## Welcome to the St. Clair College Mathematics Tutorial Website

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#### Unit 1: Whole Numbers, Fractions and Decimals

- Intro to Rational & Irrational Numbers
- Classifying Numbers: Rational & Irrational
- Classifying Numbers
- Number Sets Example
- Intro to Multiplication
- Multiplication as groups of objects
- More on the concept of Multiplication
- Multiplication Tables
- Multiple Digit Multiplication
- The Idea of Division
- Long Division Review
- Integers Review - Adding Negative Numbers
- Integers Review - Adding Numbers with Different Signs
- Integers Review - Adding and Subtracting Negative Numbers
- Multiplying Positive and Negative Numbers
- Dividing Positive and Negative Numbers
- Exponents Review - Understanding Exponents 1
- Exponents Review - Understanding Exponents 2
- Absolute Value of Integers
- Order of Operations - Introduction to Order of Operations (Remember Parenthesis has the same meaning as Brackets)
- Order of Operations - Example 1
- Order of Operations - Example 2
- Order of Operations - Example 3
- Comparing Improper Fractions Mixed Numbers
- Equivalent Fractions
- Converting Mixed Numbers into Improper Fractions
- Converting an Improper Fraction into a Mixed Numbers
- Adding Fractions with Same Denominators
- Finding a Common Denominator
- Prime Factorization
- Adding Fractions with Unlike Denominators
- Adding Mixed Numbers with Different Denominators
- Subtracting Fractions
- Subtracting Mixed Numbers
- Multiplying Fractions
- Multiplying Mixed Numbers
- Understanding Fractions as Division
- Creating a Fraction Through Division
- Creating Mixed Numbers with Fraction Division
- Understanding Dividing Fractions
- Dividing Mixed Numbers
- Representing a Number as a Decimal, Fraction and Percent Example 1
- Representing a Number as a Decimal, Fraction and Percent Example 2
- Representing a Number as a Decimal, Fraction and Percent Example 3
- Percent Problem Example 1
- Percent Problem Example 2
- Percent Problem Example 3
- Scientific Notation Examples
- Converting Decimal Number into a Number in Scientific Notation
- Multiplying in Scientific Notation
- Scientific Notation Word Problem

#### Unit 2: Equations

- Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials by Monomials
- Multiplying Monomials by Polynomials
- Introduction to Simple Equations
- Solving a Simple Equation Example 1
- Solving a Simple Equation Example 2
- Solving a Simple Equation Example 3
- Solving a Simple Equation Example 4
- Solving a Simple Equation Example 5
- Solving a Simple Equation Example 6
- Solving a Simple Equation Example
- Solving a Simple Equation Example 8
- Solving a Simple Equation Example 9
- Solving a Simple Equation Example 10
- Evaluate a Formula using Substitution
- Rearrange a Formula to Isolate a Specific Variable
- Word Problem Example
- Introduction to Ratios
- Understanding Proportions
- Equivalent Ratios
- Finding an Unknown in a Proportion
- Finding Unit Rates
- Finding Unit Prices

#### Unit 3: Graphing

- The Cartesian Plane 1
- The Cartesian Plane 2
- The Cartesian Plane 3
- Interpreting Graphs
- Modeling Linear Graphs

#### Unit 4: Measurement

#### Unit 1: Introduction to Statistics

#### Unit 2: Frequency Distributions

- Reading Pictographs
- Reading Bar Graphs
- Reading Pie Graphs
- Reading Line Graphs
- Reading Stem and Leaf Plots
- Reading Box and Whisker Graphs
- Representing Data
- Frequency Tables and Dot Plots
- Creating a Histogram
- Interpreting a Histogram

#### Unit 3: Central Tendency

- Mean Median and Mode
- Mean Median and Mode Example
- Find the Missing Value Given the Mean
- Comparing Means of Different Distributions
- Means and Medians of Different Distributions
- Impact on Median and Mean: Removing an Outlier
- Impact on Median and Mean: Increasing an Outlier
- Interquartile Range (IQR)
- Range and Mid Range
- Sample versus Population Mean

#### Unit 4: Variability

- Measures of Spread: Range, Variance & Standard Deviation
- Variance of a Population | Descriptive Statistics
- Population Standard Deviation
- Mean and Standard Deviation versus Median and IQR
- Sample Variance
- Sample Standard Deviation and Bias
- Statistics: Alternate Variance Formulas
- Why we divide by n-1 in Variance
- Simulation Showing bias in Sample Variance
- Simulation Providing Evidence that (n-1) gives us Unbiased Estimate

#### Unit 5: Probability

- Probability Explained
- Coin Flip
- Introduction to Conditional Probability
- Basic Probability
- Simple Probability
- Venn Diagrams
- Addition Rule for Probability
- Counting Outcomes Using Tree Diagrams
- Permutation Formula
- Zero Factorial or 0!
- Factorial and Counting Seat Arrangements
- Possible Three Letter Words
- Ways to Arrange Colours
- Intro to Combinations
- Combination Formula
- Handshaking Combinations
- Combinations Example: 9 Card Hands
- Probability Using Combinations | Probability and Statistics
- Probability and Combinations
- Probability with Counting Outcomes
- Getting Exactly Two Heads
- Exactly Three Heads in Five Flips
- Generalization With Binomial Coefficients
- Different Ways to Pick Officers
- Combinatorics and Probability
- Lottery Probability
- Mega Millions Jackpot Probability
- Birthday Probability Problem
- Permutations

#### Unit 6: Normal Distribution

- Introduction to Z-Scores
- Comparing Z-Scores
- Z-Scores in the Normal Distribution
- Qualitative Sense of Normal Distributions
- Normal Distribution Problems: Empirical Rule
- Standard Normal Table for Proportion Below
- Standard Normal Table or Proportion Above
- Standard Normal Table for Proportion between Values
- Finding Z-Score for Percentile
- Threshold for Low Percentile
- Z-Score Examples 1
- Introduction to t Statistics
- Simulation Showing Value of t Statistic
- Conditions for Valid t Intervals
- Finding a Critical t Value

#### Unit 8: The Distribution of Sample Means

- The Central Limit Theorem
- Sampling Distribution of the Sample Mean 1
- Sampling Distribution of the Sample Mean 2
- Standard Error of the Mean
- Example: Probability of Sample Mean Exceeding a Value

#### Unit 9: Confidence Intervals

- Confidence Interval and Margin of Error
- Confidence Interval Simulation
- Interpreting Confidence Level Example
- Confidence Interval Example
- Margin of Error 1
- Margin of Error 2
- Conditions for Valid Confidence Intervals
- Conditions for Confidence Intervals Worked Examples
- Critical Value (z*) for a Given Confidence Level
- Sample Size Based on Confidence and Margin of Error
- Example Constructing a t Interval for a Mean
- Sample Size for a Given Margin of Error for a Mean
- T-Statistic Confidence Interval
- Small Sample Size Confidence Intervals

#### Unit 1: Whole Numbers, Fractions and Decimals

- Addition: Basics
- Addition: Adding 3 Digit Numbers
- Addition: Multiple Digit Addition
- Subtraction: Basics
- Subtraction: Multiple Digit Subtraction
- Multiplication: Basics
- Multiplication 2: The Multiplication Tables
- Multiplying: 2 Digit Number
- Introduction to standard way of multiplying multidigit numbers
- Division: Basics
- Division: Introduction to Long Division
- Dividing Numbers: Long Division with Remainders
- Division: 2 Digit Long Division
- Proper and Improper Fractions | Fractions
- Equivalent Fractions
- Converting Mixed Numbers to Improper Fractions | Fractions
- Converting an Improper Fraction into a Mixed Numbers
- Fractions in Lowest Terms | Fractions
- Adding Fractions with Same Denominators
- Finding a Common Denominator
- Prime Factorization
- Adding Fractions with Unlike Denominators
- Adding Mixed Numbers with Unlike Denominators
- Subtracting Fractions with Unlike Denominators
- Subtracting Mixed Numbers with Regrouping
- Multiplying Fractions
- Multiplying Mixed Numbers
- Understanding Fractions as Division
- Creating a Fraction Through Division
- Creating Mixed Numbers with Fraction Division
- Understanding Dividing Fractions
- Dividing Mixed Numbers
- Understanding Decimals
- Decimals on a Number Line
- Adding Decimals
- Subtracting Decimals
- Multiplying Decimals by a Power of Ten
- Dividing Decimals by a Power of Ten
- Multiplying Decimals
- Dividing a Decimals by a Whole Number With Long Division
- Dividing a Decimal Number by a Decimal Number With Long Division

#### Unit 2: Percents Averages and Estimating

- Introduction to Percent
- Representing a Number as a Decimal, Fraction and Percentage 1
- Representing a Number as a Decimal, Fraction and Percentage 2
- Percentage Problem Example 1
- Percentage Problem Example 2
- Percentage Problem Example 3
- Rounding Whole Numbers
- Rounding Decimal Numbers

#### Unit 3: Measurement

- Unit Conversion
- Converting Units of Length
- Conversion Between Metric Units
- Conversion Between US and Metric Units
- Converting Within the Metric System
- Converting Gallons, Quarts, Pints and Cups

