A-level
MATHEMATICS
Paper 1
Time allowed: 2 hours
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
...
A-level
MATHEMATICS
Paper 1
Time allowed: 2 hours
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 100.
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
TOTAL
I declare this is my own work.
2
Answer all questions in the spaces provided.
1 A curve is defined by the parametric equations
x ¼ cos y and y ¼ sin y where 0 y 2p
Which of the options shown below is a Cartesian equation for this curve?
Circle your answer.
[1 mark]
y
x ¼ tan y x2 þ y2 ¼ 1 x2 y2 ¼ 1 x2y2 ¼ 1
2 A periodic sequence is defined by
Un ¼ (1)n
State the period of the sequence.
Circle your answer.
[1 mark]
10 1 2
3 The curve
y ¼ log4 x
is transformed by a stretch, scale factor 2, parallel to the y-axis.
State the equation of the curve after it has been transformed.
Circle your answer.
[1 mark]
y ¼ 1
2 log4 x y ¼ 2 log4 x y ¼ log4 2x y ¼ log8 x
Jun22/7357/1
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(02)
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
3
Turn over for the next question
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box
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Turn over s
(03)
4
4 The graph of
y ¼ f (x)
where
f (x) ¼ ax2 þ bx þ c
is shown in Figure 1.
Figure 1
x
y
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outside the
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(04)
5
Which of the following shows the graph of y ¼ f0
(x) ?
Tick (3) one box.
[1 mark]
x
y
x
y
x
y
x
y
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outside the
box
Jun22/7357/1
Turn over s
(05)
6
5 Find an equation of the tangent to the curve
y ¼ (x 2)4
at the point where x ¼ 0
[3 marks]
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(06)
7
6 (a) Find the first two terms, in ascending powers of x, of the binomial expansion of
1 x
2
1
2
[2 marks]
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6 (b) Hence, for small values of x, show that
sin 4x þ ffiffiffiffiffiffiffiffiffiffiffi
cos x p A þ Bx þ Cx2
where A, B and C are constants to be found.
[4 marks]
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Jun22/7357/1
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(07)
8
7 Sketch the graph of
y ¼ cot
x p
2
for 0 x 2p
[3 marks]
x
y
O 2
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Jun22/7357/1
(08)
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
9
Turn over for the next question
Do not write
outside the
box
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(09)
10
8 The lines L1 and L2 are parallel.
L1 has equation
5x þ 3y ¼ 15
and L2 has equation
5x þ 3y ¼ 83
L1 intersects the y-axis at the point P.
The point Q is the point on L2 closest to P, as shown in the diagram.
x
y
L2
Q
P
L1
8 (a) (i) Find the coordinates of Q.
[5 marks]
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