OCR MEI FP1 2011 June — Question 4 6 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeRational inequality algebraically
DifficultyStandard +0.3 This is a straightforward rational inequality requiring rearrangement to standard form, finding critical points by solving a quadratic, and testing intervals. While it's from FP1, the technique is routine: move everything to one side, combine fractions, solve the numerator equation, and check signs. Slightly above average due to being Further Maths content, but mechanically standard.
Spec1.02g Inequalities: linear and quadratic in single variable1.02k Simplify rational expressions: factorising, cancelling, algebraic division
4 Solve the inequality \(\frac { 5 x } { x ^ { 2 } + 4 } < x\).
Question 4:
AnswerMarks Guidance
AnswerMark Guidance
\(\frac{5x}{x^2+4} < x \Rightarrow 5x < x^3 + 4x\)M1* Method attempted towards factorisation to find critical values
\(\Rightarrow 0 < x^3 - x\)A1 \(x = 0\)
\(\Rightarrow 0 < x(x+1)(x-1)\)A1 \(x = 1, x = -1\)
\(\Rightarrow x > 1,\ -1 < x < 0\)M1dep* Valid method leading to required intervals, graphical or algebraic
A1\(x > 1\)
A1\(-1 < x < 0\)
[6]SC B2 No valid working seen: \(x>1\), \(-1 
# Question 4:

| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{5x}{x^2+4} < x \Rightarrow 5x < x^3 + 4x$ | M1* | Method attempted towards factorisation to find critical values |
| $\Rightarrow 0 < x^3 - x$ | A1 | $x = 0$ |
| $\Rightarrow 0 < x(x+1)(x-1)$ | A1 | $x = 1, x = -1$ |
| $\Rightarrow x > 1,\ -1 < x < 0$ | M1dep* | Valid method leading to required intervals, graphical or algebraic |
| | A1 | $x > 1$ |
| | A1 | $-1 < x < 0$ |
| | **[6]** | SC B2 No valid working seen: $x>1$, $-1<x<0$ |

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4 Solve the inequality $\frac { 5 x } { x ^ { 2 } + 4 } < x$.

\hfill \mbox{\textit{OCR MEI FP1 2011 Q4 [6]}}
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Q1 5 Q2 8 Q3 5 Q4 6 Q5 5 Q6 7 Q7 12 Q8 11 Q9 13