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A Level Mathematics

Sample Assessment Materials DRAFTPearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)First teaching from September 2017First certification from 2018

This draft qualification has not yet been accredited by Ofqual. It is published to enable teachers to have early sight of our proposed approach to Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0). Further changes may be required and no assurance can be given at this time that the proposed qualification will be made available in its current form, or that it will be accredited in time for first teaching in September 2017 and first award in 2018.

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Edexcel, BTEC and LCCI qualifications Edexcel, BTEC and LCCI qualifications are awarded by Pearson, the UK’s largest awarding body offering academic and vocational qualifications that are globally recognised and benchmarked. For further information, please visit our qualification websites at www.edexcel.com, www.btec.co.uk or www.lcci.org.uk. Alternatively, you can get in touch with us using the details on our contact us page at qualifications.pearson.com/contactus

About Pearson Pearson is the world's leading learning company, with 40,000 employees in more than 70 countries working to help people of all ages to make measurable progress in their lives through learning. We put the learner at the centre of everything we do, because wherever learning flourishes, so do people. Find out more about how we can help you and your learners at qualifications.pearson.com

References to third party material made in this sample assessment materials are made in good faith. Pearson does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)

All information in this document is correct at time of publication.

Original origami artwork: Mark Bolitho Origami photography: Pearson Education Ltd/Naki Kouyioumtzis

ISBN 978 1 4469 3344 2

All the material in this publication is copyright © Pearson Education Limited 2016

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Contents

Introduction 1

General marking guidance 3

Paper 1 – sample question paper and mark scheme 5



Mathematical formulae and statistical tables

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Introduction

The Pearson Edexcel Level 3 Advanced GCE in Mathematics is designed for use in schools and colleges. It is part of a suite of AS/A Level qualifications offered by Pearson.

These sample assessment materials have been developed to support this qualification and will be used as the benchmark to develop the assessment students will take.

Pearson Edexcel Level 3 Advanced GCE in Mathematics – Sample assessment materials (SAMs) – Draft 1.0 – June 2016 © Pearson Education Limited 2016

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General marking guidance

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

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

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

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/indicative content will not be exhaustive.

When examiners are in doubt regarding the application of the mark scheme to a candidate’s response, a senior examiner must be consulted before a mark is given.

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

Specific guidance for mathematics

1. These 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.

2. Abbreviations

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

bod benefit of doubt

ft follow through

this symbol is 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)

d… dependent or dep

indep independent

dp decimal places

sf significant figures

The answer is printed on the paper or ag- answer given

or d… The second mark is dependent on gaining the first mark


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3. All A marks are ‘correct answer only’ (cao.), unless shown, for example, as A1 ft to indicate that previous wrong working is to be followed through. After a misread however, the subsequent A marks affected are treated as A ft, but manifestly absurd answers should never be awarded A marks.

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. If a candidate makes more than one attempt at any question:

If all but one attempt is crossed out, mark the attempt which is NOT crossed out.

If either all attempts are crossed out or none are crossed out, mark all the attempts and score the highest single attempt.

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


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Pearson Edexcel Level 3 GCE

Mathematics Advanced Paper 1: Pure Mathematics 1

Sample assessment material for first teaching September 2017 Time: 2 hours

Paper Reference(s)

9MA0/01

You must have: Mathematical Formulae and Statistical Tables, calculator

Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for algebraic manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them.

Instructions

Use black ink or ball-point pen. If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). Fill in the boxes at the top of this page with your name, centre

number and candidate number.

Answer all questions and ensure that your answers to parts of questions are clearly labelled.

Answer the questions in the spaces provided – there may be more space than you need.

You should show sufficient working to make your methods clear. Answers without working may not gain full credit.

Answers should be given to three significant figures unless otherwise stated. Information

A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. There are 17 questions in this question paper. The total mark for this

paper is 100.

The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

Advice

Read each question carefully before you start to answer it. Try to answer every question. Check your answers if you have time at the end.


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Answer ALL questions. Write your answers in the spaces provided.

