Algebra 1 | Index

Algebra 1 teaches you to solve equations and graph lines and curves. You’ll start with linear equations, functions and systems. Later units cover exponents, polynomials, radicals, quadratics and data.

It’s for high school students taking Algebra 1 or getting ready for Geometry. It also works for review before a test.

What to know first: negative numbers, fractions, exponents and the order of operations from Pre-Algebra.

Lessons marked “coming soon” are planned but not written yet.

Units in this course

Unit 1: Expressions and Variables

  1. Variables — what variables are and how letters stand for numbers
  2. Algebraic Expressions — write expressions from words and evaluate them
  3. Combining Like Terms — simplify expressions by adding and subtracting like terms
  4. Distributive Property — multiply a number across parentheses to simplify expressions

Also see: Nested Fractions (now in Pre-Algebra, Unit 2).

Unit 2: Linear Equations and Inequalities

  1. One-Step Equations — solve equations with one inverse operation
  2. Two-Step Equations — undo addition or subtraction first, then multiplication or division
  3. Multi-Step Equations — distribute and combine like terms before you solve
  4. Equations with Variables on Both Sides — collect the variable on one side, and spot equations with no solution or every solution
  5. Literal Equations — solve a formula for one of its variables
  6. One-Step Inequalities — solve and graph inequalities, and know when to flip the sign
  7. Two-Step Inequalities — solve inequalities that take two steps and graph the solution
  8. Multi-Step Inequalities — solve inequalities with parentheses or variables on both sides
  9. Compound Inequalities — solve and graph “and” and “or” inequalities
  10. Absolute Value Equations — solve absolute value equations by splitting them into two cases
  11. Absolute Value Inequalities — solve and graph absolute value inequalities

Unit 3: Introduction to Functions

  1. Relations and Functions — decide whether a relation is a function, including the vertical line test
  2. Function Notation — read and evaluate functions written with function notation
  3. Domain and Range — find a function’s inputs and outputs from a table, graph or rule
  4. Key Features of Functions — read intercepts, maximums, minimums and where a graph rises or falls

Unit 4: Linear Functions, Slope and Graphing

  1. Two-Variable Linear Equations — find solutions as ordered pairs and graph them as a line
  2. X-Intercepts and Y-Intercepts — find where a line crosses each axis and graph with intercepts
  3. Slope — find the slope of a line from two points, a graph, an equation or a table
  4. Horizontal and Vertical Lines — graph and write equations of lines with zero or undefined slope
  5. Slope-Intercept Form — graph a line from its slope and y-intercept
  6. Writing Equations in Slope-Intercept Form — write a line’s equation from a graph, two points or a word problem
  7. Point-Slope Form — write a line’s equation from one point and the slope
  8. Standard Form of a Linear Equation — write and graph lines in standard form and convert between forms
  9. Parallel and Perpendicular Lines — use slopes to identify parallel and perpendicular lines and write their equations
  10. Direct Variation — recognize and write equations where y is a constant multiple of x
  11. Average Rate of Change — find how fast a function changes over an interval
  12. Arithmetic Sequences — find terms and write formulas for sequences that add the same amount each time

Also see: Coordinate Plane (now in Pre-Algebra, Unit 1).

Unit 5: Systems of Equations and Inequalities

  1. Systems of Equations — what a system is and how to solve one by graphing
  2. Substitution Method — solve a system by substituting one equation into the other
  3. Elimination Method — add or subtract equations to eliminate a variable
  4. Number of Solutions — tell whether a system has one solution, no solution or infinitely many
  5. Systems of Equations Word Problems — set up and solve systems from real situations
  6. Graphing Linear Inequalities — graph a linear inequality with a boundary line and shading
  7. Systems of Inequalities — graph two or more inequalities and find where they overlap

Unit 6: Exponent Rules and Exponential Functions

  1. Exponent Rules — the product, quotient and power rules for exponents with variables
  2. Zero and Negative Exponents — what zero and negative exponents mean and how to rewrite them
  3. Exponential Functions — recognize and graph functions where the variable is in the exponent
  4. Exponential Growth and Decay — model amounts that grow or shrink by the same percent each period
  5. Compound Interest — use the compound interest formula to see how money grows
  6. Geometric Sequences — find terms and write formulas for sequences that multiply by the same number each time
  7. Linear vs. Exponential Functions — compare growth patterns in tables, graphs and real situations

Unit 7: Polynomials and Factoring

  1. Polynomials — terms, degree and standard form of a polynomial
  2. Adding and Subtracting Polynomials — combine like terms across polynomials
  3. Multiplying Binomials — use the distributive property or FOIL to multiply two binomials
  4. Multiplying Polynomials — multiply any two polynomials with the distributive property or a box
  5. Special Products of Binomials — square a binomial and multiply sum-and-difference pairs quickly
  6. Factoring Out the Greatest Common Factor — pull the greatest common factor out of a polynomial
  7. Factoring Trinomials — factor trinomials whose leading coefficient is 1
  8. Factoring Trinomials When a Is Not 1 — factor trinomials with a leading coefficient other than 1
  9. Factoring by Grouping — factor four-term polynomials by grouping pairs of terms
  10. Factoring the Difference of Squares — factor an expression that is one square minus another
  11. Perfect Square Trinomials — recognize and factor trinomials that are squares of binomials
  12. Factoring Completely — choose a factoring method and keep going until nothing more factors

Unit 8: Radicals

  1. Simplifying Square Roots — pull perfect-square factors out of a square root
  2. Adding and Subtracting Radicals — combine like radicals
  3. Multiplying Radicals (coming soon) — multiply square roots and simplify the product
  4. Rationalizing the Denominator (coming soon) — divide square roots and remove a radical from the denominator

Unit 9: Quadratic Functions and Equations

  1. Graphing Quadratic Functions (coming soon) — graph parabolas in standard form and find the vertex and axis of symmetry
  2. Vertex Form (coming soon) — graph and write quadratic functions in vertex form
  3. Solving Quadratics by Graphing (coming soon) — find solutions where a parabola crosses the x-axis
  4. Solving Quadratic Equations by Factoring (coming soon) — factor and use the zero product property
  5. Solving Quadratics with Square Roots (coming soon) — isolate the squared term and take the square root of both sides
  6. Completing the Square (coming soon) — rewrite a quadratic to solve it or find its vertex
  7. Quadratic Formula (coming soon) — solve any quadratic equation with the quadratic formula
  8. The Discriminant (coming soon) — use the discriminant to find how many real solutions a quadratic has
  9. Linear-Quadratic Systems (coming soon) — solve a system of a line and a parabola
  10. Linear, Quadratic and Exponential Models (coming soon) — choose the best model for a table of data or a situation

Unit 10: Data, Scatter Plots and Lines of Fit

  1. Two-Way Tables (coming soon) — organize categorical data and find relative frequencies
  2. Scatter Plots and Correlation (coming soon) — describe how two variables are related, and tell correlation from causation
  3. Line of Best Fit (coming soon) — draw and write a line of fit and use it to make predictions

Also see: mean, median, mode and box plots in Pre-Algebra, Unit 7.

For Teachers: Standards Alignment

Lessons follow the Common Core high school standards for Algebra 1 (traditional pathway). A few Algebra 1 standards are taught in other courses. Piecewise, absolute value and inverse functions and rational exponents are in Algebra 2. Standard deviation and the correlation coefficient are in Statistics.

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