| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Combined region areas |
| Difficulty | Standard +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. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08e Area between curve and x-axis: using definite integrals |
\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]}}