AQA A-LEVEL FURTHER MATHEMATICS 7367/3S PAPER 3
FINAL EXAM QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED)
A-level
FURTHER MATHEMATICS
Paper 3 Statistics
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. 1
l You must ensure you have the other optional Question 2
Paper/Answer Book for which you are entered (either Discrete or
Mechanics). You will have 2 hours to complete both papers. 3
Instructions 4
l Use black ink or black ball-point pen. Pencil should only be used for 5
drawing.
l Fill in the boxes at the top of this page. 6
l Answer all questions. 7
l You must answer each question in the space provided for that
question. 8
If you require extra space for your answer(s), use the lined pages at 9
the end of this book. Write the question number against your
answer(s). TOTAL
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 50.
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.
(JUN2273673S01) 7367/3S
PB/Jun22/E5
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The random variable T follows a discrete uniform distribution and can take values
1, 2, 3, …, 16
Find the variance of T
Circle your answer.
[1 mark]
1.25 18.75 21.25 21.33
2 The random variable X has probability density function
>1 8
>
0<x 1
2
f (x) ¼ >8 x<
>3 2
2
1
<x 2 3
>
>
>
:
>0 otherwise
Find P(X < 1)
Circle your answer.
[1 mark]
1 3 5 7
8 8 8 8
(02)
Jun22/7367/3S
, 3
Do not write
outside the
Turn over for the next question box
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
Turn over
s
(03)
Jun22/7367/3S
, 4
Do not write
outside the
3 The random variable X has an exponential distribution with probability density function box
lx
f (x) ¼ le where x 0
lx
3 (a) Show that the cumulative distribution function, for x 0 , is given by F (x) ¼ 1 e
[3 marks]
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
3 (b) Given that l ¼ 2 , find P(X > 1), giving your answer to three decimal places.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun22/7367/3S
FINAL EXAM QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED)
A-level
FURTHER MATHEMATICS
Paper 3 Statistics
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. 1
l You must ensure you have the other optional Question 2
Paper/Answer Book for which you are entered (either Discrete or
Mechanics). You will have 2 hours to complete both papers. 3
Instructions 4
l Use black ink or black ball-point pen. Pencil should only be used for 5
drawing.
l Fill in the boxes at the top of this page. 6
l Answer all questions. 7
l You must answer each question in the space provided for that
question. 8
If you require extra space for your answer(s), use the lined pages at 9
the end of this book. Write the question number against your
answer(s). TOTAL
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 50.
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.
(JUN2273673S01) 7367/3S
PB/Jun22/E5
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The random variable T follows a discrete uniform distribution and can take values
1, 2, 3, …, 16
Find the variance of T
Circle your answer.
[1 mark]
1.25 18.75 21.25 21.33
2 The random variable X has probability density function
>1 8
>
0<x 1
2
f (x) ¼ >8 x<
>3 2
2
1
<x 2 3
>
>
>
:
>0 otherwise
Find P(X < 1)
Circle your answer.
[1 mark]
1 3 5 7
8 8 8 8
(02)
Jun22/7367/3S
, 3
Do not write
outside the
Turn over for the next question box
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
Turn over
s
(03)
Jun22/7367/3S
, 4
Do not write
outside the
3 The random variable X has an exponential distribution with probability density function box
lx
f (x) ¼ le where x 0
lx
3 (a) Show that the cumulative distribution function, for x 0 , is given by F (x) ¼ 1 e
[3 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
3 (b) Given that l ¼ 2 , find P(X > 1), giving your answer to three decimal places.
[2 marks]
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(04)
Jun22/7367/3S
