The math lessons below can be used to assist both teachers and students, including homeschool students. Teachers can gather ideas how to deliver various skills. Students can learn new mathematics lessons to avoid taking low level courses or review known skills to prepare for tests. There are three sections:

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  • College Algebra
  • Statistics
  • Trigonometry
  • Calculus
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Divisibility Check         Fractions, Decimals, and Percents         Converting Decimals, Fractions, and Percents     Reducing Fractions     Multiplying Fractions     Dividing Fractions     Adding and Subtracting Fractions     Percent Word Problems         Operations on Integers     Adding Positive and Negative Integers       Subtracting Positive and Negative Integers     Multiplying Positive and Negative Integers       Dividing Positive and Negative Integers     Order of Operations       Inequalities         Solving Equations     Two-Step: ( ax + b = c )       Three-Step, Type 1: ( ax + b + cx = d )       Three-Step, Type 2: ( ax + b = cx + d )       Head Start 1       Head Start 2     Absolute Value Equations         Solving Literal Equations       Solving the Gas Law Relation       Solving Literal Equations       Power Rules for Exponents       Change the Base         Simplifying Radical Expressions     Simplifying Radical Expressions         Addition and Subtraction         Multiplication         The Pythagorean Theorem     Finding the Hypotenuse     Finding a Leg         Operations on Polynomials     Addition     Subtraction     Multiplication     Synthetic Division         Factoring Polynomials     Factoring the Greatest Common Factor     Factoring a Difference of Two Squares     Factoring Trinomials (when a = 1 for ax2 + bx + c)     Factoring Trinomials (when a > 1 for ax2 + bx + c)     Using the Quadratic Formula         Graphing Lines     Graphing Lines in Slope-Intercept Form     Graphing Lines in Standard Form         Systems of Linear Equations   Addition   Multiplication/Addition (Linear Combination)   Substitution         Rational Expressions       Simplification     Multiplication     Division     Addition     Subtraction     Graphing: Basic       Graphing: Intermediate     Graphing: Advanced       Division with Zero       Algebra 'Magic': Simple       Algebra 'Magic': Intermediate #1       Algebra 'Magic': Intermediate #2         Characteristics of Parabolas       Parabolas in Factored Form       Parabolas in Vertex Form         Parabolas: Standard Form to Vertex Form         Word Problems - Beginner Level     Chemistry I     Distance I     Mixture I     Basic Work Problems       Similarity     Proportions 1: Simple     Proportions 2: Linear Equations     Proportions 3: Quadratic Equations       Similar Figures     Dilations         The Pythagorean Theorem     Finding the Hypotenuse     Finding a Leg         Quadrilaterals         Properties of Parallelograms         Properties of Rectangles         Properties of All Quadrilaterals         Geometry Proofs     Beginner Level Proofs     Moderate Level Proofs         Circle Properties         Circle Terminology     Central Angles and Arcs     Inscribed Angles and Arcs     Chord-Chord Partial Lengths Relationship     Chord-Chord Arcs and Angle Relationship       Secant-Secant Partial Lengths Relationship     Secant-Secant Arcs and Angle Relationship         Two Dimensional Figures: Area       Rectangles       Parallelograms       Triangles       Trapezoids       Circles       Area Tour of All Figures         Three Dimensional Figures: Surface Area     Rectangular Prisms   Cylinders   Square Pyramids   Cones     Spheres         Surface Area Tour of All Figures         Three Dimensional Figures: Volume       Rectangular Prisms     Cylinders   Square Pyramids   Cones     Spheres         Volume Tour of All Figures         Similar Figures & Solids       Similar Figures: Ratios of Lengths and Areas       Similar Solids: Ratios of Lengths and Volumes       Calculating the Diagonal Length of a Cube         Coordinate Geometry     Distance Formula     Midpoint Formula     Slope Formula     Parallel versus Perpendicular         Angled Width of a Sofa         Classifying Triangles Using Slope & Distance         Classifying Parallelograms       Classifying Parallelograms Using Slope       Classifying Parallelograms Using Slope & Distance     Partitioning a Segment       Circles       Parabolas       Matrices       Matrix Basics       Creating a Matrix     Adding Matrices     Subtracting Matrices       Scalar Matrix Multiplication   Multiplying Matrices     The Multiplicative Inverse of a Matrix       The Determinant of a 2x2 Matrix         