ALGEBRA
Understanding Notation
- Converting Between Scientific and Decimal Notation
- Factorials – Evaluating Factorials! Basic Info
- Function Notation
- Interval Notation – A basic question!
- Polynomial… or NOT?! Recognizing Polynomials, the degree and some Terminology
- Radical Notation and Simplifying Radicals
- Using Interval Notation to Express Inequalities – Ex 1
- Using Interval Notation to Express Inequalities – Ex 2
- What is a Derivative? Understanding the Definition
- What is a Sequence? Basic Sequence Info
- What is a Series?
Arithmetic
- Absolute Value: Evaluating Numbers
- Arithmetic Basics: Converting Decimals into Fractions
- Arithmetic Basics: Dividing Decimals
- Arithmetic Basics: Finding the Percent of a Number
- Arithmetic Basics: Long Division of Numbers
- Arithmetic Basics: Multiplying Decimals
- Comparing Fractions using Inequalities – Ex 1
- Comparing Fractions using Inequalities – Ex 2
- Complex Numbers: Multiplying and Dividing
- Factoring a Number
- Factoring a Number
- Fractions – Adding and Subtracting
- Fractions – Multiplying and Dividing
- Fractions: Adding and Subtracting – Numerical and Variable Examples
- Least Common Multiple
Factoring and Simplifying
- Absolute Value: Evaluating Expressions – Ex 1
- Absolute Value: Evaluating Expressions – Ex 2
- Absolute Value: Evaluating Expressions – Ex 3
- Factoring by Grouping
- Factoring by Grouping – Ex 1
- Factoring By Grouping – Ex 2
- Factoring Using the Great Common Factor, GCF – Ex 1
- Factoring Using the Great Common Factor, GCF – Ex 2 – Factoring Out Binomials
- Fractions: Adding and Subtracting – Numerical and Variable Examples
- Long Division of Polynomials
- Quadratic Formula
- Quadratic Formula: How to Derive
- Radicals: Simplifying Radical Expressions Involving Variables – Ex 1
- Rationalize the Denominator
- Rationalize the Denominator – Harder Example
- Rationalizing the Denominator – Ex 1
- Rationalizing the Denominator – Ex 3
- Simplifying Numbers under Square Roots
- Synthetic Division
- Synthetic Division – Ex 2
Graphing
- Basic Graphs that Every Algebra Student Should Know!!
- Complex Numbers: Graphing, Adding, Subtracting
- Graph Transformations about the X-axis and Y-axis
- Graphing a Polar Curve – Part 1
- Graphing a Polar Curve – Part 2
- Graphing Quadratic Functions – Ex 1
- Graphing Systems of Linear Inequalities – Ex 1
- Graphing Systems of Linear Inequalities – Ex 2
- Graphing the Greatest Integer or Floor Function
- Graphing the Trigonometric Functions
- Graphing Trigonometric Functions, Graph Transformations – Part 1
- Graphing Using Graph Transformations – Ex 1
- Graphing Using Graph Transformations – Ex 2
- Horizontal And Vertical Graph Stretches and Compressions Part 1 of 3
- Horizontal And Vertical Graph Stretches and Compressions Part 2 of 3
- Horizontal and Vertical Graph Transformations
- Linear Functions: Graphing by Finding X,Y Intercept
- Local Max/Min, Inc/Dec: On a Graph
- Parametric Curves – Basic Graphing
- Piecewise Defined Functions: Graphing
- Piecewise Functions: Find the Formula from a Graph – Ex 1
- Piecewise Functions: Find the Formula from a Graph – Ex 2
- Polar Coordinates – Basic Graphing
- Solving a Linear System of Equations by Graphing
Functions
- Binomial Theorem – Ex 1
- Binomial Theorem – Ex 2
- Composition of Functions
- Compound Interest – More than Once Per Year
