| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find normal line equation at given point |
| Difficulty | Moderate -0.3 This is a straightforward C1 integration and differentiation question with standard techniques: finding a normal (negative reciprocal of gradient), integrating to find the curve equation using a boundary condition, and analyzing when a derivative equals a constant. All parts are routine textbook exercises requiring no problem-solving insight, though the multi-step nature and 11 total marks place it slightly below average difficulty rather than being trivial. |
| Spec | 1.07m Tangents and normals: gradient and equations1.08a Fundamental theorem of calculus: integration as reverse of differentiation |
The gradient of the curve $C$ is given by
$$\frac{dy}{dx} = (3x - 1)^2.$$
The point $P(1, 4)$ lies on $C$.
\begin{enumerate}[label=(\alph*)]
\item Find an equation of the normal to $C$ at $P$. [4]
\item Find an equation for the curve $C$ in the form $y = f(x)$. [5]
\item Using $\frac{dy}{dx} = (3x - 1)^2$, show that there is no point on $C$ at which the tangent is parallel to the line $y = 1 - 2x$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q9 [11]}}