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
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 graphical or scientific calculator that meets the
requirements of the specification. 1
l 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
l Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
l Fill in the boxes at the top of this page.
6
l Answer all questions.
l 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
l Do not write outside the box around each page or on blank pages. 9
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 TOTAL
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.
(JUN2573673S01)
G/LM/Jun25/G4007/V6 7367/3S
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
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
(02)
G/Jun25/7367/3S
, 3
Do not write
outside the
3 Cosmo is carrying out a hypothesis test. box
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
(03)
G/Jun25/7367/3S
, 4
Do not write
outside the
4 The continuous random variable X has cumulative distribution function box
{
0 x<0
π
F (x) = sin 3 x0 ≤ 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]
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
(04)
G/Jun25/7367/3S
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
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 graphical or scientific calculator that meets the
requirements of the specification. 1
l 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
l Use black ink or black ball‑point pen. Pencil should only be used for drawing. 5
l Fill in the boxes at the top of this page.
6
l Answer all questions.
l 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
l Do not write outside the box around each page or on blank pages. 9
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 TOTAL
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.
(JUN2573673S01)
G/LM/Jun25/G4007/V6 7367/3S
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
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
(02)
G/Jun25/7367/3S
, 3
Do not write
outside the
3 Cosmo is carrying out a hypothesis test. box
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
(03)
G/Jun25/7367/3S
, 4
Do not write
outside the
4 The continuous random variable X has cumulative distribution function box
{
0 x<0
π
F (x) = sin 3 x0 ≤ 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]
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
(04)
G/Jun25/7367/3S
