Sophia College Algebra & Math Fundamentals

What You'll Learn

Sophia Platform Overview & Getting Started

Number Properties & Arithmetic Foundations

Linear Equations & Inequalities

Functions & Graphing in the Coordinate Plane

Systems of Equations

Polynomials & Factoring

Quadratic Equations

Rational & Radical Expressions

Course Curriculum 9 Modules · 70+ Lessons

Sophia Platform Overview & Getting Started

5 lessons · 30 min

How Sophia Learning Works: Milestones and Challenges
Navigating Your Sophia Dashboard Effectively
College Credit Transfer: Partner Institutions and Requirements
Study Tips Specific to Sophia's Self-Paced Format
Building Your College Algebra Study Schedule
Module 1 Practice Quiz

Number Properties & Arithmetic Foundations

8 lessons · 2 hrs

Real Numbers: Natural, Integer, Rational, Irrational
Properties: Commutative, Associative, Distributive
Order of Operations (PEMDAS) with Complex Expressions
Absolute Value and Distance on the Number Line
Scientific Notation: Reading and Writing Large Numbers
Simplifying Expressions with Integer Exponents
Radicals and Rational Exponents
Module Practice Quiz (10 questions)
Module 2 Practice Quiz

Linear Equations & Inequalities

10 lessons · 2.5 hrs · High-Yield

Solving One-Step and Multi-Step Linear Equations
Solving Equations with Variables on Both Sides
Translating Word Problems into Equations
Solving Linear Inequalities and Graphing on Number Lines
Compound Inequalities: 'And' vs 'Or' Statements
Absolute Value Equations
Absolute Value Inequalities
Formulas: Solving for a Specific Variable
Mixture and Rate Word Problems
Module Practice Quiz (15 questions)
Module 3 Practice Quiz

Functions & Graphing in the Coordinate Plane

9 lessons · 2.5 hrs · High-Yield

Introduction to Functions: Domain and Range
Function Notation: f(x) Explained
Graphing Linear Functions from Tables and Equations
Slope: Calculating and Interpreting Rise Over Run
Slope-Intercept Form: y = mx + b
Point-Slope Form and Standard Form
Parallel and Perpendicular Lines
Graphing Using Intercepts
Module Practice Quiz (15 questions)
Module 4 Practice Quiz

Systems of Equations

8 lessons · 2 hrs

Introduction to Systems: One Solution, No Solution, Infinite
Solving by Graphing (Visual Method)
Solving by Substitution Method
Solving by Elimination (Addition) Method
Choosing the Best Method for a Given System
Systems Word Problems: Setting Up and Solving
Systems of Inequalities and Graphing Regions
Module Practice Quiz (10 questions)
Module 5 Practice Quiz

Polynomials & Factoring

9 lessons · 2.5 hrs

Polynomial Vocabulary: Terms, Coefficients, Degree
Adding and Subtracting Polynomials
Multiplying Polynomials: Monomial by Polynomial
FOIL Method for Multiplying Binomials
Special Products: (a+b)² and (a+b)(a-b)
Factoring GCF (Greatest Common Factor)
Factoring Trinomials: x² + bx + c
Factoring Trinomials: ax² + bx + c
Module Practice Quiz (15 questions)
Module 6 Practice Quiz

Quadratic Equations

8 lessons · 2.5 hrs

Solving Quadratics by Factoring
Completing the Square Method
The Quadratic Formula
Discriminant: Identifying Number and Type of Solutions
Graphing Parabolas: Vertex, Axis of Symmetry, Intercepts
Vertex Form of Quadratic Equations
Quadratic Word Problems: Projectile Motion
Module Practice Quiz (15 questions)
Module 7 Practice Quiz

Rational & Radical Expressions

8 lessons · 2 hrs

Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions (LCD)
Solving Rational Equations
Simplifying Radical Expressions
Operations with Radicals (Add, Subtract, Multiply)
Rationalizing the Denominator
Module Practice Quiz (10 questions)
Module 8 Practice Quiz

Final Assessment Preparation & Sophia Milestone Strategies

5 lessons · 1.5 hrs

Sophia Challenge Exam Strategy: What to Expect
Common Mistakes to Avoid in the Final Assessment
Practice Milestone: Full Algebra Review (30 questions)
Time Management During Sophia Assessments
Applying for College Credit After Completion
Module 9 Practice Quiz

What's Included

Complete Study Guide

10+ Practice Questions

10+ Digital Flashcards

Expert Support

Progress Tracking

Certificate

Practice Test — 10 Questions

Full explanations provided after each answer.

20:00

Q 1 / 10

Digital Flashcards

Click any card to flip.

Study Guide & Key Concepts

Sophia College Algebra: Key Topics

Unit 1: Foundations — Real numbers, properties, order of operations
Unit 2: Linear Equations — Solving, inequalities, formulas
Unit 3: Functions — Domain/range, graphing, slope, lines
Unit 4: Systems — Graphing, substitution, elimination methods
Unit 5: Polynomials — Operations, factoring, special products
Unit 6: Quadratics — Factoring, quadratic formula, graphing
Unit 7: Rational/Radical — Simplifying, operations, solving equations

Sophia Tips for Success

Complete all practice problems before taking the Challenge
You can retake Challenges — use first attempt as a diagnostic
Review all explanations after each attempt, right and wrong
Time each unit: aim for 2-3 days per unit at 2 hours/day
Submit for credit only after scoring 75%+ consistently

$59

One-time · Lifetime access

9 comprehensive modules
10+ practice questions
Expert support included

SSL · PayPal accepted

Course Rating

★★★★★

4.7 / 5.0

1,423 students enrolled