- Deriving the Annual Compound Interest Formula
- Descartes’ Rule of Signs
- Domain and Range From a Graph
- Domain of a Function
- Equation of a Line: Point-Slope Form
- Exponential Function From a Graph
- Function Notation
- Functions: Adding and Subtracting
- Functions: Multiplying and Dividing
- Graphing Quadratic Functions – Ex 1
- Graphing the Greatest Integer or Floor Function
- Inverse of a Function
- Long Division of Polynomials
- Long Division of Polynomials – A slightly harder example
- Pascal’s Triangle and the Binomial Coefficients
- Piecewise Defined Functions: Graphing
- Piecewise Functions: Find the Formula from a Graph – Ex 1
- Piecewise Functions: Find the Formula from a Graph – Ex 2
- Polynomial… or NOT?! Recognizing Polynomials, the degree and some Terminology
- Polynomials: Adding and Subtracting
- Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 1
- Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 2
- Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 3
- Polynomials: Multiplying – Slightly Harder Ex 1
- Polynomials: Multiplying – Slightly Harder Ex 2
- Polynomials: Multiplying – Slightly Harder Ex 3
- Polynomials: Multiplying – Slightly Harder Ex 4 – Cubing Binomials
- Polynomials: Multiplying – Slightly Harder Ex 5 – Cubing Binomials
- Polynomials: Multiplying – Slightly Harder Ex 6
- Rational Expressions: Adding and Subtracting
- Rational Functions: Shortcut to Find Horizontal Asymptotes
- Rational Functions: Slant Asymptotes
- Rational Functions: Vertical Asymptotes
- Slope of a Line
- The Distance Formula
- The Midpoint Formula
- Understanding Simple Interest and Compound Interest
- Word Problem: Distance, Rate, and Time
Solving Equations / Inequalities
- Completing the Square – Solving Quadratic Equations
- Completing the Square: Solving Quadratic Equations – Ex 2
- Exponents: Applying the Rules of Exponents – Basic Ex 3
- Fundamental True/False Questions about Inequalities!
- Linear System of Equations: Row Reducing – Part 1
- Linear System of Equations: Row Reducing – Part 2
- Linear System of Equations: Solving using Elimination by Addition
- Linear System of Equations: Solving using Substitution
- Logarithms: Properties of Logarithms – Part 1
- Logarithms: Properties of Logarithms – Part 2
- Quadratic Equations – Completing the Square
- Quadratic Equations – Factoring and Quadratic Formula
- Quadratic Equations: Using the Discriminant
- Quadratic Formula
- Quadratic Formula: How to Derive
- Rational Equations: Solving
- Rational Inequalities: Solving
- Rational Roots Test
- Solving a Linear System of Equations by Graphing
- Solving a System of Linear Equations Using Inverses
- Solving Equations Involving Rational Exponents
- Solving Equations Involving Square Roots
- Solving Linear Absolute Value Equations and Inequalities
- Solving Linear Equations
- Solving Linear Inequalities
- Solving Quadratic Inequalities
- Solving Quadratic Inequalities – A Common Mistake
- Solving Quadratic Inequalities – More Examples
- Solving Quadratic Inequalities – The Basics
- Using Interval Notation to Express Inequalities – Ex 1
- Using Interval Notation to Express Inequalities – Ex 2
TRIGONOMETRY
- A Trick to Remember Values on The Unit Circle
- A way to remember the Entire Unit Circle for Trigonometry
- A Way to Remember the Unit Circle
