Cambridge IGCSE Mathematics - International 0607 — 2022 Oct/Nov Paper 3 · Variant 3

This document has 16 pages. [Turn over DC (CJ) 316553 © UCLES 2022 * 3 4 9 4 0 1 5 9 4 6 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) October/November 2022 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 [ ]. Cambridge IGCSE™

2 0607/33/O/N/22 © UCLES 2022 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/22 © UCLES 2022 [Turn over Answer all the questions. 1 (a) Write the two missing terms in this sequence. 40 33 26 … 12 … 2 - [2] (b) Work out. (i) 256 31 68 # - … [1] (ii) 4 4 3 2 - … [1] (c) Find the value of 105 3 . Give your answer correct to 4 significant figures. … [2] (d) Write 7 2 as a percentage. Give your answer correct to 3 decimal places. …% [2] (e) Find 24% of $6.50 . $ … [2] (f) Write 5 5 5 5 5 5 # # # # # as a power of 5. … [1] (g) Work out . . 3 1 10 2 6 10 5 4 # # + . Give your answer in standard form. … [2]

4 0607/33/O/N/22 © UCLES 2022 2 (a) Each diagram shows a circle, centre O. Complete each diagram with a correct straight line. O Radius O Chord O Diameter O Tangent [4] (b) A circle has radius 4 cm. Work out the circumference of this circle. … cm [2]

5 0607/33/O/N/22 © UCLES 2022 [Turn over 3 60 cm 40 cm NOT TO SCALE A flag measures 60 cm by 40 cm. In the centre of the flag is a shaded cross with all sides 10 cm. All the angles are right angles. (a) Work out the area of the cross. … cm2 [2] (b) Find the area of the cross as a percentage of the total area of the flag. …% [2] (c) Write down the order of rotational symmetry of the flag. … [1] (d) Draw all the lines of symmetry of the flag. [2]

6 0607/33/O/N/22 © UCLES 2022 4 (a) A teacher buys a packet of raisins for each of her 18 mathematics students. Each student counts the number of raisins in their packet. 28 29 28 30 28 28 29 27 29 29 30 29 28 27 27 30 28 30 (i) Complete the frequency table. Number of raisins Frequency 27 28 29 30 [2] (ii) Write down the mode. … [1] (iii) Work out the mean number of raisins in a packet. … [2] (iv) One of these 18 students is chosen at random. Find the probability that there were 29 raisins in their packet. … [1]

7 0607/33/O/N/22 © UCLES 2022 [Turn over (b) Another teacher buys a packet of raisins for each of his 24 mathematics students. The numbers of raisins in these packets are shown in the table. Number of raisins Frequency 27 4 28 7 29 8 30 5 The teacher asks his students to draw a pie chart to show the information in the table. (i) Show that the sector angle for 27 raisins is 60°. [2] (ii) Complete the pie chart to show the numbers of raisins in these packets. 60° 27 [3]

8 0607/33/O/N/22 © UCLES 2022 5 Maisy is a plumber. (a) Maisy buys 5 pipes that each cost $13 and 2 taps that each cost $32. Work out the total she pays. $ … [2] (b) Maisy has a fixed call-out charge of $25 plus a charge of $35 for each hour, h, that she works. The total charge is $T. (i) Write a formula for T in terms of h. … [2] (ii) Work out the total charge when Maisy works for 3 hours. $ … [2] (iii) Giselle pays Maisy a total charge of $200. Work out the number of hours that Maisy worked. … [2] (c) Maisy invests $3000 for 4 years at a rate of 2% per year compound interest. Calculate the amount of interest she receives at the end of the 4 years. $ … [3]

9 0607/33/O/N/22 © UCLES 2022 [Turn over 6 (a) Simplify. (i) t t t 3 2 - + … [1] (ii) x y x y 6 3 2 - - + … [2] (b) Solve. (i) x 8 2 = x = … [1] (ii) x 17 16 + = x = … [1] (iii) x 25 2 4 2 - … [2] (c) Write as a single fraction in its simplest form. (i) a a 7 2 21 2 - … [2] (ii) p p 8 9 3 4 2 # … [2]

