Course overview

Algebra 1 turns arithmetic patterns into general rules. The course begins with expressions and equations, builds a visual understanding of linear functions, then extends those tools to systems, exponents, polynomials, quadratics, and simple models.

Complete curriculum

Every chapter and lesson

32 lessons total

01
Chapter 1 · 4 lessons
Foundations and Expressions
Translate between words and algebraic expressions, use properties of real numbers, and simplify expressions without changing their value.
Why it matters
Every later equation, function, and model depends on reading symbols correctly and combining only terms that truly match.
By the end, you will be able to
- Evaluate expressions using substitution and the order of operations.
- Apply distributive, commutative, and associative properties.
- Combine like terms and translate verbal statements into algebra.
1. 1.1
  Variables and expressions
  Identify coefficients, constants, terms, and operations in an expression.
2. 1.2
  Properties of real numbers
  Rewrite expressions while preserving equality.
3. 1.3
  Combining like terms
  Simplify expressions by grouping terms with the same variable part.
4. 1.4
  Writing expressions from context
  Represent quantities and relationships with algebraic notation.
Study chapter 1 in detail
02
Chapter 2 · 4 lessons
Linear Equations and Inequalities
Solve one-variable equations and inequalities, including fractions, parentheses, variables on both sides, and real constraints.
Why it matters
Linear equations describe break-even points, missing measurements, rates, and many other situations where one unknown must be found.
By the end, you will be able to
- Solve multi-step equations and verify solutions by substitution.
- Recognize equations with one, none, or infinitely many solutions.
- Solve and graph inequalities while handling negative multiplication correctly.
1. 2.1
  Solving linear equations
  Use inverse operations and preserve equality at every step.
2. 2.2
  Variables on both sides
  Collect variable terms and diagnose identities or contradictions.
3. 2.3
  Solving inequalities
  Reverse the inequality when multiplying or dividing by a negative value.
4. 2.4
  Modeling constraints
  Translate limits such as budgets and capacities into inequalities.
Study chapter 2 in detail
03
Chapter 3 · 4 lessons
Linear Functions and Graphs
Connect equations, tables, graphs, slope, and intercepts so a line becomes a meaningful rate-and-starting-value model.
Why it matters
Linear functions are the first major function family and a foundation for comparing rates, reading trends, and choosing useful models.
By the end, you will be able to
- Calculate and interpret slope as a rate of change.
- Graph a line from an equation, table, or two points.
- Write equations in slope-intercept and point-slope forms.
1. 3.1
  Graphing linear functions
  Plot lines from equations and tables.
2. 3.2
  Slope and rate of change
  Calculate rise over run and interpret units.
3. 3.3
  Slope-intercept form
  Use y = mx + b to identify rate and starting value.
4. 3.4
  Writing a line from data
  Build a linear equation from points or a real situation.
Study chapter 3 in detail
04
Chapter 4 · 4 lessons
Systems of Equations
Find values that satisfy two equations at once by graphing, substitution, or elimination, then interpret the intersection in context.
Why it matters
Systems answer comparison questions such as when two plans cost the same or which combination of quantities meets two constraints.
By the end, you will be able to
- Solve two-variable systems by three standard methods.
- Recognize systems with one, none, or infinitely many solutions.
- Translate a two-condition word problem into a system.
1. 4.1
  Graphing systems
  Use intersection points as shared solutions.
2. 4.2
  Substitution
  Replace one variable with an equivalent expression.
3. 4.3
  Elimination
  Combine equations to remove one variable.
4. 4.4
  Systems in context
  Interpret a solution with units and real constraints.
Study chapter 4 in detail
05
Chapter 5 · 4 lessons
Exponents and Radicals
Use exponent laws, scientific notation, square roots, and rational exponents to rewrite and evaluate expressions.
Why it matters
Exponent rules make very large, very small, repeated, and root-based quantities manageable across algebra and science.
By the end, you will be able to
- Apply product, quotient, power, zero, and negative exponent rules.
- Simplify square roots and connect radicals to rational exponents.
- Calculate with scientific notation while preserving scale.
1. 5.1
  Exponent laws
  Rewrite repeated multiplication using consistent exponent rules.
2. 5.2
  Negative and zero exponents
  Interpret reciprocal powers and the zero-power rule.
3. 5.3
  Radicals and rational exponents
  Move between root and exponent notation.
4. 5.4
  Scientific notation
  Represent and calculate with extreme magnitudes.
Study chapter 5 in detail
06
Chapter 6 · 4 lessons
Polynomials and Factoring
Add, multiply, and factor polynomial expressions, with special attention to common factors and quadratic patterns.
Why it matters
Factoring reveals zeros and structure that are hidden in expanded form, making later equation solving and graph analysis possible.
By the end, you will be able to
- Classify polynomials by degree and number of terms.
- Add and multiply polynomials accurately.
- Factor greatest common factors, trinomials, and differences of squares.
1. 6.1
  Polynomial operations
  Combine and multiply polynomial terms without mixing degrees.
2. 6.2
  Greatest common factors
  Remove the largest shared factor before using other patterns.
3. 6.3
  Factoring trinomials
  Reverse multiplication to express a quadratic as two binomials.
4. 6.4
  Special products
  Recognize perfect squares and differences of squares.
Study chapter 6 in detail
07
Chapter 7 · 4 lessons
Quadratic Equations and Graphs
Solve quadratic equations by factoring, square roots, completing the square, and the quadratic formula, then connect solutions to a parabola.
Why it matters
Quadratics model area, projectile motion, and optimization while introducing equations that can have two, one, or no real solutions.
By the end, you will be able to
- Choose an efficient method for solving a quadratic equation.
- Use the discriminant to predict the number of real solutions.
- Interpret roots, vertex, axis of symmetry, and intercepts on a graph.
1. 7.1
  Solving by factoring
  Use the zero-product property after putting the equation in standard form.
2. 7.2
  Completing the square
  Rewrite a quadratic in vertex form.
3. 7.3
  The quadratic formula
  Solve any quadratic and interpret the discriminant.
4. 7.4
  Graphing parabolas
  Connect algebraic forms to roots and vertex behavior.
Study chapter 7 in detail
08
Chapter 8 · 4 lessons
Exponential Models and Data
Distinguish linear from exponential change, write growth and decay models, and judge whether a model fits data and context.
Why it matters
Repeated percentage change appears in population, depreciation, spread, and many science applications where a linear model fails.
By the end, you will be able to
- Identify constant difference versus constant ratio patterns.
- Write and interpret $y = a(b^x)$ growth and decay models.
- Use tables, graphs, and residual thinking to evaluate a simple model.
1. 8.1
  Linear versus exponential change
  Compare additive and multiplicative patterns.
2. 8.2
  Growth and decay models
  Interpret initial value and growth factor.
3. 8.3
  Reading exponential graphs
  Connect intercepts and long-run behavior to context.
4. 8.4
  Choosing a model
  Check whether data support a linear or exponential relationship.
Study chapter 8 in detail

Algebra 1

Course overview

Every chapter and lesson

Learn this with an AI teacher that starts from what you already know.