Cambridge IGCSE Mathematics - International 0607 — 2021 Oct/Nov Paper 3 · Variant 2

This document has 16 pages. Cambridge IGCSE™ DC (CE/CGW) 199832/1 © UCLES 2021 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) October/November 2021 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 [ ]. * 6 2 4 0 9 7 8 3 9 0 *

2 0607/32/O/N/21 © UCLES 2021 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/O/N/21 © UCLES 2021 [Turn over Answer all the questions. 1 (a) These are the first three patterns of a sequence made using lines. Pattern 1 Pattern 2 Pattern 4 Pattern 5 Pattern 3 (i) In the space above, draw Pattern 4 and Pattern 5. [2] (ii) Complete the table. Pattern number 1 2 3 4 5 6 Number of lines 3 5 [2] (iii) Write down the rule for continuing the sequence of lines. … [1] (b) These are the first four terms of a different sequence. 23 17 11 5 Write down the next two terms of this sequence. … , … [2] (c) The nth term of another sequence is n n 5 2 + . Find the first three terms of this sequence. … , … , … [2]

4 0607/32/O/N/21 © UCLES 2021 2 (a) Wilfred went to a shop to buy plants for his garden. Complete the bill. Item Cost ($) 8 shrubs at $9.95 each … 12 bushes at $… each 207.00 … plants at $1.60 each 25.60 Total $ … [4] (b) The shop bought 960 tomato plants. (i) In the first week they sold 800 of the tomato plants. Write 960 800 as a fraction in its simplest form. … [1] (ii) In the second week, 5% of the remaining 160 plants died and 5 3 of the remaining 160 plants were sold. Work out how many tomato plants are left at the end of the second week. … [3]

5 0607/32/O/N/21 © UCLES 2021 [Turn over (c) Olga and Zak each buy some plants. These plants are all the same price. Olga pays $67.95 for 15 plants. Zak buys 12 plants. Work out how much Zak pays for his plants. $ … [2]

6 0607/32/O/N/21 © UCLES 2021 3 (a) 0 x 2 3 4 A B C – 3 – 2 – 1 3 4 5 2 7 6 1 y 1 (i) Write down the coordinates of (a) point A, ( … , …) [1] (b) point B, ( … , …) [1] (c) point C. ( … , …) [1] (ii) Write down the coordinates of the mid-point of AC. ( … , …) [1] (iii) Write down the equation of the line AB. … [1]

7 0607/32/O/N/21 © UCLES 2021 [Turn over (b) 110° NOT TO SCALE x° z° y° R S T P Q In the diagram, PQ is parallel to TS and QS = SR. TSR is a straight line. (i) Write down the mathematical name of quadrilateral PQRT. … [1] (ii) Find the value of x. x = … [1] (iii) Find the value of y. y = … [2] (iv) Find the value of z. z = … [1]

8 0607/32/O/N/21 © UCLES 2021 4 (a) Simplify. p p p 5 7 4 - + … [1] (b) Solve. x 4 1 9 - = x = … [2] (c) Factorise fully. x xy 15 9 + … [2] (d) Complete this statement with either 2 or 1 . Show clearly how you decide. 112 … 53 [1] (e) Write down the inequality shown on the number line. 5 3 1 4 2 0 6 x … [1]

9 0607/32/O/N/21 © UCLES 2021 [Turn over 5 The results of 24 matches played by a football team are recorded below. They can Win (W), Lose (L) or Draw (D). W L W L D W L L L W W L L D L L W L L D W L L W (a) Complete the table. Result Frequency Pie chart angle W D L Total 24 360° [6] (b) Draw a pie chart to show this information. [3] (c) One of these matches is chosen at random. Find the probability that the result is a Win. … [1]

10 0607/32/O/N/21 © UCLES 2021 6 NOT TO SCALE 6 cm w° C D A B 7 cm 5 cm (a) Work out the area of quadrilateral ABCD. Give the units of your answer. … … [3] (b) Work out the perimeter of quadrilateral ABCD. … cm [3] (c) Use trigonometry to work out the value of w. w = … [2]

