Edexcel C34 2019 June — Question 6

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2019
SessionJune
TopicModulus function

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a9870c94-0910-46ec-a54a-44a431cb324e-14_988_1120_123_395} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the graph with equation \(y = | 4 x + 10 a |\), where \(a\) is a positive constant. The graph cuts the \(y\)-axis at the point \(P\) and meets the \(x\)-axis at the point \(Q\) as shown.
    1. State the coordinates of \(P\).
    2. State the coordinates of \(Q\).
  1. A copy of Figure 1 is shown on page 15. On this copy, sketch the graph with equation $$y = | x | - a$$ Show on the sketch the coordinates of each point where your graph cuts or meets the coordinate axes.
  2. Hence, or otherwise, solve the equation $$| 4 x + 10 a | = | x | - a$$ giving your answers in terms of \(a\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{a9870c94-0910-46ec-a54a-44a431cb324e-15_860_1128_447_392} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure} \(\_\_\_\_\) 7