Pearson Edexcel IAL Mathematics FP2.1 Inequalities Question Bank

Practise solving FP2 inequalities algebraically, including modulus and rational forms where graphical or numerical-only solutions are not accepted.

Exam points

split modulus inequalities into algebraic cases and combine the valid intervals
use critical values from zeros and undefined points to solve rational inequalities

Covered syllabus points

FP2.1.1 - Manipulation and solution

[Maximum number: 6]

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Use algebra to determine the values of x for which

\frac{x+1}{(x-3)(x+2)}\le 1-\frac{2}{x-3}

Critical values from the denominator are x=-2 and x=3.

Equating the two sides:

\frac{x+1}{(x-3)(x+2)}=1-\frac{2}{x-3}

x+1=x^2-x-6-2(x+2)

x^2-4x-11=0.

x=\frac{4\pm\sqrt{16+44}}{2}=2\pm\sqrt{15}

Therefore

x<-2,\qquad 2-\sqrt{15}\le x<3,\qquad x\ge 2+\sqrt{15}

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Covered syllabus points

FP2.1 - Inequalities question 1