A-level

MATHEMATICS

Paper 3

Time allowed: 2 hours

Materials

l You must have the AQA Formulae for A‑level Mathematics booklet.

l You should have a graphical or scientific calculator that meets the

requirements of the specification.

Instructions

l Use black ink or black ball-point pen. Pencil should only be used for drawing.

l Fill in the boxes at the top of this page.

l Answer all questions.

l You must answer each question in the space provided for that question.

If you need extra space for your answer(s), use the lined pages at the end

of this book. Write the question number against your answer(s).

l Show all necessary working; otherwise marks for method may be lost.

l Do all rough work in this book. Cross through any work that you do not want

to be marked.

Information

l The marks for questions are shown in brackets.

l The maximum mark for this paper is 100.

Advice

l Unless stated otherwise, you may quote formulae, without proof, from the

booklet.

l You do not necessarily need to use all the space provided.

Please write clearly in block capitals.

Centre number Candidate number

Surname ________________________________________________________________________

Forename(s) ________________________________________________________________________

Candidate signature ________________________________________________________________________

For Examiner’s Use

Question Mark

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

TOTAL

I declare this is my own work.

2

Section A

Answer all questions in the spaces provided.

1 The graph of y ¼ arccos x is shown.

P

x

y

State the coordinates of the end point P.

Circle your answer.

[1 mark]

(p, 1) (1, p)  p

2 , 1   1, p

2

Jun21/7357/3

Do not write

outside the

box

(02)

3

2 Simplify fully

(x þ 3)(6  2x)

(x  3)(3 þ x) for x 6¼ 3

Circle your answer.

[1 mark]

2 2 (6  2x)

(x  3)

(2x  6)

(x  3)

3 f (x) ¼ 3x2

Obtain lim

h! 0

f (x þ h)  f (x)

h

Circle your answer.

[1 mark]

3h2

h x3 3(x þ h)

2  3x2

h 6x

Turn over for the next question