| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Algebraic side lengths |
| Difficulty | Standard +0.3 Part (a) is a straightforward application of the cosine rule with angle 60°, requiring simple algebraic expansion. Part (b) involves binomial expansion of (16 + 3h²)^(1/2) for small h, which is a standard A-level technique. The question tests routine methods without requiring problem-solving insight, making it slightly easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
\includegraphics{figure_2}
The diagram shows triangle $ABC$ in which angle $A$ is $60°$ and the lengths of $AB$ and $AC$ are $(4 + h)$ cm and $(4 - h)$ cm respectively.
\begin{enumerate}[label=(\alph*)]
\item Show that the length of $BC$ is $p$ cm where
$$p^2 = 16 + 3h^2.$$ [2]
\item Hence show that, when $h$ is small, $p \approx 4 + \lambda h^2 + \mu h^4$, where $\lambda$ and $\mu$ are rational numbers whose values are to be determined. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2021 Q2 [6]}}