Mark Scheme (Results) Summer 2019

[Pages:41]Mark Scheme (Results)

Summer 2019

Pearson Edexcel GCE In Mathematics (9MA0) Paper 2 Pure Mathematics 2

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Summer 2019 Publications Code 9MA0_02_1906_MS All the material in this publication is copyright ? Pearson Education Ltd 2019

General Marking Guidance

All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last.

Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions.

Examiners should mark according to the mark scheme not according to their perception of where the grade boundaries may lie.

There is no ceiling on achievement. All marks on the mark scheme should be used appropriately.

All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate's response is not worthy of credit according to the mark scheme.

Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited.

When examiners are in doubt regarding the application of the mark scheme to a candidate's response, the team leader must be consulted.

Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response.

PEARSON EDEXCEL GCE MATHEMATICS

General Instructions for Marking

1. The total number of marks for the paper is 100.

2. The Edexcel Mathematics mark schemes use the following types of marks:

M marks: method marks are awarded for `knowing a method and attempting to apply it', unless otherwise indicated.

A marks: Accuracy marks can only be awarded if the relevant method (M) marks have been earned.

B marks are unconditional accuracy marks (independent of M marks) Marks should not be subdivided.

3. Abbreviations

These are some of the traditional marking abbreviations that will appear in the mark schemes.

bod ? benefit of doubt ft ? follow through the symbol will be used for correct ft cao ? correct answer only cso - correct solution only. There must be no errors in this part of the question to

obtain this mark isw ? ignore subsequent working awrt ? answers which round to SC: special case o.e. ? or equivalent (and appropriate) dep ? dependent indep ? independent dp decimal places sf significant figures The answer is printed on the paper The second mark is dependent on gaining the first mark

4. For misreading which does not alter the character of a question or materially simplify it, deduct two from any A or B marks gained, in that part of the question affected.

5. Where a candidate has made multiple responses and indicates which response they wish to submit, examiners should mark this response. If there are several attempts at a question which have not been crossed out, examiners should mark the final answer which is the answer that is the most complete.

6. Ignore wrong working or incorrect statements following a correct answer.

7. Mark schemes will firstly show the solution judged to be the most common response expected from candidates. Where appropriate, alternative answers are provided in the notes. If examiners are not sure if an answer is acceptable, they will check the mark scheme to see if an alternative answer is given for the method used.

General Principles for Further Pure Mathematics Marking

(But note that specific mark schemes may sometimes override these general principles)

Method mark for solving 3 term quadratic: 1. Factorisation

(x2 bx c) (x p)(x q), where pq c , leading to x ...

(ax2 bx c) (mx p)(nx q), where pq c and mn a , leading to x ...

2. Formula Attempt to use the correct formula (with values for a, b and c)

3. Completing the square

Solving

x2

bx c 0 :

x

b 2 2

qc

0,

q 0 , leading to

x ...

Method marks for differentiation and integration:

1. Differentiation

Power of at least one term decreased by 1. (xn xn1)

2. Integration

Power of at least one term increased by 1. (xn xn1)

Use of a formula

Where a method involves using a formula that has been learnt, the advice given in recent examiners' reports is that the formula should be quoted first.

Normal marking procedure is as follows:

Method mark for quoting a correct formula and attempting to use it, even if there are small errors in the substitution of values.

Where the formula is not quoted, the method mark can be gained by implication from correct working with values but may be lost if there is any mistake in the working.

