| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic inequality manipulation and standard quadratic inequality solving. Part (a) is linear algebra requiring simple expansion and collection of terms. Part (b) requires factorising a quadratic and determining sign regions, which is routine bookwork with no problem-solving insight needed. Both parts are below average difficulty for A-level. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| \(8 - 6x > 5 - 4x - 8\) | M1 | multiplying out correctly and \(>\) sign used |
| \(11 > 2x\) | ||
| \(x < 5\frac{1}{2}\) (or \(x < \frac{11}{2}\)) | A1 also | accept 5.5 \(>\) \(x\) OE |
| Answer | Marks | Guidance |
|---|---|---|
| \(2x^2 + 5x - 12 \geq 0\) | ||
| \((x+4)(2x-3)\) | M1 | correct factors |
| (or roots unsimplified) \(\frac{-5 \pm \sqrt{121}}{4}\) | ||
| Critical values are \(-4\) and \(\frac{3}{2}\) | A1 | both CVs correct; condone \(\frac{6}{4}, -\frac{16}{4}\) etc here but must be single fractions |
| M1 | sketch or sign diagram including values | |
| \(x \leq -4, x \geq \frac{3}{2}\) | A1 | fractions must be simplified |
| take their final line as their answer | condone use of OR but not AND |
**7(a)**
$8 - 6x > 5 - 4x - 8$ | M1 | multiplying out correctly and $>$ sign used
$11 > 2x$ | |
$x < 5\frac{1}{2}$ (or $x < \frac{11}{2}$) | A1 also | accept 5.5 $>$ $x$ OE
**7(b)**
$2x^2 + 5x - 12 \geq 0$ | |
$(x+4)(2x-3)$ | M1 | correct factors
| | (or roots unsimplified) $\frac{-5 \pm \sqrt{121}}{4}$
Critical values are $-4$ and $\frac{3}{2}$ | A1 | both CVs correct; condone $\frac{6}{4}, -\frac{16}{4}$ etc here but must be single fractions
| M1 | sketch or sign diagram including values
$x \leq -4, x \geq \frac{3}{2}$ | A1 | fractions must be simplified
take their final line as their answer | | condone use of OR but not AND
---7 Solve each of the following inequalities:
\begin{enumerate}[label=(\alph*)]
\item $\quad 2 ( 4 - 3 x ) > 5 - 4 ( x + 2 )$;
\item $\quad 2 x ^ { 2 } + 5 x \geqslant 12$.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2011 Q7 [6]}}