H640/02 Mark Scheme June 2023 5 5. Subject Specific Marking Instructions a. Annotations must be used during your marking. For a response awarded zero (or full) marks a single appropriate annotation (cross, tick, M0 or ^) is sufficient, but not required. For responses that are not awarded either 0 or full marks, you must make it clear how you have arrived at the mark you have awarded and all responses must have enough annotation for a reviewer to decide if the mark awarded is correct without having to mark it independently. It is vital that you annotate standardisation scripts fully to show how the marks have been awarded. Award NR (No Response) - if there is nothing written at all in the answer space and no attempt elsewhere in the script - OR if there is a comment which does not in any way relate to the question (e.g. ‘can’t do’, ‘don’t know’) - OR if there is a mark (e.g. a dash, a question mark, a picture) which isn’t an attempt at the question. Note: Award 0 marks only for an attempt that earns no credit (including copying out the question). If a candidate uses the answer space for one question to answer another, for example using the space for 8(b) to answer 8(a), then give benefit of doubt unless it is ambiguous for which part it is intended. 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 always 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. M A 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 H640/02 Mark Scheme June 2023 6 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. A method mark may usually be implied by a correct answer unless the question includes the DR statement, the command words “Determine” or “Show that”, or some other indication that the method must be given explicitly. A Accuracy 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. E A 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. 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. H640/02 Mark Scheme June 2023 7 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. unless a different level of accuracy has been asked for in the question, or the mark scheme specifies an acceptable range. 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 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. E marks are lost unless, by chance, the given results are established by equivalent working. Note that a miscopy of the candidate’s own working is not a misread but an accuracy error. H640/02 Mark Scheme June 2023 8 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. H640/02 Mark Scheme June 2023 9 Question Answer Marks AO Guidance 1 𝑎 1−𝑟 used M1 1.1a a and r are numerical values; a = 9 and/or 𝑟= ± 1 3 9 1±1 3 soi M1 1.1 27 4 or 6 3 4 or 6.75 cao isw A1 1.1 if unsupported allow SC2 for correct answer [3] 2 (a) (𝑥± 6)2 and (𝑦± 4)2 M1 1.1 completing the square twice soi r = 7 not from wrong working A1 1.1 NB (𝑥−6)2−36 + (𝑦+ 4)2 −16 + 3 = 0 oe allow B2 for r = 7 unsupported Alternatively ±2𝑎= −12 𝐨𝐞 and ± 2𝑏= 8 𝐨𝐞 r = 7 not from wrong working M1 A1 NB 𝑟2 = 62 + 42 −3 [2] 2 (b) (6, ‒4) B1 1.1 FT (𝑥± 6)2+ (𝑦± 4)2 or FT ±2𝑎= −12 𝐨𝐞 and ± 2𝑏= 8 𝐨𝐞 [1] H640/02 Mark Scheme June 2023 10 Question Answer Marks AO Guidance 3 take reciprocal calculate cube calculate square root to obtain 𝑚= 343, 𝑛= 512 isw or 343 512 isw B1 