| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson convergence failure |
| Difficulty | Standard +0.3 This is a straightforward Newton-Raphson question with standard parts: showing a root exists via sign change (trivial), applying the iterative formula (routine calculation), and explaining failure at a stationary point. All parts are textbook exercises requiring only direct application of learned techniques with no problem-solving insight needed. |
| Spec | 1.09a Sign change methods: locate roots1.09d Newton-Raphson method1.09e Iterative method failure: convergence conditions |
The function $f$ is defined by
$$f(x) = x^3 + 4x^2 - 3x - 1.$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation $f(x) = 0$ has a root in the interval $[0, 1]$. [1]
\item Using the Newton-Raphson method with $x_0 = 0 \cdot 8$,
\begin{enumerate}[label=(\roman*)]
\item write down in full the decimal value of $x_1$ as given in your calculator,
\item determine the value of this root correct to six decimal places. [4]
\end{enumerate}
\item Explain why the Newton-Raphson method does not work if $x_0 = \frac{1}{3}$. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2024 Q8 [7]}}