| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Express and solve equation |
| Difficulty | Moderate -0.3 This is a straightforward application of standard techniques: part (a) uses the R cos(t-α) form with R=√(144+25)=13 and tan α=5/12, requiring only routine trigonometric manipulation. Part (b) solves 13cos(t-α)=±3, which is a simple inverse cosine problem. Both parts follow textbook procedures with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc |
A particle $P$ moves along a straight line in such a way that at time $t$ seconds $P$ has velocity $v$ m s$^{-1}$, where
$v = 12\cos t + 5\sin t$.
\begin{enumerate}[label=(\alph*)]
\item Express $v$ in the form $R\cos(t - \alpha)$, where $R > 0$ and $0 < \alpha < \frac{1}{2}\pi$. Give the value of $\alpha$ correct to 4 significant figures. [3]
\item Hence find the two smallest positive values of $t$ for which $P$ is moving, in either direction, with a speed of 3 m s$^{-1}$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2021 Q5 [6]}}