| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Integration with partial fractions |
| Difficulty | Standard +0.3 This is a straightforward algebraic manipulation followed by a standard integration. Part (a) requires factorising and simplifying a rational function (routine A-level algebra), and part (b) applies direct integration of a simple form with logarithms. The question is slightly easier than average as it's highly structured with clear guidance ('show that' and 'hence'), requiring no problem-solving insight beyond standard techniques. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.08d Evaluate definite integrals: between limits |
The function $f$ is defined by $f(x) = \frac{4x^2 + 12x + 9}{2x^2 + x - 3}$, where $x > 1$.
\begin{enumerate}[label=(\alph*)]
\item Show that $f(x)$ can be written as $2 + \frac{5}{x-1}$. [3]
\item Hence find the exact value of $\int_3^7 f(x)\,dx$. [4]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q8 [7]}}