Solve linear and quadratic equations using various algebraic methods (factorisation, completing the square, quadratic formula).
Understand and use the discriminant of a quadratic equation to determine the nature and number of its real roots.
Interpret the roots, intercepts, and turning points of quadratic functions graphically.
Solve simultaneous equations involving two unknowns (linear/linear and linear/quadratic systems) algebraically and understand their graphical interpretation.
Solve equations involving absolute values by considering cases or graphical methods.
Solve irrational equations (containing square roots) by appropriate manipulation, ensuring to check for extraneous solutions.
Solve some higher-order polynomial equations that are reducible to quadratic form or can be factorised.