GCE Mathematics A H240/02: Pure Mathematics and Statistics Advanced GCE Mark Scheme for Autumn 2021. Graded A+

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Annotations and abbreviations Annotation in RM assessor Meaning and  BOD Benefit of doubt FT Follow through ISW Ignore subsequent working M0, M1 Method mark awarded 0, 1 A0, A1 Accuracy m... ark awarded 0, 1 B0, B1 Independent mark awarded 0, 1 SC Special case ^ Omission sign MR Misread BP Blank Page Seen Highlighting Other abbreviations in mark scheme Meaning dep* Mark dependent on a previous mark, indicated by *. The * may be omitted if only one previous M mark 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 question included the instruction: In this question you must show detailed reasoning.H240/02 Mark Scheme October 2021 3 2. Subject-specific Marking Instructions for A Level Mathematics A 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.H240/02 Mark Scheme October 2021 4 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 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 Question Answer Mark Guidance 1 (a) –4e–4x oe B2 B1 for e–4x seen as part of answer, not in denominator [2] 1 (b) By quotient rule 2 2 ( 1) 2 1 ( 1) x x x x + × − × + B1 B1 B1: correct denominator & 1 correct term in numerator, any form ISW Alternative method – chain rule or –(x + 1)–2 × x2 + (x + 1)–1 × 2x B1 B1 B1 for either term correct ISW (= ( 2) 2 ( 1) x x x + + or 2 2 2 2 1 x x x x + + + ) [2] 2 f(x) is positive on both sides of the 1st root oe B2 B1 for "The graph touches the x-axis" or “repeated root” Curve does not cross the x-axis (near root) or “It is a stationary point” Sign does not change (near the root) No negative value (near the root) Ignore all else, eg “inflection” [2] 3 a + 14d = 88 (i) M1 M1 for one error, eg a + 9d = 88 A1 10 2 (2a + 9d) = 310 (ii) M1 M1 for 15 2 (2a + 14d) = 310 or for one error, eg 5(2a + 18d) = 310 A1 Substitute from (i) into (ii) M1 Attempt substitution, elimination or to verify solutions found BC. Condone one arithmetical error 10 2 (2(88 – 14d) + 9d) = 310 SC for last 2 marks: Correct answers, substitution not seen: B1B0, dep M1M1 176 – 19d = 62 d = 6, a = 4 A1 cao [6]H240/02 Mark Scheme October 2021 7 Question Answer Mark Guidance 4 (a) 6000 B1 [1] 4 (b) 2000 B1f ft their (a) − 4000 [1] 4 (c) Oscillates or Goes up and down. oe B1 Ignore all else Fluctuates. Moves in a cycle NOT “Increases for 1st 6 months then decreases” [1] 4 (d) 30t = 360 M1 May be implied by answer Time to return to initial size = 12 months A1 Allow t = 12, or t = 12 months, or just 12 [2] 4 (e) 4500 = 5000 – 1000cos(30t)o M1 Substitute P = 4500 May be implied by next line cos(30t) o = 0.5 A1 Correct rearrangement 30t = 60 or 300 (both) M1 Attempt 30t = cos-1(their 0.5), giving α and 360 − α. Condone 30t = 5 3 3 , π π 2nd time P = 4500 is when t = 10 A1 or after 10 months. Allow t = 10 months, or just 10 SC. (If not gained 1st M1A1)Correct answer with no or inadequate working and/or T&I: t = 10 stated: B2; t = 10 embedded: B1B0 Alternative methods for 2nd M1A1 30t = 60 or −60 (both) (t = 2 or −2) M1 30t = 60 (t = 2) 2nd time P = 4500 is when t = −2 + 12 = 10 A1 (end of 1st cycle at t = 12) 2nd time P = 4500 is when t = 12 − 2 = 10 30t = 60 (t = 2) M1 6 − 2 = 4; t = 6 + 4 = 10 A1 [4] 4 (f) eg P = 5000 – 1000e–tcos (30t)o P = 5000 – 1000e–ktcos (30t)o (k > 0) B1 or other good answers Answers in words must be equivalent to one of these eg P = 5000 − (1000cos(30t)o)1/t P = 5000 – 1000 t cos (30t)o. (t > 0) [1]H240/02 Mark Scheme October 202 [Show More]

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