AQA Further Mathematics Paper 3m 2025 Mark Scheme Pdf

Download the official AQA A-Level Further Mathematics Paper 3 (Mechanics) mark scheme for June 2025 (7367/3M). This **final version (v1.0)** includes full worked solutions, mark allocations (M, A, B, R, E), and examiner guidance used during standardisation.

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## **Mark Scheme Overview (pages 2–4)**

The mark scheme explains how examiners award marks:

- **M (Method):** Correct approach
- **A (Accuracy):** Correct answer
- **B (Independent):** Standalone result
- **R (Reasoning):** Justification
- **E (Explanation):** Clear explanation

👉 As stated on **page 3**, examiners:
- Credit **valid alternative methods**
- Apply a **best-fit approach**
- Allow correct answers without working (where appropriate)

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## **Section A: Multiple Choice Answers (Q1–Q3)** *(page 6)*

- **Q1:** **1250 N**
- **Q2:** **30 J**
- **Q3:** **x > y**

👉 The **table on page 6** confirms correct options and marking (B1 each).

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## **Key Worked Answers & Methods**

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### **Restitution (Q4, page 6)**
- **Q4(a):**
\[
e = 0.625 = \frac{5}{8}
\]

- **Q4(b):**
\[
u = 11.2\ \text{m s}^{-1}
\]

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### **Energy Methods (Q5, page 7)**

- Initial KE:
\[
64\ \text{J}
\]

- Max GPE:
\[
29.4\ \text{J}
\]

- Minimum speed:
\[
11.8\ \text{m s}^{-1}
\]

- Key assumption:
- **No air resistance**

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### **Dimensional Analysis (Q6, page 8)**

- Final values:
\[
\alpha = -\frac{1}{3}, \quad \beta = \frac{1}{3}, \quad \gamma = 2
\]

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### **Moments & Vectors (Q7, page 8)**

- Vector product leads to:
\[
|\mathbf{r} \times \mathbf{F}| = 11\sqrt{6}
\]

- Therefore:
\[
k = 11
\]

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### **Circular Motion (Q8, page 9)**

- Tension:
\[
T \approx 2.3\ \text{N}
\]

- Speed:
\[
v \approx 1.8\ \text{m s}^{-1}
\]

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### **Momentum & Impulse (Q9, page 10)**

- Velocity of B:
\[
\begin{bmatrix}
0.6 \\
-2
\end{bmatrix}
\]

- Impulse magnitude:
\[
3.3\ \text{N s}
\]

- Force:
\[
\begin{bmatrix}
31.2 \\
12
\end{bmatrix} \text{N}
\]

---

### **Centres of Mass (Q10, page 11)**

- Distance of COM:
\[
\frac{4a}{3\pi}
\]

- Angle:
\[
23^\circ
\]

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### **Elastic Strings & Energy (Q11, page 12)**

- Elastic potential energy:
\[
96\ \text{J}
\]

- Maximum speed:
\[
8.6\ \text{m s}^{-1}
\]

- Effect of air resistance:
- Adds opposing force →
- **Maximum speed reached sooner → shorter distance travelled**

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## **Assessment Objectives (page 5)**

- **AO1:** Methods & accuracy
- **AO2:** Reasoning & proof
- **AO3:** Modelling & interpretation

👉 The **table on page 5** outlines how skills like modelling, reasoning, and interpretation are assessed.

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## **Why This Mark Scheme Matters**
- Shows **exact final answers + working steps**
- Reveals **method marks (crucial for partial credit)**
- Helps you understand **examiner expectations**
- Essential for mastering **Mechanics Paper 3**

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

This mark scheme is designed for Year 13 students studying AQA A-Level Further Mathematics, particularly the Mechanics option.

It is ideal for revision, checking answers, and improving exam technique for top grades.