Cambridge IGCSE Mathematics - International 0607 — 2015 Oct/Nov Paper 3 · Variant 3

This document consists of 16 printed pages. DC (CW/SW) 117643 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 6 0 6 0 9 9 1 7 6 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) October/November 2015 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 π, 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/O/N/15 © UCLES 2015 Formula List Area, A, of triangle, base b, height h. A = 2 1 bh 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 = 3 1 Ah Volume, V, of cylinder of radius r, height h. V = rr2h Volume, V, of cone of radius r, height h. V = 3 1 rr2h Volume, V, of sphere of radius r. V = 3 4 rr3

3 0607/33/O/N/15 © UCLES 2015 [Turn over Answer all the questions. 1 (a) Complete the list of factors of 18. Answer(a) 1, … , … , … , … , 18 [1] (b) Work out. (i) 676 Answer(b)(i) … [1] (ii) 6.73 Answer(b)(ii) … [1] (iii) . . . 2 93 63 5 26 1 - Answer(b)(iii) … [2] (c) Write 807.536 correct to (i) 2 decimal places, Answer(c)(i) … [1] (ii) 4 significant figures, Answer(c)(ii) … [1] (iii) the nearest 10, Answer(c)(iii) … [1] (iv) the nearest 100. Answer(c)(iv) … [1]

4 0607/33/O/N/15 © UCLES 2015 2 A B D E C F a° b° c° d ° 136° NOT TO SCALE 48° ABD and ECF are parallel straight lines. Find the values of a, b, c and d. Answer a = … b = … c = … d = … [4]

5 0607/33/O/N/15 © UCLES 2015 [Turn over 3 (a) Tejas, Wali and Niamh share 100 pieces of candy in the ratio 5 : 9 : 11. Find how many pieces of candy Wali receives. Answer(a) … [2] (b) Hanneke buys a gold necklace for $ 4500. She later sells it for $ 5300. Calculate her percentage profit. Answer(b) … % [3]

6 0607/33/O/N/15 © UCLES 2015 4 NOT TO SCALE A rectangular patio is 6 metres long and 3.2 metres wide. It is made up of 8 rows of grey tiles and white tiles as shown in the diagram. (a) Calculate (i) the area of the patio, Answer(a)(i) … m2 [1] (ii) the perimeter of the patio. Answer(a)(ii) … m [1] (b) All tiles have the same width. Each grey tile is twice as long as a white tile. Complete this statement. A grey tile has length … metres and width … metres. [2] (c) Find the total number of white tiles and the total number of grey tiles. Answer(c) Number of white tiles … Number of grey tiles … [2] (d) Each white tile costs $0.95 and each grey tile costs $1.35 . Find the total cost of the tiles used to make the patio. Answer(d) $ … [2]

7 0607/33/O/N/15 © UCLES 2015 [Turn over 5 Romina opens 10 packets of biscuits and counts the number of biscuits in each packet. The number of biscuits in each packet is shown below. 23 24 23 22 25 23 24 25 26 21 (a) Find (i) the range, Answer(a)(i) … [1] (ii) the mode, Answer(a)(ii) … [1] (iii) the median, Answer(a)(iii) … [1] (iv) the mean. Answer(a)(iv) … [1] (b) Complete the bar chart. The first bar has been drawn for you. 21 0 1 2 Frequency 3 4 22 23 Number of biscuits 24 25 26 [2]

8 0607/33/O/N/15 © UCLES 2015 6 Each person at a school Science Fair receives a lunchbox. There are 50 students, 7 teachers, 9 judges and 84 parents at the Science Fair. (a) Find the total number of people at the Science Fair. Answer(a) … [1] (b) Each lunchbox contains two sandwiches. Find the total number of sandwiches in all the lunchboxes. Answer(b) … [1] (c) Paul’s Snacks make the lunchboxes. The lunchbox contains two sandwiches, one piece of fruit and one bottle of water. The cost of making each lunchbox is $4.25 . Each sandwich costs $1.45 and the bottle of water costs $0.70 . Find the cost of the piece of fruit. Answer(c) $ … [2] (d) The school pays Paul’s Snacks $5 for each lunchbox. Find how much profit Paul’s Snacks make on each lunchbox. Answer(d) $ … [1]

