Edexcel F1 2021 January — Question 1 5 marks

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2021
SessionJanuary
Marks5
PaperDownload PDF ↗
TopicSign Change & Interval Methods
TypePure Interval Bisection Only
DifficultyModerate -0.8 This is a straightforward application of the interval bisection method with minimal computational complexity. Part (a) requires simple substitution to verify sign change, and part (b) involves just two iterations of bisection with clear arithmetic. The method is algorithmic with no conceptual challenges or problem-solving required—purely procedural execution of a standard technique.
Spec1.09a Sign change methods: locate roots

  1. (a) Show that the equation \(4 x - 2 \sin x - 1 = 0\), where \(x\) is in radians, has a root \(\alpha\) in the interval [0.2, 0.6]
    [0pt] (b) Starting with the interval [0.2, 0.6], use interval bisection twice to find an interval of width 0.1 in which \(\alpha\) lies.
    (3)

\begin{enumerate}
  \item (a) Show that the equation $4 x - 2 \sin x - 1 = 0$, where $x$ is in radians, has a root $\alpha$ in the interval [0.2, 0.6]\\[0pt]
(b) Starting with the interval [0.2, 0.6], use interval bisection twice to find an interval of width 0.1 in which $\alpha$ lies.\\
(3)\\

\end{enumerate}

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\hfill \mbox{\textit{Edexcel F1 2021 Q1 [5]}}