| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2021 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Easy -1.2 This is a straightforward quadratic inequality requiring factorization (x² - x - 20 > 0 gives (x-5)(x+4) > 0), identifying critical points, and testing regions. It's a standard AS-level technique with no conceptual challenges, making it easier than average but not trivial since students must correctly determine which regions satisfy the inequality and express the answer in set notation. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| Finds critical values: \(x^2 - x > 20 \Rightarrow x^2 - x - 20 > 0 \Rightarrow x = (5, -4)\) | M1 | Attempts to find critical values using an algebraic method. Condone slips but two critical values must be found |
| Chooses outside region: \(x > 5, x < -4\) | M1 | Chooses the outside region for their critical values. May appear in incorrect inequalities such as \(5 < x < -4\) |
| \(\{x : x < -4\} \cup \{x : x > 5\}\) | A1 | Accept \(\{x < -4 \cup x > 5\}\). Do not accept \(\{x < -4,\ x > 5\}\) |
## Question 1:
| Working/Answer | Marks | Guidance |
|---|---|---|
| Finds critical values: $x^2 - x > 20 \Rightarrow x^2 - x - 20 > 0 \Rightarrow x = (5, -4)$ | M1 | Attempts to find critical values using an algebraic method. Condone slips but two critical values must be found |
| Chooses outside region: $x > 5, x < -4$ | M1 | Chooses the outside region for their critical values. May appear in incorrect inequalities such as $5 < x < -4$ |
| $\{x : x < -4\} \cup \{x : x > 5\}$ | A1 | Accept $\{x < -4 \cup x > 5\}$. Do not accept $\{x < -4,\ x > 5\}$ |
**Note:** If there is a contradiction of their solution on different lines of working do not penalise intermediate working and mark what appears to be their final answer.
---\begin{enumerate}
\item In this question you should show all stages of your working.
\end{enumerate}
Solutions relying on calculator technology are not acceptable.\\
Using algebra, solve the inequality
$$x ^ { 2 } - x > 20$$
writing your answer in set notation.
\hfill \mbox{\textit{Edexcel AS Paper 1 2021 Q1 [3]}}