OCR MEI C1 — Question 3 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeSolve quadratic inequality
DifficultyModerate -0.8 This is a straightforward quadratic inequality requiring factorization (or quadratic formula) followed by standard inequality reasoning with critical values. It's a routine C1 exercise with no complications, making it easier than average but not trivial since students must correctly identify the solution interval.
Spec1.02g Inequalities: linear and quadratic in single variable

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

Question 3:
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 \((5x-c)^2 \leq d\) stage); 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 for \(-0.4 < x < 6\) 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 3:

| 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 $(5x-c)^2 \leq d$ stage); 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 for $-0.4 < x < 6$ 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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3 Solve the inequality $5 x ^ { 2 } - 28 x - 12 \leqslant 0$.

\hfill \mbox{\textit{OCR MEI C1  Q3 [4]}}