Cambridge IGCSE Mathematics - International 0607 — 2021 May/June Paper 3 · Variant 2

This document has 16 pages. Cambridge IGCSE™ DC (CE/CGW) 199830/3 © UCLES 2021 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 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 [ ]. * 2 7 1 4 5 4 1 4 0 1 *

2 0607/32/M/J/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/M/J/21 © UCLES 2021 [Turn over Answer all the questions. 1 (a) Ruri buys these items. 1 bag of lettuce $1.20 1 cucumber $0.90 1 box of 8 tomatoes $1.60 1 bag of 3 peppers $1.50 1 bag of 6 avocados $3.00 (i) Work out the total cost of the items. $ … [1] (ii) Ruri makes a salad. The items she uses are shown in the table. Complete the table. Item Cost ($) 1 bag of lettuce 2 1 a cucumber 0.45 4 tomatoes 1 pepper 1 avocado Total [3] (b) Roses cost $1.50 each. Ruri has $10.00 to spend. (i) Work out the greatest number of roses she can buy. … roses [1] (ii) Work out how much money she has left. $ … [1]

4 0607/32/M/J/21 © UCLES 2021 2 There are 200 shirts in the school shop. Lotem counts the number of shirts of each size. Size S M L XL XXL Frequency 36 64 48 32 20 (a) Complete the bar chart to show this information. 0 20 40 Frequency 60 10 30 50 70 S M L XL XXL Size of shirt [2] (b) Which size is the mode? … [1] (c) Work out how many more shirts are size S than size XL. … [1] (d) Complete the relative frequency table. Write each value as a decimal. Size S M L XL XXL Relative frequency [2] (e) Find the probability that a shirt, chosen at random, is not size L. … [1]

5 0607/32/M/J/21 © UCLES 2021 [Turn over 3 (a) Write the number 30 062 in words. … [1] (b) Write down all the factors of 50. … [2] (c) Write 6 1, 17% and 0.16 in order of size, starting with the smallest. … , … , … [1] smallest (d) Find the value of 62. Give your answer correct to 3 decimal places. … [2] (e) Work out . . . 8 4 6 4 9 3 + . Give your answer correct to 2 significant figures. … [2] (f) These are the first four terms of a sequence. 60 53 46 39 (i) Find the next two terms of this sequence. … , … [2] (ii) Find the nth term of this sequence. … [2]

6 0607/32/M/J/21 © UCLES 2021 4 0 x 2 3 4 5 6 – 3 – 2 – 5 – 6 – 4 – 1 – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 3 4 5 2 7 8 6 1 y 1 (a) On the grid, plot the points A (2, 1), B (6, 1) and C (6, -3). [2] (b) ABCD is a square. (i) On the grid, plot point D and draw the square. [1] (ii) Write down the coordinates of point D. ( … , …) [1] (c) Write down the coordinates of the mid-point of BC. ( … , …) [1] (d) Write down the equation of the line AB. … [1] (e) Reflect square ABCD in the y-axis. [1] (f) Translate square ABCD by the vector 1 - 5 b l. [2]

7 0607/32/M/J/21 © UCLES 2021 [Turn over 5 10 cm 2.5 cm 20 cm NOT TO SCALE The diagram shows a sign made from card. The card is in the shape of a rectangle with a circle cut from it. (a) Work out the perimeter of the rectangle. … cm [1] (b) Some of these signs are cut from a sheet of card measuring 1.8 metres by 1.6 metres. Work out the maximum number of these signs that can be cut from this sheet of card. … [3] (c) The radius of the circle is 2.5 cm. Work out the shaded area. … cm2 [3] (d) The rectangle is enlarged by scale factor 3. Work out the length and width of the enlarged rectangle. … cm and … cm [2]

8 0607/32/M/J/21 © UCLES 2021 6 (a) y x 6 5 4 3 2 1 – 1 – 2 – 3 – 4 – 3 – 2 – 1 1 0 2 3 4 5 6 The diagram shows the graph of y = f(x). On the same diagram, sketch the graph of (i) y = f(x) + 2, [1] (ii) y = f(x + 3). [1] (b) 6 – 3 0 3 – 1 y x (i) On the diagram, sketch the graph of y x x 2 4 2 = - for x 1 3 G G - . [2] (ii) Find the coordinates of the local minimum. ( … , …) [1]

9 0607/32/M/J/21 © UCLES 2021 [Turn over 7 An unbiased blue die has a cross on 2 faces and a circle on the other 4 faces. An unbiased red die has a cross on 1 face and a circle on the other 5 faces. (a) Micha rolls the blue die. Find the probability that he rolls (i) a circle, … [1] (ii) a tick. … [1] (b) Derk rolls both dice. (i) Find the probability that he rolls a cross on the blue die and a cross on the red die. … [2] (ii) Derk rolls the two dice 360 times. Find the expected number of times he rolls a cross on the blue die and a cross on the red die. … [1]

10 0607/32/M/J/21 © UCLES 2021 8 (a) A B NOT TO SCALE D C M 53° z° y° x° The diagram shows a rectangle, ABCD. M is the mid-point of AB and angle BMC = 53°. Find the value of each of x, y and z. x = … y = … z = … [3] (b) The diagram shows another rectangle PQRS. P Q NOT TO SCALE S R Complete each statement using one word from this list. similar congruent acute obtuse right reflex alternate corresponding The angle QPS is … The angle QRP is … Triangle PQR is … to triangle PSR. Angle QPR is equal to angle PRS because they are … angles. [4]

11 0607/32/M/J/21 © UCLES 2021 [Turn over 9 (a) 3 km NOT TO SCALE 4 km North A B x° C The diagram shows the positions of three houses, A, B and C. B is 4 km due East of A. C is 3 km due South of B. (i) Use trigonometry to calculate the value of x. x = … [2] (ii) Find the bearing of A from C. … [1] (b) Inez walks from home to Hindy’s house. The distance is 7 km. Inez walks at a speed of 4 km/h. (i) Work out how long this takes. Give your answer in hours and minutes. … hours … minutes [2] (ii) Inez leaves home at 13 20. Work out the time that she arrives at Hindy’s house. … [1]

12 0607/32/M/J/21 © UCLES 2021 10 (a) Solve. x x 4 7 8 9 + = - x = … [2] (b) Expand and simplify. ( ) ( ) x y x y 2 3 2 + - - … [2] (c) Factorise fully. p q pq 3 6 2 3 - … [2] (d) 2 2 2 n n 2 12 # = Find the value of n. n = … [1] (e) 5 5 5 t 6 4 = Find the value of t. t = … [1]

13 0607/32/M/J/21 © UCLES 2021 [Turn over (f) Write as a single fraction in its simplest form. (i) a a 2 5 2 + … [2] (ii) t t 9 2 3 # … [2] (iii) m m 5 3 4 2 ' … [2]

14 0607/32/M/J/21 © UCLES 2021 11 The cumulative frequency curve shows the time, in minutes, that 200 customers waited to be served in a restaurant. 0 20 40 Cumulative frequency 60 80 100 120 140 160 180 200 0 1 2 3 4 Time (minutes) 5 6

15 0607/32/M/J/21 © UCLES 2021 [Turn over (a) Use the curve to find (i) the median, … minutes [1] (ii) the lower quartile, … minutes [1] (iii) the interquartile range. … minutes [1] (b) (i) Complete the frequency table. Time (t minutes) Frequency t 0 1 1 G t 1 2 1 G t 2 3 1 G t 3 4 1 G t 4 5 1 G t 5 6 1 G 10 [2] (ii) Write down the modal class. … 1 t G … [1] (iii) Work out an estimate of the mean. … minutes [2] Question 12 is printed on the next page.

16 0607/32/M/J/21 © UCLES 2021 12 NOT TO SCALE 0.2 cm 13 cm h cm 5 cm 6 cm A trophy is in the shape of a solid cone on top of a solid cylinder. The cone has radius 5 cm and slant height 13 cm. The cylinder has radius 6 cm and height 0.2 cm. (a) Work out the volume of the cylinder. … cm3 [2] (b) Use Pythagoras’ Theorem to show that the vertical height, h cm, of the cone is 12 cm. [2] (c) Work out the volume of the cone. … cm3 [2] (d) Work out the curved surface area of the cone. … cm2 [2] 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.

