Cambridge IGCSE Mathematics - International 0607 — 2018 Oct/Nov Paper 3 · Variant 2

* 8 5 0 3 8 5 4 5 9 3 * This document consists of 16 printed pages. DC (ST/SG) 153615/2 © UCLES 2018 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 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, 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 0607/32/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 0607/32/O/N/18 © UCLES 2018 [Turn over Answer all the questions. 1 (a) Here is a list of numbers. 8 10 14 17 20 25 From this list, write down (i) an odd number, … [1] (ii) a multiple of 7, … [1] (iii) a square number. … [1] (b) Here are the first four numbers in a sequence. 8 11 14 17 Write down the next two terms in this sequence. … , … [2] (c) Write 3658 correct to the nearest 100. … [1] (d) Write 68.437 (i) correct to 2 decimal places, … [1] (ii) correct to 3 significant figures. … [1] (e) s m n 3 2 = + Find the value of s when m = 4.8 and n = 1.6 . s = … [2] (f) Change 2.3 kilometres into metres. …m [1]

4 0607/32/O/N/18 © UCLES 2018 2 A school shop sells the following. Cost (cents) Pencil 12 Sharpener 25 Eraser 10 Ruler 30 (a) Gigue buys 3 pencils and 1 sharpener. Work out how much he spends. … cents [2] (b) The cost of a ruler is increased by 20%. Work out the new cost of a ruler. … cents [2] (c) In a sale, the cost of a sharpener is reduced to 19 cents. Work out the percentage reduction. …% [2]

5 0607/32/O/N/18 © UCLES 2018 [Turn over 3 Some students were asked to choose their favourite colour of candy. All their choices are shown in the table. Favourite colour Red Blue Yellow Green Orange Number of students 6 5 2 2 3 (a) Find the number of students that were asked. … [1] (b) One of these students is chosen at random. Find the probability that their favourite colour of candy is blue. … [1] (c) Complete the bar chart. Red Blue Yellow Favourite colour Green Orange 0 1 2 3 4 5 6 7 Number of students [2]

6 0607/32/O/N/18 © UCLES 2018 4 There are 36 cars altogether in a car park. There are 11 black cars, 10 red cars and the rest of the cars are blue. (a) Work out the number of blue cars. … [1] (b) Write down the fraction of cars in the car park that are black. … [1] (c) The information is to be shown in a pie chart. Work out the sector angle for red cars. … [2]

7 0607/32/O/N/18 © UCLES 2018 [Turn over 5 (a) VRI ND From the letters above, write down all the letters that have (i) line symmetry, … [2] (ii) rotational symmetry, … [2] (iii) both line symmetry and rotational symmetry, … [1] (iv) neither line symmetry nor rotational symmetry. … [1] (b) On a poster, the letter I is a rectangle of width 2 cm and height 11 cm. (i) Work out the perimeter of the letter I. … cm [1] (ii) Work out the area of the letter I. … cm2 [1]

8 0607/32/O/N/18 © UCLES 2018 6 A bag contains 15 marshmallows. 8 of these are white and 7 are pink. Terry picks a marshmallow at random from the bag and eats it. He then picks a second marshmallow at random from the bag and eats it. (a) Complete the probability tree diagram. … … White Pink … … White Pink … … White Pink First marshmallow Second marshmallow [3] (b) Find the probability that both marshmallows were white. … [2]

9 0607/32/O/N/18 © UCLES 2018 [Turn over 7 A B C y x –6 –5 –4 –3 –2 –1 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 1 2 3 4 5 6 0 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) Describe fully the single transformation that maps triangle A onto triangle C. … … [2] (c) On the grid, draw the image of triangle A after a rotation of 180° about the origin. Label this image D. [2] (d) Describe fully the single transformation that maps triangle C onto triangle D. … … [2]

