Cambridge IGCSE Mathematics - International 0607 — 2017 Oct/Nov Paper 3 · Variant 3

This document consists of 16 printed pages. DC (LEG) 154696 © UCLES 2017 [Turn over * 4 6 4 7 6 6 7 1 8 3 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) October/November 2017 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. Cambridge International Examinations Cambridge International General Certificate of Secondary Education

2 0607/33/O/N/17 © UCLES 2017 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/17 © UCLES 2017 [Turn over Answer all the questions. 1 (a) Write a mathematical word in each box to describe the three lines and the shaded area. x [4] (b) Measure angle x. x = … [1] 2 Complete the table for the three sequences. Rule Sequence −4 27, 23, …, …, … … 64, 32, 16, 8, 4 × 3 then +1 2, 7, …, …, … [4]

4 0607/33/O/N/17 © UCLES 2017 3 (a) Here are some scores in a mathematics test. 15 7 10 12 20 19 16 11 9 14 (i) Work out the range of these scores. … [1] (ii) Work out the mean score. … [1] (b) A group of students were asked if they preferred lessons in mathematics or science. Complete the table. Science Mathematics Total Boys 18 Girls 15 Total 25 48 [3]

5 0607/33/O/N/17 © UCLES 2017 [Turn over (c) The results for 30 students in an English exam are shown in the table. Pass Merit Distinction 5 18 7 Complete the pie chart to show this information. You must show all your working. [5]

6 0607/33/O/N/17 © UCLES 2017 4 (a) Write in figures the number seven thousand and sixty one. … [1] (b) Write down (i) a multiple of 9, … [1] (ii) an even number between 21 and 29. … [1] (c) Find the value of (i) 625, … [1] (ii) 113, … [1] (iii) 5 729 2 - 3 . … [1] (d) Insert one pair of brackets to make this calculation correct. 3 × 6 + 5 − 4 = 29 [1] (e) Work out. . . . 6 1 3 8 25 2 + Write your answer correct to two decimal places. … [2] (f) Write 0.031 626 (i) correct to three significant figures, … [1] (ii) in standard form. … [1]

7 0607/33/O/N/17 © UCLES 2017 [Turn over 5 (a) A train takes 1 hour 30 minutes to travel from Cambridge to London. (i) The train leaves Cambridge at 07 25. Find the time that this train arrives in London. … [1] (ii) The distance from Cambridge to London is 105 km. Work out the average speed of this train. …km/h [2] (b) There are 104 trains travelling from Cambridge to London each day. (i) 3% of these trains arrive late in London. Work out how many of the trains arrive late in London. … [2] (ii) Trains from Cambridge are either express trains or local trains. The ratio express trains : local trains = 5 : 3. How many of the 104 trains are local trains? … [2]

8 0607/33/O/N/17 © UCLES 2017 6 The number 7 is drawn on a rectangular piece of paper. 8 cm NOT TO SCALE 4 cm 16 cm 4 cm 4 cm 10 cm (a) Work out the area of the rectangular piece of paper. …cm2 [2] (b) Work out the total area of the shaded number 7. …cm2 [4]

9 0607/33/O/N/17 © UCLES 2017 [Turn over (c) What fraction of the area of the rectangular piece of paper is the area of the shaded number 7? Give your answer as a fraction in its simplest form. … [2] (d) Write down the mathematical name for each of the two quadrilaterals that make up the shaded number 7. … and … [2] 7 Solve these equations to find the value of x, the value of y and the value of z. x + x + x = 42 x + y + y = 32 x + y + z = 22 x = … y = … z = … [4]

10 0607/33/O/N/17 © UCLES 2017 8 NOT TO SCALE 25 cm 24 cm 7 cm 74° x (a) (i) Work out the perimeter of the triangle. … cm [1] (ii) Write your answer to part (a)(i) in metres. …m [1] (b) Work out the size of angle x. x = … [1] (c) The triangle is enlarged by scale factor 3. Find the lengths of the sides and the sizes of the angles in the enlarged triangle. Sides … cm … cm … cm Angles …° …° …° [3] (d) Complete this statement with a mathematical word. The enlarged triangle is … to the original triangle. [1]

