Cambridge IGCSE Mathematics - International 0607 — 2023 Oct/Nov Paper 3 · Variant 1

This document has 16 pages. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 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 [ ]. * 2 3 4 5 1 0 5 1 0 3 * DC (RW/JG) 312460/1 © UCLES 2023

2 0607/31/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 0607/31/O/N/23 © UCLES 2023 [Turn over Answer all the questions. 1 (a) Write eighty thousand five hundred and two in figures. … [1] (b) Write 0.63 as a fraction. … [1] (c) Work out .7 13 . Give your answer correct to the nearest 10. … [2] (d) Work out . . . 2 16 4 12 9 84 # . Give your answer correct to 4 significant figures. … [2] (e) Find the next two terms in this sequence. 8 15 22 29 … , … [2] (f) Ahmed buys 8 roses each costing $2.20 . (i) Work out how much he pays for the 8 roses. $ … [1] (ii) Work out how much change he receives from $20. $ … [1] (g) Find the lowest common multiple (LCM) and the highest common factor (HCF) of 14 and 21. LCM = … HCF = … [3]

4 0607/31/O/N/23 © UCLES 2023 2 The ages, in years, of 15 teachers are shown below. 38 62 51 42 49 24 31 46 60 58 29 36 38 48 54 (a) Draw a stem-and-leaf diagram for the 15 ages. Key …|… = … [3] (b) Find (i) the mode … years [1] (ii) the median … years [1] (iii) the interquartile range … years [2] (iv) the mean. … years [1]

5 0607/31/O/N/23 © UCLES 2023 [Turn over 3 (a) Bettica invests $12 000 at a rate of 1.8% per year simple interest. Calculate the value of Bettica’s investment at the end of 4 years. $ … [3] (b) Melanie has $240. She spends $50 on books, $110 on food and $80 on clothes. Draw and label a pie chart to show this information. [4]

6 0607/31/O/N/23 © UCLES 2023 4 (a) The Monaco Grand Prix is a car race. The cars race around a circuit. The length of one circuit is 3.337 kilometres. The drivers each complete 78 circuits in the race. (i) Work out the total distance of the race. … km [1] (ii) One driver completes one circuit at an average speed of 162 km/h. Find the time taken. Give your answer in minutes and seconds. … min … s [3] (b) One car reaches a speed of 290 km/h. Change 290 km/h to m/s. … m/s [2] (c) The cost of entry to watch the race was $450. The total amount collected was $90 million. Work out the number of people who paid to watch the race. … [2]

7 0607/31/O/N/23 © UCLES 2023 [Turn over 5 Marius, Silvia and Greta each roll fair six-sided dice numbered 1 to 6. (a) Marius rolls one die. Find the probability that he rolls a 4. … [1] (b) Silvia rolls two dice. Find the probability that she rolls a 6 on both dice. … [2] (c) Greta rolls one die 300 times. Find the expected number of times that she rolls a 5. … [2]

8 0607/31/O/N/23 © UCLES 2023 6 1 1 2 3 4 0 2 3 4 5 –1 A y x B C D The diagram shows quadrilateral ABCD drawn on a cm 1 2 grid. (a) Write down the coordinates of point B and point C. B ( … , … ) C ( … , … ) [2] (b) Write down the mathematical name for the quadrilateral. … [1] (c) Work out the area of the quadrilateral. … cm2 [2] (d) Write down the number of lines of symmetry of the quadrilateral. … [1] (e) Write down the order of rotational symmetry of the quadrilateral. … [1]

9 0607/31/O/N/23 © UCLES 2023 [Turn over 7 Eight students play basketball. They each have ten attempts to score a basket. The number of years training and the number of baskets scored are shown in the table. Student A B C D E F G H Number of years training 1 2 2 3 3 4 7 8 Number of baskets 1 2 4 3 5 7 8 10 (a) Complete the scatter diagram. The first 4 points have been plotted for you. 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10 Number of baskets Number of years training [2] (b) What type of correlation is shown in the scatter diagram? … [1] (c) The mean number of years training is 3.75 and the mean number of baskets scored is 5. On the diagram, draw a line of best fit. [2] (d) Use your line of best fit to estimate the number of baskets scored by a student with 5 years training. … [1]

