Cambridge IGCSE Mathematics - International 0607 — 2023 May/June Paper 3 · Variant 2

This document has 16 pages. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2023 1 hour 45 minutes You must answer on the question paper. You will need: Geometrical instruments INSTRUCTIONS ● Answer all questions. ● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. ● Write your name, centre number and candidate number in the boxes at the top of the page. ● Write your answer to each question in the space provided. ● Do not use an erasable pen or correction fluid. ● Do not write on any bar codes. ● You should use a graphic display calculator where appropriate. ● You may use tracing paper. ● You must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. ● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. ● For r, use your calculator value. INFORMATION ● The total mark for this paper is 96. ● The number of marks for each question or part question is shown in brackets [ ]. * 0 9 3 9 6 1 7 5 4 5 * DC (CJ/JG) 311909/4 © UCLES 2023

2 0607/32/M/J/23 © UCLES 2023 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle, radius r. A = r2 r 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 = r 4 2 r 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 = r h 2 r 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/23 © UCLES 2023 [Turn over Answer all the questions. 1 (a) Show that, in a year of 365 days, there are 31 536 000 seconds. [2] (b) (i) Write 31 536 000 in words. … … [1] (ii) Write 31 536 000 in standard form. … [1] (c) Write down all the factors of 49. … [2] (d) Write 4 1 as a percentage. … % [1] (e) Find 604 . Give your answer correct to 3 decimal places. … [2] (f) Work out . . . 4 85 3 26 2 31 # - . Give your answer correct to 4 significant figures. … [2] (g) Write these numbers in order of size, starting with the smallest. 5.6 5.56 5.06 5.65 … … … … [2] smallest

4 0607/32/M/J/23 © UCLES 2023 2 33 students in a class write down the number of siblings they each have. The results are shown in this bar chart. 0 Frequency 8 10 12 6 4 2 0 1 2 3 4 5 Number of siblings (a) Write down the mode. … [1] (b) (i) Write down the number of students that have 0 siblings. … [1] (ii) Work out how many more students have 2 siblings rather than have 5 siblings. … [1] (c) One of the 33 students is chosen at random. (i) Find the probability that this student has 3 siblings. … [1] (ii) Find the probability that this student has more than 1 sibling. … [2]

5 0607/32/M/J/23 © UCLES 2023 [Turn over 3 (a) Petrol costs $0.76 per litre. Work out the amount of petrol that can be bought with $10. … litres [2] (b) Company A and Company B have cars to rent. Company A charges $50 for the first day and $28 for each additional day. (i) Find the cost of renting a car from Company A for 4 days. $ … [2] (ii) Company B charges $200 to rent a car for a week. Selma wants to rent a car for 2 weeks. Work out whether Company A or Company B is cheaper for Selma. You must show all your working. [3]

6 0607/32/M/J/23 © UCLES 2023 4 The Burj Khalifa has a height of 828 metres. Sky Level is a floor in the Burj Khalifa at a height of 555 metres. (a) Work out the difference in height between Sky Level and the top of the Burj Khalifa. … m [1] (b) An elevator takes visitors the 555 metres up to Sky Level. The elevator travels at an average speed of 10 metres per second. (i) Work out how many seconds it takes for the elevator to reach Sky Level. … s [1] (ii) Change 10 metres per second to kilometres per hour. … km/h [2] (c) In year 1, 1.66 million people visited the Burj Khalifa. In year 2, 13% more people visited the Burj Khalifa. Work out the number of people who visited the Burj Khalifa in year 2. … million [2]

7 0607/32/M/J/23 © UCLES 2023 [Turn over 5 (a) T a b 5 2 = - (i) Find T when . a 2 34 = and . b 1 68 = . T = … [2] (ii) Find a when . T 12 6 = and . b 1 2 = . a = … [2] (iii) Rearrange the formula to make b the subject. b = … [2] (b) ( ) ( ) x x 3 7 f = - (i) Find ( ) 10 f . … [1] (ii) Find the value of x when ( ) . f x 34 5 =- . x = … [3]

8 0607/32/M/J/23 © UCLES 2023 6 The cumulative frequency curve shows the times, in minutes, taken by 200 students to travel to school. 200 180 160 140 120 100 80 60 40 20 0 0 10 20 30 40 50 60 Cumulative frequency Time (minutes) (a) Find (i) the median … min [1] (ii) the interquartile range. … min [2] (b) Work out the number of students who took more than 36 minutes to travel to school. … [2]

