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
Solve $x^2 - 3x - 4 \le 0$ (4 marks)
Level 4 · 4 marksTry it
2
Solve $x^2 - 5x - 14 > 0$ (4 marks)
Level 4 · 4 marksTry it
3
Solve $(2x + 7)(4x - 3) < 0$

(2 marks)
Level 4 · 2 marksTry it
4
Solve the inequality $x^2 \le 16$
Level 4 · 2 marksTry it
5
$n$ is an integer and $n^2 < 30$

(a) Write down the greatest possible value of $n$ .

(b) Write down the least possible value of $n$ .
Level 4 · 3 marksTry it

1 more question on quadratic inequalities

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