OCR H240/02 2020 November — Question 1 9 marks

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2020
SessionNovember
Marks9
PaperDownload PDF ↗
TopicChain Rule
TypeFind curve equation from derivative
DifficultyEasy -1.3 This is a straightforward collection of basic calculus exercises testing standard techniques: chain rule, product rule, simple integration, and finding a particular solution. All parts are routine recall with minimal problem-solving, requiring only direct application of learned rules with no conceptual challenges or multi-step reasoning.
Spec1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08l Interpret differential equation solutions: in context

  1. Differentiate the following with respect to \(x\).
    1. \((2x + 3)^7\) [2]
    2. \(x^3 \ln x\) [3]
  2. Find \(\int \cos 5x \, dx\). [2]
  3. Find the equation of the curve through \((1, 3)\) for which \(\frac{dy}{dx} = 6x - 5\). [2]

\begin{enumerate}[label=(\alph*)]
\item Differentiate the following with respect to $x$.
\begin{enumerate}[label=(\roman*)]
\item $(2x + 3)^7$ [2]
\item $x^3 \ln x$ [3]
\end{enumerate}
\item Find $\int \cos 5x \, dx$. [2]
\item Find the equation of the curve through $(1, 3)$ for which $\frac{dy}{dx} = 6x - 5$. [2]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/02 2020 Q1 [9]}}