AQA Further Mathematics Paper 3m 2025 Question Paper Pdf

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

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## **Paper Overview (page 1)**
- **Duration:** 2 hours
- **Total marks:** 50
- **All questions compulsory**
- Requires:
- AQA formula booklet
- 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): Power & Resistance**
- Uses:
\[
P = Fv
\]
- Requires finding resistance force at max speed

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### **Q2 (page 3): Work Done**
- Area under force–displacement graph
- From **x = 5 to 10**

👉 The **graph on page 3** shows a linear force variation used for area calculation.

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### **Q3 (page 4): Centre of Mass**
- Lamina made of **three identical squares**
- Compare x and y coordinates

👉 The **diagram on page 4** shows the arrangement used to determine symmetry.

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## **Section B: Core Mechanics Problems**

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### **Collisions & Restitution (Q4, page 5)**
- Coefficient of restitution:
\[
e = \frac{\text{speed after}}{\text{speed before}}
\]
- Second scenario uses same surface → same \( e \)

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### **Energy Methods (Q5, pages 6–7)**
- Kinetic energy:
\[
\frac{1}{2}mv^2
\]
- Gravitational potential energy:
\[
mgh
\]
- Minimum speed found using **energy conservation**

- Assumption:
- No air resistance (typical expected answer)

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### **Dimensional Analysis (Q6, page 8)**
- Model:
\[
a = -k m^{\alpha} \rho^{\beta} v^{\gamma}
\]
- Requires matching **dimensions of acceleration**

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### **Moments & Vectors (Q7, page 9)**
- Moment about origin:
\[
\mathbf{r} \times \mathbf{F}
\]
- Result expressed as:
\[
k\sqrt{6}
\]

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### **Circular Motion (Q8, pages 10–11)**
- Conical pendulum:
- Radius = 0.6 m
- Length = 1.2 m

- Uses:
- Vertical: \( T\cos\theta = mg \)
- Horizontal: \( T\sin\theta = \frac{mv^2}{r} \)

- Find:
- Tension (≈ 2.3 N)
- Speed of sphere

👉 The **diagram on page 10** shows the geometry of the conical pendulum.

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### **Momentum & Impulse (Q9, pages 12–13)**
- Conservation of momentum (vector form)
- Impulse:
\[
\mathbf{J} = m(\mathbf{v} - \mathbf{u})
\]

- Force:
\[
\mathbf{F} = \frac{\mathbf{J}}{t}
\]

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### **Centres of Mass (Q10, pages 14–15)**
- Semicircular lamina:
\[
\text{distance} = \frac{4a}{3\pi}
\]

- Suspension:
- Centre of mass vertically below pivot

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### **Elastic Strings & Energy (Q11, pages 16–17)**
- Elastic potential energy:
\[
\frac{\lambda x^2}{2l}
\]

- Motion down rough slope:
- Includes:
- Gravity
- Elastic tension
- Friction

- Requires:
- Maximum speed using energy conservation
- Explanation with air resistance

👉 The **setup on page 16** shows slope angle (30°), string extension, and friction coefficient.

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## **Skills Assessed**

- Energy methods and modelling
- Vector mechanics
- Circular motion
- Collisions and impulse
- Dimensional analysis
- Mathematical reasoning and assumptions

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## **Why This Paper Matters**
- Covers **Mechanics option module**
- Integrates multiple physics-style maths topics
- Essential for **A/A*** in Further Mathematics
- Builds strong foundation for **engineering & physics degrees**

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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 Mechanics option.

It is ideal for exam practice, revision, and mastering applied mathematics concepts.