Cambridge IGCSE Mathematics - International 0607 — 2019 Oct/Nov Paper 3 · Variant 1

This document consists of 15 printed pages and 1 blank page. DC (NF/FC) 168254/3 © UCLES 2019 [Turn over * 2 5 0 1 1 7 9 7 5 8 * Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2019 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 r, 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/19 © UCLES 2019 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 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 = Ah 3 1 Volume, V, of cylinder of radius r, height h. V = rr2h 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/O/N/19 © UCLES 2019 [Turn over Answer all the questions. 1 (a) Write 5 2 as a decimal. … [1] (b) Write 16 9 as a percentage. …% [1] (c) Work out . . . 68 52 3 41 7 9 # - . … [2] (d) Write down a factor of 17. … [1] (e) Write 49 28 in its simplest form. … [1] (f) Write down the next two terms in this sequence. 81, 74, 67, 60, … … , … [2] (g) $380 is invested at a rate of 3% per year simple interest. Work out the interest at the end of 4 years. $ … [2] (h) Cupcakes cost $1.30 each. Find the largest number of these cupcakes that can be bought with $10. … [2]

4 0607/31/O/N/19 © UCLES 2019 2 Benji has 15 bags of potatoes. The number of potatoes in each bag is shown below. 38 36 42 36 36 41 40 38 37 39 39 40 37 38 36 (a) Complete the frequency table. Number of potatoes 36 37 38 39 40 41 42 Frequency 4 [2] (b) For the number of potatoes, find (i) the range, … [1] (ii) the mode, … [1] (iii) the median, … [1] (iv) the mean. … [1] (c) Complete the bar chart. Frequency Number of potatoes 36 0 1 2 3 4 5 37 38 39 40 41 42 [2]

5 0607/31/O/N/19 © UCLES 2019 [Turn over 3 (a) Write sixty thousand and twenty in figures. … [1] (b) Complete the mapping diagram for the function ( )x x 3 4 f = - . x 0 … f (x) 1 … 2 … 3 … [2] (c) Write down a prime number between 35 and 45. … [1] (d) a 15 8 75 = Find the value of a. a = … [1] (e) Write 6789 correct to the nearest 10. … [1] (f) Write 189.436 correct to 2 decimal places. … [1] (g) Write 3462 (i) correct to 3 significant figures, … [1] (ii) in standard form. … [1]

6 0607/31/O/N/19 © UCLES 2019 4 0 1 A B 2 3 4 5 6 y x 1 2 3 4 5 6 The diagram shows two points, A and B, plotted on a 1 cm2 grid. (a) Write down the co-ordinates of point A and the co-ordinates of point B. A ( … , … ) B ( … , … ) [2] (b) Calculate the length of AB. … cm [2] (c) Find the co-ordinates of the midpoint of AB. ( … , … ) [1] (d) Find the gradient of AB. … [2] (e) Write down the equation of the line parallel to AB passing through (0, 3). y = … [2]

7 0607/31/O/N/19 © UCLES 2019 [Turn over 5 Two cylindrical candles are mathematically similar. The small candle has radius 2 cm and height 5 cm. The large candle has radius 7 cm. NOT TO SCALE 5 cm 2 cm 7 cm (a) Find the height of the large candle. … cm [2] (b) The small candle burns for 4 hours and the large candle burns for 60 hours. Write the ratio 4 : 60 in its simplest form. … : … [1] (c) The price of the large candle is $28. In a sale, this price is reduced by 15%. Find the sale price. $ … [2]

8 0607/31/O/N/19 © UCLES 2019 6 (a) For each diagram, draw all the lines of symmetry. NOT TO SCALE [3] (b) NOT TO SCALE Simi makes a flower using some mathematical shapes. The centre is a circle with radius 2 cm. Each of the five petals is an isosceles triangle with base 2.3 cm and perpendicular height 4 cm. The stem is a rectangle with length 6 cm and width 1 cm. Find the total area shaded. … cm2 [4]