10 0607/31/O/N/23 © UCLES 2023 8 Adil is an electrician. He works out the total amount that he charges his customers using this formula. Total amount = hourly rate # number of hours worked + fixed call-out fee (a) Adil’s hourly rate is $50 and the fixed call-out fee is $85. (i) He works for one customer for 6 hours. Find the total amount he charges that customer. $ … [2] (ii) Adil works in Sahdna’s house. He charges Sahdna $460. Work out how many hours Adil worked for Sahdna. … h [2] (b) T rn F = + Rearrange the formula to make r the subject. r = … [2]

11 0607/31/O/N/23 © UCLES 2023 [Turn over 9 (a) Complete the mapping diagram for ( ) f x x 3 1 = - . 0 1 2 …… …… …… x f (x) [2] (b) Solve. (i) x 3 6 = x = … [1] (ii) x x 6 4 12 2 - = - x = … [2] (c) Complete this statement using one of 2 or 1 or = . ( ) 2 3 - … ( ) 2 4 - [1] (d) Factorise completely. y y 6 3 2 - … [2] (e) Find each value of x. (i) 2 2 2 x 5 10 # = x = … [1] (ii) a a a x 6 2 = x = … [1]

12 0607/31/O/N/23 © UCLES 2023 10 (a) NOT TO SCALE D A C B F E 48° AB and CD are straight lines that intersect at E. EF is perpendicular to CD and angle ° CEB 48 = . Find (i) angle DEF Angle DEF = … [1] (ii) angle AED Angle AED = … [1] (iii) angle BEF Angle BEF = … [1] (iv) angle CEA. Angle CEA = … [1]

13 0607/31/O/N/23 © UCLES 2023 [Turn over (b) NOT TO SCALE 120° x° 135° 125° 140° 115° 135° The diagram shows a seven-sided polygon. Work out the value of x. x = … [3]

14 0607/31/O/N/23 © UCLES 2023 11 NOT TO SCALE 8 cm 6 cm A B C D ABC is a right-angled triangle. BDC is a right angle. (a) Work out the area of triangle ABC. … cm2 [1] (b) Use Pythagoras’ Theorem to work out the length of AC. AC = … cm [2] (c) Use your answers to part (a) and part (b) to work out the length of BD. BD = … cm [2]

15 0607/31/O/N/23 © UCLES 2023 [Turn over 12 A solid sphere has a surface area of cm 581 2. (a) Show that the radius of the sphere is 6.8 cm, correct to 1 decimal place. [2] (b) Work out the volume of the sphere. … cm3 [2] (c) A solid cube has the same volume as this sphere. Find the length of one edge of this cube. … cm [2] Question 13 is printed on the next page.

16 0607/31/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. 13 y x 8 5 0 – 7 – 10 P Q NOT TO SCALE The diagram shows a sketch of the graph of . . y x x x 0 1 0 25 2 1 3 2 = + - - for x 7 5 G G - . Two points, P and Q, are also marked. Draw the graph of . . y x x x 0 1 0 25 2 1 3 2 = + - - on your calculator and use it to answer the following questions. (a) Find the coordinates of point P and point Q. P = ( … , … ) Q = ( … , … ) [2] (b) Find the coordinates of (i) the local maximum point ( … , … ) [2] (ii) the local minimum point. ( … , … ) [2] (c) The line y a = intercepts the graph of . . y x x x 0 1 0 25 2 1 3 2 = + - - at 3 points. Complete the range of values for a. … a 1 1 … [2]

This document consists of 7 printed pages. © UCLES 2023 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 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.

0607/31 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.

