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Khan Academy

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Omele isiZulu: Dumazile Chauke

Probability and combinatorics

LeBron Asks: What are the chances of making 10 free throws in a row?
Basic Probability
Example: 9 card hands
LeBron Asks: What are the chances of three free throws versus one three pointer?
Example rolling even three times
Combinations
Getting At Least One Heads
Frequency probability and unfair coins
Permutations
Compound Probability of Independent Events
Example probability of rolling double
Conditional Probability and Combinations
Example: Ways to pick officers
Getting atleast one heads
Exactly Three Heads in Five Flips
Example: Ways to arrange colors
Compound probability of independ
Probability using Combinations
Example: Is an event independent or dependent?
Monty Hall Problem
Probability using Combinations 2
Example: Picking a yellow marble
Example: Bag of unfair coins
Getting Exactly Two Heads (Combinatorics)
Example: Picking a non-blue marble
Example: Dependent probability
Addition Rule for Probability
Example: Marbles from a bag
Introduction to dependent probability
Probability with Playing Cards and Venn Diagrams

Probability and statistics

Variance of a population
Statistics: Alternate Variance Formulas
Example: Probability of rolling doubles
Statistics: The Average
Simulation providing evidence that (n-1) gives us unbiased estimate
Constructing a box-and-whisker plot
Statistics: Sample Variance
Sample variance
Term Life Insurance and Death Probability
Probability (part 8)
Sample standard deviation and bias
Probability Density Functions
Probability (part 7)
Range, Variance and standard deviation as measures of disperation
Law of Large Numbers
Probability (part 6)
Population standard deviation
Exploring Mean and Median Module
Probability (part 5)
Exploring standard deviation 1 module
Expected Value: E(X)
Probability (part 4)
Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance
Expected Value of Binomial Distribution
Probability (part 3)
Reading Box-and-Whisker Plots
Example finding mean, median and mode
Probability (part 2)
Poisson Process 2
Discrete and continuous random variables
Probability (part 1)
Poisson Process 1
Binomial Distribution 4
Introduction to Random Variables
Frequency Stability
Binomial Distribution 3
Intersection and union of sets
Frequency Probability and Unfair Coins
Binomial Distribution 2
Bringing the set operations together
Example: Range and mid-range
Binomial Distribution 1
Statistics: Variance of a Population
Example getting two questions right on an exam
Simulation showing bias in sample variance
Example: Rolling even three times

Special properties and parts of triangles

Area circumradius formual proof
Median centroid right triangle example
Finding central angle measure given arch length
2003 AIME 2 problem 7
Circumcenter of a right triangle
Triangle medians and centriods 2D proof
Angle bisectors theorem examples
Constructing a perpendicular line using campass and straight edge
Area of inscribed equilateral triangle some basic trig used
Point line distance and angle bisectors
Three points defining a circle
Rhombus Diagonals
Angle bisectors theorem proof
Exploring medial triangles
Perpendicular radius bisects chord
Incenter and incircles of a triangle
Euler's line proof
Whether a special quadrilateral can exist
Proof Triangle altitudes are concurrent
Review of triangle properties
Proof diagonals of a parallelogram bisect each other
Inradius perimeter and area
Area of a sector given a central angle
Length of an arch that subtends a central triangle
Circumcenter of a triangle
Proving that the centroid is 2 3rd along the median
Right triangles inscribed in circle proof
Euler line
Proof opposite sides of parallelogram congruent
Language and notation of the circle
Common orthocenter and centroid
Triangle Medians and centriods
Proof opposite angles of parallelogram congruent
Constructing a perpendicular bisect using campass straight edge
Proof Rhombus diagonal are perpendicular bisectors
Median devide into smaller triangle of equal area
Constructing an angle bisect using a campass and straight edge
Inscribed and central angles
Proof Rhombus area half product of diagonal length

