Inequalities

The diagram shows a trapezium. All lengths are in centimetres.

The area of the trapezium is less than 22cm²

Work out the greatest possible range of values of x. Give your answer in the form m x n where m and n are both positive numbers.

A garden patio is made from two rectangles. All lengths are in metres.

The area of the patio is less than 51m²

Work out the range of possible values of x. Give your answer in the form a x b where a and b are both integers. You must show your working.

2 5n² + 2 38

Work out all the possible integer values of n.

Here is a sketch of the curve y = ax² + bx + c where a, b and c are constants. The curve intersects the x-axis at (– 4, 0) and (p, 0) The turning point has x-coordinate 0.5

Work out the value of p.

Solve ax² + bx + c 0

A quadratic sequence starts – 2 – 1 4 13

Work out an expression for the n th term.

A different quadratic sequence has nth term n² + 10n

Use an algebraic method to work out how many terms in the sequence are less than 2000 Do not use trial and improvement. You must show your working.

Work out all the negative integer values of x for which 3x² 48

Solve 2x² + 4 (2x – 3)(x + 1)