9 0607/31/O/N/19 © UCLES 2019 [Turn over 7 The table shows the age, in months, and length, in centimetres, of seven babies. Age (months) 0 2 4 5 9 10 12 Length (cm) 50 58 63 64 71 73 76 (a) Complete the scatter diagram to show this information. The first three points have been plotted for you. 0 40 50 60 70 80 2 4 6 Age (months) Length (cm) 8 10 12 [2] (b) Find. (i) the mean age, … months [1] (ii) the mean length. … cm [1] (c) On the scatter diagram, draw a line of best fit. [2] (d) Use your line of best fit to find an estimate for the length of a baby aged 7 months. … cm [1]

10 0607/31/O/N/19 © UCLES 2019 8 (a) 40° 36 m Q P A NOT TO SCALE 1.8 m The diagram shows a vertical tower, PQ, standing on horizontal ground. Matthijs stands at point A. He is 1.8 m tall. The base of the tower, P, is 36 m from point A. Find the height of the tower. … m [3]

11 0607/31/O/N/19 © UCLES 2019 [Turn over (b) B 4 cm NOT TO SCALE 4 cm C O A 38° AB and AC are tangents to a circle with centre, O, and radius 4 cm. Angle ° BAC 38 = . (i) Write down the size of angle OBA. Angle OBA = … [1] (ii) Find the size of angle BOC. Angle BOC = … [1] (c) Use trigonometry to find the length of OA. OA = … cm [3]

12 0607/31/O/N/19 © UCLES 2019 9 20 people were asked if they liked banana milk shake, B, or chocolate milk shake, C. B 4 3 9 C … U (a) Complete the Venn diagram. [1] (b) Write down ( ) B C n + . … [1] (c) One of these 20 people is chosen at random. Find the probability that this person likes (i) banana milk shake, … [1] (ii) chocolate milk shake but not banana milk shake. … [1] (d) On the Venn diagram, shade C B + l . [1]

13 0607/31/O/N/19 © UCLES 2019 [Turn over 10 y 20 –25 0 –2 5 x ( )x x x x 5 2 8 f 3 2 = - + + (a) On the diagram, sketch the graph of ( ) y x f = for x 2 5 G G - . [3] (b) Write down the co-ordinates of the point where the curve crosses the y-axis. ( … , … ) [1] (c) Write down the co-ordinates of the three points where the curve crosses the x-axis. ( … , … ), ( … , … ), ( … , … ) [2] (d) Find the co-ordinates of the local maximum. ( … , … ) [2] (e) Find the number of times that the line y 9 = crosses the curve ( ) y x f = . … [1]

14 0607/31/O/N/19 © UCLES 2019 11 (a) Solve. (i) y 3 6 = y = … [1] (ii) y 6 5 13 - = y = … [2] (iii) y 3 6 2 - … [2] (b) Expand and simplify. ( )( ) y y 5 7 3 4 - - … [2] (c) P T 2 6 = - (i) Find the value of P when T 8 = . P = … [1] (ii) Rearrange the formula to make T the subject. T = … [2] (d) Simplify. y y 3 2 5 + … [2]

15 0607/31/O/N/19 © UCLES 2019 12 Angie goes to school on 5 days each week. On a school day, the probability that Angie gets up before 7 am is 10 9 . On a non-school day, the probability that Angie gets up before 7 am is 20 1 . (a) Complete the tree diagram. school day non-school day … 5 7 gets up before 7 am does not get up before 7 am … gets up before 7 am does not get up before 7 am … … … [3] (b) One day of the week is chosen at random. Find the probability that the day is a non-school day and that Angie gets up before 7 am. … [2]

16 0607/31/O/N/19 © UCLES 2019 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 Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. BLANK PAGE

This document consists of 7 printed pages. © UCLES 2019 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2019 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 2019 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 2019 © UCLES 2019 Page 2 of 7 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 2019 © UCLES 2019 Page 3 of 7 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 Question Answer Marks Partial Marks 1(a) [0].4 1 1(b) 56.25 1 1(c) 41.581 2 M1 for 26.939 1(d) 1 or 17 1 1(e) 4 7 1 1(f) 53, 46 2 B1 for 53 or their 53 – 7 1(g) 45.6[0] 2 M1 for [380 ×]0.03 × 4 or 380 × 0.03[× 4] 1(h) 7 2 M1 for 10 1.3 soi 7.692… 2(a) [4] 2 3 2 2 1 1 2 M1 for 4 or 5 correct

