OCR GCE A LEVEL 2022 MATHEMATICS A MARKSCHEMES H240-01 PAPER 1-H240/01: Pure Mathematics

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H240/01 Mark Scheme June 2022 5 • When a value is not given in the paper accept any answer that agrees with the correct value to 3 s.f. unless a different level of accuracy has been asked for in... the question, or the mark scheme specifies an acceptable range. NB for Specification B (MEI) the rubric is not specific about the level of accuracy required, so this statement reads “2 s.f”. Follow through should be used so that only one mark in any question is lost for each distinct accuracy error. Candidates using a value of 9.80, 9.81 or 10 for g should usually be penalised for any final accuracy marks which do not agree to the value found with 9.8 which is given in the rubric. g Rules for replaced work and multiple attempts: • If one attempt is clearly indicated as the one to mark, or only one is left uncrossed out, then mark that attempt and ignore the others. • If more than one attempt is left not crossed out, then mark the last attempt unless it only repeats part of the first attempt or is substantially less complete. • if a candidate crosses out all of their attempts, the assessor should attempt to mark the crossed out answer(s) as above and award marks appropriately. 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 or B mark in the question. Marks designated as cao may be awarded as long as there are no other errors. If a candidate corrects the misread in a later part, do not continue to follow through. 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 that there is nothing in the wording of the question specifying that analytical methods are required such as the bold “In this question you must show detailed reasoning”, or the command words “Show” or “Determine”. 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. H240/01 Mark Scheme June 2022 6 Question Answer Mark s AO Guidance 1 (a) 5 21 0.5 0.5 0 2 2 2 3 2 2        + + + +             B1 1.1a State the 4 correct non-zero yvalues and no others Exact values (including unsimplified) or decimal equivs (0, 1.12, 1.73, 2.29, 2.83) – 3sf or better B0 if other ordinates seen unless clearly not intended to be used M1* 1.1a Attempt to find area between x = 1 and x = 3, using k{y0 + yn + 2(y1 + ... + yn-1)} Big brackets need to be seen or implied y-values must be correctly placed Must be using attempts for at least 4 yvalues (but no need to see y = 0 explicitly) Condone using other than 4 intervals as long as values equally spaced between x =1 and x = 3 M1d* 1.1a Use k = 0.5 × 0.5 soi Dep on previous M1 Or using k = 0.5h, h consistent with their different number of intervals = 3.28 A1 1.1 Obtain 3.28, or better Allow answers to > 3sf, as long as they round to 3.28 [4] 1 (b) Under-estimate, as the tops of the trapezia are below the curve B1 3.2b Under-estimate, with any valid explanation Condone just ‘trapezia under curve’ Or curve is concave / decreasing gradient (not decreasing function) Accept explanation on diagrams Allow comparing to true value (3.36) B0 if any additional incorrect or contradictory statements [1] H240/01 Mark Scheme June 2022 7 Question Answer Mark s AO Guidance 1 (c) Use more trapezia, of a lesser width, between the same limits B1 3.2b Convincing reason Condone just ‘more trapezia’ or ‘narrower trapezia’ Could refer to strips or intervals [1] 2 (a) eg 1 > – 2, but 12 < (– 2)2 as 1 < 4 B1 2.1 Any correct counterexample, and contradiction identified Initial inequality soi and then contradiction eg –3 > –4 but 9 < 16 (or 9 ≯ 16) [1] 2 (b) (i) eg sin150o = 0.5 as well B1 2.3 Any correct statement Identifies that sinx = 0.5 could give values of x other than 30o Either specific example or general statement eg ‘many to one’ function [1] 2 (b) (ii) sinx o = 0.5 ⇐ x o = 30o B1 2.5 Any correct relationship If attempting to write general solution then must be fully correct eg x = 30o + 360n o , x = 150o + 360n o Condone ← instead of ⇐ [1] 2 (c) (4n) + (4n + 4) + (4n + 8) + (4n + 12), where n is an integer B1* 2.1 Four consecutive multiples of 4 written correctly in terms of n, or any other variable Allow BOD if n not explicitly stated to be an integer Sufficient to just list the 4 terms, rather than as a sum Not necessarily starting on 4n Could also define k as a multiple of 4 and then have k, k + 4 etc = 16n + 24 = 8(2n + 3) M1 dep* 2.1 Correctly sum terms, and correctly take out common factor of 8 Or sum and then consider each term separately Could be a different factor if using k H240/01 Mark Scheme June 2022 8 Question Answer Mark s AO Guidance 2n +3 is an integer, so 8(2n + 3) is a multiple of 8 A1 2.4 Conclude appropriately Allow BOD if 2n + 3 not explicitly stated to be an integer If using k… expect 8(0.5k + 3) then justify 0.5k as an integer, or 4(k + 6) then justify k + 6 is a multiple of 2 [3] 3 (a) DR 2x 2 – 8x + 6 = 0 x 2 – 4x + 3 = 0 M1 1.1 Equate, and rearrange to three term quadratic Attempt to gather like terms, but not necessarily on same side of equation Condone no ‘= 0’ (x – 1)(x – 3) = 0 M1 1.1 Attempt to solve quadratic If factorising then expansion should give x 2 and one other term correct Quadratic formula should be correct – allow one slip when substituting as long as general formula already seen as correct Completing the square needs to go as far as x – p = ±√q x = 1, x = 3 A1 1.1 Obtain both correct x values Or one correct (x, y) coordinate following a correct factorisation oe (1, 0) and (3, 4) A1 1.1 Obtain both correct pai [Show More]

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