Edexcel Paper 2 2021 October — Question 11

Exam BoardEdexcel
ModulePaper 2 (Paper 2)
Year2021
SessionOctober
TopicModulus function

11. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6c32000f-574f-473c-bd04-9cfe2c1bd715-30_630_630_312_721} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of the graph with equation $$y = | 2 x - 3 k |$$ where \(k\) is a positive constant.
  1. Sketch the graph with equation \(y = \mathrm { f } ( x )\) where $$f ( x ) = k - | 2 x - 3 k |$$ stating
    • the coordinates of the maximum point
    • the coordinates of any points where the graph cuts the coordinate axes
    • Find, in terms of \(k\), the set of values of \(x\) for which
    $$k - | 2 x - 3 k | > x - k$$ giving your answer in set notation.
  2. Find, in terms of \(k\), the coordinates of the minimum point of the graph with equation $$y = 3 - 5 f \left( \frac { 1 } { 2 } x \right)$$