| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find normal line equation at given point |
| Difficulty | Moderate -0.8 This is a straightforward C1 differentiation question requiring basic power rule application and finding a normal line equation. The steps are routine: differentiate using standard rules, substitute x=1 to find the gradient, calculate the perpendicular gradient, find the y-coordinate, and write the equation in the required form. No problem-solving insight needed, just mechanical application of learned procedures. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations |
For the curve $C$ with equation $y = x^4 – 8x^2 + 3$,
(a) find $\frac{dy}{dx}$.
(2)
The point $A$, on the curve $C$, has x-coordinate 1.
(b) Find an equation for the normal to $C$ at $A$, giving your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers.
(5)7. For the curve $C$ with equation $y = x ^ { 4 } - 8 x ^ { 2 } + 3$,
\begin{enumerate}[label=(\alph*)]
\item find $\frac { \mathrm { d } y } { \mathrm {~d} x }$,
The point $A$, on the curve $C$, has $x$-coordinate 1 .
\item Find an equation for the normal to $C$ at $A$, giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [7]}}