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Mathematical Foundations I

Solidify your arithmetic, learn about variables and graphs, level up your algebra, and learn the essentials of geometry.

Outcomes

Content

Arithmetic Operations

Measurement and Data

Prime Factorization

Linear Equations and Inequalities

Nonlinear Equations and Inequalities

Polynomials

Functions

Geometry

1.
Fractions
39 topics
1.1. Adding and Subtracting Fractions and Whole Numbers
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. Adding and Subtracting Fractions
1.2.1. The Least Common Multiple
1.2.2. Least Common Denominator
1.2.3. Comparing Fractions
1.2.4. Adding Fractions With Unlike Denominators Using Fraction Models
1.2.5. Subtracting Fractions With Unlike Denominators Using Fraction Models
1.2.6. Adding Fractions With Unlike Denominators
1.2.7. Subtracting Fractions With Unlike Denominators
1.3. Adding and Subtracting Mixed Numbers
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. Multiplying Fractions
1.4.1. Multiplying Fractions by Whole Numbers Using Models
1.4.2. Multiplying Fractions by Whole Numbers
1.4.3. Interpreting Multiplication of Fractions and Whole Numbers
1.4.4. Multiplying Mixed Numbers by Whole Numbers
1.4.5. Multiplying Fractions by Unit Fractions Using Models
1.4.6. Multiplying Fractions Using Models
1.4.7. Multiplying Fractions
1.4.8. Multiplying Fractions: Word Problems
1.4.9. Multiplying Mixed Numbers by Fractions
1.4.10. Multiplying Mixed Numbers
1.4.11. Multiplying Mixed Numbers: Word Problems
1.4.12. Connecting Fraction Multiplication and Area
1.4.13. Finding Areas Using Fraction Multiplication
1.5. Dividing Fractions
1.5.1. Dividing Fractions Using the Relationship Between Multiplication and Division
1.5.2. Dividing Whole Numbers by Unit Fractions Using Fraction Models
1.5.3. Dividing Whole Numbers by Unit Fractions
1.5.4. Dividing Unit Fractions by Whole Numbers Using Fraction Models
1.5.5. Dividing Unit Fractions by Whole Numbers
1.5.6. Reciprocals
1.5.7. Dividing Whole Numbers by Fractions Using Models
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.
Ratios & Percentages
27 topics
2.6. Ratios
2.6.1. Introduction to Ratios
2.6.2. Equivalent Ratios
2.6.3. Writing Ratios Using Fractions
2.6.4. Ratio Tables
2.6.5. Graphing Ratios
2.6.6. Unit Rates
2.6.7. Solving Problems Using Unit Rates
2.6.8. Speed as a Unit Rate
2.7. Working With Units
2.7.1. Units
2.7.2. Units of Area and Volume
2.7.3. Unit Conversions Using Base Units of Mass
2.7.4. Two-Step Unit Conversions
2.7.5. Unit Conversions Using Base Units of Length
2.7.6. Unit Conversions Using Units of Time
2.7.7. Unit Conversions Using Base Units of Area
2.7.8. Determining Units in Formulas
2.7.9. Selecting Units for Rates of Change
2.7.10. Degrees of Accuracy
2.8. Percentages
2.8.1. Understanding Percentages Using Models
2.8.2. Converting Between Percentages and Fractions
2.8.3. Converting Between Percentages and Decimals
2.8.4. Finding Part of a Number Given a Whole and a Percentage
2.8.5. Finding Part of a Number Given a Whole and a Percentage: Word Problems
2.8.6. Finding a Percentage Given Two Numbers
2.8.7. Finding a Percentage Given Two Numbers: Word Problems
2.8.8. Finding a Total Given a Part and a Percentage
2.8.9. Percentage Increase, Decrease, and Error
3.
The Number System
22 topics
3.9. Addition and Subtraction of Rational Numbers
3.9.1. Subtracting a Positive Number From a Smaller Positive Number
3.9.2. Subtracting a Positive Number From a Negative Number
3.9.3. Subtracting a Positive Fraction From a Smaller Fraction
3.9.4. Subtracting a Positive Decimal From a Smaller Decimal
3.9.5. Adding a Positive Number to a Negative Number
3.9.6. Adding a Negative Number
3.9.7. Subtracting a Negative Number
3.9.8. Additive Inverses of Numbers
3.9.9. Solving Problems Using Addition and Subtraction of Rational Numbers
