| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Quadratic inequality solving |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring factorisation of a quadratic (routine technique) followed by solving a quadratic inequality using the factored form. Both are standard C1 skills with no problem-solving insight required, making it easier than average but not trivial since students must correctly identify the solution interval from the inequality. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| 2(a) | \((x-1)(2x-3)\) | B1 |
| 2(b) | Critical values are \(1, 1\frac{1}{2}\) | B1 |
| Sign diagram or sketch | M1 | |
| \(\Rightarrow 1 < x < 1\frac{1}{2}\) | A1 | Full marks for correct inequality without working |
**2(a)** | $(x-1)(2x-3)$ | B1 | (1 - x)(3 - 2x) or $2(x-1)(x-1.5)$ etc
**2(b)** | Critical values are $1, 1\frac{1}{2}$ | B1 | Correct or ft their factors from (a)
| Sign diagram or sketch | M1 |
| $\Rightarrow 1 < x < 1\frac{1}{2}$ | A1 | Full marks for correct inequality without working
**Total: 4 marks**
---2
\begin{enumerate}[label=(\alph*)]
\item Factorise $2 x ^ { 2 } - 5 x + 3$.
\item Hence, or otherwise, solve the inequality $2 x ^ { 2 } - 5 x + 3 < 0$.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2009 Q2 [4]}}