AQA A-level Further Mathematics Paper 1 2025 | 7367/1 and mark scheme

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A-level
FURTHER MATHEMATICS
Paper 1


Thursday 22 May 2025 Afternoon Time allowed: 2 hours
For Examiner’s Use
Materials
l You must have the AQA Formulae and statistical tables booklet for Question Mark
A‑level Mathematics and A‑level Further Mathematics. 1
l You should have a graphical or scientific calculator that meets the
2
requirements of the specification.
3
Instructions 4
l Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
l Fill in the boxes at the top of this page.
6
l Answer all questions.
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). 9
l Do not write outside the box around each page or on blank pages.
10
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
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to be marked. 12
13
Information
14
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100. 15
16
Advice 17
l Unless stated otherwise, you may quote formulae, without proof,
from the booklet. 18
l You do not necessarily need to use all the space provided. TOTAL



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Answer all questions in the spaces provided. box




2
1 The equation x + 4 x + c =0 has non-real roots.

Find the range of possible values of c

Circle your answer.
[1 mark]

c < 4        c ≤ 4        c ≥ 4        c > 4




2 The point A on the Argand diagram represents the complex number z

The point B is the reflection in the imaginary axis of the point A


Im




O Re


A B




Which complex number does the point B represent?

Circle your answer.
[1 mark]
1
− z        z ∗        − z ∗
z




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3 Which one of the following expressions cannot be evaluated by l’Hôpital’s rule? box



Circle your answer.
[1 mark]

 x   x2   tanh x   ex − 1 
lim   lim   lim   lim  
x→0  cos x  x→0 sin x 
 x→0  2 x  x→0 ln (1+ x ) 

   




4 Which one of the following statements is always correct?

Tick () one box.
[1 mark]

1
2
sinh= x
2
(1 − cosh 2 x )

sech2 x + tanh2 x =
1



cosech2 x + coth2 x =
1


1
cosh2 x
= (cosh 2 x − 1)
2




Turn over for the next question




Turn over U


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 1
5 The complex number z1 has argument tan −1 
5
The complex number z2 = –2 – 4i

 z1 
Find arg  
 z2 
Give your answer as a number in the range – π < α < π, to two decimal places.
[3 marks]

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