Maths A Level
AQA
Please write clearly in block capitals.
Centre number Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
A-level
MATHEMATICS
Paper 3
Time allowed: 2 hours
Materials For Examiner’s Use
⚫ You must have the AQA Formulae for A‑level Mathematics booklet.
⚫ You should have a graphical or scientific calculator that meets the Question Mark
requirements of the specification. 1
2
Instructions
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 3
⚫ Fill in the boxes at the top of this page. 4
⚫ Answer all questions. 5
⚫ You must answer each question in the space provided for that question. 6
If you need extra space for your answer(s), use the lined pages at the end 7
of this book. Write the question number against your answer(s).
⚫ Do not write outside the box around each page or on blank pages. 8
⚫ Show all necessary working; otherwise marks for method may be lost. 9
⚫ Do all rough work in this book. Cross through any work that you do not want 10
to be marked. 11
12
Information 13
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100. 14
15
Advice 16
⚫ Unless stated otherwise, you may quote formulae, without proof, from the 17
booklet. 18
⚫ You do not necessarily need to use all the space provided. 19
TOTAL
(JUN227357301)
PB/Jun22/E7 7357/3
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 State the range of values of x for which the binomial expansion of
rffiffiffiffiffiffiffiffiffiffiffi
x
1—
4
is valid.
Circle your answer.
[1 mark]
1
jxj < jxj < 1 jxj < 2 jxj < 4
4
(02)
Jun22/7357/3
, 3
Do not write
outside the
2 The shaded region, shown in the diagram below, is defined by box
x 2 — 7x þ 7 ≤ y ≤ 7 — 2x
y
O 5 x
Identify which of the following gives the area of the shaded region.
Tick (3) one box.
[1 mark]
ð ð
(7 — 2x) d x — (x2 — 7x þ 7) d x
ð5
(x2 — 5x) d x
0
ð5 2
—
0 (5x x ) dx
ð5
(x 2 — 9x þ 14) d x
0
Turn over for the next question
Turn over
s
(03)
Jun22/7357/3
, 4
Do not write
outside the
3 The function f is defined by box
f (x) ¼ 2x þ 1
Solve the equation
f (x) ¼ f —1ðx)
Circle your answer.
[1 mark]
x ¼ —1 x¼0 x¼1 x¼2
4 Find
ð 1
x2 þ x 2 d x
[2 marks]
(04)
Jun22/7357/3
AQA
Please write clearly in block capitals.
Centre number Candidate number
Surname
Forename(s)
Candidate signature
I declare this is my own work.
A-level
MATHEMATICS
Paper 3
Time allowed: 2 hours
Materials For Examiner’s Use
⚫ You must have the AQA Formulae for A‑level Mathematics booklet.
⚫ You should have a graphical or scientific calculator that meets the Question Mark
requirements of the specification. 1
2
Instructions
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. 3
⚫ Fill in the boxes at the top of this page. 4
⚫ Answer all questions. 5
⚫ You must answer each question in the space provided for that question. 6
If you need extra space for your answer(s), use the lined pages at the end 7
of this book. Write the question number against your answer(s).
⚫ Do not write outside the box around each page or on blank pages. 8
⚫ Show all necessary working; otherwise marks for method may be lost. 9
⚫ Do all rough work in this book. Cross through any work that you do not want 10
to be marked. 11
12
Information 13
⚫ The marks for questions are shown in brackets.
⚫ The maximum mark for this paper is 100. 14
15
Advice 16
⚫ Unless stated otherwise, you may quote formulae, without proof, from the 17
booklet. 18
⚫ You do not necessarily need to use all the space provided. 19
TOTAL
(JUN227357301)
PB/Jun22/E7 7357/3
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 State the range of values of x for which the binomial expansion of
rffiffiffiffiffiffiffiffiffiffiffi
x
1—
4
is valid.
Circle your answer.
[1 mark]
1
jxj < jxj < 1 jxj < 2 jxj < 4
4
(02)
Jun22/7357/3
, 3
Do not write
outside the
2 The shaded region, shown in the diagram below, is defined by box
x 2 — 7x þ 7 ≤ y ≤ 7 — 2x
y
O 5 x
Identify which of the following gives the area of the shaded region.
Tick (3) one box.
[1 mark]
ð ð
(7 — 2x) d x — (x2 — 7x þ 7) d x
ð5
(x2 — 5x) d x
0
ð5 2
—
0 (5x x ) dx
ð5
(x 2 — 9x þ 14) d x
0
Turn over for the next question
Turn over
s
(03)
Jun22/7357/3
, 4
Do not write
outside the
3 The function f is defined by box
f (x) ¼ 2x þ 1
Solve the equation
f (x) ¼ f —1ðx)
Circle your answer.
[1 mark]
x ¼ —1 x¼0 x¼1 x¼2
4 Find
ð 1
x2 þ x 2 d x
[2 marks]
(04)
Jun22/7357/3
