Cambridge IGCSE Mathematics - International 0607 — 2015 May/June Paper 2 · Variant 2

This document consists of 8 printed pages. DC (AC/SG) 99283/6 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 1 0 4 9 5 4 7 5 2 6 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 Paper 2 (Extended) May/June 2015 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments 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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40.

2 0607/22/M/J/15 © UCLES 2015 Formula List For the equation ax bx c 0 2 + + = x a b b ac 2 4 2 ! = - - Curved surface area, A, of cylinder of radius r, height h. r A rh 2 = Curved surface area, A, of cone of radius r, sloping edge l. r A rl = Curved surface area, A, of sphere of radius r. r A r 4 2 = Volume, V, of pyramid, base area A, height h. V Ah 3 1 = Volume, V, of cylinder of radius r, height h. r V r h 2 = Volume, V, of cone of radius r, height h. r V r h 3 1 2 = Volume, V, of sphere of radius r. r V r 3 4 3 = sin sin sin A a B b C c = = cos a b c bc A 2 2 2 2 = + - sin bc A 2 1 Area = A C B c b a

3 0607/22/M/J/15 © UCLES 2015 [Turn over Answer all the questions. 1 (a) Work out ( . ) 0 3 2. Answer(a) … [1] (b) Find n when n 6 5 24 = . Answer(b) n = … [1] 2 (a) Find the value of (i) 250, Answer(a)(i) … [1] (ii) 100 2 3. Answer(a)(ii) … [1] (b) Write as a single power of 5. 5 5 5 3 2 12 # Answer(b) … [1] 3 Find the magnitude of 4 6 - J L KK N P OO. Write your answer in surd form as simply as possible. Answer … [3]

4 0607/22/M/J/15 © UCLES 2015 4 Anneke, Babar, Céline, and Dieter each throw the same biased die. They want to find the probability of throwing a six with this die. They each throw the die a different number of times. These are their results. Anneke Babar Céline Dieter Number of throws 200 40 100 500 Number of sixes 46 12 15 100 (a) Complete the table below to show the relative frequencies of their results. Write your answers as decimals. Anneke Babar Céline Dieter Relative frequency of throwing a six [2] (b) Whose result gives the best estimate of the probability of throwing a six with the biased die? Give a reason for your answer. Answer(b) … because … … [1] (c) The probability of throwing a six with a different biased die is 0.41. Find the expected number of sixes when this die is thrown 600 times. Answer(c) … [1]

5 0607/22/M/J/15 © UCLES 2015 [Turn over 5 A is the point (2, 8) and B is the point (6, 0). (a) Find the co-ordinates of the midpoint of AB. Answer(a) (… , …) [1] (b) Find the gradient of AB. Answer(b) … [2] 6 Simplify ( ) 5 3 2 + . Answer … [2] 7 Solve. ( ) x x 2 3 4 2 G + - Answer … [3]

6 0607/22/M/J/15 © UCLES 2015 8 3 m 10 m 6 m NOT TO SCALE The diagram shows a shape made from a cylinder and a cone. The cylinder and cone have a common radius of 6 m. The height of the cylinder is 10 m and the height of the cone is 3 m. Calculate the total volume of the shape. Leave your answer as a multiple of π. Answer … m3 [3] 9 Solve these simultaneous equations. x y 4 3 18 - = x y 5 2 11 + = Answer x = … y = … [4]

7 0607/22/M/J/15 © UCLES 2015 [Turn over 10 Solve the following equations. (a) log x + log 3 = log 12 Answer(a) x = … [1] (b) log x = 3 Answer(b) x = … [1] (c) 2log x – log 5 = log 20 Answer(c) x = … [3] 11 A, B, C and D are points on the circle, centre O. PQ is a tangent to the circle at the point C. Angle PCD = 55° and angle ADO = 40°. A B Q C P O D 40° 55° NOT TO SCALE Find (a) angle COD, Answer(a) … [2] (b) angle DAC, Answer(b) … [1] (c) angle ABC. Answer(c) … [1] Question 12 is printed on the next page.

8 0607/22/M/J/15 © UCLES 2015 12 These are sketches of the graphs of six functions. y x 0 A y x 0 B y x 0 D y x 0 C y x 0 E y x 0 F In the table below are four functions. Write the correct letter in the table to match each function with its graph. Function Graph ( )x x 2 3 f = - ( ) ( ) x x 2 f 2 = - ( )x x x 4 f 3 = - ( )x x 5 2 f = - [4] 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. 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.

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 2015 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 Paper 2 (Extended), maximum raw mark 40 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 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 22 © Cambridge International Examinations 2015 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 1 (a) 0.09 1 (b) 20 1 2 (a) (i) 1 1 (ii) 1000 1 (b) 57 1 3 2 13 3 M1 for ( ) 2 2 6 4 − + oe A1 for 52 4 (a) 0.23, 0.3, 0.15, 0.2 2 M1 for at least 2 of 46 12 15 100 , , , 200 40 100 500 soi (b) Dieter, More throws oe 1 (c) 246 1 5 (a) (4, 4) 1 (b) –2 2 M1 for clear evidence of rise run 6 28 10 3 + or ( ) 2 14 5 3 + final answer 2 M1 for 25 5 3 5 3 3 3 + + + × or better 7 x ≥ 5.5 or 1 2 5 or 11 2 final answer 3 M1 for 2x + 3 ≤ 4x – 8 oe M1 FT for 3 + 8 ≤ 4x – 2x oe 8 396π 3 M1 for π × 6² × 10 or better M1 for 1 3 × π × 6² × 3 or better

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 22 © Cambridge International Examinations 2015 9 x = 3, y = –2 4 M1 for correctly equating one set of coefficients M1FT for correct method to eliminate one variable A1 for x = 3 or y = –2 If zero scored SC1 for correct substitution into one of the original equations and correct evaluation, to find the other variable 10 (a) 4 1 (b) 1000 1 (c) 10 3 M1 for correct use of a alog x = log ax M1 for correct use of log a + log b = log ab or log log log a a b b − = 11 (a) 110 2 M1 for angle DCO = 90 – 55 (b) 55 1FT FT 1 2 their (a) (c) 105 1 12 F E D A 1 1 1 1