Refer to Khan academy: Converting recursive & explicit forms of arithmetic sequences
Geometric sequences
Binomial theorem
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.
sign
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.
sign of a polynomial
This is because polynomial functions are continuous functions (no breaks in the…
continuous functions
Polynomial long division
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.
Degrading process
Function Transformations
Refer to math is fun: Function Transformations
Express different transformations in the function.
Refer to the previous note Graph transformations.
Let’s assume:
f(x)
Inverse functions
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.
function
Map to
inverse function
Map back
f(x)=y
x
y
f'(y)=x
f'
f
Refer to math is fun: Midpoint of a Line SegmentThe midpoint is halfway between the two end points of the line segment.
Σ: Sigma Notation
Refer to math is fun: Σ: Sigma Notation
Literally means Sum up. Pronounced Sigma.
Sum up
Sigma
We can do this:
And get the result:
Or do this sum:
ARC
Mind that: it’s very basic idea for Differential calculus.
Differential calculus
Average slope
Because the slope is almost always changing in a non-linear function, and we have to specify a…
Linear growth
Exponential growth
Refer to khan academy: Linear growth vs. Exponential growth
Quite a bit like the Arithmetic sequences vs. Geometric sequences,
Arithmetic sequences
except in Exponential relationship, it's using a common exponent,instead of using a…
Exponential relationship
common exponent
Maxima
Minima
Refer to math is fun: Maxima and Minima of Functions
Absolute maximum
Polygons
Refer to math is fun: Polygons (2D shapes)
A Polygon is any flat shape with straight sides.
Polygon
flat shape
straight sides
Interior Angles
cubes
Khan lecture 1.Khan lecture 2.
# Sum of cubesa³ + b³ = (a + b)(a² - ab + b²)
# Division of cubesa³ - b³ = (a - b)(a² + ab + b²)
Refer to math is fun: Factorial !
Factorial
0! = 1
It makes no sense, but it is generally agreed this result, because: