AQA A-level FURTHER MATHEMATICS Paper 1 QP 2021
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 1
Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for A‑level
Mathematics and A‑level Further Mathematics. Question Mark
l You should have a scientific calculator that meets the requirements of the
specification. (You may use a graphical calculator.) 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.
If you require extra space for your answer(s), use the lined pages at the end 6
of this book. Write the question number against your answer(s). 7
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. 8
l Do all rough work in this book. Cross through any work you do not want to 9
be marked.
10
Information 11
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100. 12
13
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the 14
booklet. 15
l You do not necessarily need to use all the space provided.
TOTAL
(JUN217367101)
PB/Jun21/E6 7367/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Find
X
20
(r 2 2r)
r ¼1
Circle your answer.
[1 mark]
2450 2660 5320 43680
2 Given that z ¼ 1 3i is one root of the equation z 2 þ pz þ r ¼ 0 , where p and r are
real, find the value of r.
Circle your answer.
[1 mark]
8 2 6 10
(02)
Jun21/7367/1
, 3
Do not write
outside the
3 The curve C has polar equation box
r 2 sin 2y ¼ 4
Find a Cartesian equation for C.
Circle your answer.
[1 mark]
x 2
y ¼ 2x y¼ y¼ y ¼ 4x
2 x
Turn over for the next question
Turn over
s
(03)
Jun21/7367/1
, 4
Do not write
outside the
4 Show that the solutions to the equation box
3 tanh2 x 2 sech x ¼ 2
can be expressed in the form
pffiffiffi
x ¼ ln (a þ b)
where a and b are integers to be found.
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
You may use without proof the result cosh1 y ¼ ln ( y þ y 2 1)
[5 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun21/7367/1
Please write clearly in block capitals.
Centre number Candidate number
Surname _________________________________________________________________________
Forename(s) _________________________________________________________________________
Candidate signature _________________________________________________________________________
I declare this is my own work.
A-level
FURTHER MATHEMATICS
Paper 1
Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae and statistical tables booklet for A‑level
Mathematics and A‑level Further Mathematics. Question Mark
l You should have a scientific calculator that meets the requirements of the
specification. (You may use a graphical calculator.) 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.
If you require extra space for your answer(s), use the lined pages at the end 6
of this book. Write the question number against your answer(s). 7
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. 8
l Do all rough work in this book. Cross through any work you do not want to 9
be marked.
10
Information 11
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100. 12
13
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the 14
booklet. 15
l You do not necessarily need to use all the space provided.
TOTAL
(JUN217367101)
PB/Jun21/E6 7367/1
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 Find
X
20
(r 2 2r)
r ¼1
Circle your answer.
[1 mark]
2450 2660 5320 43680
2 Given that z ¼ 1 3i is one root of the equation z 2 þ pz þ r ¼ 0 , where p and r are
real, find the value of r.
Circle your answer.
[1 mark]
8 2 6 10
(02)
Jun21/7367/1
, 3
Do not write
outside the
3 The curve C has polar equation box
r 2 sin 2y ¼ 4
Find a Cartesian equation for C.
Circle your answer.
[1 mark]
x 2
y ¼ 2x y¼ y¼ y ¼ 4x
2 x
Turn over for the next question
Turn over
s
(03)
Jun21/7367/1
, 4
Do not write
outside the
4 Show that the solutions to the equation box
3 tanh2 x 2 sech x ¼ 2
can be expressed in the form
pffiffiffi
x ¼ ln (a þ b)
where a and b are integers to be found.
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
You may use without proof the result cosh1 y ¼ ln ( y þ y 2 1)
[5 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun21/7367/1