10 0607/32/O/N/18 © UCLES 2018 8 250 m 100 m NOT TO SCALE The diagram shows a rectangle joined to a semicircle. There is a path along the perimeter of this shape. (a) Show that the length of the path is 757 m, correct to the nearest metre. [3] (b) Maggie runs around the path at a speed of 220 metres per minute. Work out how long it takes Maggie to run around the path. Give your answer in minutes. …min [1] (c) Jack takes 10 minutes to walk around the path. Work out his average speed in km/h. …km/h [3] (d) Work out the total area enclosed by the path. …m2 [3] (e) The area inside the path is covered with grass. Grass cost $0.29 for one square metre. Work out the total cost for the grass. $ … [1]

11 0607/32/O/N/18 © UCLES 2018 [Turn over 9 The diagram shows a 1cm2 grid. y x 1 2 3 4 5 6 1 2 3 4 5 6 0 7 8 9 10 7 8 9 (a) On the grid, plot the points R(2, 2), S(8, 2) and T(8, 8). Join these points to form a right-angled triangle. [2] (b) Find (i) the length of RS, … cm [1] (ii) the area of the triangle, …cm2 [1] (iii) the gradient of RT. … [2] (c) Find the co-ordinates of the midpoint of RT. ( … , … ) [1] (d) Write down the equation of the line ST. … [1]

12 0607/32/O/N/18 © UCLES 2018 10 (a) A C O B E D F 15° 10° NOT TO SCALE The diagram shows a circle, centre O. AB and CD are parallel chords and the line EDF is a tangent to the circle at D. Angle ODC = 10° and angle OCB = 15°. Find the size of (i) angle ODE, Angle ODE = … [1] (ii) angle CDF, Angle CDF = … [1] (iii) angle COD, Angle COD = … [2] (iv) angle CBA. Angle CBA = … [1]

13 0607/32/O/N/18 © UCLES 2018 [Turn over (b) x + 15° x + 10° x + 20° NOT TO SCALE x° x + 25° The diagram shows a pentagon. Find the value of x. x = … [3]

14 0607/32/O/N/18 © UCLES 2018 11 The Venn diagram shows the number of students in a class wearing a T-shirt, T, or a cardigan, C. T 8 3 7 C … U (a) There are 20 students in total in the class. Complete the Venn diagram. [1] (b) Find the probability that one of these students, chosen at random, wears (i) both a T-shirt and a cardigan, … [1] (ii) a T-shirt but not a cardigan. … [1] (c) Find n(T ). … [1] (d) On the Venn diagram, shade C T + l. [1] 12 (a) T R S 5 = - Find the value of T when R = 3 and S = 4. T = … [2] (b) Simplify fully. (i) a b a b 3 6 2 - + - … [2] (ii) x x 5 10 … [1]

15 0607/32/O/N/18 © UCLES 2018 [Turn over (c) Solve. (i) x 2 5 = x = … [1] (ii) x 7 2 51 + = x = … [2] (d) Expand the brackets and simplify. ( ) ( ) x x 4 2 2 2 1 + + + … [2] (e) Write down the inequality shown by this number line. –4 –3 –2 –1 0 1 2 3 4 5 6 7 x … [1] (f) Solve these simultaneous equations. You must show all your working. x y 9 2 - = x y 3 16 + = x = … y = … [2] Question 13 is printed on the next page.

16 0607/32/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 –2 4 x y –12 10 0 NOT TO SCALE The diagram shows the graph of ( ) y x f = where ( )x x x 2 5 6 f 2 =- + + for x 2 4 G G - . (a) Use your calculator to find the zeros of ( )x f . … and … [2] (b) Use your calculator to find the co-ordinates of the local maximum. ( … , … ) [2] (c) Write down the equation of the line of symmetry. … [1]

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 0607/32 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.

0607/32 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.

