Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 Oct/Nov Paper 2 · Variant 3

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 an HB pencil for any diagrams or graphs. Do not use staples, paper clips, 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 0581/23 Paper 2 (Extended) October/November 2014 1 hour 30 minutes Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education This document consists of 12 printed pages. [Turn over IB14 11_0581_23/FP © UCLES 2014 *0528559093* PAPA CAMBRIDGE

2 0581/23/O/N/14 © UCLES 2014 1 $1 = 8.2 rand Change $350 into rands. Answer … rand [2] __________________________________________________________________________________________ 2 Write the following in order of size, smallest fi rst. 0.34 0.6 0.62 0.73 Answer … < … < … < … [2] smallest __________________________________________________________________________________________ 3 Work out 4 × 10–5 × 6 × 1012. Give your answer in standard form. Answer … [2] __________________________________________________________________________________________ 4 The four sector angles in a pie chart are 2x°, 3x°, 4x° and 90°. Find the value of x. Answer x = … [2] __________________________________________________________________________________________

3 0581/23/O/N/14 © UCLES 2014 [Turn over 5 A train takes 65 minutes to travel 52 km. Calculate the average speed of the train in kilometres per hour. Answer … km/h [2] __________________________________________________________________________________________ 6 Solve the equation. 3 2 5 x + = 8 Answer x = … [3] __________________________________________________________________________________________ 7 Find the interior angle of a regular polygon with 18 sides. Answer … [3] __________________________________________________________________________________________

4 0581/23/O/N/14 © UCLES 2014 8 Make x the subject of the formula. y = 2 + 8 x - Answer x = … [3] __________________________________________________________________________________________ 9 y varies inversely as (x + 5). y = 6 when x = 3. Find y when x = 7. Answer y = … [3] __________________________________________________________________________________________

5 0581/23/O/N/14 © UCLES 2014 [Turn over 10 Maryah borrows $12 000 to start a business. The loan is for 3 years at a rate of 5% per year compound interest. The loan has to be paid back at the end of the 3 years. Calculate the total amount to be paid back. Answer $ … [3] __________________________________________________________________________________________ 11 (a) Here are the fi rst three terms of a sequence. U1 = 13 U2 = 13 + 23 U3 = 13 + 23 + 33 The n th term is given by Un = 4 1 n2 (n + 1)2. Work out the value of U39 . Answer(a) U39 = … [2] (b) Here are the fi rst three terms of another sequence. V1 = 23 V2 = 23 + 43 V3 = 23 + 43 + 63 By comparing this sequence with the sequence in part (a), fi nd a formula for the n th term, Vn . Answer(b) Vn = … [1] __________________________________________________________________________________________

6 0581/23/O/N/14 © UCLES 2014 12 D A C B E (a) Draw the locus of the points which are 3 cm from E. [1] (b) Using a straight edge and compasses only, construct the bisector of angle DCB. [2] (c) Shade the region which is ● less than 3 cm from E and ● nearer to CB than to CD. [1] __________________________________________________________________________________________

7 0581/23/O/N/14 © UCLES 2014 [Turn over 13 Write as a single fraction, in its simplest form. 2 3 x + 3 2x + 3 + 2x Answer … [4] __________________________________________________________________________________________ 14 A O B P Q b a NOT TO SCALE The diagram shows two points, P and Q, on a straight line AB. P is the midpoint of AB and Q is the midpoint of PB. O is the origin, = a and = b. Write down, in terms of a and b, in its simplest form (a) , Answer(a) = … [2] (b) the position vector of Q. Answer(b) … [2] __________________________________________________________________________________________

8 0581/23/O/N/14 © UCLES 2014 15 The lights and brakes of 30 bicycles are tested. The table shows the results. Lights Brakes Fail test 3 9 Pass test 27 21 The lights and brakes both failed on one bicycle only. = {30 bicycles} Complete the Venn diagrams. (a) [2] (b) [2] __________________________________________________________________________________________ L i g h t s f a il B r a k e s f a i l … … … … L i g h t s p a s s B r a k e s p a s s … … … …

9 0581/23/O/N/14 © UCLES 2014 [Turn over 16 f(x) = (x – 3)2 g(x) = 4 1 x - h(x) = x3 Find (a) hf(1), Answer(a) … [2] (b) g–1(x), Answer(b) g–1(x) = … [2] (c) gh(x), Answer(c) gh(x) = … [1] (d) the solution to the equation f(x) = 0. Answer(d) x = … [1] __________________________________________________________________________________________

10 0581/23/O/N/14 © UCLES 2014 17 The mass, m grams, of cornfl akes in each of 200 boxes is recorded. The cumulative frequency diagram shows the results. 200 180 160 140 120 100 80 60 40 20 0 494 496 498 500 502 Mass (grams) 504 506 508 510 m Cumulative frequency (a) Use the diagram to estimate the inter-quartile range. Answer(a) … g [2] (b) Find the probability that a box chosen at random has a mass of 500 grams or less. Answer(b) … [2] (c) Mass (m grams) 496 < m Y 500 500 < m Y 504 504 < m Y 508 508 < m Y 510 Frequency 16 74 104 6 The data in this frequency table is to be shown in a histogram. Complete the frequency density table below. Mass (m grams) 496 < m Y 500 500 < m Y 504 504 < m Y 508 508 < m Y 510 Frequency density 4 [2] __________________________________________________________________________________________

11 0581/23/O/N/14 © UCLES 2014 [Turn over 18 6 cm 15 cm NOT TO SCALE The diagram shows a glass, in the shape of a cone, for drinking milk. The cone has a radius of 6 cm and height 15 cm. A bottle of milk holds 2 litres. (a) How many times can the glass be completely fi lled from the bottle? [The volume, V, of a cone with radius r and height h is V = 3 1 πr 2h.] Answer(a) … [4] (b) Calculate the volume of milk left in the bottle. Give your answer in cm3. Answer(b) … cm3 [3] __________________________________________________________________________________________ Question 19 is printed on the next page.

