OCR MEI C1 2013 January — Question 4 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2013
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeSolve quadratic inequality
DifficultyModerate -0.8 This is a straightforward quadratic inequality requiring factorisation (or quadratic formula), finding roots, and sketching a parabola to determine the solution set. It's a standard C1 exercise with routine steps and no complications, making it easier than average but not trivial since it requires correct execution of multiple steps.
Spec1.02g Inequalities: linear and quadratic in single variable

4 Solve the inequality \(5 x ^ { 2 } - 28 x - 12 \leqslant 0\).

Question 4:
AnswerMarks Guidance
AnswerMarks Guidance
\((5x+2)(x-6)\)M1 For factors giving at least two out of three terms correct when expanded and collected. Or use of formula or completing the square with at most one error (comp square must reach \([5](x-a)^2 \leq b\) or \((5x-c)^2 \leq d\)); if correct: \(5(x-2.8)^2 \leq 51.2\) or \((x-2.8)^2 \leq 10.24\) or \((5x-14)^2 \leq 256\)
Boundary values \(-0.4\) oe and \(6\) soiA1 A0 for just \(\frac{28 \pm \sqrt{1024}}{10}\)
\(-0.4 \leq x \leq 6\) oeA2 May be separate inequalities; mark final answer. A1 for one end correct e.g. \(x \leq 6\) or \(-0.4 < x < 6\) oe. Or B1 for \(a \leq x \leq b\) ft their boundary values. Condone unsimplified but correct \(\frac{28-\sqrt{1024}}{10} \leq x \leq \frac{28+\sqrt{1024}}{10}\); allow A1 for \(-0.4 \leq 0 \leq 6\). Condone errors in inequality signs during working towards final answer
[4]
## Question 4:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $(5x+2)(x-6)$ | M1 | For factors giving at least two out of three terms correct when expanded and collected. Or use of formula or completing the square with at most one error (comp square must reach $[5](x-a)^2 \leq b$ or $(5x-c)^2 \leq d$); if correct: $5(x-2.8)^2 \leq 51.2$ or $(x-2.8)^2 \leq 10.24$ or $(5x-14)^2 \leq 256$ |
| Boundary values $-0.4$ oe and $6$ soi | A1 | A0 for just $\frac{28 \pm \sqrt{1024}}{10}$ |
| $-0.4 \leq x \leq 6$ oe | A2 | May be separate inequalities; mark final answer. A1 for one end correct e.g. $x \leq 6$ or $-0.4 < x < 6$ oe. Or B1 for $a \leq x \leq b$ ft their boundary values. Condone unsimplified but correct $\frac{28-\sqrt{1024}}{10} \leq x \leq \frac{28+\sqrt{1024}}{10}$; allow A1 for $-0.4 \leq 0 \leq 6$. Condone errors in inequality signs during working towards final answer |
| **[4]** | | |

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4 Solve the inequality $5 x ^ { 2 } - 28 x - 12 \leqslant 0$.

\hfill \mbox{\textit{OCR MEI C1 2013 Q4 [4]}}