AQA_2024: AS Further Mathematics - Paper 2
Statistics.
(Merged Question Paper and Marking Scheme)
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 17 May 2024 Afternoon Time allowed: 1 hour 30 minutes
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
requirements of the specification. 1
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
Use black ink or black ball-point pen. Pencil should only be used for drawing.
Fill in the boxes at the top of this page.
5
Answer all questions.
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
Do not write outside the box around each page or on blank pages.
Show all necessary working; otherwise marks for method may be lost. TOTAL
Do all rough work in this book. Cross through any work that you do not want
to be marked.
Information
The marks for questions are shown in brackets.
The maximum mark for this paper is 40.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet.
You do not necessarily need to use all the space provided.
,For AS Further Mathematics - Paper 2: Statistics, focus on these key areas:
1. Probability:
Basic Probability Rules: Understand fundamental probability concepts such as conditional
probability, independent events, and mutually exclusive events.
Probability Distributions: Learn about common probability distributions, including the binomial
distribution and normal distribution.
Expected Value: Calculate the expected value and variance for both discrete and continuous
random variables.
2. Discrete Random Variables:
Binomial Distribution: Know the properties of the binomial distribution (e.g., mean, variance) and
how to apply the binomial probability formula to calculate probabilities and solve problems.
Geometric Distribution: Understand the geometric distribution, its mean, and variance, and how to
solve related problems.
3. Continuous Random Variables:
Normal Distribution: Understand the properties of the normal distribution, including the mean,
variance, and standard deviation. Be able to solve problems involving the normal distribution using
Z-scores.
Applications of the Normal Distribution: Apply the normal distribution in various contexts (e.g.,
finding probabilities, confidence intervals).
4. Sampling and Estimation:
Sampling Techniques: Learn about different sampling methods such as simple random sampling,
stratified sampling, and systematic sampling.
Sampling Distribution: Understand the concept of sampling distribution and the central limit
theorem.
Point Estimation: Be able to estimate population parameters (e.g., mean, variance) from sample data.
5. Hypothesis Testing:
Null and Alternative Hypotheses: Understand the process of hypothesis testing, including setting up
null and alternative hypotheses, and determining the critical region.
Significance Levels: Know how to use significance levels (e.g., 5%, 1%) and understand type I and
type II errors.
t-tests and chi-squared tests: Be familiar with applying t-tests for means and chi-squared tests for
goodness of fit and independence.
6. Correlation and Regression:
Scatter Diagrams and Correlation: Understand how to interpret scatter diagrams and calculate the
correlation coefficient to measure the strength of a linear relationship.
Linear Regression: Be able to find the equation of the line of best fit using least squares
regression and make predictions.
7. Combinations and Permutations:
Combinations and Permutations: Learn how to calculate permutations and combinations and
understand their applications in probability and statistics.
G/LM/Jun24/G4001/V6 7366/2S
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The discrete random variable X has probability distribution function
{
0.45 x=1
0.25 x=2
P(X = x) = 0.25 x=3
0.05 x=4
0 otherwise
State the mode of X
Circle your answer.
[1 mark]
0.25 0.45 1 2.5
2 A test for association is to be carried out.
The tables below show the observed frequencies and the expected frequencies that
are to be used for the test.
Observed X Y Z Expected X Y Z
A 28 6 66 A 45 15 40
B 8 8 4 B 9 3 8
C 54 16 10 C 36 12 32
It is necessary to merge some rows or columns before the test can be carried out.
Find the entry in the tables that provides evidence for this.
Circle your answer.
[1 mark]
Observed A-Z Observed B-Z Expected A-X Expected B-Y
G/Jun24/7366/2S
, 3
Do not write
outside the
box
3 The random variable X has a normal distribution with known variance 15.7
A random sample of size 120 is taken from X
The sample mean is 68.2
Find a 94% confidence interval for the population mean of X
Give your limits to three significant figures.
[3 marks]
Turn over for the next question
Turn over ▶
G/Jun24/7366/2S
Statistics.
