Mathematical Foundations I is the first course in a sequence specially crafted for adults seeking the most direct path to prepare for university math courses. The course starts with fraction arithmetic and covers all the way up through the algebra of linear equations. Upon completing the course, students will be prepared for Mathematical Foundations II, the second step of the journey towards university-level math.
Solidify your arithmetic, learn about variables and graphs, level up your algebra, and learn the essentials of geometry.
| 1.1.1. | Adding Fractions and Whole Numbers Using Models | |
| 1.1.2. | Adding Fractions and Whole Numbers | |
| 1.1.3. | Subtracting Fractions and Whole Numbers Using Models | |
| 1.1.4. | Subtracting Fractions and Whole Numbers |
| 1.2.1. | Least Common Multiples | |
| 1.2.2. | Least Common Denominators | |
| 1.2.3. | Comparing Fraction Models Using Common Denominators | |
| 1.2.4. | Comparing Fractions Using Common Denominators | |
| 1.2.5. | Adding Fractions With Unlike Denominators Using Models | |
| 1.2.6. | Subtracting Fractions With Unlike Denominators Using Models | |
| 1.2.7. | Adding Fractions With Unlike Denominators | |
| 1.2.8. | Subtracting Fractions With Unlike Denominators |
| 1.3.1. | Adding Mixed Numbers With Unlike Denominators | |
| 1.3.2. | Subtracting Mixed Numbers With Unlike Denominators | |
| 1.3.3. | Subtracting Mixed Numbers With Unlike Denominators Using Improper Fractions |
| 1.4.1. | Multiplying Unit Fractions by Whole Numbers Using Models | |
| 1.4.2. | Multiplying Fractions by Whole Numbers Using Models | |
| 1.4.3. | Multiplying Fractions by Whole Numbers | |
| 1.4.4. | Multiplying Fractions by Whole Numbers: Word Problems | |
| 1.4.5. | Strategies to Simplify Whole Number and Fraction Multiplication | |
| 1.4.6. | Multiplying Mixed Numbers by Whole Numbers | |
| 1.4.7. | Multiplying Fractions by Unit Fractions Using Models | |
| 1.4.8. | Multiplying Fractions Using Models | |
| 1.4.9. | Multiplying Fractions | |
| 1.4.10. | Multiplying Fractions: Word Problems | |
| 1.4.11. | Strategies to Simplify Fraction Multiplication | |
| 1.4.12. | Multiplying Mixed Numbers by Fractions | |
| 1.4.13. | Multiplying Mixed Numbers | |
| 1.4.14. | Multiplying Mixed Numbers: Word Problems |
| 1.5.1. | Dividing Whole Numbers by Unit Fractions Using Models | |
| 1.5.2. | Dividing Whole Numbers by Unit Fractions | |
| 1.5.3. | Dividing Unit Fractions by Whole Numbers Using Models | |
| 1.5.4. | Dividing Unit Fractions by Whole Numbers | |
| 1.5.5. | Reciprocals | |
| 1.5.6. | Dividing Whole Numbers by Fractions Using Models: Whole Number Results | |
| 1.5.7. | Dividing Whole Numbers by Fractions Using Models: Fractional Results | |
| 1.5.8. | Dividing Whole Numbers by Fractions | |
| 1.5.9. | Dividing Fractions by Whole Numbers Using Models | |
| 1.5.10. | Dividing Fractions by Whole Numbers | |
| 1.5.11. | Dividing Fractions Using Models | |
| 1.5.12. | Dividing Fractions |
| 2.6.1. | Introduction to Ratios | |
| 2.6.2. | Equivalent Ratios | |
| 2.6.3. | Writing Ratios Using Fractions | |
| 2.6.4. | Working With Equivalent Ratios | |
| 2.6.5. | More on Equivalent Ratios | |
| 2.6.6. | Ratio Tables | |
| 2.6.7. | Graphing Ratios | |
| 2.6.8. | Unit Rates | |
| 2.6.9. | Solving Problems Using Unit Rates | |
| 2.6.10. | Speed as a Unit Rate |
| 2.7.1. | Understanding Proportional Relationships Using Tables | |
| 2.7.2. | Understanding Proportional Relationships Using Graphs | |
| 2.7.3. | Understanding Proportional Relationships From Descriptions | |
| 2.7.4. | Modeling with Direct Variation | |
| 2.7.5. | Inverse Variation | |
| 2.7.6. | Modeling With Inverse Variation |
| 2.8.1. | Units of Length | |
| 2.8.2. | Units of Mass | |
| 2.8.3. | Units of Time | |
