Key Idea: This topic solves inequalities, either from a graph or by algebra. It is on Paper 1 by hand and on Paper 2 with the GDC.
Solving inequalities
- Boundaries — Solve f(x) = g(x).
- One side — Move everything to one side. Never cross-multiply.
- Sign analysis — Use a number line through the zeros and undefined points.
- Endpoints — Include them for ≤ or ≥, never where a denominator is 0.
Quadratic shortcut
- An upward parabola is > 0 outside its roots.
- It is < 0 between its roots.
Never multiply both sides by something that might be negative.
Solve x² − x − 6 > 0. x < −2 or x > 3.
Where are the boundaries of f ≥ g? At the solutions of f = g.
Why not cross-multiply a rational inequality? The bottom might be negative, which would flip the inequality.
When is an endpoint left out? When the sign is < or >, or a denominator is 0 there.