- Degrees and Radians
- Deriving Trigonometric Identities from Known Identities
- Graphing a Polar Curve – Part 1
- Graphing a Polar Curve – Part 2
- Graphing the Trigonometric Functions
- Graphing Trigonometric Functions, Graph Transformations – Part 1
- Integrals: Inverse Trigonometric Functions – Ex 1
- Integrals: Inverse Trigonometric Functions – Ex 2
- Inverse Trigonometric Functions: Derivatives – Ex 1
- Inverse Trigonometric Functions: Derivatives – Ex 2
- Inverse Trigonometric Functions: Derivatives – Ex 3
- Proving some Random Trigonometric Identities
- Pythagorean Theorem
- Right Triangles and Trigonometry
- Solving Trigonometric Equations
- Special Right Triangles in Geometry: 45-45-90 and 30-60-90
- The Law of Cosines
CALCULUS
Limits
- Calculating a Limit by Expanding and Simplifying
- Calculating a Limit by Factoring and Cancelling
- Calculating a Limit by Getting a Common Denominator
- Calculating a Limit by Multiplying by a Conjugate
- Calculating a Limit Involving Absolute Value
- Infinite Limits
- Infinite Limits – Basic Idea and Shortcuts for Rational Functions
- Infinite Limits with a Radical in the Expression
- sin(x)/x Limit as x Approaches Zero
- Squeeze Theorem for Limits
- Using Series to Evaluate Limits
- What is a Limit? Basic Idea of Limits
Derivatives
- Chain Rule + Product Rule + Factoring
- Chain Rule + Product Rule + Simplifying – Ex 2
- Chain Rule + Product Rule + Simplifying – Ex 1
- Chain Rule +Quotient Rule + Simplifying
- Chain Rule – Harder Ex 1
- Chain Rule – Harder Ex 2
- Chain Rule – Harder Ex 3
- Chain Rule: Basic Problems
- Concavity and Second Derivatives
- Critical Numbers – Ex 1
- Critical Numbers – Ex 2
- Derivatives – Basic Examples
- Derivatives – More Complicated Examples
- Derivatives – More Complicated Examples
- Derivatives of Logarithmic Functions – More Examples
- Derivatives of Exponential Functions
- Derivatives of Hyperbolic Functions
- Derivatives of Inverse Hyperbolic Functions
- Derivatives of Logarithmic Functions
- Derivatives of Parametric Functions
- Derivatives: Chain Rule
- Derivatives: Product Rule
- Derivatives: Quotient Rule
- Derivatives: Using the Definition to Find a Derivative
- Exponential Decay / Finding Half Life
- Generalized Chain Rule – Part 1
- Generalized Chain Rule – Part 2
- Implicit Differentiation – Basic Idea and Examples
- Implicit Differentiation – Extra Examples
- Implicit Differentiation – More Examples
- Implicit Differentiation and Second Derivatives
- Inverse Trigonometric Functions: Derivatives – Ex 1
- Inverse Trigonometric Functions: Derivatives – Ex 2
- Inverse Trigonometric Functions: Derivatives – Ex 3
- L’Hospital’s Rule – Indeterminate Differences
- L’Hospital’s Rule – Indeterminate Powers
- L’Hospital’s Rule – Indeterminate Products
- L’Hospital’s Rule – Indeterminate Quotients
- Linearization at a Point
- Local Max/Min, Inc/Dec: From a Function
- Local Max/Min, Inc/Dec: On a Graph
- Local Maximums/Minimums – Second Derivative Test
- Logarithmic Differentiation – Ex 1
- Logarithmic Differentiation – Ex 2
- Logarithmic Differentiation – Ex 3
- Mean Value Theorem
- Newton’s Method
- Optimization Problem #1
- Optimization Problem #2
- Optimization Problem #3 – Making a Rain Gutter!
- Parametric Curves: Finding Second Derivatives
- Related Rates – A Point on a Graph
- Related Rates Involving Baseball!
