GCSE · Inequalities

Quadratic inequalitiesExam-style questions

Why x² < 16 has TWO boundaries, how the parabola sketch decides "between" versus "outside", and why two-region answers must be written with "or" — never chained into one impossible inequality.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 4 Level 5

1
Find the set of possible values of $x$ for which

$x(x - 3) < 10 \qquad \text{and} \qquad 2x^2 + 9x < 5$

You must show all your working.

(5 marks)
Level 5 · 5 marksTry it
2
Find the set of possible values of $x$ for which

$x^2 + 2x > 24$ \qquad and \qquad $2x^2 < 7x + 30$

You must show all your working.

(5 marks)
Level 5 · 5 marksTry it
3
Solve the inequality $x^2 - 3x - 10 > 0$
Level 5 · 3 marksTry it
4
Solve the inequality $x^2 + x - 12 < 0$
Level 5 · 3 marksTry it
5
Solve the inequality $x^2 > 3x$
Level 5 · 3 marksTry it

4 more questions on quadratic inequalities

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