Area and Perimeter

Area and perimeter
Interesting Perimeter and Area Problems
Perimeter of a polygon
Area of an Equilateral Triangle
Part 1 proof of Heron's Formula
Perimeter and area of a non polygon
Area of Koch Snowflake (part 1) - Advanced
Part 2 proof of Heron's formula
Similar triangles
Koch Snowflake Fractal
Parts of a circle
Similar triangles example problem
Perimeter and Area Basics
Triangle Area Proofs
How we measure volume
Perimeter of a Polygon
Triangle inqequality theorem
Quadrilateral Overview
Perimeter of a shape
Area of a Parallelogram
Measuring volume with unit cubes
Area of a circle
Cylinder volume and surface area
Volume of a rectangular prism or box examples
Area of Diagonal Generated Triangles of Rectangle are Equal
Finding Area Using Similarity and Congruence
Volume of a sphere
Area of shaded region from equilateral triangles
Area of a trapezoid
Solid Geometry Volume
Challenging Perimeter Problem
Area of a kite
Volume word problem example
Circles: Radius, Diameter and Circumference
Measuring volume as area times length
Heron's Formula
Quadrilateral Properties

Indefinite and definite integrals

Antiderivative of xcosx using integration by parts
Definite Integrals (area under a curve) (part III)
Trig substitution with tangent
Basic trig and exponential antiderivatives
Definite integrals (part II)
U-substitution and back substitution
Deriving integration by parts formula
Definite integrals (part 4)
U-substitution example 2
Generalizing a left Riemann sum with equally spaced rectangles
Definite integrals (part 5)
U-substitution example 3
Indefinite integrals of x raised to a power
Evaluating simple definite integral
U-substitution with definite integral
Integral of ln x
Introduction to definite integrals
U-substitution with ln(x)
Integration by parts twice for antiderivative of (x^2)(e^x)
Intuition for Second Fundamental Theorem of Calculus
U-substitution
Integration by parts of (e^x)(cos x)
(2^ln x)/x Antiderivative Example
Applying the fundamental theorem of calculus
Rectangular and trapezoidal Riemann approximations
Another substitution with xsin (theta)
Both bounds being a function of x
Riemann sums and integrals
Another u-substitution example
Connecting the first and second fundamental theorems of calculus
Simple Riemann approximation using rectangles
Doing u-substitution twice (second time with w)
Divergent improper integral
Trapezoidal approximation of area under curve
Integrals: Trig Substitution 1
Fundamental theorem of calculus
Area between curves with multiple boundaries
Integrals: Trig Substitution 2
Improper integral with two infinite bounds
Area between curves
Integrals: Trig Substitution 3 (long problem)
Introduction to improper integrals
Challenging definite integration
Introduction to trig substitution
Proof of Fundamental Theorem of Calculus
Definite integral with substitution
Trig and U substitution together (part 1)
Swapping the bounds for definite integral
Definite integrals and negative area
Trig and U substitution together (part 2)

Taking derivatives

Derivative Intuition Module
Power Rule
Product rule for more than two functions
Graphs of functions and their derivatives
Is the power rule reasonable
Quotient rule from product rule
Identifying a function's derivative
Derivative properties and polynomial derivatives
Quotient rule for derivative of tan x
Intuitively drawing the derivative of a function
Proof: d/dx(x^n)
Using the product rule and the chain rule
Visualizing derivatives exercise
Proof: d/dx(sqrt(x))
Product Rule
Newton Leibniz and Usain Bolt
Power rule introduction
Quotient rule and common derivatives
Derivative as slope of a tangent line
Derivatives of sin x, cos x, tan x, e^x and ln x
Equation of a tangent line
Tangent slopes as limiting value of secant slope example 1
Chain rule introduction
Showing explicit and implicit differentiation give same result
Tangent slope as limiting value of secant slope example 2
Chain rule definition and example
Proofs of derivatives of ln(x) and e^x
Tangent slope as limiting value of secant slope example 3
Chain rule with triple composition
Proof: d/dx(ln x) 1/x
Calculating slope of tangent line using derivative definition
Chain rule for derivative of 2^x
Proof: d/dx(e^x) e^x
The derivative of f(x)x^2 for any x
Derivative of log with arbitrary base
Implicit differentiation
Formal and alternate forms of the derivative
Extreme Derivative Word Problem (advanced)
Implicit derivative of (x-y)^2 x + y + 1
Formal and alternate form of the derivative for Inx
The Chain Rule
Implicit derivative of y cos(5x - 3y)
Formal and alternate forms of the derivatives example 1
Chain Rule Examples
Implicit derivative of e^(xy^2) x - y
Interpreting slope of a curve exercise
Even More Chain Rule
Finding slope of tangent line with implicit differentiation
Calculus: Derivatives 1
More examples using multiple rules
Building the idea of espilon delta definition
Calculus: Derivatives 2
Applying the product rule for derivatives