3.10. Multiplication and Division of Rational Numbers
3.10.1. Multiplying Positive Numbers With Negative Numbers
3.10.2. Multiplying Negative Numbers
3.10.3. Dividing With Negative Numbers
3.10.4. Dividing With Negative Decimals and Fractions
3.10.5. Reciprocals of Rational Numbers
3.10.6. Multiplying and Dividing With Zero
3.10.7. Fractions of Fractions
3.10.8. Solving Problems Using the Four Operations on Rational Numbers
3.11. Number Theory
3.11.1. The Multiples of a Number
3.11.2. Prime and Composite Numbers
3.11.3. Prime Factorization of Integers
3.11.4. The Greatest Common Factor of Two Integers
3.11.5. The Lowest Common Multiple of Two Integers
4.
Exponents & Radicals
32 topics
4.12. Exponents
4.12.1. Introduction to Exponents
4.12.2. Evaluating Exponents
4.12.3. Evaluating Larger Exponents
4.12.4. Evaluating Exponents With Fractional Bases
4.12.5. Evaluating Exponents With Decimal Bases
4.12.6. Evaluating Whole Number Expressions Containing Exponents
4.12.7. Squaring Rational Numbers
4.12.8. Cubing Rational Numbers
4.12.9. Exponents With Rational Bases
4.12.10. The Zeroth Power
4.12.11. Powers of Negative One
4.12.12. Negative Exponents
4.13. The Rules of Exponents
4.13.1. The Product Rule for Exponents
4.13.2. The Quotient Rule for Exponents
4.13.3. The Power Rule for Exponents
4.13.4. The Power of Product Rule for Exponents
4.13.5. The Power of Quotient Rule for Exponents
4.13.6. Combining the Rules of Exponents
4.14. Order of Operations
4.14.1. Evaluating Rational Number Expressions Without Exponents
4.14.2. Evaluating Rational Number Expressions With Positive Integer Exponents
4.14.3. Evaluating Rational Number Expressions With Integer Exponents
4.15. Radicals
4.15.1. The Square Root of a Perfect Square
4.15.2. Squaring a Square Root
4.15.3. The Cube Root of a Perfect Cube
4.15.4. Surds
4.15.5. Simplifying Expressions With Surds
4.15.6. Evaluating Numerical Expressions Containing Radicals
4.15.7. Adding and Subtracting Radicals
4.15.8. Rationalizing Denominators
4.16. The Rules of Radicals
4.16.1. Radicals as Fractional Exponents
4.16.2. The Product Rule for Radicals
4.16.3. The Quotient Rule for Radicals
6.
Equations & Inequalities
46 topics
6.17. Algebraic Expressions
6.17.1. Introduction to Algebraic Expressions
6.17.2. Constructing Algebraic Expressions
6.17.3. Evaluating Linear Expressions
6.17.4. Evaluating Rational Expressions
6.17.5. Identifying Terms in Linear Expressions
6.17.6. Identifying Coefficients and Constants in Linear Expressions
6.17.7. The Greatest Common Factor of Two Linear Expressions
6.18. Simplifying Linear Expressions
6.18.1. Identifying Like Terms in a Linear Expression
6.18.2. Collecting Like Terms in a Linear Expression
6.18.3. Applying the Distributive Law With Linear Expressions
6.18.4. The Distributive Law With Three Terms
6.18.5. Distributing the Negative Sign in a Linear Expression
6.18.6. Simplifying Linear Expressions Using the Distributive Law
6.18.7. Simplifying Linear Expressions When a Group of Terms Is Subtracted
6.18.8. Simplifying Linear Expressions Containing Fractions
6.18.9. Factoring Numerical Expressions
6.18.10. Factoring Linear Expressions
6.19. Solving One-Step Linear Equations
6.19.1. Solving Linear Equations by Trial and Error
6.19.2. Solving One-Step Addition and Subtraction Equations
6.19.3. Solving One-Step Multiplication and Division Equations
6.20. Solving Multi-Step Linear Equations
6.20.1. Solving Two-Step Equations
6.20.2. Solving Linear Equations With Fractional Coefficients
6.20.3. Solving Linear Equations With Decimal Coefficients
6.20.4. Solving Linear Equations With Variables on Both Sides
6.20.5. Solving Linear Equations by Clearing a Rational Expression
6.20.6. Solving Linear Equations Using Cross-Multiplication
6.20.7. Solving Two-Variable Equations
6.20.8. Equations With Many Solutions and No Solutions
