Courses tagged with "Introduction to Macroeconomics" (14)

Basic trigonometry. Example: Using soh cah toa. Trigonometry 0.5. Basic trigonometry II. Trigonometry 1. Secant (sec), cosecant (csc) and cotangent (cot) example. Example: Using trig to solve for missing information. Reciprocal trig functions. Trigonometry 1.5. Example: Calculator to evaluate a trig function. Example: Trig to solve the sides and angles of a right triangle. Trigonometry 2. Example: Solving a 30-60-90 triangle. Special right triangles. Using Trig Functions. Using Trig Functions Part II. Introduction to radians. Radian and degree conversion practice. Example: Radian measure and arc length. Example: Converting degrees to radians. Degrees to radians. Example: Converting radians to degrees. Radians to degrees. Radians and degrees. Radians and degrees. Unit circle definition of trig functions. Example: Unit circle definition of sin and cos. Example: Using the unit circle definition of trig functions. Example: Trig function values using unit circle definition. Example: The signs of sine and cosecant. Unit Circle Manipulative. Unit circle. Example: Graph, domain, and range of sine function. Example: Graph of cosine. Example: Intersection of sine and cosine. Example: Amplitude and period. Example: Amplitude and period transformations. Example: Amplitude and period cosine transformations. Example: Figure out the trig function. Graphs of sine and cosine. Graph of the sine function. Graphs of trig functions. Graphing trig functions. More trig graphs. Determining the equation of a trigonometric function. Inverse Trig Functions: Arcsin. Inverse Trig Functions: Arccos. Inverse Trig Functions: Arctan. Example: Calculator to evaluate inverse trig function. Inverse trig functions. Tau versus Pi. Pi Is (still) Wrong.. Basic trigonometry. Example: Using soh cah toa. Trigonometry 0.5. Basic trigonometry II. Trigonometry 1. Secant (sec), cosecant (csc) and cotangent (cot) example. Example: Using trig to solve for missing information. Reciprocal trig functions. Trigonometry 1.5. Example: Calculator to evaluate a trig function. Example: Trig to solve the sides and angles of a right triangle. Trigonometry 2. Example: Solving a 30-60-90 triangle. Special right triangles. Using Trig Functions. Using Trig Functions Part II. Introduction to radians. Radian and degree conversion practice. Example: Radian measure and arc length. Example: Converting degrees to radians. Degrees to radians. Example: Converting radians to degrees. Radians to degrees. Radians and degrees. Radians and degrees. Unit circle definition of trig functions. Example: Unit circle definition of sin and cos. Example: Using the unit circle definition of trig functions. Example: Trig function values using unit circle definition. Example: The signs of sine and cosecant. Unit Circle Manipulative. Unit circle. Example: Graph, domain, and range of sine function. Example: Graph of cosine. Example: Intersection of sine and cosine. Example: Amplitude and period. Example: Amplitude and period transformations. Example: Amplitude and period cosine transformations. Example: Figure out the trig function. Graphs of sine and cosine. Graph of the sine function. Graphs of trig functions. Graphing trig functions. More trig graphs. Determining the equation of a trigonometric function. Inverse Trig Functions: Arcsin. Inverse Trig Functions: Arccos. Inverse Trig Functions: Arctan. Example: Calculator to evaluate inverse trig function. Inverse trig functions. Tau versus Pi. Pi Is (still) Wrong..

