Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 2
Monday 5 June 2024 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
⚫ You must have the AQA Formulae and statistical tables booklet for A‑level
Mathematics and A‑level Further Mathematics. Question Mark
⚫ You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
2
Instructions 3
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing.
⚫ 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 require extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s). 7
⚫ 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.
⚫ Do all rough work in this book. Cross through any work that you do not want 9
to be marked. 10
11
Information
⚫ The marks for questions are shown in brackets. 12
⚫ The maximum mark for this paper is 100. 13
14
Advice
⚫ Unless stated otherwise, you may quote formulae, without proof, from the 15
booklet. 16
⚫ You do not necessarily need to use all the space provided. TOTAL
PB/KL/Jun24/E4 7367/2
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
d 2y
1Given that y ¼ sin x þ sinh x , find d x2 þ y
Circle your answer.
[1 mark]
2 sin x 2 sin x 2 sinh x 2 sinh x
2 Which one of the expressions below is not equal to zero?
Circle your answer.
[1 mark]
ex 3 x
(x
x!1 2e x ) (x
x!0 5 ln x) x!1 x5
lim (x e )
lim lim lim x!0
(02)
Jun24/7367/2
, 3
Do not write
¼ outside the
1 1 1 box
3 2 1
3 The determinant A 2 0 2
Which one of the determinants below has a value which is not equal to the value of A?
Tick (3) one box.
[1 mark]
2 0 2
3 1 3
3 2 1
1 0 2
1 2 3
1 2 1
1 0 1
2 2 2
3 2 1
3 2 1
1 1 1
2 0 2
1
4 It is given that f (x) ¼ cosh (x 3)
Which of the sets listed below is the greatest possible domain of the function f ?
Circle your answer.
[1 mark]
fx : x 4g fx : x 3g fx : x 1g fx : x 0g
Turn over
s
(03)
Jun24/7367/2
, 4
Do not write
outside the
5 Josh and Zoe are solving the following mathematics problem: box
The curve C1 has equation
x2 y
2
16 9 ¼1
" #
0 1
The matrix M ¼ maps C1 onto C2
10
Find the equations of the asymptotes of C2
Josh says that to solve this problem you must first carry out the transformation on C1
to find C2, and then find the asymptotes of C2
Zoe says that you will get the same answer if you first find the asymptotes of C1, and
then carry out the transformation on these asymptotes to obtain the asymptotes of C2
Show that Zoe is correct.
[5 marks]
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_____________________________________________________________________________________
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun24/7367/2
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 2
Monday 5 June 2024 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
⚫ You must have the AQA Formulae and statistical tables booklet for A‑level
Mathematics and A‑level Further Mathematics. Question Mark
⚫ You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
2
Instructions 3
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing.
⚫ 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 require extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s). 7
⚫ 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.
⚫ Do all rough work in this book. Cross through any work that you do not want 9
to be marked. 10
11
Information
⚫ The marks for questions are shown in brackets. 12
⚫ The maximum mark for this paper is 100. 13
14
Advice
⚫ Unless stated otherwise, you may quote formulae, without proof, from the 15
booklet. 16
⚫ You do not necessarily need to use all the space provided. TOTAL
PB/KL/Jun24/E4 7367/2
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
d 2y
1Given that y ¼ sin x þ sinh x , find d x2 þ y
Circle your answer.
[1 mark]
2 sin x 2 sin x 2 sinh x 2 sinh x
2 Which one of the expressions below is not equal to zero?
Circle your answer.
[1 mark]
ex 3 x
(x
x!1 2e x ) (x
x!0 5 ln x) x!1 x5
lim (x e )
lim lim lim x!0
(02)
Jun24/7367/2
, 3
Do not write
¼ outside the
1 1 1 box
3 2 1
3 The determinant A 2 0 2
Which one of the determinants below has a value which is not equal to the value of A?
Tick (3) one box.
[1 mark]
2 0 2
3 1 3
3 2 1
1 0 2
1 2 3
1 2 1
1 0 1
2 2 2
3 2 1
3 2 1
1 1 1
2 0 2
1
4 It is given that f (x) ¼ cosh (x 3)
Which of the sets listed below is the greatest possible domain of the function f ?
Circle your answer.
[1 mark]
fx : x 4g fx : x 3g fx : x 1g fx : x 0g
Turn over
s
(03)
Jun24/7367/2
, 4
Do not write
outside the
5 Josh and Zoe are solving the following mathematics problem: box
The curve C1 has equation
x2 y
2
16 9 ¼1
" #
0 1
The matrix M ¼ maps C1 onto C2
10
Find the equations of the asymptotes of C2
Josh says that to solve this problem you must first carry out the transformation on C1
to find C2, and then find the asymptotes of C2
Zoe says that you will get the same answer if you first find the asymptotes of C1, and
then carry out the transformation on these asymptotes to obtain the asymptotes of C2
Show that Zoe is correct.
[5 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun24/7367/2