#### Unit 4: Ratio and Proportion

- Introduction to Ratios
- Introduction to Proportional Relationships
- Ratio as Fractions
- Simplifying Rates and Ratios
- Finding an Unknown in a Proportion
- Finding Unit Rates
- Finding Unit Prices

#### Unit 5: Applied Algebra

- Identifying the Parts of a Polynomial
- Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials by Monomials
- Multiplying Monomials by Polynomials
- Evaluate a Formula using Substitution
- Solving a Linear Equation Example 1
- Solving a Linear Equation Example 2
- Solving a Linear Equation Example 3
- Solving a More Complicated Equation
- Solving a Linear Equation Example 5

#### Unit 6: Graphs

- Reading Pictographs
- Reading Bar Graphs
- Reading Pie Graphs
- Reading Line Graphs
- Reading Stem and Leaf Plots
- Reading Box and Whisker Graphs

#### Unit 7: Applied Geometry

- Perimeter and Area Basics
- 4 Polygon Perimeter
- Perimeter and Area of non Standard Polygons
- Area of a Triangle
- Area of a Parallelogram
- Area of Trapezoids
- Area of Kites
- Circles: Radius, Diameter, Circumference and Pi
- Circles: Area
- Volume of Basic Solids
- Volume of a Cone
- Cylinder Volume and Surface Area
- Volume of a Sphere
- Acute, Right and Obtuse Angles
- Recognizing Angles
- Complementary and Supplementary Angles
- SATT- Sum of The Angles of a Triangle Theorem
- Parallel Line and Transversals
- Congruent and Similar Triangles
- Equilateral and Isosceles Triangles
- Similar Triangles

#### Unit 8: Applied Trigonometry

- Trig Ratios and Calculator Use
- Solving for a Side in Right Triangles with Trigonometry
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 1
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 2
- Proof: Law of Sines
- Proof: Law of Cosines
- Solving of a Side with the Law of Sines
- Solving for an Angle with the Law of Sines
- Solving for a Side with the Law of Cosines
- Solving for a Angle of the Law of Cosines
- Solving a Triangle Example one

#### Unit 1: Arithmetic Operations with Whole Numbers, Fractions, Decimals and Percents

- Addition: Basics
- Addition: Adding 3 Digit Numbers
- Addition: Multiple Digit Addition
- Subtraction: Basics
- Subtraction: Multiple Digit Subtraction
- Multiplication: Basics
- Multiplication: Multiplication Tables (2-9)
- Multiplication: 2 Digit Number Times a 2 Digit Number
- Multiplication: Multiple Digit Multiplication
- Division: Basics
- Division: Introduction to Long Division
- Division: Long Division with Remainders
- Division: 2 Digit Long Division
- Comparing Improper Fractions Mixed Numbers
- Equivalent Fractions
- Converting Mixed Numbers into Improper Fractions
- Converting an Improper Fraction into a Mixed Numbers
- Adding Fractions with Same Denominators
- Finding a Common Denominator
- Prime Factorization
- Adding Fractions with Unlike Denominators
- Adding Mixed Numbers with Different Denominators
- Subtracting Fractions
- Subtracting Mixed Numbers
- Multiplying Fractions
- Multiplying Mixed Numbers
- Understanding Fractions as Division
- Creating a Fraction Through Division
- Creating Mixed Numbers with Fraction Division
- Understanding Dividing Fractions
- Dividing Mixed Numbers
- Understanding Decimals
- Decimals on a Number Line
- Adding Decimals
- Subtracting Decimals
- Multiplying Decimals by a Power of Ten
- Dividing Decimals by a Power of Ten
- Multiplying Decimals
- Dividing a Decimals by a Whole Number With Long Division
- Dividing a Decimal Number by a Decimal Number With Long Division
- Introduction to Percent
- Representing a Number as a Decimal, Fraction and Percentage 1
- Representing a Number as a Decimal, Fraction and Percentage 2
- Percentage Problem Example 1
- Percentage Problem Example 2
- Percentage Problem Example 3
- Rounding Whole Numbers
- Rounding Decimal Numbers

#### Unit 2: Metric and English Measurement Systems and Methods of Conversion

- Unit Conversion
- Converting Units of Length
- Conversion Between Metric Units
- Converting Within the Metric System
- Converting Gallons, Quarts, Pints and Cups

#### Unit 3: Basic Algebraic Operations for Solving Algebraic Equations and Word Problems

- Identifying the Parts of a Polynomial
- Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials by Monomials
- Multiplying Monomials by Polynomials
- Solving a Simple Equation Example 1
- Solving a Simple Equation Example 2
- Solving a Simple Equation Example 3
- Solving a Simple Equation Example 4
- Solving a Simple Equation Example 5
- Solving a Simple Equation Example 6
- Solving a Simple Equation Example 7
- Solving a Simple Equation Example 8
- Solving a Simple Equation Example 9
- Solving a Simple Equation Example 10
- Word Problem Example

#### Unit 4: Powers and Roots

- Introduction to Exponents
- Exponent Example 1
- Exponent Example 2
- The 0 & 1
^{st}Power - Introduction to Roots

#### Unit 5: Applications of Trade Related Formulas

#### Unit 6: Trig Functions for Right Angle Triangles

#### Unit 1: Basic Algebraic Operations

- Points on a Number Line
- Absolute Value
- Intro to Rational & Irrational Numbers
- Classifying Numbers: Rational & Irrational
- Classifying Numbers
- Number Sets Example
- Adding and Subtracting Negative Numbers
- Multiplying Positive and Negative Numbers
- Dividing Positive and Negative Numbers
- Order of Operations Example 1
- Order of Operations Example 2
- Order of Operations Example 3
- Order of Operations Example 4
- Commutative Law of Addition
- Commutative Law of Multiplication
- Associative Law of Addition
- Associative Law of Multiplication
- The Distributive Property
- Rounding Decimals
- Introduction to Roots
- Converting a Number in From Scientific Notation into a Decimal Number
- Converting Decimal Number into a Number in Scientific Notation
- Multiplying in Scientific Notation
- Red Blood Cells in Human Body (Scientific Notation Word Problem)
- Simplifying Square Roots
- Finding Cube Roots
- Simplifying Cube Roots
- Simplifying Radical Expressions Example 1
- Simplifying Radical Expressions Example 2
- Radicals of Higher Roots
- Simplifying a Polynomial
*(collecting like terms)* - Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials
- Multiplying Monomials by Polynomials
- Multiplying Binomials
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial 1
- Dividing a Polynomial by a Binomial
- Dividing Polynomials with Remainders
- Solving a Linear Equation Example 1
- Solving a Linear Equation Example 2
- Solving a Linear Equation Example 3
- Solving a More Complicated Equation
- Rearrange a Formula to Isolate a Specific Variable

#### Unit 2: Functions and Graphs

- Introduction to Functions 1
- Introduction to Functions 2
- Introduction to Functions 3
- Introduction to Functions 4
- Evaluate a Formula or Function Using Substitution
- The Coordinate Plane
- Plotting (x,y) Coordinates
- Finding the Length of a Line Segment or Finding the Distance Between Two Points (Distance Formula)
- Graphing a Basic Function
- Graphing a Quadratic Function
- Graphing Exponential Functions
- Graphing Square Root Functions

#### Unit 3: The Trigonometric Functions

- Language and Notation in Geometry
- Angle Basics
- Measuring Angles in Degrees
- Solving for a Side in Right Triangles with Trigonometry
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 1
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 2

#### Unit 4: Systems of Linear Equations ; Determinants

- Checking if a Point is (or is not) a Solution in a Linear System
- Finding Slope from a Graph
- Finding Slope When Given Two Points (or Ordered Pairs) Example 1
- Finding Slope When Given Two Points (or Ordered Pairs) Example 2
- Graphing a Linear Function by the X and Y Intercept Method
- Graphing a Linear Function (Line) by the Slope Y-Intercept Method Example 1
- Graphing a Linear Function (Line) by the Slope Y-Intercept Method Example 2
- Solving Linear Systems by Graphing
- Solving Linear Systems by Substitution Method Example 1
- Solving Linear Systems by Substitution Method Example 2
- Solving Linear Systems by Elimination (Addition) Method Example 1
- Solving Linear Systems by Elimination (Addition) Method Example 2
- Solving Systems with 3 Unknowns 1
- Solving Systems with 3 Unknowns 2