B1 B1 operations may be in any order, but 3 distinct numerical steps required for 3 marks if taking reciprocal and one other step are combined into one step, allow B1B1B0 if B0B0 for cubing and square rooting, allow SC1 for (√ 49 64) 3 = 343 512 or (√ 64 49) 3 = 512 343 seen [3] eg ( 49 64) 3 2 B1 1.1 taking reciprocal; may be awarded after simplification ( 7 8) 3 B1 1.1 square roots found; may be seen before taking reciprocal 343 512 isw B1 1.1 dependent on award of both preceding marks [3] eg Alternatively ( 64 49) −3 = ( 𝑚 𝑛) 2 ( 49 64) 3 = ( 𝑚 𝑛) 2 117649 = 𝑚2 and 262144 = 𝑛2 m= 343 and n = 512 B1 B1 B1 dependent on award of both preceding marks H640/02 Mark Scheme June 2023 11 Question Answer Marks AO Guidance 4 (a) 7p + 3p = 1 oe M1 1.2 must see some reasoning; allow explanation in words p = 0.1 or 1 10 isw cao A1 1.1 if unsupported, allow SC1 for correct answer [2] 4 (b) 0.7 or 7 10 B1FT 1.1 their 7p [1] 4 (c) B(30, their 0.3) seen or used M1 1.1 FT their 3p; allow M1 for (𝑡ℎ𝑒𝑖𝑟 0.3)2 × (𝑡ℎ𝑒𝑖𝑟 0.7)28 awrt 0.0018 isw A1 1.1 not from wrong working; if unsupported, allow SC1 for correct answer [2] 5 [( 5 −3) −( 3 −1) =] ( 2 −2) or [( 3 −1) −( 5 −3) =] (−2 2 ) B1 2.1 may be in coordinate form or may see distances identified or on diagram; may be implied by √(±2)2 + (±2)2 oe √ (±2)2 + (±2)2 oe M1 1.1 or FT their evaluation of ( 5 −3) −( 3 −1) may be implied by correct answer √8 or 2√2 isw A1 1.1 if B0M0; allow SC1 for √80 or 4√5 (from addition of vectors) if supported by Pythagoras; if B0M0 allow SC1 for √8 or 2√2 unsupported [3] H640/02 Mark Scheme June 2023 12 Question Answer Marks AO Guidance 6 2cos𝜃= 𝑥+ 3 or cos𝜃= 𝑥+3 2 B1 2.1 2sin𝜃= 𝑦−1 or sin𝜃= 𝑦−1 2 B1 1.1 ( 𝑥±3 2 ) 𝟐 + ( 𝑦±1 2 ) 𝟐 = cos2𝜃+ sin2𝜃 or (𝑥± 3)2 + (𝑦± 1)2 = 4cos2𝜃+ 4sin2𝜃 oe M1 1.1 allow sign errors in their expressions for sin𝜃 and cos𝜃; allow if just see brackets expanded, but must be 3 terms in each case (𝑥+ 3)2 + (𝑦−1)2 = 4 A1 1.1 allow SC2 for (𝑥+ 3)2 + (𝑦−1)2 = 4 unsupported [4] Alternatively centre of circle is (‒3, 1) radius is 2 (𝑥+ 3)2 + (𝑦−1)2 = 22 (𝑥+ 3)2 + (𝑦−1)2 = 4 B1 B1 M1 A1 allow one sign error in bracket; 7 (2𝑥)8 soi M1 3.1a allow recovery from bracket error; may be implied by award of second M1 12C8 or 12C4 or 495 seen B1 1.1 495×256×k4 [𝑥8]= 79 200 000 [𝑥8] oe M1 1.1 allow M1 for 495×2×k4 = 79 200 000 oe; “ = 79 200 000” may be implied by k = 5 k = 5 cao isw A1 3.2a not from wrong working; but allow recovery from 𝑥8 on one side of equation only allow SC2 for k = 5 unsupported [4] H640/02 Mark Scheme June 2023 13 Question Answer Marks AO Guidance 8 (a) not a simple random sample since each possible sample does not have an equal probability of being selected B1 2.4 allow “not a simple random sample since each plant does not have an equal probability of being selected” ignore further comments unless contradictory the essential elements of the comment are in bold [1] 8 (b) 18 (shorter than 40 cm) seen B1 2.1 may be embedded in calculation 110 (shorter than 80 cm) or 10 (taller than 80 cm) seen B1 1.1 may be embedded in calculation 92 120 oe or 28 120 oe M1 1.1 FT their 18 and their 110; allow M1 for 91 120 or 29 120 oe or 75 100 × 120 = 90 oe awrt 77% > 75% oe so this supports the (owner’s) statement A1 2.2a or 92 > 90 so this