0607/31 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

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 4 of 7 Question Answer Marks Partial Marks 1(a) 80502 1 1(b) 63 100 1 1(c) 360 2 B1 for 357.9… If 0 scored, SC1 for their value correctly rounded to the nearest 10 1(d) 1.106 2 B1 for 1.1057… If 0 scored, SC1 for their value greater than 4 significant figures correctly rounded to 4 significant figures 1(e) 36 , 43 2 B1 for each 1(f)(i) 17.6[0] 1 1(f)(ii) 2.4[0] 1 1(g) [LCM=] 42 [HCF=] 7 3 B1 for [HCF =] 7 AND B2 for [LCM =] 42 or B2 for answers reversed or B1 for [LCM=] 42k, k > 0 or for14 7 2 =  and 21 3 7 = soi 2(a) Correct stem-and-leaf diagram 2 4 9 3 1 6 8 8 4 2 6 8 9 5 1 4 8 6 0 2 2 B1 for unordered stem-and-leaf diagram or 3 correct lines Correct key, e.g. 2 | 4 = 24 1 2(b)(i) 38 1 2(b)(ii) 46 1 2(b)(iii) 18 2 B1 for 54 or 36 seen 2(b)(iv) 44.4 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 5 of 7 Question Answer Marks Partial Marks 3(a) 12864 3 B2 for 864 or M2 for 12000 4 1.8 12000 100  + or M1 for   12000 4 1.8 100   3(b) 4 B3 for three correct sectors with no/wrong labels or B2 for one correct sector with correct label or 3 correct angles seen or B1 for one correct angle 4(a)(i) 260.286 1 4(a)(ii) 1 [min] 14 [s] 3 M2 for 3.337 60 60 162   soi by 74.155… or M1 for 3.337 162 soi by 0.02059 … If 0 scored, SC1 for their time greater than 60s converted correctly to minutes and seconds 4(b) 80.6 or 80.55… 2 M1 for 290 1000 or 290 3600   4(c) 200 000 2 M1 for figs 9 450 5(a) 1 6 1 5(b) 1 36 2 M1 for 1 1 6 6  or sample space diagram oe 5(c) 50 2 M1 for 1 300 6  6(a) (5, 4) (2, 0) 2 B1 for each 6(b) parallelogram 1 6(c) 12 2 M1 for   1 3 4 2 2   oe

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 6 of 7 Question Answer Marks Partial Marks 6(d) 0 1 6(e) 2 1 7(a) Correct points plotted 2 B1 for 2 or 3 correctly plotted 7(b) positive 1 7(c) Correct ruled line drawn 2 B1 for ruled line through the mean point but not in tolerance or B1 for ruled line not through mean point but in tolerance 7(d) 6 or 7 1 FT their ruled line with positive gradient 8(a)(i) 385 2 M1 for 6 50 85  + 8(a)(ii) 7.5 2 M1 for 460 50 number of hours 85 =  + 8(b) or − = − T F T F r n n n 2 M1 for or T F T F rn r n n − = = + 9(a) 2 B1 for 2 correct values 9(b)(i) 18 1 9(b)(ii) 2 2 M1 for 6 2 12 4 x x + = + or better 9(c) - 8 < 16 1 9(d) ( ) 3 2 1 − y y 2 M1 for ( ) ( ) 2 3 2 or 6 3 y y y y − − If 0 scored, SC1 for 2y(3y – 1.5) 9(e)(i) 5 1 9(e)(ii) 4 1 10(a)(i) 90 1 10(a)(ii) 48 1 10(a)(iii) 42 1 10(a)(iv) 132 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 7 of 7 Question Answer Marks Partial Marks 10(b) 130 3 M2 for 5  180 – (120 + 135 + 125 + 140 + 115 + 135) or better or M1 for 5 180  or ( ) 120 135 125 140 115 135 + + + + + soi by 900 or 770 11(a) 24 1 11(b) 10 2 M1 for 2 2 6 8 + 11(c) 4.8 2 M1 for 1 24 1 0 2 their their BD =   12(a) 2 4π 581 = r M1 r =6.79… leading to 6.8 A1 12(b) 1320 or 1317. … 2 M1 for 3 4 π 6.8 3  12(c) 11[.0] or 10.96… 2 M1 for 3 x their = (b) or better 13(a) ( ) 0, 1 − 1 ( ) 3.68 or 3.677 , 0  1 13(b)(i) ( ) ( ) 3.55, 4.78 or 3.546 , 4.776 − −   2 B1 for each If 0 scored, SC1 for ( ) 3.5,4.8 − 13(b)(ii) ( ) ( ) 1.88, 3.21 or 1.879 , 3.211 − −  2 B1 for each If 0 scored, SC1 for ( ) 1.9, 3.2 − 13(c)   3.21 4.78 −   a 2 FT their max and min B1 for each end point