| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiation from First Principles |
| Type | First principles: trigonometric functions |
| Difficulty | Standard +0.8 Part (a) requires a rigorous first principles proof using the limit definition and standard limit results (sin h/h → 1), which is conceptually demanding and rarely examined. Parts (b) and (c) are standard product rule and integration by parts (applied twice), but the 13-mark total and proof requirement elevate this above average difficulty. |
| Spec | 1.07h Differentiation from first principles: for sin(x) and cos(x)1.07q Product and quotient rules: differentiation1.08i Integration by parts |
\begin{enumerate}[label=(\alph*)]
\item Differentiate $\cos x$ from first principles. [5]
\item Differentiate $e^{3x}\sin 4x$ with respect to $x$. [3]
\item Find $\int x^2\sin 2x dx$. [5]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2024 Q6 [13]}}