Cambridge IGCSE Mathematics - International 0607 — 2022 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 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 [ ]. * 9 8 4 5 9 0 9 1 6 7 * DC (LK/CGW) 214223/2 © UCLES 2022

2 0607/31/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 0607/31/O/N/22 © UCLES 2022 [Turn over Answer all the questions. 1 Every week, a city company pays its workers travel expenses. Each worker can travel for work either by car or by bicycle. This is how travel expenses are worked out. Travel by car Number of kilometres # $0.40 Travel by bicycle $15 + number of kilometres # $0.25 (a) One week, Anna cycles a total of 45 km for work. Work out her travel expenses. $ … [2] (b) Raza has a car and a bicycle. He travels 120 km for work. Will he be paid more travel expenses if he uses his car or if he uses his bicycle? Work out how much more he would receive. … pays more by $ … [3] (c) Tyson always travels for work by car. One week he receives $14.80 in travel expenses. Work out how many kilometres he travels for work that week. … km [1] (d) A worker cycles for work. Write a formula for the travel expenses, $E, this worker receives when they travel k kilometres for work one week. … [2]

4 0607/31/O/N/22 © UCLES 2022 2 (a) This table shows how Toby spent money on his holiday. Travel Accommodation Food Entertainment $60 $168 $116 $56 (i) Work out how much Toby spent in total. $ … [1] (ii) Work out how much more money Toby spent on Food than on Entertainment. $ … [1] (iii) What fraction of the total amount did Toby spend on Travel? Give your answer as a fraction in its simplest form. … [2] (iv) Work out the percentage of the total amount that Toby spent on Travel and Accommodation. … % [2]

5 0607/31/O/N/22 © UCLES 2022 [Turn over (b) This pie chart shows how Neesha spent her money on holiday. Food Entertainment Travel Accommodation (i) Measure the angle for Travel. … [1] (ii) Work out the fraction of the total amount that was spent on Accommodation. … [1] (iii) Neesha spent $540 in total. Work out how much she spent on Food. $ … [2]

6 0607/31/O/N/22 © UCLES 2022 3 (a) The diagram shows a quadrilateral, ABCD, drawn on a 1 cm square grid. y x A C B D 4 3 2 3 1 – 3 – 2 – 1 2 1 – 1 0 (i) Write down the mathematical name of the quadrilateral. … [1] (ii) Write down the coordinates of point A, point B and point C. A = ( … , … ) B = ( … , … ) C = ( … , … ) [3] (iii) Find the area of the quadrilateral. … cm2 [2] (b) On the diagram below, draw any lines of symmetry. [1]

7 0607/31/O/N/22 © UCLES 2022 [Turn over (c) The diagram below shows quadrilateral X and one side of quadrilateral Y. Quadrilateral Y is an enlargement of quadrilateral X. X Y (i) Write down the scale factor of the enlargement. … [1] (ii) Complete the drawing of quadrilateral Y. [2] (d) Here is a quadrilateral with one of its sides extended. 60° 40° k° NOT TO SCALE Work out the value of k. k = … [3]

8 0607/31/O/N/22 © UCLES 2022 4 (a) Write the number seven thousand and twenty-four in figures. … [1] (b) Find the value of (i) .8 42 , … [1] (ii) 163 3 . Give your answer correct to 2 significant figures. … [2] (c) Work out. (i) . . . . 14 1 9 2 16 28 9 2 - + … [1] (ii) . . 3 1 18 6 - - … [1] (d) (i) Write down a square number between 30 and 40. … [1] (ii) Write down a prime number between 30 and 40. … [1]

9 0607/31/O/N/22 © UCLES 2022 [Turn over 5 (a) Factorise. x 4 10 + … [1] (b) Expand. ( ) x x x 3 3 + … [2] (c) Solve. ( ) x 2 3 5 26 - = x = … [3] (d) Write as a single fraction in its simplest form. x y 2 3 5 ' … [2]

