Algebra & Functions

Order of operations and the factoring identities you should recognize on sight.

Solving single-variable equations and reading inequality solutions as intervals.

Piecewise reasoning and distance interpretations for absolute value equations.

The quadratic formula, discriminant, vertex form, and completing the square.

Remainder and factor theorems, and Vieta's formulas for roots and coefficients.

Domain restrictions, simplifying, and catching extraneous solutions.

Rational exponent rules and rationalizing techniques for radical equations.

Substitution, elimination, and symmetric-structure tricks for solving systems.

Sign charts and the AM-GM inequality for bounding and optimizing expressions.

Arithmetic and geometric progressions, and telescoping sums.

Substitution strategies for pinning down an unknown function.

Matching bases and log properties for exponential and logarithmic equations.

Operations on a + bi, conjugates, and complex roots of quadratics.

Using the discriminant to reason about how many solutions an equation has.