000001
AQA
AQA
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
S
Forename(s) _________________________________________________________________________
C
Candidate signature _________________________________________________________________________
I declare this is my own work.
TI
A-level
A
EM
FURTHER MATHEMATICS
Paper 1
TH
Wednesday 22 May 2024 Afternoon Time allowed: 2 hours
A
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
M
Question Mark
A‑level Mathematics and A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
1
requirements of the specification. 2
ER
3
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing.
l Fill in the boxes at the top of this page. 5
TH
l Answer all questions. 6
l You must answer each question in the space provided for that question. 7
If you require extra space for your answer(s), use the lined pages at the end
8
of this book. Write the question number against your answer(s).
R
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
FU
l Do all rough work in this book. Cross through any work that you do not want
11
to be marked.
12
Information 13
l The marks for questions are shown in brackets. 14
l The maximum mark for this paper is 100.
15
Advice 16
l Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet. 18
l You do not necessarily need to use all the space provided.
TOTAL
G/LM/Jun24/G4006/V8 7367/1
Page 1 of 32
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The roots of the equation 20 x 3 – 16 x 2 – 4 x + 7 = 0 are α, β and γ
Find the value of αβ + βγ + γα
Circle your answer.
[1 mark]
–4 –1 1 4
S
5 5 5 5
C
TI
A
iπ
EM
2 The complex number z = e 3
Which one of the following is a real number?
TH
Circle your answer.
[1 mark]
z4 z5 z6 z7
A
M
ER
TH
R
FU
(02)
G/Jun24/7367/1
Page 2 of 32
,000003
3
Do not write
outside the
box
3 The function f is defined by
f (x) = x 2 (x ∈ ℝ)
Find the mean value of f (x) between x = 0 and x = 2
Circle your answer.
[1 mark]
2 4 8 16
3 3 3 3
S
C
4 Which one of the following statements is correct?
TI
Tick () one box.
[1 mark]
A
lim (x 2 ln x) = 0
EM
x 0
lim (x 2 ln x) = 1
x 0
TH
lim (x 2 ln x) = 2
x 0
A
M
lim (x 2 ln x) is not defined.
x 0
ER
Turn over for the next question
TH
R
FU
Turn over U
(03)
G/Jun24/7367/1
Page 3 of 32
, 000004
4
Do not write
outside the
box
5 The points A, B and C have coordinates A(5, 3, 4), B(8, –1, 9) and C(12, 5, 10)
The points A, B and C lie in the plane ∏
5 (a) Find a vector that is normal to the plane ∏
[3 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
S
_____________________________________________________________________________________
C
_____________________________________________________________________________________
TI
_____________________________________________________________________________________
A
_____________________________________________________________________________________
EM
_____________________________________________________________________________________
_____________________________________________________________________________________
TH
_____________________________________________________________________________________
_____________________________________________________________________________________
A
_____________________________________________________________________________________
M
_____________________________________________________________________________________
ER
_____________________________________________________________________________________
_____________________________________________________________________________________
TH
_____________________________________________________________________________________
_____________________________________________________________________________________
R
_____________________________________________________________________________________
FU
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
G/Jun24/7367/1
Page 4 of 32
AQA
AQA
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
S
Forename(s) _________________________________________________________________________
C
Candidate signature _________________________________________________________________________
I declare this is my own work.
TI
A-level
A
EM
FURTHER MATHEMATICS
Paper 1
TH
Wednesday 22 May 2024 Afternoon Time allowed: 2 hours
A
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
M
Question Mark
A‑level Mathematics and A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
1
requirements of the specification. 2
ER
3
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing.
l Fill in the boxes at the top of this page. 5
TH
l Answer all questions. 6
l You must answer each question in the space provided for that question. 7
If you require extra space for your answer(s), use the lined pages at the end
8
of this book. Write the question number against your answer(s).
R
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
FU
l Do all rough work in this book. Cross through any work that you do not want
11
to be marked.
12
Information 13
l The marks for questions are shown in brackets. 14
l The maximum mark for this paper is 100.
15
Advice 16
l Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet. 18
l You do not necessarily need to use all the space provided.
TOTAL
G/LM/Jun24/G4006/V8 7367/1
Page 1 of 32
,000002
2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The roots of the equation 20 x 3 – 16 x 2 – 4 x + 7 = 0 are α, β and γ
Find the value of αβ + βγ + γα
Circle your answer.
[1 mark]
–4 –1 1 4
S
5 5 5 5
C
TI
A
iπ
EM
2 The complex number z = e 3
Which one of the following is a real number?
TH
Circle your answer.
[1 mark]
z4 z5 z6 z7
A
M
ER
TH
R
FU
(02)
G/Jun24/7367/1
Page 2 of 32
,000003
3
Do not write
outside the
box
3 The function f is defined by
f (x) = x 2 (x ∈ ℝ)
Find the mean value of f (x) between x = 0 and x = 2
Circle your answer.
[1 mark]
2 4 8 16
3 3 3 3
S
C
4 Which one of the following statements is correct?
TI
Tick () one box.
[1 mark]
A
lim (x 2 ln x) = 0
EM
x 0
lim (x 2 ln x) = 1
x 0
TH
lim (x 2 ln x) = 2
x 0
A
M
lim (x 2 ln x) is not defined.
x 0
ER
Turn over for the next question
TH
R
FU
Turn over U
(03)
G/Jun24/7367/1
Page 3 of 32
, 000004
4
Do not write
outside the
box
5 The points A, B and C have coordinates A(5, 3, 4), B(8, –1, 9) and C(12, 5, 10)
The points A, B and C lie in the plane ∏
5 (a) Find a vector that is normal to the plane ∏
[3 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
S
_____________________________________________________________________________________
C
_____________________________________________________________________________________
TI
_____________________________________________________________________________________
A
_____________________________________________________________________________________
EM
_____________________________________________________________________________________
_____________________________________________________________________________________
TH
_____________________________________________________________________________________
_____________________________________________________________________________________
A
_____________________________________________________________________________________
M
_____________________________________________________________________________________
ER
_____________________________________________________________________________________
_____________________________________________________________________________________
TH
_____________________________________________________________________________________
_____________________________________________________________________________________
R
_____________________________________________________________________________________
FU
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
G/Jun24/7367/1
Page 4 of 32