10 0607/31/O/N/22 © UCLES 2022 6 Karim asked ten students how much time, in minutes, they spent revising for a Maths test and what score they gained. His results are shown in the table. Time spent revising (minutes) 120 64 70 22 45 100 34 115 0 50 Score 88 58 82 36 23 100 54 88 16 45 (a) Complete the scatter diagram. The first five points have been plotted for you. 0 10 0 10 20 30 40 50 Score 60 70 80 90 100 20 30 40 50 60 Time spent revising (min) 70 80 90 100 110 120 [2] (b) What type of correlation is shown in the scatter diagram? … [1] (c) (i) Work out the mean time spent revising and the mean score. Mean time = … min Mean score = … [2] (ii) On the scatter diagram, draw a line of best fit. [2] (d) Sonya revised for 90 minutes but was absent for the test. Use your line of best fit to estimate a score for Sonya. … [1]

11 0607/31/O/N/22 © UCLES 2022 [Turn over 7 (a) A small lake has an area of m 3500 2. One winter, 68% of this area is covered with ice. All the ice is 0.12 m thick. Calculate the volume of ice on this lake. … m3 [3] (b) Another lake has an area of 124 m 000 2. One winter, the surface is covered in the ratio ice : water = 5 : 3. Calculate the area covered by ice and the area covered by water. ice … m2 water … m2 [2] (c) An ice crystal is . m 8 6 10 7 # - thick. Write .8 6 10 7 # - as an ordinary number. … [1] (d) Lake Superior, Lake Erie and Lake Manitoba are three lakes in North America. (i) Lake Erie has an area of 25 700 000 000 square metres. Write 25 700 000 000 in standard form. … [1] (ii) Lake Superior has an area of .8 2 1010 # square metres and Lake Manitoba has an area of .4 6 109 # square metres. Calculate the difference between the areas of these two lakes. Give your answer in standard form. … m2 [1]

12 0607/31/O/N/22 © UCLES 2022 8 (a) A flower bed is a circle of radius 130 cm. A layer of compost, 15 cm thick, is spread on the flower bed. (i) Work out the volume of compost used. … cm3 [2] (ii) Compost is sold in 120-litre bags. Work out the number of these bags of compost that are needed. … [3] (b) A bag of compost is a cuboid measuring 80 cm by 30 cm by 50 cm. 80 cm 30 cm 50 cm NOT TO SCALE Work out the total surface area of the cuboid. … cm2 [3]

13 0607/31/O/N/22 © UCLES 2022 [Turn over 9 Nina asks 100 students the time, in minutes, they spent exercising one weekend. Her results are shown in the table. Time (t minutes) Frequency t 0 20 1 G 2 t 20 0 4 1 G 4 t 40 0 6 1 G 9 t 60 0 8 1 G 34 t 80 0 10 1 G 27 t 100 120 1 G 24 (a) Calculate an estimate of the mean time. … min [3] (b) Write down the modal group. … t 1 G … [1] (c) One of the 100 students is chosen at random. Work out the probability that this student exercised for less than one hour. … [2] (d) Complete the grouped frequency diagram for these results. 0 20 0 5 10 15 20 25 30 35 40 60 Time (t minutes) Frequency 80 100 120 [2]

14 0607/31/O/N/22 © UCLES 2022 10 (a) x° 5.5 m NOT TO SCALE 2.7 m h m The diagram shows a ladder of length 5.5 m standing on horizontal ground and leaning against a vertical wall. The bottom of the ladder is 2.7 m away from the wall. (i) Show that . h 4 79 = , correct to 3 significant figures. [3] (ii) Calculate the value of x, the angle between the ladder and the ground. x = … [2]

15 0607/31/O/N/22 © UCLES 2022 [Turn over (b) 70° 5.5 m NOT TO SCALE The bottom of the ladder is moved closer to the wall. The ladder now makes an angle of 70° with the ground. Work out the distance the top of the ladder has moved up the wall. … m [3] Question 11 is printed on the next page.

16 0607/31/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 0 y x – 2 2 – 7 7 (a) (i) On the diagram, sketch the graph of y x 1 2 = - for x 2 2 G G - . [2] (ii) Find the coordinates of the local minimum. ( … , … ) [1] (b) (i) On the diagram, sketch the graph of y x x 3 = - for x 2 2 G G - . [2] (ii) Find the coordinates of the local maximum. ( … , … ) [2] (c) Find the x-coordinate of each point of intersection of y x x 3 = - and y x 1 2 = - . x = … and x = … [2]

This document consists of 7 printed pages. © UCLES 2022 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 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.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 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 2022 © UCLES 2022 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

