Cambridge IGCSE Mathematics - International 0607 — 2022 Feb/March Paper 3 · Variant 2

This document has 20 pages. [Turn over DC (RW/CGW) 214153/1 © UCLES 2022 * 1 9 4 4 0 0 7 0 7 7 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) February/March 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 0607/32/F/M/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 0607/32/F/M/22 © UCLES 2022 [Turn over Answer all the questions. 1 (a) Simon swims 25 metres. Change 25 metres to centimetres. … cm [1] (b) Aroon swims four lengths of a 50-metre pool. Here is the time, in seconds, for each length. 44.8 45.3 44.5 44.4 Work out the total time. Give your answer in minutes and seconds. … minutes … seconds [2] (c) Tam swims 200 metres in a total time of 3.2 minutes. Calculate her average speed in metres per second. … m/s [3]

4 0607/32/F/M/22 © UCLES 2022 2 (a) These are the first three patterns in a sequence. Pattern 1 Pattern 2 Pattern 3 Pattern 4 Pattern 5 (i) In the space above, draw Pattern 4 and Pattern 5. [2] (ii) Complete the table for the number of squares in each pattern. Pattern number 1 2 3 4 5 8 Number of squares 5 [3] (b) These are the first four terms of another sequence. 5 9 13 17 For this sequence, (i) write down the rule for continuing the sequence, … [1] (ii) find the nth term. … [2]

5 0607/32/F/M/22 © UCLES 2022 [Turn over (c) The nth term, T, of a different sequence is given by this formula. T n 5 2 = - (i) Work out the value of T when n 4 = . T = … [1] (ii) Rearrange the formula to make n the subject. n = … [2]

6 0607/32/F/M/22 © UCLES 2022 3 Students in a college carry out a science experiment. (a) At the start of the experiment, the temperature of a gas was - 42 °C. During the experiment, the temperature of the gas rises to 28 °C. (i) Work out how much the temperature of the gas rises during the experiment. … °C [1] (ii) Work out the temperature that is half-way between - 42 °C and 28 °C. … °C [1] (b) The experiment began at 07 50 and ended at 15 25. Work out the length of time the experiment lasted. Give your answer in hours and minutes. … h … min [1] (c) When the results were posted online, there were 1279 views in the first day. Write 1279 correct to the nearest 10. … [1] (d) By the end of the week, there had been 15 503 views. (i) Write 15 503 in words. … [1] (ii) Write 15 503 in standard form, correct to two significant figures. … [2]

7 0607/32/F/M/22 © UCLES 2022 [Turn over (e) In the college, 53 students study science. 32 study physics (P). 24 study chemistry (C). 18 study both physics and chemistry. Complete the Venn diagram. P C … … … … U [3]

8 0607/32/F/M/22 © UCLES 2022 4 50 students were asked the number of magazines they bought in a week. The results are shown in the table. Number of magazines 0 1 2 3 4 Number of students 18 8 14 7 3 (a) Work out how many more students bought 2 magazines than bought 1 magazine. … [1] (b) Write down the most common number of magazines bought. … [1] (c) One of the students is chosen at random. Find the probability that this student bought 3 or 4 magazines. Give your answer as a fraction in its simplest form. … [2] (d) Work out the mean number of magazines bought. … [2]

9 0607/32/F/M/22 © UCLES 2022 [Turn over (e) On the grid, draw a bar chart to show the information in the table. 0 0 Number of magazines Number of students 2 4 6 8 10 12 14 16 18 20 1 2 3 4 [2]

10 0607/32/F/M/22 © UCLES 2022 5 In the diagram, all lengths are in centimetres and all angles are right angles. 4 7 5 6 7 7 NOT TO SCALE 3 12 (a) Work out the area of the shaded shape. Give the units of your answer. … … [4] (b) Work out the perimeter of the shaded shape. … cm [3]

11 0607/32/F/M/22 © UCLES 2022 [Turn over 6 In a school there are 960 students. 540 of the students are girls. (a) Write the ratio girls : boys in its simplest form. … : … [3] (b) Two thirds of the 540 girls and 45% of the boys travel to school by bus. Work out how many more girls than boys travel to school by bus. … [3]

