Equations and Inequalities
Relations and Introduction to Functions
Linear Relations and Functions
Systems of Equations and Inequalities
Matrices
- Basic matrix operations
- Matrix multiplication
- All matrix operations combined
- Determinants
- Matrix inverses
- Cramer’s rule
- Matrix equations
- Geometric transformations with matrices
Complex Numbers
Quadratic Functions and Inequalities
- Properties of parabolas
- Vertex form
- Graphing quadratic inequalities
- Factoring quadratic expressions
- Solving quadratic equations w/ square roots
- Solving quadratic equations by factoring
- Completing the square
- Solving equations by completing the square
- Solving equations with the quadratic formula
- The discriminant
Polynomial Functions
- Naming and simple operations
- Factoring a sum/difference of cubes
- Factoring by grouping
- Factoring quadratic form
- Factoring using all techniques
- Factors and Zeros
- The Remainder Theorem
- Irrational and Imaginary Root Theorems
- Descartes’ Rule of Signs
- More on factors, zeros, and dividing
- The Rational Root Theorem
- Polynomial equations
- Basic shape of graphs of polynomials
- Graphing polynomial functions
- The Binomial Theorem
General Functions
Radical Functions and Rational Exponents
Conic Sections
Rational Expressions
Exponential and Logarithmic Functions
- The meaning of logarithms
- Properties of logarithms
- The change of base formula
- Writing logs in terms of others
- Logarithmic equations
- Inverse functions and logarithms
- Exponential equations not requiring logarithms
- Exponential equations requiring logarithms
- Graphing logarithms
- Graphing exponential functions
- Discrete exponential growth and decay word problems
- Continuous exponential growth and decay word problems
Sequences and Series
Trigonometry
- Right triangle trig: Evaluating ratios
- Right triangle trig: Missing sides/angles
- Angles and angle measure
- Co-terminal angles and reference angles
- Arc length and sector area
- Trig ratios of general angles
- Exact trig ratios of important angles
- The Law of Sines
- The Law of Cosines
- Graphing trig functions
- Translating trig functions
- Angle Sum/Difference Identities
- Double-/Half-Angle Identities