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2023 AQA AS FURTHER MATHEMATICS 7366/1 Paper 1 Question Paper & Mark scheme (Merged)
June 2023 [VERIFIED]
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) 7366/1
G/LM/Jun23/E7
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
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
3 The matrices A and B are given by box
A= [30 1
] = [07
5 B 4
1 ]
Calculate AB
Circle your answer.
[1 mark]
[37 56] [210 12
20
] [00 4
5 ] [ 357 135]
4 The roots of the equation
3 2
5x + 2x – 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
, 4
Do not write
outside the
5 The function f is defined by box
f (x) = 3x2 1≤x≤5
5 (a) Find the mean value of f
[2 marks]
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