| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Resultant of two forces (triangle/parallelogram law) |
| Difficulty | Standard +0.3 This is a straightforward application of the cosine rule to find an angle in a force triangle, followed by a basic component calculation. While it requires knowledge of the triangle law of forces and trigonometry, it's a standard two-part mechanics question with no conceptual challenges—slightly easier than average for A-level. |
| Spec | 3.03e Resolve forces: two dimensions3.03p Resultant forces: using vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(X = 14 - 13\cos\theta\) and \(Y = 13\sin\theta\) or triangle with sides 13, 14, 15 and \(\theta\) opposite 15 | B1 | |
| \([14^2 + 13^2 - 2 \times 13 \times 14\cos\theta = 15^2]\) | M1 | For using \(X^2 + Y^2 = R^2\) or cosine rule |
| \(\theta = 67.4\) | A1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| M1 | For evaluating \(X\) or \(15\cos[\tan^{-1}(Y/X)]\) | |
| Component is 9 N | A1ft [2] |
## Question 2(i):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $X = 14 - 13\cos\theta$ and $Y = 13\sin\theta$ or triangle with sides 13, 14, 15 and $\theta$ opposite 15 | B1 | |
| $[14^2 + 13^2 - 2 \times 13 \times 14\cos\theta = 15^2]$ | M1 | For using $X^2 + Y^2 = R^2$ or cosine rule |
| $\theta = 67.4$ | A1 [3] | |
## Question 2(ii):
| Working/Answer | Mark | Guidance |
|---|---|---|
| | M1 | For evaluating $X$ or $15\cos[\tan^{-1}(Y/X)]$ |
| Component is 9 N | A1ft [2] | |
---2\\
\includegraphics[max width=\textwidth, alt={}, center]{01e73486-5a95-4e65-bf18-518d1adc7cfb-2_318_632_482_753}
Forces of magnitudes 13 N and 14 N act at a point $O$ in the directions shown in the diagram. The resultant of these forces has magnitude 15 N . Find\\
(i) the value of $\theta$,\\
(ii) the component of the resultant in the direction of the force of magnitude 14 N .
\hfill \mbox{\textit{CAIE M1 2012 Q2 [5]}}