SPS SPS SM 2020 June — Question 10

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2020
SessionJune
TopicInequalities

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2033889-3cc5-48de-9bdb-cb1861921a2a-10_883_885_283_644} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of the curve \(C\) with equation \(y = 3 x - 2 \sqrt { x } , x \geqslant 0\) and the line \(l\) with equation \(y = 8 x - 16\) The line cuts the curve at point \(A\) as shown in Figure 3.
  1. Using algebra, find the \(x\) coordinate of point \(A\).
    (5)
  2. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{f2033889-3cc5-48de-9bdb-cb1861921a2a-10_656_814_1786_662} \captionsetup{labelformat=empty} \caption{Figure 4}
    \end{figure} The region \(R\) is shown unshaded in Figure 4. Identify the inequalities that define \(R\).