12 0581/23/O/N/14 © UCLES 2014 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. 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. 19 (a) N = 1 0 1 0 - f p Describe fully the single transformation represented by N. Answer(a) … … [3] (b) Find the matrix which represents the single transformation that maps triangle A onto triangle B. A B 2 4 6 8 10 1 3 5 7 9 7 6 5 4 3 2 1 0 y x Answer(b) f p [2] (c) On the grid, draw the image of triangle A under a stretch, factor 3, with the y-axis invariant. [2]

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 2014 series 0581 MATHEMATICS 0581/23 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 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components. PAPA CAMBRIDGE

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 23 © Cambridge International Examinations 2014 Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Qu. Answers Mark Part Marks 1 2870 2 M1 for 350 × 8.2 2 6.0 6.0 7.0 34 .0 2 3 2 M1 for decimal conversion: 0.7 [7…] or 0.8 for 6.0 and 0.36 for 0.62 and 0.343 for 0.73 or B1 for three in the correct order 3 8 10 4.2 × 2 B1 for 240 000 000 oe or B1 for 8 10 × k or k 10 4.2 × 4 30 2 M1 for 2x + 3x + 4x + 90 = 360 oe 5 48 2 M1 for 52 ÷ 65 [× 60] oe implied by 0.8 6 9.5 or 2 19 3 M2 for 2x = (8 × 3) – 5 or better oe or M1 for 2x + 5 = 8 × 3 or better 7 160 3 M2 for 18 360 180 − or ( ) 18 2 18 180 − × oe or M1 for 180 × (18 – 2) or 18 360 8 8 + (y – 2)2 oe final answer 3 M1 for y – 2 = √(x – 8) M1 for squaring both sides completed correctly M1 for adding their 8 completed correctly on answer line 9 4 3 M2 for 6(3 + 5) = y(7 + 5) oe or M1 for 5 + = x k y oe A1 for k = 48 10 13891.5[0] 3 M2 for 3 100 5 1 12000      + × oe or M1 for n      + × 100 5 1 12000 oe 2 > n

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 23 © Cambridge International Examinations 2014 11 (a) (b) 608 400 cao 2n2(n + 1)2 oe 2 1 M1 for ( )2 2 1 39 39 4 1 + × × 12 (a) (b) (c) Complete circle centre E radius 3cm Correct ruled bisector with two pairs of correct arcs 1 2 1 B1 for correct bisector with no/wrong arcs dep on attempt at bisector of C and enclosed region 13 x x x 6 9 18 16 2 + + final answer 4 M2 for 9 [+] 4x2 [+] 18x [+] 12x2 or better or M1 for 2 of these and M1FT for adding their four ‘numerators’ together correctly and B1 for denominator 6x to a maximum of 3 marks 14 (a) (b) a b 2 1 2 1 − oe b a 4 3 4 1 + oe 2 2 M1 for 2 1 ( AO + OB) oe or correct unsimplified route e.g. AO + OB + BP or –a + b + 2 1 BA = –a + b + 2 1 (a – b) M1 for OA + AQ oe or correct unsimplified route 15 (a) (b) 8 1 2 19 2 19 8 1 2 2FT B1 for any two correct B2FT for a correct ft from (a) or B1FT for any two correct or for any correct two ft from (a) 16 (a) (b) (c) (d) 64 4x + 1 oe 4 1 3 − x oe final answer 3 nfww 2 2 1 1 B1 for [f(1) =] 4 or M1 for ((x – 3)2)3 or better M1 for 4 1 − = y x or 4y = x – 1

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 23 © Cambridge International Examinations 2014 17 (a) (b) (c) 3.08 to 3.22 nfww 200 16 oe 18.5 26 3 2 2 2 B1 for 502.5 to 502.62 or 505.7 to 505.8 B1 for 16 soi or M1 for 200 16 their B1 for 18.5 and 26 B1 for 3 18 (a) (b) 3 303 to 304 4 3 B3 for 3.536 to 3.54 as an answer or M2 for 15 6 π 3 1 2000 2 × × ÷ or M1 for 15 6 π 3 1 2 × × and SC1 for truncating their 3.54 to a whole number M2 for 2000 – their 3 × their volume or M1 for their 3 × their volume 19 (a) (b) (c) rotation 90 clockwise [about] origin oe       0 1 1 0 Triangle at (3, 3), (6, 3) and (3, 5) 3 2 2 B1 for each M1 for any one column or row correct M1 for any two vertices correct or correct answer translated horizontally