WJEC Unit 1 2023 June — Question 13 12 marks

Exam BoardWJEC
ModuleUnit 1 (Unit 1)
Year2023
SessionJune
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAreas by integration
TypeCombined region areas
DifficultyStandard +0.3 Part (a) is routine integration of power functions requiring only the power rule—straightforward recall. Part (b) requires expanding the cubic, integrating, finding roots, splitting the integral at zeros, and taking absolute values to find total area. While multi-step with 9 marks, these are all standard AS-level techniques with no novel insight required, making it slightly easier than average overall.
Spec1.08b Integrate x^n: where n != -1 and sums1.08e Area between curve and x-axis: using definite integrals

  1. Find \(\int \left(4x^{-\frac{2}{3}} + 5x^3 + 7\right) dx\). [3]
  2. The diagram below shows the graph of \(y = x(x + 6)(x - 3)\). \includegraphics{figure_13} Calculate the total area of the regions enclosed by the graph and the \(x\)-axis. [9]

\begin{enumerate}[label=(\alph*)]
\item Find $\int \left(4x^{-\frac{2}{3}} + 5x^3 + 7\right) dx$. [3]

\item The diagram below shows the graph of $y = x(x + 6)(x - 3)$.

\includegraphics{figure_13}

Calculate the total area of the regions enclosed by the graph and the $x$-axis. [9]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 1 2023 Q13 [12]}}