A detailed look at shapes that are prevalent in science: conic sections. Introduction to Conic Sections. Recognizing conic sections. Radius and center for a circle equation in standard form. Equation of a circle in factored form. Conic Sections: Intro to Circles. Graphing circles. Equation of a circle in non-factored form. Graphing circles 2. Conic Sections: Intro to Ellipses. Equation of an ellipse. Foci of an Ellipse. Parabola Focus and Directrix 1. Focus and Directrix of a Parabola 2. Parabola intuition 1. Parabola intuition 2. Conic Sections: Intro to Hyperbolas. Conic Sections: Hyperbolas 2. Conic Sections: Hyperbolas 3. Equation of a hyperbola. Foci of a Hyperbola. Proof: Hyperbola Foci. Identifying an ellipse from equation. Identifying a hyperbola from an equation. Identifying circles and parabolas from equations. Hyperbola and parabola examples. Tangent Line Hyperbola Relationship (very optional). IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Circle Hyperbola Intersection. Introduction to Conic Sections. Recognizing conic sections. Radius and center for a circle equation in standard form. Equation of a circle in factored form. Conic Sections: Intro to Circles. Graphing circles. Equation of a circle in non-factored form. Graphing circles 2. Conic Sections: Intro to Ellipses. Equation of an ellipse. Foci of an Ellipse. Parabola Focus and Directrix 1. Focus and Directrix of a Parabola 2. Parabola intuition 1. Parabola intuition 2. Conic Sections: Intro to Hyperbolas. Conic Sections: Hyperbolas 2. Conic Sections: Hyperbolas 3. Equation of a hyperbola. Foci of a Hyperbola. Proof: Hyperbola Foci. Identifying an ellipse from equation. Identifying a hyperbola from an equation. Identifying circles and parabolas from equations. Hyperbola and parabola examples. Tangent Line Hyperbola Relationship (very optional). IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Circle Hyperbola Intersection.

An look at exponential and logarithmic functions including many of their properties and graphs. Exponential Growth Functions. Ex: Graphing exponential functions. Subtracting Rational Expressions. Word Problem Solving- Exponential Growth and Decay. Exponential Growth. Graphing Logarithmic Functions. Logarithmic Scale. Vi and Sal Explore How We Think About Scale. Vi and Sal Talk About the Mysteries of Benford's Law. Benford's Law Explanation (Sequel to Mysteries of Benford's Law). Solving Logarithmic Equations. Solving Logarithmic Equations. Introduction to interest. Interest (part 2). Introduction to compound interest and e. Compound Interest and e (part 2). Compound Interest and e (part 3). Compound Interest and e (part 4). Exponential Growth Functions. Ex: Graphing exponential functions. Subtracting Rational Expressions. Word Problem Solving- Exponential Growth and Decay. Exponential Growth. Graphing Logarithmic Functions. Logarithmic Scale. Vi and Sal Explore How We Think About Scale. Vi and Sal Talk About the Mysteries of Benford's Law. Benford's Law Explanation (Sequel to Mysteries of Benford's Law). Solving Logarithmic Equations. Solving Logarithmic Equations. Introduction to interest. Interest (part 2). Introduction to compound interest and e. Compound Interest and e (part 2). Compound Interest and e (part 3). Compound Interest and e (part 4).