The Determinant of a 3x3 Matrix     Matrix Equations     Partial Fraction Decomposition         The Point-Slope Formula: Calculating an Equation of a Line   Use the Formula Given a Point and a Slope   Use the Formula Given Two Points         Systems of Linear Equations   Addition   Multiplication/Addition (Linear Combination)   Substitution       Reduced Row Echelon Form       Matrix Equations     Three Equations and Three Unknowns         Graphing Inequalities   Graphing Linear Inequalities: Slope-Intercept Form   Graphing Linear Inequalities: Standard Form   Graphing Systems of Linear Inequalities         Solving Inequalities     Solving Absolute Value Inequalities       Solving Quadratic Inequalities by Algebra         Solving Quadratic Inequalities by Graphing         Linear Programming     Converting Words into Symbols     Determining the Profit (Objective) Function     Graphing Systems of Inequalities     Finding the Feasible Region     Finding the Vertices     Finding the Maximum Value (Profit)         Complex Numbers     Graphing     Addition   Subtraction     Powers of I   Multiplication   Division         Simplifying Radical Expressions     Modulus (Absolute Value)         Solve Quadratic Equations     Method: Factoring     Method: Completing the Square     Method: Using the Quadratic Formula         Method: Graphing         Solving Quadratic Equations Involving Area         Solving Complicated Proportions     Proportions 2: Linear Equations     Proportions 3: Quadratic Equations       Polynomials, Factors, and Zeros       Finding Zeros and Factors, Given a Polynomial     Finding a Polynomial, Given its Real Zeros       Finding a Polynomial, Given its Complex Zeros         Polynomial Graphs to Factors         Polynomial Tables     Translations: From Equations to Statements     Translations: From Statements to Equations     End Behavior       Even and Odd Degree       Even, Odd, or Neither (Symmetry)     The Rational Root Theorem       Finding the Coefficients of a 2nd Degree Polynomial Function         Polynomial Models       Picture Frame Problem     Open Box Problem   Flight of a Projectile         Solving Radical Equations     Solve Radical Equations     Solve Radical Equations 2         Relations   Domain and Range   Inverses     Functions     Translations / Transformations     Testing Relations for Symmetry         Functions       Determining Functions from Non-Functions   Evaluating Functions   Composite Functions       Determine the Function       Find the Pattern   Domain and Range   Finding Inverses       Piecewise Functions: Beginner Level       Piecewise Functions: Intermediate Level     Piecewise Functions: Advanced Level     Parent Functions       Even and Odd Functions         Parabolic Functions         Exponential Functions     Calculating Value Over Time       Translating Exponential Functions         Logarithms       Graphing Logarithmic Functions   Converting Between Logarithmic and Exponential Forms   Expanding and Contracting Logarithmic Expressions   Exponential Equations       Word Problem: Bacterial Growth     Word Problem: Radioactive Decay     Word Problem: Human Population Growth     Word Problem: Value Over Time       Solving Logarithmic Equations         Arithmetic Sequences and Series     Calculating the nth Term in a Sequence     Finding the Number of Terms in a Finite Sequence       Deriving the Sum Formula for a Series     Finding the Sum of a Series       Geometric Sequences and Series       Calculating the nth Term in a Sequence       Finding the Number of Terms in a Finite Sequence     Finding the Sum of a Finite Series     Finding the Sum of an Infinite Series         Sigma Notation       Arithmetic Series       Geometric Series         Arithmetic, Geometric, or Neither         Rational Expressions     Expressions with Basic Exponents     Expressions with Complex Exponents       Expressions with Negative Exponents       Algebra 'Magic': Advanced         Conic Sections   Parabolas     Circles   Ellipses   Hyperbolas       Identify the Conic Section     General Form to Standard Form         Word Problems - Advanced Level   Chemistry II     Distance II       Average Velocity     Mixture II     Delayed Start Work Problems     Unknown Rate Work Problems       Relative Rates Work Problems     Standardized Test Questions and Solutions         Basic Counting (Fundamental Counting Principle)   Clothing Problems   License Plate Problems       Complex Counting (Combinations & Permutations)   Tickets Problems   Card Deck Problems   Horse Race Problems   Election Problems     Placement Counting (Placement Problems)   Bookshelf Problems   Scrambled Letters Problems   Seating People Problems   Town Maps and Grids Problems         