| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic inequality manipulation and factorising a simple quadratic. Part (a) requires only linear algebra (expanding brackets, collecting terms), and part (b) is a standard quadratic inequality requiring factorisation of x²-x-6 into (x-3)(x+2) and identifying the negative region. Both are routine textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(3x - 3 > 3 - 5x - 30\) | M1 | Multiplying out (condone one slip) |
| \(\Rightarrow 8x > -24\) | A1 | Or correct equivalent e.g. \(-8x < 24\) |
| \(\Rightarrow x > -3\) | A1 | (Penalise \(\leqslant\), \(\geqslant\) once only in (a) and (b)) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(x^2 - x - 6 = (x-3)(x+2)\) | M1 | Attempt to use quad formula or factorise |
| (critical points are) \(3\) and \(-2\) | A1 | May be seen in diagram or solution |
| Sketch or sign diagram | M1 | |
| \(2 < x < 3\) | A1 |
## Question 7:
**Part (a)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $3x - 3 > 3 - 5x - 30$ | M1 | Multiplying out (condone one slip) |
| $\Rightarrow 8x > -24$ | A1 | Or correct equivalent e.g. $-8x < 24$ |
| $\Rightarrow x > -3$ | A1 | (Penalise $\leqslant$, $\geqslant$ once only in (a) and (b)) |
**Part (b)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $x^2 - x - 6 = (x-3)(x+2)$ | M1 | Attempt to use quad formula or factorise |
| (critical points are) $3$ and $-2$ | A1 | May be seen in diagram or solution |
| Sketch or sign diagram | M1 | |
| $2 < x < 3$ | A1 | |
**Total: 7 marks**
---7 Solve each of the following inequalities:
\begin{enumerate}[label=(\alph*)]
\item $3 ( x - 1 ) > 3 - 5 ( x + 6 )$;
\item $\quad x ^ { 2 } - x - 6 < 0$.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2005 Q7 [7]}}