| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Tangent parallel to given line |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic differentiation, finding x-intercepts by factoring, and using the gradient condition for parallel lines. All parts use standard techniques with clear signposting, requiring minimal problem-solving insight. Part (d) involves solving a quadratic equation but the setup is routine. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations |
\includegraphics{figure_2}
Figure 2 shows part of the curve $C$ with equation
$$y = (x - 1)(x^2 - 4).$$
The curve cuts the $x$-axis at the points $P$, $(1, 0)$ and $Q$, as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Write down the $x$-coordinate of $P$ and the $x$-coordinate of $Q$. [2]
\item Show that $\frac{dy}{dx} = 3x^2 - 2x - 4$. [3]
\item Show that $y = x + 7$ is an equation of the tangent to $C$ at the point $(-1, 6)$. [2]
\end{enumerate}
The tangent to $C$ at the point $R$ is parallel to the tangent at the point $(-1, 6)$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find the exact coordinates of $R$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q9 [12]}}