- Related Rates Involving Trigonometry
- Related Rates Problem Using Implicit Differentiation
- Related Rates Using Cones
- Sketching the Curve Summary – Example 2 – Part 2 of 4
- Sketching the Curve Summary – Example 2 – Part 3 of 4
- Sketching the Curve Summary – Example 2 – Part 4 of 4
- Sketching the Curve Summary – Example 2, Part 1 of 4
- Sketching the Curve Using Calculus – Part 1 of 2
- Sketching the Curve Using Calculus – Part 2 of 2
- Sketching the Derivative of a Function
- Tangent Line: Finding the Equation
- Tangent Plane Approximations
- Vector Fields – Sketching
- What is a Derivative? Understanding the Definition
Antiderivatives/Integrals
- Approximating a Definite Integral Using Rectangles
- Approximating Integrals: Simpsons Rule
- Approximating Integrals: Simpsons Rule Error Bound
- Approximating Integrals: Trapezoid Rule
- Arc Length Using Parametric Curves – Ex 1
- Arc Length Using Parametric Curves – Ex 2
- Area Between Curves – Integrating with Respect to y
- Area Between Curves – Integrating with Respect to y – Part 2
- Areas Between Curves
- Centroids / Centers of Mass – Part 1 of 2
- Centroids / Centers of Mass – Part 2 of 2
- Definite Integral – Understanding the Definition
- Fundamental Theorem of Calculus Part 1
- Improper Integral – Basic Idea and Example
- Improper Integral – Infinity in Upper and Lower Limits
- Improper Integral – More Complicated Example
- Improper Integral with Infinite Discontinuity at Endpoint
- Improper Integral with Infinite Discontinuity in the Middle
- Integral Test for Series
- Integrals: Exponential Functions – Ex 1 and 2
- Integrals: Exponential Functions – Ex 3 and 4
- Integrals: Hyberbolic Functions
- Integrals: Inverse Trigonometric Functions – Ex 1
- Integrals: Inverse Trigonometric Functions – Ex 2
- Integration by Partial Fractions and a Rationalizing Substitution
- Integration by Partial Fractions: A Complete Problem
- Integration by Partial Fractions: Determining Coefficients
- Integration by Partial Fractions: Long Division
- Integration by Parts – A Loopy Example!
- Integration by Parts – Definite Integral
- Integration by Parts – Ex 1
- Integration By Parts – Using IBP’s Twice
- Integration by U-Substitution – Indefinite Integral, Another 2 Examples
- Integration by U-Substitution, Definite Integral
- Integration by U-substitution, More Complicated Examples
- Integration by U-Substitution: Antiderivatives
- Parametric Curves – Calculating Area
- Polar Coordinates: Finding Areas
- Probability Density Functions: Continuous Random Variables
- Riemann Sums: Calculating a Definite Integral – Part 1
- Riemann Sums: Calculating a Definite Integral – Part 2
- Surface Area – Part 1
- Trigonometric Integrals – Part 1 of 6
- Trigonometric Integrals – Part 2 of 6
- Trigonometric Integrals – Part 3 of 6
- Trigonometric Integrals – Part 4 of 6
- Trigonometric Integrals – Part 5 of 6
- Trigonometric Integrals – Part 6 of 6
- Trigonometric Substitution – Ex 2
- Trigonometric Substitution – Ex 3 / Part 2
- Trigonometric Substitution – Ex 3/ Part 1
- Volumes of Revolution: Cylindrical Shells
- Volumes of Revolution: Cylindrical Shells – Longer Version
- Volumes of Revolution: Disk/Washers – Ex 1
- Volumes of Revolution: Disk/Washers – Ex 2
- Volumes of Revolution: Disk/Washers – Ex 3
- Volumes of Revolution: Disk/Washers – Longer Version
- Volumes of Revolution: Disk/Washers about Vertical Lines
- Work and Hooke’s Law – Ex 1
- Work and Hooke’s Law – Ex 2
- Work Required to Drain a Tank
- Work: The Cable/Rope Problem – Part 2
- Work: The Cable/Rope Problem Part 1
Sequences and Series
- Absolute Convergence, Conditional Convergence and Divergence
- Alternating Series
- Alternating Series Estimation Theorem
- Alternating Series: More Examples
- Arithmetic Sequences: A Formula for the ‘ n – th ‘ Term
- Arithmetic Sequences: A Quick Intro
- Binomial Series – Ex 1
- Binomial Series – Ex 2
- Factorials – Evaluating Factorials! Basic Info
- Finding the Sum of a Finite Arithmetic Series
- Geometric Sequences: A Formula for the’ n – th ‘ Term.
