| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | September |
| Marks | 7 |
| Topic | Product & Quotient Rules |
| Type | Find derivative of quotient |
| Difficulty | Moderate -0.8 This is a straightforward differentiation question testing basic quotient rule and chain rule application with standard functions. Part (a) can be done with chain rule alone (rewriting as a power), part (b) is a direct quotient rule application with ln(x+2) and x, and part (ii) is a routine integration by inspection. All are textbook exercises requiring only mechanical application of rules with no problem-solving or insight needed, making it easier than average. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
1 (i) Differentiate the following with respect to $x$.
\begin{enumerate}[label=(\alph*)]
\item $\frac { 1 } { ( 3 x - 4 ) ^ { 2 } }$
\item $\frac { \ln ( x + 2 ) } { x }$\\
(ii) Find $\int \mathrm { e } ^ { ( 2 x + 3 ) } \mathrm { d } x$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2018 Q1 [7]}}