Cambridge IGCSE Mathematics - International 0607 — 2016 May/June Paper 3 · Variant 3

This document consists of 18 printed pages and 2 blank pages. DC (LK/CGW) 115325/4 © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 7 6 5 8 3 7 4 3 0 9 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2016 1 hour 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments Graphics Calculator 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. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For r, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, 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 96.

2 0607/33/M/J/16 © UCLES 2016 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle, radius r. A = rr2 Circumference, C, of circle, radius r. C = 2rr Curved surface area, A, of cylinder of radius r, height h. A = 2rrh Curved surface area, A, of cone of radius r, sloping edge l. A = rrl Curved surface area, A, of sphere of radius r. A = 4rr2 Volume, V, of prism, cross-sectional area A, length l. V =Al Volume, V, of pyramid, base area A, height h. V= Ah 3 1 Volume, V, of cylinder of radius r, height h. V = rr2h Volume, V, of cone of radius r, height h. V = r h 3 1 2 r Volume, V, of sphere of radius r. V = r 3 4 3 r

3 0607/33/M/J/16 © UCLES 2016 [Turn over Answer all the questions. 1 1 0 2 1 2 3 4 5 6 A C B 7 8 3 4 5 6 7 8 y x (a) Write down the co-ordinates of C. ( … , … ) [1] (b) Write down the mathematical name of triangle ABC. … [1] (c) Measure angle ACB. … [1] (d) On the diagram, draw the line of symmetry of triangle ABC. [1]

4 0607/33/M/J/16 © UCLES 2016 2 Sophie is tiling three of the rectangular walls of a small bathroom. The diagram shows the dimensions of the three walls. 1.5 m 2.1 m 2.1 m 3 m NOT TO SCALE 3 m (a) Work out the total area of these three walls. Give your answer in square centimetres. … cm2 [4]

5 0607/33/M/J/16 © UCLES 2016 [Turn over (b) Sophie chooses tiles measuring 30 cm by 30 cm to cover the three walls. (i) Work out how many of these tiles she needs to cover all three walls. … [3] (ii) The tiles can be plain or patterned. Each type of tile is sold in boxes of 10. Sophie decides to use 1 patterned tile for every 4 plain tiles. Work out the number of boxes of each type of tile that Sophie needs to buy. … boxes of patterned tiles … boxes of plain tiles [5] (c) The bathroom is a cuboid. Work out the volume of the bathroom. … m3 [2]

6 0607/33/M/J/16 © UCLES 2016 3 Ravi has 1 green sweet, 2 red sweets, 3 orange sweets and 6 yellow sweets in a bag. (a) He picks a sweet at random from the bag. (i) Which colour sweet is least likely to be picked? … [1] (ii) Which colour sweet has a 50% chance of being picked? … [1] (iii) Find the probability that he picks a red sweet. … [1] (iv) Find the probability that he picks a purple sweet. … [1] (b) Ravi eats two of the sweets from the bag. From the ten sweets remaining in the bag • the probability of picking a yellow sweet stays the same • two of the colours have equal probability of being picked. Work out the number of sweets of each colour that could be in the bag now. Green … Red … Orange … Yellow … [3]

7 0607/33/M/J/16 © UCLES 2016 [Turn over 4 (a) An electrician charges his customers using this formula. Charge = $65 × Number of hours + $30 (i) Work out the charge when the job takes 4 hours. $ … [2] (ii) For another job, the electrician charges $485. Work out the length of time this job takes. … hours [2] (b) The electrician uses his van to travel to work. One journey of 8 km takes 20 minutes. Calculate the average speed of this journey. … km/h [2]

8 0607/33/M/J/16 © UCLES 2016 5 (a) 15 students go on a school trip. The age of each student in years, correct to 1 decimal place, is listed below. 13.4 14.7 13.1 15.5 15.3 15.2 14.1 14.2 16.4 14.7 15.2 15.9 13.1 15.1 16.0 (i) Complete the ordered stem and leaf diagram to show this information. 16.0 has been entered for you. 13 14 15 16 0 Key: … … represents … [3] (ii) Work out the range. … years [1] (iii) Find the median. … years [1] (b) Another student is 14 years 7 months old. Write this student’s age in years as a decimal, correct to 1 decimal place. … years [2]

