Cambridge IGCSE Mathematics - International 0607 — 2018 Oct/Nov Paper 3 · Variant 1

This document consists of 16 printed pages. DC (LEG/CGW) 153614/2 © UCLES 2018 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 6 6 0 7 8 5 3 3 3 3 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2018 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 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 0607/31/O/N/18 © UCLES 2018 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/18 © UCLES 2018 [Turn over Answer all the questions. 1 (a) (i) Write 88% as a decimal. … [1] (ii) Write 0.3 as a fraction. … [1] (iii) Shade 60% of this diagram. [1] (b) Find the value of (i) 63, … [1] (ii) .6 4, giving your answer correct to 1 decimal place, … [2] (iii) . . 21 2 8 8 489 + . … [1] (c) Complete the list of factors of 12. 1 , … , … , … , … , 12 [1]

4 0607/31/O/N/18 © UCLES 2018 2 One day, Pat and Terry walk to school. (a) It takes Pat 10 minutes 7 seconds to walk to school. It takes Terry 14 minutes 49 seconds to walk to school. (i) Who takes the least time and by how much? … takes the least time by … minutes … seconds [1] (ii) When Pat left home, her watch showed this time. Hours Minutes Seconds 7 58 45 What time did the watch show when Pat arrived at school? Hours Minutes Seconds … … … [2] (b) Pat lives 0.78 km from school. Terry lives 8 7 km from school. Work out who lives closer to school and by how much. Give your answer in metres. … lives closer by … metres [2]

5 0607/31/O/N/18 © UCLES 2018 [Turn over (c) One day Pat takes 1180 steps on her way to school. The next day she takes 15% more steps. Work out how many more steps she takes. … [1] (d) On a different day Pat takes 1240 steps on her way to school and Terry takes 1400 steps. Write the ratio 1240 : 1400 in its simplest form. … : … [2]

6 0607/31/O/N/18 © UCLES 2018 3 Here is a rectangle drawn on a 1 cm2 grid. (a) Work out the perimeter and the area of the rectangle. Perimeter = … cm2 [2] Area = … cm2 [2] (b) A square has the same area as the rectangle. Work out the length of one side of the square. … cm [2] (c) h b NOT TO SCALE Work out a value for b and a value for h so that this triangle has the same area as the rectangle. b = … cm [3] h = … cm [3]

7 0607/31/O/N/18 © UCLES 2018 [Turn over 4 (a) Here are the first four terms of a sequence. 1 4 7 10 (i) Write down the next two terms of this sequence. … , … [1] (ii) Write down the rule to find the next term. … [1] (b) Here are the first four terms of another sequence. 80 40 20 10 Write down the next four terms of this sequence. … , … , … , … [2] (c) Here are the first five terms of a different sequence. 1 3 5 7 9 (i) Find the nth term. … [2] (ii) Explain why multiplying together any two terms in this sequence gives an answer that is also a term in the sequence. … … [1]

8 0607/31/O/N/18 © UCLES 2018 5 –2 –1 1 2 3 4 5 6 7 8 9 –3 –2 –1 0 1 2 3 4 5 y x A B C (a) Write down the co-ordinates of (i) point B, ( … , … ) [1] (ii) point A. ( … , … ) [1] (b) ABCD is a kite. (i) On the grid, plot the point D and complete the kite. [1] (ii) Write down the co-ordinates of point D. ( … , … ) [1] (c) On the grid, draw the line of symmetry of the kite. [1] (d) The equation of the line BC is 2y + x = 10. (i) Rearrange 2y + x = 10 to make y the subject. y = … [2] (ii) Write down the gradient of the line BC. … [1] (e) The equation of the line AB is y = x + 2. Write down the equation of the line parallel to AB, passing through the point (0, −4). … [2]

9 0607/31/O/N/18 © UCLES 2018 [Turn over 6 (a) (i) Work out the value of 9y + 12 when y = 5. … [1] (ii) Factorise 9y + 12. … [1] (b) Solve these equations. (i) x 2 = 8 x = … [1] (ii) 3x – 5 = 7 x = … [2] (c) Multiply out the brackets and simplify. (x + 3)(x + 2) … [2] (d) Write down the value of x0. … [1] (e) Simplify fully. (i) t t 5 3 # … [1] (ii) (p4)2 … [1] (iii) y y 6 18 3 9 … [2]

