| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Small angle approximation |
| Type | Simplify expression to polynomial form |
| Difficulty | Standard +0.3 This is a straightforward application of the small angle approximation cos θ ≈ 1 - θ²/2. Students substitute this into the expression and simplify algebraically to reach the given result. It requires recall of a standard approximation and basic polynomial manipulation, making it slightly easier than average but not trivial since it involves squaring the approximation and collecting terms carefully. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.05e Small angle approximations: sin x ~ x, cos x ~ 1-x^2/2, tan x ~ x |
4 For a small angle $\theta$, where $\theta$ is in radians, show that $1 + \cos \theta - 3 \cos ^ { 2 } \theta \approx - 1 + \frac { 5 } { 2 } \theta ^ { 2 }$.
\hfill \mbox{\textit{OCR H240/03 Q4 [4]}}