Table of Contents for the Prerequisite Chapter from Sullivan’s Algebra and Trigonometry (most editions — 9th through 11th — follow this structure closely):
Chapter P: Prerequisites: Fundamental Concepts of Algebra
P.1 Real Numbers and Their Properties
- Sets of numbers (natural, integers, rational, irrational, real)
- The number line and absolute value
- Order of operations
- Properties of real numbers (commutative, associative, distributive)
P.2 Exponents and Radicals
- Rules of exponents
- Simplifying expressions with exponents
- Radicals and rational exponents
- Simplifying radical expressions
P.3 Polynomials and Operations
- Addition, subtraction, and multiplication of polynomials
- Special products (difference of squares, perfect square trinomials)
- Factoring techniques
P.4 Rational Expressions
- Simplifying rational expressions
- Multiplication and division of rational expressions
- Addition and subtraction with common denominators
- Complex fractions
P.5 Equations
- Linear equations
- Quadratic equations (factoring, completing the square, quadratic formula)
- Rational and radical equations
- Problem-solving applications
P.6 Inequalities
- Linear inequalities
- Compound inequalities
- Quadratic inequalities
- Absolute value equations and inequalities
P.7 The Coordinate Plane and Graphs
- Cartesian coordinate system
- Distance and midpoint formulas
- Graphing equations and intercepts
- Circles and basic graph shapes