AQA-7367-1-FURTHER MATHEMATICS QUESTION PAPER 1-A LEVEL-22May24-PM

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AQA
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A-level



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FURTHER MATHEMATICS
Paper 1
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Wednesday 22 May 2024 Afternoon Time allowed: 2 hours
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Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for
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Question Mark
A‑level Mathematics and A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
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requirements of the specification. 2
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Instructions 4
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. 5
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l Answer all questions. 6
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
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of this book. Write the question number against your answer(s).
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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. 10
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l Do all rough work in this book. Cross through any work that you do not want
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to be marked.
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Information 13
l The marks for questions are shown in brackets. 14
l The maximum mark for this paper is 100.
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Advice 16
l Unless stated otherwise, you may quote formulae, without proof, 17
from the booklet. 18
l You do not necessarily need to use all the space provided.
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Answer all questions in the spaces provided.



1 The roots of the equation 20 x 3 – 16 x 2 – 4 x + 7 = 0 are α, β and γ

Find the value of αβ + βγ + γα

Circle your answer.
[1 mark]

–4 –1 1 4




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iπ




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2 The complex number z = e 3

Which one of the following is a real number?
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Circle your answer.
[1 mark]

z4 z5 z6 z7
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3 The function f is defined by
f (x) = x 2 (x ∈ ℝ)

Find the mean value of f (x) between x = 0 and x = 2

Circle your answer.
[1 mark]
2 4 8 16
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4 Which one of the following statements is correct?




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Tick () one box.
[1 mark]




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lim (x 2 ln x) = 0



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x 0




lim (x 2 ln x) = 1
x 0
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lim (x 2 ln x) = 2
x 0
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lim (x 2 ln x) is not defined.
x 0
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Turn over for the next question
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5 The points A, B and C have coordinates A(5, 3, 4), B(8, –1, 9) and C(12, 5, 10)

The points A, B and C lie in the plane ∏


5 (a) Find a vector that is normal to the plane ∏
[3 marks]

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