GCSE · Inequalities

Inequalities as regions on a graphExam-style questions

Why an inequality in x and y claims a HALF-PLANE, why testing one point settles which side, and how several inequalities carve out a region together.

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

DifficultyAll Level 3 Level 4 Level 5

1
A region is defined by the three inequalities

$x \ge 1, \qquad y \le x + 1, \qquad x + y < 8$

The point $(a, 3)$ lies in the region, where $a$ is an integer.

Find all the possible values of $a$ .
Level 5 · 3 marksTry it
2
A region is defined by the three inequalities

$y \ge 1, \qquad y < 2x + 1, \qquad x + y \le 7$

The point $(2, b)$ , where $b$ is an integer, lies in the region.

Write down all the possible values of $b$ .
Level 5 · 3 marksTry it