10 0607/31/O/N/18 © UCLES 2018 7 The table shows how the value of a car changes as it gets older. Age (years) 1 1.5 2 3 4 4.5 5 6 Value ($) 9000 8000 5000 4500 3000 2500 2000 2000 (a) Complete the scatter diagram. The first four points have been plotted for you. 0 0 2000 4000 6000 8000 10 000 1 2 3 4 Age (years) Value ($) 5 6 [2] (b) What type of correlation is shown in your scatter diagram? … [1] (c) (i) Find the mean age and the mean value. Mean age = … years [2] Mean value = $ … [2] (ii) On the scatter diagram, draw a line of best fit. [2] (d) Use your line of best fit to estimate the value of the car when it was 2.5 years old. $ … [1]

11 0607/31/O/N/18 © UCLES 2018 [Turn over 8 (a) In the diagram, BCD is a straight line and CE = CD. 110° NOT TO SCALE 80° 125° x° y° D E A B C Work out the value of (i) x, x = … [2] (ii) y. y = … [2] (b) On a map, two towns are 8.5 cm apart. The scale of the map is 1 centimetre represents 5 kilometres. Work out the actual distance between the two towns. … km [1] (c) North 70° Y X North NOT TO SCALE The bearing of Y from X is 070°. Work out the bearing of X from Y. … [2]

12 0607/31/O/N/18 © UCLES 2018 9 A bag contains black counters, white counters and red counters only. Tam takes a counter, at random, from the bag. He records the colour of the counter and then replaces the counter in the bag. He does this 500 times. The table below shows his results. Colour of counter Black White Red Number of times 163 128 209 (a) Complete the relative frequency table below. Give each of your answers as a decimal. Colour of counter Black White Red Relative frequency [2] (b) Tam chooses another counter from the bag at random. Work out an estimate of the probability that it is either black or white. … [2] (c) There is a total of 24 counters in the bag. Work out an estimate of the number of red counters. … [2]

13 0607/31/O/N/18 © UCLES 2018 [Turn over 10 (a) Work out . . 8 4 10 1 5 10 3 8 # # # - ` ` j j, giving your answer (i) in standard form, … [1] (ii) as an ordinary number. … [1] (b) The Sun is a sphere of radius 696 000 km. (i) Write 696 000 in standard form. … [1] (ii) Work out the surface area of the Sun. Write your answer in standard form correct to 2 significant figures. …km2 [3]

14 0607/31/O/N/18 © UCLES 2018 11 Nur recorded the distance, d cm, that 100 people each sit from their computer screen. The table shows her results. Distance from screen (d cm) Frequency d 0 0 3 4 1 G 4 d 0 0 4 5 1 G 50 d 0 0 5 6 1 G 27 d 0 0 6 7 1 G 16 d 0 0 7 8 1 G 3 (a) Write down the modal class. … d 1 G … [1] (b) Work out an estimate of the mean distance. … cm [2] (c) Draw a bar chart to show this data. 30 0 20 40 50 70 Distance from screen (cm) Frequency 40 60 80 10 30 50 d [2]

15 0607/31/O/N/18 © UCLES 2018 [Turn over 12 27 cm x cm 51 cm NOT TO SCALE 34 cm The diagram shows two rectangular computer screens. The screens are mathematically similar. (a) Find the value of x. x = … [2] (b) 27 cm 34 cm NOT TO SCALE y cm p° For the smaller computer screen, work out (i) the value of y, y = … [2] (ii) the value of p. p = … [2] Question 13 is printed on the next page.

16 0607/31/O/N/18 © UCLES 2018 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. 13 Here is a sketch of the graph y = x x 3 4 + + for values of x between −6 and 2. –4 –6 x –4 4 –6 2 0 y (a) (i) On the sketch, draw the asymptotes for this graph. [1] (ii) Find the equation of each asymptote you have drawn. … [2] … [2] (b) Solve the equation x x 3 4 + + = 3. x = … [1] (c) Describe fully the single transformation that maps the graph of y = x x 3 4 + + onto the graph of y = x x 3 4 + + – 1. … [2]

This document consists of 6 printed pages. © UCLES 2018 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2018 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 2018 series for most Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 2 of 6 Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • the specific content of the mark scheme or the generic level descriptors for the question • the specific skills defined in the mark scheme or in the generic level descriptors for the question • the standard of response required by a candidate as exemplified by the standardisation scripts. GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate • marks are awarded when candidates clearly demonstrate what they know and can do • marks are not deducted for errors • marks are not deducted for omissions • answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 3 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

