AQA_2024: AS Further Mathematics - Paper 2 Statistics. (Merged Question Paper and Marking Scheme)

AQA_2024: AS Further Mathematics - Paper 2
Statistics.
(Merged Question Paper and Marking Scheme)



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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