11 0607/33/O/N/17 © UCLES 2017 [Turn over 9 In a class of students, 11 like classical music (C ), 15 like pop music (P), 8 like both and 6 like neither. (a) Complete the Venn diagram to show this information. C P … … … … U [2] (b) Find the total number of students in the class. … [1] (c) One student is chosen at random. Find the probability that this student likes both classical music and pop music. … [1]

12 0607/33/O/N/17 © UCLES 2017 10 A cycle track has two straight sections, each 78 m long. Each of the two semi-circular ends has diameter 30 m. NOT TO SCALE 30 m 78 m Work out the perimeter of the cycle track. …m [3] 11 (a) Factorise. 5x – 15 … [1] (b) Solve. 4(3x – 2) = 28 … [3]

13 0607/33/O/N/17 © UCLES 2017 [Turn over (c) Simplify. a a b 4 2 3 2 2 # b … [2] (d) On the number line, show the inequality x G 3. –5 –4 –3 –2 –1 0 1 2 3 4 5 x [1] (e) Solve. 7x > 3x + 6 … [2] (f) Solve these simultaneous equations. x + y = 5 x – y = 7 x = … y = … [2]

14 0607/33/O/N/17 © UCLES 2017 12 Find the highest common factor (HCF) and the lowest common multiple (LCM) of 54 and 72. Highest common factor … Lowest common multiple … [4] 13 Sandy is playing a game with a fair dice numbered 1 to 6. To win the game she needs a 6 on each of the next two throws. (a) Complete the tree diagram. First throw Second throw Not a 6 Not a 6 Not a 6 1 6 6 6 6 … … … … … [2] (b) Work out the probability that Sandy does not win the game. … [3]

15 0607/33/O/N/17 © UCLES 2017 [Turn over 14 The line AB is drawn on a 1 cm2 grid. 6 5 4 3 2 1 0 –3 –2 –1 3 2 1 x y A B (a) Write down the co-ordinates of the midpoint of AB. (… , …) [1] (b) Use Pythagoras’ Theorem to work out the length of AB. AB = … cm [2] (c) Work out the gradient of AB. … [2] (d) Write down the equation of AB in the form y = mx + c. y = … [2] Question 15 is printed on the next page.

16 0607/33/O/N/17 © UCLES 2017 15 25 –25 0 –1 3 x y (a) On the diagram, sketch the graph of y = 8x2 −18x − 5 for −1 G x G 3. [2] (b) Solve the equation 8x2 −18x − 5 = 0. x = … or x = … [2] 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 a registered trademark. This document consists of 6 printed pages. © UCLES 2017 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) October/November 2017 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 International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the October/November 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 2 of 6 MARK SCHEME NOTES The following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons outside the scope of these notes. Types of mark M Method marks, awarded for a valid method applied to the problem. A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For accuracy marks to be given, the associated Method mark must be earned or implied. B Mark for a correct result or statement independent of Method marks. When a part of a question has two or more ‘method’ steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. The notation ‘dep’ is used to indicate that a particular M or B mark is dependent on an earlier mark in the scheme. Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working nfww not from wrong working oe or equivalent rot rounded or truncated SC Special Case soi seen or implied

