AQA QP 2023 AS MATHEMATICS Paper 2
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
AS
MATHEMATICS
Paper 2
Time allowed: 1 hour 30 minutes
Materials For Examiner’s Use
l You must have the AQA Formulae for A‑level Mathematics booklet.
Question Mark
l You should have a graphical or scientific calculator that meets the
requirements of the specification. 1
2
Instructions 3
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. 4
l Answer all questions. 5
l You must answer each question in the space provided for that question. 6
l If you need extra space for your answer(s), use the lined pages at the end of 7
this book. Write the question number against your answer(s). 8
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. 9
l Do all rough work in this book. Cross through any work that you do not want 10
to be marked. 11
12
Information 13
l The marks for questions are shown in brackets.
14
l The maximum mark for this paper is 80.
15
Advice 16
l Unless stated otherwise, you may quote formulae, without proof, from the 17
booklet. 18
l You do not necessarily need to use all the space provided. 19
TOTAL
PB/KL/Jun23/E4 7356/2
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 Simplify log2 8a
Circle your answer.
[1 mark]
a3 2a 3a 8a
4
2 It is given that sin y ¼ and 90 < y < 180
5
Find the value of cos y
Circle your answer.
[1 mark]
3 3 3 3
4 5 5 4
(02)
Jun23/7356/2
, 3
Do not write
ð outside the
3 8 box
3 (a) Find 2x þ 2 d x
x [3 marks]
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
dy 8
3 (b) A curve has gradient function ¼ 2x3 þ 2
dx x
The x-intercept of the curve is at the point (2, 0)
Find the equation of the curve.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
Turn over
s
(03)
Jun23/7356/2
, 4
Do not write
outside the
4 Find the exact solution of the equation ln (x þ 1) þ ln (x 1) ¼ ln 15 2 ln 7 box
Fully justify your answer.
[5 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun23/7356/2
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
AS
MATHEMATICS
Paper 2
Time allowed: 1 hour 30 minutes
Materials For Examiner’s Use
l You must have the AQA Formulae for A‑level Mathematics booklet.
Question Mark
l You should have a graphical or scientific calculator that meets the
requirements of the specification. 1
2
Instructions 3
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. 4
l Answer all questions. 5
l You must answer each question in the space provided for that question. 6
l If you need extra space for your answer(s), use the lined pages at the end of 7
this book. Write the question number against your answer(s). 8
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. 9
l Do all rough work in this book. Cross through any work that you do not want 10
to be marked. 11
12
Information 13
l The marks for questions are shown in brackets.
14
l The maximum mark for this paper is 80.
15
Advice 16
l Unless stated otherwise, you may quote formulae, without proof, from the 17
booklet. 18
l You do not necessarily need to use all the space provided. 19
TOTAL
PB/KL/Jun23/E4 7356/2
, 2
Do not write
outside the
Section A box
Answer all questions in the spaces provided.
1 Simplify log2 8a
Circle your answer.
[1 mark]
a3 2a 3a 8a
4
2 It is given that sin y ¼ and 90 < y < 180
5
Find the value of cos y
Circle your answer.
[1 mark]
3 3 3 3
4 5 5 4
(02)
Jun23/7356/2
, 3
Do not write
ð outside the
3 8 box
3 (a) Find 2x þ 2 d x
x [3 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
dy 8
3 (b) A curve has gradient function ¼ 2x3 þ 2
dx x
The x-intercept of the curve is at the point (2, 0)
Find the equation of the curve.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
Turn over
s
(03)
Jun23/7356/2
, 4
Do not write
outside the
4 Find the exact solution of the equation ln (x þ 1) þ ln (x 1) ¼ ln 15 2 ln 7 box
Fully justify your answer.
[5 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun23/7356/2
