AS
MATHEMATICS
Paper 2
Time allowed: 1 hour 30 minutes
Materials
l You must have the AQA Formulae for A‑level Mathematics booklet.
l You should have a graphical or scientific calculator that meets the
requirement
...
AS
MATHEMATICS
Paper 2
Time allowed: 1 hour 30 minutes
Materials
l You must have the AQA Formulae for A‑level Mathematics booklet.
l You should have a graphical or scientific calculator that meets the
requirements of the specification.
Instructions
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.
l Answer all questions.
l 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).
l Do not write outside the box around each page or on blank pages.
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
to be marked.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 80.
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the
booklet.
l You do not necessarily need to use all the space provided.
Please write clearly in block capitals.
Centre number Candidate number
Surname ________________________________________________________________________
Forename(s) ________________________________________________________________________
Candidate signature ________________________________________________________________________
For Examiner’s Use
Question Mark
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
TOTAL
I declare this is my own work.
2
Section A
Answer all questions in the spaces provided.
1 Find ð
12x3 dx
Circle your answer.
[1 mark]
36x2 þ c 3x4 þ c 3x2 þ c 36x4 þ c
2 Given that
cos (y 20) ¼ cos 60
which one of the following is a possible value for y?
Circle your answer.
[1 mark]
40 140 280 320
Jun22/7356/2
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(02)
3
3 A curve has equation y ¼ k ffiffiffi
x p where k is a constant.
Find d2y
dx2 at the point (4, 2k) on the curve, giving your answer as an expression in
terms of k.
[5 marks]
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Jun22/7356/2
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(03)
4
4 The equation 9x2 þ 4x þ p2 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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Jun22/7356/2
(04)
5
5 Kaya is investigating the function
f (x) ¼ 2x3 7x2 12x þ 45
Kaya makes two statements.
Statement 1: f (3) ¼ 0
Statement 2: this shows that (x þ 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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Statement 2: ________________________________________________________________________
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5 (b) Fully factorise f (x).
[3 marks]
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(05)
6
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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Jun22/7356/2
(06)
7
7 The expression
3 pn
2 þ pn
can be written in the form a þ b
pn , where a and b and n are rational but pn is
irrational.
Find expressions for a and b in terms of n.
[4 marks]
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(07)
8
8 Triangle ABC has sides of length (m n) , m and (m þ n) 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 (m þ n).
[1 mark]
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8 (a) (ii) Using the cosine rule, show that cosA ¼ m 4n
2(m n)
[3 marks]
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Jun22/7356/2
(08)
9
8 (b) You are given that BC is the diameter of a circle, and A lies on the circumference of
the circle. The value of m is 8
Calculate the value of n.
[3 marks]
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