| 2.8.4. | Units of Volume | |
| 2.8.5. | Units of Area and Volume | |
| 2.8.6. | Unit Conversions Using Base Units of Mass | |
| 2.8.7. | Two-Step Unit Conversions | |
| 2.8.8. | Unit Conversions Using Base Units of Length | |
| 2.8.9. | Unit Conversions Using Units of Time | |
| 2.8.10. | Converting Units of Area to Smaller Units | |
| 2.8.11. | Converting Units of Area to Larger Units | |
| 2.8.12. | Converting Between Mixed Units | |
| 2.8.13. | Determining Units in Formulas | |
| 2.8.14. | Selecting Units for Rates of Change | |
| 2.8.15. | Degrees of Accuracy |
| 2.9.1. | Understanding Percentages Using Models | |
| 2.9.2. | Converting Between Percentages and Fractions | |
| 2.9.3. | Converting Between Percentages and Decimals | |
| 2.9.4. | Finding Part of a Number Given a Whole and a Percentage | |
| 2.9.5. | Finding Part of a Number Given a Whole and a Percentage: Word Problems | |
| 2.9.6. | Finding a Percentage Given Two Numbers | |
| 2.9.7. | Finding a Percentage Given Two Numbers: Word Problems | |
| 2.9.8. | Finding a Total Given a Part and a Percentage | |
| 2.9.9. | Percentage Increase, Decrease, and Error |
| 3.10.1. | Subtracting a Positive Number From a Smaller Positive Number | |
| 3.10.2. | Subtracting a Positive Number From a Negative Number | |
| 3.10.3. | Subtracting a Positive Fraction From a Smaller Fraction | |
| 3.10.4. | Subtracting a Positive Decimal From a Smaller Decimal | |
| 3.10.5. | Adding a Positive Number to a Negative Number | |
| 3.10.6. | Adding a Negative Number | |
| 3.10.7. | Subtracting a Negative Number | |
| 3.10.8. | Additive Inverses of Numbers | |
| 3.10.9. | Solving Problems Using Addition and Subtraction of Rational Numbers | |
| 3.10.10. | Absolute Value |
| 3.11.1. | Multiplying Positive Numbers With Negative Numbers | |
| 3.11.2. | Multiplying Negative Numbers | |
| 3.11.3. | Dividing With Negative Numbers | |
| 3.11.4. | Equivalent Fractions With Negative Numbers | |
| 3.11.5. | Dividing With Negative Decimals and Fractions | |
| 3.11.6. | Reciprocals of Rational Numbers | |
| 3.11.7. | Multiplying and Dividing With Zero | |
| 3.11.8. | Fractions of Fractions | |
| 3.11.9. | Solving Problems Using the Four Operations on Rational Numbers |
| 3.12.1. | Divisibility of Integers by 2, 5, 10, 4, and 8 | |
| 3.12.2. | Divisibility of Integers by 3, 9, 6, and 7 | |
| 3.12.3. | Prime and Composite Numbers | |
| 3.12.4. | Prime Factors | |
| 3.12.5. | The Fundamental Theorem of Arithmetic | |
| 3.12.6. | Finding Greatest Common Factors Using Prime Factorization | |
| 3.12.7. | Finding Lowest Common Multiples Using Prime Factorization | |
| 3.12.8. | Natural Numbers, Integers, and Rational Numbers |
| 4.13.1. | Introduction to Exponents | |
| 4.13.2. | Evaluating Exponents | |
| 4.13.3. | Evaluating Larger Exponents | |
| 4.13.4. | Evaluating Exponents With Fractional Bases | |
| 4.13.5. | Evaluating Exponents With Decimal Bases | |
| 4.13.6. | Evaluating Whole Number Expressions Containing Exponents | |
| 4.13.7. | Squaring Rational Numbers | |
| 4.13.8. | Cubing Rational Numbers | |
| 4.13.9. | Exponents With Rational Bases | |
| 4.13.10. | The Zeroth Power | |
| 4.13.11. | Powers of Negative One | |
| 4.13.12. | Negative Exponents |
| 4.14.1. | The Product Rule for Exponents | |
| 4.14.2. | The Quotient Rule for Exponents | |
| 4.14.3. | The Power Rule for Exponents | |
| 4.14.4. | The Power of Product Rule for Exponents | |
| 4.14.5. | The Power of Quotient Rule for Exponents | |
| 4.14.6. | Combining the Rules of Exponents |
| 4.15.1. | Evaluating Rational Number Expressions Without Exponents | |
| 4.15.2. | Evaluating Expressions With Positive Integer Exponents | |
| 4.15.3. | Evaluating Expressions With Integer Exponents |
