Cambridge IGCSE Mathematics - International 0607 — 2016 Oct/Nov Paper 3 · Variant 1

* 3 8 7 9 8 2 5 3 3 5 * This document consists of 16 printed pages. DC (SLM/JG) 114970/2 © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 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, highlighters, glue or correction fluid. You may use a 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 0607/31/O/N/16 © UCLES 2016 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 0607/31/O/N/16 © UCLES 2016 [Turn over Answer all the questions. 1 A B C NOT TO SCALE x cm y cm 12 cm The diagram shows three regular shapes A, B and C. (a) Write down the correct mathematical name of each shape. Shape A … Shape B … Shape C … [4] (b) Each shape has the same perimeter. Find the value of x and the value of y. x = … cm y = … cm [3]

4 0607/31/O/N/16 © UCLES 2016 2 A conference centre has 6 rooms. One day all the rooms are used. Room Number Number of people 1 7 2 6 3 12 4 10 5 9 6 11 (a) Find the total number of people in the six rooms. … [1] (b) Complete the bar chart for the information above. 1 2 3 4 5 6 0 Number of people Room number 4 2 6 8 10 12 [2]

5 0607/31/O/N/16 © UCLES 2016 [Turn over (c) The cost of using each of the rooms for the day is $300. The cost is shared equally between the people using it. (i) Calculate the total cost of using all six rooms. $ … [1] (ii) For Room 4, find the cost per person to use the room. $ … [1] (iii) Each person in Room 2 has a lunch that costs $8 per person. Find the total amount paid by all six people in Room 2. $ … [2]

6 0607/31/O/N/16 © UCLES 2016 3 (a) 3 9 8 5 21 -6 r -0.75 0.33 -18 3 5 2 From this list, write down (i) a positive integer, … [1] (ii) a negative integer, … [1] (iii) a square number, … [1] (iv) a number between 0.5 and 1, … [1] (v) an irrational number. … [1] (b) Write 3 as a decimal (i) correct to 4 decimal places, … [1] (ii) correct to 4 significant figures. … [1]

7 0607/31/O/N/16 © UCLES 2016 [Turn over (c) Write 0.33 as a fraction. … [1] (d) Write 3 5 2 as a decimal. … [1] (e) Write 8 5 as a percentage. … % [1]

8 0607/31/O/N/16 © UCLES 2016 4 (a) MONEY Write down all the letters from this word that have (i) line symmetry, … [2] (ii) rotational symmetry. … [2] (b) A B C 15 cm 9 cm D E F 4 cm 3 cm NOT TO SCALE The diagram shows two right-angled triangles. Triangle ABC is similar to triangle DEF. (i) Work out the lengths AB and DF. AB = … cm DF = … cm [3] (ii) Find the ratio area of triangle ABC : area of triangle DEF. … : … [2]

9 0607/31/O/N/16 © UCLES 2016 [Turn over 5 Tutku counts the number of petals on each of 100 flowers. Her results are shown in the table. Number of petals Frequency 15 5 16 10 17 12 18 24 19 27 20 14 21 6 22 2 Find (a) the mode, … [1] (b) the median, … [1] (c) the interquartile range, … [2] (d) the mean. … [2]

10 0607/31/O/N/16 © UCLES 2016 6 These are the first four terms of a sequence. 326 319 312 305 (a) Find the next two terms in this sequence. … , … [2] (b) Find an expression for the nth term of this sequence. … [2] (c) Pedro says that 249 is a term in this sequence. Is he correct? Show working to support your answer. [1]

11 0607/31/O/N/16 © UCLES 2016 [Turn over 7 (a) A B D C E a° b° c° d ° NOT TO SCALE 107° 42° The diagram shows a parallelogram ABCD and a straight line CDE. Find the values of a, b, c and d. a = … b = … c = … d = … [4] (b) B A D C O E p° 62° q° r° NOT TO SCALE The diagram shows a circle, centre O, with diameter EB. The line AC is a tangent to the circle at B. D is a point on the circumference and angle ABD = 62°. Find the values of p, q and r. p = … q = … r = … [3]

