Precalculus
Functions and Graphs
Domain and Range
Function Notation
Types of Functions: Linear, Quadratic, Polynomial, Rational, Exponential, Logarithmic, Piecewise
Transformations of Functions: Shifts, Reflections, Stretching, and Shrinking
Inverse Functions
Composition of Functions
Polynomial Functions
Degree and Leading Coefficient
Roots/Zeros of Polynomials
Factoring Polynomials
Rational Root Theorem
Descartes' Rule of Signs
Synthetic Division
Rational Functions
Simplifying Rational Expressions
Asymptotes: Vertical, Horizontal, and Oblique
Analyzing Graphs of Rational Functions
Exponential and Logarithmic Functions
Properties of Exponents
Exponential Growth and Decay
Logarithmic Functions and Properties
Change of Base Formula
Solving Exponential and Logarithmic Equations
Trigonometry
Unit Circle and Radian Measure
Trigonometric Functions: Sine, Cosine, Tangent, etc.
Graphs of Trigonometric Functions
Trigonometric Identities: Pythagorean, Reciprocal, Quotient
Inverse Trigonometric Functions
Solving Trigonometric Equations
Angles and their Measurement
Degrees vs. Radians
Converting between Degrees and Radians
Reference Angles
Coterminal Angles
Law of Sines and Cosines
Solving Triangles: SSA, AAS, and SAS cases
Area of a Triangle
Heron's Formula
Sequences and Series
Arithmetic Sequences and Series
Geometric Sequences and Series
Recursive Sequences
Sigma Notation
Convergence and Divergence of Series
Matrices and Determinants
Matrix Operations: Addition, Subtraction, Multiplication
Inverse of a Matrix
Determinants and Cramer's Rule
Conic Sections
Parabolas, Circles, Ellipses, and Hyperbolas
Equations and Graphs of Conic Sections
Focus and Directrix of Parabolas
Vectors
Vector Operations: Addition, Scalar Multiplication
Dot Product
Magnitude and Direction of a Vector
Applications of Vectors
Complex Numbers
Imaginary and Real Parts
Operations with Complex Numbers
Polar Form of Complex Numbers
De Moivre’s Theorem
Limits and Continuity (Introduction to Calculus)
Concept of a Limit
Continuity of Functions
Left-hand and Right-hand Limits