Geometry

Triangle Angle Example 3
Angles (part 2)
Example involving an isosceles triangle and parallel liness
Triangle Angle Example 2
Angles formed between transversals and parallel lines
Another Isosceles Example Problem
Triangle Angle Example 1
Angles of parallel lines 2
Equilateral and Isosceles Example Problems
The Angle Game
Challenging Triangle Angle Problem
Equilateral Triangle Sides and Angles Congruent
Angle basics
Example using algebra to find measure of complementary angles
Congruent legs and base angles of Isosceles Triangles
Angles Formed by Parallel Lines and Transversals
Complementary and supplementary angles
Congruent Triangle Example 2
CA Geometry: Deducing Angle Measures
Finding More Angles
Congruent Triangle Proof Example
Figuring out angles between transversal and parellel lines
Introduction to angles (old)
Perpendicular Radius Bisects Chord
Identifying Parallel and Perpendicular Lines
Proof corresponding angle equivalence implies parallel lines
More on why SSA is not a postulate
Introduction to vertical angles
Sum of the exterior angles of convex polygon
Finding Congruent Triangles
Measuring angles in degrees
Proof - Sum of Measures of Angles in a Triangle are 180
Two column proof showing segments are perpendicular
Proof-Vertical Angles are Equal
Sum of interior angle of a polygon
Other Triangle Congruence Postulates
Using a protractor
Problem involving angle derived from square and circle
SSS to Show a Radius is Perpendicular to a Chord that it Bisects
Using algebra to find measure of angles formed
Wrong statements in proofs example 1
Congruent Triangles and SSS
Vertical adjacent and Limearly paired angels
Fill-in-the-blank triangle proofs example 2
Example using algebra to find measure of Supplimentary angles
Acute, right, obtuse angles
Basic Triangle Proofs Module Example 2
Example using algebra to find measure of Complemetary angles
Angle Game (part 2)
Basic Triangle Proofs Module Example
Angles (part 3)
Figuring out all the angles for congruent triangles example

Derivative applications

Testing critical points for local extrema
Using algebra to find measures of supplementary angles
Rate of change of balloon height
Proof of special case of L'Hopital's Rule
Expression for combined area of triangle and square
Rate of change of distance between approaching cars
Minima, maxima and critical points
Falling ladder related rates
Rates of change between radius and area of circle
Introduction to L'Hôpital's Rule
Minimizing combined area
Related rates of water pouring into cone
Inflection Points
Minimizing sum of squares
Speed of shadow of diving bird
Identifying minima and maxima for x^3 - 12x - 5
Minimizing the cost of a storage container
Antiderivative of hairier expression
Graphing using derivatives
Optimizing box volume analytically
Antiderivatives and indefinite integrals
Concavity, concave upwards and concave downwards intervals
Optimizing box volume graphically
Another example graphing with derivatives
Optimizing profit at a shoe factory

