1. Annotations and abbreviations
Annotation in scoris Meaning
and
BOD Benefit of doubt
FT Follow through
ISW Ignore subsequent
... [Show More] 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.
2. Subject-specific Marking Instructions for 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.
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
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.
3
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. This rule should be applied to each case. When a value is not given in the paper accept any answer that agrees with the correct value to 2 s.f. Follow through should be used so that only one mark is lost for each distinct accuracy error, except for errors due to premature approximation which should be penalised only once in the examination. There is no penalty for using a wrong value for g. E marks will be lost except when results agree to the accuracy required in the question.
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 graphical 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.
Question Answer Marks AOs Guidance
1 2 5x21
6
dy 6 10x3
dx M1 B1
A1 [3] 1.1
1.1
1.1 soi
or correct differentiation of 6x + 3
Allow equivalent form, but constant must be simplified to 10.
2 (i) Symmetrical with one possible outlier B1
[1] 1.2 or negative skew
2 (ii) 24th value ‒ 8th value M1 1.1
27 ‒ 16 = 11 A1 1.1
[2]
2 (iii) 16 ‒ 1.5 × 11 = ‒ 0.5 M1 1.1 Check for outliers using their
Q1 ‒ 1.5×IQR
3 > ‒ 0.5 so it is not an outlier. A1 2.2a
[2]
3 (i) [384 ‒ 400 +8 + 8 =] 0 B1
[1] 1.1
3 (ii) Long division or equating coefficients M1 2.1 DR
6x2 x 2 seen A1 1.1
x 43x 22x 1 M1 1.1
x 43x 22x 1
A1
1.1
[4]
5
Question Answer Marks AOs Guidance
4 2x5 5(2x)4 (3) 10(2x)3 (3)2 10(2x)2 (3)3
5(2x)(3)4 (3)5 M1
M1 2.1
1.1 Binomial coefficents
6 terms in powers of x from 0 to 5 May be unsimplified eg 5C2
or 1 5 10 10 5 1 seen
From 5 to 0
32x5 240x4 720x3 1080x2 810x 243 A1 A1 1.1
1.1 Five terms correct Six terms correct
[4]
5 (i)
k[P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ] = 1
M1
1.1
k (1 + 1 + 2 + 6 ) = 1 so k = 0.1 A1 3.1a
[2]
5 (ii) P(X = 3) = 0.6 B1
[1] 1.1
5 (iii) X ~ B (32, 0.6) M1 3.3 FT their 0.6
0.073 A1 3.4 BC FT their 0.6 or 0.0728 or 0.07283
[2]
Question Answer Marks AOs Guidance
6 3x2 6x 6 M1 A1 2.1
1.1 Differentiation All correct
6x ‒ 6 = 0
x = 1 M1
A1 2.1
1.1 Differentiates again
or completes the square or uses the discriminant NB 3(x ‒ 1)2 + 3
NB ‒ 36
gradient has a minimum value of 3 at x =1. This is a minimum value because the gradient function is parabolic and the coefficient of x2 is positive. As the gradient is always positive the function is always increasing oe
E1 [5]
2.2a alternatively gradient is never zero since discriminant is negative / can’t solve from completing square, and must therefore be always positive since term in x2 is positive oe
7 (i) Consistent use of midpoints in either calculation M1 1.1 soi
Mean £36.25 A1 1.1 BC
Sample sd 8.313… A1 1.1 BC
£36 250 and £8313 A1 1.1
[4] FT their calculator values
7 (ii) We are using grouped data not the original values B1
[1] 2.4
(iii) Any valid reason which suggests that the sample is
not necessarily representative B1 3.2b
[1]
(iv) It would increase B1
[1] 2.2a
7
Question Answer Marks AOs Guidance
8 H0 : p = 0.49
H1 : p ≠ 0.49 B1
B1 1.1
1.1 DR
p is the probability that a voter selected at random B1 2.5
supports Mr Evans
X is the number of voters who support Mr. Evans.
Under H0 X ~ B (38, 0.49)
p (X ≤ 13) = 0.047(46439…) B1 1.1 BC
0.047 > 0.025 M1 1.1 Compares their 0.047 with 0.025
Not significant A1 2.2b Or reject H0
There is insufficient evidence at the 5% level to E1 2.4 Conclusion in context
suggest that support for Mr Evans has changed.
[7]
9 (i) c = 4.45 B1
[1] 3.3
9 (ii) log10 y = ‒ 0.37 log10 t + 4.45
y = 10‒ 0.37 log t + 4.45
10 M1 2.1 may be awarded after combining logarithms
log10 t‒ 0.37 seen M1 1.1
104.45 × t‒ 0.37
21183.829..≈ 28 200
so y ≈ 28 200 t ‒ 0.37 A1 1.1 AG
[3]
Question Answer Marks AOs Guidance
9 (iii) 18 781 is close to 18776 B1
[1] 3.5a BC NB t = 3
9 (iv) A 12 507 or 12 508 B1
[1] 3.4 BC to 3, 4 or 5 s.f.
9 B 8986 B1
[1] 3.4 BC
9 (v) Answer to A interpolation so more likely to be B1 3.5a
reliable
Answer to B extrapolation beyond 2015 so B1 3.5b
unreliable
[2]
10 1
3
y x 4x 2 6x
1 3
2
y x 8 x 2x3 c
Substitution of y = 122 and x = 4 in their
y x 8 x 2x3 c y x 8 x 2x3 6
M1
2.1
Must be three terms
at least two terms correct
A1
1.1
8√x or 8x½
A1 1.1 All correct including + c
M1 1.1
A1
1.1
[5]
9
Question Answer Marks AOs Guidance
11 (i) Population because these are all the countries of B1 1.1
interest. [1]
11 (ii) Eg Consistent with the correlation for all countries oe
And
Eg You would expect countries with higher populations to tend to have higher numbers of both mobile phone subscribers and internet users.
Or
Eg people who use mobile phones will be more likely to use the internet E1
E1 2.4
2.2b
[2]
11 (iii) Ukraine B1 1.1
Has high mobile phone usage with lower internet
provision.
Suggests people are used to and/or like technology E1 3.2a
so potential customers for the internet. [2] [Show Less]