| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Combined linear and quadratic inequalities |
| Difficulty | Moderate -0.3 Part (i) is a routine compound linear inequality requiring simple rearrangement. Part (ii) involves rearranging to standard form, factorising a quadratic, and determining the correct inequality region—standard C1 fare but requires more steps than pure recall. Overall slightly easier than average due to straightforward algebra and no conceptual subtlety. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(-14 \leq 6y \leq -5\) | M1 | 2 equations or inequalities both dealing with all 3 terms resulting in \(a \leq 6x \leq b\), \(a \neq -9\), \(b \neq 0\) |
| \(-\frac{7}{3} \leq x \leq -\frac{5}{6}\) | A1, A1, 3 | -14 and -5 seen www |
| (ii) \(0 < x^2 - 4x - 12\) | M1 | Rearrange to collect all terms on one side |
| \((x-6)(x+2)\) | M1 | Correct method to find roots |
| \(6, -2\) seen | A1 | |
| \(x > 6, x < -2\) | M1, 5, 8 | Correct method to solve quadratic inequality i.e. x > their higher root, x < their lower root (not wrapped, strict inequalities, no 'and') |
**(i)** $-14 \leq 6y \leq -5$ | M1 | 2 equations or inequalities both dealing with all 3 terms resulting in $a \leq 6x \leq b$, $a \neq -9$, $b \neq 0$ | Do not ISW after correct answer if contradictory inequality seen.
$-\frac{7}{3} \leq x \leq -\frac{5}{6}$ | A1, A1, 3 | -14 and -5 seen www | Accept as two separate inequalities provided not linked by "or" (must be ≤) | Allow $-\frac{14}{6} \leq x \leq -\frac{5}{6}$
**(ii)** $0 < x^2 - 4x - 12$ | M1 | Rearrange to collect all terms on one side |
$(x-6)(x+2)$ | M1 | Correct method to find roots |
$6, -2$ seen | A1 | |
$x > 6, x < -2$ | M1, 5, 8 | Correct method to solve quadratic inequality i.e. x > their higher root, x < their lower root (not wrapped, strict inequalities, no 'and') | Do not ISW after correct answer if contradictory inequality seen. | e.g. for last two marks, -2 > x > 6 scores M1 A07 Solve the inequalities\\
(i) $- 9 \leqslant 6 x + 5 \leqslant 0$,\\
(ii) $6 x + 5 < x ^ { 2 } + 2 x - 7$.
\hfill \mbox{\textit{OCR C1 2011 Q7 [8]}}