#### Unit 5: Factoring and Fractions

- Binomial Squared(Special Products in Algebra)
- Difference of Squares(Special Products in Algebra)
- Finding The Greatest Common Factor (GCF)
- More GCF Examples
- Common Factoring Example
- More Common Factoring Examples
- Factor by Grouping (Triple Common Factor)
- Factoring a Trinomial with a Common Factor First
- Factoring a Perfect Square Trinomial
- Factoring a Difference of Squares
- Strategy in Factoring Quadratics 1
- Strategy in Factoring Quadratics 2
- Factoring a Sum of Cubes
- Factoring a Difference of Cubes
- Simplifying Rational Expressions
- Simplifying Rational Expressions: Common Monomial Factors
- Simplifying Rational Expressions: Common Binomial Factors
- Simplifying Rational Expressions: Opposite Common Binomial
- Simplifying Rational Expressions: Grouping
- Simplifying Rational Expressions: Higher Degree Terms
- Multiplying & Dividing Rational Expressions: Monomials
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Adding & Subtracting Rational Expressions: Like Denominators
- Intro to Adding Rational Expressions with Unlike Denominators
- Adding Rational Expressions: Unlike Denominators
- Subtracting Rational Expressions: Unlike Denominators
- Least Common Multiple
- Least Common Multiple: Repeating Factors
- Subtracting Rational Expressions: Factored Denominators
- Least Common Multiple of Polynomials
- Subtracting Rational Expressions
- Solving Rational Equations Example

#### Unit 6: Quadradic Equations

- Zero Product Property
- Solving Quadratics by Factoring
- Solving Quadratics by Factoring: Leading Coefficient not = 1
- Completing the Square
- Completing the Square to Solve Quadratics
- Quadratic Formula 1
- Quadratic Formula 2
- Quadratic Formula 3
- Quadratic Formula 4
- Graphing a Quadratic Function

#### Unit 7: Trig Functions For Any Angle

- The Unit Circle
- The Trig Functions & Right Triangle Trig Ratios
- Intro to Radians
- Radians & Degrees
- Degrees to Radians
- Radians to Degrees
- Radian Angles & Quadrants

#### Unit 8: Vectors and Oblique Triangles

- Introduction to Scalars and Vectors
- Visualizing Vectors in Two Dimensions
- Additing and Subtracting Vectors Examples
- Proof: Law of Sines
- Proof: Law of Cosines
- Solving of a Side with the Law of Sines
- Solving for an Angle with the Law of Sines
- Solving for a Side with the Law of Cosines
- Solving for a Angle of the Law of Cosines
- Solving a Triangle Example one

#### Unit 9: Graphs of Trig Functions

- Graphs of Trigonometric Functions - Sine
- Graphs of Trigonometric Functions - Cosine
- Graphs of Trigonometric Functions - Tangent
- Graphing Trigonometric Functions: Transformations
- Determining the Trigonometric Equation From a Graph
- Finding the Trigonometric Equation From the Graph 2

#### Unit 10: Exponents and Radicals

- Exponent Properties 1
- Exponent Properties 2
- Exponent Properties 3
- Simplifying Rational Expressions Using Exponent Laws - Example
- Exponents Properties with Products
- Exponent Properties with Parentheses
- Exponent Properties with Quotients
- Rational Exponents and Exponent Laws
- Simplifying Radical Expressions Example 1
- Simplifying Radical Expressions Example 2
- How to Rationalize a Denominator
- Addition of Radical Expressions
- Subtraction of Radical Expressions
- Adding and Subtracting Radical Expressions
- Multiplying Rational Expressions Example 1
- MultiplyingRational Expressions Example 2
- How to Rationalize a Denominator

#### Unit 11: Complex Numbers

- Introduction to i and Complex Numbers
- Real and Imaginary Parts of a Complex Number
- Basic Operations with Complex Numbers
- Complex Conjugates
- Graphical Representation of a Complex Number
- Adding Complex Numbers
- Subtracting Complex Numbers
- Multiplying Complex Numbers
- Dividing Complex Numbers
- Operations of Complex Numbers Addition
- Operations of Complex Numbers Subtraction
- Operations of Complex Numbers Multiplication
- Operations of Complex Numbers Division
- Polar Form of a Complex Number
- Exponential Form of a Complex Number

#### Unit 12: Exponential and Logarithmic Functions

- Graphing Exponential Functions
- Solving Exponentials with Logarithms
- Logarithm Properties
*(Sum and Difference Properties)* - Logarithm Properties
*(Multiple Property and Change of Base)* - Proof of the Sum Property of Logarithms
- Proof of the Difference and Multiple Property of Logarithms
- Simplifying Logarithms
- Change of Base Formula
- Calculating a Logarithm with a Calculator
- Logarithmic Equations: Variable in the Argument
- Logarithmic Equations: Variable in the Base
- Solving Logarithmic Equations
- Solving Exponential Equations Using Logarithms: Base-10
- Solving Exponential Equations Using Logarithms: Base-2

#### Unit 1: Basic Algebraic Operations Overview

- Commutative Law of Addition
- Commutative Law of Multiplication
- Associative Law of Addition
- Associative Law of Multiplication
- The Distributive Property
- Law of Exponents: Multiplication (LEM)
- Law of Exponents: Division (LED)
- Law of Exponents: Powers (LEP)
- Simplifying Rational Expressions Using Exponent Laws - Example
- Law of Exponents: Extension of LEP 1
- Law of Exponents: Extension of LEP 2
- Law of Exponents: Negative Exponents
- Introduction to Roots
- Finding Cube Roots
- Simplifying a Polynomial (collecting like terms)
- Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials
- Multiplying Monomials by Polynomials
- Multiplying Binomials
- Multiplying Polynomials
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial 1
- Dividing a Polynomial by a Monomial 2
- Dividing a Polynomial by a Binomial
- Dividing Polynomials with Remainders
- Solving a Simple Equation Example 1
- Solving a Simple Equation Example 2
- Solving a Simple Equation Example 3
- Solving a Simple Equation Example 4
- Solving a Simple Equation Example 5
- Solving a Simple Equation Example 6
- Solving a Simple Equation Example 7
- Solving a Simple Equation Example 8
- Solving a Simple Equation Example 9
- Solving a Simple Equation Example 10
- Rearrange a Formula to Isolate a Specific Variable

#### Unit 2: Functions

- Introduction to Functions 1
- Introduction to Functions 2
- Introduction to Functions 3
- Introduction to Functions 4
- Evaluate a Formula or Function Using Substitution
- Domain of a Function
- Domain and Range of a Function 1
- Domain and Range of a Function 2
- Domain and Range of a Function 3
- The Coordinate Plane
- Plotting (x,y) Coordinates
- Finding the Length of a Line Segment or Finding the Distance Between Two Points (Distance Formula)
- Graphing a Basic Function
- Graphing a Quadratic Function

#### Unit 3: Linear Equations

- Checking if a Point is (or is not) a Solution in a Linear System
- Finding Slope from a Graph
- Finding Slope When Given Two Points (or Ordered Pairs) Example 1
- Finding Slope When Given Two Points (or Ordered Pairs) Example 2
- Graphing a Linear Function by the X and Y Intercept Method
- Graphing a Linear Function (Line) by the Slope Y-Intercept Method Example 1
- Graphing a Linear Function (Line) by the Slope Y-Intercept Method Example 2
- Solving Linear Systems by Graphing
- Solving Linear Systems by Substitution Method Example 1
- Solving Linear Systems by Substitution Method Example 2
- Solving Linear Systems by Elimination (Addition) Method Example 1
- Solving Linear Systems by Elimination (Addition) Method Example 2

#### Unit 4: Factoring Fractions

- Binomial Squared(Special Products in Algebra)
- Difference of Squares(Special Products in Algebra)
- Finding The Greatest Common Factor (GCF)
- More GCF Examples
- Common Factoring Example
- More Common Factoring Examples
- Factoring Easy Trinomials (Trinomial with a Leading One Coefficient)
- Factor by Grouping (Triple Common Factor)
- Factoring Hard Trinomials (Trinomials with a Non-One Coefficicent)
- Factoring a Trinomial with a Common Factor First
- Factoring a Perfect Square Trinomial

#### Unit 5: Quadratic Equations

- Solving Quadratics by Factoring
- Completing the Square
- Completing the Square to Solve Quadratics
- Quadratic Formula 1
- Quadratic Formula 2
- Quadratic Formula 3
- Quadratic Formula 4
- Graphing a Quadratic: Standard form
- Graphing a Quadratic: Vertex form
- Graphing a Quadratic: Factored form

#### Unit 6: Exponents and Radicals

- Law of Exponents: Multiplication(LEM)
- Law of Exponents: Division(LED)
- Law of Exponents: Powers(LEP)
- Simplifying Rational Expressions Using Exponent Laws - Example
- Law of Exponents: Extension of LEP 1
- Law of Exponents: Extension of LEP 2
- Law of Exponents: Negative Exponents
- Rational Exponents and Exponent Laws
- Simplifying Expressions With Rational Exponents
- Simplifying Radical Expressions Example 1
- Simplifying Radical Expressions Example 2
- Simplifying Radical Expressions Example 3
- How to Rationalize a Denominator
- Addition of Radical Expressions
- Subtraction of Radical Expressions
- Adding Radical Expressions
- Subtracting Radical Expressions
- Multiplying Rational Expressions Example 1
- MultiplyingRational Expressions Example 2
- How to Rationalize a Denominator

#### Unit 7: Exponential and Logarithmic Functions

- Graphing Exponential Functions
- Solving Exponentials with Logarithms
- Logarithm Properties(Sum and Difference Properties)
- Logarithm Properties(Multiple Property and Change of Base)
- Proof of the Sum Property of Logarithms
- Proof of the Difference and Multiple Property of Logarithms
- Change of Base Formula
- Simplifying Logarithms
- Calculating a Logarithm with a Calculator
- Logarithmic Equations: Variable in the Argument
- Logarithmic Equations: Variable in the Base
- Solving Logarithmic Equations

