2025 AQA A-LEVEL FURTHER MATHEMATICS Paper 3
Statistics Question Paper & Mark Scheme (Merged) Friday 13
June 2025 [VERIFIED]
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 3 Statistics
Friday 13 June 2025 Afternoon Time allowed: 2 hours
Materials
For Examiner’s Use
You must have the AQA Formulae and statistical tables booklet for
A‑ level Mathematics and A‑ level Further Mathematics. Question Mark
You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
You must ensure you have the other optional Question Paper/Answer Book 2
for which you are entered (either Discrete or Mechanics). You will have
2 hours to complete both papers. 3
4
Instructions
Use black ink or black ball‑ point pen. Pencil should only be used for drawing. 5
Fill in the boxes at the top of this page.
6
Answer all questions.
You must answer each question in the space provided for that question. 7
If you require extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s). 8
Do not write outside the box around each page or on blank pages. 9
Show all necessary working; otherwise marks for method may be lost.
Do all rough work in this book. Cross through any work that you do not want TOTAL
to be marked.
Information
The marks for questions are shown in brackets.
The maximum mark for this paper is 50.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet.
You do not necessarily need to use all the space provided.
G/LM/Jun25/G4007/V6 7367/3S
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The continuous random variable X has standard deviation 16
Find Var(5X – 12)
Circle your answer.
[1 mark]
80 400 6388 6400
2 The discrete random variable Y has probability distribution
y –6 2 3 18
P(Y = y) 0.56 0.02 0.21 0.21
Find the mode of Y
Circle your answer.
[1 mark]
–6 0.21 0.56 18
G/Jun25/7367/3S
, 3
Do not write
outside the
box
3 Cosmo is carrying out a hypothesis test.
He rejects the null hypothesis.
State which of the following statements is correct.
Tick () one box.
[1 mark]
He could have made a Type I error but not a Type II error.
He could have made a Type II error but not a Type I error.
He could have made both a Type I error and a Type II error.
He has made neither a Type I nor a Type II error.
Turn over for the next question
Turn over U
G/Jun25/7367/3S
, 4
4
{
The continuous random variable X has cumulative distribution function
0
sin 3x
x<0
0x
π
Do not write
outside the
box
F(x) = 6
π
1 x
6
4 (a) Find P(0.1 < X < 0.3)
Give your answer to three decimal places.
[2 marks]
4 (b) Show that the median of X is equal to
π
18
[2 marks]
G/Jun25/7367/3S
Statistics Question Paper & Mark Scheme (Merged) Friday 13
June 2025 [VERIFIED]
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 3 Statistics
Friday 13 June 2025 Afternoon Time allowed: 2 hours
Materials
For Examiner’s Use
You must have the AQA Formulae and statistical tables booklet for
A‑ level Mathematics and A‑ level Further Mathematics. Question Mark
You should have a graphical or scientific calculator that meets the
1
requirements of the specification.
You must ensure you have the other optional Question Paper/Answer Book 2
for which you are entered (either Discrete or Mechanics). You will have
2 hours to complete both papers. 3
4
Instructions
Use black ink or black ball‑ point pen. Pencil should only be used for drawing. 5
Fill in the boxes at the top of this page.
6
Answer all questions.
You must answer each question in the space provided for that question. 7
If you require extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s). 8
Do not write outside the box around each page or on blank pages. 9
Show all necessary working; otherwise marks for method may be lost.
Do all rough work in this book. Cross through any work that you do not want TOTAL
to be marked.
Information
The marks for questions are shown in brackets.
The maximum mark for this paper is 50.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet.
You do not necessarily need to use all the space provided.
G/LM/Jun25/G4007/V6 7367/3S
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The continuous random variable X has standard deviation 16
Find Var(5X – 12)
Circle your answer.
[1 mark]
80 400 6388 6400
2 The discrete random variable Y has probability distribution
y –6 2 3 18
P(Y = y) 0.56 0.02 0.21 0.21
Find the mode of Y
Circle your answer.
[1 mark]
–6 0.21 0.56 18
G/Jun25/7367/3S
, 3
Do not write
outside the
box
3 Cosmo is carrying out a hypothesis test.
He rejects the null hypothesis.
State which of the following statements is correct.
Tick () one box.
[1 mark]
He could have made a Type I error but not a Type II error.
He could have made a Type II error but not a Type I error.
He could have made both a Type I error and a Type II error.
He has made neither a Type I nor a Type II error.
Turn over for the next question
Turn over U
G/Jun25/7367/3S
, 4
4
{
The continuous random variable X has cumulative distribution function
0
sin 3x
x<0
0x
π
Do not write
outside the
box
F(x) = 6
π
1 x
6
4 (a) Find P(0.1 < X < 0.3)
Give your answer to three decimal places.
[2 marks]
4 (b) Show that the median of X is equal to
π
18
[2 marks]
G/Jun25/7367/3S