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 3 of 6 Question Answer Marks Partial Marks 1(a) Radius Sector Chord Tangent 4 B1 for each 1(b) 56 to 60 1 2 19, 15, 11 1 ÷2 oe 1 22, 67, 202 2 B1 for 1 value correct 3(a)(i) 13 1 3(a)(ii) 13.3 1 3(b) 8 – 26 – 7 22 23 – – 3 B2 for 3 or 4 correct or B1 for 1 or 2 correct 3(c) Two of 60, 216, 84 seen B3 B2 for 1 angle correct or M1 for 360 ÷ 30 soi by 12 3 correct sectors drawn B1 Correct labels B1 FT if 3 sectors in approx. correct proportions 4(a) 7061 1 4(b)(i) Any multiple of 9 1 4(b)(ii) One of 22, 24, 26, 28 1 4(c)(i) 25 1 4(c)(ii) 1331 1 4(c)(iii) 16 1 4(d) ( ) 3 6 5 4 29 × + − = 1 4(e) 2.55 2 B1 for 2.545… 4(f)(i) 0.0316 1 4(f)(ii) 3.1626 × 10−2 1 FT from (f)(i) 5(a)(i) 08 55 oe 1 5(a)(ii) 70 2 M1 for 105 ÷ 1h 30min soi 5(b)(i) 3 2 M1 for 104 × 0.03 oe soi by 3.12

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 4 of 6 Question Answer Marks Partial Marks 5(b)(ii) 39 2 M1 for 104 ÷ (5 + 3) soi If zero scored SC1 for answer 65 6(a) 280 2 M1 for (16 + 4) × (4 + 10) 6(b) 116 4 M3 for 1 1 20 14 10 20 8 16 2 2       × − × × + × ×             or M2 for 1 10 20 2 × × and 1 8 16 2 × × or M1 for 1 10 20 2 × × or 1 8 16 2 × × A1 for 100 or 64 OR M3 for ( ) 1 8 10 4 4 20 2 × + × + × oe or M2 for ( ) 1 8 10 4 2 × + × or M1 4 20 × 6(c) 29 70 2 M1 for (b) (a) their their 6(d) Trapezium 1 Parallelogram 1 7 [x =] 14 1 [y =] 9 2 M1 for (32 − their x) ÷ 2 [z =] –1 1 8(a)(i) 56 1 8(a)(ii) [0].56 1 FT their(a)(i) ÷100 8(b) 16 1 8(c) 75, 72, 21 2 B1 for 1 or 2 values correct 90, 74, their16 1 FT 8(d) Similar 1 9(a) 6 3 8 7 2 B1 for 2 or 3 values correct 9(b) 24 1 FT their diagram

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 5 of 6 Question Answer Marks Partial Marks 9(c) 8 (b) their 1 FT 10 250 or 250.2 to 250.3 3 M2 for 78 + 78 + π × 30 oe or M1 for 1 2   × π×30     11(a) 5(x – 3) final answer 1 11(b) 3 3 M1 for 12x – 8 = 28 or 3x – 2 = 7 M1 for 12x = 28 + 8 or 3x = 7 + 2 oe 11(c) 6b a or 6ba−1 2 M1 for any correct cancelling once 11(d) Enclosed circle and indication from 3 to the left 1 11(e) x > 1 12 oe 2 B1 for 7x – 3x > 6 oe 11(f) x = 6, y = −1 2 B1 for each If zero scored SC1 for correct sub. and evaluation to find their other variable 12 HCF = 18 LCM = 216 4 B2 for each or B1 for 2 × 3 × 3 × 3 oe B1 for 2 × 4 × 3 × 3 oe If 0 scored SC2 for correct answers reversed or SC1 for answer HCF = 3, 6 or 9 and SC1 for answer LCM any multiple of 216 (eg 3888) 13(a) Complete, correct tree 2 B1 for 5 6 correctly placed once 13(b) 35 36 3 M2 for 1 5 1 5 5 5 6 6 6 6 6 6 × + × + × or 1 1 1 6 6   − ×     or M1 for 1 5 6 6 × or 1 5 6 6 × or 5 5 6 6 × 14(a) (0, 3) 1 14(b) 5.66 or 5.656 to 5.657 2 M1 for 42 + 42

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 6 of 6 Question Answer Marks Partial Marks 14(c) 1 2 M1 for any correct rise run 14(d) [1]x + 3 2 FT their m from their (c) B1 for mx + 3 or [1]x + c 15(a) Correct sketch 2 M1 for correct U shape or for minimum to right of y-axis and curve intersects y-axis below origin 15(b) 2.5 and −0.25 oe 2 B1 for one value correct