| Exam Board | Edexcel |
|---|---|
| Module | PMT Mocks (PMT Mocks) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Show derivative equals expression - algebraic/trigonometric identity proof |
| Difficulty | Standard +0.3 Part (a) requires straightforward differentiation using chain rule (d/dx of sin 2x) and a standard trigonometric identity (1 - cos 2x = 2sin²x). Part (b) requires finding second derivative, setting it to zero, and solving sin 2x = 0, which is routine A-level calculus. This is slightly easier than average due to being a standard 'show that' followed by mechanical application of inflection point method. |
| Spec | 1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07p Points of inflection: using second derivative |
\begin{enumerate}
\item The curve $C$ has equation
\end{enumerate}
$$y = \frac { 1 } { 2 } x - \frac { 1 } { 4 } \sin 2 x \quad 0 < x < \pi$$
a. Show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \sin ^ { 2 } x$\\
b. Find the coordinates of the points of inflection of the curve.\\
\hfill \mbox{\textit{Edexcel PMT Mocks Q15 [6]}}