Cambridge IGCSE Mathematics - International 0607 — 2021 Feb/March Paper 3 · Variant 2

This document has 16 pages. Any blank pages are indicated. Cambridge IGCSE™ DC (CE/CGW) 199834/2 © UCLES 2021 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) February/March 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 [ ]. * 5 4 8 5 3 1 3 6 7 7 *

2 0607/32/F/M/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/F/M/21 © UCLES 2021 [Turn over Answer all the questions. 1 (a) 6 13 21 25 27 38 39 41 43 49 From the list above, write down (i) an even number, … [1] (ii) a factor of 50, … [1] (iii) a multiple of 7, … [1] (iv) a triangle number, … [1] (v) a cube number, … [1] (vi) a prime number. … [1] (b) Find 421 3 . Give your answer correct to 4 significant figures. … [2] (c) Work out 27 49 41 # . Give your answer correct to 5 decimal places. … [2]

4 0607/32/F/M/21 © UCLES 2021 2 Here is the price list in a restaurant. You can choose a 1-course meal or a 2-course meal or a 3-course meal. 1-course meal $28 2-course meal $35 3-course meal $42 Coffee or Tea $3 Anna and Alexa eat a meal in this restaurant. Anna has a 3-course meal and a cup of coffee. Alexa has a 2-course meal and two cups of tea. (a) Work out how much this costs altogether. $ … [2] (b) They pay a service charge of 15% of this cost. (i) Work out the total cost including the service charge. $ … [2] (ii) They each pay half of the total cost including the service charge. Work out how much they each pay. $ … [1]

5 0607/32/F/M/21 © UCLES 2021 [Turn over 3 A B D C E 6 cm 10 cm 100° x° NOT TO SCALE ABCD is a rectangle. AD = 6 cm, AE = 10 cm and angle AEB = 100°. (a) Write down the size of one interior angle of a rectangle. … [1] (b) Use trigonometry to show that the value of x is 37, correct to the nearest whole number. [2] (c) Find the size of (i) angle DAE, Angle DAE = … [1] (ii) angle ABE, Angle ABE = … [2] (iii) angle EBC. Angle EBC = … [1]

6 0607/32/F/M/21 © UCLES 2021 4 Hikaru throws a die 40 times. The results are shown in the bar chart. 2 4 6 Frequency Number on die 8 10 1 0 3 5 7 9 1 2 3 4 5 6 (a) Write down the mode. … [1] (b) Find how many more times she throws 2 than 1. … [1] (c) Calculate the mean. … [2] (d) Hikaru represents her results in a pie chart. Work out the sector angle for throwing a 3. … [2]

7 0607/32/F/M/21 © UCLES 2021 [Turn over 5 The diagram shows a 1 cm2 grid. 0 y x 2 4 6 8 1 3 5 7 1 3 5 7 9 2 4 6 8 (a) On the grid, plot and label the points A (3, 5), B (6, 5), C (8, 1) and D (1, 1). Join the points to form a quadrilateral. [2] (b) Write down the mathematical name for quadrilateral ABCD. … [1] (c) Write down the coordinates of the mid-point of BC. ( … , …) [1] (d) Work out the gradient of DA. … [2] (e) Use Pythagoras’ Theorem to work out the length of BC. … cm [2] (f) Work out the perimeter of ABCD. … cm [2]

8 0607/32/F/M/21 © UCLES 2021 6 Piotr works at a pottery making solid spheres. (a) Each sphere has a radius of 2 cm. (i) Calculate the volume of one sphere. … cm3 [2] (ii) Calculate the surface area of one sphere. … cm2 [2] (b) A sphere costs $4.50 to make. The selling price of a sphere is $25. (i) Work out the profit made when a sphere is sold. $ … [1] (ii) In a sale, the selling price of a sphere is reduced by 16%. Work out the sale price of a sphere. $ … [2]

9 0607/32/F/M/21 © UCLES 2021 [Turn over 7 (a) Solve. (i) x 6 3 + = - x = … [1] (ii) ( ) x 5 2 1 6 - = x = … [2] (b) Show the inequality x 2 H on the number line. 4 2 0 3 1 – 1 5 x – 2 [1] (c) Simplify. r r r 3 2 + - … [1] (d) a a a n n 16 # = Find the value of n. n = … [1] (e) Write as a single fraction in its simplest form. (i) m m 7 2 3 + … [2] (ii) m m 4 3 9 8 # … [2]

