7367-2-QP3-Mathematics-AS-6Jun25-PM 2 (1) 1

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A-level
FURTHER MATHEMATICS
Paper 2

Friday 6 June 2025 Afternoon Time allowed: 2 hours
Materials
For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
A‑level Mathematics and A‑level Further Mathematics. Question Mark
l You should have a graphical or scientific calculator that meets the 1
requirements of the specification.
2
Instructions 3
l Use black ink or black ball‑point pen. Pencil should only be used for drawing. 4
l Fill in the boxes at the top of this page. 5
l Answer all questions.
6
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 7
of this book. Write the question number against your answer(s). 8
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.
l Do all rough work in this book. Cross through any work that you do not want
10
to be marked. 11
12
Information 13
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100.
14
15
Advice 16
l Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet.
l You do not necessarily need to use all the space provided. TOTAL




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




a  c 
1 The vectors   and   are perpendicular.
b   1
Which one of the following statements must be true?

Tick () one box.
[1 mark]

a = bc


b = ac


a = – bc


b = – ac




2 The quadrilateral Q1 has an area of 5 cm2

 4 −1
The matrix   represents the transformation T
2 1 
The transformation T acts on Q1 to give the quadrilateral Q2

Find the area of Q2

Circle your answer.
[1 mark]

5 cm2       10 cm2       30 cm2       180 cm2




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, Page 3

d
3 Find
dx
( sin −1 x − 2 cos−1 x ) 3
Do not write
Circle your answer. outside the
d
( )
box
3 Find sin−1 x − 2 cos−1 x
dx [1 mark]

−3 answer.
Circle your −1 1 3
1− x 2
1− x 2
1− x 2
1 − x 2 [1 mark]
−3 −1 1 3

1− x2 1− x2 1− x2 1− x2




4 The
The f isf defined
function
function is defined
by by )f ( x16
f ( x= x 2− x 2
) −16
= ( x ∈ )
OnOn
which of the
which following
of the intervals
following is the
intervals mean
is the value
mean value f the
of fofthe greatest?
greatest?
Tick ()()
Tick oneone
box.
box.
[1 mark][1 mark]

0≤x≤1

0 ≤ 𝑥𝑥𝑥𝑥 𝑥 1
0≤x≤2


0≤x≤3 0 ≤ 𝑥𝑥𝑥𝑥 𝑥 2



0≤x≤4 0 ≤ 𝑥𝑥𝑥𝑥 𝑥 3



0 ≤ 𝑥𝑥𝑥𝑥 𝑥 4
Turn over for the next question




3
7367.2 G4007 QP draft 3
Turn over U


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, 4
Do not write
outside the

5 ( 3 4i )( 5 + ci ) , where c is an integer.
The complex number z =+
box



It is given that Re ( z ) = 7

Find the value of c
[2 marks]

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