| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2016 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Tangent meets curve/axis — further geometry |
| Difficulty | Moderate -0.8 This is a structured, multi-part question guiding students through the first principles definition of differentiation with a simple quadratic, followed by a routine tangent line and area calculation. While it has multiple parts (13 marks total), each step is straightforward and heavily scaffolded, requiring only basic algebraic manipulation and standard techniques well below average A-level difficulty. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.07a Derivative as gradient: of tangent to curve1.07g Differentiation from first principles: for small positive integer powers of x1.07m Tangents and normals: gradient and equations |
\begin{enumerate}[label=(\roman*)]
\item Calculate the gradient of the chord of the curve $y = x^2 - 2x$ joining the points at which the values of $x$ are 5 and 5.1. [2]
\item Given that $\mathrm{f}(x) = x^2 - 2x$, find and simplify $\frac{\mathrm{f}(5 + h) - \mathrm{f}(5)}{h}$. [4]
\item Use your result in part (ii) to find the gradient of the curve $y = x^2 - 2x$ at the point where $x = 5$, showing your reasoning. [2]
\item Find the equation of the tangent to the curve $y = x^2 - 2x$ at the point where $x = 5$.
Find the area of the triangle formed by this tangent and the coordinate axes. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2016 Q10 [13]}}