Algebra

Introduction to basic algebraic equations of the form Ax=B.

Slightly more complicated equations.

Equations with the variable on both sides.

Solving linear equations with variable expressions in the denominators of fractions.

Graphing linear equations.

Getting a feel for slope and y-intercept.

Figuring out the slope of a line.

Second part of determining the slope of a line.

Part 3 of slope.

Introduction to averages and algebra problems involving averages.

Adding sums of consecutive integers.

Taking a percentage of a number.

Growing a quantity by a percentage.

Finding the full price when you know the discount price.

Slightly harder percent problems.

Systems of equations.

What a ratio is. Simple ratio problems.

A slightly more involved ratio problem with algebra.

More advance ratio problem with algebra.

An alternate solution to the advanced ratio problem in the last video.

Basic ratio problems.

More advanced ratio problems.

Age word problems.

Second set of age word problems.

Part 3 of the presentation on age word problems.

(Ax+By)(Ax+By).

Factoring quadratics.

Introduction to i. Raising i to arbitrary exponents.

Introduction to complex numbers. Adding, subtracting and multiplying complex numbers.

Dividing complex numbers. Complex conjugates.

Introduction to using the quadratic equation to solve 2nd degree polynomials.

2 more examples of solving equations using the quadratic equation.

Solving a quadratic by completing the square.

Deriving the quadratic formula by completing the square.

Solving quadratic inequalities using factoring.

An introduction to functions.

More examples of solving function problems.

Even more examples of function exercises. Introduction of a graph as definition of a function.

An example of a functions problem submitted by a youtube viewer.

Figuring out the domain of a function.

Proof of the logarithm property: log a + log b = log ab.

Proofs of the logarithm properties: A(log B) = log (B^A) and log A - log B = log (A/B).

Proof of the logarithm property.

Dividing one polynomial into another.

What are conic sections and why are they called "conic sections"?

Introduction to the Circle.

Introduction to the ellipse.

Introduction to the hyperbola.

Continuation of the intro to hyperbolas.

Part 3 of the intro to hyperbolas.

Part 1 of identifying and graphic conic sections.

Part 2 of identifying and graphing conic sections.

Let's identify (and graph) a couple of more conics!

Calculating the foci (or focuses) of an Ellipse.

Introduction to the foci (focuses) of a hyperbola.

Proof of the hyperbola foci formula.

Introduction to partial fraction expansion.

A more complex problem.

Dealing with repeated factors.

Parabola as the locus of all points equidistant from a point and a line.

Finding the focus and directrix of a parabola.

Algebra word problem involving two bicycles passing each other.

Fun algebra word problem involving a train passing a bike.

Trains passing at different rates.

3 people overtaking each other at different rates.

Fun word problem that is almost a brain teaser.

Not quite a brain teaser but fun nonetheless!

Two ways to solve a rational inequality (or an inequality involving a fractional expression).

Slightly harder rational inequality problem.

Finding the coefficients of a third degree polynomial given 2 roots and the y-intercept.

Figuring out the formula for fixed mortgage payments using the sum of a geometric series.

Function Inverse Example 1.

Function Inverse Example 2.

Function Inverse Example 3.