| 4.16.1. | The Square Root of a Perfect Square | |
| 4.16.2. | Squaring a Square Root | |
| 4.16.3. | The Cube Root of a Perfect Cube | |
| 4.16.4. | Surds | |
| 4.16.5. | Simplifying Expressions With Surds | |
| 4.16.6. | Evaluating Numerical Expressions Containing Radicals | |
| 4.16.7. | Adding and Subtracting Radicals | |
| 4.16.8. | Rationalizing Denominators |
| 4.17.1. | Radicals as Fractional Exponents | |
| 4.17.2. | The Product Rule for Radicals | |
| 4.17.3. | The Quotient Rule for Radicals |
| 5.18.1. | Introduction to Algebraic Expressions | |
| 5.18.2. | Constructing Algebraic Expressions | |
| 5.18.3. | Evaluating Linear Expressions | |
| 5.18.4. | Evaluating Rational Expressions | |
| 5.18.5. | Identifying Terms in Linear Expressions | |
| 5.18.6. | Identifying Coefficients and Constants in Linear Expressions | |
| 5.18.7. | The Greatest Common Factor of Two Linear Expressions |
| 5.19.1. | Identifying Like Terms in a Linear Expression | |
| 5.19.2. | Collecting Like Terms in a Linear Expression | |
| 5.19.3. | Applying the Distributive Law With Linear Expressions | |
| 5.19.4. | The Distributive Law With Three Terms | |
| 5.19.5. | Distributing the Negative Sign in a Linear Expression | |
| 5.19.6. | Simplifying Linear Expressions Using the Distributive Law | |
| 5.19.7. | Simplifying Linear Expressions When a Group of Terms Is Subtracted | |
| 5.19.8. | Simplifying Linear Expressions Containing Fractions | |
| 5.19.9. | Factoring Linear Expressions |
| 5.20.1. | Solving Linear Equations by Trial and Error | |
| 5.20.2. | Solving One-Step Addition and Subtraction Equations | |
| 5.20.3. | Solving One-Step Multiplication and Division Equations |
| 5.21.1. | Solving Two-Step Equations | |
| 5.21.2. | Solving Linear Equations With Fractional Coefficients | |
| 5.21.3. | Solving Linear Equations With Decimal Coefficients | |
| 5.21.4. | Solving Linear Equations With Variables on Both Sides | |
| 5.21.5. | Solving Linear Equations by Clearing a Rational Expression | |
| 5.21.6. | Solving Linear Equations Using Cross-Multiplication | |
| 5.21.7. | Solving Two-Variable Equations | |
| 5.21.8. | Equations With Many Solutions and No Solutions | |
| 5.21.9. | Solving Linear Equations With Unknown Coefficients | |
| 5.21.10. | Solving Linear Equations With Unknown Coefficients by Factoring | |
| 5.21.11. | Solving Many-Variable Equations |
| 5.22.1. | Interpreting Linear Expressions | |
| 5.22.2. | Modeling With Linear Equations |
| 5.23.1. | Inequalities | |
| 5.23.2. | Compound Inequalities | |
| 5.23.3. | Verifying Solutions of Linear Inequalities | |
| 5.23.4. | Solving One-Step Linear Inequalities | |
| 5.23.5. | Solving Two-Step Inequalities | |
| 5.23.6. | Representing Solutions to Inequalities on Number Lines | |
| 5.23.7. | Further Solving Linear Inequalities | |
| 5.23.8. | Solving Compound Inequalities | |
| 5.23.9. | Interval Notation | |
| 5.23.10. | Unbounded Intervals | |
| 5.23.11. | Unions of Intervals | |
| 5.23.12. | Intersections of Intervals | |
| 5.23.13. | Compound OR Inequalities | |
| 5.23.14. | Compound AND Inequalities |
| 5.24.1. | Solving Equations Using the Square Root Method | |
| 5.24.2. | Solving Equations With Odd Exponents Using the Nth Root Method | |
| 5.24.3. | Solving Equations With Even Exponents Using the Nth Root Method |
| 6.25.1. | The Cartesian Coordinate System | |
| 6.25.2. | Distances Between Points in the Coordinate Plane | |
| 6.25.3. | Two-Variable Linear Equations and Their Solutions | |
| 6.25.4. | Graphing Linear Equations | |
| 6.25.5. | Horizontal and Vertical Lines | |
| 6.25.6. | Calculating Slopes of Straight Lines | |
| 6.25.7. | Equations of Lines in Slope-Intercept Form | |
| 6.25.8. | Finding Properties of Lines Given in Slope-Intercept Form | |