Minima, maxima, inflection points and critical points

Sequences and induction

Sequences and induction

Proof by Induction

Quadratics

Graphs of Quadratic Functions
Example 2: Factoring by grouping
Solving Quadratic Equations by Completing the Square
Factoring Quadratic Expressions
Example 3: Factoring by grouping
Example: Solving simple quadratic
Examples: Factoring simple quadratics
Example 4: Factoring by grouping
Solving Quadratic Equations by Square Roots
Example 1: Factoring quadratic expressions
Example 6: Factoring by grouping
Quadratic Inequalities (Visual Explanation)
Example 2: Solving a quadratic equation by factoring
Example 5: Factoring by grouping
Quadratic Formula (proof)
Example 3: Solving a quadratic equation by factoring
Parabola Focus and Directrix 1
How to Use the Quadratic Formula
Example 4: Solving a quadratic equation by factoring
Focus and Directrix of a Parabola 2
Quadratic Inequalities
Example: Graphing a quadratic
Focus and Directrix of a Parabola 2
Example: Quadratics in standard form
Example 1: Factoring trinomials with a common factor
Applying Quadratic Functions 2
Example: Complex roots for a quadratic
Example 1: Factoring difference of squares
Applying Quadratic Functions 1
Example 5: Using the quadratic formula
Factoring Special Products
Examples: Graphing and interpreting quadratics
Example 3: Using the quadratic formula
Example 2: Factoring difference of squares
Example: Parabola vertex and axis of symmetry
Example 2: Using the quadratic formula
Example: Factoring perfect square trinomials
Example: Roots and vertex of a parabola
Example 1: Using the quadratic formula
Example: Factoring a fourth degree expression
Example 3: Completing the square
Discriminant of Quadratic Equations
Example: Basic grouping
Example 2: Completing the square
Discriminant for Types of Solutions for a Quadratic
Factor by Grouping and Factoring Completely
Example 1: Completing the square
Example 4: Applying the quadratic formula
Example: Factoring special products
Example: Completing perfect square trinomials
Example 5: Completing the square
Example 1: Factoring by grouping
Completing the square (old school)
Example 4: Completing the square

Negative numbers and absolute value

Adding decimals of different signs word problem

Fractions

Adding fractions with different signs
Adding subtracting mixed numbers 0.5 (ex 1)
Equivalent Fractions Example
Adding fractions examples
Adding subtracting mixed numbers 0.5 (ex 2)
Comparing Fractions
Dividing fractions
Adding subtracting mixed numbers 1 (ex 1)
Fractions in lowest terms
Proper and Improper Fractions
Adding subtracting mixed numbers 1 (ex 2)
Finding Common Denominators
Comparing improper fractions and mixed numbers
Multiplying Fractions and Mixed Numbers
Ordering Fractions
Mixed numbers and improper fractions
Multiplying Mixed Numbers
Comparing Fractions 2
Converting Mixed Numbers to Improper Fractions
Reciprocal of a Mixed Number
Adding Fractions with Like Denominators
Changing an Improper Fraction to a Mixed Number
Dividing Mixed Numbers
Subtracting Fractions
Changing a Mixed Number to an Improper Fraction
Dividing Mixed Numbers and Fractions
Adding and subtracting fractions
Ordering improper fractions and mixed numbers
Number Sets
Adding Fractions with Unlike Denominators
Adding Mixed Numbers
Number Sets 1
Multiplying Fractions
Adding Mixed Numbers Word Problem
Number Sets 2
Multiplying Fractions Word Problem
Subtracting Mixed Numbers
Number Sets 3
Dividing Fractions Word Problem
Adding Mixed Numbers with Unlike Denominators
Identifying Fraction Parts
Dividing Fractions Example
Subtracting Mixed Numbers 2
Numerator and Denominator of a Fraction
Subtracting Mixed Numbers Word Problem
Equivalent Fractions

