| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | June |
| 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 inequality question requiring standard techniques: linear inequality manipulation for part (a), finding critical points and testing intervals for the quadratic inequality in part (b), and set intersection for part (c). All methods are routine textbook exercises with no problem-solving insight required, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(3x - 6 < 8 - 2x \rightarrow 5x < 14\) | M1 | For attempt to rearrange to \(kx < m\); either \(k=5\) or \(m=14\) should be correct. Allow \(5x=14\) or even \(5x>14\) |
| \(x < 2.8\) or \(\frac{14}{5}\) or \(2\frac{4}{5}\) | A1 | Condone \(\leq\). Accept \(5x - 14 < 0\) (o.e.) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Critical values \(x = \frac{7}{2}\) and \(-1\) | B1 | For both correct critical values (may be implied by correct inequality) |
| Choosing "inside" \(-1 < x < \frac{7}{2}\) | M1 A1 | M1: ft their values and choose "inside" region. A1: fully correct inequality. Allow 3.5 instead of \(\frac{7}{2}\). Also \(\left(-1, \frac{7}{2}\right)\) scores M1A1. \(x < -1, x < \frac{7}{2}\) is M0A0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(-1 < x < 2.8\) | B1ft | For \(-1 < x < 2.8\) ignoring previous answers, or ft their answers to parts (a) and (b) provided both were regions not single values |
## Question 3:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $3x - 6 < 8 - 2x \rightarrow 5x < 14$ | M1 | For attempt to rearrange to $kx < m$; either $k=5$ or $m=14$ should be correct. Allow $5x=14$ or even $5x>14$ |
| $x < 2.8$ or $\frac{14}{5}$ or $2\frac{4}{5}$ | A1 | Condone $\leq$. Accept $5x - 14 < 0$ (o.e.) |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Critical values $x = \frac{7}{2}$ and $-1$ | B1 | For both correct critical values (may be implied by correct inequality) |
| Choosing "inside" $-1 < x < \frac{7}{2}$ | M1 A1 | M1: ft their values and choose "inside" region. A1: fully correct inequality. Allow 3.5 instead of $\frac{7}{2}$. Also $\left(-1, \frac{7}{2}\right)$ scores M1A1. $x < -1, x < \frac{7}{2}$ is M0A0 |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $-1 < x < 2.8$ | B1ft | For $-1 < x < 2.8$ ignoring previous answers, or ft their answers to parts (a) and (b) provided both were regions not single values |
---3. Find the set of values of $x$ for which
\begin{enumerate}[label=(\alph*)]
\item $3 ( x - 2 ) < 8 - 2 x$
\item $( 2 x - 7 ) ( 1 + x ) < 0$
\item both $3 ( x - 2 ) < 8 - 2 x$ and $( 2 x - 7 ) ( 1 + x ) < 0$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2010 Q3 [6]}}