Revisiting what a function is and how we can define and visualize one. What is a function. Function example problems. Ex: Constructing a function. Functions Part 2. Functions as Graphs. Understanding function notation exercise. Understanding function notation. Functions (Part III). Functions (part 4). Sum of Functions. Difference of Functions. Product of Functions. Quotient of Functions. Evaluating expressions with function notation. Evaluating composite functions. Domain of a function. Domain of a function. Domain of a function. Domain and Range of a Relation. Domain and range from graph. Domain and Range of a Function Given a Formula. Domain and Range 1. Domain of a Radical Function. Domain of a function. Domain and Range 2. Domain and Range of a Function. Range of a function. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Inverses of functions. When a function is positive or negative. Positive and negative parts of functions. Recognizing odd and even functions. Connection between even and odd numbers and functions. Even and odd functions. Shifting and reflecting functions. Shifting functions. Shifting and reflecting functions. Recognizing features of functions (Example 1). Recognizing features of functions 2 (example 2). Recognizing features of functions 2 (example 3). Recognizing features of functions 2. Interpreting features of functions 2 (Example 1). Interpreting features of functions 2 (Example 2). Interpreting features of functions 2. Comparing features of functions 2 (example 1). Comparing features of functions 2 (example 2). Comparing features of functions 2 (example 3). Comparing features of functions 2. Why Dividing by Zero is Undefined. Why Zero Divided by Zero is Undefined/Indeterminate. Undefined and Indeterminate. A more formal understanding of functions. Introduction to the inverse of a function. What is a function. Function example problems. Ex: Constructing a function. Functions Part 2. Functions as Graphs. Understanding function notation exercise. Understanding function notation. Functions (Part III). Functions (part 4). Sum of Functions. Difference of Functions. Product of Functions. Quotient of Functions. Evaluating expressions with function notation. Evaluating composite functions. Domain of a function. Domain of a function. Domain of a function. Domain and Range of a Relation. Domain and range from graph. Domain and Range of a Function Given a Formula. Domain and Range 1. Domain of a Radical Function. Domain of a function. Domain and Range 2. Domain and Range of a Function. Range of a function. Introduction to Function Inverses. Function Inverse Example 1. Function Inverses Example 2. Function Inverses Example 3. Inverses of functions. When a function is positive or negative. Positive and negative parts of functions. Recognizing odd and even functions. Connection between even and odd numbers and functions. Even and odd functions. Shifting and reflecting functions. Shifting functions. Shifting and reflecting functions. Recognizing features of functions (Example 1). Recognizing features of functions 2 (example 2). Recognizing features of functions 2 (example 3). Recognizing features of functions 2. Interpreting features of functions 2 (Example 1). Interpreting features of functions 2 (Example 2). Interpreting features of functions 2. Comparing features of functions 2 (example 1). Comparing features of functions 2 (example 2). Comparing features of functions 2 (example 3). Comparing features of functions 2. Why Dividing by Zero is Undefined. Why Zero Divided by Zero is Undefined/Indeterminate. Undefined and Indeterminate. A more formal understanding of functions. Introduction to the inverse of a function.

Thinking about graphing on a coordinate plane, slope and other analytic geometry. Descartes and Cartesian Coordinates. The Coordinate Plane. Plot ordered pairs. Graphing points. Quadrants of Coordinate Plane. Graphing points and naming quadrants. Points on the coordinate plane. Ordered pair solutions of equations. Ordered Pair Solutions of Equations 2. Ordered pair solutions to linear equations. Recognizing Linear Functions. Interpreting linear relationships. Slope of a line. Slope of a Line 2. Slope and Rate of Change. Graphical Slope of a Line. Slope of a Line 3. Identifying slope of a line. Slope and Y-intercept Intuition. Line graph intuition. Graphing a line in slope intercept form. Converting to slope-intercept form. Graphing linear equations. Multiple examples of constructing linear equations in slope-intercept form. Constructing equations in slope-intercept form from graphs. Constructing linear equations to solve word problems. Linear equation from slope and a point. Finding a linear equation given a point and slope. Constructing the equation of a line given two points. Solving for the y-intercept. Slope intercept form. Linear Equations in Point Slope Form. Point slope form. Linear Equations in Standard Form. Point-slope and standard form. Converting between slope-intercept and standard form. Converting between point-slope and slope-intercept. Finding the equation of a line. Midpoint formula. Midpoint formula. Distance Formula. Distance formula. Perpendicular Line Slope. Equations of Parallel and Perpendicular Lines. Parallel Line Equation. Parallel Lines. Parallel Lines 2. Parallel lines 3. Perpendicular Lines. Perpendicular lines 2. Equations of parallel and perpendicular lines. Distance between point and line. Graphing Inequalities. Solving and graphing linear inequalities in two variables 1. Graphing Linear Inequalities in Two Variables Example 2. Graphing Inequalities 2. Graphing linear inequalities in two variables 3. Graphs of inequalities. Graphing linear inequalities. Graphing and solving linear inequalities. Descartes and Cartesian Coordinates. The Coordinate Plane. Plot ordered pairs. Graphing points. Quadrants of Coordinate Plane. Graphing points and naming quadrants. Points on the coordinate plane. Ordered pair solutions of equations. Ordered Pair Solutions of Equations 2. Ordered pair solutions to linear equations. Recognizing Linear Functions. Interpreting linear relationships. Slope of a line. Slope of a Line 2. Slope and Rate of Change. Graphical Slope of a Line. Slope of a Line 3. Identifying slope of a line. Slope and Y-intercept Intuition. Line graph intuition. Graphing a line in slope intercept form. Converting to slope-intercept form. Graphing linear equations. Multiple examples of constructing linear equations in slope-intercept form. Constructing equations in slope-intercept form from graphs. Constructing linear equations to solve word problems. Linear equation from slope and a point. Finding a linear equation given a point and slope. Constructing the equation of a line given two points. Solving for the y-intercept. Slope intercept form. Linear Equations in Point Slope Form. Point slope form. Linear Equations in Standard Form. Point-slope and standard form. Converting between slope-intercept and standard form. Converting between point-slope and slope-intercept. Finding the equation of a line. Midpoint formula. Midpoint formula. Distance Formula. Distance formula. Perpendicular Line Slope. Equations of Parallel and Perpendicular Lines. Parallel Line Equation. Parallel Lines. Parallel Lines 2. Parallel lines 3. Perpendicular Lines. Perpendicular lines 2. Equations of parallel and perpendicular lines. Distance between point and line. Graphing Inequalities. Solving and graphing linear inequalities in two variables 1. Graphing Linear Inequalities in Two Variables Example 2. Graphing Inequalities 2. Graphing linear inequalities in two variables 3. Graphs of inequalities. Graphing linear inequalities. Graphing and solving linear inequalities.

