Quadratic Inequalities worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 33 marks Sheet 1

2 marks
\(x^2 {bb:coefsigned}x {cc:+} \lt 0\)

Is \(x = {vv}\) a solution of this inequality?

You must show your working.
4 marks
The graph of \(y = x^2 - 6x + 5\) is drawn on the grid.

(a)
Use the graph to solve \(x^2 - 6x + 5 < 0\)

(b)
Use the graph to solve \(x^2 - 6x + 5 > 0\)
3 marks
Solve \(4x^2 \gt 64\)
3 marks
\(x^2 -x - 6 < 0\)

Find the set of values of \(x\) for which this is true.
3 marks
\(x^2 + 8x + 15 \geq 0\)

Find the set of values of \(x\) for which this is true.
3 marks
List all the integers that satisfy \(x^2 + 8x + 7 \leq 0\)
4 marks
Solve the inequality \(x^2 > -5x + 14\)
3 marks
The solution of the inequality

\(x^2 + bx + c < 0\)

is \(-8 < x < -1\).

Calculate the value of \(b\) and the value of \(c\).
4 marks
\(x(x + 1) \gt 12\)

Find the set of values of \(x\) for which this is true.
4 marks
\(4x^2 -x - 3 \leq 0\)

Find the set of values of \(x\) for which this is true.

Answers

{verdict}. When \(x = {vv}\) the expression is equal to \({val}\), which is {sizeword} zero.
(a) \(1 < x < 5\)
(b) \(x < 1\) or \(x > 5\)
\(x \lt -4\) or \(x \gt 4\)
\(-2 < x < 3\)
\(x \leq -5\) or \(x \geq -3\)
\(-7,\ -6,\ -5,\ -4,\ -3,\ -2,\ -1\)
\(x < -7\) or \(x > 2\)
\(b = 9\) and \(c = 8\)
\(x \lt -4\) or \(x \gt 3\)
\(-\frac{3}{4} \leq x \leq 1\)