Moderate -0.8 This is a straightforward application of the interval bisection algorithm requiring only three iterations of a mechanical procedure (evaluate at midpoint, check sign, select new interval). No conceptual difficulty beyond understanding the basic method, and the arithmetic is simple with a calculator. Easier than average A-level questions which typically require more problem-solving.
$$f(x) = 1 - e^x + 3 \sin 2x$$
The equation \(f(x) = 0\) has a root \(\alpha\) in the interval \(1.0 < x < 1.4\).
Starting with the interval \((1.0, 1.4)\), use interval bisection three times to find the value of \(\alpha\) to one decimal place.
[3]
$$f(x) = 1 - e^x + 3 \sin 2x$$
The equation $f(x) = 0$ has a root $\alpha$ in the interval $1.0 < x < 1.4$.
Starting with the interval $(1.0, 1.4)$, use interval bisection three times to find the value of $\alpha$ to one decimal place.
[3]
\hfill \mbox{\textit{Edexcel FP1 Q23 [3]}}