Cambridge IGCSE Mathematics - International 0607 — 2023 Oct/Nov Paper 3 · Variant 3

This document has 16 pages. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) October/November 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 [ ]. * 5 6 7 1 0 2 7 8 3 4 * DC (AP) 331339 © UCLES 2023

2 0607/33/O/N/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 0607/33/O/N/23 © UCLES 2023 [Turn over Answer all the questions. 1 The line AB is drawn on a 1 cm square grid. - 4 - 4 - 3 - 3 - 2 - 2 - 1 - 1 1 2 3 4 0 1 2 3 4 x y B A (a) Write down the coordinates of point A and point B. A = ( … , …) B = ( … , …) [2] (b) Write down the coordinates of the mid-point of AB. ( … , …) [1] (c) On the grid, plot point C at (2, 2 - ). [1] (d) On the grid, draw a straight line through C, parallel to AB. [1] (e) On the grid, draw a straight line through B, perpendicular to AB. [1]

4 0607/33/O/N/23 © UCLES 2023 2 (a) (i) Write 17 852 in words. … … [1] (ii) Write 17 852 correct to the nearest 100. … [1] (iii) Write 17 852 correct to 2 significant figures. … [1] (b) (i) Write down a multiple of 10. … [1] (ii) Write down a factor of 20. … [1] (iii) Write down a prime number between 10 and 20. … [1] (c) Find the value of (i) 62 … [1] (ii) 45. … [1] (d) (i) Find the value of n when n 10 3 30 = . n = … [1] (ii) Write these fractions in order of size, starting with the smallest. 5 2 3 1 30 11 10 3 … … … … [2] smallest

5 0607/33/O/N/23 © UCLES 2023 [Turn over (e) Work out the following, giving your answers as fractions. (i) 5 2 3 1 - … [1] (ii) 1 2 1 30 11 # … [1] 3 (a) Simplify. x y x y 3 5 7 2 4 9 + + - - + … [3] (b) Factorise completely. x x 6 15 2 + … [2] (c) Solve. ( ) x 4 7 20 + = x = … [2] (d) (i) Solve the inequality x 3 2 4 1 - . … [2] (ii) Write down the largest possible integer value of x for x 3 2 4 1 - . x = … [1]

6 0607/33/O/N/23 © UCLES 2023 4 Inaya surveys the eye colour of everyone in her class. The table shows her results. Eye colour Blue Brown Green Grey Other Number of students 5 8 10 7 2 (a) Find how many students are in the survey. … [1] (b) What is the most common eye colour? … [1] (c) One of the students is chosen at random. Find the probability that this student has grey eyes. … [1] (d) One of the students is chosen at random. Find the probability that this student has blue eyes or brown eyes. … [1] (e) There are 256 students in the school. Work out an estimate of how many of these students have green eyes. … [2]

7 0607/33/O/N/23 © UCLES 2023 [Turn over (f) Complete the bar chart to show the information in the table. 0 1 2 3 5 4 6 7 8 9 10 Blue Brown Green Eye colour Number of students Grey Other [2]

8 0607/33/O/N/23 © UCLES 2023 5 This is a sign at a golf club. AAA GOLF CLUB One round of golf: $24 each player Golf balls: $2.25 each (a) 4 friends go to the golf club to play one round of golf. They each buy 3 golf balls. Work out the total that they pay. $ … [3] (b) Ali and Ben are senior golf players. The golf club offers each senior player a 12% discount. Ali pays for them both to play one round of golf. Work out how much he pays. $ … [3] (c) There are 288 members of AAA Golf Club. The members are in the ratio male : female = 5 : 4 . Work out how many males and how many females are members of AAA Golf Club. male … female … [2]

9 0607/33/O/N/23 © UCLES 2023 [Turn over (d) These are the scores Lennie has in 10 rounds of golf. 91 76 102 73 82 89 88 71 92 86 (i) Find the mean. … [1] (ii) Find the median. … [1] (iii) Draw a stem-and-leaf diagram for the ten scores. Key : … | … means … [3] (iv) Find the range of the ten scores. … [1] (v) Lennie plays one more round of golf. After this, the range of his scores is 35. Work out the possible scores for that last round of golf. … [2]

