AQA Further Mathematics Paper 3s 2025 Question Paper Pdf

Download the official AQA A-Level Further Mathematics Paper 3 (Statistics) question paper for June 2025 (7367/3S), sat on **Friday 13 June 2025 (afternoon)**. This paper is worth **50 marks over 2 hours** and focuses on advanced statistical techniques and modelling.

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## **Paper Overview (page 1)**

- **Duration:** 2 hours
- **Total marks:** 50
- **All questions compulsory**
- Requires:
- AQA formula booklet
- Statistical tables
- Scientific/graphical calculator

👉 As stated on **page 1**, you must *“show all necessary working; otherwise marks for method may be lost.”*

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## **Section A: Short Questions (Q1–Q3)**

- **Q1 (page 2):** Variance transformation
- **Q2 (page 2):** Mode of a discrete distribution
- **Q3 (page 3):** Hypothesis testing (Type I/II errors)

👉 These are **1-mark conceptual questions** testing core understanding.

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## **Core Topics & Questions**

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### **Continuous Distributions (Q4, pages 4–5)**
- Cumulative distribution function:
\[
F(x) =
\begin{cases}
0 & x < 0 \\
\sin(3x) & 0 \le x \le \frac{\pi}{6} \\
1 & x > \frac{\pi}{6}
\end{cases}
\]

Tasks:
- Probability calculation
- Median proof
- Deriving PDF

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### **Discrete & Continuous Models (Q5, pages 6–7)**
- Discrete uniform + continuous rectangular distributions
- Independence assumption

Key result:
- Show:
\[
\text{Var}(D + R) = \frac{n^2}{12}
\]

- Use expectation to find:
\[
n = 16
\]

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### **Confidence Intervals & Hypothesis Testing (Q6, pages 8–9)**
- Sample data:
- \( \sum x = 1003.2 \)
- \( \sum x^2 = 91747.84 \)

Tasks:
- Construct **90% confidence interval**
- Perform hypothesis test at **10% significance level**

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### **Discrete Probability Modelling (Q7, pages 10–11)**
- Game scoring system:
- Outcomes: 0, 10, 100

Tasks:
- Transform variable \( X \to X^n \)
- Match new mean to **50× original mean**
- Adjust values to multiples of 10

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### **Chi-Squared Test (Q8, page 12)**
- Test for **association (independence)**
- Data:
- 300 villagers
- Coffee shop vs restaurant preference

👉 Requires:
- Contingency table
- Expected frequencies
- χ² test statistic
- Comparison with critical value

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### **Poisson Process & Exponential Distribution (Q9, pages 14–15)**

- Given:
- Mean = 60 messages per 30 minutes

Tasks:
- Show mean inter-arrival time = **0.5 minutes**
- Calculate:
\[
P(X > 130) = 0.169
\]
- Binomial-style extension over 7 hours

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## **Question Structure**

- **Q1–Q3:** 1 mark each
- **Q4–Q6:** Mid-level (2–5 marks)
- **Q7–Q9:** Extended problems (6–8 marks each)

Example:
- Q6: 8 marks (CI + hypothesis test)
- Q8: 8 marks (chi-squared test)
- Q9: 11 marks total (Poisson + modelling)

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## **Skills Assessed**

- Statistical modelling
- Probability distributions
- Hypothesis testing
- Data interpretation
- Mathematical reasoning

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## **Why This Paper Matters**
- Covers the **Statistics option module**
- Tests **real-world data analysis skills**
- Essential for **A/A*** performance
- Useful for **economics, data science, and research fields**

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Fully updated for the 2025/2026 academic year and optimised for instant download on markscheme.net.

This paper is designed for Year 13 students studying AQA A-Level Further Mathematics, particularly those taking the Statistics option.

It is ideal for exam practice, revision, and mastering statistical techniques for high grades.