| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | 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 equation. Part (a) is routine differentiation of a polynomial. Part (b) involves standard steps: finding y-coordinate, evaluating gradient, finding perpendicular gradient, and writing the line equation. All techniques are standard textbook exercises with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature of part (b). |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations |
For the curve $C$ with equation $y = x^4 - 8x^2 + 3$,
\begin{enumerate}[label=(\alph*)]
\item find $\frac{dy}{dx}$. [2]
\end{enumerate}
The point $A$, on the curve $C$, has $x$-coordinate 1.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item 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]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q28 [7]}}