Question paper: Paper 1 - June 2019 - AQA
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Surname
_________________________________________________________________________
Forename(s)
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A-level MATHEMATICS
Paper 1
Wednesday 5 June 2019
Morning
Time allowed: 2 hours
Materials l You must have the AQA Formulae for Alevel 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 require extra space, use an AQA supplementary answer book; do not use the space provided for a different question. 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.
For Examiner's Use
Question
Mark
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
TOTAL
(JUN197357101)
PB/Jun19/E4
7357/1
2 Answer all questions in the spaces provided.
Do not write outside the
box
1
Given that a > 0 , determine which of these expressions is not equivalent to the
others.
Circle your answer. 1
?2 log10 a
2 log10 (a)
log10 (a2)
[1 mark] pffiffiffi
?4 log10 ( a)
2
Given y ? ekx , where k is a constant, find dy
dx
Circle your answer.
[1 mark]
dy ? ekx dx
dy ? kekx dx
dy ? kxekx?1 dx
d d
y x
?
e kx k
3
The diagram below shows a sector of a circle.
The radius of the circle is 4 cm and y ? 0:8 radians.
Find the area of the sector. Circle your answer.
1.28 cm2
3.2 cm2
6.4 cm2
[1 mark] 12.8 cm2
(02)
Jun19/7357/1
3
4
The point A has coordinates (?1, a) and the point B has coordinates (3, b)
Do not write outside the
box
The line AB has equation 5x ? 4y ? 17
Find the equation of the perpendicular bisector of the points A and B.
[4 marks]
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(03)
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5 5 (a)
4 An arithmetic sequence has first term a and common difference d.
Do not write outside the
box
The sum of the first 16 terms of the sequence is 260
Show that 4a ? 30d ? 65
[2 marks]
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5 (b)
Given that the sum of the first 60 terms is 315, find the sum of the first 41 terms. [3 marks]
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(04)
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5 (c)
5
Sn is the sum of the first n terms of the sequence. Explain why the value you found in part (b) is the maximum value of Sn
Do not write outside the
box
[2 marks]
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(05)
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6 6 (a)
6
The function f is defined by
f
(x)
?
1 2
(x 2
?
1),
x
!
0
Find the range of f .
Do not write outside the
box
[1 mark]
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6 (b) (i) Find f ?1(x)
[3 marks]
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6 (b) (ii) State the range of f ?1(x)
[1 mark]
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(06)
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6 (c)
7
State the transformation which maps the graph of y ? f (x) onto the graph of y ? f ?1(x)
[1 mark]
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box
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6 (d)
Find the coordinates of the point of intersection of the graphs of y ? f (x) and y ? f ?1(x)
[2 marks]
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(07)
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7 (a)
8
By
sketching
the
graphs
of
y
?
1
x
and
y
?
sec 2x
on
the
axes
below,
show
that
the
equation
Do not write outside the
box
1
x
?
sec
2x
has exactly one solution for x > 0
y
[3 marks]
O
2
x
7 (b)
By considering a suitable change of sign, show that the solution to the equation lies between 0.4 and 0.6
[2 marks]
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7 (c)
Show that the equation can be rearranged to give
x ? 1 cos?1 x
2
[2 marks]
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(08)
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