[PDF] 2015 Mathematics Advanced Higher Finalised Marking Instructions

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2015 Mathematics

Advanced Higher

Finalised Marking Instructions

Scottish Qualifications Authority 2015

The information in this publication may be reproduced to support SQA qualifications only on a non-

commercial basis. If it is to be used for any other purposes written permission must be obtained from

Where the publication includes materials from sources other than SQA (secondary copyright), this material should only be reproduced for the purposes of examination or assessment. If it needs to be These Marking Instructions have been prepared by Examination Teams for use by SQA Appointed Markers when marking External Course Assessments. This publication must not be reproduced for commercial or trade purposes.

Page 2

Part One: General Marking Principles for Mathematics Advanced Higher This information is provided to help you understand the general principles you must apply when

marking candidate responses to questions in this Paper. These principles must be read in conjunction

with the specific Marking Instructions for each question. (a) Marks for each candidate response must always be assigned in line with these general marking principles and the specific Marking Instructions for the relevant question. If a specific candidate response does not seem to be covered by either the principles or detailed Marking Instructions, and you are uncertain how to assess it, you must seek guidance from your

Principal Assessor.

(b) Marking should always be positive ie, marks should be awarded for what is correct and not deducted for errors or omissions. GENERAL MARKING ADVICE: Mathematics Advanced Higher listing every possible correct and incorrect answer. The following notes are offered to support assessments and course assessments.

General Marking Principles

These principles describe the approach taken when marking Advanced Higher Mathematics papers. For more detailed guidance please refer to the detailed Marking Instructions.

1 The main principle is to give credit for the skills demonstrated and the criteria met. Failure to have

a correct method may not preclude a candidate gaining credit for their solution.

2 The answer to one part of a question, even if incorrect, can be accepted as a basis for subsequent

dependent parts of the question.

3 The following are not penalised:

working subsequent to a correct answer (unless it provides firm evidence that the requirements of the question have not been met) legitimate variation in numerical values/algebraic expressions.

4 Full credit will only be given where the solution contains appropriate working. Where the correct

answer might be obtained by inspection or mentally, credit may be given.

5 Sometimes the method to be used in a particular question is explicitly stated; no credit will be

given where a candidate obtains the correct answer by an alternative method.

6 Where the method to be used in a particular question is not explicitly stated in the question paper,

full credit is available for an alternative valid method. (Some likely alternatives are included but

these should not be assumed to be the only acceptable ones.)

In the detailed Marking Instructions which follow, marks are shown alongside the line for which they are

awarded. When marking, no comments at all should be made on the script. The total mark for each question should appear in one of the right-hand margins. The following codes should be used where applicable:

3 - correct; X wrong; working underlined wrong;

tickcross mark(s) awarded for follow-through from previous answer; ^ ^ - mark(s) lost through omission of essential working or incomplete answer; wavy or broken underline bad form, but not penalised.

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Part Two: Marking Instructions for each Question

Question Expected Answer/s Max

Mark

Additional Guidance

1

5 4 3122 2 2

5 5 5 0 1 2

23 4 522

5 5 5 3 4 5 22
3 3 3 2 2 2 33
x x xC C Cxx xxC C Cx x x

10 7 4

2510 40 80 80 32

243 81 27 9 3

x x x x xx 4

1 correct unsimplified

expansion

2 fully simplified powers of x

3 powers of 3 and binomial

coefficients. OR powers of 2 correct.

4 Completes and simplifies

correctly.

Notes:

1.1 Accept negative powers of x.

1.2 Coefficients must be fully processed to simplified fractions and whole numbers.

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Question Expected Answer/s Max

Mark

Additional Guidance

2 a 2 22

5 2 2 5 1

2 x x xdy dxx 2 22

5 2 10

2 xx x

3 1 For using quotient rule and

correct denominator3.

2 correct differentiation for

both parts of numerator

3 simplified form2.

2 b

2 2 22 sin 3 .2.3.sin3 cos3xxf' x e x e x x

22 sin3 sin3 3cos3xe x x x

or

222sin 3 3sin6xe x x

3 4 evidence of using product

rule

5 first term

6 second term

Notes:

2.1 Alternative Method

Product rule

12 2122
2 22
5 1 2

5 1 2 .2 5 2

5 2 10

2 y x x dyx x x xdx xx x

2.2 Where a candidate has a wrong, but factorisable expression in the

numerator, factorisation is not required for award of this mark.

2.3 Where terms are the wrong way round, lose 1

2.4

2205 1 2 ... 15 2 10:award .3

dx x x xdx

1 for evidence of using

product rule and one term correct.

2 for second term

3 simplified fraction

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Question Expected Answer/s Max

Mark

Additional Guidance

3 20 21
10

20320 2 192

2 19 32

37 20 20 37

2 40 74

21 42
2 3 10292
60
s a d ad u a d a d ad d d a s a d OR 21
10 20 37

320 37 357

21357 372

3 2

5 6 18 60

ad s a a d s

5 1 for correct

substitution into formula1.

2 for correct

substitution into formula1. 3 1d 4 1a 5 10s 1

20 37ad

2 for correct

substitution into formula1. 3 a 4 d 5 10s

Notes:

3.1 Accept correct equations for 1 and 2 without explicit statement of general formulae. However, simply

stating values for a and d, is not sufficient, so do not award 1 or 2, ie working required.

3.2 Candidates can also obtain two simultaneous equations using S20 and S21 formulae. One mark each, then

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