Chapter 1: Fundamentals
Chapter 1 builds the algebraic foundation for everything that follows. Real numbers, exponents, radicals, algebraic expressions, equations, inequalities, and coordinate geometry — the bedrock skills you use constantly in every later chapter.
Textbook alignment
Sections
1.1Real Numbers
Real numbers include everything on the number line: integers, fractions, and irrational numbers like π and √2. This section reviews the types of real numbers, their properties, and interval notation for describing sets of numbers.
1.2Exponents and Radicals
Exponent rules let you simplify expressions with powers efficiently. Radicals are just fractional exponents in disguise. These rules appear constantly in algebra, trig, and calculus.
1.3Algebraic Expressions
Polynomials, FOIL, factoring, and special products — the core of algebra. Being fast and accurate with these operations is a prerequisite for everything from solving equations to calculus.
1.4Rational Expressions
A rational expression is a fraction where the numerator and denominator are polynomials. The operations (simplify, multiply, divide, add, subtract) follow the same rules as fractions with numbers.
1.5Equations
Solving equations — linear, quadratic, and beyond — is the core skill of algebra. This section covers the main solving strategies: isolating the variable, factoring, quadratic formula, and radical equations.
1.6Modeling with Equations
Setting up equations from word problems is a skill unto itself. This section develops a systematic approach: define variables, write the equation, solve, and check that the answer makes sense in context.
1.7Inequalities
Inequalities find ranges of values that satisfy a condition — not just exact answers. The key rule: when you multiply or divide both sides by a negative number, FLIP the inequality sign.
1.8Coordinate Geometry
The coordinate plane connects algebra and geometry. The distance formula, midpoint formula, and equation of a circle are the core tools. These show up directly in later sections on circles, conics, and complex numbers.
1.10Lines
Lines are the simplest non-trivial functions. Every key concept — slope, intercepts, parallel and perpendicular relationships — connects directly to later work with linear functions, derivatives, and tangent lines.
What's included — free
- ✓Visual concept explanations with diagrams for every section
- ✓Step-by-step worked examples you can study at your pace
- ✓Key vocabulary and memory aids for each topic
- ✓Printable worksheets generated for each section
Upgrade for unlimited practice, private tutoring, study planner, and exam mode. View plans