(Merged Question Paper and Marking Scheme)
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 17 May 2024 Afternoon Time allowed: 1 hour 30 minutes
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
requirements of the specification. 1
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
Use black ink or black ball-point pen. Pencil should only be used for drawing.
Fill in the boxes at the top of this page.
5
Answer all questions.
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
Do not write outside the box around each page or on blank pages.
Show all necessary working; otherwise marks for method may be lost. TOTAL
Do all rough work in this book. Cross through any work that you do not want
to be marked.
Information
The marks for questions are shown in brackets.
The maximum mark for this paper is 40.
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet.
You do not necessarily need to use all the space provided.
,For AS Further Mathematics - Paper 2: Statistics, focus on these key areas:
1. Probability:
Basic Probability Rules: Understand fundamental probability concepts such as conditional
probability, independent events, and mutually exclusive events.
Probability Distributions: Learn about common probability distributions, including the binomial
distribution and normal distribution.
Expected Value: Calculate the expected value and variance for both discrete and continuous
random variables.
2. Discrete Random Variables:
Binomial Distribution: Know the properties of the binomial distribution (e.g., mean, variance) and
how to apply the binomial probability formula to calculate probabilities and solve problems.
Geometric Distribution: Understand the geometric distribution, its mean, and variance, and how to
solve related problems.
3. Continuous Random Variables:
Normal Distribution: Understand the properties of the normal distribution, including the mean,
variance, and standard deviation. Be able to solve problems involving the normal distribution using
Z-scores.
Applications of the Normal Distribution: Apply the normal distribution in various contexts (e.g.,
finding probabilities, confidence intervals).
4. Sampling and Estimation:
Sampling Techniques: Learn about different sampling methods such as simple random sampling,
stratified sampling, and systematic sampling.
Sampling Distribution: Understand the concept of sampling distribution and the central limit
theorem.
Point Estimation: Be able to estimate population parameters (e.g., mean, variance) from sample data.
5. Hypothesis Testing:
Null and Alternative Hypotheses: Understand the process of hypothesis testing, including setting up
null and alternative hypotheses, and determining the critical region.
Significance Levels: Know how to use significance levels (e.g., 5%, 1%) and understand type I and
type II errors.
t-tests and chi-squared tests: Be familiar with applying t-tests for means and chi-squared tests for
goodness of fit and independence.
6. Correlation and Regression:
Scatter Diagrams and Correlation: Understand how to interpret scatter diagrams and calculate the
correlation coefficient to measure the strength of a linear relationship.
Linear Regression: Be able to find the equation of the line of best fit using least squares
regression and make predictions.
7. Combinations and Permutations:
Combinations and Permutations: Learn how to calculate permutations and combinations and
understand their applications in probability and statistics.
G/LM/Jun24/G4001/V6 7366/2S
, 2
Do not write
outside the
box
Answer all questions in the spaces provided.
1 The discrete random variable X has probability distribution function
{
0.45 x=1
0.25 x=2
P(X = x) = 0.25 x=3
0.05 x=4
0 otherwise
State the mode of X
Circle your answer.
[1 mark]
0.25 0.45 1 2.5
2 A test for association is to be carried out.
The tables below show the observed frequencies and the expected frequencies that
are to be used for the test.
Observed X Y Z Expected X Y Z
A 28 6 66 A 45 15 40
B 8 8 4 B 9 3 8
C 54 16 10 C 36 12 32
It is necessary to merge some rows or columns before the test can be carried out.
Find the entry in the tables that provides evidence for this.
Circle your answer.
[1 mark]
Observed A-Z Observed B-Z Expected A-X Expected B-Y
G/Jun24/7366/2S
, 3
Do not write
outside the
box
3 The random variable X has a normal distribution with known variance 15.7
A random sample of size 120 is taken from X
The sample mean is 68.2
Find a 94% confidence interval for the population mean of X
Give your limits to three significant figures.
[3 marks]
Turn over for the next question
Turn over ▶
G/Jun24/7366/2S