6.20.9. Solving Linear Equations With Unknown Coefficients
6.20.10. Solving Linear Equations With Unknown Coefficients by Factoring
6.20.11. Solving Many-Variable Equations
6.21. Modeling With Linear Equations
6.21.1. Interpreting Linear Expressions
6.21.2. Modeling With Linear Equations
6.22. Solving Linear Inequalities
6.22.1. Representing Inequalities on Number Lines
6.22.2. Representing Compound Inequalities on Number Lines
6.22.3. Verifying Solutions of Linear Inequalities
6.22.4. Solving Linear Inequalities
6.22.5. Solving Compound Inequalities
6.22.6. Expressing Inequalities Using Interval Notation
6.22.7. Unions of Intervals
6.22.8. Intersections of Intervals
6.22.9. Compound OR Inequalities
6.22.10. Compound AND Inequalities
6.23. Nonlinear Equations
6.23.1. Solving Equations Using the Square Root Method
6.23.2. Solving Equations With Odd Exponents Using the Nth Root Method
6.23.3. Solving Equations With Even Exponents Using the Nth Root Method
7.
Two-Variable Equations
22 topics
7.24. Graphs of Linear Equations
7.24.1. The Cartesian Coordinate System
7.24.2. The Distance Between Two Points in the Coordinate Plane
7.24.3. Two-Variable Linear Equations and Their Solutions
7.24.4. Graphing Linear Equations
7.24.5. Horizontal and Vertical Lines
7.24.6. Calculating Slopes of Straight Lines
7.24.7. Equations of Lines in Slope-Intercept Form
7.24.8. Finding Properties of Lines Given in Slope-Intercept Form
7.24.9. Equations of Lines in Point-Slope Form
7.24.10. Equations of Lines in Standard Form
7.24.11. Determining Properties of Lines Given in Standard Form
7.25. Modeling With Two-Variable Linear Equations
7.25.1. Modeling With Linear Equations in Two Variables
7.25.2. Further Modeling With Linear Equations in Two Variables
7.25.3. Analyzing and Interpreting Graphs of Linear Equations
7.26. Systems of Linear Equations
7.26.1. Introduction to Systems of Linear Equations
7.26.2. Solving Systems of Two Linear Equations Using Substitution
7.26.3. Solving Systems of Two Linear Equations Using Elimination
7.26.4. Systems of Linear Equations With Fractional Coefficients
7.26.5. Systems of Linear Equations With Decimal Coefficients
7.26.6. Solving Systems of Nonlinear Equations Using Graphs
7.26.7. Systems of Equations With No Solutions and Infinitely Many Solutions
7.26.8. Calculating the Intersection of Two Lines
8.
Radical & Rational Expressions
15 topics
8.27. Radical Expressions
8.27.1. Writing Radical Expressions Using Fractional Exponents
8.27.2. The Square Root of a Perfect Square With Algebraic Expressions
8.27.3. The Square Root of a Perfect Square With Domain Restrictions
8.27.4. The Cube Root of a Perfect Cube With Algebraic Expressions
8.27.5. Simplifying Square Root Expressions Using the Product Rule
8.27.6. Combining Radical Expressions Using the Product Rule
8.27.7. Evaluating Algebraic Radical Expressions
8.27.8. Adding and Subtracting Radical Expressions
8.28. Rational Expressions
8.28.1. Equivalent Expressions With Fractions
8.28.2. Simplifying Rational Expressions
8.28.3. Simplifying Rational Expressions by Factoring
8.28.4. Splitting Rational Expressions Into Separate Terms
8.29. Rational Equations
8.29.1. Solving Rational Equations Containing One Fractional Term
8.29.2. Solving Rational Equations Using Cross-Multiplication
8.29.3. Solving Rational Equations Containing Binomials Using Cross-Multiplication
9.
Functions
12 topics
9.30. Functions
9.30.1. Introduction to Functions
9.30.2. Visual Representations of Functions
9.30.3. Graphs of Functions
9.30.4. The Domain of a Function
9.30.5. Global Extrema of Functions
9.30.6. End Behavior of Functions
9.30.7. The Range of a Function
9.30.8. The Range of a Function: Advanced Cases
9.30.9. The Roots of a Function
9.30.10. Increasing and Decreasing Functions
9.30.11. Piecewise Functions
9.30.12. Modeling With Linear Functions
