| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Sign Change & Interval Methods |
| Type | Pure Interval Bisection Only |
| Difficulty | Moderate -0.8 This is a straightforward application of the interval bisection method with minimal computational complexity. Part (a) requires simple substitution to verify a sign change, and part (b) is a mechanical three-step bisection process with clear instructions. While it's from FP1, the question requires only routine execution of a standard algorithm with no problem-solving insight or conceptual challenges. |
| Spec | 1.09a Sign change methods: locate roots |
$$f(x) = 0.25x - 2 + 4 \sin \sqrt{x}.$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation $f(x) = 0$ has a root $\alpha$ between $x = 0.24$ and $x = 0.28$. [2]
\item Starting with the interval $[0.24, 0.28]$, use interval bisection three times to find an interval of width 0.005 which contains $\alpha$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q34 [5]}}