AQA QP 2023 AS FURTHER MATHEMATICS Paper 1
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
AS
FURTHER MATHEMATICS
Paper 1
Monday 15 May 2023 Afternoon Time allowed: 1 hour 30 minutes
Materials For Examiner’s Use
You must have the AQA Formulae and statistical tables booklet for
Question Mark
A-level Mathematics and A-level Further Mathematics.
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. 4
Fill in the boxes at the top of this page.
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
Information 11
The marks for questions are shown in brackets. 12
The maximum mark for this paper is 80.
13
Advice 14
Unless stated otherwise, you may quote formulae, without proof,
from the booklet. TOTAL
You do not necessarily need to use all the space provided.
(JUN237366101)
G/LM/Jun23/E7 7366/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Which expression below is equivalent to tanh x ?
Circle your answer.
[1 mark]
sinh x cosh x sinh x cosh x sinh x + cosh x
cosh x sinh x
2 The two vectors a and b are such that a.b = 0
State the angle between the vectors a and b
Circle your answer.
[1 mark]
0° 45° 90° 180°
(02)
G/Jun23/7366/1
, 3
Do not write
outside the
box
3 The matrices A and B are given by
A= [ ] 3
0
1
5
B= [ ]
0
7
4
1
Calculate AB
Circle your answer.
[1 mark]
[ ]
3
7
5
6 [ 0
21
20
12 ] [ ]
0
0
4
5 [ 7 13
35 5 ]
4 The roots of the equation
5x 3 + 2x 2 – 3x + p = 0
are α, β and γ
Given that p is a constant, state the value of αβ + βγ + γα
Circle your answer.
[1 mark]
–3 –2 2 3
5 5 5 5
Turn over 8
(03)
G/Jun23/7366/1
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
AS
FURTHER MATHEMATICS
Paper 1
Monday 15 May 2023 Afternoon Time allowed: 1 hour 30 minutes
Materials For Examiner’s Use
You must have the AQA Formulae and statistical tables booklet for
Question Mark
A-level Mathematics and A-level Further Mathematics.
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. 4
Fill in the boxes at the top of this page.
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
Information 11
The marks for questions are shown in brackets. 12
The maximum mark for this paper is 80.
13
Advice 14
Unless stated otherwise, you may quote formulae, without proof,
from the booklet. TOTAL
You do not necessarily need to use all the space provided.
(JUN237366101)
G/LM/Jun23/E7 7366/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Which expression below is equivalent to tanh x ?
Circle your answer.
[1 mark]
sinh x cosh x sinh x cosh x sinh x + cosh x
cosh x sinh x
2 The two vectors a and b are such that a.b = 0
State the angle between the vectors a and b
Circle your answer.
[1 mark]
0° 45° 90° 180°
(02)
G/Jun23/7366/1
, 3
Do not write
outside the
box
3 The matrices A and B are given by
A= [ ] 3
0
1
5
B= [ ]
0
7
4
1
Calculate AB
Circle your answer.
[1 mark]
[ ]
3
7
5
6 [ 0
21
20
12 ] [ ]
0
0
4
5 [ 7 13
35 5 ]
4 The roots of the equation
5x 3 + 2x 2 – 3x + p = 0
are α, β and γ
Given that p is a constant, state the value of αβ + βγ + γα
Circle your answer.
[1 mark]
–3 –2 2 3
5 5 5 5
Turn over 8
(03)
G/Jun23/7366/1