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 4 of 6 Question Answer Marks Partial Marks 1(a)(i) 0.88 1 1(a)(ii) 3 10 1 1(a)(iii) 6 parts shaded 1 1(b)(i) 216 1 1(b)(ii) 2.5 2 B1 for 2.529 to 2.53[0] seen 1(b)(iii) 16.3 1 1(c) [1], 2, 3, 4, 6, [12] 1 2(a)(i) [Pat] by 4 min 42 sec 1 2(a)(ii) 8 h 8 m 52 s 2 B1 for 8 h 2(b) [Pat] by 95 m 2 B1 for 0.875 seen or for 0.095 or 19 200 2(c) 177 1 2(d) 31 : 35 2 M1 for any correct cancelling 3(a) [P =] 26 [A =] 36 2 B1 for one correct If 0 scored SC1 for answers reversed 3(b) 6 2 FT their A in part (a) M1 for squaring values in attempt to find their 36 or for 36 their seen 3(c) Any correct pair of values with a product of 2 × their A 3 FT their A in part (a) M2 for using b × h in an attempt to find 2 × their 36 or M1 for using 2 b h × in an attempt to find their 36 4(a)(i) 13, 16 1 4(a)(ii) +3 oe 1 4(b) 5, 2.5, 1.25, 0.625 oe 2 B1 for 2 values correct If 0 scored SC1 for halving correctly any two terms 4(c)(i) 2n – 1 2 B1 for 2n + c or kn – 1 for k ≠ 0 4(c)(ii) odd × odd = odd 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 5 of 6 Question Answer Marks Partial Marks 5(a)(i) (2, 4) 1 5(a)(ii) (–1, 1) 1 5(b)(i) Plot at (2, –2) 1 5(b)(ii) (2, –2) 1 FT their D in part (b)(i) 5(c) One horizontal line of symmetry only 1 5(d)(i) [y =] −1 2 x + 5 oe 2 M1 for 2y = –x + 10 or for y + 1 2 x = 5 oe 5(d)(ii) – 1 2 oe 1 FT part (d)(i) but only from their y = mx + c 5(e) y = x – 4 oe 2 B1 for x – 4 or y = mx – 4 or y = x + k 6(a)(i) 57 1 6(a)(ii) 3(3y + 4) 1 6(b)(i) 16 1 6(b)(ii) 4 2 M1 for 3x = 7 + 5 soi or for x – 5 3 = 7 3 6(c) x2 + 5x + 6 2 B1 for three of x2, [+]3x, [+]2x, [+]6 6(d) 1 1 6(e)(i) t8 1 6(e)(ii) p8 1 6(e)(iii) 3y6 2 B1 for ny6 or 3yn 7(a) 4 points correctly plotted 2 M1 for 2 or 3 points correctly plotted 7(b) negative 1 7(c)(i) 3.375 or 3.38 4500 2 B1 for each 7(c)(ii) Correct ruled line 2 B1 for ruled line through their mean point or for line with negative gradient that is within the tolerance 7(d) Correct value from their line 1 FT their (c)(ii) 8(a)(i) 45 2 M1 for 360 – (125+110 + 80) oe 8(a)(ii) 55 2 M1 for ECD=70

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 6 of 6 Question Answer Marks Partial Marks 8(b) 42.5 1 8(c) 250 2 B1 for XYN = 110 or NY? = 70 or XYS = 70 soi 9(a) 0.326, 0.256, 0.418 oe 2 B1 for ÷ 500 soi 9(b) 0.582 oe 2 M1 for their(0.326) + their(0.256) oe or for 163 128 500 + oe 9(c) 10 2 M1 for their(0.418) × 24 10(a)(i) 1.26×10−4 1 10(a)(ii) 0.000126 1 FT their (a)(i) 10(b)(i) 6.96[000] ×105 1 10(b)(ii) 6.1×1012 3 B2 for 6.084… to 6.089 × 1012 oe or M1 for 4 × π × 6960002 11(a) 40 [ ] d < ≤ 50 1 11(b) 51.4 2 M1 for Σd × f soi by 5140 11(c) Correct bar chart 2 M1 for any 4 of the heights correct 12(a) 40.5 2 B1 for 51 34 or 34 51 or 27 34 or 34 27 oe seen 12(b)(i) 43.4 or 43.41 to 43.42 2 M1 for 2 2 34 27 + 12(b)(ii) 38.5 or 38.45… 2 M1 for tan [=] 27 34 or better oe 13(a)(i) Correct two asymptotes drawn 1 13(a)(ii) x = –3 y = 1 2 B1 for each If 0 scored SC1 for x = 1 and y = –3 13(b) –2.5 1 13(c) Translation cao 0 1     −   2 B1 for each