| Exam Board | WJEC |
|---|---|
| Module | Further Unit 4 (Further Unit 4) |
| Year | 2024 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Partial fractions then inverse trig integration |
| Difficulty | Challenging +1.8 Part (a) requires partial fractions decomposition with a quadratic factor, leading to ln and arctan terms—a standard Further Maths technique but multi-step. Part (b) involves hyperbolic functions with a substitution (u = cosh x) to simplify the radical, requiring recognition of the derivative relationship and algebraic manipulation. Both parts demand solid technical facility beyond standard A-level, though they follow recognizable patterns for Further Maths integration questions. |
| Spec | 1.08j Integration using partial fractions4.05c Partial fractions: extended to quadratic denominators4.07d Differentiate/integrate: hyperbolic functions |
Find each of the following integrals.
\begin{enumerate}[label=(\alph*)]
\item $\int \frac{3-x}{x(x^2+1)} \mathrm{d}x$ [8]
\item $\int \frac{\sinh 2x}{\sqrt{\cosh^4 x - 9\cosh^2 x}} \mathrm{d}x$ [6]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 4 2024 Q5 [14]}}