Developmental Mathematics: North Carolina Curriculum
1.1 Introduction to Integers
- Examples
- Example 1: Finding Opposites
- Example 2: Graphing Integers
- Example 3: Graphing Integers
- Example 4: Using Inequality Symbols
- Example 5: Absolute Value
- Example 6: Absolute Value
- Example 7: Absolute Value
- Example 8: Absolute Value
- Example 9: Absolute Value
- Example 10: Finding the Possible Integer Values
- Bonus Videos
- Bonus 1: Introduction to Integers
- Bonus 2: Introduction to Integers
- Bonus 3: Introduction to Integers
1.2 Addition with Integers
- Examples
- Example 1: Addition with Whole Numbers
- Example 2: Addition with Integers
- Example 3: Finding the Additive Inverse
- Example 4: The Properties of Addition
- Example 6: Addition with Integers
- Example 7: Solutions to Equations
- Example 8: Application
- Bonus Videos
- Bonus 1: Addition with Integers
- Bonus 2: Addition with Integers
1.3 Subtraction with Integers
- Examples
- Example 1: Subtraction with Integers
- Example 2: Subtraction with Integers
- Example 3: Addition and Subtraction with Integers
- Example 4: Subtraction with Integers
- Example 5: Subtraction with Integers
- Example 6: Subtraction with Integers
- Example 7: Solutions to Equations
- Example 8: Application
- Example 9: Application
- Bonus Videos
- Bonus 1: Subtraction with Integers
- Bonus 2: Subtraction with Integers
1.4 Multiplication and Division with Integers
- Examples
- Example 1: Multiplication with Integers
- Example 2: Multiplication with Integers
- Example 3: The Properties of Multiplication
- Example 5: Multiplication with Integers
- Example 6: The Distributive Property
- Example 7: Division with Integers
- Example 8: Division Involving 0
- Example 9: Application
- Example 10: Application
- Example 11: Application
- Bonus Videos
- Bonus 1: Multiplication and Division with Integers
- Bonus 2: Multiplication and Division with Integers
1.5 Applications: Change in Value and Average
1.6 Exponents and Order of Operations
- Examples
- Example 1: Exponents
- Example 2: Reading Exponents
- Example 4: Order of Operations with Integers
- Example 5: Order of Operations with Integers
- Example 6: Order of Operations with Integers
- Bonus Videos
- Bonus 1: Exponents and Order of Operations
- Bonus 2: Exponents and Order of Operations
- Bonus 3: Exponents and Order of Operations
1.7 Square Roots and the Pythagorean Theorem
- Examples
- Example 1: Calculating Squares and Square Roots
- Example 3: Right Triangles
- Example 4: Finding the Length of the Hypotenuse
- Example 5: Finding the Length of the Hypotenuse
- Example 6: Finding the Length of the Hypotenuse
- Bonus Videos
- Bonus 1: Square Roots and the Pythagorean Theorem
- Bonus 2: Square Roots and the Pythagorean Theorem
1.8 Angles
1.9 Perimeter
1.10 Area
2.1a Tests for Divisibility
2.1b Prime Numbers
2.1c Prime Factorization
2.2 Least Common Multiple (LCM)
2.3 Introduction to Fractions
- Examples
- Example 1: Understanding Fractions
- Example 2: Proper Fractions
- Example 3: Improper Fractions
- Example 4: The Number 0 in Fractions
- Example 5: Placement of Negative Signs in Fractions
- Example 6: Multiplication with Fractions
- Example 7: Multiplication with Fractions
- Example 8: Application
- Example 9: Finding Equivalent Fractions
- Example 10: Finding Equivalent Fractions
- Example 12: Reducing Fractions to Lowest Terms
- Example 13: Reducing Fractions to Lowest Terms
- Example 14: Reducing Fractions to Lowest Terms
- Example 16: Changing a Mixed Number to an Improper Fraction
- Example 18: Changing an Improper Fraction to a Mixed Number
- Bonus Videos
- Bonus 1: Introduction to Fractions
- Bonus 2: Introduction to Fractions
- Bonus 3: Introduction to Fractions
2.4 Multiplication and Division with Fractions and Mixed Numbers
- Examples
- Example 1: Multiplying with Mixed Numbers
- Example 2: Multiplying with Fractions and Mixed Numbers
- Example 3: Multiplying and Reducing with Fractions
- Example 4: Multiplying and Reducing with Fractions
