| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2015 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Find maximum or minimum value |
| Difficulty | Moderate -0.3 This is a standard harmonic form question requiring routine application of the R cos(x - α) transformation formula and solving R = √(1 + λ²) = 2. The method is well-practiced in C4, involving straightforward algebraic manipulation with no novel insight required, making it slightly easier than average. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc |
**Question 4:** [2 marks]
Explanation of how 188 seconds derived from 8 stops calculation4 You are given that $\mathrm { f } ( x ) = \cos x + \lambda \sin x$ where $\lambda$ is a positive constant.\\
(i) Express $\mathrm { f } ( x )$ in the form $R \cos ( x - \alpha )$, where $R > 0$ and $0 < \alpha < \frac { 1 } { 2 } \pi$, giving $R$ and $\alpha$ in terms of $\lambda$.\\
(ii) Given that the maximum value (as $x$ varies) of $\mathrm { f } ( x )$ is 2 , find $R , \lambda$ and $\alpha$, giving your answers in exact form.
\hfill \mbox{\textit{OCR MEI C4 2015 Q4 [8]}}