OCR GCE A LEVEL 2022 MATHEMATICS A MARKSCHEMES H240-03 PAPER 3-H240/03: Pure Mathematics and Mechanics

H240/03 Mark Scheme June 2022 5 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 yo ...

H240/03 Mark Scheme June 2022 5 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. 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 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. H240/03 Mark Scheme June 2022 6 Question Answer Marks AO Guidance 1 x = 6 B1 1.1 B0 for x = 6 unless replaced with x = 6 2 3 9 2 3 9 x x − =  − = − M1 1.1a oe e.g. ( ) 2 2 3 81 x − = or 2 3 9 x − =  M0 for ( ) 2 2 3 9 x − = x =−3 A1 1.1 A0 for x = - 3 unless replaced with x = - 3 The correct answer implies the previous M mark Two marks maximum if more than two answers given [3] H240/03 Mark Scheme June 2022 7 Question Answer Marks AO Guidance 2 (a) Translation B1 2.5 Do not accept shift, move, transformation, etc. for first B1 - 8 units parallel to the y-axis or ( 0 −8 ) B1 1.1 Correct description e.g. correct vector (not as a coordinate), ‘8 units down’. Do not allow second B1 after incorrect type of transformation e.g. stretch/rotation etc. but allow after shift/move etc. Condone lack of ‘units’ but do not accept ‘factor - 8’, ‘8 places/spaces/steps down’ etc. For ‘parallel to the y axis’ allow ‘vertically’, ‘in the y direction’. Do not accept across/up/along/to/in/ towards the y axis’ [2] If more than a single transformation, then no marks (unless two translations equivalent to the correct answer) Mark vector before description/words 2 (b) 3 3 y x y x = −  + = 8 8 x = ... M1 1.1 Attempt to make x the subject (allow sign errors only) May use either f(x) or y ( ) ( ) 1 3 1 f 8 x x − = + A1 1.1 Must be in terms of x. Allow the expression only e.g. ( ) 1 x +8 3 , 3 x +8 , oe Ignore what this expression is equated to [2] 2 (c) One graph is the reflection of the other graph in the line y x = B1 1.2 Must include both ‘reflection’ or ‘mirror image’ or ‘mirrored’ and ‘y = x’ B0 for ‘symmetrical’ unless clearly describing reflective symmetry [1] H240/03 Mark Scheme June 2022 8 Question Answer Marks AO Guidance 3 2 3 5 1 , 2 2   + − +     M1* 2.1 Attempt at the midpoint (3 out of 4 values used correctly or one correct coordinate) If correct 5 , 2 2     −   ( ) ( ) 2 2 2 d = − + − − 2 3 5 1 M1* 1.1 Attempt to calculate diameter d or radius r (or the square of either of these two) e.g. ( ) ( ( )) 2 2 2 5 2 r = − + − − − 2 5 2 M0 if implying that ( ) ( ) 2 2 2 r = − + − − 2 3 5 1 . If the value is not labelled (as either r or d) then consider how this value is used in their circle equation 3 out of 4 values used correctly – if correct 2 d = 37 or 2 37 4 r = ( ) 2 5 37 2 2 2 4 x y     − + + =   M1dep* 1.1 Correct form for the equation of a circle with their values for the centre and radius Dependent on both previous M marks 2 2 25 37 5 4 4 4 4 x x y y − + + + + = 2 2 x y x y + − + + = 5 4 1 0 A1 2.2a Must have = 0 Order of terms on the lhs irrelevant a, b and c need not be explicitly stated [4] H240/03 Mark Scheme June 2022 9 Question Answer Marks AO Guidance 4 (a) GP: 15 15 , , 15 y z x z y x y  = M1* 3.1a M1 for un-simplified correct use of 1 n n u r u − = so allow this mark for stating that 15 r xy = or 15 yz r = or 2 r x z = oe Or for the terms of the GP as 15 y y 4, , 4 y + − in y only AP: x y z y x , , 4  − = − or z y − = −4 M1* 1.1 M1 for y x − = 4 or z y − = 4 or z x − = 8 oe Or for the terms of the AP as y y y + − 4, , 4 in y only For reference: 2 xy z = 225 , x y = + 4 and z y = − 4 ( ) ( ) 2 y y y + − = 4 4 225 M1dep* 1.1 Eliminate x and z to form an equation in y only (must be equivalent to a quartic in y) Or for 2 2 4 15 / 15 / 4 225 16 y y y y y y − = +      − =   2 2 4 2 y y y y y y ( 4 4 16) 225 16 225 0 − + − =  − − = A1 2.2a AG so sufficient working must be shown www – note that y x = + 4 and y z = - 4 (from d = +4) can lead to the correct equation (which can score the M marks only)