1. Given that

y = 31

27x

express each of the following in the form ,nkx where k and n are constants.

(a) 1

3y

(1)

(b) 3y –1

(1)

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(Total for Question 1 is 2 marks)


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2. 3 2f ( ) 2 5 8x x x x a

Given that ( 3)x is a factor of f ( ),x use the factor theorem to find the value of

the constant a.

(2)

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3. The point ( 2,5)P lies on the curve with equation f ( ).y x

State the coordinates of the point to which P is transformed on the curve with equation

(a) f ( ) 4y x

(1)

(b) 5 f ( )y x

(1)

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4. A class of A level students were given the following question.

Solve, for 90 90 , the equation

cos 2sin

The attempts of two of the students are shown below

(a) Identify the error made by student A.

(1)

(b) Identify the error made by student B, and explain how this effects their solution.

(2)

(c) Write down the correct answer to the question.

(1)

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Total for Question 4 is 4 marks)

Student

cos 2sin

tan 2

63.4

A

2 2

2 2

Student

cos 2sin

cos 4sin

1 sin 4sin

1sin

5

26.6

B


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5. Given

3

2 6, 0y x xx

(a) find d

d

y

x

(3)

(b) Hence find the value of d

d

y

x when 8,x writing your answer in the form 2a where

a is a rational number.

(2)

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6. A circle C has equation

2 2 4 10x y x y k

where k is a constant.

(a) Find the coordinates of the centre of C.

(2)

(b) State the range of possible values for k. (2)

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7. The curve 1C has equation 2 ,a

yx

where a is a positive constant.

The curve 2C has equation 2(2 ),y x x b where b is a positive constant.

(a) Sketch 1C and 2C on the same set of axes.

Show on your sketch the coordinates of any point where either curve cuts or touches the

coordinate axes.

(5)

(b) Using your sketch, state, giving a reason, the number of real solutions to the equation

4(2 )x x b a

where a and b are positive constants.

(1)

y

O x

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8. Given that A is constant and

show that there are two possible values for A and find these values.

(5)

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4

2

1

3 d 2x A x A


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9.

Figure 1

Figure 1 shows a rectangle ABCD.

The point A lies on the y-axis and the points B and D lie on the x-axis as shown in Figure 1.

Given that the straight line through the points A and B has equation 5 2 10y x

(a) show that the straight line through the points A and D has equation 2 5 4y x

(4)

(b) Find the area of the rectangle ABCD.

(3)

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Question 9 continued

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10.

Figure 2

Figure 2 shows a sketch of a triangle ABC.

Given = 2 +3AB i j and =3 6 ,AC i j

(a) find ,BC

(2)

(b) find the size of BAC , in degrees, to one decimal place.

(4)

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11. 5

g( ) 2 ,x kx where k is a constant

Given that the coefficient of 3x in the binomial expansion of g(x) is 5, find the value of k.

(3)

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12. The mass, m grams, of a radioactive substance t years after first being observed, is modelled by the equation

0.0525e tm

According to the model,

(a) state the value of m when the radioactive substance was first observed,

(1)

(b) show that d

,d

mkm

t where k is a constant that should be found.

(2)

(c) With reference to the model, interpret the significance of the sign of the value

of k found in part (b).

(1)

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13. (a) Show that the equation

5 sin x – cos2 x + 2 sin2 x = 1

can be written in the form

3 sin2 x + 5 sin x – 2 = 0

(2)

(b) Hence solve, for –180° θ < 180°, the equation

5 sin 2θ – cos2 2θ + 2 sin2 2θ = 1

giving your answers to 2 decimal places.

(7)

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14.

The finite region R, which is shown shaded in Figure 3, is bounded by the straight line l

with equation y = 4x + 3 and the curve C with equation y = 23

2x – 2x + 3, x 0

The line l meets the curve C at the point A on the y-axis and l meets C again at the point B,

as shown in Figure 3.

(a) Find the coordinates of point A and point B.

(4)

(b) Find the area of the region R.

(6)

(Solutions based entirely on graphical or numerical methods are not acceptable.)

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