| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find tangent equation at point |
| Difficulty | Moderate -0.3 This is a straightforward implicit differentiation question with standard techniques. Part (i) requires differentiating x with respect to y and inverting (routine), while part (ii) involves substituting a value and finding a tangent line equation. The algebra is simple and the methods are textbook standard, making it slightly easier than average. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
3. A curve has the equation $x = y ^ { 2 } - 3 \ln 2 y$.\\
(i) Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y } { 2 y ^ { 2 } - 3 }$$
(ii) Find an equation for the tangent to the curve at the point where $y = \frac { 1 } { 2 }$.
Give your answer in the form $a x + b y + c = 0$ where $a , b$ and $c$ are integers.\\
\hfill \mbox{\textit{OCR C3 Q3 [6]}}