Cambridge IGCSE Mathematics - International 0607 — 2018 May/June Paper 3 · Variant 3

* 3 4 1 0 3 0 4 6 4 2 * This document consists of 16 printed pages. DC (ST/CT) 153518/2 © UCLES 2018 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 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 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 0607/33/M/J/18 © UCLES 2018 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 0607/33/M/J/18 © UCLES 2018 [Turn over Answer all the questions. 1 (a) Work out. . . 3 6 2 5 1 # + … [1] (b) Find. (i) 81 … [1] (ii) 812 … [1] (c) Change 4 1 to a decimal. … [1] (d) Write 56.3942 (i) correct to 2 decimal places, … [1] (ii) correct to 3 significant figures, … [1] (iii) correct to the nearest 10. … [1] (e) Calculate the interest received when (i) $600 is invested for 3 years at a rate of 2% per year simple interest, $ … [2] (ii) $600 is invested for 3 years at a rate of 2% per year compound interest. $ … [3]

4 0607/33/M/J/18 © UCLES 2018 2 Here is a list of numbers. 9 12 35 41 56 (a) From the list of numbers above, write down (i) an even number, … [1] (ii) a prime number. … [1] (b) Charee picks one of the five numbers from the list above at random. Find the probability that this number is (i) an odd number, … [1] (ii) a multiple of 4, … [1] (iii) a factor of 18. … [1]

5 0607/33/M/J/18 © UCLES 2018 [Turn over 3 (a) Three brothers, Al, Bob and Cole, go to the cinema. Their mother gives them $60 to share in the ratio of their ages. Al : Bob : Cole = 15 : 16 : 17 Al receives $18.75 . Show that Cole receives $21.25 . [2] (b) Cinema tickets cost $14 each. Al, Bob and Cole each buy a cinema ticket. Find how much money Al has left. $ … [1] (c) Popcorn (large box) $3.50 Popcorn (medium box) $2.50 Popcorn (small box) $1.50 Water $2.00 Cola $2.50 After paying for his cinema ticket, Bob wants to buy a large box of popcorn and a cola. Does he have enough money from his share of the $60? Show how you decide. [3]

6 0607/33/M/J/18 © UCLES 2018 4 Here are the ages, in years, of 21 teachers. 26 31 28 64 42 35 58 60 32 49 53 38 29 47 26 48 33 24 63 32 51 (a) Complete an ordered stem-and-leaf diagram, including the key, for these ages. Key … | … represents … [3] (b) For these ages, find (i) the range, … [1] (ii) the median, … [1] (iii) the upper quartile, … [1] (iv) the inter-quartile range. … [1]

7 0607/33/M/J/18 © UCLES 2018 [Turn over 5 4 3 2 1 –1 –1 1 2 3 4 5 –2 –3 –4 –5 –2 –3 –4 0 x y A B (a) Write down the co-ordinates of point A and point B. A ( … , … ) B ( … , … ) [2] (b) Find the co-ordinates of the midpoint of AB. ( … , … ) [1] (c) Find the gradient of AB. … [2] (d) Find the equation of the line AB. Give your answer in the form y mx c + = . y = … [2]

8 0607/33/M/J/18 © UCLES 2018 6 (a) A triangle, a rectangle and a semicircle are joined to form this shape. B 11 cm 12 cm 9 cm C E A D NOT TO SCALE CD is the diameter of the semicircle. (i) Show that the length of BE is 15 cm. [2] (ii) Find the perimeter of the shape ABCDE. … cm [3] (iii) Find the total area of the shape ABCDE. …cm2 [4]

9 0607/33/M/J/18 © UCLES 2018 [Turn over (b) The diagram shows two similar triangles, ABC and DEC. NOT TO SCALE t cm 9.6 cm 6.3 cm 85° 39° 3.2 cm r cm 2.4 cm C A B E D AB is parallel to ED. (i) Find the value of r and the value of t. r = … t = … [3] (ii) Find angle ACB. Angle ACB = … [1] (iii) Find angle CDE. Angle CDE = … [1]