12 0607/32/F/M/22 © UCLES 2022 7 (a) x° 26° NOT TO SCALE Find the value of x. x = … [1] (b) NOT TO SCALE 50° 155° p° r° q° B A X Y Z The diagram shows a triangle XYZ and a straight line AB. AB is parallel to XZ. Find the value of p, the value of q and the value of r. p = … q = … r = … [3]

13 0607/32/F/M/22 © UCLES 2022 [Turn over (c) 106° 42° 75° NOT TO SCALE y° Find the value of y. y = … [1] (d) D C e° B P A Q NOT TO SCALE ABCD is part of a regular octagon. PBCQ is part of a regular hexagon. Find the value of e. e = … [4]

14 0607/32/F/M/22 © UCLES 2022 8 In a competition, each diver is given a score out of 10 by each of two judges. The table shows the scores for eight divers. Judge 1 2.3 7.3 7.9 4.4 8.5 7.7 1.8 8.1 Judge 2 2.4 7.7 7.9 4.7 8.8 7.9 2.4 7.8 (a) Complete the scatter diagram. The first four points have been plotted for you. 0 0 1 2 3 4 5 6 7 8 9 10 Judge 2 score Judge 1 score 1 2 3 4 5 6 7 8 9 10 [2] (b) What type of correlation is shown in the scatter diagram? … [1]

15 0607/32/F/M/22 © UCLES 2022 [Turn over (c) Calculate the mean of the scores given by each judge. Judge 1 … Judge 2 … [2] (d) On the scatter diagram, draw a line of best fit. [2] (e) Judge 1 gives another diver a score of 5.6 . Use your line of best fit to estimate the score given to this diver by Judge 2. … [1]

16 0607/32/F/M/22 © UCLES 2022 9 A C B y x 0 5 4 3 2 1 – 1 – 2 – 3 – 4 – 5 1 2 3 4 5 – 5 – 4 – 3 – 2 – 1 The diagram shows three triangles A, B and C. (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) Describe fully the single transformation that maps triangle A onto triangle C. … … [2] (c) Rotate triangle A through 180° about (0, 0). Label the image P. [2] (d) Enlarge triangle A, scale factor 2, centre (1, 4). Label the image Q. [2]

17 0607/32/F/M/22 © UCLES 2022 [Turn over 10 (a) Solve. (i) x 7 11 + = x = … [1] (ii) ( ) x 4 3 2 10 - = x = … [3] (iii) x 5 1 9 + = x = … [2] (b) Multiply out the brackets and simplify. ( )( ) x x 6 8 + - … [2]

18 0607/32/F/M/22 © UCLES 2022 11 x° A C 75 cm 25 cm NOT TO SCALE 25 cm 75 cm O D B 96 cm h cm The diagram shows a table standing on a horizontal floor. The table top is horizontal and is supported by two legs AOB and COD. (a) Use trigonometry to find the value of x. x = … [3] (b) Use similar triangles to find DB. DB = … cm [2]

19 0607/32/F/M/22 © UCLES 2022 [Turn over (c) Use Pythagoras’ Theorem to find the height, h cm, of O above the floor. … cm [3] Question 12 is printed on the next page.

20 0607/32/F/M/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. 12 0 A B y x – 6 4 – 10 20 The diagram shows the graph of ( )( ) y x x 4 2 = + - for x 6 4 G G - . A and B are two of the points where the graph crosses the axes. (a) Find the coordinates of (i) point A, ( … , … ) [1] (ii) point B, ( … , … ) [1] (iii) the local minimum. ( … , … ) [1] (b) On the diagram, sketch the graph of y x 1 = - for x 6 4 G G - . [2] (c) Find the x-coordinate of each point of intersection of ( )( ) y x x 4 2 = + - and y x 1 = - . x = … and … [2]

