| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Combined linear and quadratic inequalities |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic quadratic and linear inequalities. Part (a) requires factorising x² + 3x - 10 > 0 to get (x+5)(x-2) > 0, giving x < -5 or x > 2. Part (b) adds a simple linear inequality (3x - 2 < x + 3 gives x < 2.5) and asks for the intersection. All techniques are routine with no problem-solving insight required, making this easier than the average A-level question. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation |
| Answer | Marks | Guidance |
|---|---|---|
| \((x+5)(x-2) > 0\) | M1 | |
| M1 | ||
| \(x < -5\) or \(x > 2\) | A1 | |
| (b) \(3x - 2 < x + 3 \Rightarrow 2x < 5\) | M1 | |
| \(x < \frac{5}{2}\) | A1 | |
| both satisfied when \(x < -5\) or \(2 < x < \frac{5}{2}\) | A1 | (6 marks) |
(a) $x^2 + 3x - 10 > 0$
$(x+5)(x-2) > 0$ | M1 |
| M1 |
$x < -5$ or $x > 2$ | A1 |
(b) $3x - 2 < x + 3 \Rightarrow 2x < 5$ | M1 |
$x < \frac{5}{2}$ | A1 |
both satisfied when $x < -5$ or $2 < x < \frac{5}{2}$ | A1 | (6 marks)\begin{enumerate}[label=(\alph*)]
\item Solve the inequality
$$x^2 + 3x > 10.$$ [3]
\item Find the set of values of $x$ which satisfy both of the following inequalities:
$$3x - 2 < x + 3$$
$$x^2 + 3x > 10$$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4 [6]}}