#### Unit 8: Variation

- Introduction to Ratios
- Understanding Proportions
- Equivalent Ratios
- Finding an Unknown in a Proportion
- Finding Unit Rates
- Finding Unit Prices

#### Unit 9: Trigonometric Functions

- Language and Notation in Geometry
- Lines Segments & Rays
- Parallel & Perpendicular Lines Intro
- Parallel & Perpendicular Lines
- Angle Basics
- Measuring Angles in Degrees
- Radian Angles & Quadrants
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 1
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 2

#### Unit 10: Trigonometric Functions of Any Angle

#### Unit 11: Vectors and Oblique Triangles

- Introduction to Scalars and Vectors
- Visualizing Vectors in Two Dimensions
- Vector Addition and Subtraction Examples
- Proof: Law of Sines
- Proof: Law of Cosines
- Solving of a Side with the Law of Sines
- Solving for an Angle with the Law of Sines
- Solving for a Side with the Law of Cosines
- Solving for a Angle of the Law of Cosines
- Solving a Triangle Example one

#### Unit 12: Graphing Trig Functions

- Graphs of Trigonometric Functions - Sine
- Graphs of Trigonometric Functions - Cosine
- Graphs of Trigonometric Functions - Tangent
- Graphing Trigonometric Functions: Transformations
- Finding the Trigonometric Equation From the Graph

#### Unit 13: Trig Identities

- Sum, Difference and Double Angle Identities
- Review of Trig Angle Addition Identities
- Using the Cosine Angle Addition Identity
- Using Cosine Double Angle Identity
- Proof of the Sine Angle Addition Identity
- Proof of the Cosine Angle Addition Identity
- Finding Trig Values Using Angle Addition Identities
- Using Trig Angle Addition Identities: Finding Side Lengths
- Using Trig Angle Addition Identities: Manipulation Expressions
- Using Trig Identities

#### Unit 1: Units of Measurement

- Unit Conversion
- Converting Units of Length
- Conversion Between Metric Units
- Converting Within the Metric System
- Converting Gallons, Quarts, Pints and Cups
- Conversion Between US and Metric Units

#### Unit 2: Introduction to Algebra

- Identifying the Parts of a Polynomial
- Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials by Monomials
- Multiplying Monomials by Polynomials

#### Unit 3: Simple Equations

- Solving a Linear Equation Example 1
- Solving a Linear Equation Example 2
- Solving a Linear Equation Example 3
- Solving a More Complicated Equation

#### Unit 4: Introduction to Geometry

- Perimeter and Area Basics
- 4 Polygon Perimeter
- Perimeter and Area of non Standard Polygons
- Area of a Triangle
- Area of a Parallelogram
- Area of Trapezoids
- Area of Kites
- Circles: Radius, Diameter, Circumference and Pi
- Circles: Area
- Volume of Basic Solids
- Volume of a Cone
- Cylinder Volume and Surface Area
- Volume of a Sphere

#### Unit 5: Geometry and the Right Triangle Trigonometry

- Acute, Right and Obtuse Angles
- Recognizing Angles
- Complementary and Supplementary Angles
- SATT- Sum of The Angles of a Triangle Theorem
- Parallel Line and Transversals
- Congruent and Similar Triangles
- Equilateral and Isosceles Triangles
- Trig Ratios and Calculator Use
- Solving for a Side in Right Triangles with Trigonometry
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 1
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 2

#### Unit 6: Oblique Triangles and Vectors

- Introduction to Scalars and Vectors
- Visualizing Vectors in Two Dimensions
- Vector Addition and Subtraction Examples
- Proof: Law of Sines
- Proof: Law of Cosines
- Solving of a Side with the Law of Sines
- Solving for an Angle with the Law of Sines
- Solving for a Side with the Law of Cosines
- Solving for a Angle of the Law of Cosines
- Solving a Triangle Example one

#### Unit 1: Review of Fundamental Mathematics

- Order of Operations - Introduction to Order of Operations
*(Remember Parenthesis had the same meaning as Brackets)* - Order of Operations - Example 1
- Order of Operations - Example 2
- Order of Operations - Example 3
- Proper and Improper Fractions | Fractions
- Equivalent Fractions
- Converting Mixed Numbers to Improper Fractions | Fractions
- Converting an Improper Fraction into a Mixed Numbers
- Fractions in Lowest Terms | Fractions
- Adding Fractions with Same Denominators
- Finding a Common Denominator
- Prime Factorization
- Adding Fractions with Unlike Denominators
- Adding Mixed Numbers with Unlike Denominators
- Subtracting Fractions with Unlike Denominators
- Subtracting Mixed Numbers with Regrouping
- Multiplying Fractions
- Multiplying Mixed Numbers
- Understanding Fractions as Division
- Creating a Fraction Through Division
- Creating Mixed Numbers with Fraction Division
- Understanding Dividing Fractions
- Dividing Mixed Numbers
- Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials by Monomials
- Multiplying Monomials by Polynomials
- Exponent Properties 1
- Exponent Properties 2
- Exponent Properties 3
- Simplifying Rational Expressions Using Exponent Laws - Example
- Exponents Properties with Products
- Exponent Properties with Parentheses
- Exponent Properties with Quotients
- Solving a Linear Equation Example 1
- Solving a Linear Equation Example 2
- Solving a Linear Equation Example 3
- Solving a More Complicated Equation
- Introduction to Percent
- Converting a Percent to a Decimal and a Fraction
- Representing a Number as a Decimal, Percent and Fraction
- Percentage Problem Example 1
- Percentage Problem Example 2
- Percentage Problem Example 3
- Introduction to Ratios
- Introduction to Proportional Relationships
- Ratio as Fractions
- Simplifying Rates and Ratios
- Finding an Unknown in a Proportion
- Finding Unit Rates
- Finding Unit Prices

#### Unit 2: Computing Interest

- Introduction to Simple and Compound Interest
- Compound Interest
- The Rule of 72 with Compound Interest
- Nominal and Effective Interest Rates
- Payday Loans
- Time Value of Money
- Introduction to Present Value
- Present Value Example 1
- Present Value Example 2
- Present Value Example 3

#### Unit 3: Annuities

- N/A

#### Unit 4: Mathematics Merchandising

- N/A

#### Unit 1: Geometry

- Lines, Line Segements and Rays
- Angle Basics
- Acute Right and Obtuse Angles
- Complementary and Supplementary Angles
- Angles at the Intersection of Two Lines
- Angles Formed Between Transversals and Parallel Lines
- Sum of the Angles in Triangles Example 1
- Sum of the Angles in Triangles Example 2
- Sum of the Angles in Triangles Example 3
- Pythagoreans Theorem
- Pythagoreans Theorem and Area
- Congruent and Similar Triangles
- Introduction of Quadrilaterals
- Quadrilateral Properties
- Area of a Parallelogram
- Language and Notation of the Circle
- Circles: Radius, Diameter, Circumference and Pi
- Area of a Circle
- Degrees to Radians
- Radians to Degrees
- Solid Geometry Volume
- Cylinder Volume and Surface Area
- Volume of a Sphere

#### Unit 2: Plane Analytic Geometry

- Distance Formula
- Slope of a Line (Rise over Run)
- Slope of a Line (Given Two Points)
- Slope Example
- Parallel Lines
- Perpendicular Lines 1
- Perpendicular Lines 2
- Midpoint of a Line Segment
- Finding Linear Equations given the Slope and Y Intercept
- Finding Linear Equations Given Slope and a Point
- Converting to Slope Y Intercept Form
- Point Slope and Standard Form of a Line
- Parallel and Perpendicular Lines Intro
- Parallel and Perpendicular Lines
- Graphing a Line from the Slope Y Intercept Form of a Line
- Circle Glossary
- Radius, Diameter, Circumference & pi
- 3 Points Defining a Circle
- Introduction to Directrix and Focus
- Intro to Focus & Directrix
- Equation of a Parabola from Focus & Directrix
- Focus & Directrix of a Parabola from Equation
- Introduction to Ellipses
- Foci of an Ellipse
- Hyperbolas 1
- Hyperbolas 2
- Hyperbolas 3
- Foci of a Hyperbola
- Polar Coordinates 1
- Polar Coordinates 2
- Polar Coordinates 3

#### Unit 1: Whole Numbers

- Intro to Rational & Irrational Numbers
- Classifying Numbers: Rational & Irrational
- Classifying Numbers
- Number Sets Example
- Intro to Multiplication
- Multiplication as groups of objects
- More on the concept of Multiplication
- Multiplication Tables
- Multiple Digit Multiplication
- The Idea of Division
- Long Division Review
- Multiplying Positive and Negative Numbers
- Dividing Positive and Negative Numbers
- Exponents Review - Understanding Exponents 1
- Exponents Review - Understanding Exponents 2
- Order of Operations - Introduction to Order of Operations (Remember Parenthesis has the same meaning as Brackets)
- Order of Operations - Example 1
- Order of Operations - Example 2
- Order of Operations - Example 3

