = 3x oe or 5 = 5x – 19 oe 6 (a) 6 2 oe 1 (b) 200 1FT FT 600 × their (a) providing their (a) is a probability 7 435, 445 cao 2 B1 for one value in the correct place or SC1 for both values correct but reversed 8 134 3 M2 for 5 3 100 1. 20 × × oe or M1 for 1. 20 100 5 3 = × × x or 3% = 4.02 oe If 0 scored SC1 for answer of figs 134 9 (a) 2 + n n oe final answer 1 (b) n2–1 oe final answer 2 B1 for any quadratic in final answer 10 [±] 2 2 a c − oe final answer 3 M1 for correct square M1 for correct re-arrangement M1 for correct square root

Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 21 © Cambridge International Examinations 2013 11 150 3 M1 for m3 to cm3 or cm3 to m3 12 (a) 110 1 (b) 79 2 B1 for DAC = 42 or ACB = 79 or ACD = 28 13 (a) 4 5 oe 1 (b) 4y6 2 B1 for ky6 or y6 or 4yk or 4 as final answer 14 1 5 2 − − t t final answer 3 B1 for 1 )1 ( 3 − − t t or better B1 for 3(t – 1) – (t + 2) oe or better 15 (a) 12 1 12 9 − oe [=] 12 8 oe [=] 3 2 M1 M1 Must be shown Both fractions must be shown (b) 25 4 2 5 × oe Cancelling shown or 50 20 oe [=] 5 2 M1 M1 Must be shown Dependent and cancelling shown or a fraction and then 5 2 must be shown 16 (a)       6 9 1 (b) 10.8 or 10.81 to 10.82 2FT M1 for 2 2 ) 6 ( ) 9 ( their their + A1 for 10.8 or FT correctly evaluated (c) (17, 13) 1FT FT their 9 and 6. (8 + their 9, 7 + their 6) correctly evaluated 17 (a) (a + b)(1 + t) 2 B1 for 1(a + b) + t(a + b) or a(1 + t) + b(1 + t) (b) (x – 6)(x + 4) 2 SC1 for answer of (x + a)(x + b) where ab = –24 or a + b = –2 18 486 cao 4 M1 for π π π 243 4 2 2 2 1 = + × r r or better A1 for [r =] 9 M1 for ( )3 3 4 2 1 their ] [ r π ×

Page 4 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 21 © Cambridge International Examinations 2013 19 (a) 40 2 M1 for 60 60 1000 144 × × oe (b) 3.5 2FT FT 140 ÷ their (a) M1 for dist ÷ their (a) or dist ÷ 40 or dist × 1000 144 60 60 × × or B1 for 140 seen 20 (a) (i) Accurate bisector of angle B with correct arcs 2 B1 for correct line or correct arcs (ii) Accurate perpendicular bisector of BC with correct arcs 2 B1 for correct line or correct arcs (b) correct region shaded 1 21 (a) 73.7 or 73.73 to 73.74 3 M1 for 2 2 3 20 × + or B1 for BX = 8 M1 for tan [ ] = 8 6 their or better (b) 120 2 M1 for 12 20 2 1 × × oe 22 (a) (i) 50 5 oe 1 (ii) 50 11 oe 1 (b) 16 11 oe 1 (c) 2450 380 oe 2 M1 for 49 19 50 20 × (d) 1