Motivation and understanding of hyperbolic trig functions. Hyperbolic Trig Function Inspiration. Hyperbolic Trig Functions and the Unit Hyperbola. Hyperbolic Trig Function Inspiration. Hyperbolic Trig Functions and the Unit Hyperbola.

Understanding i and the complex plane. Introduction to i and Imaginary Numbers. Calculating i Raised to Arbitrary Exponents. Imaginary unit powers. Imaginary Roots of Negative Numbers. i as the Principal Root of -1 (a little technical). Complex numbers. Complex numbers (part 1). Complex numbers (part 2). The complex plane. Adding Complex Numbers. Subtracting Complex Numbers. Complex number polar form intuition. Complex plane operations. Adding and subtracting complex numbers. Multiplying Complex Numbers. Multiplying complex numbers. Dividing Complex Numbers. Dividing complex numbers. Multiplying and dividing complex numbers in polar form. Complex Conjugates. Complex Conjugates Example. Absolute value of complex numbers. Basic Complex Analysis. Complex number polar form intuition exercise. Complex number polar form intuition. Exponential form to find complex roots. Multiplying and dividing complex numbers in polar form. Powers of complex numbers. Complex Conjugates. IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). Complex Determinant Example. Introduction to i and Imaginary Numbers. Calculating i Raised to Arbitrary Exponents. Imaginary unit powers. Imaginary Roots of Negative Numbers. i as the Principal Root of -1 (a little technical). Complex numbers. Complex numbers (part 1). Complex numbers (part 2). The complex plane. Adding Complex Numbers. Subtracting Complex Numbers. Complex number polar form intuition. Complex plane operations. Adding and subtracting complex numbers. Multiplying Complex Numbers. Multiplying complex numbers. Dividing Complex Numbers. Dividing complex numbers. Multiplying and dividing complex numbers in polar form. Complex Conjugates. Complex Conjugates Example. Absolute value of complex numbers. Basic Complex Analysis. Complex number polar form intuition exercise. Complex number polar form intuition. Exponential form to find complex roots. Multiplying and dividing complex numbers in polar form. Powers of complex numbers. Complex Conjugates. IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). Complex Determinant Example.

Preview of the calculus topic of limits. Introduction to limits. Introduction to Limits. Limits 1. Limits 2. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part 3). Limit Examples w/ brain malfunction on first prob (part 4). More Limits. Introduction to limits. Introduction to Limits. Limits 1. Limits 2. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part 3). Limit Examples w/ brain malfunction on first prob (part 4). More Limits.

An alternative to Cartesian coordinates. Parametric Equations 1. Parametric Equations 2. Parametric Equations 3. Parametric Equations 4. Polar Coordinates 1. Polar Coordinates 2. Polar Coordinates 3. Parametric Equations 1. Parametric Equations 2. Parametric Equations 3. Parametric Equations 4. Polar Coordinates 1. Polar Coordinates 2. Polar Coordinates 3.

Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions. Factoring quadratic expressions. Examples: Factoring simple quadratics. Factoring polynomials 1. Example 1: Solving a quadratic equation by factoring. Example 2: Solving a quadratic equation by factoring. Solving quadratics by factoring. Example 1: Factoring trinomials with a common factor. Factoring polynomials 2. Solving quadratics by factoring 2. Factoring Special Products. Example 1: Factoring difference of squares. Factoring difference of squares 1. Example 2: Factoring difference of squares. Factoring difference of squares 2. Factoring to produce difference of squares. Factoring difference of squares 3. Example 5: Factoring by grouping. Example 6: Factoring by grouping. Factoring polynomials by grouping. Solving Quadratic Equations by Square Roots. Solving quadratics by taking the square root. Solving Quadratic Equations by Completing the Square. Completing the square 1. Completing the square 2. How to use the Quadratic Formula. Proof of Quadratic Formula. Quadratic formula. Example: Complex roots for a quadratic. Discriminant of Quadratic Equations. Discriminant for Types of Solutions for a Quadratic. Solutions to quadratic equations. Quadratic Inequalities. Quadratic Inequalities (Visual Explanation). Terms coefficients and exponents in a polynomial. Addition and Subtraction of Polynomials. Adding and subtracting polynomials. Multiplying Polynomials. Multiplying Polynomials 3. Multiplying polynomials. Polynomial Division. Dividing polynomials 1. Dividing polynomials with remainders. Synthetic Division. Synthetic Division Example 2. Why Synthetic Division Works. Factoring Sum of Cubes. Difference of Cubes Factoring. Binomial Theorem (part 1). Binomial Theorem (part 2). Binomial Theorem (part 3). Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Simplifying Rational Expressions 2. Simplifying Rational Expressions 3. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Subtracting Rational Expressions. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Extraneous Solutions to Rational Equations. Rational Inequalities. Rational Inequalities 2. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Partial Fraction Expansion 1. Partial Fraction Expansion 2. Partial Fraction Expansion 3. Partial fraction expansion. Factoring quadratic expressions. Examples: Factoring simple quadratics. Factoring polynomials 1. Example 1: Solving a quadratic equation by factoring. Example 2: Solving a quadratic equation by factoring. Solving quadratics by factoring. Example 1: Factoring trinomials with a common factor. Factoring polynomials 2. Solving quadratics by factoring 2. Factoring Special Products. Example 1: Factoring difference of squares. Factoring difference of squares 1. Example 2: Factoring difference of squares. Factoring difference of squares 2. Factoring to produce difference of squares. Factoring difference of squares 3. Example 5: Factoring by grouping. Example 6: Factoring by grouping. Factoring polynomials by grouping. Solving Quadratic Equations by Square Roots. Solving quadratics by taking the square root. Solving Quadratic Equations by Completing the Square. Completing the square 1. Completing the square 2. How to use the Quadratic Formula. Proof of Quadratic Formula. Quadratic formula. Example: Complex roots for a quadratic. Discriminant of Quadratic Equations. Discriminant for Types of Solutions for a Quadratic. Solutions to quadratic equations. Quadratic Inequalities. Quadratic Inequalities (Visual Explanation). Terms coefficients and exponents in a polynomial. Addition and Subtraction of Polynomials. Adding and subtracting polynomials. Multiplying Polynomials. Multiplying Polynomials 3. Multiplying polynomials. Polynomial Division. Dividing polynomials 1. Dividing polynomials with remainders. Synthetic Division. Synthetic Division Example 2. Why Synthetic Division Works. Factoring Sum of Cubes. Difference of Cubes Factoring. Binomial Theorem (part 1). Binomial Theorem (part 2). Binomial Theorem (part 3). Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Simplifying Rational Expressions 2. Simplifying Rational Expressions 3. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Subtracting Rational Expressions. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Extraneous Solutions to Rational Equations. Rational Inequalities. Rational Inequalities 2. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Partial Fraction Expansion 1. Partial Fraction Expansion 2. Partial Fraction Expansion 3. Partial fraction expansion.