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 4 of 7 Question Answer Marks Partial Marks 2(b)(i) 6 1 2(b)(ii) 36 1 2(b)(iii) 38 1 2(b)(iv) 38.2 1 2(c) Correct bar chart 2 FT from their (a) B1 for 4 or 5 correct heights with equal widths or 6 correct heights and unequal widths. 3(a) 60 020 1 3(b) –4 , –1, 2, 5 2 M1 for 2 or 3 correct 3(c) 37 or 41 or 43 1 3(d) 40 1 3(e) 6790 1 3(f) 189.44 1 3(g)(i) 3460 1 3(g)(ii) 3 3.462 10 × 1 4(a) [A] (1, 1) [B] (3, 5) 2 B1 for each 4(b) 4.47 or 4.472… 2 M1 for 2 2 4 2 + 4(c) (2, 3) 1 4(d) 2 2 M1 for correct rise run fraction or their rise run from suitable triangle on diagram 4(e) y = 2x + 3 2 FT their (d) M1 for y = 2x + k 5(a) 17.5 2 M1 for 5 2 or 2 5 or 2 7 or 7 2 5(b) 1 : 15 1 5(c) 23.8[0] 2 M1 for 15 1 28 100   − ×     or 15 28 100 ×

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 5 of 7 Question Answer Marks Partial Marks 6(a) Correct ruled lines of symmetry 3 B1 for triangle correct with no extras B2 for rectangle correct with no extras or B1 for 1 correct line with no extras or 2 correct lines and only 1 extra. 6(b) 41.6 or 41.56 to 41.57 4 M3 for 2 1 2 5 2.3 4 1 6 2 π× + × × × + × or M2 for two of 2 1 2 , 5 2.3 4 2 π× × × × or 1 6 × or M1 for 1 correct product 7(a) Correct points plotted 2 B1 for 2 or 3 correct 7(b)(i) 6 1 7(b)(ii) 65 1 7(c) Ruled line correctly drawn 2 B1 for positive slope passing through the mean but not in tolerance or B1 for line in tolerance but not through the mean. 7(d) 65 to 70 1 FT from their line with positive slope 8(a) 32[.0] 3 M1 for tan 40 36 = x M1 for their 30.2 + 1.8 8(b)(i) 90 1 8(b)(ii) 142 1 8(c) 12.3 or 12.28 to 12.29 3 M2 for 4 38 sin 2 = OA or 4 1 42 cos 2       their or M1 for 38 4 sin 2 OA = or 1 42 4 cos 2 their OA  =     9(a) 4 1 9(b) 3 1 9(c)(i) 7 20 1 9(c)(ii) 9 20 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 6 of 7 Question Answer Marks Partial Marks 9(d) 1 10(a) Correct sketch 3 B1 for y-intercept approximately correct B1 for x-intercepts approximately correct B1 for turning points approximately correct 10(b) (0, 8) 1 10(c) (–1, 0), (2, 0), (4, 0) 2 B1 for 1 correct 10(d) (0.214, 8.21) or (0.2137… , 8.208 to 8.209) 2 B1 for each If 0 scored, SC1 for (0.21 , 8.21) 10(e) 1 1 11(a)(i) 2 1 11(a)(ii) 3 2 M1 for 6y = 13 + 5 or 5 13 6 6 − = y 11(a)(iii) y < –3 2 M1 for 6 – 3 or 3 6 −> − > y y 11(b) 2 15 41 28 − + y y 2 B1 for any three of 2 15 , 20 , 21 y y y − − or 28 11(c)(i) 10 1 11(c)(ii) 6 2 + = P T oe 2 M1 for 6 2 + = P T or 3 2 = − P T 11(d) 13 15 y 2 M1 for a common denominator 15k

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 7 of 7 Question Answer Marks Partial Marks 12(a) 3 B1 for each pair of branches correct. 12(b) 2 140 oe or 0.0143 2 M1 for 2 1 7 20 × their their