OCR C1 2005 June — Question 1 4 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2005
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeSolve quadratic inequality
DifficultyModerate -0.8 This is a straightforward quadratic inequality requiring factorisation to (x-10)(x+4)≥0, identifying critical values, and determining solution regions. It's a standard C1 exercise with routine technique and no complications, making it easier than average but not trivial since students must correctly interpret the inequality sign and solution regions.
Spec1.02f Solve quadratic equations: including in a function of unknown1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation
1 Solve the inequality \(x ^ { 2 } - 6 x - 40 \geqslant 0\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(x^2 - 6x - 40 \geq 0\)
\((x+4)(x-10) \geq 0\)M1 Correct method to find roots
\(-4, 10\)A1
[sketch of positive quadratic]M1 Correct method to solve quadratic inequality e.g. +ve quadratic graph
\(x \leq -4, \quad x \geq 10\)A1 4 Not wrapped, not strict inequalities, no 'and' 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $x^2 - 6x - 40 \geq 0$ | | |
| $(x+4)(x-10) \geq 0$ | M1 | Correct method to find roots |
| $-4, 10$ | A1 | |
| [sketch of positive quadratic] | M1 | Correct method to solve quadratic inequality e.g. +ve quadratic graph |
| $x \leq -4, \quad x \geq 10$ | A1 **4** | Not wrapped, not strict inequalities, no 'and' |

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1 Solve the inequality $x ^ { 2 } - 6 x - 40 \geqslant 0$.

\hfill \mbox{\textit{OCR C1 2005 Q1 [4]}}
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