Assessment Objectives

Assessment Objective

A01 A02 A03

Definition

Use and apply standard techniques Reason, interpret and communicate mathematically Solve problems within mathematics and in other contexts

Elements

Element

1.1a 1.1b 1.2

2.1 2.2a 2.2b 2.3 2.4 2.5

3.1a 3.1b 3.2a 3.2b 3.3 3.4 3.5a 3.5b 3.5c

Definition

Select routine procedures Correctly carry out routine procedures Accurately recall facts, terminology and definitions

Construct rigorous mathematical arguments (including proofs) Make deductions Make inferences Assess the validity of mathematical arguments Explain their reasoning Uses mathematical language and notation correctly

Translate problems in mathematical contexts into mathematical processes Translate problems in non-mathematical contexts into mathematical processes Interpret solutions to problems in their original context Evaluate (the) accuracy and limitations (of solutions to problems) Translate situations in context into mathematical models Use mathematical models Evaluate the outcomes of modelling in context Recognise the limitations of models Where appropriate, explain how to refine (models)

Question 1

Special Case

Way 1

Way 2

Way 3

Way 4

Scheme

2x 4y 1 22

2

4

If 0 marks are scored on application of the mark scheme then allow

Special Case B1 M0 A0 (total of 1 mark) for any of

2x 4y 2x2y

2x

4y

1 xy

42

1

x 3

2 2

2x2 2

log 2x log 4y xlog 2 ylog 4 or xlog 2 2ylog 2

ln 2x ln 4y xln 2 yln 4 or xln 2 2yln 2

y

log

2x

1 2

2 o.e. {base of 4 omitted}

2x

22y

2

3 2

2x2y

3

2 2

x 2 y 3 y ...

2

E.g. y 1 x 3 or y 1 (2x 3)

24

4

log(

2x

4

y

)

log

2

1

2

log 2x

log 4y

log

1 22

xlog 2 y log 4 log1 log(2 2) y ...

y log(2 2) x log 2 log 4

y 1 2

x

3 4

log(

2x

4

y

)

log

2

1

2

log 2x

log 4y

log

2

1

2

log 2x

y log 4

log

2

1

2

y

...

log

1

log

(2x

)

y 2 2

log 4

y1x 2

3 4

log

2

(

2

x

4

y

)

log

2

2

1

2

log2 2x log2 4y

log2

2

1

2

x2y

3 2

y ...

E.g. y 1 x 3 or y 1 (2x 3)

24

4

Marks AOs

B1

1.1b

M1

2.1

A1

1.1b

(3)

B1

1.1b

M1

2.1

A1

1.1b

(3)

B1

1.1b

M1

2.1

A1

1.1b

(3)

B1

1.1b

M1

2.1

A1

1.1b

(3) (3 marks)

Question

Scheme

Marks AOs

Way 5

1x

42

4y

4

3 4

1 x y

3

42 4 4

1 x y 3 y ...

2

4

E.g. y 1 x 3 or y 1 (2x 3)

24

4

B1

1.1b

M1

2.1

A1

1.1b

(3)

Notes for Question 1

Way 1

B1:

Writes a correct equation in powers of 2 only

M1: Complete process of writing a correct equation in powers of 2 only and using correct index laws to

obtain y written as a function of x.

A1:

y 1 x 3 o.e.

24

Way 2, Way 3 and Way 4

B1:

Writes a correct equation involving logarithms

M1: Complete process of writing a correct equation involving logarithms and using correct log laws to

obtain y written as a function of x.

log

1

log

(2x

)

A1:

y log(2 2) x log 2 or y ln(2 2) x ln 2 or y 2 2

log 4

ln 4

log 4

or y 1 x 3 or y 1 (2x 3) o.e.

24

4

B1: M1:

A1: Note: Note:

Way 5 Writes a correct equation in powers of 4 only Complete process of writing a correct equation in powers of 4 only and using correct index laws to obtain y written as a function of x. y 1 x 3 o.e.

24

Allow equivalent results for A1 where y is written as a function of x You can ignore subsequent working following on from a correct answer.

Note:

Allow B1 for 2x 4y 1 22

4y 1 2x2 2

log

4

(4

y

)

log

4

2x

1 2

2

followed by M1 A1 for

y

log4

2x

1 2

2

or

y

log

4

2 2

x

2

or

2 y log4 4(2x )

or

x3 y log4 2 2

or

y log4 (

2 (2x1))

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