| 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 -0.3 This is a standard C1 inequality question with routine techniques: (a) requires simple linear inequality manipulation, (b) requires factorizing/solving a quadratic and applying inequality reasoning, and (c) requires finding the intersection of solution sets. While multi-part, each step follows textbook procedures with no novel insight required, making it slightly easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks |
|---|---|
| \(6x - 7 < 2x + 3 \Rightarrow 4x < 10\) | M1 |
| \(x < \frac{5}{2}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(2x^2 - 11x + 5 < 0 \Rightarrow (2x-1)(x-5) < 0\) | M1 A1 | M1 for attempt to factorise or solve |
| \(\frac{1}{2} < x < 5\) | A1 A1 | A1 for critical values, A1 for correct inequality |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2} < x < \frac{5}{2}\) | B1 | Follow through from (a) and (b) |
# Question 5:
## Part (a):
| $6x - 7 < 2x + 3 \Rightarrow 4x < 10$ | M1 | |
| $x < \frac{5}{2}$ | A1 | |
## Part (b):
| $2x^2 - 11x + 5 < 0 \Rightarrow (2x-1)(x-5) < 0$ | M1 A1 | M1 for attempt to factorise or solve |
| $\frac{1}{2} < x < 5$ | A1 A1 | A1 for critical values, A1 for correct inequality |
## Part (c):
| $\frac{1}{2} < x < \frac{5}{2}$ | B1 | Follow through from (a) and (b) |
---5. Find the set of values for $x$ for which
\begin{enumerate}[label=(\alph*)]
\item $6 x - 7 < 2 x + 3$,
\item $2 x ^ { 2 } - 11 x + 5 < 0$,
\item both $6 x - 7 < 2 x + 3$ and $2 x ^ { 2 } - 11 x + 5 < 0$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q5 [7]}}