| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Quadratic inequality solving |
| Difficulty | Easy -1.2 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 parts are standard textbook exercises with no problem-solving or novel insight required, making it easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| \(eg\ 3x^2 - 21x + 2x - 14\) | M1 | Any valid attempt at factorisation, three out of four terms correct or signs opposite |
| \((3x + 2)(x - 7)\) | A1 | isw after factorisation; solutions to eq=0 if no factorisation M0A0; accept \(3(x+\frac{2}{3})(x-7)\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(-\frac{2}{3}\) and \(7\) identified | M1FT | FT from part(a) |
| \(-\frac{2}{3} < x < 7\) | A1FT | accept \(x<7 \cap x>-\frac{2}{3}\) or '\(x<7\) and \(x>-\frac{2}{3}\)'; Not \(\leq\) or \(\geq\) |
## Question 2(a):
$eg\ 3x^2 - 21x + 2x - 14$ | **M1** | Any valid attempt at factorisation, three out of four terms correct or signs opposite
$(3x + 2)(x - 7)$ | **A1** | isw after factorisation; solutions to eq=0 if no factorisation M0A0; accept $3(x+\frac{2}{3})(x-7)$
## Question 2(b):
$-\frac{2}{3}$ and $7$ identified | **M1FT** | FT from part(a)
$-\frac{2}{3} < x < 7$ | **A1FT** | accept $x<7 \cap x>-\frac{2}{3}$ or '$x<7$ and $x>-\frac{2}{3}$'; Not $\leq$ or $\geq$
---2
\begin{enumerate}[label=(\alph*)]
\item Factorise $3 x ^ { 2 } - 19 x - 14$.
\item Solve the inequality $3 x ^ { 2 } - 19 x - 14 < 0$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2022 Q2 [4]}}