Moderate -0.8 This is a straightforward application of the linear interpolation formula with given interval endpoints. Students only need to evaluate f(1) and f(2), then apply the standard formula—no iteration, problem-solving, or conceptual depth required. While it's FP1, this particular question is more mechanical than typical A-level questions.
$$f(x) = 2^x + x - 4.$$
The equation \(f(x) = 0\) has a root \(\alpha\) in the interval \([1, 2]\).
Use linear interpolation on the values at the end points of this interval to find an approximation to \(\alpha\).
[2]
$$f(x) = 2^x + x - 4.$$
The equation $f(x) = 0$ has a root $\alpha$ in the interval $[1, 2]$.
Use linear interpolation on the values at the end points of this interval to find an approximation to $\alpha$.
[2]
\hfill \mbox{\textit{Edexcel FP1 Q17 [2]}}