10 0607/33/O/N/23 © UCLES 2023 6 (a) The diagram shows a quadrilateral ABCD. A D C B (i) Write down the mathematical name for this quadrilateral. … [1] (ii) Give a geometric reason for choosing your answer to part (i). … [1] (iii) Measure angle BAD. Angle BAD = … [1] (b) P Q x° y° 75° NOT TO SCALE Here is another quadrilateral. PQ is a straight line. (i) Find the value of x. x = … [1] (ii) Find the value of y. y = … [1]

11 0607/33/O/N/23 © UCLES 2023 [Turn over (c) Here is a different quadrilateral. NOT TO SCALE 5.3 m 4.5 m 2.1 m (i) Find the area of this quadrilateral. … m2 [3] (ii) Find the perimeter of this quadrilateral. … m [4]

12 0607/33/O/N/23 © UCLES 2023 7 The graph shows the cost of hiring a car. The cost, $y, depends on the distance, x km, travelled in the car. 0 0 10 20 30 40 50 60 70 80 Distance travelled (km) 90 100 110 120 130 140 150 160 x 10 20 30 40 50 60 Cost ($) 70 80 90 100 y (a) Paul hires a car and travels a distance of 120 km. Find how much this costs him. $ … [1] (b) Bushra hires a car. It costs her $50. Find the distance she travels. … km [1] (c) Find the equation of the line drawn on the grid. Give your answer in the form y mx c = + . … [3]

13 0607/33/O/N/23 © UCLES 2023 [Turn over (d) Carmen hires a car and travels a distance of 350 km. Using your answer to part (c), work out how much this costs her. $ … [2] 8 4.5 cm NOT TO SCALE x cm The area of the circle is equal to the area of the square. The length of one side of the square is x cm. Find the value of x. x = … [4]

14 0607/33/O/N/23 © UCLES 2023 9 (a) Simplify. (i) x x 6 3 # … [1] (ii) x x 5 10 2 7 … [2] (b) Expand and simplify. ( )( ) x x 9 4 + - … [2] (c) Rearrange P K B 2 = + to make K the subject. K = … [2]

15 0607/33/O/N/23 © UCLES 2023 [Turn over 10 590 km Z X Y NOT TO SCALE North X, Y and Z are three towns. Z is 590 km due South of X. Y is due West of Z. The bearing of Y from X is 220°. (a) Use trigonometry to calculate the distance XY. … km [4] (b) Work out the bearing of X from Y. … [1] Question 11 is printed on the next page.

16 0607/33/O/N/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. 11 y x 10 4 0 -2 - 10 (a) (i) On the diagram, sketch the graph of y x x 4 2 = - - for x 2 4 G G - . [2] (ii) Find the coordinates of the local minimum. ( … , …) [2] (b) On the diagram, sketch the graph of y x x 3 2 2 =- + + for x 2 4 G G - . [2] (c) Find the x-coordinate of each point of intersection of y x x 4 2 = - - and y x x 3 2 2 =- + + . x = … and x = … [2]

This document consists of 7 printed pages. © UCLES 2023 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) October/November 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 October/November 2023 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 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 October/November 2023 © UCLES 2023 Page 3 of 7 Mathematics-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, non-integer 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 or sign 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 A or B 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

