AQA A-LEVEL MATHEMATICS 7357/3 PAPER 3 FINAL
EXAM QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED).
A-level
MATHEMATICS
Paper 3
Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae for A-level Mathematics booklet.
l You should have a graphical or scientific calculator that Question Mark
meets the requirements of the specification. 1
Instructions 2
l Use black ink or black ball-point pen. Pencil should only be used for 3
drawing. 4
l Fill in the boxes at the top of this page. 5
l Answer all questions. 6
l You must answer each question in the space provided for that
7
question. If you need extra space for your answer(s), use the
lined pages at the end of this book. Write the question number 8
against your answer(s). 9
l Do not write outside the box around each page or on blank pages. 10
l Show all necessary working; otherwise marks for method may be 11
lost.
12
l Do all rough work in this book. Cross through any work that you do
13
not want to be marked.
14
Information 15
l The marks for questions are shown in brackets. 16
l The maximum mark for this paper is 100. 17
18
Advice
l Unless stated otherwise, you may quote formulae, without 19
proof, from the booklet. TOTAL
l You do not necessarily need to use all the space provided.
(JUN227357301) 7357/3
PB/Jun22/E7
, 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
rffiffiffiffiffiffiffiffiffiffiffiffi
1 x
4
is valid.
Circle your answer.
[1 mark]
1
jxj < 4 jxj < 1 jxj < 2 jxj < 4
(02)
Jun22/7357/3
, 3
Do not write
outside the
2 The shaded region, shown in the diagram below, is defined by box
2
x 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
2
(7 2x) d x (x 7x þ 7) d x
ð5
2
(x 5x ) d x
0
ð5
2
(5x x )dx
0
ð5
2
(x 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
1
f (x) ¼ f ðx)
Circle your answer.
[1 mark]
x¼ 1 x¼0 x¼1 x¼2
4 Find
ð 1
2 2
x þx dx
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun22/7357/3
EXAM QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED).
A-level
MATHEMATICS
Paper 3
Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae for A-level Mathematics booklet.
l You should have a graphical or scientific calculator that Question Mark
meets the requirements of the specification. 1
Instructions 2
l Use black ink or black ball-point pen. Pencil should only be used for 3
drawing. 4
l Fill in the boxes at the top of this page. 5
l Answer all questions. 6
l You must answer each question in the space provided for that
7
question. If you need extra space for your answer(s), use the
lined pages at the end of this book. Write the question number 8
against your answer(s). 9
l Do not write outside the box around each page or on blank pages. 10
l Show all necessary working; otherwise marks for method may be 11
lost.
12
l Do all rough work in this book. Cross through any work that you do
13
not want to be marked.
14
Information 15
l The marks for questions are shown in brackets. 16
l The maximum mark for this paper is 100. 17
18
Advice
l Unless stated otherwise, you may quote formulae, without 19
proof, from the booklet. TOTAL
l You do not necessarily need to use all the space provided.
(JUN227357301) 7357/3
PB/Jun22/E7
, 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
rffiffiffiffiffiffiffiffiffiffiffiffi
1 x
4
is valid.
Circle your answer.
[1 mark]
1
jxj < 4 jxj < 1 jxj < 2 jxj < 4
(02)
Jun22/7357/3
, 3
Do not write
outside the
2 The shaded region, shown in the diagram below, is defined by box
2
x 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
2
(7 2x) d x (x 7x þ 7) d x
ð5
2
(x 5x ) d x
0
ð5
2
(5x x )dx
0
ð5
2
(x 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
1
f (x) ¼ f ðx)
Circle your answer.
[1 mark]
x¼ 1 x¼0 x¼1 x¼2
4 Find
ð 1
2 2
x þx dx
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun22/7357/3
