| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Tangent meets curve/axis — further geometry |
| Difficulty | Moderate -0.8 This is a straightforward C1 differentiation question requiring quotient rule or rewriting, finding a tangent equation using y-y₁=m(x-x₁), and solving a linear equation. All steps are routine textbook exercises with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations |
The curve $C$ has equation $y = 4x^2 + \frac{5-x}{x}$, $x \neq 0$. The point $P$ on $C$ has $x$-coordinate $1$.
\begin{enumerate}[label=(\alph*)]
\item Show that the value of $\frac{dy}{dx}$ at $P$ is $3$. [5]
\item Find an equation of the tangent to $C$ at $P$. [3]
\end{enumerate}
This tangent meets the $x$-axis at the point $(k, 0)$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the value of $k$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [10]}}