supports the (owner’s) statement; need comparison and comment [4] 8 (c) must refer to sample in answer eg since different samples give different results, not all samples would necessarily support owner’s statement eg no since another sample may contain all the tallest plants (and/or shortest) eg no since the heights in other samples may be different B1 2.4 ignore superfluous comments referring to eg growing conditions, soil type etc do not allow eg no, conditions different for other plants eg no, different plants on different rows eg no, might be biggest and smallest plants on other rows eg the first sample is not representative [1] H640/02 Mark Scheme June 2023 14 Question Answer Marks AO Guidance 9 (a) eg sample, since only some data used oe eg sample, since data for 2009 not used oe B1 2.2a sample, since not all data used; ignore further reasoning unless contradictory [1] 9 (b) £27 085 or £27 100 or £27 000 B1 3.4 [1] 9 (c) it’s interpolation oe eg because we use 2009 oe which is between 2008 and 2010 B1 2.2a do not allow eg 27085 lies between 2008 and 2010 eg 27085 lies between the values for 2008 and 2010 eg a straight line model appears to be justified eg relationship seems to be linear eg median income seems to be directly proportional to time eg positive correlation [between median income and year] B1 2.2b do not allow eg positive association eg positive relationship [2] H640/02 Mark Scheme June 2023 15 Question Answer Marks AO Guidance 9 (d) not reasonable oe since eg (median taxable) income varies considerably across different regions of London eg (median) income different in Croydon and Camden eg (median) income lower in Croydon (than Camden) eg pattern of change in income over time different in Camden to Croydon B1 2.4 LDS advantage [1] 10 4𝑥× 1 2 sin2𝑥−∫ 1 2 sin2𝑥× 4 d𝑥 M1* 3.1a allow sign errors only, condone omission of dx 2𝑥sin2𝑥−∫2sin2𝑥 d𝑥 oe A1 1.1 allow omission of dx; may be unsimplified F[𝑥] = 2𝑥sin2𝑥+ cos2𝑥 A1 1.1 ignore + c F [ 𝜋 4] −F[0] M1dep* 1.1 must see substitution if F[x] incorrect, otherwise may be implied by correct answer; 𝜋 2 −1 or 𝜋−2 2 isw A1 3.2a allow recovery from bracket error [5] 11 (a) d𝑦 d𝑥= 𝑘√𝑥 B1 2.1 may be implied by final answer 3 = 𝑘× √4 M1 1.1 𝑘= 3 2 𝐨𝐫 d𝑦 d𝑥= 3 2 √𝑥 isw A1 2.2a if B0M0 allow SC1 for d𝑦 d𝑥= 𝑘 √𝑥 and 𝑘= 6 as final answer or d𝑦 d𝑥= 6 √𝑥 as final answer [3] H640/02 Mark Scheme June 2023 16 Question Answer Marks AO Guidance 11 (b) their 𝑘× 𝑥 3 2 3 2 oe B1 3.1a FT their k 10 = (√4) 3 + 𝑐 M1 1.1 FT their integration, one term in x with index 1.5 𝑐= 2 or 𝑦= 𝑥 3 2 + 2 or 𝑦= 𝑥√𝑥+ 2 isw A1 1.1 must see ‘y =’ at some point if B0M0 allow SC2 for 𝑦= 12𝑥 1 2 −14 or 𝑦= 12√𝑥−14 or 𝑦= 12𝑥 1 2 + 𝑐 and 𝑐= −14 [3] 12 (a) because it’s neither a one-to-one nor a many-to-one (mapping) do not allow eg because it’s neither a one-to-one nor a many-to-one function B1 2.4 allow because it’s one-to-many (mapping) allow eg because each value of x is mapped to two values oe do not allow eg because it’s a one-to-many function [1] 12 (b) 𝑥2+2 𝑥2+2−3 M1 1.1 𝑥2+2 𝑥2−1 or 𝑥2+2 (𝑥−1)(𝑥+1) A1 1.1 [2] H640/02 Mark Scheme June 2023 17 Question Answer Marks AO Guidance 12 (c) |𝑥| > 1 or x < ‒1 or x > 1 or x < ‒1, x > 1 or 𝑥< −1 ∪𝑥> 1 B1 1.1 do not allow eg x < ‒1 and x > 1 eg ‒1 > x > 1 [1] 13 (a) H0: μ = 0.14 H1: μ < 0.14 B1 1.1 allow any other symbol except 𝑥̅ or 𝑋̅, as long as it is correctly defined; allow hypotheses stated in words their μ is the population mean mass of this variety of apple B1 2.5 allow weight; correct definition of μ may be embedded in hypotheses written out as a sentence; do not allow 𝑥̅ or 𝑋̅ [2] 13 (b) [𝑋̅~]N (0.14, 0.01992 80 ) B1 B1 3.3 2.2a Normal distribution with correct mean or variance allow variance = awrt 4.95 × 10−6 or awrt 0.002222 all correct, but allow full credit if no symbol used; allow symbol other than 𝑋̅ if correctly defined as sample mean, but do not allow 𝜇 [2] 13 (c) awrt 0.136 seen BC B1 1.1 𝑋̅ < 0.136 only or 𝑋̅ ≤0.136 only B1 3.4 FT other correctly defined symbol [2] H640/02 Mark Scheme June 2023 18 Question Answer Marks AO Guidance 13 (d) 0.1316 < 0.136 or 0.1316 is in the critical region (must be correct critical region) oe or p = awrt 0.00008 < 0.05 oe NB 0.0000799 or z = awrt ‒3.78 < ‒1.645 oe M1 3.4 condone p = awrt 0.00007 < 0.05 oe NB 0.0000740 or z = awrt ‒3.79 < ‒1.645 oe from use of 𝑋̅~N (0.14, 0.01982 80 ) reject H0 A1 1.1 allow accept H1 or result is significant there is sufficient evidence at the 5% level to suggest that the mean mass of the apples is less than 0.14 kg A1 2.2b allow weight; do not allow eg conclude / prove / indicate or other assertive statement instead of suggest [3] 14 (a) discard City of London (as part of the data not available) or discard any regions where one or more pieces of data are missing oe B1 2.4 LDS advantage do not allow if answer spoiled eg because it’s an anomaly, eg because it’s an outlier, [1] 14 (b) scatter does not look linear oe B1 3.4 ignore extra comments unless they contradict an otherwise correct answer pmcc not close to 1 oe B1 3.4 ignore extra comments unless they contradict an otherwise correct answer [2] H640/02 Mark Scheme June 2023 19 Question Answer Marks AO Guidance 14 (c) 27216 ± 2×4177.5 or 61.0 ± 2×5.32 M1 1.1 use of 2 standard deviation check for one of the 4 calculations soi m < 18861 or m > 35 571 A1 1.1 allow ≤ and ≥ percentage < 50.36 or percentage > 71.64 A1 1.1 allow ≤ and ≥ if M1A0A0 allow M1 SCB1 for all 4 correct values seen A1 1.1 [4] 14 (d) between 0 and 0.3743 since eg outliers gave a false impression of linearity eg scatter will be more like a circle B1 2.4 need to refer to the shape of the scatter oe [1] H640/02 Mark Scheme June 2023 20 Question Answer Marks AO Guidance 15 y = 1 then x = 2 only B1 3.1a 1 𝑦× d𝑦 d𝑥 𝑥3 × d𝑦 d𝑥+ 3𝑥2𝑦 B1 M1 2.1 1.1 first term correct; allow 𝑦′ for d𝑦 d𝑥 Product Rule; allow one coefficient error or one index error 1 𝑦× d𝑦 d𝑥+ 𝑥3 × d𝑦 d𝑥+ 3𝑥2𝑦[= 0] A1 1.1 substitution of their x = 2 and y = 1 to obtain numerical value for d𝑦 d𝑥 M1* 1.1 NB − 4 3 dependent on at least two of 3 terms correct on LHS following differentiation; if expression for d𝑦 d𝑥 or evaluation of d𝑦 d𝑥 is incorrect, need to see substitution for award of M1 𝑦−1 = (𝑡ℎ𝑒𝑖𝑟 3 4) (𝑥−𝑡ℎ𝑒𝑖𝑟 2) oe M1dep* 3.1a FT negative reciprocal of their − 4 3 and their 2 may see eg 1 = 3 4 × 2 + 𝑐 3x ‒ 4y ‒ 2= 0 or ‒3x + 4y + 2= 0 oe A1 3.2a must be in required form, but coefficients may be fractions [7] H640/02 Mark Scheme June 2023 21 Question Answer Marks AO Guidance 16 (a) 0.16×0.84×2 or B(2, 0.16) or B(2, 