A-level

MATHEMATICS

Paper 1

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

TOTAL

I declare this is my own work.

2

Answer all questions in the spaces provided.

1 State the set of values of x which satisfies the inequality

(x  3)(2x þ 7) > 0

Tick (3) one box.

[1 mark]

x :  7

2 < x < 3

x : x < 3 or x >

7

2

x : x <  7

2 or x > 3

x : 3 < x <

7

2

2 Given that y ¼ ln (5x)

find dy

dx

Circle your answer.

[1 mark]

dy

dx

¼ 1

x

dy

dx

¼ 1

5x

dy

dx

¼ 5

x

dy

dx

¼ ln 5

Jun21/7357/1

Do not write

outside the

box

(02)

3

3 A geometric sequence has a sum to infinity of 3

A second sequence is formed by multiplying each term of the original sequence by 2

What is the sum to infinity of the new sequence?

Circle your answer.

[1 mark]

The sum to

infinity does not 6 3 6

exist

4 Millie is attempting to use proof by contradiction to show that the result of multiplying

an irrational number by a non-zero rational number is always an irrational number.

Select the assumption she should make to start her proof.

Tick (3) one box.

[1 mark]

Every irrational multiplied by a non-zero rational

is irrational.

Every irrational multiplied by a non-zero rational

is rational.

There exists a non-zero rational and

an irrational whose product is irrational.

There exists a non-zero rational and

an irrational whose product is rational.