Cambridge IGCSE Mathematics - International 0607 — 2023 May/June Paper 2 · Variant 1

This document has 8 pages. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2023 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. ● Calculators must not be used in this paper. ● You may use tracing paper. ● You must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. ● All answers should be given in their simplest form. INFORMATION ● The total mark for this paper is 40. ● The number of marks for each question or part question is shown in brackets [ ]. * 3 9 4 0 0 6 8 4 6 9 * DC (LK/CT) 311890/3 © UCLES 2023

2 0607/21/M/J/23 © UCLES 2023 Formula List For the equation ax bx c 0 2 + + = x a b b ac 2 4 2 ! = - - Curved surface area, A, of cylinder of radius r, height h. r A rh 2 = Curved surface area, A, of cone of radius r, sloping edge l. r A rl = Curved surface area, A, of sphere of radius r. r A r 4 2 = Volume, V, of pyramid, base area A, height h. V Ah 3 1 = Volume, V, of cylinder of radius r, height h. r V r h 2 = Volume, V, of cone of radius r, height h. r V r h 3 1 2 = Volume, V, of sphere of radius r. r V r 3 4 3 = sin sin sin A a B b C c = = cos a b c bc A 2 2 2 2 = + - sin bc A 2 1 Area = A C B c b a

3 0607/21/M/J/23 © UCLES 2023 [Turn over Answer all the questions. 1 (a) Insert one pair of brackets to make the statement correct. 3 # 7 + 2 + 9 = 36 [1] (b) Work out ( . ) 0 2 3. … [1] (c) Write down a prime number between 80 and 90. … [1] 2 Solve the equation. x 7 5 3 - =- x = … [2] 3 (a) Work out 1 2 5 3 - - e e o o. f p [1] (b) P is the point (-3, 6). Q is the point (0, 2). Find the translation vector that maps the point P onto the point Q. f p [2]

4 0607/21/M/J/23 © UCLES 2023 4 (a) Factorise. p pq 2 2 - … [1] (b) Expand the brackets and simplify. ( )( ) p p 7 3 - + … [2] 5 (a) Work out 12 11 4 3 + . Give your answer as a mixed number in its simplest form. … [2] (b) Simplify x a y b 2 ' . Give your answer as a single fraction. … [1]

5 0607/21/M/J/23 © UCLES 2023 [Turn over 6 0 4 x y 3 2 1 –1 –2 4 3 2 1 T Rotate triangle T 90° clockwise about the point (2, 1). [2] 7 The interior angle of a regular polygon is 140°. Find the number of sides of this polygon. … [3] 8 Rearrange this equation to make x the subject. y x 7 2 = + x = … [2]

6 0607/21/M/J/23 © UCLES 2023 9 Simplify w 3 3 3 ` j . … [2] 10 NOT TO SCALE B P A 62° x° 39° APB is a tangent to the circle at P. Work out the value of x. x = … [2] 11 Simplify 27 12 108 + - . … [2]

7 0607/21/M/J/23 © UCLES 2023 [Turn over 12 ( ) ( °) f sin x x 3 4 = Find the amplitude and period of ( ) f x . Amplitude = … Period = … [2] 13 y varies inversely as x. When , x y 9 2 = = . Find y in terms of x. y = … [2] 14 ( ) f x x 7 1 = Find ( ) f x 1 - . ( ) f x 1 = - … [1] Question 15 is printed on the next page.

8 0607/21/M/J/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. 15 Simplify. (a) x x 2 3 1 2 + - - … [3] (b) x x ax a x 6 12 6 8 3 4 2 + - - - + … [5]

This document consists of 5 printed pages. © UCLES 2023 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2023 MARK SCHEME Maximum Mark: 40 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 2023 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/21 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 2 of 5 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.

0607/21 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 3 of 5 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

0607/21 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 4 of 5 Question Answer Marks Partial Marks 1(a) 3 × (7 + 2) + 9 = 36 1 1(b) 0.008 oe 1 1(c) 83 or 89 1 2 2 2 M1 for 7 3 7 3 5 or 5 3 7 or 5 5       x x x 3(a) 6 1        1 3(b) 3 4        2 B1 for 3    k or 4 k        If 0 scored, SC1 for   3, 4  4(a) (2 )  p p q final answer 1 4(b) 2 4 21   p p final answer 2 B1 for three terms correct in 2 7 3 21    p p p 5(a) 2 13 cao 2 M1 for 11 9 12 12  5(b) 2ay bx final answer 1 6 Image at (2, 1), (3, 2), (2, 3) 2 B1 for correct orientation wrong position or for rotation 90˚ anticlockwise about (2, 1) 7 9 3 M2 for [n =]   360 180 140  their or 40 360  n or M1 for 180 – 140 or   180 2 140   n n 8 2 2 or 7 7 7   y y final answer 2 M1 for 2 2 7 or 7 7     y y x x 9 9 27w final answer 2 B1 for 9 kw or 27 k w 10 79 2 B1 for 79, 39 or 62 correctly added to diagram or M1 for 180 – (39 + 62) oe 11 3  2 B1 for two of 3 3 or 2 3 or 6 3 12 Amplitude = 3 Period = 90 oe 2 B1 for each or SC1 for answers reversed

0607/21 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 5 of 5 Question Answer Marks Partial Marks 13 6 x oe 2 M1 for k y x or  y x k 14 7x 1 15(a) 7 ( 2)( 1)    x x x final answer 3 B1 for 3 3 2 4   x x oe or better B1 for common denominator ( 2)( 1)   x x or 2 2   x x 15(b) 2 3 2 1   x a or 2 3 1 2    x a final answer 5 B2 for    2 3 3 4   x x or B1 for      ax b cx d with ac = 6 and either bd = –12 or ad + bc = 1 or for 2 (3 4) 3(3 4) or 3 (2 3) 4(2 3)       x x x x x x B2 for   2 1 3 4   a x or B1 for 2a(3x – 4) – (3x–4) or 3x(2a – 1) – 4(2a – 1)