| 6.25.9. | Equations of Lines in Point-Slope Form | |
| 6.25.10. | Equations of Lines in Standard Form | |
| 6.25.11. | Determining Properties of Lines Given in Standard Form | |
| 6.25.12. | Parallel Lines in the Coordinate Plane |
| 6.26.1. | Modeling With Linear Equations in Two Variables | |
| 6.26.2. | Further Modeling With Linear Equations in Two Variables | |
| 6.26.3. | Analyzing and Interpreting Graphs of Linear Equations | |
| 6.26.4. | Distance-Time Graphs | |
| 6.26.5. | Calculating Acceleration From a Speed-Time Graph | |
| 6.26.6. | Calculating Distance From a Speed-Time Graph |
| 6.27.1. | Introduction to Systems of Linear Equations | |
| 6.27.2. | Solving Systems of Equations by Substitution | |
| 6.27.3. | Introduction to the Elimination Method | |
| 6.27.4. | Solving Systems of Linear Equations Using Elimination: One Transformation | |
| 6.27.5. | Solving Systems of Linear Equations Using Elimination: Two Transformations | |
| 6.27.6. | Systems of Linear Equations With Fractional Coefficients | |
| 6.27.7. | Systems of Linear Equations With Decimal Coefficients | |
| 6.27.8. | Solving Systems of Nonlinear Equations Using Graphs | |
| 6.27.9. | Systems of Equations With No Solutions and Infinitely Many Solutions | |
| 6.27.10. | Consistency and Dependency in Linear Systems | |
| 6.27.11. | Calculating the Intersection of Two Lines |
| 7.28.1. | Writing Radical Expressions Using Fractional Exponents | |
| 7.28.2. | The Square Root of a Perfect Square With Algebraic Expressions | |
| 7.28.3. | The Square Root of a Perfect Square With Domain Restrictions | |
| 7.28.4. | The Cube Root of a Perfect Cube With Algebraic Expressions | |
| 7.28.5. | Simplifying Square Root Expressions Using the Product Rule | |
| 7.28.6. | Combining Radical Expressions Using the Product Rule | |
| 7.28.7. | Evaluating Algebraic Radical Expressions | |
| 7.28.8. | Adding and Subtracting Radical Expressions |
| 7.29.1. | Equivalent Expressions With Fractions | |
| 7.29.2. | Simplifying Rational Expressions | |
| 7.29.3. | Simplifying Rational Expressions by Factoring | |
| 7.29.4. | Splitting Rational Expressions Into Separate Terms |
| 7.30.1. | Solving Rational Equations Containing One Fractional Term | |
| 7.30.2. | Solving Rational Equations Using Cross-Multiplication | |
| 7.30.3. | Solving Rational Equations Containing Binomials Using Cross-Multiplication | |
| 7.30.4. | Solving Rational Equations Using the Flip Method |
| 8.31.1. | Introduction to Functions | |
| 8.31.2. | Visual Representations of Functions | |
| 8.31.3. | Graphs of Functions | |
| 8.31.4. | The Domain of a Function | |
| 8.31.5. | Global Extrema of Functions | |
| 8.31.6. | End Behavior of Functions | |
| 8.31.7. | The Range of a Function | |
| 8.31.8. | The Range of a Function: Advanced Cases | |
| 8.31.9. | The Roots of a Function | |
| 8.31.10. | Increasing and Decreasing Functions | |
| 8.31.11. | Piecewise Functions | |
| 8.31.12. | Modeling With Linear Functions |
| 9.32.1. | Absolute Value Expressions | |
| 9.32.2. | Rules of Absolute Value | |
| 9.32.3. | Further Rules of Absolute Value | |
| 9.32.4. | Absolute Value Equations | |
| 9.32.5. | Further Absolute Value Equations | |
| 9.32.6. | Absolute Value Inequalities | |
| 9.32.7. | Absolute Value Graphs | |
| 9.32.8. | Vertical Reflections of Absolute Value Graphs | |
| 9.32.9. | Stretches of Absolute Value Graphs | |
| 9.32.10. | Combining Transformations of Absolute Value Graphs | |
| 9.32.11. | Domain and Range of Absolute Value Functions |
| 10.33.1. | The Product Rule for Exponents With Algebraic Expressions | |
| 10.33.2. | The Quotient Rule for Exponents With Algebraic Expressions | |
| 10.33.3. | The Power Rule for Exponents With Algebraic Expressions | |