9 0607/32/M/J/23 © UCLES 2023 [Turn over (c) (i) Use the cumulative frequency curve to complete the frequency table. Time (m minutes) Frequency 0 1 m G 10 10 1 m G 20 20 1 m G 30 30 1 m G 40 40 1 m G 50 50 1 m G 60 [2] (ii) Write down the mid-point of the group m 0 10 1 G . … [1] (iii) Using the mid-point of each group, work out an estimate for the mean. … min [2]

10 0607/32/M/J/23 © UCLES 2023 7 (a) Use a ruler to draw a suitable angle in each of the spaces provided. Mark each angle with an arc. A right angle An obtuse angle An acute angle A reflex angle [3] (b) G F H E 52° 94° a° b° d° c° A B C D NOT TO SCALE AB is parallel to CD. EF and GH are straight lines. Work out the size of angle a, angle b, angle c and angle d. Angle a = … Angle b = … Angle c = … Angle d = … [5]

11 0607/32/M/J/23 © UCLES 2023 [Turn over 8 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 y A B C x 1 – 1 – 2 –3 – 4 – 5 4 5 6 7 8 3 2 (a) Describe fully the single transformation that maps shape A onto shape B. … … [2] (b) Describe fully the single transformation that maps shape A onto shape C. … … [3] (c) Translate shape A by vector 5 3 - - e o . [2]

12 0607/32/M/J/23 © UCLES 2023 9 A S B C D T NOT TO SCALE The diagram shows a pyramid, ABCDS. The base, ABCD, is a square of side 8.4 cm. This diagram shows the square base. NOT TO SCALE 8.4 cm D A B C (a) Show that . cm BD 11 9 = , correct to 3 significant figures. [2]

13 0607/32/M/J/23 © UCLES 2023 [Turn over (b) 50° S T D B T is the mid-point of diagonal DB with S vertically above T. ST is the height of the pyramid. Angle SBT is 50°. Use trigonometry to work out the length of ST. … cm [2] (c) Work out the volume of the pyramid. … cm3 [2]

14 0607/32/M/J/23 © UCLES 2023 10 (a) Complete this statement using one of or or 1 2 =. … 4 4096 2 3 [1] (b) Solve. x 2 5 9 - =- x = … [2] (c) Factorise completely. x x 6 2 2 + … [2] (d) Expand and simplify. ( ) x 3 1 2 - … [2] (e) On the number line, show the inequality x 2 G- . – 4 – 5 – 3 – 2 – 1 0 1 2 3 4 5 x [1] (f) Write as a single fraction in its simplest form. (i) a a 5 6 3 2 + … [2] (ii) c c 3 8 16 3 # … [2]

15 0607/32/M/J/23 © UCLES 2023 [Turn over 11 On any school day, the probability that Mindy wakes before 7am is 0.80 . When Mindy wakes before 7am, the probability that she gets to school on time is 0.92 . When Mindy does not wake before 7am, the probability that she gets to school on time is 0.23 . (a) Complete the tree diagram. 0.80 wakes before 7am does not wake before 7am does not get to school on time gets to school on time does not get to school on time gets to school on time …… …… …… …… …… [3] (b) Find the probability that, on one school day, Mindy does not wake before 7am and gets to school on time. … [2] Question 12 is printed on the next page.

16 0607/32/M/J/23 © UCLES 2023 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 Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. 12 y x 0 – 10 25 – 2 5 (a) On the diagram, sketch the graph of for y x x x 2 5 3 2 5 2 G G = - - - . [2] (b) On the same diagram, sketch the graph of for y x x 5 2 5 G G = + - . [2] (c) Find the x-coordinate of each point of intersection of and y x x y x 2 5 3 5 2 = - - = + . x = … and x = … [2]