9 0607/33/O/N/15 © UCLES 2015 [Turn over 7 A taxi company charges a fixed amount of $F for each journey. It also charges $2 for each kilometre of the journey. A taxi journey is M km. (a) Find an expression, in terms of F and M, for the total cost of this journey. Answer(a) $ … [2] (b) When F = 3 find the total cost of a journey of 6 km. Answer(b) $ … [2] (c) Find the distance travelled when F = 3 and the total cost of the journey is $21. Answer(c) … km [2]

10 0607/33/O/N/15 © UCLES 2015 8 U , , , , , , , , , 1 2 3 4 5 6 7 8 9 10 = " , , , , , , A 1 3 5 6 7 8 = " , , , , , B 1 3 4 7 9 = " , A U B (a) Write the elements of U in the correct places in the Venn diagram. [2] (b) Write down the elements in the set (i) A B + , Answer(b)(i) … [1] (ii) A B , l ^ h , Answer(b)(ii) … [1] (iii) A B + l . Answer(b)(iii) … [1]

11 0607/33/O/N/15 © UCLES 2015 [Turn over (c) A number is chosen at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Find the probability that it is (i) an odd number, Answer(c)(i) … [1] (ii) a number less than 4, Answer(c)(ii) … [1] (iii) a triangle number. Answer(c)(iii) … [1] 9 These are the first five terms of a sequence. −2 1 6 13 22 (a) Write down the next two terms in this sequence. Answer(a) … , … [2] (b) Find an expression for the nth term. Answer(b) … [3]

12 0607/33/O/N/15 © UCLES 2015 10 Kensuke travels to school either by train or by car. The probability that he travels by train is 5 4 . If Kensuke travels by train then the probability that he is late for school is 20 1 . If Kensuke travels by car then the probability that he is late for school is 15 1 . (a) Complete the tree diagram. late not late … … late train 4 5 car not late … … … [3] (b) Find the probability that Kensuke travels by train and is late for school. Answer(b) … [2] (c) Find the probability that Kensuke is not late for school. Answer(c) … [3]

13 0607/33/O/N/15 © UCLES 2015 [Turn over 11 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 1 2 3 4 5 6 x P y –2 –3 –4 –5 –6 (a) Reflect shape P in the line x 1 = . Label the image A. [2] (b) Translate shape P by the vector 3 2 - - c m. Label the image B. [2] (c) Rotate shape P by 180° about the point (0, 0). Label the image C. [2]

14 0607/33/O/N/15 © UCLES 2015 12 –3 –2 –1 0 1 2 3 4 5 –1 1 2 3 4 5 6 7 8 x y –2 –3 –4 The axes are drawn on a 1 cm2 grid. A is the point (2, 3) and B is the point (8, −3). (a) Plot the points A and B on the grid. [2] (b) Find the co-ordinates of the midpoint of AB. Answer(b) (… , …) [2] (c) Calculate the length of AB. Give your answer correct to 2 decimal places. Answer(c) … cm [3] (d) Find the gradient of AB. Answer(d) … [2] (e) Find the equation of the straight line that passes through point A and point B. Answer(e) … [2]

15 0607/33/O/N/15 © UCLES 2015 [Turn over 13 NOT TO SCALE 6 cm A B O C A circle, centre O, is inscribed in a regular pentagon. Each side of the pentagon has length 6 cm. (a) Find angle AOB. Answer(a) Angle AOB = … [1] (b) Find the size of an interior angle of the regular pentagon. Answer(b) … [2] (c) Use trigonometry to find the radius, OC, of the circle. Answer(c) … cm [2] (d) Find the area of the pentagon. Answer(d) … cm2 [3] Question 14 is printed on the next page.

