Algebra

AdvancedMaths revision

Equations and Inequalities (Advanced)

Solve equations and inequalities involving absolute values, rational expressions and polynomial structure.

Open calculator

Focus points

✓Solve non-linear equations.

✓Analyse sign intervals.

✓Check domain restrictions.

orin

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions

Question 1FluencyCore

Original practice · Free Online Revision

Skill · absolute value equation

Solve |2x−5|=9.

Question 2FluencyCore

Original practice · Free Online Revision

Skill · absolute inequality

Solve |x+1|<4.

Question 3FluencyCore

Original practice · Free Online Revision

Skill · quadratic inequality

Solve x²−5x+4 ≤ 0.

Question 4FluencyCore

Original practice · Free Online Revision

Skill · rational inequality

Solve (x−2)/(x+1) > 0.

Question 5FluencyCore

Original practice · Free Online Revision

Skill · radical equation

Solve √(x+5)=x−1.

Question 6FluencyCore

Original practice · Free Online Revision

Skill · reducible equation

Solve x⁴−5x²+4=0.

Question 7ReasoningCore

Original practice · Free Online Revision

Skill · solution checking

Explain why squaring both sides of an equation can introduce extraneous solutions.

Question 8ChallengeStretch

Original practice · Free Online Revision

Skill · piecewise inequality

Find all real x satisfying |x−2| ≥ x+4.