| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find normal equation at point |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question requiring students to differentiate both sides with respect to x (using product rule for the middle term), substitute the point to find dy/dx, then find the negative reciprocal for the normal gradient and write the equation. While it involves multiple techniques, these are standard C4 procedures with no conceptual surprises, making it slightly easier than average. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.07s Parametric and implicit differentiation |
4 Find the equation of the normal to the curve
$$x ^ { 3 } + 4 x ^ { 2 } y + y ^ { 3 } = 6$$
at the point $( 1,1 )$, giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.
\hfill \mbox{\textit{OCR C4 2008 Q4 [6]}}