Materials You must have the AQA Formulae for A‑ level Mathematics booklet.
You should have a graphical or scientific calculator that meets the
... [Show More] requirements
of the specification.
Instructions Use black ink or black ball‑ point pen. Pencil should only be used
for drawing. Fill in the boxes at the top of this page. Answer all questions.
For Examiner’s Use
Question Mark
1
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10
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16
TOTAL
3
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You must answer each question in the space provided for that question. If you need extra space for
your answer(s), use the lined pages at the end of this book. Write the question number against your
answer(s).
Do not write outside the box around each page or on blank pages. 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 to be marked.
Information The marks for questions are shown in brackets. The maximum mark for this paper is
80.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet. You do not
necessarily need to use all the space provided.
(JUN227356201) PB/Jun22/E6 7356/2
Section A
Answer all questions in the spaces provided.
1
ð
Find 12x
3dx
Circle your answer.
[1 mark]
Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
I declare this is my own work.
4
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36x
2þc 3x
4þc 3x
2þc 36x
4þc
2 Given that
cos (y 20) ¼ cos 60
which one of the following is a p
Circle your answer.
ossible value for y?
[1 mark]
40 140 280 320
(02)
5
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3 pffix where k is a constant.
A curve has equation y¼k d2y
Find at the point (4, 2k) on the curve, giving your answer as an expression in dx2
terms of k.
[5 marks]
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(03)
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4 The equation 9x
2þ 4xþp
2 ¼ 0 has no real solutions for x.
Find the set of possible values of p.
Fully justify your answer.
[4 marks]
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(04)
5
Kaya is investigating the function
f (x) ¼ 2x
3 7x
2 12xþ 45
Kaya makes two statements.
Statement 1: f (3) ¼ 0
Statement 2: this shows that (xþ 3) must be a factor of f (x).
5 (a) State, with a reason, whether each of Kaya’s statements is correct.
[2 marks]
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5 (b)
Fully factorise f (x).
[3 marks]
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(05)
6
An on-line science website states:
‘To find a dog’s equivalent human age in years, multiply the natural logarithm of the dog’s age
in years by 16 then add 31.’
6 (a) Calculate the equivalent age to the nearest human year of a dog aged 5 years.
[1 mark]
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6 (b)
A dog’s equivalent age in human years is 40 years. Find the dog’s actual age to the nearest
month.
[3 marks]
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6 (c)
Explain why the behaviour of the natural logarithm for values close to zero means that the
formula given on the website cannot be true for very young dogs.
[2 marks]
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(06)
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7 The expression
p
3 n p
2 þ n
p p
can be written in the form aþb n , where a and b and n are rational but n is irrational.
Find expressions for a and b in terms of n.
[4 marks]
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(07)
8
Triangle ABC has sides of length (mn) , m and (mþn) where 0 < 2n < m
Angle A is the largest angle in the triangle.
8 (a) (i) Explain why angle A must be opposite the side of length (mþn).
[1 mark]
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8 (a) (ii) m 4n
Using the cosine rule, show that cos A¼
2(mn)... [Show Less]