OCR PURE — Question 4 9 marks

Exam BoardOCR
ModulePURE
Marks9
PaperDownload PDF ↗
TopicTangents, normals and gradients
TypeIncreasing/decreasing intervals
DifficultyModerate -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.
Spec1.07i 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

  1. It is given that \(y = x^2 + 3x\).
    1. Find \(\frac{dy}{dx}\). [2]
    2. Find the values of \(x\) for which \(y\) is increasing. [2]
  2. Find \(\int(3 - 4\sqrt{x})dx\). [5]

\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]}}