Cambridge IGCSE Mathematics - International 0607 — 2019 May/June Paper 3 · Variant 2

This document consists of 16 printed pages. DC (SC/TP) 168252/2 © UCLES 2019 [Turn over * 9 2 5 2 8 9 8 3 3 1 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 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. Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education

2 0607/32/M/J/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 0607/32/M/J/19 © UCLES 2019 [Turn over Answer all the questions. 1 (a) Write in words the number 27 003. … [1] (b) Write 0.37 as a fraction. … [1] (c) Write down a square number between 30 and 50. … [1] (d) Complete the list of factors of 12. … , 2 , … , … , 6 , … [2] (e) Work out . . 2 6 0 72 - . … [1] 2 Mr and Mrs Tan and their three children go on a boat trip. (a) One adult fare costs $15 and one child fare costs $8. (i) Find the total cost of their fares. $ … [2] (ii) Find how much change they receive from $100. $ … [1] (b) The boat sails 6 km in 90 minutes. Work out the speed of the boat in km/h. …km/h [3]

4 0607/32/M/J/19 © UCLES 2019 3 (a) The bar chart shows the number of pieces of different types of fruit in a basket. Oranges Apples Grapes Bananas Cherries 0 2 4 6 8 10 12 14 Number of pieces of fruit (i) Find the total number of pieces of fruit in the basket. … [1] (ii) Find how many more cherries there are than oranges. … [1] (iii) One piece of fruit is chosen at random from the basket. Find the probability that it is a banana. … [1] (iv) Find the percentage of pieces of fruit in the basket that are apples. …% [2]

5 0607/32/M/J/19 © UCLES 2019 [Turn over (b) 15 18 21 32 11 8 34 17 21 6 45 From this list of eleven numbers, find (i) the mode, … [1] (ii) the range, … [1] (iii) the median, … [1] (iv) the mean, … [1] (v) the lower quartile, … [1] (vi) the inter-quartile range. … [1]

6 0607/32/M/J/19 © UCLES 2019 4 (a) Write down the correct mathematical name for each shape. … … … … [4]

7 0607/32/M/J/19 © UCLES 2019 [Turn over (b) 52° 88° NOT TO SCALE A D E F C B ABC is parallel to DEF, DB is parallel to EC and BE is parallel to CF. Angle ABD = 52° and angle DEB = 88°. Find the size of (i) angle BDE, Angle BDE = … [1] (ii) angle DBE, Angle DBE = … [1] (iii) angle CFE, Angle CFE = … [1] (iv) angle CBE, Angle CBE = … [1] (v) angle BEC. Angle BEC = … [1]

8 0607/32/M/J/19 © UCLES 2019 5 (a) Siobhan makes a rabbit run in the shape of a right-angled triangle. She uses x metres of the garden fence for one side of the run. The other two sides are made from 36 metres of wire mesh, as shown in the diagram. x m 20 m 16 m NOT TO SCALE FENCE (i) Work out the value of x. x = … [3] (ii) Find the area of garden used for the run. …m2 [1] (b) Siobhan’s friend makes a rabbit run in the shape of a square. She uses y metres of the garden fence for one side of the run. The other three sides are made from 36 metres of wire mesh. y m NOT TO SCALE FENCE (i) Work out the value of y. y = … [1] (ii) Find the area of garden used for the square run. …m2 [1]

9 0607/32/M/J/19 © UCLES 2019 [Turn over 6 –2 2 4 6 8 10 12 14 – 4 – 6 –8 –10 –12 –14 6 4 8 10 12 2 –2 – 4 – 6 0 y x The diagram shows the graph of ( ) y x f = . (a) Write down the zeros of ( ) y x f = . x = … or x = … [1] (b) On the diagram, draw the line of symmetry of ( ) y x f = . [1] (c) Write down the co-ordinates of the y-intercept. ( … , … ) [1] (d) On the diagram (i) sketch the image of the graph of ( ) y x f = after reflection in the x-axis, [1] (ii) sketch the graph of ( ) y x 2 f = + , [1] (iii) sketch the graph of ( ) y x 3 f = + . [1]

