AQA LEVEL 2 CERTIFICATE FURTHER MATHEMATICS (8365/2)

AQA LEVEL 2 CERTIFICATE FURTHER MATHEMATICS (8365/2)

Paper 2

Mark scheme

Specimen 2020

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MARK SCHEME ? AQA LEVEL 2 CERTIFICATE FURTHER MATHS ? 8365/2 ? SPECIMEN

Principal Examiners have prepared these mark schemes for specimen papers. These mark schemes have not, therefore, been through the normal process of standardising that would take place for live papers.

Further copies of this Mark Scheme are available from .uk

Glossary for Mark Schemes

AQA examinations are marked in such a way as to award positive achievement wherever possible. Thus, for these Mathematics papers, marks are awarded under various categories.

If a student uses a method which is not explicitly covered by the mark scheme the same principles of marking should be applied. Credit should be given to any valid methods. Examiners should seek advice from their senior examiner if in any doubt.

M A

B ft SC M dep B dep oe

[a, b]

Method marks are awarded for a correct method which could lead to a correct answer.

Accuracy marks are awarded when following on from a correct method. It is not necessary to always see the method. This can be implied.

Marks awarded independent of method.

Follow through marks. Marks awarded for correct working following a mistake in an earlier step.

Special case. Marks awarded within the scheme for a common misinterpretation which has some mathematical worth.

A method mark dependent on a previous method mark being awarded.

A mark that can only be awarded if a previous independent mark has been awarded.

Or equivalent. Accept answers that are equivalent. eg accept 0.5 as well as 1

2

Accept values between a and b inclusive.

3.14 ...

Allow answers which begin 3.14 eg 3.14, 3.142, 3.1416

Use of brackets It is not necessary to see the bracketed work to award the marks.

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MARK SCHEME ? AQA LEVEL 2 CERTIFICATE FURTHER MATHS ? 8365/2 ? SPECIMEN

Examiners should consistently apply the following principles

Diagrams Diagrams that have working on them should be treated like normal responses. If a diagram has been written on but the correct response is within the answer space, the work within the answer space should be marked. Working on diagrams that contradicts work within the answer space is not to be considered as choice but as working, and is not, therefore, penalised.

Responses which appear to come from incorrect methods Whenever there is doubt as to whether a student has used an incorrect method to obtain an answer, as a general principle, the benefit of doubt must be given to the student. In cases where there is no doubt that the answer has come from incorrect working then the student should be penalised.

Questions which ask students to show working Instructions on marking will be given but usually marks are not awarded to students who show no working.

Questions which do not ask students to show working As a general principle, a correct response is awarded full marks.

Misread or miscopy Students often copy values from a question incorrectly. If the examiner thinks that the student has made a genuine misread, then only the accuracy marks (A or B marks), up to a maximum of 2 marks are penalised. The method marks can still be awarded.

Further work Once the correct answer has been seen, further working may be ignored unless it goes on to contradict the correct answer.

Choice When a choice of answers and/or methods is given, mark each attempt. If both methods are valid then M marks can be awarded but any incorrect answer or method would result in marks being lost.

Work not replaced Erased or crossed out work that is still legible should be marked.

Work replaced Erased or crossed out work that has been replaced is not awarded marks.

Premature approximation Rounding off too early can lead to inaccuracy in the final answer. This should be penalised by 1 mark unless instructed otherwise.

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MARK SCHEME ? AQA LEVEL 2 CERTIFICATE FURTHER MATHS ? 8365/2 ? SPECIMEN

Q

Answer

Mark

Comments

x-coordinate of Q = 6 ? 2 or 3

M1

may be implied or seen on diagram

0.5 ? 6 ? their 3

1

9

M1dep A1

Additional Guidance

x2 + y2 = 100 or x2 + y2 = 102

B2

B1 radius = 10

2

Additional Guidance

p = 2.5 or 5 or 2 1

2

2

3

r = ?5

x > 6 4(a)

x ?4 or x 4 4(b)

(2, 0) 5(a)

B1 B1 Additional Guidance

B1 Additional Guidance

B1 Additional Guidance

B1 Additional Guidance

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MARK SCHEME ? AQA LEVEL 2 CERTIFICATE FURTHER MATHS ? 8365/2 ? SPECIMEN

Q

6 5(b)

Answer

4s + 5 = ?1 or ?7s ? 10 = t

s = ?1.5 6(a)

t = 0.5

Mark

B1 Additional Guidance

Comments

oe equation M1

A1 A1ft ft ?7 ? their s ? 10 Additional Guidance

4 6(b)

A1 Additional Guidance

(gradient =) 0.5 or 1

M1

2

0 = their 0.5 ? 4 + c or c = ?2 or y ? 0 = their 0.5(x ? 4) 7 y = 0.5x ? 2 or y = 0.5(x ? 4)

oe M1

oe simplified equation A1

Additional Guidance

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MARK SCHEME ? AQA LEVEL 2 CERTIFICATE FURTHER MATHS ? 8365/2 ? SPECIMEN

Q

Answer

8(a)

ab ? ad

cd bc

a 2 c2

Mark

M1

oe

A1 Additional Guidance

Comments

Common denominator with at least one numerator correct

M1

eg 21 + 8x or 21x + 8x2

6x2 6x2

6x3 6x3

21 + 8x

8(b)

6x2

A1

Additional Guidance

x + 62 = 2(2x ? 50)

62 + 100 = 4x ? x or 3x = 162

x = 54 9

180 - 62 - their 54 2

32

M1 oe

M1dep

oe

correct expansion and collection of terms

A1

M1dep

A1ft ft their x with first and third M1 gained Additional Guidance

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MARK SCHEME ? AQA LEVEL 2 CERTIFICATE FURTHER MATHS ? 8365/2 ? SPECIMEN

Q

Answer

Mark

Comments

6x9 + x8 or 3x5 or 1 x4

2x4 2x4

2

3x5 + 1 x4

2

15x4 or 2x3 10

60x3 + 6x2

9

M1

A1 M1dep differentiates at least one term correctly M1dep differentiates their 2-term dy correctly

dx A1 Additional Guidance

k2 = 2(14k + 30) k2 ? 28k ? 60 (= 0)

M1 M1dep

oe correct equation with fractions eliminated

oe equation

(k + 2)(k ? 30) (= 0)

- -28 ? (-28)2 - 4 ?1? -60

11

or

2?1

or 14 ? 256

oe

correct attempt to solve their 3-term

M1

quadratic equation

30

A1

30 and ?2 is A0

Additional Guidance

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MARK SCHEME ? AQA LEVEL 2 CERTIFICATE FURTHER MATHS ? 8365/2 ? SPECIMEN

Q

Answer

Mark

Comments

12(a)

30x + 20x + 15x + 10x + 15x + y + y =

oe

252

M1

or 90x + 2y = 252

y = 252 - 90x

2

and y = 126 ? 45x

must see working for M1 A1

Additional Guidance

12(b)

30x ? 15x + 20x ? (126 ? 45x) or 15x ? 10x + 20x ? (126 ? 45x + 15x) or 15x ? 10x + 20x ? (126 ? 30x)

oe M1

450x2 + 2520x ? 900x2 = 2520x ? 450x2

or 150x2 + 2520x ? 900x2 + 300x2 = 2520x ? 450x2

or 150x2 + 2520x ? 600x2 = 2520x ? 450x2

must see correct expansion of brackets A1

Additional Guidance

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