AQA A Level Further Mathematics Paper 1 2025 Question Pdf

Download the official AQA A-Level Further Mathematics Paper 1 question paper for the May 2025 exam (7367/1), sat on **Thursday 22 May 2025 (afternoon)**. This paper is worth **100 marks over 2 hours** and assesses core pure mathematics topics.

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

- **Exam duration:** 2 hours
- **Total marks:** 100
- **All questions compulsory**
- Requires:
- AQA formula booklet
- Scientific/graphical calculator

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## **Key Topics Covered**

This paper tests a wide range of Further Maths concepts:

### **Complex Numbers & Argand Diagrams**
- Reflection in imaginary axis (Q2, page 2)
- Arguments and division of complex numbers (Q5, page 4)
- Polynomial roots and conjugates (Q13, pages 16–17)

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### **Calculus & Series**
- Simpson’s Rule approximation (Q6, page 5)
- Maclaurin expansions (Q11, pages 12–13)
- L’Hôpital’s rule (Q3, page 3)

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### **Algebra & Proof**
- Inequalities and discriminants (Q1, page 2)
- Proof by induction (Q10, pages 10–11)
- Transforming roots of equations (Q7, page 6)

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### **Vectors & Geometry**
- Vector magnitudes using dot & cross products (Q9, page 9)
- Planes and lines of intersection (Q15, pages 20–21)
- Matrix transformations & eigenvalues (Q12, pages 14–15)

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### **Hyperbolic Functions**
- Identities and proofs (Q14, page 18)
- Inequalities and integration with sinh/cosh (Q18, pages 28–30)

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### **Differential Equations & Modelling**
- Damped motion with resistance (Q17, pages 24–26)
- Second-order differential equations
- Real-world modelling (particle in oil system)

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### **Advanced Integration & Geometry**
- Surface area of revolution (Q16, page 22)
- Area between curves (Q18c, page 30 diagram)

👉 The **diagram on page 30** shows a shaded region bounded by
- \( y = 4\sinh x + \frac{1}{2} \)
- \( y = 15 \cosech x \)
- the axes and \( x = \ln 9 \),
which is used for a **7-mark integration problem**.

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## **Question Structure**

- **Short MC-style questions (1–4):** 1 mark each
- **Mid questions (3–5 marks):** Skills + working
- **Long questions (6–7 marks):** Extended reasoning, proofs, modelling

Example:
- Q16 (7 marks): Surface area via integration
- Q17 (11 marks total): Differential equation + solution
- Q18 (15 marks total): Inequality, differentiation, area

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## **Skills Assessed**

- Algebraic manipulation & proof
- Advanced calculus techniques
- Mathematical modelling
- Problem-solving under exam conditions
- Clear logical working (method marks emphasized)

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## **Why This Paper Matters**
- Core **Further Maths Paper 1** (pure content)
- Builds skills needed for **STEP / university maths**
- Essential for achieving **top A-Level grades (A/A*)**

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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 focusing on pure mathematics.

It is ideal for exam practice, mock testing, and mastering advanced mathematical techniques required for top grades and university preparation.