| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 5 |
| Topic | Small angle approximation |
| Type | Solve equation using small angle approximation |
| Difficulty | Standard +0.3 This question requires knowledge of small angle approximations (cos θ ≈ 1 - θ²/2, tan θ ≈ θ) and algebraic manipulation to derive the given result, then solving a linear equation. While it involves multiple steps and careful expansion, the techniques are standard A-level material with no novel insight required. The 5 marks and straightforward structure place it slightly easier than average. |
| Spec | 1.05e Small angle approximations: sin x ~ x, cos x ~ 1-x^2/2, tan x ~ x |
\begin{enumerate}[label=(\alph*)]
\item For a small angle $\theta$, where $\theta$ is in radians, show that $2\cos\theta + (1 - \tan\theta)^2 \approx 3 - 2\theta$. [3]
\item Hence determine an approximate solution to $2\cos\theta + (1 - \tan\theta)^2 = 28\sin\theta$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q1 [5]}}