10 0607/33/M/J/18 © UCLES 2018 7 Eight people were asked their age and the number of attempts they took to pass their driving test. The results are shown in the table. Age (years) 17 18 19 20 22 25 30 45 Number of attempts 1 2 3 3 6 5 4 8 (a) Complete the scatter diagram. The first 4 points have been plotted for you. 0 1 5 10 15 20 25 30 35 40 45 2 3 4 5 6 7 8 Number of attempts Age (years) [2] (b) Find (i) the mean age, … [1] (ii) the mean number of attempts. … [1]

11 0607/33/M/J/18 © UCLES 2018 [Turn over (c) (i) On the scatter diagram, plot the mean point. [1] (ii) On the scatter diagram, draw a line of best fit. [2] (iii) Use your line of best fit to estimate the number of attempts a 40 year old person might take to pass their driving test. … [1]

12 0607/33/M/J/18 © UCLES 2018 8 (a) Here are six Venn diagrams. A Diagram 1 B ∪ A Diagram 2 B ∪ A Diagram 3 B ∪ A Diagram 4 B ∪ A Diagram 5 B ∪ A Diagram 6 B ∪ Complete the table. Shaded area Venn diagram number A B , 3 A B + Al A B + l [3]

13 0607/33/M/J/18 © UCLES 2018 [Turn over (b) (i) 20 students are asked if they study history (H) or geography (G). 10 study history, 12 study geography and 3 study both history and geography. Complete the Venn diagram. ∪ H G … … … … [3] (ii) Write down the number of students who do not study history or geography. … [1]

14 0607/33/M/J/18 © UCLES 2018 9 The diagram shows a bridge for a model train set. The bridge is a cuboid with two identical tunnels. Each tunnel is a cuboid. 38 cm NOT TO SCALE 2 cm 2 cm 8 cm 2 cm 7 cm 12 cm (a) Find the shaded area. …cm2 [4] (b) Find the volume of the bridge. …cm3 [2]

15 0607/33/M/J/18 © UCLES 2018 [Turn over 10 (a) Solve. x 3 8 2 + = x = … [2] (b) (i) Solve. x 3 2 3 G - … [2] (ii) Show your answer to part (b)(i) on the number line. x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 [1] (c) Simplify. a b a b 3 2 3 + + - … [2] (d) Expand the brackets and simplify. ( )( ) x x 3 1 2 4 - + … [2] (e) Factorise completely. x y x y 3 2 3 2 - … [2] (f) P a b 3 2 2 = + (i) Find the value of P when a 2 = and b 1 =- . P = … [2] (ii) Rearrange the formula to make a the subject. a = … [2] Question 11 is printed on the next page.

16 0607/33/M/J/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. 11 x y 50 10 –20 0 ( ) ( )( ) x x x 2 5 8 f = - - (a) On the diagram, sketch the graph of ( ) y x f = for x 0 10 G G . [2] (b) Find the co-ordinates of the point where the graph crosses the y-axis. ( … , … ) [1] (c) Write down the x co-ordinate of each point where the graph crosses the x-axis. x = … and x = … [2] (d) Find the co-ordinates of the local minimum. ( … , … ) [2] (e) ( ) . x 1 4 10 g x = - Find the x co-ordinate of each point of intersection of ( ) y x f = and ( ) y x g = . x = … and x = … [2]

IGCSE™ is a registered trademark. This document consists of 7 printed pages. © UCLES 2018 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 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 May/June 2018 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 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.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 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