10 0607/32/M/J/19 © UCLES 2019 7 (a) Joska and Sem go to the cinema to see a film. The film starts at 15 45 and lasts for 1 hour 53 minutes. Work out the time that the film ends. … [1] (b) NOT TO SCALE 6 cm 6 cm 10 cm The cinema shop sells popcorn in small boxes and large boxes. Each box is a cuboid and the cuboids are mathematically similar. The small box has dimensions 6 cm by 6 cm by 10 cm. The ratio of dimensions small box : large box = 2 : 3. Work out the dimensions of a large box. … cm by … cm by … cm [2] (c) Find the volume of a small box and the volume of a large box. small box = …cm3 large box = …cm3 [2] (d) A small box of popcorn costs $2.50 and a large box of popcorn costs $4.00 . Find which box of popcorn is the better value. Show all your working. … [2] (e) Write your answers to part (c) as a ratio in its simplest form. volume of small box : volume of large box = … : … [1]

11 0607/32/M/J/19 © UCLES 2019 [Turn over 8 (a) Show x 2 2- on the number line. – 4 –5 –3 –2 –1 0 1 2 x [1] (b) Solve. (i) x 3 5 = x = … [1] (ii) x 11 9 13 - = x = … [2] (c) Expand and simplify. ( )( ) x x 2 7 3 - + … [2] (d) Factorise completely. xy y 2 6 2 - … [2] (e) Simplify fully. x x 4 7 5 3 # … [2]

12 0607/32/M/J/19 © UCLES 2019 9 The mass of each of eight cars, in kg, and the time taken, in seconds, each takes to reach a speed of 100 km/h is recorded. Mass (kg) 1200 1290 1320 1410 1430 1490 1580 1650 Time (seconds) 11.4 10.3 10.9 6.1 7.0 4.4 4.2 3.9 (a) Complete the scatter diagram. The first four points have been plotted for you. 1100 0 1 2 3 4 5 6 7 8 9 11 10 12 1200 1300 Mass (kg) Time (seconds) 1400 1500 1600 1700 [2] (b) Write down the type of correlation shown in the scatter diagram. … [1]

13 0607/32/M/J/19 © UCLES 2019 [Turn over (c) (i) Find the mean mass. … kg [1] (ii) Find the mean time. … seconds [1] (iii) On the scatter diagram, draw a line of best fit. [2] (d) Use your line of best fit to find an estimate of the time taken to reach 100 km/h for a car that has a mass of 1550 kg. … seconds [1] 10 Some students are asked if they travel to school by tram (T) or bicycle (B) or both. 17 travel by tram, 14 travel by bicycle and 6 travel by both tram and bicycle. (a) Show this information on the Venn diagram. T B … … … U [2] (b) The total number of students asked is 30. Work out the number of students who do not travel to school by tram or bicycle or both. … [1] (c) One of the 30 students is chosen at random. Find the probability that this student travels to school by bicycle and not by tram. … [1] (d) On the Venn diagram, shade the region ( ) T B , l. [1]

14 0607/32/M/J/19 © UCLES 2019 11 The shape, , is shown on the diagram. – 4 –3 –2 –1 1 0 2 3 4 5 6 7 8 6 5 4 3 9 8 7 6 2 1 –1 –2 –3 – 4 y x On the diagram, draw the image of after (a) a rotation of 180° about the origin, [2] (b) a translation by the vector 1 3 - e o, [2] (c) an enlargement, scale factor 2, with centre (0, 0). [2]

15 0607/32/M/J/19 © UCLES 2019 [Turn over 12 Here is a sequence of patterns. Pattern 1 Pattern 2 Pattern 3 Pattern 4 (a) In the space above, draw Pattern 4. [1] (b) Complete the table. Pattern number 1 2 3 4 5 Number of dots 2 [2] (c) Write down the rule for continuing the sequence of numbers of dots. … [1] (d) Find an expression for the nth term of the sequence of numbers of dots. … [2] (e) Zoe thinks that 134 is a term in this sequence. Is she correct? Show how you decide. … because … [2] Question 13 is printed on the next page.

16 0607/32/M/J/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. 13 5 –5 5 –5 y x 0 ( )x x 2 f = (a) On the diagram, sketch the graph of ( ) y x f = for values of x between 5 - and 5. [2] (b) Write down the equation of the vertical asymptote. … [1] (c) On the same diagram, sketch the graph of y x 2 = for x 5 5 G G - . [2] (d) Find the values of x when x x 2 2 = . x = … or x = … [2]

