| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Resultant of three coplanar forces |
| Difficulty | Moderate -0.8 This is a straightforward M1 vector addition problem requiring resolution of two forces into components and finding the resultant magnitude using Pythagoras. It's a standard textbook exercise with clear setup and routine calculation, making it easier than average but not trivial due to the bearing conversion and component work required. |
| Spec | 1.10g Problem solving with vectors: in geometry |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Correct triangle with sides 8, 10 and angle \(120°\) | M1 | Correct triangle with lengths and angle (arrows not needed), seen or implied |
| \((F^2) = 8^2 + 10^2 - 2 \times 8 \times 10\cos\theta\) where \(\theta < 180°\) | M1 | Use of cosine rule with correct structure but any angle \(< 180°\) |
| \((F^2) = 8^2 + 10^2 - 2 \times 8 \times 10\cos120°\) | A1 | Correct expression with or without root |
| \(F = \sqrt{244} = 2\sqrt{61}\) or 16 (N) or better (15.620499..) | A1 (4) | cao |
| Answer | Marks | Guidance |
|---|---|---|
| \(\pm(10 + 8\cos60°)\) and \(\pm8\sin60°\) | M1 | Two correct components |
| Use of Pythagoras on their combined components | M1 | Use of Pythagoras using combined i and j components |
| \(F^2 = (10 + 8\cos60°)^2 + (8\sin60°)^2\) | A1 | Correct expression with or without root |
| \(F = \sqrt{244} = 2\sqrt{61}\) or 16 (N) or better (15.620499..) | A1 (4) | cao; N.B. scale drawing scores Max M1M0A0A0 |
# Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Correct triangle with sides 8, 10 and angle $120°$ | M1 | Correct triangle with lengths and angle (arrows not needed), seen or implied |
| $(F^2) = 8^2 + 10^2 - 2 \times 8 \times 10\cos\theta$ where $\theta < 180°$ | M1 | Use of cosine rule with correct structure but any angle $< 180°$ |
| $(F^2) = 8^2 + 10^2 - 2 \times 8 \times 10\cos120°$ | A1 | Correct expression with or without root |
| $F = \sqrt{244} = 2\sqrt{61}$ or 16 (N) or better (15.620499..) | A1 (4) | cao |
**OR (component method):**
| $\pm(10 + 8\cos60°)$ **and** $\pm8\sin60°$ | M1 | Two correct components |
| Use of Pythagoras on their combined components | M1 | Use of Pythagoras using combined **i** and **j** components |
| $F^2 = (10 + 8\cos60°)^2 + (8\sin60°)^2$ | A1 | Correct expression with or without root |
| $F = \sqrt{244} = 2\sqrt{61}$ or 16 (N) or better (15.620499..) | A1 (4) | cao; N.B. scale drawing scores Max M1M0A0A0 |
---\begin{enumerate}
\item Two forces, $\mathbf { P }$ and $\mathbf { Q }$, act on a particle.
\end{enumerate}
\begin{itemize}
\item $\mathbf { P }$ has magnitude 10 N and acts due west
\item Q has magnitude 8 N and acts on a bearing of $330 ^ { \circ }$
\end{itemize}
Given that $\mathbf { F } = \mathbf { P } + \mathbf { Q }$, find the magnitude of $\mathbf { F }$.
\hfill \mbox{\textit{Edexcel M1 2024 Q2 [4]}}