Cambridge IGCSE Mathematics - International 0607 — 2023 Feb/March Paper 3 · Variant 2

This document has 16 pages. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) February/March 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 [ ]. * 1 8 7 8 6 4 1 3 4 9 * DC (PQ/SG) 312450/2 © UCLES 2023

2 0607/32/F/M/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/F/M/23 © UCLES 2023 [Turn over Answer all the questions. 1 (a) 121 122 123 124 125 126 127 From this list, write down a number that is (i) even … [1] (ii) a square … [1] (iii) a cube … [1] (iv) a multiple of 7 … [1] (v) prime. … [1] (b) (i) Find the value of .3 628 3 . Give your answer correct to 3 decimal places. … [2] (ii) Find the value of . . . 0 23 36 2 21 4 # . Give your answer correct to the nearest hundred. … [2]

4 0607/32/F/M/23 © UCLES 2023 2 The table shows the number of babies born to each of 25 hamsters. Number of babies 2 3 4 5 6 7 8 Frequency 3 3 4 2 5 6 2 (a) Write down how many hamsters had 6 babies. … [1] (b) Find (i) the range … [1] (ii) the median … [1] (iii) the mean. … [2] (c) Use the information to complete the bar chart. 2 0 1 2 3 4 5 6 3 4 5 Number of babies 6 7 8 Frequency [2]

5 0607/32/F/M/23 © UCLES 2023 [Turn over 3 In 2019 the Louvre museum had 9 609 900 visitors. (a) Write 9 609 900 in words. … … [1] (b) The Louvre museum is open 309 days of the year. Work out the average number of visitors per day. … [1] (c) 40% of all visitors are admitted free. (i) Write down the percentage of visitors who have to pay. …% [1] (ii) The admission price is 15 euros (€). Work out how much money, on average, was paid to the Louvre museum each day for admissions. € … [3]

6 0607/32/F/M/23 © UCLES 2023 4 (a) Prija changes 600 pounds (£) to US dollars ($) at a bank. (i) The bank charges 2% of the £600 to change the money. Show that the bank charges £12. [1] (ii) The bank takes the £12 charge and then changes the rest of the money. The exchange rate is £ $ . 1 1 335 = . Work out how much money, in $, Prija receives. $ … [2] (b) From the money Prija receives, she spends $150 on food, $225 on entertainment and $130 on gifts. Work out how much, in $, Prija has left. $ … [2] (c) Prija changes the remaining dollars back to pounds at a rate of $ . 1 1 347 £ = . The bank does not charge to make the change. Work out how much money, in £, she receives. £ … [1]

7 0607/32/F/M/23 © UCLES 2023 [Turn over 5 Sabhina asks 180 parents how many children they have. The results are shown in the pie chart. 130° 50° 60° 30° 1 child 2 children 3 children 4 children 5 children (a) Write down the mode. … children [1] (b) Work out how many parents have (i) 1 child … [1] (ii) 4 children. … [2] (c) One of these parents is picked at random. Find the probability that they have 5 children. Give your answer as a fraction in its simplest form. … [2]

8 0607/32/F/M/23 © UCLES 2023 6 (a) This is the start of a sequence. The first term and the fifth term are missing. … 55 63 71 … 87 95 (i) Find the first term and the fifth term of this sequence. First term = … Fifth term = … [2] (ii) Find the nth term of this sequence. … [2] (b) Another sequence has nth term n n 2 3 2 + . Work out the first 3 terms of this sequence. … , … , … [2]

9 0607/32/F/M/23 © UCLES 2023 [Turn over 7 66° B C O A D NOT TO SCALE The diagram shows a circle, centre O. AC is a tangent to the circle at B and angle ° BOC 66 = . DOC is a straight line. (a) Find (i) angle OBC Angle OBC = … [1] (ii) angle OCB Angle OCB = … [1] (iii) angle ODB Angle ODB = … [2] (iv) angle DBA. Angle DBA = … [1] (b) The circle has radius 3.2 cm. (i) Work out the area of the circle. … cm2 [2] (ii) Work out the length of OC. OC = … cm [3]

