| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 7 |
| 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 routine manipulation of linear and quadratic inequalities. Part (a) requires simple rearrangement, part (b) involves factorising a quadratic and applying standard inequality rules, and part (c) combines the results using set intersection. All techniques are standard textbook exercises with no problem-solving insight required, making it easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5x > 10,\ x > 2\) | M1, A1 | M1 for collecting like terms leading to \(ax>b\), \(ax |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((2x+3)(x-4)=0\), critical values \(-\dfrac{3}{2}\) and \(4\) | M1, A1 | M1 for attempt to factorise/solve giving potentially 2 critical values; A1 for \(-\frac{3}{2}\) and 4. May write \(x<-\frac{3}{2}\), \(x<4\) and still get A1 |
| \(-\dfrac{3}{2} < x < 4\) | M1 A1ft | 2nd M1 for choosing "inside region"; A1ft follow through their 2 distinct critical values. \(x\in(-\frac{3}{2},4)\) is M1A1; \(x\in[-\frac{3}{2},4]\) is M1A0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2 < x < 4\) | B1ft | Allow if correct answer seen or follow through from (a) and (b) — both must be regions. Empty set accept \(\varnothing\) or \(\{\}\). Use of \(\leq\) instead of \(<\) loses one accuracy mark at first occurrence |
# Question 4:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5x > 10,\ x > 2$ | M1, A1 | M1 for collecting like terms leading to $ax>b$, $ax<b$, or $ax=b$. Must have $a$ or $b$ correct. Condone $x>\frac{10}{2}=2$ for M1A1 |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(2x+3)(x-4)=0$, critical values $-\dfrac{3}{2}$ and $4$ | M1, A1 | M1 for attempt to factorise/solve giving potentially 2 critical values; A1 for $-\frac{3}{2}$ and 4. May write $x<-\frac{3}{2}$, $x<4$ and still get A1 |
| $-\dfrac{3}{2} < x < 4$ | M1 A1ft | 2nd M1 for choosing "inside region"; A1ft follow through their 2 distinct critical values. $x\in(-\frac{3}{2},4)$ is M1A1; $x\in[-\frac{3}{2},4]$ is M1A0 |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2 < x < 4$ | B1ft | Allow if correct answer seen or follow through from (a) and (b) — both must be regions. Empty set accept $\varnothing$ or $\{\}$. Use of $\leq$ instead of $<$ loses one accuracy mark at first occurrence |
---4. Find the set of values of $x$ for which
\begin{enumerate}[label=(\alph*)]
\item $4 x - 3 > 7 - x$
\item $2 x ^ { 2 } - 5 x - 12 < 0$
\item both $4 x - 3 > 7 - x$ and $2 x ^ { 2 } - 5 x - 12 < 0$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2009 Q4 [7]}}