This document consists of 8 printed pages. © UCLES 2023 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2023 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 2023 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 2023 © UCLES 2023 Page 2 of 8 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 2023 © UCLES 2023 Page 3 of 8 Maths-Specific Marking Principles 1 Unless a particular method has been specified in the question, full marks may be awarded for any correct method. However, if a calculation is required then no marks will be awarded for a scale drawing. 2 Unless specified in the question, answers may be given as fractions, decimals or in standard form. Ignore superfluous zeros, provided that the degree of accuracy is not affected. 3 Allow alternative conventions for notation if used consistently throughout the paper, e.g. commas being used as decimal points. 4 Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw). 5 Where a candidate has misread a number in the question and used that value consistently throughout, provided that number does not alter the difficulty or the method required, award all marks earned and deduct just 1 mark for the misread. 6 Recovery within working is allowed, e.g. a notation error in the working where the following line of working makes the candidate’s intent clear. 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 May/June 2023 © UCLES 2023 Page 4 of 8 Question Answer Marks Partial Marks 1(a) 365 24 60 60[ ]31536000     M2 M1 for [365 ] 24  60 or [365 ] 60  60 1(b)(i) Thirty-one million, five hundred [and] thirty-six thousand 1 1(b)(ii) 7 3.15[36] 10  1 1(c) 1, 7, 49 2 B1 for 2 correct factors and no extras or for 3 correct and 1 extra 1(d) 25 1 1(e) 24.576 2 M1 for 24.5764… or for their answer to more than 3dp correctly rounded to 3dp. 1(f) ‒2.681 2 M1 for [‒]2.680[6] or for their answer to more than 4sf correctly rounded to 4sf 1(g) 5.06 5.56 5.6 5.65 2 B1 for 3 correct when one is covered up 2(a) 1 1 2(b)(i) 4 1 2(b)(ii) 8 1 2(c)(i) 5 33 oe 1 2(c)(ii) 18 33 oe 2 B1 for 9 + 5 + 3 + 1 soi by 18 3(a) 13.1 to 13.2 2 M1 for 10 0.76 oe 3(b)(i) 134 2 M1 for [50 ]3 28   3(b)(ii) Company A: 50 13 28 414    M1 Company B: 2 200 400   M1 Company B clearly indicated as cheapest A1 Dep on at least M1 If 0 scored, SC1 for their correct conclusion after seeing a price for A and B

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 5 of 8 Question Answer Marks Partial Marks 4(a) 273 1 4(b)(i) 55.5 1 4(b)(ii) 36 2 M1 for dividing by 1000 or multiplying by 60  60 4(c) 1.88 or 1.8758 2 M1 for 13 1.66 100  oe soi by 0.2158 5(a)(i) 8.34 2 M1 for 5(2.34) or –2(1.68) 5(a)(ii) 3 2 M1 for 12.6 5 2(1.2)   a oe 5(a)(iii) 5 2   T a or 5 2  a T or 5 2 2  a T oe final answer 2 M1 for 5 2   T a b or 5 2 2   T a b or 2 5   T b a 5(b)(i) 9 1 5(b)(ii) –4.5 3 M1 for 3 21 34.5   x or 34.5 7 3    x M1 for their correct next step to isolate the x term 6(a)(i) 30 1 6(a)(ii) 16 2 B1 for 38 or 22 seen 6(b) 60 2 B1 for 140 seen 6(c)(i) 20 20 60 60 30 10 2 B1 for 4 or 5 correct 6(c)(ii) 5 1 6(c)(iii) 29.5 2 M1 for correct use of mid- points and their frequencies

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 6 of 8 Question Answer Marks Partial Marks 7(a) Correct drawing e.g. 3 B2 for 3 correct or B1 for 1 correct 7(b) [a =] 94 1 [b =] 52 1 [c =] 86 1 [d =] 138 2 FT their b + their c M1 for 180 – (their b + their c) soi by 42 8(a) Reflection y–axis or x = 0 2 B1 for each 8(b) Rotation 90 clockwise oe (0, 0) or origin 3 B1 for each 8(c) Correct translation (–4, –3), (–4, –1), (–1, –3), (–1, –1), (–2, –2) 2 B1 for translation of 5 y        or 3 x         9(a) 8.42 + 8.42 M1 11.87… or 11.88 [= 11.9 to 3sf] A1 9(b) 7.09 or 7.090 to 7.091 2 M1 for tan 50 = 11.9 2 ST or 11.9 2  ST oe 9(c) 167 or 166.7 to 166.8 2 M1 for 1 8.4 8.4 3   their(b) 10(a) = 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 7 of 8 Question Answer Marks Partial Marks 10(b) –2 2 M1 for 2 9 5  x or 5 9 2 2   x 10(c) 2 (3 1)  x x final answer 2 M1 for   2 2 3  x x or (6 2)  x x 10(d) 2 9 6 1   x x final answer 2 M1 for any three correct from 9x2, –3x, –3x, +1 10(e) 1 10(f)(i) 28 15 a final answer 2 M1 for correct denominator 10(f)(ii) 2 2 c final answer 2 M1 for correctly cancelling the 8 and 16 or the threes or for 2 24 48 c or better 11(a) Correct tree diagram 3 B2 for 3 or 4 correct probabilities correctly placed or B1 for 2 correct probabilities correctly placed 11(b) 0.046 oe isw 2 M1 for their 0.20  0.23 3 2 1 0 –5 –1 –2 –3 –4

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 8 of 8 Question Answer Marks Partial Marks 12(a) Correct sketch 2 B1 for correct shape B1 for minimum in correct quadrant 12(b) Correct line drawn 2 B1 for line with positive gradient B1 for crossing the y-axis closer to 0 than 25 12(c) –1 and 4 2 B1 for each