| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Write inequalities from graph |
| Difficulty | Moderate -0.8 This question requires finding equations from given information (quadratic from roots, line from two points) and writing inequalities for a shaded region. While it involves multiple steps, each is a standard AS-level technique with no novel problem-solving required. The graphical context makes the inequalities straightforward to identify. |
| Spec | 1.02i Represent inequalities: graphically on coordinate plane |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Gradient \(= \frac{80-60}{10} = 2\), intercept \(= 60\) | M1 | 1.1b — Complete method to find RHS of equation for \(l\) |
| \(y = 2x + 60\) | A1 | 1.1b |
| Deduces RHS of equation for \(C\) is \(y = ax(x-6)\), attempts to use \((10, 80)\) to find \(a\) | M1 | 3.1a |
| \(y = 2x(x-6)\) | A1 | 1.1b |
| \(2x(x-6) \leqslant y \leqslant 2x+60\) | B1ft | 2.5 — Follow through on their quadratic \(C\) and linear \(l\); do not allow mixed strict/non-strict inequalities |
## Question 8:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Gradient $= \frac{80-60}{10} = 2$, intercept $= 60$ | M1 | 1.1b — Complete method to find RHS of equation for $l$ |
| $y = 2x + 60$ | A1 | 1.1b |
| Deduces RHS of equation for $C$ is $y = ax(x-6)$, attempts to use $(10, 80)$ to find $a$ | M1 | 3.1a |
| $y = 2x(x-6)$ | A1 | 1.1b |
| $2x(x-6) \leqslant y \leqslant 2x+60$ | B1ft | 2.5 — Follow through on their quadratic $C$ and linear $l$; do not allow mixed strict/non-strict inequalities |
---8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{ce4f8375-0d88-4e48-85de-35f7e90b014d-16_661_855_283_605}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
Figure 3 shows a sketch of a curve $C$ and a straight line $l$.\\
Given that
\begin{itemize}
\item $C$ has equation $y = \mathrm { f } ( x )$ where $\mathrm { f } ( x )$ is a quadratic expression in $x$
\item $C$ cuts the $x$-axis at 0 and 6
\item $l$ 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.
\end{itemize}
\hfill \mbox{\textit{Edexcel AS Paper 1 2023 Q8 [5]}}