10.
Absolute Value
6 topics
10.31. Absolute Value Expressions, Equations & Inequalities
10.31.1. Evaluating Absolute Value Expressions
10.31.2. Rules of Absolute Value
10.31.3. Further Rules of Absolute Value
10.31.4. Absolute Value Equations
10.31.5. Absolute Value Inequalities
10.31.6. Absolute Value Graphs
11.
Exponential Functions
17 topics
11.32. Rules of Exponents
11.32.1. The Product Rule for Exponents With Algebraic Expressions
11.32.2. The Quotient Rule for Exponents With Algebraic Expressions
11.32.3. The Power Rule for Exponents With Algebraic Expressions
11.32.4. The Power of Product Rule With Algebraic Expressions
11.32.5. The Power of Quotient Rule With Algebraic Expressions
11.33. Exponential Expressions and Equations
11.33.1. Solving Exponential Equations with Integer Solutions
11.33.2. Creating Exponential Growth Expressions
11.33.3. Creating Exponential Decay Expressions
11.34. Exponential Functions
11.34.1. Exponential Functions
11.34.2. Modeling Exponential Growth With Functions
11.34.3. Interpreting Exponential Growth
11.34.4. Solving Exponential Growth Problems
11.34.5. Modeling Exponential Decay With Functions
11.34.6. Interpreting Exponential Decay
11.34.7. Solving Exponential Decay Problems
11.34.8. Graphing Exponential Growth Functions
11.34.9. Graphing Exponential Decay Functions
12.
Polynomials
19 topics
12.35. Polynomials
12.35.1. Introduction to Polynomials
12.35.2. The Degree of a Polynomial
12.35.3. Simplifying Polynomials
12.35.4. The Distributive Law for Polynomials
12.35.5. Adding and Subtracting Polynomials
12.35.6. Monomials, Binomials and Trinomials
12.35.7. Multiplying Binomials
12.35.8. Multiplying Polynomials
12.35.9. Squaring Binomials
12.35.10. Expanding Binomials Using Pascal's Triangle
12.35.11. The Difference of Squares Formula
12.36. Factoring Polynomials
12.36.1. The Greatest Common Factor of Two Monomials
12.36.2. Factoring Simple Polynomials Using Greatest Common Factors
12.36.3. Factoring Perfect Square Trinomials
12.36.4. Factoring Perfect Square Trinomials With Leading Coefficients
12.36.5. Factoring Differences of Squares
12.36.6. Factoring Trinomials
12.36.7. Factoring Trinomials Using Common Factors
12.36.8. Factoring Trinomials With Leading Coefficients
13.
Geometry Fundamentals
21 topics
13.37. Introduction to Geometry
13.37.1. Points, Lines, Rays, and Parallel Lines
13.37.2. Segments and Measures of Segments
13.37.3. Congruent Segments
13.37.4. Midpoints
13.37.5. Collinear Points
13.37.6. The Segment Addition Postulate
13.38. Angles
13.38.1. Angles and Measures of Angles
13.38.2. Congruent Angles
13.38.3. Sums of Angles
13.38.4. Null, Right, Straight, and Full Angles
13.38.5. Vertical Angles
13.38.6. Acute, Obtuse, and Reflex Angles
13.38.7. Solving Problems With Angles
13.39. Advanced Angles
13.39.1. Complementary Angles
13.39.2. Supplementary Angles
13.39.3. Parallel Lines and Transversals
13.39.4. Perpendicular Lines and Bisectors
13.40. Circles
13.40.1. Introduction to Circles
13.40.2. Arcs, Segments, and Sectors of Circles
13.40.3. The Circumference of a Circle
13.40.4. Areas of Circles
14.
Polygons
20 topics
14.41. Triangles
14.41.1. Interior Angles of Triangles
14.41.2. Exterior Angles of Triangles
14.41.3. Classifying Triangles
14.41.4. The Triangle Inequality
14.41.5. The Isosceles Triangle Theorem
14.41.6. Heights of Triangles
14.41.7. The Pythagorean Theorem
14.41.8. The 45-45-90 Triangle
14.41.9. The 30-60-90 Triangle
14.42. Polygons
14.42.1. Polygons
14.42.2. Interior Angles of Polygons
14.42.3. Exterior Angles of Polygons
14.42.4. Congruent Polygons
14.42.5. Regular Polygons
14.42.6. The Perimeter of a Polygon
14.42.7. Classifying Quadrilaterals
14.42.8. Properties of Rectangles and Squares
14.43. Area and Perimeter
14.43.1. Areas of Rectangles and Squares
14.43.2. Areas of Triangles
14.43.3. Areas of Trapezoids