| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Combined linear and quadratic inequalities |
| Difficulty | Moderate -0.5 This is a standard C1 inequalities question with routine techniques: solving a linear inequality by rearranging, factorizing a quadratic to solve a quadratic inequality, then finding the intersection of solution sets. While it requires multiple steps and careful attention to inequality signs, all methods are textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| \(6x - 2x < 3 + 7\) | M1 | Method for solving linear inequality |
| \(x < 2\frac{1}{2}\) | A1 | (2 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \((2x-1)(x-5)\) | M1 | Attempt to factorise |
| Critical values \(\frac{1}{2}\) and \(5\) | A1 | |
| \(\frac{1}{2} < x < 5\) | M1 A1 ft | (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2} < x < 2\frac{1}{2}\) | B1 ft | Intersection of (a) and (b) (1 mark) |
## Question 4:
### Part (a)
$6x - 2x < 3 + 7$ | M1 | Method for solving linear inequality
$x < 2\frac{1}{2}$ | A1 | (2 marks)
### Part (b)
$(2x-1)(x-5)$ | M1 | Attempt to factorise
Critical values $\frac{1}{2}$ and $5$ | A1 |
$\frac{1}{2} < x < 5$ | M1 A1 ft | (4 marks)
### Part (c)
$\frac{1}{2} < x < 2\frac{1}{2}$ | B1 ft | Intersection of (a) and (b) (1 mark)
---4. Find the set of values for $x$ for which
\begin{enumerate}[label=(\alph*)]
\item $6 x - 7 < 2 x + 3$,
\item $\quad 2 x ^ { 2 } - 11 x + 5 < 0$,
\item both $6 x - 7 < 2 x + 3$ and $2 x ^ { 2 } - 11 x + 5 < 0$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4 [7]}}