- Example 6: Multiplying and Reducing with Mixed Numbers
- Example 7: Multiplying and Reducing with Fractions
- Example 8: Multiplying and Reducing with Fractions
- Example 9: Application
- Example 10: Reciprocals
- Example 11: Reciprocals
- Example 12: Dividing with Fractions
- Example 13: Dividing and Reducing with Fractions and Mixed Numbers
- Example 15: Multiplying and Dividing with Fractions and Mixed Numbers
- Example 16: Application
- Bonus Videos
- Bonus 1: Multiplication and Division with Fractions and Mixed Numbers
- Bonus 2: Multiplication and Division with Fractions and Mixed Numbers
- Bonus 3: Multiplication and Division with Fractions and Mixed Numbers
2.5 Addition and Subtraction with Fractions
- Examples
- Example 1: Adding Fractions with the Same Denominator
- Example 2: Adding Fractions with the Same Denominator
- Example 3: Adding Fractions with Different Denominators
- Example 4: Adding Fractions with Different Denominators
- Example 5: Adding Fractions with Different Denominators
- Example 6: Subtracting Fractions with the Same Denominator
- Example 7: Subtracting Fractions with the Same Denominator
- Example 8: Subtracting Fractions with Different Denominators
- Example 9: Subtracting Fractions with Different Denominators
- Example 11: Application
- Bonus Videos
- Bonus 1: Addition and Subtraction with Fractions
- Bonus 2: Addition and Subtraction with Fractions
2.6 Addition and Subtraction with Mixed Numbers
- Examples
- Example 1: Adding Mixed Numbers with the Same Denominator
- Example 2: Adding Mixed Numbers with Different Denominators
- Example 3: Adding Mixed Numbers with Different Denominators
- Example 4: Adding Mixed Numbers and Whole Numbers
- Example 5: Subtracting Mixed Numbers with the Same Denominator
- Example 6: Subtracting Mixed Numbers with Different Denominators
- Example 7: Subtracting Mixed Numbers by Borrowing
- Example 8: Subtracting Mixed Numbers from Whole Numbers
- Example 9: Subtracting Mixed Numbers by Borrowing
- Example 11: Finding the Algebraic Sum of Mixed Numbers
- Example 12: Finding the Algebraic Sum of Mixed Numbers
- Example 13: Adding Mixed Numbers Using Improper Fractions
- Example 14: Adding Mixed Numbers Using Improper Fractions
- Example 15: Subtracting Mixed Numbers Using Improper Fractions
- Bonus Videos
- Bonus 1: Addition and Subtraction with Mixed Numbers
2.7 Order of Operations with Fractions and Mixed Numbers
- Examples
- Example 1: Comparing Fractions
- Example 2: Comparing Fractions
- Example 3: Comparing Fractions
- Example 4: Order of Operations with Fractions
- Example 5: Order of Operations with Fractions
- Example 7: Order of Operations with Mixed Numbers
- Example 8: Order of Operations with Mixed Numbers
- Example 9: Average of Mixed Numbers
- Bonus Videos
- Bonus 1: Order of Operations with Fractions and Mixed Numbers
2.8 Reading, Writing, and Rounding Decimal Numbers
- Examples
- Example 1: Reading and Writing Decimal Numbers
- Example 2: Reading and Writing Decimal Numbers
- Example 4: Reading and Writing Decimal Numbers
- Example 5: Comparing Decimal Numbers
- Example 6: Comparing Decimal Numbers
- Example 7: Comparing Decimal Numbers
- Example 8: Rounding Decimal Numbers
- Example 9: Rounding Decimal Numbers
- Bonus Videos
- Bonus 1: Reading, Writing, and Rounding Decimal Numbers
2.9 Addition and Subtraction with Decimal Numbers
- Examples
- Example 1: Adding Decimal Numbers
- Example 2: Adding Decimal Numbers
- Example 3: Subtracting Decimal Numbers
- Example 4: Application
- Example 5: Adding Signed Decimal Numbers
- Example 6: Subtracting Signed Decimal Numbers
- Example 7: Estimating the Sum of Decimal Numbers
- Bonus Videos
- Bonus 1: Addition and Subtraction with Decimal Numbers
2.10 Multiplication and Division with Decimal Numbers
- Examples
- Example 1: Multiplying Positive Decimal Numbers
- Example 2: Multiplying Signed Decimal Numbers
- Example 3: Multiplying by Powers of 10
- Example 4: Dividing Decimal Numbers
