Edexcel IGCSE Math B 3.K Quadratic inequalities Question Bank

Practise solving quadratic inequalities by finding boundary roots, selecting intervals and combining them with linear constraints.

Exam points

factorise a quadratic inequality and choose the interval from the sign of each factor
combine linear and quadratic conditions to give the final range of possible x values
read a range from a curve or number line, using open or closed endpoints correctly

[Maximum number: 1]

The width of a rectangle is x metres.
The length of the rectangle is 8 metres longer than the width of the rectangle.

Hence write down the range of values of x for which the area of the rectangle is greater than $20\text{ m}^2$ .

From part (b):
$x^{2}+8x-20=(x+10)(x-2)$
For the rectangle area to be greater than $20\text{ m}^{2}$ :
$x^{2}+8x>20$
so
$x^{2}+8x-20>0$
Final answer:
x>2

Marking notes:
Follow through their part (b) where the factorised form has only one positive critical value and only one region is given. Condone $x\ge2$ .

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3.K Quadratic inequalities question 1