Edexcel P3 2022 October — Question 7

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2022
SessionOctober
TopicModulus function

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{83e12fa4-1abb-4bea-bff4-8d36757bd9c3-20_624_798_219_575} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of the graph of \(C _ { 1 }\) with equation $$y = 5 - | 3 x - 22 |$$
  1. Write down the coordinates of
    1. the vertex of \(C _ { 1 }\)
    2. the intersection of \(C _ { 1 }\) with the \(y\)-axis.
  2. Find the \(x\) coordinates of the intersections of \(C _ { 1 }\) with the \(x\)-axis. Diagram 1, shown on page 21, is a copy of Figure 3.
  3. On Diagram 1, sketch the curve \(C _ { 2 }\) with equation $$y = \frac { 1 } { 9 } x ^ { 2 } - 9$$ Identify clearly the coordinates of any points of intersection of \(C _ { 2 }\) with the coordinate axes.
  4. Find the coordinates of the points of intersection of \(C _ { 1 }\) and \(C _ { 2 }\) (Solutions relying entirely on calculator technology are not acceptable.) \includegraphics[max width=\textwidth, alt={}, center]{83e12fa4-1abb-4bea-bff4-8d36757bd9c3-21_629_803_1137_573} \section*{Diagram 1} Solutions relying entirely on calculator technology are not acceptable.