Basics of probability and combinatorics. Basic Probability. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Probability 1. Probability with Playing Cards and Venn Diagrams. Addition Rule for Probability. Compound Probability of Independent Events. Getting At Least One Heads. Example: Probability of rolling doubles. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Frequency Probability and Unfair Coins. Example: Getting two questions right on an exam. Example: Rolling even three times. Independent probability. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Dependent probability. Monty Hall Problem. Permutations. Combinations. Counting 2. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Permutations. Combinations. Permutations and combinations. Example: Probability through counting outcomes. Example: All the ways you can flip a coin. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Generalizing with Binomial Coefficients (bit advanced). Conditional Probability and Combinations. Conditional Probability (Bayes Theorem) Visualized. Birthday Probability Problem. Probability with permutations and combinations. Basic Probability. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Probability 1. Probability with Playing Cards and Venn Diagrams. Addition Rule for Probability. Compound Probability of Independent Events. Getting At Least One Heads. Example: Probability of rolling doubles. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Frequency Probability and Unfair Coins. Example: Getting two questions right on an exam. Example: Rolling even three times. Independent probability. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Dependent probability. Monty Hall Problem. Permutations. Combinations. Counting 2. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Permutations. Combinations. Permutations and combinations. Example: Probability through counting outcomes. Example: All the ways you can flip a coin. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Generalizing with Binomial Coefficients (bit advanced). Conditional Probability and Combinations. Conditional Probability (Bayes Theorem) Visualized. Birthday Probability Problem. Probability with permutations and combinations.

An assortment of concepts in math that help us deal with sequences and proofs. Proof by Induction. Alternate Proof to Induction for Integer Sum. Explicit and recursive definitions of sequences. Arithmetic sequences. Finding the 100th Term in a Sequence. Arithmetic sequences 1. Equations of Sequence Patterns. Arithmetic sequences 2. Geometric sequences introduction. Geometric sequences. Geometric sequences 1. Geometric sequences 2. Converting an explicit function to a recursive function. Recursive and explicit functions. Sum of arithmetic sequence (arithmetic series). Formula for arithmetic series. Arithmetic series. Difference between inductive and deductive reasoning. Deductive Reasoning 2. Deductive Reasoning 3. Inductive Reasoning 1. Inductive Reasoning 2. Inductive Reasoning 3. Inductive Patterns. Convergent and divergent sequences. Definition of limit of a sequence and sequence convergence. Proving a sequence converges. Series as sum of sequence. Formula for finite geometric series. 2003 AIME II Problem 8. Advanced: Geometric series sum to figure out mortgage payments. Series Sum Example. Proof by Induction. Alternate Proof to Induction for Integer Sum. Explicit and recursive definitions of sequences. Arithmetic sequences. Finding the 100th Term in a Sequence. Arithmetic sequences 1. Equations of Sequence Patterns. Arithmetic sequences 2. Geometric sequences introduction. Geometric sequences. Geometric sequences 1. Geometric sequences 2. Converting an explicit function to a recursive function. Recursive and explicit functions. Sum of arithmetic sequence (arithmetic series). Formula for arithmetic series. Arithmetic series. Difference between inductive and deductive reasoning. Deductive Reasoning 2. Deductive Reasoning 3. Inductive Reasoning 1. Inductive Reasoning 2. Inductive Reasoning 3. Inductive Patterns. Convergent and divergent sequences. Definition of limit of a sequence and sequence convergence. Proving a sequence converges. Series as sum of sequence. Formula for finite geometric series. 2003 AIME II Problem 8. Advanced: Geometric series sum to figure out mortgage payments. Series Sum Example.

