| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Easy -1.2 This is a straightforward two-part inequality question testing basic skills: (a) requires simple linear inequality manipulation, and (b) requires factorising or using the quadratic formula then identifying the correct region. Both are standard textbook exercises with no problem-solving insight required, making this easier than average for A-level. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(6x + x > 1 - 8\) | M1 | Attempts to expand the bracket and collect \(x\) terms on one side and constant terms on the other. Condone sign errors and allow one error in expanding the bracket. Allow \(<, \leq, \geq, =\) instead of \(>\). |
| \(x > -1\) | A1 | Cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((x+3)(3x-1)[=0] \Rightarrow x = -3\) and \(\frac{1}{3}\) | M1A1 | M1: Attempt to solve the quadratic to obtain two critical values. A1: \(x = -3\) and \(\frac{1}{3}\) (may be implied by their inequality). Allow all equivalent fractions for \(-3\) and \(1/3\). (Allow \(0.333\) for \(1/3\)) |
| \(-3 < x < \frac{1}{3}\) | M1A1ft | M1: Chooses "inside" region (letter \(x\) does not need to be used). A1ft: Allow \(x < \frac{1}{3}\) and \(x > -3\) or \(\left(-3, \frac{1}{3}\right)\) or \(x < \frac{1}{3} \cap x > -3\). Follow through their critical values (must be in terms of \(x\)). Both \((x < \frac{1}{3}\) or \(x > -3)\) and \((x < \frac{1}{3},\ x > -3)\) as a final answer score A0. |
## Question 5:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $6x + x > 1 - 8$ | M1 | Attempts to expand the bracket and collect $x$ terms on one side and constant terms on the other. Condone sign errors and allow one error in expanding the bracket. Allow $<, \leq, \geq, =$ instead of $>$. |
| $x > -1$ | A1 | Cao |
**Total: (2)**
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(x+3)(3x-1)[=0] \Rightarrow x = -3$ and $\frac{1}{3}$ | M1A1 | M1: Attempt to solve the quadratic to obtain two critical values. A1: $x = -3$ **and** $\frac{1}{3}$ (may be implied by their inequality). Allow all equivalent fractions for $-3$ and $1/3$. (Allow $0.333$ for $1/3$) |
| $-3 < x < \frac{1}{3}$ | M1A1ft | M1: Chooses "inside" region (letter $x$ does not need to be used). A1ft: Allow $x < \frac{1}{3}$ **and** $x > -3$ or $\left(-3, \frac{1}{3}\right)$ or $x < \frac{1}{3} \cap x > -3$. Follow through their critical values (must be in terms of $x$). Both $(x < \frac{1}{3}$ **or** $x > -3)$ and $(x < \frac{1}{3},\ x > -3)$ as a final answer score A0. |
**Total: (4) [6]**
---5. Find the set of values of $x$ for which
\begin{enumerate}[label=(\alph*)]
\item $2 ( 3 x + 4 ) > 1 - x$
\item $3 x ^ { 2 } + 8 x - 3 < 0$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2013 Q5 [6]}}