| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | December |
| Marks | 8 |
| Topic | Differentiation from First Principles |
| Type | Integration after differentiation |
| Difficulty | Moderate -0.8 Part (a) is a standard first principles differentiation of a simple quadratic—routine but requires careful algebraic manipulation. Part (b) is straightforward integration with a constant of integration determined by a given point. Both parts are textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.07g Differentiation from first principles: for small positive integer powers of x1.08a Fundamental theorem of calculus: integration as reverse of differentiation |
5
\begin{enumerate}[label=(\alph*)]
\item Given that $\mathrm { f } ( x ) = x ^ { 2 } - 4 x$, use differentiation from first principles to show that $\mathrm { f } ^ { \prime } ( x ) = 2 x - 4$.
\item Find the equation of the curve through $( 2,7 )$ for which $\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 x - 4$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2018 Q5 [8]}}