#### Unit 2: Fractions

- Equivalent Fractions
- Converting Mixed Numbers into Improper Fractions
- Converting an Improper Fraction into a Mixed Numbers
- Adding Fractions with Same Denominators
- Finding a Common Denominator
- Prime Factorization
- Adding Fractions with Unlike Denominators
- Adding Mixed Numbers with Different Denominators
- Subtracting Fractions
- Subtracting Mixed Numbers
- Multiplying Fractions
- Multiplying Mixed Numbers
- Understanding Fractions as Division
- Creating a Fraction Through Division
- Creating Mixed Numbers with Fraction Division
- Understanding Dividing Fractions
- Dividing Mixed Numbers
- Representing a Number as a Decimal, Fraction and Percent Example 1
- Representing a Number as a Decimal, Fraction and Percent Example 2
- Representing a Number as a Decimal, Fraction and Percent Example 3

#### Unit 3: Decimals

- Introduction to Decimals
- Decimals on a Number Line
- Rounding Decimals
- Decimals and Fractions
- Converting Fractions into Decimals
- Converting Repeating Decimals Into Fractions Part 1
- Converting Repeating Decimals Into Fractions Part 2
- Decimal Addition
- Decimal Subtraction
- Decimal Multiplication
- Dividing a Decimals by a Whole Number With Long Division
- Dividing a Decimal Number by a Decimal Number With Long Division
- Multiplying a Decimal by a Power of Ten
- Dividing a Decimal by a Power of Ten
- Subtracting Decimal Word Problem

#### Unit 4: Basic Algebra

- Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials by Monomials
- Multiplying Monomials by Polynomials
- Solving a Simple Equation Example 1
- Solving a Simple Equation Example 2
- Solving a Simple Equation Example 3
- Solving a Simple Equation Example 4
- Solving a Simple Equation Example 5
- Solving a Simple Equation Example 6
- Solving a Simple Equation Example 7
- Solving a Simple Equation Example 8
- Solving a Simple Equation Example 9
- Solving a Simple Equation Example 10
- Evaluate a Formula using Substitution
- Rearrange a Formula to Isolate a Specific Variable
- Word Problem Example

#### Unit 5: Ratios and Proportions

- Introduction to Ratios
- Understanding Proportions
- Equivalent Ratios
- Finding an Unknown in a Proportion
- Finding Unit Rates
- Finding Unit Prices

#### Unit 6: Percents

- The Meaning of Percent Part 1
- The Meaning of Percent Part 2
- Identifying the Percent Amount and Base
- Representing a Number as a Decimal, Fraction and Percent Example 1
- Representing a Number as a Decimal, Fraction and Percent Example 2
- Representing a Number as a Decimal, Fraction and Percent Example 3
- Percent Problem Example 1
- Percent Problem Example 2
- Percent Problem Example 3

#### Unit 7: Signed Numbers

- Introduction to Negative Numbers
- Adding Negative Numbers
- Adding Integers With Different Signs
- Subtracting Negative Numbers
- Multiplying Positive and Negative Numbers
- Dividing Positive and Negative Numbers
- Adding Fractions With Different Signs
- Absolute Value of Integers

#### Unit 8: Basic Statistics

- Mean, Median and Mode
- Range and Mid-Range
- Pictographs
- Bar Graphs
- Line Graphs
- Reading Pie Graphs
- Stem and Leaf Plots
- Box and Leaf Plots
- The Average
- Variance of a Population
- Sample Variance
- Standard Deviation

#### Unit 9: Measurement and Units

- Finding Unit Rates
- Finding Unit Prices
- Unit Conversion
- Converting Metric Units
- Converting Within the Metric System
- Converting Fahrenheit to Celsius
- Unit Conversion Example: Drug Dosage

#### Unit 10: Basic Geometry

- Perimeter and Area Basics
- Perimeter of a Polygon
- Perimeter and Area of non Standard Polygons
- Area of a Triangle
- Area of a Parallelogram
- Area of Trapezoids
- Area of Kites
- Circles: Radius Diameter and Circumference
- Circles: Area
- Volume of Basic Solids
- Volume of a Cone
- Cylinder Volume and Surface Area
- Volume of a Sphere
- Acute, Right and Obtuse Angles
- Recognizing Angles
- Complementary and Supplementary Angles
- SATT- Sum of The Angles of a Triangle Theorem
- Parallel Line and Transversals
- Congruent and Similar Triangles
- Equilateral and Isosceles Triangles

#### Unit 1: Additional Topics in Trigonometry

- Sum, Difference and Double Angle Identities
- Inverse trig functions: arcsin
- Inverse trig functions: arccos
- Inverse trig functions: arctan
- Review of Trig Angle Addition Identities
- Using the Cosine Angle Addition Identity
- Using Cosine Double Angle Identity
- Proof of the Sine Angle Addition Identity
- Proof of the Cosine Angle Addition Identity
- Finding Trig Values Using Angle Addition Identities
- Using Trig Angle Addition Identities: Finding Side Lengths
- Using Trig Angle Addition Identities: Manipulation Expressions
- Using Trig Identities

#### Unit 2: The Derivative

- Introduction to Limits | Limits
- Formal Definition of Limits Part 1: Intuition Review
- Formal Definition of Limits Part 2: Building the Idea
- Formal Definition of Limits Part 3: the Definition
- Formal Definition of Limits Part 4: Using the Definition
- Derivative as Slope of a Tangent Line
- Calculating Slope of a Tangent Line Using Derivative Definition
- Equation of a Tangent Line | Taking Derivatives
- Basic Derivative Rules (Part 1)
- Basic Derivative Rules (Part 2)
- Basic Derivative Rules: Find the error
- Basic Derivative Rules: Table
- Power Rule
- Justifying the Power Rule
- Proof of the Power Rule for Positive Integer Powers
- Proof of Power Rule for Square Root Function
- Basic Derivative Rules
- Differentiating Polynomials
- Tangents of Polynomials
- Differentiating Integer Powers (Mixed Positive and Negative)
- Worked Example: Tangent to the Graph of 1/x
- Fractional Powers Differentiation
- Radical Functions Differentiation Intro
- The Product Rule
- Differentiating Products
- Worked Example: Product Rule with Table
- Worked Example: Product Rule with Mixed Implicit and Explicit
- Product Rule to Find Derivative of Product of Three Functions
- Product Rule Proof
- The Quotient Rule
- Worked Example: Quotient Rule with Table
- Differentiating Rational Functions
- Chain Rule
- Common Chain Rule Misunderstandings
- Identifying Composite Functions
- Worked Example: Derivative of cos³(x) Using the Chain Rule
- Worked Example: Derivative of √(3x²-x)
- Worked Example: Derivative of ln(√x) Using the Chain Rule
- Worked Example: Chain Rule with Table
- Implicit Differentiation
- Worked Example: Implicit Differentiation
- Worked Example: Evaluating Derivative with Implicit Differentiation
- Showing Explicit and Implicit Differentiation Give the Same Result
- Implicit Differentiation 1
- Implicit Differentiation 2
- Implicit Differentiation 3
- Implicit Differentiation 4
- Differentiating Functions: Finding the Error
- Manipulating Functions Before Differentiation
- Differentiation Using multiple Rules: Strategy
- Applying the Chain Rule and Product Rule
- Applying the Chain Rule Twice
- Product Rule to Find Derivative of Product of Three Functions

#### Unit 3: Applications of the Derivative

- Second Derivatives
- Second Derivatives (implicit equations): Find Expression
- Second Derivatives (implicit equations): Evaluate Derivative
- Introduction to One-Dimensional Motion with Calculus
- Interpreting Direction of Motion from Position-Time Graph
- Interpreting Direction of Motion from Velocity-Time Graph
- Interpreting Change in Speed from Velocity-Time Graph
- Worked Example: Motion Problems with Derivatives
- Analyzing Straight-Line Motion Graphically
- Total Distance Traveled with Derivatives
- Tangent to y=?ˣ/(2+x³)
- Normal to y=?ˣ/x²
- Related Rates Intro
- Analyzing Related Rate Problems: Expressions
- Analyzing Related Rate Problems: Equations (Pythagoras)
- Analyzing Related Rate Problems: Equations (Trig)
- Differentiating Related Functions Intro
- Worked Example: Differentiating Related Functions
- Related Rates: Approaching Cars
- Related Rates: Falling Ladder
- Related Rates: Pouring Water into a Cone
- Related Rates: Shadow
- Related Rates: Balloon
- Extreme Value Theorem
- Critical Points Introduction
- Finding Critical Points
- Finding Decreasing Interval Given the Functions
- Finding Increasing Interval Given the Derivative
- Introduction to Minimum and Maximum Points
- Finding Relative Extrema
- Worked Example: Finding Relative Extrema
- Analyzing Mistakes When Finding Extrema Example 1
- Analyzing Mistakes When Finding Extrema Example 2
- Concavity Introduction
- Analyzing Concavity (graphical)
- Inflection Points Introduction
- Inflection Points (graphical)
- Analyzing Concavity (algebraic)
- Inflection Points (algebraic)
- Mistakes When Finding Inflection Points: Second Derivative Undefined
- Mistakes When Finding Inflection Points: Not Checking Candidates
- Second Derivative Test
- Curve Sketching with Calculus: Polynomial
- Curve Sketching with Calculus: Logarithm
- Analyzing a Function with its Derivative
- Optimization: Sum of Squares
- Optimization: Box Volumes (Part 1)
- Optimization: Box Volumes (Part 2)
- Optimization: Profit
- Optimization: Cost of Materials
- Optimization: Area of Triangle & Square (Part 1)
- Optimization: Area of Triangle & Square (Part 2)
- Optimization Problem: Extreme Normaline to y=x²