Probability Basics     Spinner Problems   Marble Bag Problems   Dice Problems     Expected Values     The Monty Hall Problem: A Game Show Probability         Binomial Theorem     Expansion     Term           Parametric Equations   Parametric Equations           Statistics       Frequency Tables         Dice Roller: Mean and Standard Deviation     Bell Curve: Standard Deviation     Bell Curve: 68-95-99 Rule         Confidence Intervals and Margin of Error with TI-Nspire       Margin of Error to Confidence Interval       Margin of Error from Confidence Interval   Confidence Intervals Using a Formula       Mean, Standard Deviation, and Margin of Error         Trigonometry Basics       Labeling Triangles       The Three Main Trigonometric Functions       The Other Three Trigonometric Functions       Deriving The 30-60-90 Special Right Triangle       Deriving The 45-45-90 Special Right Triangle         Right Triangle Trigonometry     Sine Problem     Cosine Problem     Tangent Problem     Area of Regular Polygons       Law of Sines     Law of Sines: Ambiguous Case (SSA)   Law of Sines: Find a Side   Law of Sines: Find an Angle       Law of Cosines   Law of Cosines: Find a Side   Law of Cosines: Find an Angle         Area of Polygons     Area of Regular Polygons       Area of an Irregular Quadrilateral: SASSS       Area of an Irregular Quadrilateral: SASAS         Trigonometric Angles     Reference Angles     Degrees to Radians     Radians to Degrees       Trigonometric Functions of Special Angles       Inverse Trigonometric Functions     The Unit Circle: Ratios     The Unit Circle: Angles         Graphing Sine, Cosine, and Tangent Functions       The Basics   Sine: Amplitude and Period   Cosine: Amplitude and Period   Sine: Amplitude, Period, Phase Shift, Vertical Shift   Cosine: Amplitude, Period, Phase Shift, Vertical Shift       Tangent: Period and Phase Shift     Equations of Musical Notes     Tide STEM Problem   Trigonometric Expressions: Simplifying/Verifying Identities       Deriving The Pythagorean Trigonometric Identities           Angle Formulas     Sum and Difference Angle Formulas (Sine, Cosine)         Sum and Difference Angle Formulas (Tangent)         Double Angle Formulas (Sine, Cosine, Tangent)         Half Angle Formulas (Sine, Cosine)           Negative Angle Identities         Negative Angle Identities         Negative Angle Identity Proofs         Solving Trigonometric Equations       Solving Simple Trigonometric Equations       Solving Trigonometric Equations by Factoring         Solving Trigonometric Equations by Graphing         Vectors   Horizontal and Vertical Components       Adding Vectors       Subtracting Vectors     Calculating the Magnitude from Components     Calculating the Direction from Components         Engineering Notation       Combining Vectors: Two Forces       Combining Vectors: Three Forces     Unit Vectors     Dot Product     Calculating the Angle Between Two Vectors     Projection       Work: Force times a Distance     Vectors: Inclined Planes         Polar Coordinates and Equations     Polar Coordinates and Rectangular Conversions         Rectangular Equations to Polar Equations         Polar Equations to Rectangular Equations         Limits         Limits of the Extreme       Limits of Ratios of Polynomials     Limits by Factoring     Limits of Piecewise Functions     Limits: Numerical Approach     Limits by Conjugates       Sine Coefficient Limit Problem       Continuity           Derivatives         Derivatives: Derivation and Explanation     Derivatives: Polynomials         Derivatives: Radical Functions         Derivatives: Deriving the Sum Rule         Derivatives: Deriving the Difference Rule         Derivatives: Deriving the Product Rule         Derivatives: Product Rule Examples         Derivatives: Deriving the Quotient Rule         Derivatives: Quotient Rule Examples         Derivatives: Deriving the Chain Rule         Derivatives: Chain Rule Examples         Derivatives: Deriving the Power Rule         Deriving the Derivative of the Sine Function         Deriving the Derivative of the Cosine Function           Areas         Approximating the Area Under a Curve         Approximating the Area Under a Curve: Left Rectangles         Approximating the Area Under a Curve: Right Rectangles         Approximating the Area Under a Curve: Trapezoids           Related Rates         Ladder Problem         Conical Tank Problem

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   Quizmasters test students' abilities by:

1. generating random problems,
2. waiting for student input,
3. checking student input, and
4. instantly reporting whether or not the input is correct.

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