Question 2 - A-Level Maths

Edexcel FP2 2013 June — Question 2 7 marks

Exam Board	Edexcel
Module	FP2 (Further Pure Mathematics 2)
Year	2013
Session	June
Marks	7
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Inequalities
Type	Rational inequality algebraically
Difficulty	Standard +0.3 This is a standard rational inequality requiring algebraic manipulation: bringing terms to one side, finding a common denominator, identifying critical points from numerator and denominator, and testing intervals. While it's FP2, this is a routine technique that stronger students practice extensively, making it slightly easier than average overall.
Spec	1.02g Inequalities: linear and quadratic in single variable

2. Use algebra to find the set of values of $x$ for which $$\frac { 6 x } { 3 - x } > \frac { 1 } { x + 1 }$$

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Question 2:

Answer	Marks	Guidance
Answer/Working	Mark	Guidance
$\frac{6x}{3-x} > \frac{1}{x+1}$
$6x(3-x)(x+1)^2 - (3-x)^2(x+1) > 0$	M1	For multiplying through by $(x+1)^2(3-x)^2$ OR collecting one side and forming single fraction
$(3-x)(x+1)(6x^2+6x-3+x) > 0$
$(3-x)(x+1)(3x-1)(2x+3) > 0$	M1dep	For factorising the quadratic; dependent on first M mark
Critical values $3, -1$	B1
$-\frac{3}{2}, \frac{1}{3}$	A1, A1
$-\frac{3}{2} < x < -1 \quad \frac{1}{3} < x < 3$	M1A1cso	Using all 4 critical values to obtain both ranges

Total: 7 Marks

# Question 2:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{6x}{3-x} > \frac{1}{x+1}$ | | |
| $6x(3-x)(x+1)^2 - (3-x)^2(x+1) > 0$ | M1 | For multiplying through by $(x+1)^2(3-x)^2$ **OR** collecting one side and forming single fraction |
| $(3-x)(x+1)(6x^2+6x-3+x) > 0$ | | |
| $(3-x)(x+1)(3x-1)(2x+3) > 0$ | M1dep | For factorising the quadratic; dependent on first M mark |
| Critical values $3, -1$ | B1 | |
| $-\frac{3}{2}, \frac{1}{3}$ | A1, A1 | |
| $-\frac{3}{2} < x < -1 \quad \frac{1}{3} < x < 3$ | M1A1cso | Using all 4 critical values to obtain both ranges |

**Total: 7 Marks**

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2. Use algebra to find the set of values of $x$ for which

$$\frac { 6 x } { 3 - x } > \frac { 1 } { x + 1 }$$

\hfill \mbox{\textit{Edexcel FP2 2013 Q2 [7]}}

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Q1 4 Q2 7 Q3 8 Q4 9 Q5 10 Q6 11 Q7 13 Q8 13