Edexcel P3 2023 January — Question 6

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2023
SessionJanuary
TopicModulus function

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5abaa077-1da4-4023-b442-194f6972095b-16_652_835_292_616} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a sketch of the graph with equation $$y = | 3 x - 5 a | - 2 a$$ where \(a\) is a positive constant.
The graph
  • cuts the \(y\)-axis at the point \(P\)
  • cuts the \(x\)-axis at the points \(Q\) and \(R\)
  • has a minimum point at \(S\)
    1. Find, in simplest form in terms of \(a\), the coordinates of
      1. point \(P\)
      2. points \(Q\) and \(R\)
      3. point \(S\)
    2. Find, in simplest form in terms of \(a\), the values of \(x\) for which
$$| 3 x - 5 a | - 2 a = | x - 2 a |$$