16 0607/33/O/N/15 © UCLES 2015 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. 14 0 –5 25 –30 6 x y ( ) . . x x x x 0 5 9 5 10 f 3 2 = - - + (a) On the diagram, sketch the graph of ( ) y x f = for x 5 6 G G - . [2] (b) Find the co-ordinates of (i) the points where the curve crosses the x-axis, Answer(b)(i) (… , …), (… , …), (… , …) [2] (ii) the point where the curve crosses the y-axis, Answer(b)(ii) (… , …) [1] (iii) the local minimum point. Answer(b)(iii) (… , …) [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 2015 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core), maximum raw mark 96 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 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 – October/November 2015 0607 33 © 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) 2, 3, 6, 9 1 (b) (i) 26 1 (ii) 300.763 1 (iii) 12.8 or 12.76… 2 B1 for 37.4 seen (c) (i) 807.54 cao 1 (ii) 807.5 cao 1 (iii) 810 cao 1 (iv) 800 cao 1 2 a = 48 b = 44 c = 44 d = 88 1 1 1 FT 1 FT FT their (b) FT 180 – 48 – their 44 or 180 – their (a) + their (b) 3 (a) 36 2 M1 for 25 or 4 seen (b) 17.8 or 17.77… 3 M2 for 100 4500 4500 5300 × − oe or M1 for 5300 4500 5300 or 100 4500 4500 − × 4 (a) (i) 19.2 1 (ii) 18.4 1 (b) 0.5 0.4 1 1 If 0 scored SC1 if reversed (c) 64 64 1 1 (d) 147.2[0] 2 FT M1 for their 64 × [0].95 and their 64 × 1.35 oe

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2015 0607 33 © Cambridge International Examinations 2015 5 (a) (i) 5 1 (ii) 23 1 (iii) 23.5 oe 1 (iv) 23.6 1 (b) 2 B1 for 4 correct bars 6 (a) 150 1 (b) 300 1 FT FT their (a) × 2 (c) [0].65 2 M1 for 2 × 1.45 + [0].7[0] or better (d) [0].75 1 7 (a) F + 2M 2 B1 for 2M seen (b) 15 2 FT M1 for correct substitution in their formula (c) 9 2 FT M1 for correct substitution in their formula 8 (a) 2 B1 for 2 correct regions (b) (i) 1 3 7 1 FT (ii) 2 10 1 FT (iii) 4 9 1 FT (c) (i) 5 10 oe 1 (ii) 3 10 oe 1 (iii) 4 10 oe 1 0 1 2 3 4 21 22 23 24 25 26

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2015 0607 33 © Cambridge International Examinations 2015 9 (a) 33 46 1 1 (b) 2 3 n − 3 B2 for 2 n k ± or M1 for finding second differences or any quadratic 10 (a) 3 B1 for each branch (b) 4 100 oe 2 M1FT for 4 1 5 20 their × (c) 75 71 or 0.947 or 0.9466… 3 M2 for 4 19 1 14 5 20 5 15 their their   × + ×     or M1 for 4 19 1 14 or 5 20 5 15 their their   × ×     11 (a) Vertices at (3, 1) (3, 2) (4, 2) (4, 4) (5, 4) (5, 1) 2 If 0 scored SC1 for reflection in y = 1 or x = 0 (b) Vertices at (–5, –2) (–3, –1) (–4, –1) (–4, 1) (–5, –1) (–3, –2) 2 If 0 scored SC1 for translation of       − −       −      − 2 3 or 3 or 2 k k (c) Vertices at (1, –1) (1, –2) (2, –2) (3, –1) (2, –4) (3, –4) 2 If 0 scored SC1 for any rotation about (0, 0) or a rotation of 180° 12 (a) Points plotted correctly 2 B1 for each point (b) (5, 0) 2 B1 for each co-ordinate If 0 scored SC1 for (0, 5) (c) 8.49 3 M1 for 2 2 6 6 + or better A1 for 8.485 to 8.486 (d)
1 2 M1 for rise run (e) 5 y x = −+ oe 2 FT M1 for [ ] y x k = − + or x y k + = FT from (d)

Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2015 0607 33 © Cambridge International Examinations 2015 13 (a) 72 1 (b) 108 2 M1 for ( ) 2 180 72 2 their − or 5 360 180 − oe or B1 for 54 (c) 4.13 or 4.129… 2 FT M1 for tan54 3 r = oe FT ( ) angle in 2 their a or ( ) angle in 2 b (d) 61.9 – 62.[0] 3 FT M2 for 1 6 4.13 5 2 their   × × ×     or M1 for 1 6 4.13 2 their × × 14 (a) Fully correct curve 2 B1 for correct cubic shape (maximum then minimum) (b) (i) (–4, 0) (1, 0) (5,0) 2 B1 for 2 correct (ii) (0, 10) 1 (iii) (3.27, –14.3) or (3.270.., –14.28 to –14.27) 2 B1 for each co-ordinate