This document consists of 6 printed pages. © UCLES 2022 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) February/March 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 February/March 2022 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 February/March 2022 © UCLES 2022 Page 2 of 6 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 February/March 2022 © UCLES 2022 Page 3 of 6 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 February/March 2022 © UCLES 2022 Page 4 of 6 Question Answer Marks Partial Marks 1(a) 2500 1 1(b) 2m 59s 2 B1 for figs 179 seen 1(c) 1.04 or 1.041 to 1.042 3 M1 for 3.2 × 60 soi by 192 M1 for 200 time their 2(a)(i) Two correct patterns 2 B1 for each 2(a)(ii) 7, 9, 11, 13 2 B1 for two or three correct terms 19 1 2(b)(i) +4 oe 1 2(b)(ii) 4n + 1 oe 2 B1 for 4n + c any c 2(c)(i) 11 1 2(c)(ii) 5 T + 2 M1 for T + 5 = n2 If 0 scored, SC1 for ( ) 5 + their T 3(a)(i) 70 1 3(a)(ii) −7 1 3(b) 7[h] 35[m] 1 3(c) 1280 1 3(d)(i) Fifteen thousand five hundred [and] three 1 3(d)(ii) 1.6×104 2 B1 for 1.5[503] × 104 or 16 000 oe seen 3(e) 14 18 6 15 3 Maximum of 2 marks if diagram not fully correct B1 for 18 B1 for 14 or 6 B1 for 53 – their(14 + 18 + 6) 4(a) 6 1 4(b) 0 1 4(c) 1 5 cao 2 M1 for 7 3 50 + soi 4(d) 1.38 2 M1 for [0×18 +] 1×8 + 2×14 + 3×7 + 4×3 soi by 69

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2022 © UCLES 2022 Page 5 of 6 Question Answer Marks Partial Marks 4(e) Correct ruled bar chart 2 M1 for 3, 4 or 5 correct heights, ignore widths 5(a) 125 3 M2 for 7 × 5 + 12 × 4 + 7 × 6 oe or M1 for any one correct relevant area cm2 1 5(b) 64 3 B1 for 11 or 2 soi M1 for adding the given lengths soi by 51 6(a) 9 : 7 3 B1 for [boys=]420 M1 for 540 : their (960 – 540) or their (960 – 540) : 540 cancelled correctly at least once If 0 scored, SC1 for 9 : 16 6(b) 171 3 M1 for 2 540 3 × oe M1 for 0.45 × their420 oe 7(a) 64 1 7(b) [p =] 50 [q =]155 [r =] 25 3 B1 for each 7(c) 137 1 7(d) 105 4 B3 for 45 and 60 or 120 and 135 seen or B2 for 45 or 60 or 120 or 135 or M1 for 360 n or 180 360 × − n n with n = 6 or 8 If 0 scored, SC1 for 8 and 6 seen for the number of sides 8(a) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted 8(b) Positive 1 8(c) [J1 =] 6 [J2 =] 6.2 2 B1 for each 8(d) Ruled, straight line through the mean point and within tolerance 2 B1 for Ruled straight line through their mean point but not within tolerance or Ruled straight line within tolerance but not through their mean point 8(e) 5.4 to 6.2 1 FT their ruled straight line 9(a) Reflection y = 0 oe 2 B1 for each

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2022 © UCLES 2022 Page 6 of 6 Question Answer Marks Partial Marks 9(b) Translation 5 1 −       oe 2 B1 for each 9(c) Correct ruled image (–1, –2) (–2, –2) (–2, –4) 2 B1 for correct orientation, wrong position 9(d) Correct ruled image (3, 4) (3, 0) (1, 0) 2 B1 for correct size, wrong position 10(a)(i) 4 1 10(a)(ii) 1 12 oe 3 M1 for 12x – 8 = 10 or 3x – 2 = 10 4 or better M1 for FT correct second step 10(a)(iii) 40 2 M1 for x + 5 = 45 or 5 x = 9 – 1 10(b) x2 – 2x – 48 final answer 2 B1 for three of x2, –8x, [+]6x, – 48 11(a) 50.2 or 50.20 to 50.21 3 B1 for 96 ÷ 2 oe soi by 48 M1 for cos = (96 2) 75 ÷ their oe 11(b) 32 2 M1 for scale factor 75 25 or 25 75 soi by 3 or 1 3 11(c) 57.6 or 57.62 to 57.63 3 M2 for 752 – (their(96÷2))2 or M1 for 752 = x2 + (their (96÷2))2 12(a)(i) (−4, 0) 1 12(a)(ii) (0, −8) 1 12(a)(iii) (−1, −9) 1 12(b) Correct straight line 2 B1 for straight line with negative slope or for straight line passing through positive y- axis 12(c) 4.85 1.85 − 2 B1 for each If 0 scored, SC1 for –4.9 and 1.9