- Geometric Sequences: A Quick Intro
- Geometric Series and the Test for Divergence
- Geometric Series and the Test for Divergence – Part 2
- Geometric Series: Expressing a Decimal as a Rational Number
- Integral Test for Series
- Limit Comparison Test and Direct Comparison Test – 1
- Limit Comparison Test and Direct Comparison Test – 2
- Maclaurin/Taylor Series: Approximate a Definite Integral to a Desired Accuracy
- Power Series Representation of a Function
- Power Series Solutions of Differential Equations
- Power Series: Differentiating and Integrating
- Power Series: Finding the Interval of Convergence
- Power Series: Multiplying and Dividing
- Radius of Convergence for a Power Series
- Ratio Test for Series – Ex 1
- Ratio Test for Series – Ex 2
- Remainder Estimate for the Integral Test
- Root Test for Series
- Sequences – Examples Showing Convergence or Divergence
- Showing a Series Diverges using Partial Sums
- Strategy for Testing Series – Practice Problems
- Taylor and Maclaurin Series – Ex 1
- Taylor and Maclaurin Series – Ex 2
- Taylor’s Inequality
- Telescoping Series Example
- Using Series to Evaluate Limits
- What is a Sequence? Basic Sequence Info
- What is a Series?
Multivariable Calculus
- Arc Length of a Vector Function
- Conic Sections: Graphing Ellipses – Part 1
- Conic Sections: Graphing Ellipses – Part 2
- Conservative Vector Fields – The Definition and a Few Remarks
- Conservative Vector Fields – Showing a Vector Field on R_2 is Conservative
- Cross Product
- Curl and Showing a Vector Field is Conservative on R_3 – Ex 1
- Curl and Showing a Vector Field is Conservative on R_3 – Ex 2
- Double Integral Using Polar Coordinates – Part 1 of 3
- Double Integral Using Polar Coordinates – Part 2 of 3
- Double Integral Using Polar Coordinates – Part 3 of 3
- Double Integrals – Basic Idea and Examples
- Double Integrals – Changing Order of Integration
- Double Integrals over General Regions
- Double Integrals: Changing Order of Integration – Full Example
- Evaluating a Line Integral Along a Straight Line Segment
- Finding and Sketching the Domain
- Finding the Directional Derivative – Ex 1
- Finding the Domain of a Vector Function
- Finding the Point Where a Line Intersects a Plane
- Finding the Scalar Equation of a Plane
- Finding the Vector Equation of a Line
- Fundamental Theorem for Line Integrals
- Generalized Chain Rule – Part 1
- Generalized Chain Rule – Part 2
- Gradient Vector – Notation and Definition
- Green’s Theorem
- Implicit Differentiation – Ex 1
- Implicit Differentiation – Ex 2
- Implicit Function Theorem
- Jacobian
- LaGrange Multipliers
- Lagrange Multipliers: Two Constraints – Part 1
- Lagrange Multipliers: Two Constraints – Part 2
- Laplace Transform
- Line Integrals – Evaluating a Line Integral
- Local Maximum and Minimum Values/ Function of Two Variables
- Local Maximum and Minimum Values/ Function of Two Variables part 2
- Partial Derivatives
- Partial Derivatives: Higher Order
- Polar Coordinates – The Basics
- Potential for a Conservative Vector Field – Ex 1
- Potential of a Conservative Vector Field – Ex 2
- Showing a Limit Does NOT Exist
- Surface Integral – Basic Example
- Tangent Plane Approximations
- Torque: An application of the cross product
- Triple Integral in Spherical Coordinates
- Triple Integrals
- Vector Basics: Algebraic Representations – Part 1
- Vector Basics: Algebraic Representations – Part 2
- Vector Basics: Drawing Vectors/Vector Addition
- Vectors: Finding Magnitude or Length
- Vectors: The Dot Product
MISC
Probability and Statistics
- Binomial Distribution: Binomial Probability Function
- Binomial Theorem – Ex 1
- Binomial Theorem – Ex 2
- Box and Whisker Plot
- Calculating Probability – ” And ” Statements, independent events
- Calculating Probability: “And” Statements, Dependent Events.