This document consists of 7 printed pages. © UCLES 2021 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 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 May/June 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 May/June 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 May/June 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 May/June 2021 © UCLES 2021 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) 8.2[0] 1 1(a)(ii) 1.2[0] [0.45] 0.8[0] 0.5[0] 0.5[0] 3.45 3 B2 for 3 or 4 correct B1 for 2 correct 1(b)(i) 6 1 1(b)(ii) 1 1 FT their integer (b)(i) < 6 2(a) Correct bar chart drawn 2 B1 for 2 or 3 bars correct height and equal width or all bars correct height but not equal width 2(b) M 1 2(c) 4 1 2(d) 0.18 0.32 0.24 0.16 0.1[0] 2 B1 for at least 2 correct or all correct fractions 2(e) 0.76 oe 1 3(a) thirty thousand [and] sixty-two 1 3(b) 1, 2, 5, 10, 25, 50 2 B1 for four or five correct 3(c) 0.16, 1 6 , 17% 1 3(d) 7.874 2 B1 for 7.87 or 7.8740… 3(e) 1.9 2 B1 for 1.869... or 1.87 If 0 scored, SC1 for their answer seen and correctly rounded to 2 sf 3(f)(i) 32 25 2 B1 for each 3(f)(ii) 67 – 7n 2 B1 for k – 7n or 67 – jn, j ≠ 0 4(a) Points plotted correctly 2 B1 for 2 points plotted correctly 4(b)(i) Point plotted correctly 1 4(b)(ii) (2, –3) 1 FT their plotted point 4(c) (6, –1) 1 4(d) y = 1 1 4(e) Correct reflection 1 FT their shape

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 5 of 7 Question Answer Marks Partial Marks 4(f) Correct translation 2 B1 for translation 1 k −       or 5 k    5(a) 60 1 5(b) 144 3 B2 for 180 160 10 20 × or 180 160 20 10 × oe soi or B1 for 180 10 or 160 20 or 180 20 or 160 10 oe soi 5(c) 180 or 180.3 to 180.4 3 M1 for 20 × 10 soi by 200 M1 for π × 2.52 soi by 19.63… 5(d) 60 and 30 2 B1 for each 6(a)(i) Correct translation of 2 units up 1 6(a)(ii) Correct translation of 3 units to the left 1 If 0 scored in (a)(i) and (a)(ii) SC1 for (a)(i) 2 small squares up and (a)(ii) 3 small squares to the left 6(b)(i) Correct sketch 2 B1 for correct shape B1 for minimum in correct quadrant 6(b)(ii) (1, –2) 1 7(a)(i) 2 3 oe 1 7(a)(ii) 0 1 7(b)(i) 1 18 oe 2 B1 for 2 1 6 6 × 7(b)(ii) 20 1 FT 360 × their (b)(i), 0 < their (b)(i) < 1 8(a) [x =] 37 [y =] 53 [z =] 74 3 B1 for each 8(b) Right Acute Congruent Alternate 4 B1 for each Accept similar in place of congruent

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 6 of 7 Question Answer Marks Partial Marks 9(a)(i) 53.1 or 53.13… 2 M1 for tan [ ] = 4 3 oe 9(a)(ii) 306.9 or 307 1 FT 360 – their acute x 9(b)(i) 1 h 45 min 2 M1 for 7 4 oe 9(b)(ii) 15 05 or 3 05 pm 1 FT 13 20 + their (b)(i) 10(a) 4 2 M1 for 7 + 9 = 8x – 4x oe 10(b) 7y final answer 2 M1 for 2x + 6y or –2x + y seen 10(c) 3pq(p – 2q2) final answer 2 M1 for correct partial factorisation 3(p2q – 2pq3) or 3p(pq – 2q3) or 3q(p2 – 2pq2) or p(3pq – 6q3) or q(3p2 – 6pq2) or pq(3p – 6q2) 10(d) 4 1 10(e) 2 1 10(f)(i) 9 10 a final answer 2 M1 for correct common denominator 10(f)(ii) 2 6 t final answer 2 M1 for 2 3 18 t or evidence of cancelling the 3 and 9 10(f)(iii) 12 5m final answer 2 M1 for 2 3 4 5 m m × 11(a)(i) 3 1 11(a)(ii) 2 1 11(a)(iii) 1.8 1 11(b)(i) 20, 30, 50, 60, 30 2 B1 for 3 or 4 correct 11(b)(ii) 3 < t ⩽ 4 1 FT their table 11(b)(iii) 2.9 2 M1 for multiplying mid-points by frequencies – at least 3 seen 12(a) 22.6 or 22.61 to 22.63 2 M1 for π × 62 × 0.2 12(b) 2 2 13 5 − soi 2 M1 for h2 + 52 = 132 oe 12(c) 314 or 314.1 to 314.2 2 M1 for 2 1 5 12 3 × π× ×

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 7 of 7 Question Answer Marks Partial Marks 12(d) 204 or 204.2… 2 M1 for π × 5 × 13