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 4 of 7 Question Answer Marks Partial Marks 1(a) 13.8 1 1(b)(i) 9 1 1(b)(ii) 6561 1 1(c) [0].25[0] 1 1(d)(i) 56.39 1 1(d)(ii) 56.4 1 1(d)(iii) 60 1 1(e)(i) 36 2 M1 for 600 × 3 × [0.0]2 1(e)(ii) 36.72 3 M2 for 600(1 + 0.02)3 oe soi by 636.72… or M1 for 600 × 0.02 oe soi by 12 If 0 scored, SC1 for 36 2(a)(i) 12 or 56 1 2(a)(ii) 41 1 2(b)(i) 3 5 oe 1 2(b)(ii) 2 5 oe 1 2(b)(iii) 1 5 oe 1 3(a) [ ] 60 1.25 15 16 17 = + + M1 [ ] 18.75 1.25 15 = 1.25 17 21.25 × = M1 3(b) 4.75 1 3(c) 60 – (18.75 + 21.25) [=20] M1 or 1.25 × 16 [=20] $3.50 + $2.50 + $14 [=20] oe M1 Yes A1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 5 of 7 Question Answer Marks Partial Marks 4(a) 2 4 6 6 8 9 3 1 2 2 3 5 8 4 2 7 8 9 5 1 3 8 6 0 3 4 2 B1 for correct order with 1 or 2 errors or for incorrect order with 0 or 1 error [Key] 2 4 = 24 oe 1 4(b)(i) 40 1 4(b)(ii) 38 1 4(b)(iii) 52 1 4(b)(iv) 22 1 5(a) (–4, –3) (4, 1) 2 B1 for each 5(b) (0, –1) 1 5(c) [0].5 oe 2 M1 for rise run their their 5(d) [0].5x – 1 2 FT their gradient in (c) B1 for [ ] 1 or 0 .5 kx x k − − 6(a)(i) [BE2 =] 92 + 122 M1 [ ] 225 15 BE = = M1 6(a)(ii) 66.6 or 66.56 to 66.57 3 M2 for 7.5 11 11 12 9 π + + + + or M1 for 7.5 or1 1 11 12 9 π + + + 6(a)(iii) 307 or 307.3 to 307.4 4 M3 for [ ] 2 0 .5 12 9 11 15 0.5 7.5 × × + × + × π× or M2 for two correct areas or M1 for one correct area 6(b)(i) [r = ] 2.1 [t = ] 7.2 3 B2 for one correct answer seen or M1 for 9.6 3.2 or 3.2 9.6 soi 6(b)(ii) 56 1 6(b)(iii) 85 1 7(a) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted 7(b)(i) 24.5 1 7(b)(ii) 4 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 6 of 7 Question Answer Marks Partial Marks 7(c)(i) Point plotted correctly 1 FT their (b)(i) and (b)(ii) 7(c)(ii) Correct straight ruled line 2 B1 for ruled line through their mean point or for ruled line with positive gradient 7(c)(iii) 7 1 FT from their straight ruled line with positive gradient 8(a) 1 4 5 3 B1 for each 8(b)(i) 3 B1 for “3” in correct place B1 for one other number in correct place 8(b)(ii) 1 1 FT their diagram 9(a) 232 4 M3 for 3 × (2 × 12) + 2 × (16 × 5) or for 38 × 5 + 3 × (7 × 2) or for 38 × 12 – 2 × 7 × 16 or M2 for two correct areas or M1 for one correct area If M0 scored, SC1 for 16 or 5 seen 9(b) 1856 2 FT their (a) × 8 evaluated M1 for their (a) × 8 10(a) 2 − 2 M1 for 3x = – 6 10(b)(i) 0 x . 2 M1 for −2x ⩽ 3 – 3 or 3 – 3 ⩽ 2x oe If 0 scored, SC1 for x = 0 as final answer 10(b)(ii) Filled in circle at 0 and arrow in correct direction. 1 FT their (b)(i) as long as it is an inequality 10(c) 4a – [1]b final answer 2 B1 for 4a or – [1]b 10(d) 6x2 +10x – 4 final answer 2 B1 for any three of 6x2, [+]12x, −2x, −4 10(e) x2y ([1]y2 – 3) final answer 2 M1 for correct partial factorisation 10(f)(i) 8 2 M1 for 3(2) + 2(–1)2 10(f)(ii) 2 2 3 P b − oe 2 M1 for correct rearrangement to isolate “a” or for correct division by 3

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 7 of 7 Question Answer Marks Partial Marks 11(a) Correct sketch 2 B1 for minimum under positive x-axis or for intercepts in approximately the correct place 11(b) (0, 40) 1 11(c) 2.5 8 2 B1 for each 11(d) (5.25, –15.125) 2 B1 for each 11(e) 3.24 or 3.237 to 3.238 8.7[0] or 8.699 to 8.7[00] 2 B1 for each If 0 scored, SC1 for 3.2 and 8.7