9 0607/33/M/J/16 © UCLES 2016 [Turn over 6 Here is a set of numbers. A = {1, 4, 6, 7, 8, 9, 15} (a) From this set choose (i) a factor of 12, … [1] (ii) 81, … [1] (iii) a multiple of 5, … [1] (iv) 23, … [1] (v) a prime number. … [1] (b) Here is another set of numbers. B = {2, 4, 6, 8, 10, 12, 14} Complete the diagram for set A and set B. A B 1 15 4 12 [3]

10 0607/33/M/J/16 © UCLES 2016 7 (a) Reflect the triangle in the line PQ. P Q [1] (b) Rotate the triangle through 90° clockwise about point C. C [2]

11 0607/33/M/J/16 © UCLES 2016 [Turn over (c) Translate the triangle by the vector 3 2 J L KK N P OO . [2] (d) Write down as much information as you can about the single transformation that maps triangle A onto triangle B. A B … [2]

12 0607/33/M/J/16 © UCLES 2016 8 (a) Solve these equations. (i) x 2 = 4 x = … [1] (ii) x + 3 = − 1 x = … [1] (iii) 2(6x – 5) = 8 x = … [3] (b) Solve these simultaneous equations. x + y = 3 x – y = −7 x = … y = … [2]

13 0607/33/M/J/16 © UCLES 2016 [Turn over 9 (a) Here are some test results for Akbar. Subject English (out of 60) Mathematics (out of 40) Science (out of 70) Mark 48 34 49 In which subject did Akbar get the highest percentage? Show clearly how you decide. [3] (b) Last year Akbar’s mark in his History test was 60. This year his mark increased by 35%. Work out Akbar’s mark in his History test this year. … [3]

14 0607/33/M/J/16 © UCLES 2016 10 (a) Show that (4, 5) is a point on the line y = 2x – 3. [2] (b) Write down the gradient of the line y = 2x – 3. … [1] (c) Write down the equation of the line parallel to y = 2x – 3 that passes through the point (0, 1). … [2] (d) Rearrange this equation to make x the subject. y = 2x – 3 x = … [2]

15 0607/33/M/J/16 © UCLES 2016 [Turn over 11 The probability that Joe is late for school on any day is 0.3 . (a) Complete the tree diagram for two days. First day Second day Late … … … Not late Not late Late Not late Late 0.3 … … [2] (b) Work out the probability that Joe will be late for school on both days. … [2]

16 0607/33/M/J/16 © UCLES 2016 12 (a) Simplify. x x 2 18 2 … [2] (b) Factorise fully. 3x2 + 6x … [2] (c) Show the inequality x 3 H on the number line. 1 0 –1 –2 –3 5 x 4 3 2 [1] (d) List the integer values which satisfy the inequality x 4 7 1 G . … [1] (e) Multiply out the brackets and simplify. (x + 3)(x – 2) … [2]

17 0607/33/M/J/16 © UCLES 2016 [Turn over 13 The diagram shows a flagpole that is held in position by two straight wires. The wires are attached to the flagpole 11.8 m above the ground. 11.8 m NOT TO SCALE y° x 7.2 m 15.2 m (a) Calculate the length of the wire, x. … m [2] (b) Use trigonometry to calculate the size of angle y. … [2]

18 0607/33/M/J/16 © UCLES 2016 14 0 −3.5 2.5 25 x y −10 (a) On the diagram, sketch the graph of y = 2x3 + 3x2 – 12x for . . x 3 5 2 5 G G - . [2] (b) Write down the co-ordinates of the local maximum and the local minimum. Local maximum ( … , … ) Local minimum ( … , … ) [2] (c) Write down the co-ordinates of the points where the curve crosses the axes. ( … , … ) ( … , … ) ( … , … ) [3]

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20 0607/33/M/J/16 © UCLES 2016 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. bLank page

® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 5 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2016 MARK SCHEME Maximum Mark: 96 Published 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 2016 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 2016 0607 33 © Cambridge International Examinations 2016 Abbreviations awrt answers which round to 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 Question Answer Mark Part Marks 1 (a) (7, 2) 1 (b) Right-angled or isosceles 1 (c) 45 1 (d) Straight line from (3, 2) to (5, 4) at least 1 2 (a) 171 000 4 M3 for 300 × (210 + 150 + 210) oe or M2 for 3 × (2.1 + 1.5 + 2.1) oe soi or M1 for 3 × 2.1 or 3 × 1.5 oe soi (b) (i) 190 3 M2 for 300 570 30 30 × oe or B1 for ÷ 30 soi (ii) 38 pattern tiles 152 plain tiles 16 boxes plain, 4 boxes pattern 2 2 1FT M1 for their190 ÷ 5 (× 1) oe M1 for their190 ÷ 5 × 4 oe (c) 9.45 2 M1for 3 × 2.1 × 1.5 3 (a) (i) Green 1 (ii) Yellow 1 (iii) 2 12 oe isw 1 (iv) 0 1 (b) G 1 or 1 R 2 1 O 2 3 Y 5 5 3 B1 for G + R + O + Y = 10 B1 for 5 yellow 4 (a) (i) 290 2 M1 for 65×4 (ii) 7 2 M1 for (485 – 30) ÷ 65 soi (b) 24 2 M1 for distance ÷ time soi

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 33 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 5 (a) (i) 13 1 1 4 14 1 2 7 7 15 1 2 2 3 5 9 16 [0] 4 e.g. 16 0 represents 16.0 [years] 2 1 B1 for correct table with 1 or 2 errors or ‘correct’ table but unordered leaves (ii) 3.3 1 (iii) 15.1 1 (b) 14.6 2 M1 for 7 ÷ 12 soi 6 (a) (i) 1 or 4 or 6 1 (ii) 9 1 (iii) 15 1 (iv) 8 1 (v) 7 1 (b) 7, 9 in A 6, 8 in A B ∩ 2, 10, 14 in B 1 1 1 If 0 scored SC1 for 2, 4, 6, 8, 10, 12, 14 only anywhere in B 7 (a) Correct reflection 1 (b) Correct rotation 2 B1 for correct rotation 90 anti-clockwise or for correct orientation, wrong position (c) Correct translation 2 B1 for either 3 horizontal to right or 2 vertical up or for correct 2 3    translation (d) Enlargement [Scale factor] 2 1 1 If more than one transformation, question scores zero.

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 33 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 8 (a) (i) 8 1 (ii) –4 1 (iii) 1 12 oe 3 B1 for 12x – 10 = 8 or 6x – 5 = 4 B1 for 12x = 8 + their10 Or for 6x = their 4 + 5 (b) x = –2 y = 5 2 B1 for 2 x = − B1 for 5 y = If 0 scored SC1 for two values satisfying one of the original equations 9 (a) Maths and E:80% M:85% S: 70% 3 B2 for 2 values correct or M1 for mark ÷ total implied by 1 value correct (b) 81 3 M2 for 60 × 1.35 oe or M1 for 60 × 0.35 oe 10 (a) Substitute x = 4 and y = 5 Show this balances 1 1 OR Substitute x = 4 into equation Show get y = 5 (b) 2 1 (c) y = 2x + 1 oe final answer 2 B1 for y = 2x + n oe n ≠ –3 or for y = px + 1 oe p ≠ 0 or for 2x + 1 (d) [x =] y + 3 oe final answer 2 2 M1 for correct first step M1FT for correct second step 11 (a) Correct diagram 2 B1 for 0.7 oe correctly placed once (b) 0.09 oe 2 M1 for 0.3 × their 0.3 12 (a) 9x final answer 2 B1 for 2 9 [1] x x or 18 2 x seen (b) 3x([1]x + 2) final answer 2 B1 for 3([1]x2 + 2x) or x(3x + 6) (c) 3 1 (d) 5, 6, 7 1 (e) x2 + [1]x – 6 final answer 2 B1 for any three of x2, − 2x, (+)3x, − 6 seen 13 (a) 13.8 or 13.82… 2 M1 for 7.22 + 11.82 soi (b) 37.8 or 37.82… 2 M1 for tan [y =] 11.8 ÷ 15.2

Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 33 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 14 (a) Correct shape Correct position 1 1 (b) Max (–2, 20) Min (1, –7) 1 1 (c) (−3.31, 0) (0, 0) (1.81, 0) 1 1 1 If 0 scored SC1 for − 3.3, 0, 1.8 seen as x