AQA A-LEVEL FURTHER MATHEMATICS 7367/2 PAPER 2
FINAL EXAM QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED).
A-level
FURTHER MATHEMATICS
Paper 2
Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet
for A-level Mathematics and A-level Further Mathematics. Question Mark
l You should have a scientific calculator that meets the
requirements of the specification. 1
2
Instructions
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.
l Answer all questions. 5
l You must answer each question in the space provided for that
question. 6
If you require extra space for your answer(s), use the lined pages 7
at the end of this book. Write the question number against your
answer(s). 8
l Do not write outside the box around each page or on blank pages.
9
l Show all necessary working; otherwise marks for method may be
lost. 10
l Do all rough work in this book. Cross through any work that you do
11
not want to be marked.
12
Information
l The marks for questions are shown in brackets. 13
l The maximum mark for this paper is 100. 14
Advice TOTAL
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.
(JUN227367201) 7367/2
PB/Jun22/E7
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Find the imaginary part of
5þi
1 i
Circle your answer.
[1 mark]
3 2 2 3
4
2 Find the mean value of the function f (x) ¼ 10x between x ¼ 0 and x ¼ a
Circle your answer.
[1 mark]
3 3 4 5
10a 40a 2a 4a
(02)
Jun22/7367/2
, 3
Do not write
outside the
2
3 The roots of the equation x px 6 ¼ 0 are a and b box
2 2
Find a þ b in terms of p
Circle your answer.
[1 mark]
2 2 2 2
p 6 p þ6 p 12 p þ 12
4 Which of the following graphs intersects the graph of y ¼ sinh x at exactly one point?
Circle your answer.
[1 mark]
y ¼ cosech x y ¼ cosh x y ¼ coth x y ¼ sech x
Turn over for the next question
Turn over
s
(03)
Jun22/7367/2
, 4
Do not write
outside the
5 Prove by induction that, for all integers n 1, box
X
n 1 2
3
r ¼1 r ¼ 2 n(n þ 1)
[4 marks]
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(04)
Jun22/7367/2
FINAL EXAM QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED).
A-level
FURTHER MATHEMATICS
Paper 2
Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet
for A-level Mathematics and A-level Further Mathematics. Question Mark
l You should have a scientific calculator that meets the
requirements of the specification. 1
2
Instructions
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.
l Answer all questions. 5
l You must answer each question in the space provided for that
question. 6
If you require extra space for your answer(s), use the lined pages 7
at the end of this book. Write the question number against your
answer(s). 8
l Do not write outside the box around each page or on blank pages.
9
l Show all necessary working; otherwise marks for method may be
lost. 10
l Do all rough work in this book. Cross through any work that you do
11
not want to be marked.
12
Information
l The marks for questions are shown in brackets. 13
l The maximum mark for this paper is 100. 14
Advice TOTAL
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.
(JUN227367201) 7367/2
PB/Jun22/E7
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Find the imaginary part of
5þi
1 i
Circle your answer.
[1 mark]
3 2 2 3
4
2 Find the mean value of the function f (x) ¼ 10x between x ¼ 0 and x ¼ a
Circle your answer.
[1 mark]
3 3 4 5
10a 40a 2a 4a
(02)
Jun22/7367/2
, 3
Do not write
outside the
2
3 The roots of the equation x px 6 ¼ 0 are a and b box
2 2
Find a þ b in terms of p
Circle your answer.
[1 mark]
2 2 2 2
p 6 p þ6 p 12 p þ 12
4 Which of the following graphs intersects the graph of y ¼ sinh x at exactly one point?
Circle your answer.
[1 mark]
y ¼ cosech x y ¼ cosh x y ¼ coth x y ¼ sech x
Turn over for the next question
Turn over
s
(03)
Jun22/7367/2
, 4
Do not write
outside the
5 Prove by induction that, for all integers n 1, box
X
n 1 2
3
r ¼1 r ¼ 2 n(n þ 1)
[4 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun22/7367/2