- Example 5: Dividing Decimal Numbers
- Example 6: Dividing Decimal Numbers
- Example 7: Dividing Decimal Numbers
- Example 8: Dividing by Powers of 10
- Example 9: Estimating Products of Decimal Numbers
- Example 10: Estimating Quotients of Decimal Numbers
- Example 11: Buying a Car
- Example 12: Fuel Efficiency
- Example 13: Jogging
- Example 14: Price of Gasoline
- Bonus Videos
- Bonus 1: Multiplication and Division with Decimal Numbers
2.11 Decimals, Fractions, and Scientific Notation
- Examples
- Example 1: Changing a Decimal Number to a Fraction
- Example 2: Changing a Fraction to a Decimal Number
- Example 3: Changing a Fraction to a Decimal Number
- Example 4: Changing a Fraction to a Decimal Number
- Example 5: Changing a Fraction to a Decimal Number
- Example 6: Operating with Both Decimal Numbers and Fractions
- Example 7: Operating with Both Decimal Numbers and Fractions
- Example 8: Operating with Both Decimal Numbers and Fractions
- Example 9: Operating with Both Decimal Numbers and Fractions
- Example 10: Absolute Value
- Example 11: Decimal Numbers in Scientific Notation
- Bonus Videos
- Bonus 1: Decimals, Fractions, and Scientific Notation
- Bonus 2: Decimals, Fractions, and Scientific Notation
- Bonus 3: Decimals, Fractions, and Scientific Notation
- Bonus 4: Decimals, Fractions, and Scientific Notation
2.12 Circles
3.1 Ratios and Proportions
3.2 Solving Proportions
3.3 Basics of Percent
- Examples
- Example 1: Writing Fractions with 100 in the Denominator as Percents
- Example 2: Percent of Profit
- Example 4: Changing a Decimal Number to a Percent
- Example 5: Changing a Percent to a Decimal Number
- Example 6: Changing a Fraction to a Percent
- Example 7: Changing a Fraction to a Percent
- Example 9: Changing a Fraction to a Percent
- Example 10: Application
- Example 11: Changing a Percent to a Fraction
- Bonus Videos
- Bonus 1: Basics of Percent
- Bonus 2: Basics of Percent
3.4 Solving Percent Problems
3.5 Applications: Discount, Sales Tax, Commission, and Percent Increase/Decrease
- Examples
- Example 1: Solving Discount Problems
- Example 2: Solving Discount Problems
- Example 3: Solving Sales Tax Problems
- Example 4: Solving Commission Problems
- Example 5: Finding the Percent Increase
- Example 6: Finding the Percent Decrease
- Bonus Videos
- Bonus 1: Applications: Discount, Sales Tax, Commission, and Percent Increase/Decrease
- Bonus 2: Applications: Discount, Sales Tax, Commission, and Percent Increase/Decrease
3.6 Applications: Profit, Simple Interest, and Compound Interest
- Examples
- Example 1: Calculating Percent of Profit
- Example 2: Calculating Simple Interest
- Example 4: Calculating Principal Using the Simple Interest Formula
- Example 5: Calculating Time Using the Simple Interest Formula
- Example 6: Calculating Compound Interest
- Example 7: Calculating Compound Interest
- Bonus Videos
- Bonus 1: Applications: Profit, Simple Interest, and Compound Interest
- Bonus 2: Applications: Profit, Simple Interest, and Compound Interest
- Bonus 3: Applications: Profit, Simple Interest, and Compound Interest
3.7 Similar Triangles
3.8 U.S. Measurements
3.9 The Metric System - Length
- Examples
- Example 1: Converting Metric Units of Length
- Example 2: Converting Metric Units of Length
- Example 3: Converting Metric Units of Length
- Example 4: The Prefixes Mega-, Giga-, and Tera-
- Bonus Videos
- Bonus 1: The Metric System - Length
- Bonus 2: The Metric System - Length
- Bonus 3: The Metric System - Length
3.10 The Metric System - Capacity and Weight
- Examples
- Example 1: Common Metric Units of Capacity
- Example 2: Converting Metric Units of Capacity
- Example 3: Converting Metric Units of Capacity
- Example 4: Converting Metric Units of Capacity
- Example 5: Converting Metric Units of Capacity
- Example 6: Common Metric Units of Weight
- Example 7: Converting Metric Units of Weight
- Example 8: Converting Metric Units of Weight
- Bonus Videos
- Bonus 1: The Metric System - Capacity and Weight
