Solving Inequalities (AQA GCSE Further Maths): Exam Questions

Work out the integer values of $x$ for which $x^2-20x+96<0$

Work out the range of values of $x$ for which $25x^2\ge 16$

Work out the range of values of $x$ for which

$x^2–11x+28>0$

You must show your working.

Work out the range of values of $m$ for which

$3m\left(4m+1\right)\le 5m+2$

You must show your working.

The graph of $y=\left(4-x\right)\left(1+x\right)$ is shown below.

Use this graph to work out the range of values of $x$ for which

$4+3x<x^2$

A small stone is kicked off the ground and flies through the air.

The vertical movement of the stone is given by the equation

$h=12t-5t^2$

where $h$ is the vertical height of the stone above the ground (in metres) and $t$ is the time after being kicked (in seconds).

By forming and solving a suitable inequality, find the range of time, $t$, for which the stone is above a vertical height of 4 metres.

A rectangular picture frame has a height of $x$ cm and a width of $y$ cm.

The total perimeter of the frame is 120 cm.

If the area of the frame must be less than 800 cm², form and solve an inequality in terms of $x$ to find the range of values the height can take.

Work out the range of values of $p$ for which

${\left(p+2\right)}^3\ge 17+p\left(p+\sqrt{3}\right)\left(p-\sqrt{3}\right)$