12 0607/31/O/N/16 © UCLES 2016 8 On any evening, the probability that Elise goes to a café is 5 2 . If Elise goes to a café, the probability that she then goes to the cinema is 3 1 . If she does not go to a café, the probability that she then goes to the cinema is 7 4 . (a) Complete the tree diagram. cinema not cinema cinema not cinema … café 2 5 not café … … … 1 3 [3] (b) Find the probability that, on one evening, Elise goes to a café and goes to the cinema. … [2] (c) Find the probability that, on one evening, Elise goes to the cinema. … [3]

13 0607/31/O/N/16 © UCLES 2016 [Turn over 9 Sally leaves home to go to school at 07 45. She walks 100 metres to the bus stop and arrives at 07 50. (a) Work out her average walking speed in km/h. … km/h [3] (b) The bus leaves the bus stop at 07 55. It travels the 6 km to school at an average speed of 40 km/h. (i) Calculate the number of minutes that the bus takes to get to school.  min [3] (ii) Work out the time that the bus gets to school. … [1] (iii) Sally takes 5 minutes to walk from the bus to the classroom. The lesson starts at 08 15. Show that Sally gets to the classroom before the lesson starts. [1]

14 0607/31/O/N/16 © UCLES 2016 10 (a) Solve. (i) x x 5 2 3 6 + = + … [2] (ii) x 4 10 10 1 - … [2] (b) Show x 2 2- on the number line. –5 –4 –3 –2 –1 0 1 2 3 4 x [1] (c) Simplify. (i) x x 6 2 2 6 # … [2] (ii) y y 5 15 2 8 … [2] (d) Yassar buys 2 bottles of drink and 3 bars of chocolate for $5.25 . Hassan buys 1 bottle of drink and 2 bars of chocolate for $3.05 . Find the cost of 1 bottle of drink and the cost of 1 bar of chocolate. Show all your working. 1 bottle of drink = $ … 1 bar of chocolate = $ … [4]

15 0607/31/O/N/16 © UCLES 2016 [Turn over 11 NOT TO SCALE 12 m 0.5 m 1.5 m 6 m The diagram shows a rectangular garden, 6 m by 12 m. In the garden there is a circular pond with radius 1.5 m. There is a circular path of width 0.5 m around the pond. (a) The pond is 0.6 m deep. Work out the volume of water in the pond when it is full. …m3 [2] (b) Work out the area of the path. …m2 [2] (c) The rest of the garden, apart from the pond and the path, is covered by grass. Work out the area covered by grass. …m2 [2] Question 12 is printed on the next page.

16 0607/31/O/N/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. 12 –3 –6 y x 4 8 0 ( )x x x 6 f 2 = + - (a) (i) On the diagram, sketch the graph of ( ) y x x 3 4 f for G G = - . [2] (ii) Find the co-ordinates of the point where the graph cuts the y-axis. (… , …) [1] (iii) Find the co-ordinates of the points where the graph cuts the x-axis. (… , …) and (… , …) [2] (iv) Find the co-ordinates of the local maximum point. (… , …) [1] (b) ( )x x 4 g = + (i) On the diagram, sketch the graph of ( ) y x g = . [2] (ii) Find the co-ordinates of the points of intersection of the graph of ( )x f and the graph of ( )x g . (… , …) and (… , …) [2]

® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 6 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 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 October/November 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 – October/November 2016 0607 31 © UCLES 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) Square equilateral triangle hexagon 1 2 1 B1 for each word (b) [x =] 16 [y = ] 8 3 B2 for 1 correct or M1 for 12 4 × soi 2 (a) 55 1 (b) 2 B1 for 3 bars with correct height and equal width or 5 bars with correct height (c) (i) 1800 1 (ii) 30 1 (iii) 348 2 M1 for 6 8 × oe 3 (a) (i) 21 or 9 1 (ii) –6 or –18 1 (iii) 9 1 (iv) 5 8 oe 1 0 2 4 6 8 10 12 14 1 2 3 4 5 6 number of people room