- Bonus 2: The Metric System - Capacity and Weight
3.11 U.S. Customary Measurements and Metric Equivalents
4.1a Variables and Algebraic Expressions
4.1b Simplifying Expressions
4.1c Evaluating Algebraic Expressions
4.2 Translating English Phrases and Algebraic Expressions
4.3a Solving Linear Equations: x + b = c
4.3b Solving Linear Equations: ax = c
4.4 Solving Linear Equations: ax + b = c
- Examples
- Example 1: Solving Linear Equations of the Form ax + b = c
- Example 2: Solving Linear Equations of the Form ax + b = c
- Example 3: Solving Linear Equations Involving Decimals
- Example 4: Solving Linear Equations Involving Decimals
- Example 5: Solving Linear Equations with Fractional Coefficients
- Example 6: Solving Linear Equations with Fractional Coefficients
- Bonus Videos
- Bonus 1: Solving Linear Equations: ax + b = c
- Bonus 2: Solving Linear Equations: ax + b = c
4.5 Solving Linear Equations: ax + b = cx + d
- Examples
- Example 1: Solving Equations of the Form ax + b = cx + d
- Example 2: Solving Equations of the Form ax + b = cx + d
- Example 3: Solving Linear Equations Involving Decimals
- Example 4: Solving Linear Equations with Fractional Coefficients
- Example 5: Solving Equations with Parentheses
- Example 6: Solving Equations with Parentheses
- Example 8: Solutions of Equations
- Example 9: Solutions of Equations
- Example 10: Solutions of Equations
- Bonus Videos
- Bonus 1: Solving Linear Equations: ax + b = cx + d
- Bonus 2: Solving Linear Equations: ax + b = cx + d
- Bonus 3: Solving Linear Equations: ax + b = cx + d
- Bonus 4: Solving Linear Equations: ax + b = cx + d
4.6 Linear Inequalities
- Examples
- Example 1: Graphing Intervals
- Example 2: Graphing Intervals
- Example 3: Graphing Intervals
- Example 4: Graphing Intervals
- Example 5: Sets of Real Numbers Illustrating Union
- Example 6: Sets of Real Numbers Illustrating Intersection
- Example 7: Solving Linear Inequalities
- Example 8: Solving Linear Inequalities
- Example 9: Solving Linear Inequalities
- Example 11: Solving Compound Inequalities
- Example 12: Solving Compound Inequalities
- Example 13: Solving Compound Inequalities
- Bonus Videos
- Bonus 1: Linear Inequalities
- Bonus 2: Linear Inequalities
- Bonus 3: Linear Inequalities
4.7 Applications: Number Problems, Consecutive Integers, and Inequalities
- Examples
- Example 2: Number Problems
- Example 3: Number Problems
- Example 4: Number Problems
- Example 5: Consecutive Integers
- Example 6: Consecutive Integers
- Example 7: Application using a Linear Equation
- Example 8: Application using a Linear Equation
- Example 9: Application using an Inequality
- Example 10: Application using an Inequality
- Bonus Videos
- Bonus 1: Applications: Number Problems, Consecutive Integers, and Inequalities
- Bonus 2: Applications: Number Problems, Consecutive Integers, and Inequalities
- Bonus 3: Applications: Number Problems, Consecutive Integers, and Inequalities
4.8 Working with Formulas
- Examples
- Example 1: Evaluating Formulas
- Example 2: Evaluating Formulas
- Example 3: Evaluating Formulas
- Example 4: Evaluating Formulas
- Example 5: Solving for Different Variables
- Example 6: Solving for Different Variables
- Example 7: Solving for Different Variables
- Example 8: Solving for Different Variables
- Bonus Videos
- Bonus 1: Working with Formulas
- Bonus 2: Working with Formulas
- Bonus 3: Working with Formulas
4.9 Applications: Distance - Rate - Time, Interest, Average, Cost
5.1 Reading Graphs
5.2 The Cartesian Coordinate System
5.3 Graphing Linear Equations in Two Variables
- Examples
- Example 1: Graphing a Linear Equation in Two Variables
- Example 2: x- and y-Intercepts
- Bonus Videos
- Bonus 1: Graphing Linear Equations in Two Variables
- Bonus 2: Graphing Linear Equations in Two Variables
- Bonus 3: Graphing Linear Equations in Two Variables
- Bonus 4: Graphing Linear Equations in Two Variables
5.4 The Slope - Intercept Form
5.5a The Point - Slope Form
- Examples
