| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find tangent equation at point |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question with standard techniques. Part (i) requires routine application of implicit differentiation rules (differentiating cos x and sin y), then rearranging to show the given result. Part (ii) is a standard tangent line problem requiring substitution of the point to find the gradient, then using point-slope form. The trigonometric values at the given point are standard (π/3, π/6). This is slightly easier than average because it's a textbook exercise with clear steps and no novel problem-solving required. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item A curve has the equation
\end{enumerate}
$$4 \cos x + 2 \sin y = 3$$
(i) Show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 \sin x \sec y$.\\
(ii) Find an equation for the tangent to the curve at the point ( $\frac { \pi } { 3 } , \frac { \pi } { 6 }$ ), giving your answer in the form $a x + b y = c$, where $a$ and $b$ are integers.\\
\hfill \mbox{\textit{OCR C4 Q3 [7]}}