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 4 of 7 Question Answer Marks Partial Marks 1(a) 26.25 2 M1 for 45 × 0.25 soi by 11.25 1(b) Car by $3 3 B1 for 48 B1 for 45 1(c) 37 1 1(d) E = 15 + 0.25k 2 B1 for 15 + 0.25k 2(a)(i) 400 1 2(a)(ii) 60 1 2(a)(iii) 3 20 cao 2 B1 for 60 400 their oe fraction 2(a)(iv) 57 2 M1 for 60 168 400 their + [× 100] 2(b)(i) 75 1 2(b)(ii) 130 360 oe isw 1 2(b)(iii) 135 2 B1 for 90 or 1 4 soi 3(a)(i) kite 1 3(a)(ii) A (3, 1) B ( 1 1 , 2 −2) C (0, 1) 3 B1 for each 3(a)(iii) 6 2 B1 for answer 5 to 1 6 2 or M1 for 3 4 2  or 3 3 2  or 3 1 2  soi 3(b) Correct ruled vertical line 1 3(c)(i) 2 1 3(c)(ii) Correct ruled diagram 2 B1 for 1 other side correct 3(d) 80 3 M2 for 360 – (120 +120 +40) oe or M1 for 120 seen 4(a) 7024 1 4(b)(i) 70.56 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 5 of 7 Question Answer Marks Partial Marks 4(b)(ii) 5.5 2 B1 for 5.46… 4(c)(i) 5.2 1 4(c)(ii) 6 1 4(d)(i) 36 1 4(d)(ii) 31 or 37 1 5(a) 2(2x + 5) final answer 1 5(b) x4 + 3x2 final answer 2 B1 for x4 or [+]3x2 5(c) 6 3 M1 for 6x – 10 = 26 or 3x – 5 = 13 M1 for correct next step after their ax – b = c 5(d) 3xy final answer 10 2 M1 for 3 2 5 x y  6(a) 5 points correctly plotted 2 B1 for 3 points correctly plotted 6(b) Positive 1 6(c)(i) Mean time = 62 Mean score = 59 2 B1 for each 6(c)(ii) Straight line through their mean point and within tolerance 2 B1 for straight line through their mean point but not within tolerance or straight line within tolerance but not through their mean point 6(d) 70 to 90 1 FT their ruled line with positive gradient 7(a) 285.6 3 M2 for 3500 × 0.68 × 0.12 oe or M1 for 3500 × 0.68 oe or 3500×0.12 7(b) [Ice =] 77 500 [Water =] 46 500 2 B1 for one correct or M1 for 124000 5 3 + soi by 15 500 7(c) 0.000 000 86 1 7(d)(i) 2.57 ×1010 1 7(d)(ii) 7.74 ×1010 1 8(a)(i) 796 000 or 796 300 to 796 500 2 M1 for   2 15  

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 6 of 7 Question Answer Marks Partial Marks 8(a)(ii) 7 nfww 3 B1 for 120 000 or their (i) ÷ 1000 M1 for 796394 figs12 their seen 8(b) 15 800 3 M2 for [2×]{(80×30) + (80×50) + (50×30)} oe or M1 for 80×30 or 80×50 or 50×30 9(a) 80.4 3 M1 for at least 3 mid-values seen M1 for ∑t × f soi by 8040 9(b) 60 ⩽ t < 80 1 9(c) 15 100 oe 2 B1 for 15 9(d) Correct grouped frequency bar chart 2 M1 for 2 or 3 more bars with correct width and height or for 4 correct heights but with any incorrect widths 10(a)(i) [h2 =] 5.52 – 2.72 M2 M1 for 2 2 2 2.7 5.5 h + = oe 4.791 to 4.792 A1 10(a)(ii) 60.6 or 60.56 to 60.61 2 M1 for cos[ ] = 2.7 5.5 or sin[ ] = 4.79 5.5 or tan[ ] = 4.79 2.7 10(b) 0.377 or 0.376 to 0.38[0] 3 B2 for 5.1683… or 5.17 or M1 for sin70 =  5.5 soi 11(a)(i) Correct curve 2 B1 for correct shape B1 for vertex on negative y-axis 11(a)(ii) (0, −1) 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 7 of 7 Question Answer Marks Partial Marks 11(b)(i) Correct curve 2 B1 for correct shape B1 for passing through origin 11(b)(ii) (−0.577, 0.385) 2 B1 for each If 0 scored, SC1 for (−0.58, 0.38) 11(c) −1 1 2 B1 for each