Standard +0.8 This question requires students to: (1) deduce the quadratic equation from given roots and a point, (2) find the linear equation from two points, and (3) correctly formulate three inequalities with appropriate inequality signs. While each step is standard A-level content, combining them all with correct inequality directions (especially determining which side of each boundary) makes this moderately challenging, requiring careful geometric reasoning beyond routine exercises.
\includegraphics{figure_3}
Figure 3 shows a sketch of a curve \(C\) and a straight line \(l\).
Given that
• \(C\) has equation \(y = f(x)\) where \(f(x)\) is a quadratic expression in \(x\)
• \(C\) cuts the \(x\)-axis at \(0\) and \(6\)
• \(l\) cuts the \(y\)-axis at \(60\) and intersects \(C\) at the point \((10, 80)\)
use inequalities to define the region \(R\) shown shaded in Figure 3. [5]
\includegraphics{figure_3}
Figure 3 shows a sketch of a curve $C$ and a straight line $l$.
Given that
• $C$ has equation $y = f(x)$ where $f(x)$ is a quadratic expression in $x$
• $C$ cuts the $x$-axis at $0$ and $6$
• $l$ cuts the $y$-axis at $60$ and intersects $C$ at the point $(10, 80)$
use inequalities to define the region $R$ shown shaded in Figure 3. [5]
\hfill \mbox{\textit{SPS SPS SM 2023 Q3 [5]}}