GCE Mathematics B (MEI) H630/02: Pure Mathematics and Statistics Advanced Subsidiary GCE Mark Scheme for Autumn 2021

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GCE Mathematics B (MEI) H630/02: Pure Mathematics and Statistics Advanced Subsidiary GCE Mark Scheme for Autumn 2021 Oxford Cambridge and RSA Examinations GCE Mathematics B (MEI) H630/02: ... Pure Mathematics and Statistics Advanced Subsidiary GCE Mark Scheme for Autumn 2021Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing a wide range of qualifications to meet the needs of candidates of all ages and abilities. OCR qualifications include AS/A Levels, Diplomas, GCSEs, Cambridge Nationals, Cambridge Technicals, Functional Skills, Key Skills, Entry Level qualifications, NVQs and vocational qualifications in areas such as IT, business, languages, teaching/training, administration and secretarial skills. It is also responsible for developing new specifications to meet national requirements and the needs of students and teachers. OCR is a not-for-profit organisation; any surplus made is invested back into the establishment to help towards the development of qualifications and support, which keep pace with the changing needs of today’s society. This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. It shows the basis on which marks were awarded by examiners. It does not indicate the details of the discussions which took place at an examiners’ meeting before marking commenced. All examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes should be read in conjunction with the published question papers and the report on the examination. © OCR 2021H630/02 Mark Scheme November 2021 1. Annotations and abbreviations Annotation in scoris Meaning and  BOD Benefit of doubt FT Follow through ISW Ignore subsequent working M0, M1 Method mark awarded 0, 1 A0, A1 Accuracy mark awarded 0, 1 B0, B1 Independent mark awarded 0, 1 SC Special case ^ Omission sign MR Misread Highlighting Other abbreviations in mark scheme Meaning E1 Mark for explaining a result or establishing a given result dep* Mark dependent on a previous mark, indicated by * cao Correct answer only oe Or equivalent rot Rounded or truncated soi Seen or implied www Without wrong working AG Answer given awrt Anything which rounds to BC By Calculator DR This indicates that the instruction In this question you must show detailed reasoning appears in the question.H630/02 Mark Scheme November 2021 2. Subject-specific Marking Instructions for AS/A Level Mathematics B (MEI) a Annotations should be used whenever appropriate during your marking. The A, M and B annotations must be used on your standardisation scripts for responses that are not awarded either 0 or full marks. It is vital that you annotate standardisation scripts fully to show how the marks have been awarded. For subsequent marking you must make it clear how you have arrived at the mark you have awarded. b An element of professional judgement is required in the marking of any written paper. Remember that the mark scheme is designed to assist in marking incorrect solutions. Correct solutions leading to correct answers are awarded full marks but work must not be judged on the answer alone, and answers that are given in the question, especially, must be validly obtained; key steps in the working must always be looked at and anything unfamiliar must be investigated thoroughly. Correct but unfamiliar or unexpected methods are often signalled by a correct result following an apparently incorrect method. Such work must be carefully assessed. When a candidate adopts a method which does not correspond to the mark scheme, escalate the question to your Team Leader who will decide on a course of action with the Principal Examiner. If you are in any doubt whatsoever you should contact your Team Leader. c The following types of marks are available. MA suitable method has been selected and applied in a manner which shows that the method is essentially understood. Method marks are not usually lost for numerical errors, algebraic slips or errors in units. However, it is not usually sufficient for a candidate just to indicate an intention of using some method or just to quote a formula; the formula or idea must be applied to the specific problem in hand, e.g. by substituting the relevant quantities into the formula. In some cases the nature of the errors allowed for the award of an M mark may be specified. AA ccuracy mark, awarded for a correct answer or intermediate step correctly obtained. Accuracy marks cannot be given unless the associated Method mark is earned (or implied). Therefore M0 A1 cannot ever be awarded. B Mark for a correct result or statement independent of Method marks. EA given result is to be established or a result has to be explained. This usually requires more working or explanation than the establishment of an unknown result. Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored. Sometimes this is reinforced in the mark scheme by the abbreviation isw. However, this would not apply to a case where a candidate passes through the correct answer as part of a wrong argument.H630/02 Mark Scheme November 2021 d 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 mark is dependent on an earlier, asterisked, mark in the scheme.) Of course, in practice it may happen that when a candidate has once gone wrong in a part of a question, the work from there on is worthless so that no more marks can sensibly be given. On the other hand, when two or more steps are successfully run together by the candidate, the earlier marks are implied and full credit must be given. e The abbreviation FT implies that the A or B mark indicated is allowed for work correctly following on from previously incorrect results. Otherwise, A and B marks are given for correct work only – differences in notation are of course permitted. A (accuracy) marks are not given for answers obtained from incorrect working. When A or B marks are awarded for work at an intermediate stage of a solution, there may be various alternatives that are equally acceptable. In such cases, what is acceptable will be detailed in the mark scheme. If this is not the case, please escalate the question to your Team Leader who will decide on a course of action with the Principal Examiner. Sometimes the answer to one part of a question is used in a later part of the same question. In this case, A marks will often be ‘follow through’. In such cases you must ensure that you refer back to the answer of the previous part question even if this is not shown within the image zone. You may find it easier to mark follow through questions candidate-by-candidate rather than question-by-question. f Unless units are specifically requested, there is no penalty for wrong or missing units as long as the answer is numerically correct and expressed either in SI or in the units of the question. (e.g. lengths will be assumed to be in metres unless in a particular question all the lengths are in km, when this would be assumed to be the unspecified unit.) We are usually quite flexible about the accuracy to which the final answer is expressed; over-specification is usually only penalised where the scheme explicitly says so. • When a value is given in the paper only accept an answer correct to at least as many significant figures as the given value. • When a value is not given in the paper accept any answer that agrees with the correct value to 2 s.f. NB for Specification A the rubric specifies 3 s.f. as standard, so this statement reads “3 s.f” Follow through should be used so that only one mark is lost for each distinct accuracy error. g Rules for replaced work: if a candidate attempts a question more than once, and indicates which attempt he/she wishes to be marked, then examiners should do as the candidate requests; if there are two or more attempts at a question which have not been crossed out, examiners should mark what appears to be the last (complete) attempt and ignore the others. NB Follow these maths-specific instructions rather than those in the assessor handbook. h For a genuine misreading (of numbers or symbols) which is such that the object and the difficulty of the question remain unaltered, mark according to the scheme but following through from the candidate’s data. A penalty is then applied; 1 mark is generally appropriate, though this may differ for some units. This is achieved by withholding one A mark in the question. Marks designated as cao may be awarded as long as there are no other errors. E marks are lost unless, by chance, the given results are established by equivalent working. ‘Fresh starts’ will not affect an earlier decision about a misread. Note that a miscopy of the candidate’s own working is not a misread but an accuracy error. i If a calculator is used, some answers may be obtained with little or no working visible. Allow full marks for correct answers (provided, of course, that there is nothing in the wording of the question specifying that analytical methods are required). Where an answer is wrong but there is some evidence of method, allow appropriate method marks. Wrong answers with no supporting method score zero. If in doubt, consult your Team Leader. j If in any case the scheme operates with considerable unfairness consult your Team Leader.H630/02 Mark Scheme November 2021 Question Answer Marks Guidance 1 6C4 , 6C4 , 6! 