| 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 | Rational inequality algebraically |
| Difficulty | Easy -1.2 This is a straightforward rational inequality requiring basic algebraic manipulation. Part (a) is a standard sketch of a reciprocal function, and part (b) can be solved either graphically (reading off where the curve is below y=2) or algebraically by multiplying through and considering sign cases. This is simpler than average A-level content, requiring only routine techniques with minimal problem-solving insight. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02o Sketch reciprocal curves: y=a/x and y=a/x^2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Shape in quadrant 1 or 3 | M1 | Correct shape; must not cross either axis; ignore incorrect asymptotes |
| Correct shape and position (curve in quadrants 1 and 3 only) | A1 | No curve in quadrants 2 or 4; curve must not bend back on itself |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Deduces \(x < 0\) | B1 | Condone \(x \leq 0\) for this mark |
| Attempts \(\frac{16}{x} \ldots 2 \Rightarrow x \ldots \pm\frac{16}{2}\) | M1 | Any equality or inequality |
| \(x < 0\) or \(x \geq 8\) | A1 cso | Both required; accept \(\{x: x<0\} \cup \{x: x \geq 8\}\) or \(x \in (-\infty, 0) \cup [8, \infty)\); must not be combined incorrectly |
# Question 4:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Shape in quadrant 1 **or** 3 | M1 | Correct shape; must not cross either axis; ignore incorrect asymptotes |
| Correct shape **and** position (curve in quadrants 1 and 3 only) | A1 | No curve in quadrants 2 or 4; curve must not bend back on itself |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Deduces $x < 0$ | B1 | Condone $x \leq 0$ for this mark |
| Attempts $\frac{16}{x} \ldots 2 \Rightarrow x \ldots \pm\frac{16}{2}$ | M1 | Any equality or inequality |
| $x < 0$ **or** $x \geq 8$ | A1 cso | Both required; accept $\{x: x<0\} \cup \{x: x \geq 8\}$ or $x \in (-\infty, 0) \cup [8, \infty)$; must not be combined incorrectly |\begin{enumerate}
\item (a) Sketch the curve with equation
\end{enumerate}
$$y = \frac { k } { x } \quad x \neq 0$$
where $k$ is a positive constant.\\
(b) Hence or otherwise, solve
$$\frac { 16 } { x } \leqslant 2$$
\hfill \mbox{\textit{Edexcel AS Paper 1 2023 Q4 [5]}}