- Example 1: Graphing a Line Given a Point and the Slope
- Example 2: Finding Equations of Lines Using the Slope and a Point
- Example 3: Finding Equations of Lines Using Two Points
- Example 4: Finding Equations of Lines Using a Graph
- Bonus Videos
- Bonus 1: The Point - Slope Form
- Bonus 2: The Point - Slope Form
- Bonus 3: The Point - Slope Form
5.5b Parallel and Perpendicular Lines
5.6 Introduction to Functions
6.1 Introduction to Polynomials
6.2 Addition and Subtraction with Polynomials
6.3a Exponents I
- Examples
- Example 1: Product Rule for Exponents
- Example 2: Product Rule for Exponents
- Example 3: The Exponent 0
- Example 4: Quotient Rule for Exponents
- Example 5: Dividing Terms with Coefficients
- Example 6: Negative Exponents
- Example 7: Combining Rules for Exponents
- Bonus Videos
- Bonus 1: Exponents I
- Bonus 2: Exponents I
6.3b Exponents II
- Examples
- Example 9: Power Rule for Exponents
- Example 10: Rule for Power of a Product
- Example 11: Rule for Power of a Quotient
- Example 12: Using Combinations of Rules for Exponents
- Example 13: Two Approaches with Fractional Expressions and Negative Exponents
- Example 14: A More Complex Example
- Bonus Videos
- Bonus 1: Exponents II
- Bonus 2: Exponents II
6.4 Multiplication with Polynomials
6.5a The FOIL Method
- Examples
- Example 1: FOIL Method
- Bonus Videos
- Bonus 1: The FOIL Method
- Bonus 2: The FOIL Method
6.5b Special Products of Polynomials
6.6a Division by a Monomial
- Examples
- Example 1: Dividing Polynomials by Monomials
- Bonus Videos
- Bonus 1: Division by a Monomial
6.6b Greatest Common Factor of a Set of Terms
- Examples
- Example 2: Finding the GCF
- Bonus Videos
- Bonus 1: Greatest Common Factor of a Set of Terms
6.6c Greatest Common Factor of a Polynomial
6.6d Factor Polynomials by Grouping
6.7 Factoring Trinomials: x^2 + bx + c
6.8a Factoring Trinomials Using the Trial - and - Error Method
6.8b Factoring Trinomials Using the ac - Method
6.9 Special Factoring Techniques
6.10 Solving Quadratic Equations by Factoring
- Examples
- Example 1: Solving Factored Quadratic Equations
- Example 2: Solving Quadratic Equations by Factoring
- Example 4: Solving Higher Degree Equations
- Example 5: Using the Factor Theorem to Find Equations with Given Roots
- Bonus Videos
- Bonus 1: Solving Quadratic Equations by Factoring
- Bonus 2: Solving Quadratic Equations by Factoring
6.11 Applications of Quadratic Equations
6.12 Quadratic Functions: y = ax^2 + bx + c
7.1 Introduction to Rational Expressions
7.2 Multiplication and Division with Rational Expressions
7.3 Addition and Subtraction with Rational Expressions
- Examples
- Example 1: Adding Rational Expressions with a Common Denominator
- Example 2: Adding Rational Expressions with Different Denominators
- Example 4: Subtracting Rational Expressions with a Common Denominator
- Example 5: Subtracting Rational Expressions with Different Denominators
- Bonus Videos
- Bonus 1: Addition and Subtraction with Rational Expressions
- Bonus 2: Addition and Subtraction with Rational Expressions
- Bonus 3: Addition and Subtraction with Rational Expressions
7.4 Solving Rational Equations
7.5 Applications: Rational Expressions
7.6 Applications: Variation
8.1 Radical Expressions
8.2 Simplifying Radical Expressions
- Examples
- Example 1: Simplifying Radical Expressions with Square Roots
- Example 2: Simplifying Square Roots with Variables
- Example 3: Simplifying Square Roots with Variables
- Example 4: Simplifying Radical Expressions with Cube Roots
- Bonus Videos
- Bonus 1: Simplifying Radical Expressions
- Bonus 2: Simplifying Radical Expressions
8.3 Rational Exponents
- Examples
- Example 1: Evaluating Principal Roots
- Example 2: Conversion Between Exponential Notation and Radical Notation
- Example 3: Simplifying Expressions with Rational Exponents
- Example 4: Simplifying Radical Notation by Changing to Exponential Notation
- Bonus Videos
- Bonus 1: Rational Exponents
- Bonus 2: Rational Exponents
- Bonus 3: Rational Exponents