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 31 © UCLES 2016 Question Answer Mark Part Marks (v) 3 or π 1 (b) (i) 1.7321 1 (ii) 1.732 1 (c) 33 100 1 (d) 3.4 1 (e) 62.5 1 4 (a) (i) M O E Y cao 2 B1 for 2 correct and none incorrect or 3 correct and 1 extra (ii) O N 2 B1 for 1 correct and none incorrect or 2 correct and 1 extra (b) (i) [AB = ] 12 [DF = ] 5 3 B2 for 1 correct or M1 for a correct ratio, equation or correct Pythagoras statement. (ii) 54 : 6 oe 2 FT FT their AB B1 for 54 or 6 seen or 23 seen or M1 for 0.5 × 4 × 3 or 0.5 × 9 × their AB 5 (a) 19 1 (b) 18 1 (c) 2 2 M1 for 17 or 19 seen (d) 18.34 2 M1 for multiplying number of petals by frequencies 6 (a) 298 291 1 1 FT FT their298 – 7 (b) 333 7n − oe 2 B1 for 333 kn − or 7 k n − (c) Yes, with correct justification soi 1

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 31 © UCLES 2016 Question Answer Mark Part Marks 7 (a) [ ] 31 a = [ ] 42 b = [ ]1 07 c = [ ]1 07 d = 1 1 1 1 (b) [ ] 28 p = [ ] 90 q = [ ] 62 r = 1 1 1 8 (a) Not cinema cafe Not cafe cinema Not cinema cinema 2 5    3 5 1 3    2 3 4 7 3 7 3 B1 for 3 5 B1 for 2 3 B1 for 4 7 or 3 7 (b) 2 15 oe 2 M1 for 2 5 × 1 3 (c) 10 21 oe 3 M2 for ( ) 3 4 b 5 7 their their their + × or M1 for their 3 5 their × 4 7 9 (a) 1.2 3 M2 for 100 1000 5 60 oe seen or M1 for 100 1000 or 5 60 or 100 5 oe seen (b) (i) 9 3 M2 for 6 60 40 × oe or M1 for 6 40 (ii) [0]8 04 1 FT FT 07 55 + their(b)(i) (iii) [0]7 55 + their (b)(i) + 5 minutes oe 1 FT FT providing before 08 15

Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 31 © UCLES 2016 10 (a) (i) 2 2 M1 for correct first step (ii) x < 5 2 M1 for correct first step. Allow , , , = > - . for M1 (b) ○ 1 (c) (i) 8 12x 2 B1 for 12 kx or 8 kx (ii) 6 3y 2 B1 for 3 ky or 6 ky (d) 2 drink + 4 chocolate = 6.10 oe [1] chocolate 0.85 = [1] drink + 2(0.85) = 3.05 oe [1] drink 1.35 = M1 A1 M1 A1 SC2 for correct answer with no working. 11 (a) 4.24 or 4.241 to 4.242 2 M1 for [ ] 2 π 1.5 0.6 × × or better (b) 5.5[0] or 5.497 to 5.498 2 FT M1 for 2 π 2 × seen (c) 59.4 or 59.43 to 59.44 2 M1 for 6 12 an area × − seen 12 (a) (i) Fully correct sketch 2 B1 for axes intercepts approximately correct B1 for correct shape (ii) (0, 6) 1 (iii) (–2, 0) (3, 0) 1 1 (iv) (0.5, 6.25) 1

Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 31 © UCLES 2016 (b) (i) Correct line 2 B1 for approximately correct slope B1 for approximately correct y intercept (ii) (1.41, 5.41 ) ( 1.41 − , 2.59) 1 1