- Calculating Probability: “At Least One” statements
- Calculating the Probability of Simple Events
- Calculating the Probability of Winning the Texas Lottery
- Expected Value
- Laplace Transform
- Multiplication Principle: Counting Techniques
- Pascal’s Triangle and the Binomial Coefficients
- Poisson Distribution
- Probability Density Functions: Continuous Random Variables
- Statistics: Calculating Variance
Discrete Math
- Binomial Theorem – Ex 1
- Binomial Theorem – Ex 2
- Combinations – Counting Using Combinations
- Greatest Common Factor, GCF
- Pascal’s Triangle and the Binomial Coefficients
- Permutations – Counting Using Permutations
Differential Equations
- Exact Differential Equations
- First Order Linear Differential Equations
- Homogeneous Second Order Linear DE – Complex Roots Example
- Homogeneous Second Order Linear Differential Equations
- Method of Undetermined Coefficients/2nd Order Linear DE – Part 1
- Method of Undetermined Coefficients/2nd Order Linear DE – Part 2
- Power Series Solutions of Differential Equations
- Separable Differential Equations: Mixing Problems
- Solving Separable First Order Differential Equations – Ex 1
Linear Algebra
- Cross Product
- Finding the Determinant of a 3 x 3 matrix
- Linear Programming
- Linear System of Equations: Row Reducing – Part 1
- Linear System of Equations: Row Reducing – Part 2
- Markov Chains – Intro Part 1
- Markov Chains – Intro Part 2
- Matrices: Basic Matrix Operations (add, subtract, multiply by constant)
- Matrices: Multiplying a Matrix by another Matrix
- Solving a System of Linear Equations Using Inverses
- The Law of Cosines
- Torque: An application of the cross product
- Vector Basics: Algebraic Representations – Part 1
- Vector Basics: Algebraic Representations – Part 2
- Vector Basics: Drawing Vectors/Vector Addition
- Vectors: Finding Magnitude or Length
- Vectors: The Dot Product
SAT
- A complete SAT Math practice test – Part 1
- A complete SAT Math practice test – Part 2
- SAT Math Question #1
- SAT Math Question #2
- SAT Math Question #3
- SAT Math Question #4
- SAT Math Question #5
- SAT Math Question #6
- SAT Math Question #7
- SAT Math Question #8
ACT
GRE
AP AB Calculus Test
- AB Free Response Question 1a
- AB Free Response Question 1b
- AB Free Response Question 1c
- AB Sample Questions 01 & 02
- AB Sample Questions 03 & 04
- AB Sample Questions 05 & 06
- AB Sample Questions 07 & 08
- AB Sample Questions 09 & 10
- AB Sample Questions 11 & 12
- AB Sample Questions 13 & 14
- AB Sample Questions 15 & 16
- AB Sample Questions 17 & 18
- AB Sample Questions 19 & 20
- AB Sample Questions 21 & 22
- AB Sample Questions 23 & 24
- AB Sample Questions 25 & 26
- AB Sample Questions 27 & 28
AP BC Calculus Test
- BC Sample Questions 01 & 02
- BC Sample Questions 03 & 04
- BC Sample Questions 05 & 06
- BC Sample Questions 07 & 08
- BC Sample Questions 09 & 10
- BC Sample Questions 11 & 12
- BC Sample Questions 13 & 14
- BC Sample Questions 15 & 16
