Cambridge IGCSE Mathematics - International 0607 — 2015 May/June Paper 3 · Variant 1

This document consists of 16 printed pages. DC (ST/CGW) 99289/4 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 0 1 9 2 3 0 5 3 9 3 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 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 p, 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 0607/31/M/J/15 © UCLES 2015 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle, radius r. A = pr2 Circumference, C, of circle, radius r. C = 2pr Curved surface area, A, of cylinder of radius r, height h. A = 2prh Curved surface area, A, of cone of radius r, sloping edge l. A = prl Curved surface area, A, of sphere of radius r. A = 4pr2 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 = pr2h 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 0607/31/M/J/15 © UCLES 2015 [Turn over Answer all the questions. 1 (a) Write down three hundred thousand and fifty eight as a number. Answer(a) … [1] (b) Work out. 42 8 6 # - Answer(b) … [1] (c) Write 21 648 correct to the nearest hundred. Answer(c) … [1] (d) Write 0.05625 correct to 2 decimal places. Answer(d) … [1] (e) Find 7 3 of 182. Answer(e) … [1] (f) The average temperature in Amsterdam in February is −2°C. In July the average temperature is 21°C. Find the difference between these two temperatures. Answer(f) …°C [1] (g) Write 65% as a fraction in its lowest terms. Answer(g) … [2] (h) Divide 133 in the ratio 4 : 3. Answer(h) … : … [2]

4 0607/31/M/J/15 © UCLES 2015 2 (a) Simplify. x y x y 6 3 2 - + + Answer(a) … [2] (b) Find the value of a b c 2 3 + + when , a b 3 2 = =- and c 4 = . Answer(b) … [2] (c) L x y 2 3 = + Find the value of x when . L 18 6 = and . y 2 8 = . Answer(c) x = … [2] (d) Solve the equation. x 5 3 7 - = Answer(d) x = … [2] (e) Complete the mapping diagram for : f x x 2 1 " - . x 0 1 2 3 f(x) … 1 … … [2]

5 0607/31/M/J/15 © UCLES 2015 [Turn over 3 R P S U T d° c° NOT TO SCALE a° 26° b° Q PQ and RS are parallel lines. QR is a straight line and TU is a straight line perpendicular to PQ and RS. Angle PQR = 26°. Find the values of a, b, c and d. Answer a = … b = … c = … d = … [4] 4 Thirty students and three teachers go by bus on a school trip to the zoo. (a) The entrance fee is $10 for each student and $15 for each teacher. Find the total cost of the entrance fees. Answer(a) $ … [2] (b) The bus costs $600 to hire. Lunch costs $5 for each person. Find the total cost of the trip including the entrance fees. Answer(b) $ … [2] (c) The total cost of the trip is divided between the 30 students. Calculate the cost of the trip for each student. Answer(c) $ … [2]

6 0607/31/M/J/15 © UCLES 2015 5 A list of numbers is shown below. 5 8 6 2 8 4 5 8 (a) For the list of numbers, find (i) the mode, Answer(a)(i) … [1] (ii) the median, Answer(a)(ii) … [1] (iii) the lower quartile, Answer(a)(iii) … [1] (iv) the range, Answer(a)(iv) … [1] (v) the mean. Answer(a)(v) … [1]

7 0607/31/M/J/15 © UCLES 2015 [Turn over (b) (i) Using the list of numbers, complete the frequency table. Number Frequency 2 3 4 5 6 7 8 [1] (ii) Complete the bar chart. One bar has been drawn for you. 1 2 3 4 5 6 7 8 0 2 3 Frequency Number 4 5 [2]

8 0607/31/M/J/15 © UCLES 2015 6 75 cm 25 cm 2 cm NOT TO SCALE The diagram shows a bookshelf. It is made from a piece of wood 75 cm long, 25 cm wide and 2 cm thick. (a) Find the volume of this piece of wood. Answer(a) … cm3 [2] (b) (i) Find the total surface area of this piece of wood. Answer(b)(i) … cm2 [3] (ii) Write your answer to part (b)(i) in square metres. Answer(b)(ii) … m2 [1]

9 0607/31/M/J/15 © UCLES 2015 [Turn over (c) NOT TO SCALE 75 cm MATHS E N G L I S H H I S T O R Y S C I E N C E A R T Jessie wants to stand 18 books on the bookshelf. • 5 books are each 3 cm wide • 6 books are each 4 cm wide • 4 books are each 2.5 cm wide • 3 books are each 7 cm wide Can Jessie stand all these books on the bookshelf? Show all your working. [2]

10 0607/31/M/J/15 © UCLES 2015 7 23, 16, 9, 2, … (a) Find the next two terms in this sequence. Answer(a) … , … [2] (b) Find an expression for the nth term of this sequence. Answer(b) … [2] 8 The equation of line L is y x 2 3 = - . (a) Find the gradient of line L. Answer(a) … [2] (b) Write down the gradient of a line parallel to L. Answer(b) … [1] (c) Find the equation of the line parallel to L that passes through the point (0, 6). Answer(c) y = … [1]

11 0607/31/M/J/15 © UCLES 2015 [Turn over 9 A B 2 U 3 6 4 5 1 List the elements in each of the following sets. (a) (i) A Answer(a)(i) … [1] (ii) A B + Answer(a)(ii) … [1] (iii) A B , Answer(a)(iii) … [1] (iv) Bl Answer(a)(iv) … [1] (v) A B + l Answer(a)(v) … [1] (b) Find n(U). Answer(b) … [1]

12 0607/31/M/J/15 © UCLES 2015 10 1 2 3 4 5 6 0 –3 –2 –1 –1 –3 –2 x y P 1 2 3 4 5 6 7 8 9 10 R Q S (a) Triangle Q is a reflection of triangle P. On the grid, draw the line of reflection. Write down the equation of this line. Answer(a) … [2] (b) Triangle S is a translation of triangle P. Find the vector for this translation. Answer(b) ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ [2] (c) Triangle R is a rotation of triangle P. Find the centre and the angle of rotation. Answer(c) Centre = ... (… , …) Angle = … [2]

13 0607/31/M/J/15 © UCLES 2015 [Turn over 11 (a) Campbell can text at an average speed of 100 characters per minute. Find how long it takes her to text a message of 320 characters. Give your answer in minutes and seconds. Answer(a) … min … s [2] (b) Diago texts a message of 168 characters in 1 minute 36 seconds. Find the average speed at which he texts. Give your answer in characters per minute. Answer(b) … characters per minute [3]

14 0607/31/M/J/15 © UCLES 2015 12 On the way to work Herr Smit drives over a bridge. The probability that the bridge is closed is 80 1 . If the bridge is closed then the probability that Herr Smit is late for work is 3 2 . If the bridge is open then the probability that he is late for work is 50 1 . (a) Complete the tree diagram. 1 80 … … … … … bridge closed late late not late not late bridge open [3] (b) Find the probability that the bridge is closed and Herr Smit is not late for work. Answer(b) … [2] (c) In 2014, Herr Smit worked for 250 days. Estimate the number of days that the bridge was closed and Herr Smit was not late for work. Answer(c) … [2]

15 0607/31/M/J/15 © UCLES 2015 [Turn over 13 A B O 46 cm NOT TO SCALE 60° The diagram shows a sector of a circle, centre O, radius 46 cm. Angle AOB = 60°. (a) Explain why AB = 46 cm. [2] (b) Calculate the length of arc AB. Answer(b) … cm [2] (c) Calculate the area of sector AOB. Answer(c) …cm2 [2] (d) Find the area of triangle AOB. Answer(d) … cm2 [3] (e) Use your answers to part (c) and part (d) to find the area of the shaded segment. Answer(e) … cm2 [1] Question 14 is printed on the next page

16 0607/31/M/J/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 y x 3 8 –3 –10 0 ( ) f x 3 2 1 ( . )x 0 5 # = - (a) On the diagram, sketch the graph of ( ) f y x = for x 10 3 G G - . [2] (b) Write down the x co-ordinate of the point where the curve crosses the x-axis. Answer(b) x = … [1] (c) Write down the equation of the horizontal asymptote. Answer(c) … [1] (d) On the same diagram, sketch the graph of y x 2 3 =- + . [2] (e) Find the co-ordinates of the point where the two graphs intersect. Answer(e) ( … , … ) [2]

® 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 0607/31 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 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 31 © 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 Question Answer Mark Part Marks 1 (a) 300 058 1 (b) −6 1 (c) 21 600 1 (d) 0.06 1 (e) 78 1 (f) 23 1 (g) 20 13 2 M1 for 100 65 (h) 76, 57 2 M1 for dividing by 7 soi 2 (a) y x 2 8 − as final answer 2 B1 for ky x − 8 or y kx 2 − as final answer (b) 16 2 M1 for 2 × 3 + −2 + 3 × 4 seen or B1 for 6 and 12 seen (c) 5.1 2 B1 for 8.4 seen or M1 for 18.6 = 2x + 3 × 2.8 seen (d) 2 2 M1 for correct first step (e) 0 –1 2 3 3 5 2 B1 for −1 B1 for 3 and 5 3 a = 90 b = 26 c = 64 d = 116 1 1 1 1 FT FT 180 − their c 4 (a) 345 2 M1 for 30 × 10 + 3 × 15 (b) 1110 2 FT M1 for 5 × 33 + 600 + their 345 (c) 37 2 FT M1 for their 30 1110

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 31 © Cambridge International Examinations 2015 5 (a) (i) 8 1 (ii) 5.5 1 (iii) 4.5 1 (iv) 6 1 (v) 5.75 1 (b) (i) 2 1 3 0 4 1 5 2 6 1 7 0 8 3 1 (ii) Correct bar chart 2 FT B1 FT for 4 bars correct 6 (a) 3750 2 M1 for 25 × 75 × 2 (b) (i) 4150 3 M2 for 2(25 × 2 + 75 × 2 + 25 × 75) or B1 for 50, 150, 1875 soi (ii) 0.415 1 FT FT their (b)(i) ÷ 10 000 (c) 5 × 3 + 6 × 4 + 4 × 2.5 + 3 × 7 [= 70] yes 1 1 FT M1 for correct method A1 FT dep their 70 [strict] 7 (a) −5 −12 1 1 (b) 30 − 7n 2 B1 for 30 − kn , k ≠ 0, or j − 7n 8 (a) 2 1 − oe 2 M1 for dividing by 2 oe (b) 2 1 − oe 1 FT FT their 2 1 − (c) [y =] 2 1 − x + 6 1 FT FT their (b)

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 31 © Cambridge International Examinations 2015 9 (a) (i) 2, 3, 6 1 (ii) 3, 6 1 (iii) 2, 3, 4, 5, 6 1 (iv) 1, 2 1 (v) 4, 5 1 (b) 6 1 10 (a) Correct line 3 = y 1 1 FT FT their line y = k, 2 < k < 4 or 4 = x (b)       −3 4 2 B1 for       −3 k or       k 4 If 0 scored SC1 for      − 3 4 or      − 4 3 (c) (0, 0) 90° [anti-clockwise] or −270° 1 1 11 (a) 3 min 12 seconds 2 B1 for 3.2 (b) 105 3 M2 for 6.1 168 oe or M1 for a correct time conversion. 12 (a) 1 79 , 80 80 2 1 , 3 3 1 49 , 50 50 3 B1 for each pair (b) 240 1 2 M1 for 3 1 80 1 × (c) Accept 1 or 2 days 2 FT M1 FT for 250 × their (b)

Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 31 © Cambridge International Examinations 2015 13 (a) [The triangle is] equilateral OA = 46 or angles A and B are 60° 1 1 (b) 48.2 or 48.17 to 48.18 2 M1 for 60 2 46 360 π × × × (c) 1110 or 1107 to 1108 2 M1 for 2 60 46 360 π × × (d) 916 or 915.4 to 916.3 3 M1 for 46cos30 oe (= 39.837…) and M1 FT dep for 0.5 × 46 × their 39.837… (e) 194 or 195 or 190.7 to 194.6 1 FT FT their (c) – their (d) 14 (a) 2 M1 for correct shape through 3 quadrants A1 for approximately correct axis intercepts (less than half way on both axes) (b) −3.17 or −3.170 to −3.169 1 (c) 1 − = y 1 (d) 2 B1 for negative gradient B1 for correct y-intercept at approximately 3 (e) [x =] 0.323 or 0.3225 to 0.3226 [y =] 2.35 or 2.354 to 2.355 1 1 If 0 scored SC1 for correct co-ordinates reversed.