Refer to Khan academy: Converting recursive & explicit forms of arithmetic sequences

Geometric sequences

Refer to math is fun: Binomial theorem

It actually is a hard term to understand at beginning. One way to do this, is to learn how to solve first, then learn what’s the theory behind it.

Refere to khan academy: The sign of a polynomial

The sign of a polynomial between ANY two CONSECUTIVE roots is either always positive or always negative.

This is because polynomial functions are continuous functions (no breaks in the…

Refer to Wiki: Polynomial long division

It’s very import to understand it in the first place. Once get the idea, it’s easy to solve this problem.

First need to understand, 
this usually is a Degrading process.

Refer to math is fun: Function Transformations

Express different transformations in the function.

Refer to the previous note Graph transformations.

Let’s assume:

• the function is f(x)…

Refer to math is fun: Inverse functions

If a function means Map to, then inverse function means Map back. f(x)=y maps x to y, then f'(y)=x maps y back to x. Note that f' is the inverse function of f.

Refer to math is fun: Midpoint of a Line Segment
The midpoint is halfway between the two end points of the line segment.

Refer to math is fun: Σ: Sigma Notation

Literally means Sum up. Pronounced Sigma.

We can do this:

And get the result:

Or do this sum:

Refer to khan academy: Linear growth vs. Exponential growth

Quite a bit like the Arithmetic sequences vs. Geometric sequences,

except in Exponential relationship, it's using a common exponent,
instead of using a…

Refer to math is fun: Maxima and Minima of Functions

• Absolute maximum: means the…

Refer to math is fun: Polygons (2D shapes)

A Polygon is any flat shape with straight sides.

Interior Angles of Polygons

Khan lecture 1.
Khan lecture 2.

# Sum of cubes
a³ + b³ = (a + b)(a² - ab + b²)

# Division of cubes
a³ - b³ = (a - b)(a² + ab + b²)

Refer to math is fun: Factorial !

0! = 1

It makes no sense, but it is generally agreed this result, because: