Cambridge IGCSE Mathematics - Additional 0606 — 2025 Feb/March Paper 2 · Variant 2

This document has 16 pages. [Turn over * 2 8 3 6 6 0 7 5 5 1 * Cambridge IGCSE™ ADDITIONAL MATHEMATICS 0606/22 Paper 2 February/March 2025 2 hours You must answer on the question paper. No additional materials are needed. 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 scientific calculator where appropriate. ● You must show all necessary working clearly. ● 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 either your calculator value or 3.142. INFORMATION ● The total mark for this paper is 80. ● The number of marks for each question or part question is shown in brackets [ ]. DC (DE/SG) 346700/1 © UCLES 2025 ,










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2 0606/22/F/M/25 © UCLES 2025 List of formulas Equation of a circle with centre (a, b) and radius r. ( ) ( ) x a y b r 2 2 2 - + - = Curved surface area, A, of cone of radius r, sloping edge l. A rl r = Surface area, A, of sphere of radius r. A r 4 2 r = Volume, V, of pyramid or cone, base area A, height h. V Ah 3 1 = Volume, V, of sphere of radius r. V r 3 4 3 r = Quadratic equation For the equation , ax bx c 0 2 + + = x a b b ac 2 4 2 ! = - - Binomial theorem ( ) a b a n a b n a b n r a b b 1 2 … … n n n n n r r n 1 2 2 + = + + + + + + - - - J L KK J L KK J L KK N P OO N P OO N P OO , where n is a positive integer and ( )! ! ! n r n r r n = - J L KK N P OO Arithmetic series ( ) u a n d 1 n = + - ( ) { ( ) } S n a l n a n d 1 2 2 1 2 1 n = + = + - Geometric series u ar n n 1 = - ( ) ( ) S a r r r 1 1 1 n n ! = - - ( ) S r a r 1 1 1 = - 3 Identities sin cos A A 1 2 2 + = sec tan A A 1 2 2 = + cosec cot A A 1 2 2 = + Formulas for ABC T sin sin sin A a B b C c = = cos a b c bc A 2 2 2 2 = + - sin ab C 2 1 T = * 0000800000002 * ,










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3 0606/22/F/M/25 © UCLES 2025 [Turn over 1 O A B The diagram shows a circle with centre O and radius 5 cm. The point A lies on the circle. The point B is such that the line AB is a tangent to the circle. OB has length 13 cm. (a) Find angle AOB, giving your answer in radians. [2] (b) Find the perimeter of the shaded region. [3] (c) Find the area of the shaded region. [3] * 0000800000003 * ,










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4 0606/22/F/M/25 © UCLES 2025 2 (a) Find the x-coordinates of the stationary points on the curve ( )( ) y x x 2 1 3 2 2 2 = - + . [4] * 0000800000004 * ,










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5 0606/22/F/M/25 © UCLES 2025 [Turn over (b) On the axes, sketch the graph of ( )( ) y x x 2 1 3 2 2 2 = - + stating the intercepts with the coordinate axes. [3] O x y (c) Find the values of k for which the equation ( )( ) x x k 2 1 3 2 2 2 - + = has three real and distinct roots. [2] * 0000800000005 * ,










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6 0606/22/F/M/25 © UCLES 2025 3 Solve the equation x x 6 1 12 5 3 5 3 + = , giving your answers correct to 2 decimal places. [4] * 0000800000006 * ,










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7 0606/22/F/M/25 © UCLES 2025 [Turn over 4 (a) A team of 10 players is to be chosen from 15 players. (i) Find the number of different teams that can be chosen if there are no restrictions. [1] The 15 players include 3 sisters who must not be separated. (ii) Find the number of different teams that can be chosen. [3] (b) A 6-digit number is to be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The 6-digit number cannot start with 0 and all six digits must be different. Find how many 6-digit numbers can be formed if the 6-digit number is even. [3] * 0000800000007 * ,










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8 0606/22/F/M/25 © UCLES 2025 5 When ey is plotted against x2, a straight-line graph with gradient 3 - is obtained. The line passes through the point (4.30, 5.85). (a) Find y in terms of x. [4] (b) Find the values of x for which y exists. [3] * 0000800000008 * ,










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9 0606/22/F/M/25 © UCLES 2025 [Turn over 6 It is given that ln y x x 2 1 2 2 = + + ` j . (a) Find x y d d . [3] (b) Given that x increases from 2 to h 2+ , where h is small, find the approximate change in y. [2] (c) Given that y is decreasing by 0.4 units per second, find the corresponding rate of change in x when x 2 = . [3] * 0000800000009 * ,










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10 0606/22/F/M/25 © UCLES 2025 7 It is given that ( )x a 2 f ex = + for x 0 H , where a is an integer and ( )x x 1 g = - for x 1 H . (a) Find the least value of a so that the function gf exists for all x 0 H . [2] (b) In the case where a 5 = , solve the equation ( )x 3 gf = . Give your answer correct to 3 decimal places. [3] * 0000800000010 * ,










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11 0606/22/F/M/25 © UCLES 2025 [Turn over 8 (a) Show that sin tan tan 1 2 2i i i + can be written as sin3i. [2] (b) Hence solve the equation tan sin tan x x x 1 3 3 3 8 1 2 2 + = for ° ° x 180 180 G G - . [5] * 0000800000011 * ,









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12 0606/22/F/M/25 © UCLES 2025 9 In this question, all lengths are in metres and time is in seconds. A particle, P, moves in a straight line such that t seconds after passing through a fixed point O its displacement, s, is given by ( ) ln s t t 5 2 1 5 = + - . (a) Find the value of t for which P is instantaneously at rest. [4] (b) Find the distance P travels between t 0 = and t 2 = . [4] * 0000800000012 * ,









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13 0606/22/F/M/25 © UCLES 2025 [Turn over (c) Find an expression for the acceleration of P in terms of t. [2] (d) Find the acceleration when . t 4 5 = . [1] * 0000800000013 * ,









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14 0606/22/F/M/25 © UCLES 2025 10 The expansion of ( ) ax x b 2 1 4 3 - + b l is written in descending powers of x. The first 3 terms of this expansion are x x cx 81 999 4 3 2 + + . It is given that a, b and c are positive integers. Find the values of a, b and c. [10] * 0000800000014 * ,









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15 0606/22/F/M/25 © UCLES 2025 [Turn over Continuation of working space for Question 10. Question 11 is printed on the next page. * 0000800000015 * ,









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16 0606/22/F/M/25 © UCLES 2025 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 Solve the equation ( . ) cot y 1 5 3 + = where y is in radians and y 0 6 1 1 . [4] * 0000800000016 * ,









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This document consists of 10 printed pages. © Cambridge University Press & Assessment 2025 [Turn over Cambridge IGCSE™ ADDITIONAL MATHEMATICS 0606/22 Paper 2 February/March 2025 MARK SCHEME Maximum Mark: 80 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 February/March 2025 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 2 of 10 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 descriptions 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.

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 3 of 10 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.

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 4 of 10 Annotations guidance for centres Examiners use a system of annotations as a shorthand for communicating their marking decisions to one another. Examiners are trained during the standardisation process on how and when to use annotations. The purpose of annotations is to inform the standardisation and monitoring processes and guide the supervising examiners when they are checking the work of examiners within their team. The meaning of annotations and how they are used is specific to each component and is understood by all examiners who mark the component. We publish annotations in our mark schemes to help centres understand the annotations they may see on copies of scripts. Note that there may not be a direct correlation between the number of annotations on a script and the mark awarded. Similarly, the use of an annotation may not be an indication of the quality of the response. The annotations listed below were available to examiners marking this component in this series. Annotations Annotation Meaning More information required Accuracy mark awarded zero Accuracy mark awarded one Accuracy mark awarded two Accuracy mark awarded three Independent mark awarded zero Independent mark awarded one Independent mark awarded two Benefit of the doubt Communication mark Incorrect point Follow through Highlighter Highlight a key point in the working Ignore subsequent work Method mark awarded zero Method mark awarded one Method mark awarded two Misread Omission

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 5 of 10 Annotation Meaning Off-page comment Allows comments to be entered at the bottom of the RM marking window and then displayed when the associated question item is navigated to. On-page comment Allows comments to be entered in speech bubbles on the candidate response. Premature rounding/approximation Special case Indicates that work/page has been seen Transcription error Correct point Not from wrong working 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

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 6 of 10 Question Answer Marks Guidance 1(a) 5 arccos 13   =     AOB oe M1 For a complete method to find AOB 1.18 A1 1(b) 25.9 cm 3 M1 for 12 = AB soi M1 for arc length = 5theirAOB in radians 1(c) Area = 15.3 cm2 3 M1 for area of triangle = 30 soi M1 for area of sector = 1 25 2  theirAOB in radians 2(a) ( )( ) ( ) ( ) 2 d 1 2 2 3 2 2 2 d 2 = + − − + y x x x x oe or ( ) 2 d 1 6 10 4 d 2 = − − + y x x x oe 2 M1 for attempt to differentiate a product, or expansion and differentiation When d 1 0, 2, d 3 = = − = y x x x nfww 2 M1 for equating their d d y x to zero and attempt to solve a quadratic equation to obtain 2 x-values 2(b) 3 B1 for correct shape with maximum in the first quadrant, continuing into the 4th quadrant. B1 for correct intercepts 2 − and 1.5 on the x-axis or stated and no others; must have a cubic graph B1 for 6 on the y-axis or stated; must have a cubic graph 2(c) 343 54 or 6.35 M1 For finding the y-coordinate of the maximum point. 343 0 54   k or 0 6.35   k A1 A0 if additional values are given.