#### Unit 4: Derivatives of Transcendental Functions

- Derivatives of sin(x) and cos(x)
- Worked Example: Derivatives of sin(x) and cos(x)
- Derivatives of tan(x) and cot(x)
- Derivatives of sec(x) and csc(x)
- Derivatives of Inverse Functions
- Derivatives of Inverse Functions: from Equation
- Derivatives of Inverse Functions: from Table
- Derivative of Inverse Sine
- Derivative of Inverse Cosine
- Derivative of Inverse Tangent
- Derivative of ?ˣ
- Derivative of ln(x)
- Derivatives of Sine, Cosine, Tangent, e and ln
- Proof: The Derivative of ?ˣ is ?ˣ
- Proof: The Derivative of ln(x) is 1/(x)
- Worked Example: Derivatives of sin(x) and cos(x)
- Trigonometric Implicit Differentiation
- Derivative of eᶜᵒˢˣ⋅cos(eˣ)
- Derivative of sin(ln(x²))
- L’Hopital’s Rule Introduction
- L’Hopital’s Rule: Limit at 0 Example
- L’Hopital’s Rule: Limit at Infinity
- L’Hopital’s Rule: Solve for a Variable

#### Unit 1: Fundamentals of Plane Geometry

- Lines, Line Segments and Rays
- Angle Basics
- Measuring Angles in Degrees
- Acute Right and Obtuse Angles
- Complementary and Supplementary Angles
- Angles at the Intersection of Two Lines
- Angles Formed Between Transversals and Parallel Lines
- Sum of the Angles in Triangles Example 1
- Sum of the Angles in Triangles Example 2
- Sum of the Angles in Triangles Example 3
- Pythagoreans Theorem
- Pythagoreans Theorem and Area
- Congruent and Similar Triangles
- Language and Notation of the Circle
- Circles: Radius Diameter and Circumference
- Area of a Circle

#### Unit 2: Trigonometry

- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 1
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 2
- Proof: Law of Sines
- Proof: Law of Cosines
- Solving of a Side with the Law of Sines
- Solving for an Angle with the Law of Sines
- Solving for a Side with the Law of Cosines
- Solving for a Angle of the Law of Cosines
- Solving a Triangle Example one

#### Unit 1: Additional Topics in Trigonometry and Matrices

- Sum, Difference and Double Angle Identities
- Arcsine (inverse trig functions)
- Arccos (inverse trig functions)
- Arctan (inverse trig functions)
- Review of Trig Angle Addition Identities
- Using the Cosine Angle Addition Identity
- Using Cosine Double Angle Identity
- Proof of the Sine Angle Addition Identity
- Proof of the Cosine Angle Addition Identity
- Finding Trig Values Using Angle Addition Identities
- Using Trig Angle Addition Identities: Finding Side Lengths
- Using Trig Angle Addition Identities: Manipulation Expressions
- Using Trig Identities
- Intro to Matrices
- Multiplying Matrices by Scalars
- Adding and Subtracting Matrices
- Multiplying Matrices
- Introduction Matrix Inverses
- Invertible Matrices and Determinants
- Invertible Matrices and Transformations
- Finding Inverses of 2x2 Matrices
- Finding a 3x3 Matrix Using Gaussian Elimination
- Inverting a 3x3 Matrix Using Determinants 1
- Inverting a 3x3 Matrix Using Determinants 2

#### Unit 2: The Derivative

- Introduction to Limits
- Formal Definition of Limits Part 1: Intuition Review
- Formal Definition of Limits Part 2: Building the Idea
- Formal Definition of Limits Part 3: the Definition
- Formal Definition of Limits Part 4: Using the Definition
- Slope of a Tangent Line 1
- Slope of a Tangent Line 2
- Slope of a Tangent Line 3
- Basic Derivative Rules (Part 1)
- Basic Derivative Rules (Part 2)
- Basic Derivative Rules: Find the error
- Basic Derivative Rules: Table
- Power Rule
- Justifying the Power Rule
- Proof of the Power Rule for Positive Integer Powers
- Proof of Power Rule for Square Root Function
- Basic Derivative Rules
- Differentiating Polynomials
- Tangents of Polynomials
- Differentiating Integer Powers (Mixed Positive and Negative)
- Worked Example: Tangent to the Graph of 1/x
- Fractional Powers Differentiation
- Radical Functions Differentiation Intro
- The Product Rule
- Differentiating Products
- Worked Example: Product Rule with Table
- Worked Example: Product Rule with Mixed Implicit and Explicit
- Product Rule to Find Derivative of Product of Three Functions
- Product Rule Proof
- The Quotient Rule
- Worked Example: Quotient Rule with Table
- Differentiating Rational Functions
- Chain Rule
- Common Chain Rule Misunderstandings
- Identifying Composite Functions
- Worked Example: Derivative of cos³(x) Using the Chain Rule
- Worked Example: Derivative of √(3x²-x)
- Worked Example: Derivative of ln(√x) Using the Chain Rule
- Worked Example: Chain Rule with Table
- Implicit Differentiation
- Worked Example: Implicit Differentiation
- Worked Example: Evaluating Derivative with Implicit Differentiation
- Showing Explicit and Implicit Differentiation Give the Same Result
- Implicit Differentiation 1
- Implicit Differentiation 2
- Implicit Differentiation 3
- Implicit Differentiation 4
- Differentiating Functions: Finding the Error
- Manipulating Functions Before Differentiation
- Differentiation Using multiple Rules: Strategy
- Applying the Chain Rule and Product Rule
- Applying the Chain Rule Twice
- Product Rule to Find Derivative of Product of Three Functions

#### Unit 3: Applications of the Derivative

- Second Derivatives
- Second Derivatives (implicit equations): Find Expression
- Second Derivatives (implicit equations): Evaluate Derivative
- Introduction to One-Dimensional Motion with Calculus
- Interpreting Direction of Motion from Position-Time Graph
- Interpreting Direction of Motion from Velocity-Time Graph
- Interpreting Change in Speed from Velocity-Time Graph
- Worked Example: Motion Problems with Derivatives
- Analyzing Straight-Line Motion Graphically
- Total Distance Traveled with Derivatives
- Tangent to y=𝑒ˣ/(2+x³)
- Normal to y=𝑒ˣ/x²
- Related Rates Intro
- Analyzing Related Rate Problems: Expressions
- Analyzing Related Rate Problems: Equations (Pythagoras)
- Analyzing Related Rate Problems: Equations (Trig)
- Differentiating Related Functions Intro
- Worked Example: Differentiating Related Functions
- Related Rates: Approaching Cars
- Related Rates: Falling Ladder
- Related Rates: Pouring Water into a Cone
- Related Rates: Shadow
- Related Rates: Balloon
- Extreme Value Theorem
- Critical Points Introduction
- Finding Critical Points
- Finding Decreasing Interval Given the Functions
- Finding Increasing Interval Given the Derivative
- Introduction to Minimum and Maximum Points
- Finding Relative Extrema
- Worked Example: Finding Relative Extrema
- Analyzing Mistakes When Finding Extrema Example 1
- Analyzing Mistakes When Finding Extrema Example 2
- Concavity Introduction
- Analyzing Concavity (graphical)
- Inflection Points Introduction
- Inflection Points (graphical)
- Analyzing Concavity (algebraic)
- Inflection Points (algebraic)
- Mistakes When Finding Inflection Points: Second Derivative Undefined
- Mistakes When Finding Inflection Points: Not Checking Candidates
- Second Derivative Test
- Curve Sketching with Calculus: Polynomial
- Curve Sketching with Calculus: Logarithm
- Analyzing a Function with its Derivative
- Optimization: Sum of Squares
- Optimization: Box Volumes (Part 1)
- Optimization: Box Volumes (Part 2)
- Optimization: Profit
- Optimization: Cost of Materials
- Optimization: Area of Triangle & Square (Part 1)
- Optimization: Area of Triangle & Square (Part 2)
- Optimization Problem: Extreme Normal Line to y=x²