| 10.33.4. | The Power of Product Rule With Algebraic Expressions | |
| 10.33.5. | The Power of Quotient Rule With Algebraic Expressions |
| 10.34.1. | Solving Exponential Equations | |
| 10.34.2. | Creating Exponential Growth Expressions | |
| 10.34.3. | Creating Exponential Decay Expressions |
| 10.35.1. | Exponential Functions | |
| 10.35.2. | Modeling Exponential Growth With Functions | |
| 10.35.3. | Interpreting Exponential Growth | |
| 10.35.4. | Solving Exponential Growth Problems | |
| 10.35.5. | Modeling Exponential Decay With Functions | |
| 10.35.6. | Interpreting Exponential Decay | |
| 10.35.7. | Solving Exponential Decay Problems | |
| 10.35.8. | Graphing Exponential Growth Functions | |
| 10.35.9. | Graphing Exponential Decay Functions |
| 11.36.1. | Introduction to Polynomials | |
| 11.36.2. | The Degree of a Polynomial | |
| 11.36.3. | Simplifying Polynomials | |
| 11.36.4. | The Distributive Law for Polynomials | |
| 11.36.5. | Adding and Subtracting Polynomials | |
| 11.36.6. | Monomials, Binomials and Trinomials | |
| 11.36.7. | Multiplying Binomials | |
| 11.36.8. | Multiplying Polynomials | |
| 11.36.9. | Squaring Binomials | |
| 11.36.10. | Expanding Binomials Using Pascal's Triangle | |
| 11.36.11. | The Difference of Squares Formula |
| 11.37.1. | The Greatest Common Factor of Two Monomials | |
| 11.37.2. | Factoring Simple Polynomials Using Greatest Common Factors | |
| 11.37.3. | Factoring Perfect Square Trinomials | |
| 11.37.4. | Factoring Perfect Square Trinomials With Leading Coefficients | |
| 11.37.5. | Factoring Differences of Squares | |
| 11.37.6. | Factoring Trinomials | |
| 11.37.7. | Factoring Trinomials Using Common Factors | |
| 11.37.8. | Factoring Trinomials With Leading Coefficients | |
| 11.37.9. | Further Factoring Trinomials With Leading Coefficients |
| 12.38.1. | Points, Lines, Rays, and Segments | |
| 12.38.2. | Parallel and Perpendicular Lines | |
| 12.38.3. | Measures of Segments | |
| 12.38.4. | Congruent Segments | |
| 12.38.5. | Midpoints | |
| 12.38.6. | Collinear Points | |
| 12.38.7. | The Segment Addition Postulate |
| 12.39.1. | Angles and Measures of Angles | |
| 12.39.2. | Measuring Angles Using a Protractor | |
| 12.39.3. | Sums of Angles | |
| 12.39.4. | Right, Straight, Full, and Null Angles | |
| 12.39.5. | Acute, Obtuse, and Reflex Angles | |
| 12.39.6. | Congruent Angles | |
| 12.39.7. | Vertical Angles | |
| 12.39.8. | Solving Problems With Angles |
| 12.40.1. | Complementary Angles | |
| 12.40.2. | Supplementary Angles | |
| 12.40.3. | Corresponding Angles | |
| 12.40.4. | Alternate Angles | |
| 12.40.5. | Consecutive Angles | |
| 12.40.6. | Angle Bisectors | |
| 12.40.7. | Segment Bisectors |
| 12.41.1. | Circles | |
| 12.41.2. | Arcs, Segments, and Sectors of Circles | |
| 12.41.3. | The Circumference of a Circle | |
| 12.41.4. | Areas of Circles |
| 13.42.1. | Interior Angles of Triangles | |
| 13.42.2. | Exterior Angles of Triangles | |
| 13.42.3. | Classifying Triangles | |
| 13.42.4. | The Triangle Inequality | |
| 13.42.5. | The Isosceles Triangle Theorem | |
| 13.42.6. | Heights of Triangles | |
| 13.42.7. | The Pythagorean Theorem | |
| 13.42.8. | The 45-45-90 Triangle | |
| 13.42.9. | The 30-60-90 Triangle |
| 13.43.1. | Polygons | |
| 13.43.2. | Interior Angles of Polygons | |
| 13.43.3. | Exterior Angles of Polygons | |
| 13.43.4. | Congruent Polygons | |
| 13.43.5. | Regular Polygons | |
| 13.43.6. | The Perimeter of a Polygon | |
| 13.43.7. | Classifying Quadrilaterals | |
| 13.43.8. | Properties of Rectangles and Squares |
| 13.44.1. | Areas of Rectangles and Squares | |
| 13.44.2. | Areas of Triangles | |
| 13.44.3. | Areas of Trapezoids | |
| 13.44.4. | Areas and Perimeters of Composite Shapes |