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 4 of 7 Question Answer Marks Partial Marks 1(a) [A=] (−1, −3) [B=] (2, 3) 2 B1 for each 1(b) (½, 0) or (0.5, 0) 1 1(c) (2, −2) plotted correctly 1 1(d) Straight line through their C parallel to AB 1 1(e) Straight line through B perpendicular to AB 1 2(a)(i) Seventeen thousand eight hundred [and] fifty two 1 2(a)(ii) 17 900 1 2(a)(iii) 18 000 1 2(b)(i) One of 10, 20, 30, 40, etc 1 2(b)(ii) One of 1, 2, 4, 5, 10, 20 1 2(b)(iii) One of 11, 13, 17, 19 1 2(c)(i) 36 1 2(c)(ii) 1024 1 2(d)(i) 9 1 2(d)(ii) 3 1 11 2 10 3 30 5 2 M1 for correct order with one misplaced 2(e)(i) 1 15 oe fraction 1 2(e)(ii) 11 20 oe fraction 1 3(a) [1]x + 9y – 2 3 B1 for each part 3(b) 3x(2 + 5x) final answer 2 B1 for 3(2x + 5x2) or x(6 + 15x) If 0 scored, SC1 for 2x(3 + 7.5x) 3(c) −2 2 M1 for 4x + 28 = 20 or x + 7 = 5 3(d)(i) x < 2 2 M1 for 3x < 4 + 2 or better 3(d)(ii) 1 1 FT their x < n 4(a) 32 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 5 of 7 Question Answer Marks Partial Marks 4(b) Green 1 4(c) 7 32 their 1 4(d) 13 32 their 1 4(e) 80 2 M1 for 10 32 their × 256 4(f) 4 correct bars, heights [5], 8, 10, 7, 2 2 M1 for 2 or 3 correct 5(a) 123 3 M2 for 4 × 24 + 12 × 2.25 oe or M1 for 4 × 24 or 12 × 2.25 or 24 + 3 × 2.25 5(b) 42.24 3 B2 for 21.12 or M2 for 0.88 × 48 oe or M1 for 0.88 × 24 oe or for 0.12 × 24 or 0.12 × 48 oe 5(c) [Male = ] 160 [Female = ] 128 2 M1 for 288 ÷ 9 soi by 32 5(d)(i) 85 1 5(d)(ii) 87 1 5(d)(iii) 7| 1 3 6 8| 2 6 8 9 9| 1 2 10| 2 2 M1 for correct leaves unordered or for 3 correct rows Key : 10| 2 means 102 oe 1 5(d)(iv) 31 1 5(d)(v) 67 and 106 2 B1 for each 6(a)(i) trapezium 1 6(a)(ii) [only] one pair of parallel sides oe 1 6(a)(iii) 34 1 6(b)(i) 105 1 6(b)(ii) 105 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 6 of 7 Question Answer Marks Partial Marks 6(c)(i) 16.65 3 M2 for 4.5 × 2.1 + (5.3 2.1) 4.5 2 −  oe or for 4.5 × 5.3 ‒ (5.3 2.1) 4.5 2 −  oe or M1 for 4.5 × 2.1 or 4.5 × 5.3 or (5.3 2.1) 4.5 2 −  6(c)(ii) 17.4 or 17.42… 4 B3 for 5.52… or M2 for 3.22 + 4.52 or M1 for 2.1 + 4.5 + 5.3 + their 5.52 7(a) 80 1 7(b) 60 1 7(c) y = ½x + 20 3 B2 for ½x + 20 or y = ½x + k or y = mx + 20 m ≠ 0 or M1 for rise run for their triangle 7(d) 195 2 FT their y = mx + c for 2 marks M1 for substituting 350 into their y = ½x + 20 8 7.98 or 7.97 to 7.977 4 B2 for 63.5 to 63.62 or M1 for π×4.52 B1 for x2 soi 9(a)(i) x9 final answer 1 9(a)(ii) 2x5 final answer 2 B1 for 2 or x5 in answer 9(b) x2 + 5x – 36 final answer 2 B1 for three of x2 , [+] 9x , − 4x , – 36 9(c) 2P – B final answer 2 M1 for 2P = K + B or P – 2 B = 2 K

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 7 of 7 Question Answer Marks Partial Marks 10(a) 770 or 770.1 to 770.2 4 B1 for YXZ = 40 M2 for 590 cos 40 their or 590 sin 50 their or M1for cos their 40 = 590 x or sin their 50 = 590 x 10(b) 040 1 11(a)(i) 2 B1 for correct quadratic U shape 11(a)(ii) (½, −4¼) oe 2 B1 for each 11(b) 2 B1 for correct quadratic ∩ shape 11(c) −1 and 3 2 B1 for each