What happens when we have many variables but also many constraints. Trolls, Tolls, and Systems of Equations. Solving the Troll Riddle Visually. Solving Systems Graphically. Graphing systems of equations. King's Cupcakes: Solving Systems by Elimination. Simple Elimination Practice. Systems of equations with simple elimination. How many bags of potato chips do people eat?. Systems with Elimination Practice. Systems of equations with elimination. Talking bird solves systems with substitution. Practice using substitution for systems. Systems of equations with substitution. Systems of equations. Systems of equations word problems. Inconsistent systems of equations. Infinite solutions to systems. Consistent and Inconsistent Systems. Independent and Dependent Systems. Practice thinking about number of solutions to systems. Solutions to systems of equations. Visualizing the solution set for a system of inequalities. Graphing systems of inequalities. Graphing systems of inequalities 2. Graphing systems of inequalities. Graphing and solving systems of inequalities. Systems of Three Variables. Systems of Three Variables 2. Solutions to Three Variable System. Solutions to Three Variable System 2. Three Equation Application Problem. Non-Linear Systems of Equations 1. Non-Linear Systems of Equations 2. Non-Linear Systems of Equations 3. Systems of nonlinear equations 1. Systems of nonlinear equations 2. Systems of nonlinear equations 3. Systems of nonlinear equations. Trolls, Tolls, and Systems of Equations. Solving the Troll Riddle Visually. Solving Systems Graphically. Graphing systems of equations. King's Cupcakes: Solving Systems by Elimination. Simple Elimination Practice. Systems of equations with simple elimination. How many bags of potato chips do people eat?. Systems with Elimination Practice. Systems of equations with elimination. Talking bird solves systems with substitution. Practice using substitution for systems. Systems of equations with substitution. Systems of equations. Systems of equations word problems. Inconsistent systems of equations. Infinite solutions to systems. Consistent and Inconsistent Systems. Independent and Dependent Systems. Practice thinking about number of solutions to systems. Solutions to systems of equations. Visualizing the solution set for a system of inequalities. Graphing systems of inequalities. Graphing systems of inequalities 2. Graphing systems of inequalities. Graphing and solving systems of inequalities. Systems of Three Variables. Systems of Three Variables 2. Solutions to Three Variable System. Solutions to Three Variable System 2. Three Equation Application Problem. Non-Linear Systems of Equations 1. Non-Linear Systems of Equations 2. Non-Linear Systems of Equations 3. Systems of nonlinear equations 1. Systems of nonlinear equations 2. Systems of nonlinear equations 3. Systems of nonlinear equations.

Trigonometry Identity Review/Fun. Trigonometric Identities. Examples using Pythagorean identities to simplify trigonometric expressions. Pythagorean identities. Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b). Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b). Trig identities part 2 (part 4 if you watch the proofs). Trig identies part 3 (part 5 if you watch the proofs). Cosine addition identity example. Double angle formula for cosine example. Addition and subtraction trig identities. Navigation Word Problem. Fun Trig Problem. IIT JEE Trigonometry Problem 1. IIT JEE Trigonometric Maximum. IIT JEE Trigonometric Constraints. Trigonometric System Example. 2003 AIME II Problem 11. 2003 AIME II Problem 14. Trigonometry word problems (part 1). Trigonometry word problems (part 2). Ferris Wheel Trig Problem. Ferris Wheel Trig Problem (part 2). Law of cosines example. Proof of the law of cosines. Law of cosines. Proof: Law of Sines. Trigonometry Identity Review/Fun. Trigonometric Identities. Examples using Pythagorean identities to simplify trigonometric expressions. Pythagorean identities. Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b). Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b). Trig identities part 2 (part 4 if you watch the proofs). Trig identies part 3 (part 5 if you watch the proofs). Cosine addition identity example. Double angle formula for cosine example. Addition and subtraction trig identities. Navigation Word Problem. Fun Trig Problem. IIT JEE Trigonometry Problem 1. IIT JEE Trigonometric Maximum. IIT JEE Trigonometric Constraints. Trigonometric System Example. 2003 AIME II Problem 11. 2003 AIME II Problem 14. Trigonometry word problems (part 1). Trigonometry word problems (part 2). Ferris Wheel Trig Problem. Ferris Wheel Trig Problem (part 2). Law of cosines example. Proof of the law of cosines. Law of cosines. Proof: Law of Sines.