Algebra: From Fundamentals to Advanced Concepts
Build a complete algebra foundation through variables, expressions, equations, inequalities, functions, graphs, systems, powers, polynomials, factoring, and quadratic relationships. Extend your skills with rational expressions, radicals, composition, and inverse functions. Learn why methods work through purposeful visuals, interactive graphs, worked examples, and explained practice.
Understand the Relationships Behind the Symbols
Algebra helps you describe an unknown quantity, compare two changing amounts, and find values that make a relationship true. Variables, equations, and graphs become easier to use when you can connect them to something you understand.
This course builds from the language of algebra through equations, inequalities, functions, systems, polynomials, and quadratics. Visual models and carefully explained examples show why the methods work, while short interactive activities help you put each idea into practice.
What You’ll Learn
Build a foundation you can use in everyday problems and carry into more advanced math.
Read and Simplify Expressions
Understand variables, terms, coefficients, and grouping. Use equivalent forms to make a relationship easier to work with.
Solve Equations and Inequalities
Find unknown values, rearrange formulas, and describe the range of answers that fit a condition.
Understand Functions and Graphs
Connect rules to tables and graphs, interpret slope, and solve systems that must meet two conditions at once.
Work with Polynomials and Quadratics
Expand and factor expressions, read a parabola, and choose a useful way to solve a quadratic. Extend those ideas to algebraic fractions and roots.
Learn by Trying the Ideas
Choose answers and read the explanations, follow worked examples step by step, and change graph settings to see how a rule affects its shape.
Who This Course Is For
This course is for learners starting algebra, adults returning to math, and anyone who wants a stronger foundation before geometry, precalculus, or calculus. Familiarity with basic arithmetic, signed numbers, and fractions will help.
Skills You’ll Develop
The broader competencies and practical skills this guide is designed to build.
Mathematical Relationships & Change
- Algebraic Reasoning
- Functions & Mathematical Modeling
Numerical & Proportional Reasoning
- Proportional Reasoning
Guide Sections
See how algebra helps you find unknown values, compare choices, and understand how things change.
Read algebraic notation, translate relationships, substitute values, and distinguish an expression from an equation.
Use properties, combine like terms, and distribute with signs while preserving the original expression’s meaning.
Solve multi-step equations, handle variables on both sides, and recognize one, no, or infinitely many solutions.
Clear denominators, solve equations involving fractions, and rearrange formulas for a chosen variable.
Define quantities, represent relationships, solve practical problems, and interpret answers in context.
Solve inequalities, understand negative multipliers, and represent compound solution sets with number lines and intervals.
Solve absolute-value equations and inequalities by interpreting distance, including two-sided and outside intervals.
Plot points, read intercepts, calculate slope, and distinguish horizontal, vertical, increasing, and decreasing lines.
Understand function notation, domain and range, multiple representations, and the difference between a relation and a function.
Interpret and build linear rules, use different equation forms, and compare lines through rates and intercepts.
Solve systems graphically and algebraically, choose substitution or elimination, and interpret intersection and consistency.
Use integer exponent laws, distinguish addition from multiplication, and simplify powers with stated restrictions.
Identify degree and coefficients, combine polynomials, multiply using distribution, and derive important product patterns.
Factor common terms, trinomials, differences of squares, and grouped polynomials, checking each result by expansion.
Connect quadratic expressions to parabolas, identify vertices and intercepts, and interpret transformations and changing rates.
Use the zero-product property, preserve all solutions, and choose a direct method when the equation’s structure allows it.
Derive a general solving method, interpret the discriminant, and connect the number of real solutions with the graph.
Solve quadratic inequalities with a graph and sign chart, including repeated roots and boundary decisions.
Simplify algebraic fractions through factors, combine denominators, and solve rational equations without accepting excluded values.
Simplify square roots, connect radicals with rational exponents, and solve radical equations with domain and substitution checks.
Recognize linear, quadratic, exponential, and reciprocal patterns, and explore shifts, scaling, composition, and inverse relationships.
Integrate equations, functions, systems, and quadratic reasoning in complete practical problems with assumptions and checks.
Review the connected algebra skills, use a focused readiness check, and choose a useful next step.
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