#### Unit 4: Derivatives of Transcendental Functions

- Derivatives of x and cos x
- Worked Example: Derivatives of sin x and cos x
- Derivatives of tan x and cot x
- Derivatives of sec x and csc x
- Derivatives of Inverse Functions
- Derivatives of Inverse Functions: from Equation
- Derivatives of Inverse Functions: from Table
- Derivative of Inverse Sine
- Derivative of Inverse Cosine
- Derivative of Inverse Tangent
- Derivative of 𝑒ˣ
- Derivative of ln x
- Derivatives of Sine, Cosine, Tangent, e and ln
- Proof: The Derivative of 𝑒ˣ is 𝑒ˣ
- Proof: The Derivative of ln x is 1/x
- Worked Example: Derivatives of sin x and cos x
- Trigonometric Implicit Differentiation
- Derivative of eᶜᵒˢˣ⋅cos(eˣ)
- Derivative of sin(ln(x²))
- LHopitals Rule Introduction
- LHopitals Rule: Limit at 0 Example
- LHopitals Rule: Limit at Infinity
- LHopitals Rule: Solve for a Variable

#### Unit 1: Descriptive Statistics

- Identifying Individuals, variables and categorical variables in a data set
- Categorical Data Example
- Reading Pictographs
- Reading Bar Graphs
- Reading Pie Graphs
- Reading Line Graphs
- Reading Stem and Leaf Plots
- Reading Box and Whisker Graphs
- Representing Data
- Frequency Tables and Dot Plots
- Creating a Histogram
- Interpreting a Histogram
- Mean Median and Mode
- Mean Median and Mode Example
- Find the Missing Value Given the Mean
- Comparing Means of Different Distributions
- Means and Medians of Different Distributions
- Impact on Median and Mean: Removing an Outlier
- Impact on Median and Mean: Increasing an Outlier
- Interquartile Range (IQR)
- Range and Mid Range
- Sample Versus Population Mean
- The Average
- Sample vs. Population Means
- Variance of a Population | Descriptive Statistics
- Sample Variance
- Statistics: Standard Deviation
- Measures of Spread: Range, Variance & Standard Deviation
- Population Standard Deviation
- Mean and Standard Deviation versus Median and IQR
- Sample Variance
- Sample Standard Deviation and Bias
- Statistics: Alternate Variance Formulas
- Why we divide by n-1 in Variance
- Simulation Showing bias in Sample Variance
- Simulation Providing Evidence that (n-1) gives us Unbiased Estimate

#### Unit 2: Probability Theory and Distributions

- Probability Explained
- The Coin Flip Example
- More Coin Flip
- Introduction to Conditional Probability
- Basic Probability
- Simple Probability
- Venn Diagrams
- Addition Rule for Probability
- Counting Outcomes Using Tree Diagrams
- Permutation Formula
- Zero Factorial or 0!
- Factorial and Counting Seat Arrangements
- Possible Three Letter Words
- Ways to Arrange Colours
- Intro to Combinations
- Combination Formula
- Handshaking Combinations
- Combinations Example: 9 Card Hands
- Probability Using Combinations | Probability and Statistics
- Probability and Combinations
- Probability with Counting Outcomes
- Getting Exactly Two Heads
- Exactly Three Heads in Five Flips
- Generalization With Binomial Coefficients
- Different Ways to Pick Officers
- Combinatorics and Probability
- Lottery Probability
- Mega Millions Jackpot Probability
- Birthday Probability Problem
- Permutations
- Multiplication Rule for Probability
- Combinations
- Permutations
- Permutations and Combinations Example 1
- Permutations and Combinations Example 2
- Permutations and Combinations Example 3
- Permutations and Combinations Example 4
- Introduction to the Binomial Distribution 1
- Introduction to the Binomial Distribution 2
- Binomial Distribution Example 1
- Binomial Distribution Example 2
- Introduction to Z-Scores
- Comparing Z-Scores
- Z-Scores in the Normal Distribution
- Qualitative Sense of Normal Distributions
- Normal Distribution Problems: Empirical Rule
- Standard Normal Table for Proportion Below
- Standard Normal Table or Proportion Above
- Standard Normal Table for Proportion between Values
- Finding Z-Score for Percentile
- Threshold for Low Percentile
- Z-Score Examples 1
- Introduction to t Statistics
- Simulation Showing Value of t Statistic
- Conditions for Valid t Intervals
- Finding a Critical t Value

#### Unit 3: Inferential Statistics

- The Central Limit Theorem
- Sampling Distribution of the Sample Mean 1
- Sampling Distribution of the Sample Mean 2
- Standard Error of the Mean
- Example: Probability of Sample Mean Exceeding a Value
- Confidence Interval and Margin of Error
- Confidence Interval Simulation
- Interpreting Confidence Level Example
- Confidence Interval Example
- Margin of Error 1
- Margin of Error 2
- Conditions for Valid Confidence Intervals
- Conditions for Confidence Intervals Worked Examples
- Critical Value (z*) for a Given Confidence Level
- Sample Size Based on Confidence and Margin of Error
- Example Constructing a t Interval for a Mean
- Sample Size for a Given Margin of Error for a Mean
- T-Statistic Confidence Interval
- Small Sample Size Confidence Intervals
- Simple Hypothesis Testing
- Idea Behind Hypothesis Testing
- Example of Null and Alternative Hypotheses
- P-Values and Significance Tests
- Comparing P-Values to Different Significant Levels
- Comparing P-Value from a Simulation
- Introduction of Type 1 and Type 2 Errors
- Type 1 Errors
- Examples of Identifying Type 1 and Type 2 Errors
- Introduction to Power in Significance Tests
- Examples Thinking About Power in Significance Tests
- Constructing Hypotheses for a Significance Test About a Proportion
- Conditions for a Z Test About a Proportion
- Calculating a Z Statistic in a Test About a Proportion
- Making Conclusions in a Z Test for a Proportion
- Writing Hypotheses for a Significance Test About a Mean
- Conditions for a t Test about a mean
- When to use Z or t Statistics in Significance Tests
- Example Calculating t Test statistic for a Test About a Mean
- One-Tailed and Two-Tailed Tests
- Z-Statistics vs. T-Statistics
- Small Sample Hypothesis Test
- Large Sample Proportion Testing

#### Unit 1: Functions and Graphs

- Introduction to Functions 1
- Introduction to Functions 2
- Functions (Part III)
- Introduction to Functions 4
- Evaluate a Formula or Function Using Substitution
- The Coordinate Plane
- Plotting (x,y) Coordinates
- Finding the Length of a Line Segment or Finding the Distance Between Two Points (Distance Formula)
- Graphing a Basic Function
- Graphing a Quadratic Function
- Graphing Exponential Functions
- Graphing Square Root Functions

#### Unit 2: Factoring and Fractions

- Binomial Squared
*(Special Products in Algebra)* - Difference of Squares
*(Special Products in Algebra)* - Finding The Greatest Common Factor (GCF)
- More GCF Examples
- Common Factoring Example
- More Common Factoring Examples
- Example 1: Factoring Trinomials with a Common Factor
- Factor by Grouping (Triple Common Factor)
- Factoring a Trinomial with a Common Factor First
- Factoring a Perfect Square Trinomial
- Factoring a Difference of Squares
- Strategy in Factoring Quadratics 1
- Strategy in Factoring Quadratics 2
- Factoring a Sum of Cubes
- Factoring a Difference of Cubes
- Simplifying Rational Expressions
- Simplifying Rational Expressions: Common Monomial Factors
- Simplifying Rational Expressions: Common Binomial Factors
- Simplifying Rational Expressions: Opposite Common Binomial
- Simplifying Rational Expressions: Grouping
- Simplifying Rational Expressions: Higher Degree Terms
- Multiplying & Dividing Rational Expressions: Monomials
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Adding & Subtracting Rational Expressions: Like Denominators
- Intro to Adding Rational Expressions with Unlike Denominators
- Adding Rational Expressions: Unlike Denominators
- Subtracting Rational Expressions: Unlike Denominators
- Least Common Multiple
- Least Common Multiple: Repeating Factors
- Subtracting Rational Expressions: Factored Denominators
- Least Common Multiple of Polynomials
- Subtracting Rational Expressions
- Solving Rational Equations

#### Unit 3: Quadratic Equations

- Solving Equations with Zero Product Property
- Solving Quadratics by Factoring
- Solving Quadratics by Factoring: Leading Coefficient not = 1
- Completing the Square
- Completing the Square to Solve Quadratics
- Quadratic Formula 1
- Quadratic Formula 2
- Quadratic Formula 3
- Quadratic Formula 4
- Graphing a Quadratic Function

#### Unit 4: Graphing Trig Functions

- Graphs of Trigonometric Functions - Sine
- Graphs of Trigonometric Functions - Cosine
- Graphs of Trigonometric Functions - Tangent
- Graphing Trigonometric Functions: Transformations
- Determining the Equation of a Trig Function
- Finding the Trigonometric Equation From the Graph 2

#### Unit 5: Exponents and Radicals

- Exponent Properties 1 | Exponent Expressions and Equations
- Exponent Properties 2
- Exponent Properties 3
- Simplifying Rational Expressions Using Exponent Laws - Example
- Exponents Properties with Products
- Exponent Properties with Parentheses
- Exponent Properties with Quotients
- Rational Exponents and Exponent Laws
- Simplifying Radical Expressions 1
- Simplifying Radical Expressions Example 2
- How to Rationalize a Denominator
- Addition of Radical Expressions
- Subtraction of Radical Expressions
- Adding and Subtracting Radical Expressions
- Multiplying Rational Expressions Example 1
- MultiplyingRational Expressions Example 2
- How to Rationalize a Denominator