0607/32 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

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 4 of 6 Question Answer Marks Partial Marks 1(a)(i) 17 or 25 1 1(a)(ii) 14 1 1(a)(iii) 25 1 1(b) 20 23 2 B1 for 20 B1 for 23 or their 20 + 3 1(c) 3700 1 1(d)(i) 68.44 1 1(d)(ii) 68.4 1 1(e) 14.4 2 B1 for 2 × (4.8) + 3 × (1.6) seen 1(f) 2300 1 2(a) 61 2 B1 for 3 × 12 2(b) 36 2 M1 for 20 120 30 or better or 30 100 100 × × oe 2(c) 24 2 B1 for 25 19 25 − or 76% 3(a) 18 1 3(b) 5 oe 18 1 FT their (a) 3(c) Bars correctly drawn 2 B1 for 2 or 3 bars correct 4(a) 15 1 4(b) 11 36 1 4(c) 100 2 M1 for 10 360 or 36 36 5(a)(i) V I E D 2 B1 for any 2 correct 5(a)(ii) I N 2 B1 for one correct or one or two correct and some incorrect 5(a)(iii) I 1 5(a)(iv) R 1 5(b)(i) 26 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 5 of 6 Question Answer Marks Partial Marks 5(b)(ii) 22 1 6(a) 8 7 and 15 15 oe 7 7 and 14 14 oe 8 6 and 14 14 oe 3 B1 for each branch correct 6(b) 56 oe 210 2 M1 for 8 7 15 14 their × 7(a) Reflection x-axis oe 2 B1 for each 7(b) Translation 6 2 −     −   2 B1 for each 7(c) Triangle with vertices at (–3, –2), (–4, –5) and (–1, –5) 2 B1 for correct rotation about another point. 7(d) Rotation about (–3 , –1) through 180o 2 FT their (c) B1 for reflection or rotation 8(a) 100 250 250 0.5 2 50 + + + × ×π× M2 or for1 00 250 250 or 0.5 2 50 + + × × π× M1 757.0 to 757.1 A1 8(b) 3.44 or 3.440 to 3.441... 1 8(c) 4.54 or 4.542 to 4.543 3 757 for 60 1000× M2 or M1 for dividing by 1000 or multiplying by 60 10 or seen 60 or B1 for 75.7 8(d) 28900 or 28920 to 28930 3 M1 for 100 250 × and M1 for [ ] 2 0.5 50 × π× 8(e) 8380 to 8390 1 FT from their (d) 9(a) Points plotted correctly 2 B1 for 2 points plotted correctly 9(b)(i) 6 1 FT their (a) 9(b)(ii) 18 1 FT their (a) 9(b)(iii) 1 oe 2 rise for run their their M1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2018 © UCLES 2018 Page 6 of 6 Question Answer Marks Partial Marks 9(c) (5, 5) 1 9(d) x = 8 1 10(a)(i) 90 1 10(a)(ii) 80 1 10(a)(iii) 160 2 M1 for recognising OCD = 10 10(a)(iv) 25 1 10(b) 94 3 M2 for (5 – 2) × 180 = (5x + 70) oe or M1 for (5 – 2) × 180 or x + x + 25 + x +15 + x +10 + x + 20 11(a) 2 1 11(b)(i) 7 oe 20 1 11(b)(ii) 8 oe 20 1 11(c) 15 1 11(d) Correct shading 1 12(a) 11 2 M1 for 5 × 3 12(b)(i) 5a – 7b 2 M1 for 5a or –7b 12(b)(ii) 2 1 12(c)(i) 10 1 12(c)(ii) 7 2 M1 for 7x = 49 12(d) 8x + 10 or 2(4x + 5) 2 M1 for (4x + 8) or (4x + 2) 12(e) x < 3 1 12(f) [x = ] 5 [y = ] 1 with working 2 B1 for each number with working If 0 scored, SC1 for correct substitution and evaluation to find the other variable SC1 if no working shown but answers are correct 13(a) – 0.886 or – 0.8660… and 3.39 or 3.386… 2 B1 for each number If 0 scored, SC1 for (–0.89, 3.4) 13(b) (1.25 , 9.125) 2 B1 for each number 13(c) x = 1.25 1 FT their (b)