| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Increasing/decreasing intervals |
| Difficulty | Moderate -0.8 This question tests basic differentiation and integration with straightforward applications. Part (i)(a) is routine power rule differentiation, (i)(b) requires solving a simple linear inequality, and part (ii) involves integrating a polynomial with a square root term rewritten as a fractional power. All techniques are standard with no problem-solving insight required, making this easier than average but not trivial due to the multiple parts and marks allocated. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07o Increasing/decreasing: functions using sign of dy/dx1.08b Integrate x^n: where n != -1 and sums |
\begin{enumerate}[label=(\roman*)]
\item It is given that $y = x^2 + 3x$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dy}{dx}$. [2]
\item Find the values of $x$ for which $y$ is increasing. [2]
\end{enumerate}
\item Find $\int(3 - 4\sqrt{x})dx$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q4 [9]}}