2025 AQA A-LEVEL FURTHER MATHEMATICS Paper 1 Question Paper & Mark Scheme (Merged) Thursday 22 May 2025 [VERIFIED]

2025 AQA A-LEVEL FURTHER MATHEMATICS Paper 1
Question Paper & Mark Scheme (Merged) Thursday 22 May
2025 [VERIFIED]



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I declare this is my own work.




A-level
FURTHER MATHEMATICS
Paper 1


Thursday 22 May 2025 Afternoon Time allowed: 2 hours
For Examiner’s Use
Materials
 You must have the AQA Formulae and statistical tables booklet for Question Mark
A‑ level Mathematics and A‑ level Further Mathematics. 1
 You should have a graphical or scientific calculator that meets the 2
requirements of the specification.
3
Instructions 4
 Use black ink or black ball‑ point pen. Pencil should only be used for drawing. 5
 Fill in the boxes at the top of this page.
6
 Answer all questions.
 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
 Do not write outside the box around each page or on blank pages.
10
 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
11
to be marked. 12
13
Information 14
 The marks for questions are shown in brackets.
 The maximum mark for this paper is 100. 15
16
Advice 17
 Unless stated otherwise, you may quote formulae, without proof,
18
from the booklet.
 You do not necessarily need to use all the space provided. TOTAL




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, 2
Do not write
outside the
box
Answer all questions in the spaces provided.



1 The equation x2  4x  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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Do not write
outside the
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  2x  x0  ln 1 x 








4 Which one of the following statements is always correct?

Tick () one box.
[1 mark]
1
sinh2 x  1  cosh 2x 
2


sech2 x  tanh2 x  1



cosech2 x  coth2 x  1


1
cosh2 x  (cosh 2x 1)
2




Turn over for the next question




Turn over U


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, 4
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1
1  outside the
box
5 The complex number z 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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