10 0607/33/O/N/22 © UCLES 2022 7 The frequency table shows the length of time, t seconds, of 60 telephone calls answered by a doctor’s receptionist. Time (t seconds) Frequency t 0 15 1 G 2 t 15 30 1 G 4 t 30 45 1 G 9 t 45 60 1 G 12 t 60 75 1 G 15 t 75 90 1 G 12 t 90 105 1 G 4 t 105 120 1 G 2 (a) Write down the modal class. … t 1 G … [1] (b) Complete the cumulative frequency table. Time (t seconds) Cumulative frequency t 15 G 2 t 30 G 6 t 45 G t 60 G t 75 G t 90 G t 105 G t 120 G 60 [1]

11 0607/33/O/N/22 © UCLES 2022 [Turn over (c) Complete the cumulative frequency curve. 0 0 10 20 30 40 50 60 20 40 60 80 Time (seconds) 100 120 Cumulative frequency t [3] (d) Use your curve to find (i) the median, … s [1] (ii) the lower quartile, … s [1] (iii) the number of calls that lasted more than 80 seconds. … [2]

12 0607/33/O/N/22 © UCLES 2022 8 y x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 – 1 1 2 3 4 5 – 2 – 3 – 4 – 5 C The diagram shows a 1cm2 grid with the point C plotted. (a) On the grid, plot the points A( 4 - , 2) and B(2, 4). [2] (b) Join the points A, B and C to form a triangle and write down the mathematical name of triangle ABC. … [1]

13 0607/33/O/N/22 © UCLES 2022 [Turn over (c) Find (i) the coordinates of the mid-point of AB, ( … , … ) [1] (ii) the gradient of the line AB. … [2] (d) Use Pythagoras’ Theorem to calculate the length of AB. … [2] (e) Reflect triangle ABC in the x-axis. [1]

14 0607/33/O/N/22 © UCLES 2022 9 (a) U = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21} A is the set of odd numbers. B is the set of multiples of 3. (i) List the elements of the following sets. (a) A … [1] (b) B … [1] (c) A B + … [1] (ii) Complete the Venn diagram by writing each element in the correct subset. U A B [2] (b) Use set notation to describe the region shaded in each Venn diagram. U P Q U P Q … … [2]

15 0607/33/O/N/22 © UCLES 2022 [Turn over 10 20 m 20 m 22 m N M Y X O B A 35° NOT TO SCALE The diagram shows a circular Big Wheel with radius 20 metres. The centre, O, of the Big Wheel is 22 metres vertically above horizontal ground. A and B mark the positions of two seats on the Big Wheel. OA makes an angle of 35° with the horizontal line XOY. (a) Find the vertical distance, AM, of A above the ground. AM = … m [3] (b) The vertical distance of B above the ground, BN, is 38 metres. Work out the size of angle XBO. Angle XBO = … [3] Question 11 is printed on the next page.

16 0607/33/O/N/22 © UCLES 2022 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 6 – 2 – 7 0 10 (a) On the diagram, sketch the graph of y x x 4 5 2 =- + + for x 2 6 G G - . [2] (b) Find the coordinates of the points where the graph crosses the x-axis. ( … , … ) and ( … , … ) [2] (c) Find the coordinates of the point where the graph crosses the y-axis. ( … , … ) [1] (d) Find the coordinates of the local maximum. ( … , … ) [1]

This document consists of 8 printed pages. © UCLES 2022 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) October/November 2022 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 2022 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 2022 © UCLES 2022 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.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 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

