| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiation from First Principles |
| Type | Chord gradient with h (algebraic) |
| Difficulty | Moderate -0.8 This is a straightforward first-principles differentiation question requiring students to find a chord gradient and take the limit as h→0. While it involves algebraic manipulation, it's a standard FP1 exercise testing basic understanding of derivatives from first principles with no conceptual challenges—easier than average A-level questions. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.07g Differentiation from first principles: for small positive integer powers of x |
A curve $C$ has equation $y = x(x + 3)$.
\begin{enumerate}[label=(\alph*)]
\item Find the gradient of the line passing through the point $(-5, 10)$ and the point on $C$ with $x$-coordinate $-5 + h$. Give your answer in its simplest form. [3 marks]
\item Show how the answer to part (a) can be used to find the gradient of the curve $C$ at the point $(-5, 10)$. State the value of this gradient. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA FP1 2014 Q5 [5]}}