11 0607/32/O/N/21 © UCLES 2021 [Turn over 7 An aircraft flies 40 000 km around the Earth. (a) Write 40 000 in words. … [1] (b) Change 40 000 km to metres. Give your answer in standard form. … m [2] (c) The flight takes 67 hours. (i) Change 67 hours to seconds. Give your answer correct to 2 significant figures. … s [3] (ii) Calculate the average speed of the aircraft. Give your answer in metres per second. … m/s [1]

12 0607/32/O/N/21 © UCLES 2021 8 5 cm This shape is made by joining four identical semi-circles to the sides of a square. (a) Work out the perimeter of the shape. … cm [2] (b) Write down the order of rotational symmetry of the shape. … [1] (c) On the diagram, draw all the lines of symmetry. [2]

13 0607/32/O/N/21 © UCLES 2021 [Turn over 9 0 x 2 3 4 5 6 7 B A – 3 – 2 – 1 – 6 – 7 – 5 – 4 3 4 5 2 7 6 1 y 1 Shape A is mapped onto shape B by a single transformation. Describe fully three different types of transformation that will map shape A onto shape B. 1 … … 2 … … 3 … … [7]

14 0607/32/O/N/21 © UCLES 2021 10 Tilda recorded the time, in minutes, that each of 100 cars was parked in a hospital car park. Her results are shown in the frequency table. Time (t minutes) Frequency Time (t minutes) Cumulative frequency 0 1 t G 20 0 t G 20 20 1 t G 40 12 t G 40 40 1 t G 60 18 t G 60 60 1 t G 80 16 t G 80 80 1 t G 100 38 t G 100 100 1 t G 120 16 t G 120 100 (a) Complete the cumulative frequency table. [2] (b) On the grid, draw a cumulative frequency curve to show the information. 0 20 40 Cumulative frequency 60 10 30 50 70 90 80 100 10 30 50 70 90 20 0 40 60 120 t 110 80 100 Time (minutes) [3]

15 0607/32/O/N/21 © UCLES 2021 [Turn over (c) Use your cumulative frequency curve to find an estimate of (i) the median, … min [1] (ii) the interquartile range. … min [2] (d) Tilda thinks that approximately three quarters of the cars were parked in the car park for between 50 and 110 minutes. Is Tilda correct? Use information from the curve to justify your answer. [4] Question 11 is printed on the next page.

16 0607/32/O/N/21 © UCLES 2021 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. 11 0 y x – 3 3 – 3 10 (a) (i) On the diagram, sketch the graph of y x 7 2 = - for x 3 3 G G - . [2] (ii) Find the coordinates of the local maximum. ( … , …) [1] (b) (i) On the diagram, sketch the graph of y x 6 2 = for values of x from -3 to 3. [2] (ii) Write down the equation of each asymptote of y x 6 2 = . … and … [2] (c) Find the x-coordinate of each point of intersection of y x 7 2 = - and y x 6 2 = . … [4]