10 0607/32/F/M/23 © UCLES 2023 8 On one day ten students record the number of hours they are online and the number of hours they sleep that night. Number of hours online 1 1 1.5 2 2.5 2.5 3 3 3.5 5 Number of hours sleeping 10 9.5 10 8.5 7 9 6 7.5 7 5.5 (a) Complete the scatter diagram. The first 5 points have been plotted for you. 0 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 Number of hours sleeping Number of hours online [2] (b) What type of correlation is shown in the scatter diagram? … [1]

11 0607/32/F/M/23 © UCLES 2023 [Turn over (c) Find (i) the mean number of hours online … h [1] (ii) the mean number of hours sleeping. … h [1] (d) On the diagram, draw a line of best fit. [2] (e) Another student is online for 4 hours in the day. Use your line of best fit to estimate the number of hours sleeping for this student. … h [1]

12 0607/32/F/M/23 © UCLES 2023 9 1 0 1 2 3 4 5 6 7 2 3 4 x y A B The diagram shows the line AB drawn on a 1 cm2 grid. (a) Write down the coordinates of point A and point B. A ( … , …) B ( … , …) [2] (b) Calculate the length of AB. AB = … cm [2] (c) Find the coordinates of the mid-point of AB. ( … , …) [1] (d) Work out the gradient of AB. … [1] (e) Find the equation of the line AB. … [2] (f) Does the point (1.37, 3.36) lie on the line AB? Show how you decide. [2]

13 0607/32/F/M/23 © UCLES 2023 [Turn over 10 – 7 – 6 – 5 – 4 – 3 – 2 – 1 – 1 1 2 3 4 5 – 2 – 3 – 4 – 5 1 2 3 4 5 6 7 8 9 10 x y 0 C D B A (a) Shape B is a reflection of shape A in the line y m = . Write down the value of m. m = … [1] (b) Shape C is an anticlockwise rotation of shape A through t° about the origin. Write down the value of t. t = … [1] (c) Shape D is a translation of shape A by the vector y x e o. Write down the value of x and the value of y. x = … y = … [2] (d) Enlarge shape A with centre (0, 0) and scale factor 2. [2]

14 0607/32/F/M/23 © UCLES 2023 11 (a) Solve. x 6 3 2 - - … [1] (b) Solve the simultaneous equations. x y 2 3 17 + = x y 2 5 - = x = … y = … [2] (c) Simplify. r s r s 2 5 3 - - + … [2] (d) Expand. ( ) x x y 2 3 4 2 - … [2]

15 0607/32/F/M/23 © UCLES 2023 [Turn over (e) Find each value of x. (i) 3 3 3 x 9 = x = … [1] (ii) 2 2 2 x 3 6 # = x = … [1] (f) Write as a single fraction in its simplest form. (i) x x 3 7 6 - … [2] (ii) d d 9 5 3 ' … [3] Question 12 is printed on the next page.

16 0607/32/F/M/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 – 3 6 – 3 3 x y 0 (a) On the diagram, sketch the graph of y x x 3 2 = + for values of x from 3 - to 3. [2] (b) Write down the equations of the two asymptotes. … … [2] (c) On the same diagram, sketch the graph of y x 3 = + for x 3 3 G G - . [2] (d) Find the x-coordinates of the points of intersection of y x x 3 2 = + and y x 3 = + . x = … and x = … [2]

This document consists of 7 printed pages. © UCLES 2023 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) February/March 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 February/March 2023 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 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.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 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 February/March 2023 © UCLES 2023 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) 122 or 124 or 126 1 1(a)(ii) 121 1 1(a)(iii) 125 1 1(a)(iv) 126 1 1(a)(v) 127 1 1(b)(i) 1.537 2 B1 for 1.5365… or their answer to more than 3 decimal places correctly rounded to 3 decimal places. 1(b)(ii) 3400 2 B1 for 3368…. or their answer correctly rounded to the nearest hundred. 2(a) 5 1 2(b)(i) 6 1 2(b)(ii) 6 1 2(b)(iii) 5.16 2 for 2 3 3 3 4 4 5 2 6 5 7 6 8 2 orbetter + +  +  + +  +  M1 2(c) Correct ruled bar chart 2 B1 for 4 or 5 correct bars with equal widths or 6 correct heights with unequal widths 3(a) Nine million, six hundred [and] nine thousand, nine hundred 1 3(b) 31 100 1 3(c)(i) 60 cao 1 3(c)(ii) 279 900 3 M2 for 60 31100 15 100   their their oe or M1 for 60 31100 100 their their  or 15 31100 their  oe 4(a)(i) 2 600 100  1 or an equivalent method 4(a)(ii) 784.98 2 M1 for 600 – 12 soi by 588