2!4! or �6 4� oe or 1 6 15 20 15 6 1 soi M1 6C2 , 6C2 , 46!2! ! or �6 2� 34 seen B1 Allow for (3�)4 seen 1215 A1 Condone 1215�4 [3] 2 (a) Positive skew B1 Oe [1] 2 (b) (discrete) uniform B1 Oe [1] 3 tan(−30°) = − 1 3√ B1 Marks may be gained in a different order; allow for any correct method. tan(−30° + 4 × 180°) = tan(690°) B1 Or tan(−30° + 2 × 360°) = tan 690° Accept −30° + 4 × 180° = 690° completion to tan(690°) = − 1 √3 B1 [3] 4 9�3 3 oe B1 ��½ M1 3x³ +12x½ + c A1 A1 2 elements correct all 3 elements correct [4] 5 (a) B = 31 B1 [1]H630/02 Mark Scheme November 2021 Question Answer Marks Guidance 5 (b) 71 = Aln12 + 31 M1 A = 16 A1 CAO May see 16.097…A0 [2] 5 (c) 79 or 78.9 or better B1 from 16ln20 + 31 and 78.9317 Condone 79.2… from unrounded value of A [1] 5 (d) 120 = 16lnX + 31 M1 FT their A and B; allow sign error exp(their 120−31 16 ) M1 Allow slip in rearrangement awrt X = 260 A1 CAO A = 16.097… leads to 250, A0. [3] 6 (a) 3p² + 0.5p² + 2p +1.5p + 1.5 p² + 0.5p = 1 M1 Allow if only 3 probs added, or if = 1 omitted. 5p² + 4p ‒ 1 = 0 A1 Allow if one coeff or one sign wrong p = 0.2 or ‒1 BC A1 p = 0.2 only A1 [4] 6 (b) Use of their p to calculate at least two probabilities B1 Their p must be < 1. Mode is 1 B1 WWW NB 0.12, 0.42, 0.3, 0.16 [2] 7 (a) Remove Western Sahara since there is no data available (#N/A) B1 Ignore any comments about removing outliers advantageH630/02 Mark Scheme November 2021 Question Answer Marks Guidance [1] 7 (b) 6.79 + 2×2.78 or 6.79 − 2×2.78 soi M1 NB 1.23 or 12.35 implies M1 None of the smallest values are outliers A1 soi At least 1 of largest values identified A1 13.7,13.7,16.5,17.1,17.1 only A1 CAO [4] 7 (c) Not simple random sampling because every possible sample does not have an equal chance of being selected B2 oe Allow B1 for: He is using systematic sampling [2] 8 (a) �6 8� − �−203� M1 May see �−912� or �−129� ��� �����⃑� = 15 or √225 so �|��� �������⃗| < 200 or |���� �������⃗| is not greater than 200 A1 May see 9 ( 12) 2 2 + − oe CWO [2] 8 (b) �� �����⃗ = �−18 24� = 2 × �−912� M1 FT their comparison of their ��; allow mark for AB and AC so A, B and C are collinear A1 [2] 9 (a) The sample is not from the pre-release material because Arun has data from capital cities. The prerelease material only has data for countries B1 advantage [1]H630/02 Mark Scheme November 2021 Question Answer Marks Guidance 9 (b) It is possible for the same value to be selected in two different random samples. B1 Different samples (especially when small) might lead to different conclusions being made. B1 So there is no evidence to suggest Arun’s statement is correct B1 [3] 9 (c) Many African countries have a lower physician density (and often have a high death rate) B1 OR European countries generally have a higher physician density (and often have a low death rate) advantage [1] 10 (a) 5−7 11− −3 or −9−5 9−11 soi M1 All signs reversed in a fraction is correct − 2 14 and 14 2 oe A1 Fractions may be cancelled − 2 14 × 14 2 = ‒ 1 oe so lines are perpendicular A1 [3] 10 (b) PR is a diameter by angle in a semi-circle B1 Stated Detailed reasoning required �−3+9 2 , 7−9 2 � M1 allow one slip eg sign error (3, ‒1) A1H630/02 Mark Scheme November 2021 Question Answer Marks Guidance [3] 11 (a) This is a self-selecting sample. B1 Syllabus says ‘self-selected’ it may introduce bias B1 Or an explanation of why the sample is biased [2] 11 (b) 12.2×15 + 14×15 + 8.4×30 + 7.3×60 + 3.1×120 = 1455 M1 A1 at least 3 correct terms AG WWW. May see 183 + 210 + 252 + 438 + 372 [2] 11 (c) 7.3×60+3.1×120 1455 M1 = 54 97 or 0.5567 correct to 2, 3 or 4 sf. A1 [2] 12 (a) X = 2.1 B1 604−100×2.1² 99 oe M1 variance = 1.64646… A1 Accept to 3 or 4 sf or as recurring decimal or accept 163 99 [3] 12 (b) n = 10 p = 0.21 B1 B1FT Ft from their 2.1 [2] 12 (c) binomPdf(n, p, 2) used M1 FT their n and their calculated p; may be implied by 0.301…H630/02 Mark Scheme November 2021 Question Answer Marks Guidance 100 × binomPdf(10,0.21,2) M1 FT 100 x their prob from Binomial distribution fe = 30.1 A1 Accept 30 for final answer [3] 13 2 3 d 7 6 3 yd x x x       = − + M1 A1 at least two of three terms correct all correct their d 2 ydx = M1 x3 ‒ 7x + 6 = 0 M1 their d 2 ydx = rearranged to give cubic expression equal to zero Use of Factor theorem with factor of their 6 M1 Long division oe to obtain (x ‒ 1)(x2 + x ‒ 6) or (x ‒ 2)(x2 + 2x ‒ 3) or (x + 3)(x2 ‒3x + 2) M1 Allow sign error in quotient; quotient and factor may appear separately in algebraic division (x ‒ 1)( x + 3)(x ‒ 2) A1 Evaluation of f(their 1), f(their 2) and f(their‒3) seen M1 (1,7) (2, 35 4 ) and (‒3, ‒35 3 ) A1 [9]OCR (Oxford Cambridge and RSA Examinations) The Triangle Building Shaftesbury Road Cambridge CB2 8EA [Show More]

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