Please write clearly in block capitals.
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
AS
FURTHER MATHEMATICS
Paper 2 Statistics
Friday 15 May 2026 Afternoon Time allowed: 1 hour 30 minutes
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
1
requirements of the specification.
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
1 hour 30 minutes to complete both papers. 3
Instructions 4
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. 5
l Answer all questions.
l You must answer each question in the space provided for that question. 6
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). 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 that you do not want
to be marked. TOTAL
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 40.
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.
, 2
Do not write
outside the
There are no questions printed on this page box
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
, 3
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The continuous random variable T has probability density function f (t ) given by
5 (16t – 20t 2 + 8t 3 – t 4) 0 ≤ t ≤ 3
f (t ) = 27
0 otherwise
Find E(T )
Circle your answer.
[1 mark]
7 3 15
1
6 2 7
2 The continuous random variable X has variance 5
The discrete random variable Y has a Poisson distribution with mean 4
The random variables X and Y are independent.
Find the standard deviation of X + Y
Circle your answer.
[1 mark]
3 22++ 5 21 9
, 4
Do not write
outside the
3 A hypothesis test is carried out using a Poisson distribution and the following box
hypotheses
H0: λ = 7
H1: λ < 7
The test is carried out using the 5% level of significance.
The observed value for the test is 2
It is given that P(X ≤ 2) = 0.0296 correct to four decimal places, where X ~ Po(7)
State which of the following conclusions to the hypothesis test is correct.
Tick () one box.
[1 mark]
0.0296 > 0.025
Do not reject H0
0.0296 > 0.025
Reject H0
0.0296 < 0.05
Do not reject H0
0.0296 < 0.05
Reject H0
Centre number Candidate number
Surname __________________________________________________________________________
Forename(s) __________________________________________________________________________
Candidate signature __________________________________________________________________________
I declare this is my own work.
AS
FURTHER MATHEMATICS
Paper 2 Statistics
Friday 15 May 2026 Afternoon Time allowed: 1 hour 30 minutes
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
1
requirements of the specification.
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
1 hour 30 minutes to complete both papers. 3
Instructions 4
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. 5
l Answer all questions.
l You must answer each question in the space provided for that question. 6
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). 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 that you do not want
to be marked. TOTAL
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 40.
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.
, 2
Do not write
outside the
There are no questions printed on this page box
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
, 3
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The continuous random variable T has probability density function f (t ) given by
5 (16t – 20t 2 + 8t 3 – t 4) 0 ≤ t ≤ 3
f (t ) = 27
0 otherwise
Find E(T )
Circle your answer.
[1 mark]
7 3 15
1
6 2 7
2 The continuous random variable X has variance 5
The discrete random variable Y has a Poisson distribution with mean 4
The random variables X and Y are independent.
Find the standard deviation of X + Y
Circle your answer.
[1 mark]
3 22++ 5 21 9
, 4
Do not write
outside the
3 A hypothesis test is carried out using a Poisson distribution and the following box
hypotheses
H0: λ = 7
H1: λ < 7
The test is carried out using the 5% level of significance.
The observed value for the test is 2
It is given that P(X ≤ 2) = 0.0296 correct to four decimal places, where X ~ Po(7)
State which of the following conclusions to the hypothesis test is correct.
Tick () one box.
[1 mark]
0.0296 > 0.025
Do not reject H0
0.0296 > 0.025
Reject H0
0.0296 < 0.05
Do not reject H0
0.0296 < 0.05
Reject H0