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 Page 5 of 7 Question Answer Marks Partial Marks 4(b) 279.98 2 FT their(a)(ii) – 505 for 1 50 225 130 soi by 505 + + M1 4(c) 207.85 1 FT ( ) 1.347 their b 5(a) 2 1 5(b)(i) 45 1 5(b)(ii) 30 2 M1 for 60 180 or 360 360 5(c) 1 12 cao 2 M1 for 30 360 oe 6(a)(i) 47 79 2 B1 for each 6(a)(ii) 8n + 39 oe final answer 2 B1 for 8n + q 6(b) 5, 14, 27 2 B1 for 2 correct If 0 scored, SC1 for 0, 5, 14 7(a)(i) 90 1 7(a)(ii) 24 1 7(a)(iii) 33 2 B1 for 180 – 66 soi by 114 7(a)(iv) 57 1 FT 90 – their (a)(iii) 7(b)(i) 32.2 or 32.16 to 32.18 2 M1 for 2 π 3.2  7(b)(ii) 7.87 or 7.867… 3 M2 for ( ) 3.2 3.2 or sin 24 cos66 their or M1 for ( ) 3.2 sin 24 their OC = 3.2 or cos66 OC = 8(a) Correct points plotted 2 B1 for 3 or 4 points correctly plotted 8(b) negative 1 8(c)(i) 2.5 1 8(c)(ii) 8 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 Page 6 of 7 Question Answer Marks Partial Marks 8(d) Correct ruled line 2 B1 for ruled line through mean point but not in tolerance or for ruled line in tolerance but not through the mean point. 8(e) 6 to 6.5 1 FT their ruled line 9(a) (0, 6) (3, 0) 2 B1 for each 9(b) 6.71 or 6.708… 2 M1 for 32 + 62 9(c) (1.5, 3) 1 9(d) –2 oe 1 9(e) 2 6 oe = − + y x 2 FT their (d) B1 for (their – 2)x + 6 or y = (their – 2) + n or y = kx + 6, k  their – 2. 9(f) ( ) 2 1.37 6 3.26 = −  + = y M1 FT their equation for M1 only   3.26 3.36  Point is not on the line. A1 10(a) 1 − 1 10(b) 90 1 10(c) [x =] 7 − [y =] 3 − 2 B1 for each If 0 scored, SC1 for x = 7 and y = 3 10(d) Correct enlargement (2, 2), (8, 2), (8, 4), (2, 4) 2 B1 for enlargement with different scale factor or from a different centre 11(a) 3  x 1 11(b) [x = ] 4 [y = ] 3 2 B1 for each If 0 scored, SC1 for correct substitution and evaluation to find other variable 11(c) 1 4 final answer − − r s 2 B1 for 1 − r or 4 −s 11(d) 3 6 8 final answer − x xy 2 B1 for 3 6x or 8 −xy 11(e)(i) 8 1 11(e)(ii) 3 1 11(f)(i) 13 6 x 2 M1 for a multiple of 6 as common denominator

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 Page 7 of 7 Question Answer Marks Partial Marks 11(f)(ii) 5 3 3 15 2 for or better seen 9 d d B or M1 for 5 3 9  d d or 5 3 9 9  d d 12(a) Correct sketch 2 B1 for correct shape not crossing y-axis 12(b) 0 = x 3 = y 2 B1 for each 12(c) Correct ruled line drawn 2 B1 for positive gradient or B1 for crossing y-axis above the origin 12(d) 1.41 − (–1.414 … ) and 1.41 (1.414…) 2 B1 for each If 0 scored, SC1 for 1.4 and1 .4 −