10 0607/32/F/M/21 © UCLES 2021 8 11 males were asked to score how pleased they were to receive socks as a present. For each male, their score from 0 to 10 and their age in years are shown in the table. Age (years) 10 15 20 25 30 35 45 50 60 70 80 Score 1 2 3 7 5.5 6.5 5 7.5 10 9.5 9 (a) Complete the scatter diagram. The first 6 points have been plotted for you. 0 2 4 Score 6 1 3 5 7 9 8 10 10 30 50 70 20 0 40 60 80 Age (years) [2] (b) What type of correlation is shown in the scatter diagram? … [1]

11 0607/32/F/M/21 © UCLES 2021 [Turn over (c) Find (i) the mean age, … years [1] (ii) the mean score. … [1] (d) On the scatter diagram, draw a line of best fit. [2] (e) Use your line of best fit to find a score for a male aged 55 years. … [1]

12 0607/32/F/M/21 © UCLES 2021 9 (a) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 4, 6, 8, 10} B = {1, 2, 5, 10} (i) Complete each statement. A B + = {…} n(B) = … 5 g … [3] (ii) Write each element in the correct region of the Venn diagram. A B U [2] (b) On the Venn diagram, shade the region ( ) P Q , l . P Q U [1]

13 0607/32/F/M/21 © UCLES 2021 [Turn over 10 A birthday cake is in the shape of a cylinder of radius 11 cm and height 10 cm. (a) Calculate the volume of the cake. Give the units of your answer. … … [3] (b) The top of the cake and the curved surface area of the cake are covered in icing. Calculate the area of the cake that is covered in icing. … cm2 [3] (c) The top of the cake is divided into 12 equal sectors. Work out the arc length of one sector. Give your answer correct to the nearest centimetre. … cm [3]

14 0607/32/F/M/21 © UCLES 2021 11 A B D C 0 y x 9 8 7 6 5 4 3 2 1 – 1 – 2 – 3 – 4 1 2 3 4 5 6 7 8 9 – 5 – 6 – 4 – 3 – 2 – 1 (a) Describe fully the single transformation that maps shape A onto shape B. … … [2] (b) Describe fully the single transformation that maps shape A onto shape C. … … [3] (c) Describe fully the single transformation that maps shape A onto shape D. … … [2] (d) Draw the enlargement of shape A with scale factor 2 and centre (0, 0). [2]

15 0607/32/F/M/21 © UCLES 2021 12 0 y x – 3 3 – 5 8 (a) On the diagram, sketch the graph of . y 0 5x = for x 3 3 G G - . [2] (b) Write down the equation of the horizontal asymptote. … [1] (c) On the same diagram, sketch the graph of y x 4 2 =- + for x 3 3 G G - . [2] (d) Find the zeros of the graph of y x 4 2 =- + . … and … [2] (e) Find the x-coordinate of each point where the graphs of . y 0 5x = and y x 4 2 =- + intersect. x = … and x = … [2]

16 0607/32/F/M/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. BLANK PAGE

This document consists of 7 printed pages. © UCLES 2021 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) March 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 March 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 March 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 March 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 March 2021 © UCLES 2021 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) 6 or 38 1 1(a)(ii) 25 1 1(a)(iii) 21 or 49 1 1(a)(iv) 6 or 21 1 1(a)(v) 27 1 1(a)(vi) 13 or 41 or 43 1 1(b) 7.495 2 B1 for 7.4948… If 0 scored, SC1 for their value greater than 4 sf correctly rounded to 4 sf. 1(c) 0.03099 2 B1 for 0.30990… If 0 scored, SC1 for their value greater than 5 dp correctly rounded to 5 dp. 2(a) 86 2 B1 for 42 + 3 soi by 45 or 35 2 3 + × soi by 41 2(b)(i) 98.9[0] 2 M1 for 15 100 × their (a) oe 2(b)(ii) 49.45 1 FT their (b)(i) 3(a) 90 1 3(b) sin […] = 6 10 or sin […] = 0.6 M1 36.9 or 36.86 to 36.87 A1 3(c)(i) 53 1 3(c)(ii) 43 2 B1 for angle EAB = 37 or angle BEC = 43 soi 3(c)(iii) 47 1 FT 90 – their (c)(ii) 4(a) 4 1 4(b) 3 1 4(c) 3.775 2 M1 for at least three of 4 1 × , 7 2 × , 5 3 × , 9 4 × , 8 5 × or 7 6 × seen or for dividing a total by 40 4(d) 45 2 M1 for 5 40 or 360 40 soi 5(a) All points plotted correctly 2 B1 for 2 or 3 points plotted correctly

