Math Doctor Bob

Basic College Algebra

BCA1. Integer Exponent Rules

BCA1.1. Example: Like Bases

BCA1.2. Example: Mixed Bases

BCA2.0. Review: Manipulating Equalities

BCA2.1. Linear Equations in Two Variables

BCA2.2. Slope of a Line

BCA2.3. Slope-Intercept Equation of a Line

BCA2.4. Point-Slope Equation of a Line

BCA3.1. SLE 1 - The Graphing Method

BCA3.2. SLE 2 - Substitution Method

BCA3.3. SLE 3 - Addition Method

BCA4.1. Polynomials: Addition

BCA4.1.1. Polynomial Example: Subtraction with Parentheses

BCA4.2. Polynomials: Multiplication

BCA4.3. Polynomials: Division

BCA4.4. Factoring: Greatest Common Factor and Grouping

BCA4.5. Factoring: Quadratics 1

BCA4.5. Factoring: Quadratics 2: Difference of Two Squares

BCA4.5.X. Factoring Example: DO2S x 2

BCA4.6. Solving Quadratic Equations Using Zero Product Rule

BCA4.6.X Example 1: Solving Quadratics Equations Using ZPR

BCA4.6.X. Example 2: Solving Quadratic Equations

BCA5.1. Simplifying Rational Expressions

BCA5.2. Rational Expressions: Multiplication and Division

BCA5.3. Rational Expressions: Addition and Subtraction

BCA5.4. Solving Rational Equations

BCA5.4.X. Example: Solving a Rational Equation

BCA6.1. Definition of Square Root

BCA6.2. Simplifying Radical Expressions

Basic Algebra II

The Bellhop Problem: 27 + 2 = 30

Evaluating Logarithms 1

Evaluating Logarithms 2

Evaluating Logarithms 3

Logarithmic Equations 1

Logarithmic Equations 2

Logarithmic Equations 3

Domain of log_6(x^2 - 7x + 6)

Example of Compound Interest

Exponential Growth

Inverse Functions with Logarithm

Precalculus

Example of Arithmetic Sequence

Example of Arithmetic Sum

Geometric Proof of Integer Sum Formula

Example of Geometric Sum

Example of Proof By Induction 1: Sum 3n+2 = n(3n+7)/2

Example of Proof by Induction 2: 3 divides 5^n-2^n

Example of Proof by Induction 3: n! <= n^n

Example of Proof by Induction 4: Increasing Sequence (Hard)

Example of Binomial Theorem

Example of a Piecewise-Defined Function

Domain of sqrt(x+1) - 1/sqrt(9-x^2)

Graph of y = -2sqrt(x+4) - 3

Example of Projectile Motion

Example of Composition of Functions

Inverse Function for f(x) = (x-2)/(x+2)

Using Synthetic Division to Evaluate a Polynomial

Fast Factorization of Polynomial

Multiplying Complex Numbers

Complex Conjugate Roots of a Real Polynomial

Factoring 3x^4-2x^3+3x-2 Over The Complex Numbers

Sketch of Rational Function

Domain and Range of 1/(x^2-2x-8)

Partial Fraction Expansion of (x^4+x^3+1)/(x(x^2+1)^2)

Domain of ln((x+1)/(x-1)) +ln(x-1)-ln(x+1)

Evaluation of 3ln(2e^2) + 2ln(3/e) - ln(72e)

Solving an Exponential Equation

Example of Exponential Growth - Two Populations

Memorizing Trig Values

Examples of Values of Trig Functions

Calculating Trig Values

Examples of Inverse Trig Evaluations

Graph of y = -4sin(3x-pi)

Graph of y = 2 sec(pi x - pi/3)

Example of Converting to Polar Coordinates

Example of Graph of Polar Equation

Example of Proof of Trig Identity

Example of Double Angle Formulas

Trig Values for Multiples of pi/5

Example of Half Angle Formula

Example of Trig Equation

Example of De Moivre's Theorem

Cube Roots of -8

Example of Law of Sines

Example of Law of Cosines