This document consists of 7 printed pages. © UCLES 2021 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) October/November 2021 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 2021 series for most Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 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 October/November 2021 © UCLES 2021 Page 3 of 7 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 October/November 2021 © UCLES 2021 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) Pattern 4 and Pattern 5 drawn 2 B1 for each 1(a)(ii) 7, 9, 11, 13 2 B1 for two or three correct 1(a)(iii) +2 oe 1 or 2n + 1 1(b) −1, −7 2 B1 for each 1(c) 6, 14, 24 2 B1 for two correct in correct place If 0 scored, SC1 for 0, 6, 14 2(a) 79.6[0] 17.25 16 312.2[0] 4 B1 for each FT 232.6[0] + their 79.6[0] 2(b)(i) 5 6 cao 1 2(b)(ii) 56 3 M1 for 5 100 × 160 oe soi by 8 M1 for 3 5 × 160 oe soi by 96 2(c) 54.36 2 M1 for 12 ÷ 15 soi or 67.95 ÷ 15 soi 3(a)(i)(a) (4, 3) 1 3(a)(i)(b) (0, 3) 1 3(a)(i)(c) (6, −1) 1 3(a)(ii) (5, 1) 1 3(a)(iii) y = 3 1 3(b)(i) Trapezium 1 3(b)(ii) 70 1 3(b)(iii) 35 2 M1 for 180 110 2 − soi 3(b)(iv) 110 1 FT 180 – their (b)(ii) 4(a) 2p final answer 1 4(b) 1 2 2 or 2.5 or 5 2 2 M1 for 4x = 9 + 1 or x − 1 4 = 9 4 4(c) 3x(5 + 3y) final answer 2 B1 for x(15 + 9y) or 3(5x + 3xy) 4(d) < with 121 and 125 seen 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 5 of 7 Question Answer Marks Partial Marks 4(e) x ⩾ 3 1 5(a) [Frequencies] 8, 3, 13 2 B1 for two correct [Angles] 120, 45, 195 4 FT their frequencies B3 for two correct or B2 for one correct or M1 for 24 f soi or 360 24 soi 5(b) Correct labelled diagram 3 FT their angles provided they add to 360 B2 for correct sectors, no/wrong labels or B1 for one correct sector 5(c) 8 24 oe 1 6(a) 51 2 M1 for 6 × 5 or 1 2 × 7 × 6 soi cm2 1 6(b) 32.2 or 32.21 to 32.22 3 M1 for 5 + 6 + 5 + 7 + k , k > 0 M1 for 62 + 72 soi 6(c) 40.6 or 40.6 to 40.7 2 M1 for tan[ ] = 6 7 oe 7(a) Forty thousand 1 7(b) 4[.0] × 107 2 B1 for 1 km = 1000 m soi or M1 for their number of metres correctly converted to standard form 7(c)(i) 240 000 3 B2 for 241 200 or M1 for 60 seen 7(c)(ii) 166 or 167 or 165.8 to 166.7 1 8(a) 31.4 or 31.41 to 31.42 2 M1 for π × 5 or π × 2.5 soi 8(b) 4 1 8(c) 4 correct lines drawn 2 B1 for two or three lines correct and none incorrect

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 6 of 7 Question Answer Marks Partial Marks 9 Reflection x-axis oe B2 B1 for each Translation 0 7     −   B2 B1 for each Rotation 90 clockwise oe [centre] (0, 0) oe OR Rotation 180 [centre] 1 3 , 0 2       OR Rotation 90 anticlockwise [centre] (7, 0) B3 B1 for each 10(a) 0, 12, 30, 46, 84, [100] 2 M1 for 2 or 3 correct 10(b) Correct cumulative frequency curve 3 M1 for points plotted correctly horizontally M1FT for at least 4 correct vertical plots, dep. on increasing graph 10(c)(i) 81 to 85 1 FT their increasing graph 10(c)(ii) 36 to 44 2 FT their increasing graph for 2 marks B1 for [UQ =] 93 to 97 or [LQ =] 53 to 57 10(d) [50 min , cf =] 18 to 22 B1 FT their increasing graph [110 min, cf =] 93 to 97 B1 FT their increasing graph 73 100 0.73 ≈ 0.75, yes OR 3 4 × 100 = 75 73 ≈ 75, yes B2 B1 for 75 or 0.75 soi

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 7 of 7 Question Answer Marks Partial Marks 11(a)(i) Correct quadratic sketch 2 B1 for correct shape or for maximum approximately on y-axis 11(a)(ii) (0, 7) 1 11(b)(i) Correct sketch 2 B1 for one branch correct If 0 scored, SC1 for two branches correct shape but meet/cross the axes 11(b)(ii) x = 0 and y = 0 2 B1 for each If 0 scored, SC1 for x-axis and y-axis as answer 11(c) 1 −1 2.45 or 2.449… −2.45 or −2.449… 4 B1 for each or SC1 for 2.4 and −2.4 If 0 scored, SC3 for 4 correct coordinates or SC2 for 3 correct coordinates or SC1 for 2 or 1 correct coordinates