| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 4 |
| Topic | Small angle approximation |
| Type | Simplify expression to polynomial form |
| Difficulty | Standard +0.3 This is a straightforward small angle approximation question requiring substitution of cos θ ≈ 1 - θ²/2 and algebraic simplification. It's slightly easier than average as it's a 'show that' question with a clear target, requiring only standard technique application without problem-solving or insight. |
| Spec | 1.05e Small angle approximations: sin x ~ x, cos x ~ 1-x^2/2, tan x ~ x |
For a small angle $\theta$, where $\theta$ is in radians, show that $1 + \cos \theta - 3\cos^2 \theta \approx -1 + \frac{3}{2}\theta^2$. [4]
\hfill \mbox{\textit{OCR H240/03 2017 Q4 [4]}}