# Online Precalculus Tutoring Topics

## Functions and Their Graphs

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions: Composite Functions

Inverse Functions

Mathematical Modeling and Variation

## Exponential and Logarithmic Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

## Polynomial and Rational Functions

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

## Exponential and Logarithmic Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions: Composite Functions

Inverse Functions

Mathematical Modeling and Variation

## Trigonometry

Trigonometric Functions: The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

## Systems of Equations and Inequalities

Linear and Nonlinear Systems of Equations

Two-Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

## Analytic Trigonometry

Using Fundamental Identities

Verifying Trigonometric Identities

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple-Angle and Product-to-Sum Formulas

## Matrices and Determinants

Matrices and Systems of Equations

Operations with Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

## Topics in Analytic Geometry

Linear Programming

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics: Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Graphs of Polar Equations

Polar Equations of Conics

## Analytic Geometry in Three Dimensions

The Three-Dimensional Coordinate System

Vectors in Space

The Cross Product of Two Vectors

Lines and Planes in Space

## Limits and an Introduction to Calculus

Introduction to Limits

Techniques for Evaluating Limits

The Tangent Line Problem

Limits at Infinity and Limits of Sequences

The Area Problem

## Review of Fundamental Concepts of Algebra

Real Numbers and Their Properties

Polynomials and Factoring

Rational Expressions

Solving Equations

Linear Inequalities in One Variable

Errors and the Algebra of Calculus

## Concepts in Statistics

Representing Data

Measures of Central Tendency and Dispersion

Least Squares Regression