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED March 2021 © UCLES 2021 Page 5 of 7 Question Answer Marks Partial Marks 5(b) Trapezium 1 FT a mathematical name if correct from their plotted points 5(c) (7, 3) 1 5(d) 2 2 M1 for 5 1 3 1 − − oe or for a suitable triangle on the grid with the lengths marked 5(e) 4.47 or 4.472… 2 M1 for ( ) ( ) 2 2 6 8 5 1 − + − oe 5(f) 18.9 or 18.94… 2 FT 7 + 3 + 2× their (e) M1 for sum involving at least 2 correct lengths 6(a)(i) 33.5 or 33.51… 2 M1 for 3 4 2 3 ×π× oe 6(a)(ii) 50.3 or 50.26 to 50.28 2 M1 for 2 4 2 × π× oe 6(b)(i) 20.5[0] 1 6(b)(ii) 21 2 M1 for 84 25 100 × oe or 16 25 100 × oe 7(a)(i) 9 − 1 7(a)(ii) 1.1 oe 2 M1 for 10 5 6 x −= or 6 2 1 5 x −= 7(b) Filled circle at 2 and arrow in positive direction 1 7(c) 4r 1 7(d) 8 1 7(e)(i) 23 14 m final answer 2 M1 for correct common denominator 7(e)(ii) 2 3 final answer 2 B1 for 24 36 m m or better or M1 for correct cancelling of 8 and 4 or 3 and 9 or m and m 8(a) All points plotted correctly 2 B1 for 3 or 4 points plotted correctly 8(b) positive 1 8(c)(i) 40 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED March 2021 © UCLES 2021 Page 6 of 7 Question Answer Marks Partial Marks 8(c)(ii) 6 1 8(d) Correct ruled line 2 B1 for ruled line with positive gradient through their mean point but not in tolerance or ruled line in tolerance but not through their mean point. 8(e) 7.5 to 8 1 FT their ruled line with positive gradient 9(a)(i) {2, 10} 4 A 3 B1 for each 9(a)(ii) Correct diagram 2 B1 for 2 correct regions 9(b) Correct shading 1 10(a) 3800 or 3801. … 2 M1 for π 2 11 10 × × oe cm3 1 10(b) 1070 or 1071. … 3 M1 for π 2 11 × oe M1 for 2π 11 10 × × oe 10(c) 6 nfww 3 B2 for 5.76 or 5.75 to 5.76 OR M2 for 2 11 12 π× oe or M1 for 2 11 π× oe 11(a) reflection 𝑥= 3 2 B1 for each 11(b) rotation 90° clockwise oe (0, 0) oe 3 B1 for each

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED March 2021 © UCLES 2021 Page 7 of 7 Question Answer Marks Partial Marks 11(c) translation 5 6 −     −   2 B1 for each 11(d) Correct enlargement (6, 2), (6, 8), (8, 6), (8, 8) 2 B1 for enlargement scale factor 2 from another centre 12(a) Correct sketch 2 B1 for approximately correct shape in 1st and 2nd quadrants only B1 for crossing y-axis in approximately correct place 12(b) 0 y = 1 12(c) Correct sketch 2 B1 for approximately the correct shape B1 for crossing the axes in approximately the correct places. 12(d) 2 − and 2 2 B1 for each If 0 scored, SC1 for (–2, 0), (2, 0) 12(e) 1.26 − or 1.264... − 1.93 or 1.933... 2 B1 for each If 0 scored, SC1 for –1.3 and 1.9