Graphing points, equations and inequalities

Plot Ordered Pairs
Graphing Inequalities 2
Equation of a line 3
Quadrants of Coordinates Plane
Graphing Linear Inequalities in Two Variables Example 2
Linear Equations in Point Slope Form
Ordered pair solutions of equations
Solving and graphing linear inequalities in two variables 1
Linear Equations in Standard Form
Ordered Pair Solutions of Equations 2
Graphing Inequalities
Fitting a Line to Data
Plotting (x,y) relationships
Slope of a line
Point-slope and standard form
Graphs of Linear Equations
Slope of a Line 2
Midpoint Formula
Application problem with graph
Slope and Rate of Change
Distance Formula
Interpreting Linear Graphs
Graphical Slope of a Line
Perpendicular Line Slope
Exploring linear relationships
Slope of a Line 3
Equations of Parallel and Perpendicular Lines
Recognizing Linear Functions
Slope Example
Parallel Line Equation
Graphing lines 1
Hairier Slope of Line
Parallel Lines
X and Y intercepts
Slope and Y-intercept Intuition
Parallel Lines 2
X and Y intercepts 2
Algebra: Slope
Parallel Lines 3
Graphing using X and Y intercepts
Algebra: Slope 2
Perpendicular Lines
Graphing Using Intercepts
Algebra: Slope 3
Perpendicular lines 2
Linear Equations in Slope Intercept Form
Graphs Using Slope-Intercept Form
Algebra: Slope and Y-intercept intuition
Graphing a line in slope intercept form
Word Problem Solving 4
Algebra: Equation of a line
CA Algebra I: Graphing Inequalities
Equation of a line 1
CA Algebra I: Slope and Y-intercept
Graphing Inequalities 1
Equation of a Line 2
Graphing linear inequalities in two variables 3
Equation of a Line hairier example

Systems of equations and inequalities

Trolls, tolls and systems of euqation
Old video on systems of equations
Systems of Three Variables 2
Solving the troll riddle visually
Testing a solution for a system of equations
Solution to three variable systems
King's Cupcakes: Solving Systems by Elimination
Graphing systems of equations
Solutions to Three Variable System 2
Solving Systems Graphically
Graphical systems application problem
Three Equation Application Problem
How many bags of potato chips do people eat?
Example 2: Graphically Solving Systems
Non-Linear Systems of Equations 1
Simple Elimination Practice
Example 3: Graphically Solving Systems
Non-Linear Systems of Equations 2
Systems with elimination practice
CA Algebra I: Systems of Inequalities
Non-Linear Systems of Equations 3
Talking bird solves with substitution
Testing Solutions for a System of Inequalities
Consistent and Inconsistent Systems
Solving linear systems by graphing
Graphical system inequalities
Practice thinking about number of solutions to systems
Solving linear systems by substitution
Graphing systems of Inequalities
Inconsistent systems of equations
Solving systems of equation by elimination
Graphing systems of inequalities 2
Infinite solutions to systems
Solving systems of equations by multiplication
System of Inequalities Application
Independent and Dependent Systems
Special Types of Linear Systems
Systems of Three Variables

Ratios, proportions, units and rates

Conversion between metric units
Speed Translation
Comparing Celsius and Farenheit temperature scales
Converting pounds to ounces
Simplifying rates and ratios
Converting Fahrenheit to Celsius
Converting units of length
Understanding Proportions
Converting Gallons to quarts pints and cups
Converting within the metric system
Unit conversion
Converting Yards into Inches
Finding Unit Prices
Usain Bolt's Average Speed
Application problems involving units of weight
Finding Unit Rates
Writing proportions
Unit Conversion with Fractions
Introduction to ratios
Writing Proportions
Performing arithmetic calculations on units of volume
Ratios and Proportions
U S customary and metric units
Perimeter and Unit Conversion
Ratios as Fractions in Simplest Form
Applying the metric system
Solving application problems involving units of volume

Linear equations

What is a variable
Example 1: Variables on both sides
Taking percentages
Why aren't we using the multiplication sign
Example 2: Variables on both sides
Challenge example: Sum of integers
Example: evaluating an expression
Equations with special cases
Finding the 100th Term in a Sequence
Example: evaluate a formula using substitution
Interpreting Inequalities
Averages
Evaluating exponential expressions 2
Absolute Value Inequalities
Algebra: Linear Equations 4
Expressions with two variables
Absolute Value Inequalities Example 1
Patterns in Sequences 2
Example: Evaluating expressions with 2 variables
Absolute value inequalities example 3
Algebra: Linear Equations 3
Algebraic Expression Least Common Multiple
Ex 1 Age word problem
Patterns in Sequences 1
Examples of evaluating variable expressions
Absolute Value Equations
Algebra: Linear Equations 2
Variables Expressions and Equations
Ex 3 Age word problem
Early Train Word Problem
Simple Equations
Absolute Value Equation Example 2
Algebra: Linear Equations 1
Solving One-Step Equations
Ex 2 Age word problem
Basic Rate Problem
Solving One-Step Equations 2
Absolute Value Equations 1
Absolute value inequalities Example 3
One step equations
Basic linear equation word problem
Absolute inequalities
Two-Step Equations
Solving for a variable
Absolute Value Equations Example 1
Solving Ax+B C
Solving for a Variable 2
Evaluating expressions with unknown variables 2
Example: Two-step equation with x/4 term
Another Percent Word Problem
Evaluating expressions where individual variable values are unknown
Example: Dimensions of a garden
Rearrange formulas to isolate specific variables
Ex 3: Distributive property to simplify
Combining like terms
Another percent example
Ex 2: Distributive property to simplify
Combining Like Terms 1
Example: Solving for a variable
Ex 1: Distributive property to simplify
Combining like terms and the distributive property
Bunch of Examples
Solving equations with the distributive property 2
Combining Like Terms 3
More Percent Problems
Solving Equations with the Distributive Property
Combining Like Terms 2
2003 AIME II Problem 1
Ex 2 Multi-step equation
Variables on both sides
Integer sums
Ex 1 Multi step equation

Polynomials

Terms coefficients and exponents in a polynomial
Subtracting polynomials with multiple variables
Multiplying Binomials
Polynomials1
Multiplying Polynomials
Multiplication of Polynomials
Evaluating a polynomial at a given value
Multiplying Monomials by Polynomials
Multiplying Binomials with Radicals
Simply a polynomial
Special Products of Polynomials 2
Factoring and the Distributive Property 3
Adding Polynomials
Special Products of Polynomials 1
Factoring and the Distributive Property 2
Example: Adding polynomials with multiple variables
Factor polynomials using the GCF
Factoring and the Distributive Property
Addition and Subtraction of Polynomials
Special Polynomials Products 1
Monomial Greatest Common Factor
Adding and Subtracting Polynomials 1
Special Products of Binomials
Multiplying and Dividing Monomials 3
Adding and Subtracting Polynomials 2
Square a Binomial
Multiplying and Dividing Monomials 1
Adding and Subtracting Polynomials 3
Multiplying Polynomials 2
Multiplying Monomials
Subtracting Polynomials
Multiplying Polynomials 1
Dividing Monomials

Decimals and percent

Describing the meaning of percent
Significant Figures
Multiplying a Decimal by a Power of 10
Describing the meaning of percent 2
Addition and Subtraction with Significant Figures
Deviding a decimal by a power of 10
Representing a number as a decimal,percent and fraction
Multiplying and Dividing with Significant Figures
Dividing decimals
Representing-a-number-as-a-decimal--percent--and-fraction-2
Points on a number line
Deviding decimal
Ordering-numeric-expressions_DUP_3
Decimal Place Value
Decimals and Fractions
Growing by a Percentage
Decimal Place Value 2
Dividing Decimals 2.1
converting-decimals-to-percents--ex-1
Comparing Decimals
Converting fractions to decimals
converting-decimals-to-percents--ex-2
Decimals on a number line
Converting fractions to decimals (ex1)
identifying-percent-amount-and-base
Points on a number line
Converting fractions to decimals (ex2)
Solving Percent Problems
Adding Decimals
Converting Fractions to Decimals Example
Solving Percent Problems 2
Subtracting Decimals
Converting decimals to fractions 1 (ex 1)
Solving Percent Problems 3
Subtracting Decimals Word Problem
Converting decimals to fractions 1 (ex 2)
Rounding Decimals
Subtracting decimals (old)
Converting decimals to fractions 1 (ex 3)
Estimation with Decimals
Multiplying Decimals
Converting decimals to fractions 2 (ex 1)
More on significant figures
Multiplying Decimals 3