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 0607/32 Paper 3 (Core) May/June 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 May/June 2019 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 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.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 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) Twenty-seven thousand [and] three 1 1(b) 37 100 1 1(c) 36 or 49 1 1(d) 1, … , 3, 4, … ,12 2 B1 for 2 correct factors. 1(e) 1.12 or 1.122… 1 2(a)(i) 54 2 M1 for 2 15 × or 3 8 × 2(a)(ii) 46 1 FT 100 – their (a)(i) 2(b) 4 3 M2 for 6 60 90 × oe or M1 for 6 90

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 4 of 7 Question Answer Marks Partial Marks 3(a)(i) 36 1 3(a)(ii) 7 1 3(a)(iii) 5 36 1 FT their (a) 3(a)(iv) 16.7 or 16.66 to 16.67 or 16 2 3 2 M1 for 6 their(a) 3(b)(i) 21 1 3(b)(ii) 39 1 3(b)(iii) 18 1 3(b)(iv) 20.7 or 20.72 to 20.73 1 3(b)(v) 11 1 3(b)(vi) 21 1 4(a) Equilateral triangle Trapezium Cuboid Cone 4 B1 for each 4(b)(i) 52 1 4(b)(ii) 40 1 4(b)(iii) 88 1 4(b)(iv) 88 1 4(b)(v) 40 1 FT their (b)(ii) 5(a)(i) 12 3 M2 for 2 2 2 20 16 = − x or M1 for 2 2 2 20 16 = + x 5(a)(ii) 96 1 FT their (a)(i) 5(b)(i) 12 1 5(b)(ii) 144 1 Strict FT their (b)(i) 6(a) 2 and 6 1 6(b) Correct ruled line of symmetry 1 6(c) (0, 12) 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 5 of 7 Question Answer Marks Partial Marks 6(d)(i) Correct sketch 1 6(d)(ii) Correct sketch 1 6(d)(iii) Correct sketch 1 7(a) 17 38 or 5.38 pm 1 7(b) 9 by 9 by 15 2 B1 for 9 or 15 7(c) 360 1215 2 B1 for each FT their (b) 7(d) Correctly finding one ratio B1 for 2.5 0.00694... 360 = or 360 144... 2.5 = or 4 0.00329... 1215 = their or 1215 303.75 4 = their Correctly finding the second ratio in the same form leading to the correct conclusion. B1 large box is the best buy 7(e) 8 : 27 1 FT their (c) 8(a) 1 8(b)(i) 15 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 6 of 7 Question Answer Marks Partial Marks 8(b)(ii) 2 2 M1 for 11x = 13 + 9 or 9 13 11 11 − = x 8(c) 2 2 21 + − x x 2 M1 for any 2 of 2 2x or 6 −x or 7x or 21 − 8(d) 2 ( 3 ) − y x y 2 M1 for 2 2( 3 ) − xy y or ( ) 2 6 − y x y or 2 ( 3 ) + y x y 8(e) 8 28x 2 M1 for 8 28 or kx kx 9(a) Points plotted correctly 2 B1 for 2 or 3 correct 9(b) negative 1 9(c)(i) 1421.25 1 9(c)(ii) 7.275 1 9(c)(iii) Ruled line of best fit 2 M1 for negative slope through mean but not in tolerance or M1 for line in tolerance but not through mean 9(d) 4.5 to 5 1 FT their line of best fit with negative gradient. 10(a) 2 B1 for 6 in intersection 10(b) 5 1 FT from their diagram 10(c) 8 30 oe 1 FT from their diagram 10(d) Correct shading 1 11(a) Correct image (−1, −1), (−1, −2.5), (−1, −4), (−3, −1), (−3, −4), 2 B1 for 180° rotation about another point 11 6 8 T B U

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 7 of 7 Question Answer Marks Partial Marks 11(b) Correct image (2, 1), (2, −0.5), (2, −2), (4, 1), (4, −2), 2 B1 for translation of 1 or 3 k k       −    11(c) Correct image (2, 2), (6, 2), (2, 5), (2, 8), (6, 8) 2 B1 for enlargement, scale factor 2, from different centre 12(a) Correct pattern 1 12(b) [2] 5 8 11 14 2 B1 for 2 correct 12(c) Add 3 oe 1 12(d) 3n – 1 2 M1 for 3n – k or jn – 1, j ≠ 0 12(e) Equating their nth term to 134 M1 Solving and correct conclusion A1 13(a) Correct sketch 2 M1 for part of curve correctly drawn in 1st quadrant or 3rd quadrant 13(b) x = 0 1 13(c) Correct ruled line 2 M1 for positive slope M1 for passing through (0, 0) 13(d) 2 − 2 2 B1 for each