0.84) seen or 1 −(0.842 + 0.162) M1 1.1 condone omission of 2 allow recovery from bracket error 168 625 or 0.2688 or 0.269 or 0.27 cao A1 1.1 mark the final answer allow SC1 for correct answer unsupported [2] 16 (b) 0.75 ‒ 0.66 = 0.09 M1 3.1a allow 0.09 embedded in correct place in Venn diagram or contingency table; allow M1 for 9% [0.16 ‒ 0.09 = ] 0.07 isw A1 1.1 allow SC1 for correct answer unsupported [2] 16 (c) 0.09 0.75 M1 3.1a M0 for 0.12 from wrong working 0.12 A1 1.1 allow SC1 for correct answer unsupported [2] 16 (d) 0.12 ≠ 0.16 M1 2.1 so not independent A1 2.2a if M0 allow SCB1 for 0.16 × 0.75 ≠0.09 so not independent [2] H640/02 Mark Scheme June 2023 22 Question Answer Marks AO Guidance 17 divide through by cos x to obtain 2tan𝑥+ sec2𝑥= 4 B1 2.1 2tan𝑥+ tan2𝑥+ 1 = 4 M1* 3.1a use of Pythagoras to obtain equation in tan𝑥 only; allow 1 sign error tan2𝑥+ 2tan𝑥−3[= 0] A1 1.1 tan𝑥= 1 𝑜𝑟−3 M1*dep 1.1 2 values obtained for tan x from their quadratic [x =] ‒1.24905 to ‒1.249 or ‒1.25 or ‒1.2 [x =] 1.8925 to 1.893 or 1.89 or 1.9 A1 3.2a any two correct [x =] 𝜋 4 or 0.785 to 0.7854 or 0.79 [x =] − 3𝜋 4 or ‒2.3562 to ‒2.356 or ‒2.36 or ‒2.4 A1 2.2a all four correct and no extra values in range; ignore correct extra values outside range but A0 if incorrect values outside range [6] H640/02 Mark Scheme June 2023 23 Question Answer Marks AO Guidance alternatively multiply through by cos x to obtain 2sin𝑥cos𝑥+ 1 = 4cos2𝑥 B1 sin2𝑥+ 1 = 2cos2𝑥+ 2 M1* use of double angle formulae, allow 1 sign error 5cos22𝑥 + 4cos2x [= 0] NB square both sides: sin22𝑥= 4cos22𝑥 + 4cos2x + 1 oe A1 or √5cos(2𝑥+ 0.4636 … ) = −1 or √5sin(2𝑥−1.1071 … ) = 1 cos2x = 0 or ‒0.8 2 values obtained for cos2 x from their quadratic M1dep* cos(2𝑥+ 0.4636 … ) = − 1 √5 or sin(2𝑥−1.1071 … ) = 1 √5 [x =] ‒1.24905 to ‒1.249 or ‒1.25 or ‒1.2 [x =] 1.8925 to 1.893 or 1.89 or 1.9 A1 any two correct [x =] 𝜋 4 or 0.785 to 0.7854 or 0.79 [x =] − 3𝜋 4 or ‒2.3562 to ‒2.356 or ‒2.36 or ‒2.4 A1 all four correct and no extra values in range; ignore correct extra values outside range but A0 if incorrect values outside range H640/02 Mark Scheme June 2023 24 Question Answer Marks AO Guidance 18 (a) 260 cao B1 1.1 [1] 18 (b) 31 cao B1 1.1 mark the final answer [1] 18 (c) any 2 distinct reasons eg (approximately) symmetrical (about the mean) eg approximately bell-shaped / unimodal eg data is continuous B1 B1 3.5a 3.5a ignore extra comments unless they contradict an otherwise correct answer [2] 18 (d) [variance is] awrt 62.2 or [sd is] 7.89 seen BC 0.26287 – 0.263134 or 0.26 M1 A1 3.3 3.4 NB 62.15567…may be implied by sd = 7.88 or 7.89 NB 0.263047…from √62.2 or 0.263133… from 7.89 NB 0.262871… from 7.88, 0.262973…from unrounded sd allow B2 for correct answer unsupported [2] 18 (e) B(28, p) used, where p is value calculated in (d) M1 3.1a 0.888 ≤ p < 0.896 A1 1.1 may be given to 2 sf; allow B2 for correct answer unsupported [2] H640/02 Mark Scheme June 2023 25 Question Answer Marks AO Guidance 18 (f) 7.8 + 0.18 × 260 0.182 × 62.2 oe N(54.6, 2.0138 – 2.02) M1 M1 A1 3.1a 3.5c 1.1 or 0.18 × √62.2 allow eg 1.422 for variance [3] H640/02 Mark Scheme June 2023 26 APPENDIX Exemplar responses for Q2(b) Response Mark Need to get in touch? 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