| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Tangent meets curve/axis — further geometry |
| Difficulty | Moderate -0.3 This is a straightforward C1 integration and differentiation question requiring standard techniques: integrate to find y (using the point to find the constant), verify a point lies on the curve, find a tangent equation, and solve for where gradients are equal. All steps are routine with no novel problem-solving required, though the multi-part structure and finding parallel tangents adds slight complexity beyond the most basic questions. |
| Spec | 1.07m Tangents and normals: gradient and equations1.08b Integrate x^n: where n != -1 and sums |
The curve $C$ has equation $y = f(x)$. Given that
$$\frac{dy}{dx} = 3x^2 - 20x + 29$$
and that $C$ passes through the point $P(2, 6)$,
\begin{enumerate}[label=(\alph*)]
\item find $y$ in terms of $x$. [4]
\item Verify that $C$ passes through the point $(4, 0)$. [2]
\item Find an equation of the tangent to $C$ at $P$. [3]
\end{enumerate}
The tangent to $C$ at the point $Q$ is parallel to the tangent at $P$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Calculate the exact $x$-coordinate of $Q$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q20 [14]}}