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 4 of 8 Question Answer Marks Partial Marks 1(a) 19 5 2 B1 for each 1(b)(i) 1852 − 1 1(b)(ii) 48 1 1(c) 4.718 2 B1 for 4.7176… If 0 scored, SC1 for their value greater than 4 sf correctly rounded to 4 sf 1(d) 28.571 2 B1 for 28.5714… If 0 scored, SC1 for their value greater than 3 dp correctly rounded to 3 dp 1(e) 1.56 2 M1 for 24 [ 6.50] 100  or 6.50[ 24] 100  1(f) 6 5 1 1(g) 5 3.36 10  2 B1 for 336 figs 2(a) 4 B1 for each 2(b) 25.1 or 25.13 to 25.14 2 M1 for 2π 4  oe 3(a) 500 2 M1 for an attempt to find one relevant area e.g. 10 10  or 10 30  3(b) 20.8 or 20.83… 2 M1 for 60 40  soi by 2400 3(c) 2 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 5 of 8 Question Answer Marks Partial Marks 3(d) Two correct straight lines only 2 B1 for 1 correct straight line only or 2 correct straight lines with 1 extra If 0 scored, SC1 for 4 correct lines of symmetry on the cross 4(a)(i) [27] 3 [28] 6 [29] 5 [30] 4 2 B1 for 2 or 3 correct 4(a)(ii) 28 1 FT their (a) 4(a)(iii) 28.6 or 28.55 to 28.56 2 M1 for 27 3 28 6 29 5 30 4 + + +  soi by 514 4(a)(iv) 5 18 1 FT their (a) 4(b)(i) 4 360 24  2 M1 for 4 24 or 360 24 4(b)(ii) Correct pie chart with labels 3 B2 for 3 correct sectors drawn or for seeing 105, 120 and 75 OR B1 for 1 or 2 correct sectors drawn or seeing 1 or 2 of 105, 120, 75 B1 for 3 correct labels for sectors in appropriate proportions 5(a) 129 2 M1 for 5 13  or 2 32  5(b)(i) 25 35 T h = + final answer 2 B1 for 25 35h + or correct with units 5(b)(ii) 130 2 M1 for [25 ]35 3 +  oe 27 28 2 30

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 6 of 8 Question Answer Marks Partial Marks 5(b)(iii) 5 2 M1 for 200 25 35 h = +  oe or 200 – 25 5(c) 247.30 3 B2 for 3247.30 or 3247 or 3247.2 to 3247.3 or M1 for 2 3000(1 ) 100 k + , k > 0 6(a)(i) 2t final answer 1 6(a)(ii) 3x y + final answer 2 B1 for 3x or y seen 6(b)(i) 16 1 6(b)(ii) 1 − 1 6(b)(iii) 10.5 x  2 M1 for 2 4 25 x −  − or 25 2 2 x −  6(c)(i) 4 21 a final answer 2 B1 for correct common denominator ( 21k ) 6(c)(ii) 3 2 p final answer 2 B1 for correct cancellation of p or numbers or 2 36 24 p p oe 7(a) 60 75 t  1 7(b) [t ⩽15] [2] [t ⩽ 30] [6] [t ⩽ 45] 15 [t ⩽ 60] 27 [t ⩽ 75] 42 [t ⩽ 90] 54 [t ⩽ 105] 58 [t ⩽ 120] [60] 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 7 of 8 Question Answer Marks Partial Marks 7(c) correct cumulative frequency curve drawn 3 B2 for all correct points correctly plotted OR B1 for 3, 4 or 5 points correctly plotted FT their increasing points B1 for smooth line connecting increasing points 7(d)(i) 62 to 64 1 7(d)(ii) 45 1 7(d)(iii) 12 to 14 2 B1 for 46 to 48 seen or M1 for 60 – their 47 8(a) Points correctly plotted 2 B1 for each 8(b) scalene 1 8(c)(i) ( 1,3) − 1 8(c)(ii) 1 3 2 M1 for 4 2 2 4 − −− oe or suitable right-angled triangle drawn on line with correct lengths marked 8(d) 6.32 or 6.324 to 6.325 2 M1 for 2 2 ( 4 2) (2 4) −− + − oe 8(e) Correct reflection in x-axis (4,0), (2, 4), ( 4, 2) − −− 1 FT their triangle 9(a)(i)(a) 11, 13, 15, 17, 19, 21 1 9(a)(i)(b) 12, 15, 18, 21 1 9(a)(i)(c) 15, 21 1 FT their (a)(i)(a) and (a)(i)(b)

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 8 of 8 Question Answer Marks Partial Marks 9(a)(ii) Correct Venn diagram 2 B1 for 1 or 2 regions correct 9(b) P Q  Q P  2 B1 for each 10(a) 33.5 or 33.47… 3 B2 for 11.47… or 11.5 OR M1 for [...] sin35 20 = oe M1 for adding 22 to their AY following trigonometry 10(b) 36.9 or 36.86 to 36.87 3 M1 for 38 – 22 soi by 16 M1 for 16 cos[...] 20 their = 11(a) Correct sketch 2 B1 for correct shape B1 for maximum in correct quadrant 11(b) ( 1,0) (5,0) − 2 B1 for each 11(c) (0,5) 1 11(d) (2,9) 1 11 13 17 19 15 21 12 18 10 14 16 20 A B