AQA
A-level
FURTHER MATHEMATICS
7367/1
Paper 1
Version: 1.0 Final
PB/KL/Jun23/E6 7367/1
A-level
FURTHER MATHEMATICS
Paper 1
Time allowed: 2
... [Show More] hours
Materials
l You must have the AQA Formulae and statistical tables booklet for A‑level
Mathematics and A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
requirements of the specification.
Instructions
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.
l Answer all questions.
l You must answer each question in the space provided for that question.
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).
l Do not write outside the box around each page or on blank pages.
l Show all necessary working; otherwise marks for method may be lost.
l Do all rough work in this book. Cross through any work that you do not want
to be marked.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100.
Advice
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.
Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
For Examiner’s Use
Question Mark
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
TOTAL
I declare this is my own work.
2
Answer all questions in the spaces provided.
1 Find the number of solutions of the equation tanh x ¼ cosh x
Circle your answer.
[1 mark]
0 12 3
2 The diagram below shows a locus on an Argand diagram.
2 Re
Im
–3
O
Which of the equations below represents the locus shown above?
Circle your answer.
[1 mark]
jz 2 þ 3ij ¼ 2 jz þ 2 3ij ¼ 2 jz 2 þ 3ij ¼ 4 jz þ 2 3ij ¼ 4
Jun23/7367/1
Do not write
outside the
box
(02)
3
3 The matrix A ¼ 1 2
0 1 represents a transformation.
Which one of the points below is an invariant point under this transformation?
Circle your answer.
[1 mark]
(1, 1) (0, 2) (3, 0) (2, 1)
4 The solution of a second order differential equation is f (t)
The differential equation models heavy damping.
Which one of the statements below could be true?
Tick (3) one box.
[1 mark]
f (t) ¼ 2et cos (3t) þ 5et sin (3t)
f (t) ¼ 3et þ 4tet
f (t) ¼ 7et þ 2e2t
f (t) ¼ 8et cos (3t 0:1)
Turn over for the next question
Do not write
outside the
box
Jun23/7367/1
Turn over s
(03)
4
5 The function f is defined by
f (r) ¼ 2r
(r 2) (r 2 Z)
5 (a) Show that
f (r þ 1) f (r) ¼ r2r
[2 marks]
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Do not write
outside the
box
Jun23/7367/1
(04)
5
5 (b) Use the method of differences to show tha [Show Less]