Algebra - Overview

Algebra is the largest and most important domain on the SAT. It focuses on solving equations, interpreting graphs, modeling real-world situations, and understanding relationships between variables.

Many SAT questions across other domains also rely on Algebra skills, making this the foundation of success throughout the test.

TipWhat You’ll Learn

By working through this domain, you’ll learn how to:

  • Simplify and manipulate algebraic expressions
  • Solve equations and inequalities efficiently
  • Interpret and create graphs of linear relationships
  • Model real-world situations using equations
  • Solve systems of equations and inequalities
  • Analyze rates of change and linear trends

Course Structure

The Algebra domain is organized into five units.

Foundations

Build the core skills needed for all later Algebra topics.

Topics include:

  • Basic algebra vocabulary
  • Numbers and operations
  • Order of operations (PEMDAS)
  • Absolute value
  • Properties of operations
  • Fractions and decimals
  • Basic exponent rules
  • Arithmetic and geometric sequences
  • Simplifying simple radicals

Linear Expressions & Equations

Learn how to manipulate expressions and solve increasingly complex equations.

Topics include:

  • Simplifying linear expressions
  • One-step and two-step equations
  • Multi-step equations
  • Variables on both sides
  • Inequalities
  • Compound inequalities
  • Systems of inequalities
  • Literal equations

Linear Equations & Graphs

Develop graphing and equation-writing skills that frequently appear on the SAT.

Topics include:

  • Slope and rate of change
  • Slope-intercept form
  • Standard form
  • Writing equations from graphs
  • Point-slope form
  • Parallel and perpendicular lines

Linear Word Problems

Apply Algebra to realistic SAT scenarios.

Topics include:

  • Translating word problems into equations
  • Linear modeling
  • Linear trends and rate of change
  • Interpreting relationships in context

Systems of Equations & Inequalities

Solve problems involving multiple equations and constraints.

Topics include:

  • Introduction to systems
  • Substitution
  • Elimination
  • Graphing systems
  • Special cases (no solution and infinitely many solutions)
  • Systems word problems

SAT Algebra Tips

  • Always check whether a problem can be simplified before solving.
  • Pay close attention to negative signs and distribution.
  • Learn to recognize common equation structures quickly.
  • Understand what slope means in context—not just how to calculate it.
  • For systems, choose the solution method that requires the least work.
  • Translate word problems carefully before performing calculations.

Assess Your Progress

After completing the lessons in each unit, test your understanding with:

  • Unit assessments
  • The Algebra Domain Test
  • Full-Length SAT Practice Tests

Select a unit from the sidebar to begin.