#### Unit 6: Exponental and Logrithmic Functions

- Graphing Exponential Functions
- Solving Exponentials with Logarithms
- Logarithm Properties
*(Sum and Difference Properties)* - Using Multiple Logarithm Properties to Simplify
- Proof: log a + log b = log ab
- Proof: a log b = log(b^a), log a - log b = log(a/b)
- Simplifying Logarithms
- Change of Base Formula
- Calculating a Logarithm with a Calculator
- Logarithmic Equations: Variable in the Argument
- Logarithmic Equations: Variable in the Base
- Solving Logarithmic Equations
- Solving Exponential Equations Using Logarithms: Base-10
- Solving Exponential Equations Using Logarithms: Base-2

#### Unit 1: Methods of Integration

- Introduction to Integral Calculus
- Definite Integrals Intro
- Worked Example: Accumulation of Change
- Riemann Approximation Introduction
- Over and Under Estimation of Riemann Sums
- Worked Example: Finding a Riemann Sum Using a Table
- Worked Example: Over Under Estimation of Riemann Sums
- Midpoint Sums
- Trapezoidal Sums
- Motion Problem with Riemann Sum Approximation
- Summation Notation Review
- Worked Examples: Summation Review
- Riemann Sums in Summation Notation
- Worked Example: Riemann Sums in Summation Notation
- Midpoint and Trapezoidal Sums in Summation Notation
- Defining Integrals with Riemann Sums
- The Fundamental Theorem of Calculus and Accumulation Functions
- Functions Defined by Definite Integrals (Accumulation Functions)
- Finding Derivative with Fundamental Theorem of Calculus
- Finding Derivative with Fundamental Theorem of Calculus: Chain Rule
- Interpreting Behaviour of Accumulation Functions
- Negative Definite Integrals
- Finding Definite Integrals Using Area Formulas
- Definite Integral Over a Single Point
- Integrating Scaled Version of Function
- Switching Bound of Definite Integral
- Integrating Sums of Functions
- Worked Examples: Finding Definite Integrals Using Algebraic Properties
- Definite Integrals on Adjacent Intervals
- Worked Example: Breaking up the Integrals Interval
- Worked Example: Merging Definite Integrals Over Adjacent Intervals
- Functions Defined by Integrals: Switched Interval
- Finding Derivative with Fundamental Theorem of Calculus: x is on lower bound
- Finding Derivative with Fundamental Theorem of Calculus: x is on both bounds
- The Fundamental Theorem of Calculus and Definite Integrals
- Antiderivatives and Indefinite Integrals
- Reverse Power Rule
- Indefinite Integrals: Sums & Multiples
- Rewriting Before Integrating
- Rewriting Before Integrating: Challenge Problem
- Indefinite Integral for 1/x
- Indefinite Integrals for sin x, cos x, and 𝑒ˣ
- Definite Integrals: Reverse Power Rule
- Definite Integral of Rational Function
- Definite Integral of Radical Function
- Definite Integral of Trig Function
- Definite Integral Involving Natural Log
- Definite Integral of Piecewise Function
- Definite Integral of Absolute Value Function
- U-Substitution Intro
- U-Substitution: Multiplying by a Constant
- U-Substitution: Defining U
- U-Substitution: Defining U (more examples)
- U-Substitution: Rational Function
- U-Substitution: Logarithmic Function
- U-Substitution: Definite Integrals
- U-Substitution: Definite Integral of Exponential Function
- U-Substitution: Special Application
- U-Substitution: Double Substitution
- Integration Using Long Division
- Integration Using Completing the Square and the Derivative of arctan(x)
- Integral of Cos^3(x)
- Integral of sin^2(x)cos^3(x)
- Integral of sin^4(x)
- Introduction to Trigonometric Substitution
- Substitution with x=sin(theta)
- More Trig Practice
- Trig and u Substitution Together 1
- Trig and u Substitution Together 2
- Trig Substitution With Tangent
- More Trig Substitution With Tangent
- Long Trig Sub Problem
- Integration by Parts Intro
- Integration by Parts Example 1
- Integration by Parts Example 2
- Integration by Parts Example 3
- Integration by Parts Example 4
- Integration by Parts: Definite Integrals
- Integration by Partial Fractions
- Introduction to Improper Integrals
- Divergent Improper Integral
- Improper Integral With Two Infinite Bounds
- Average Value Over a Closed Interval
- Calculating Average Value of Function Over Interval
- Mean Value Theorem for Integrals
- Motion Problem with Integrals: Displacement vs. Distance
- Analyzing Motion Problems: Position
- Analyzing Motion Problems: Total Distance Traveled
- Worked Example: Motion Problems (with definite integrals)
- Average Acceleration Over Interval
- Area Under Rate Function Gives the Net Change
- Interpreting Definite Integral as Net Change
- Worked Examples: Interpreting Definite Integrals in Context
- Analyzing Problems Involving Definite
- Worked Example: Problem Involving Definite Integral (algebraic)
- Area Between a Curve and the X-Axis
- Area Between a Curve and the X-Axis: Negative area
- Area Between Curves
- Worked Example: Area Between Curves
- Composite Area Between Curves
- Area Between a Curve and the Y-Axis
- Horizontal Area Between Curves
- Volume With Cross Sections: Intro
- Volume With Cross Sections: Squares and Rectangles
- Volume With Cross Sections Perpendicular to Y-Axis
- Volume With Cross Sections: Semicircle
- Volume With Cross Sections: Triangle
- Disc Method Around X-Axis
- Generalizing Disc Method Around X-Axis
- Disc Method Around Y-Axis
- Disc Method Rotation Around Horizontal Line
- Disc Method Rotating Around Vertical Line
- Calculating Integral Disc Around Vertical Line
- Solid of Revolution Between Two Functions
- Generalizing the Washer Method
- Washer Method Rotation Around Horizontal Line (not x-axis), Part 1
- Washer Method Rotation Around Horizontal Line (not x-axis), Part 2
- Washer Method Rotation Around Vertical Line (not y-axis), Part 1
- Washer Method Rotation Around Vertical Line (not y-axis), Part 2

#### Unit 2: Differential Equations

- Differential Equations Introduction
- Writing a Differential Equation
- Verifying Solutions to Differential Equations
- Slope Fields Introduction
- Worked Example: Equation From Slope Field
- Worked Example: Slope Field From Equation
- Worked Example: Slope Fields & Equations
- Approximating Solution Curves in Slope Fields
- Worked Example: Range of Solutions Curve From Slope Field
- Separable Equations Introduction
- Addressing Treating Differentials Algebraically
- Worked Example: Separable Differential Equations
- Worked Example: Identifying Separable Equations
- Particular Solutions to Differential Equations: Rational Function
- Particular Solutions to Differential Equations: Exponential Functions
- Worked: Example: Finding a Specific Solution to a Separable Equations
- Worked Example: Separable Equation with an Implicit Solution
- Exponential Models & Differential Equations (Part 1)
- Exponential Models & Differential Equations (Part 2)
- Worked Example: Exponential Solution to Differential Equation
- Eulers Method
- Worked Example: Eulers Method
- Exact Equations Intuition 1
- Exact Equations Intuition 2
- Exact Equations Example 1
- Exact Equations Example 2
- Exact Equations Example 3
- Integrating Factors 1
- Integrating Factors 2
- First Order Homogenous Equations 1
- First Order Homogenous Equations 2
- 2
^{nd}Order Linear Homogeneous Differential Equations 1 - 2
^{nd}Order Linear Homogeneous Differential Equations 2 - 2
^{nd}Order Linear Homogeneous Differential Equations 3 - 2
^{nd}Order Linear Homogeneous Differential Equations 4 - Complex Roots of the Characteristic Equations 1
- Complex Roots of the Characteristic Equations 2
- Complex Roots of the Characteristic Equations 3
- Repeated Roots of the Characteristic Equation 1
- Repeated Roots of the Characteristic Equation 2
- Undetermined Coefficients 1
- Undetermined Coefficients 2
- Undetermined Coefficients 3
- Undetermined Coefficients 4
- Laplace Transform 1
- Laplace Transform 2
- L{sin(at)} transform of sin(at)
- Part two of the transform of sin(at)
- Laplace as Linear Operator and Laplace of Derivatives
- Laplace Transform of cos t and Polynomials
- Shifting Transform by Multiplying Function by Exponential
- Laplace Transform of t: L{t}
- Laplace Transform of t^n: L{t^n}
- Laplace Transform of the Unit Step Function
- Inverse Laplace Examples
- Dirac Delta Function
- Laplace Transform of the Dirac Delta Function
- Laplace Transform to Solve an Equation 1
- Laplace Transform to Solve an Equation 2
- Using the Laplace transform to Solve a Nonhomogeneous Equation
- Laplace/Step Function Differential Equation
- Introduction to the Convolution
- The Convolution and Laplace Transform
- Using the Convolution Theorem to Solve an Initial Value Prob