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 7 of 10 Question Answer Marks Guidance 3 6 3 5 5 6 12 0 + − = x x M1 For attempt to obtain a 3-term quadratic in terms of 3 5 x , allow one sign error. Allow use of substitution 3 3 5 5 4 3 , 3 2 = = − x x M1 Dep for solution of their quadratic equation to obtain 2 solutions in terms of 3 5 x 1.62, 1.97 − 2 M1 for correct attempt to solve an equation of the form 3 5 = x k , 1  k A1 for both 4(a)(i) 3003 B1 4(a)(ii) With the sisters: 792 soi B1 Without the sisters: 66 soi B1 Total 858 B1 4(b) 68 880 3 B1 Starts with 1, 3, 5, 7, 9: 42 000 soi B1 Starts with 2, 4, 6 or 8: 26 880 soi Alternative 68 880 (3) B1 Ends with 0: 15 120 soi B1 Ends with 2, 4, 6 or 8: 53 760 soi 5(a) 2 e = + y mx c soi B1 3 = − m used correctly B1 18.75 = c B1 ( ) 2 ln 18.75 3 = − y x oe B1 Allow 18.8 B0 for poor use of brackets 5(b) ( ) 2 18.75 3 0 −  their x B1 May be implied by final answer Critical values 2.5 oe seen B1 May be implied by final answer 2.5 2.5 −   x B1 Mark final answer

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 8 of 10 Question Answer Marks Guidance 6(a) ( ) ( ) ( ) 2 2 2 4 2 ln 2 1 2 1 2    + − +   +   + x x x x x oe, isw 3 B1 for 2 4 2 1 + x x M1 for attempt at differentiation of a quotient or correct product A1 for all terms apart from 2 4 2 1 + x x correct 6(b) When d 2, 0.0849 d = = y x x and attempt at correct use of small changes M1 Substitution of 2 = x needs to be seen if simplification of (a) is incorrect. Change = 0.0849h A1 Must have full marks in part (a) 6(c) d 0.4 d = − y t soi B1 2 d 0.4 d d d = = − x x y t their x M1 awrt 4.71 − A1 7(a) Least value of a when 2 1 + = a so 1. = − a 2 B1 for range of f: 2+ a , may be implied by 1 + a or 1 + a 7(b) ( )   2e 5 1 3 + − = x M1 For correct order 0.916 = x 2 M1 for correct attempt to solve to obtain x = … 8(a) Numerator: 2 2 sin sin cos     or Denominator: 2 1 cos  soi B1 Allow for a correct step and equivalent methods 2 2 2 sin sin cos 1 cos      = 3 sin  B1 Must have sufficient detail

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 9 of 10 Question Answer Marks Guidance 8(b) 1 sin3 2 = x B1 o 3 30 ... x = M1 Any correct triple angle o o o o o o 110 , 70 , 10 , 50 , 130 , 170 = − − x 3 M1 for one correct solution A1 for three further correct solutions A1 for a further two correct solutions and no extra solutions in the range 9(a) 10 5 2 1 = − + v t 2 M1 for 5 2 1 = − + A v t When 1 0, 2 = = v t 2 Dep M1 for attempt to solve their v = 0 9(b) When 1 2 = t , 0.9657 = s or 5ln2 2.5 − and when 2 = t 1.9528 = − s or 5ln5 10 − 2 FT on their t from part (a) B1FT for when 1 2 = t , 0.9657 = s or 5ln2 2.5 − 3.88 2 M1 for distance = ( ) 2 0.9657 1.9528 + their 9(c) ( ) 2 20 2 1 − + t oe 2 M1 for ( ) 2 2 1 + B t , where B is an integer 9(d) 0.2 − B1 Mark final answer, do not isw. 10 4 4 3 3 2 2 8 24 ... − + a x a x a x soi 3 B1 for each term 2 2 3 3 1 ... + + b b x x soi 2 B1 for two correct terms 3 = a B1 5 = b 2 B1 for 3 4 8 3 999 − + = a a b oe or 243 216 999 − = b oe 3051 = c 2 B1 for 4 2 3 2 3 24 24 − + = a b a b a c oe or 6075 3240 216 − + = c oe

0606/22 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 10 of 10 Question Answer Marks Guidance 11 ( ) 1 tan 1.5 3 + = y B1 Allow 1.96 or 1.9625 to 1.964 Allow 5.10 to 5.11 3 M1 for a correct order of operations, may be implied by 1.178 = − y oe A1 for one correct solution A1 for a second correct solution and no extras