Reflection of Math Video

ANGLE

 Angle is two rays connected in same point.

First ray is initial ray, and the second ray is terminal ray.

Vertex is a parts on an angle that connects two rays.

Direction the terminal side goes in

-positive angle, if an angle is generated by a-counter clockwise rotation.
-negative angle, if an angle is generated by a clockwise rotation.

To measure an angle, need to know how far terminal side rotates from the initial side.
To measure amount of rotation for an angle, we use x,y graph

 
x-axis is positive on right side of y-axis and negative on other side.
y-axis is positive above x-axis and negative below it.
Angle getting bigger if counterclockwise.

Angle can be measured by two unit, the units are:

1. Radian
2. Degree

There are some angles that called special angle, the angles is:

0˚, 30˚, 45˚, 60˚, 90˚. It is important to memorize special angle.

DEGREE

A degree usually denoted by ° (the degree symbol), One full counterclockwise rotation of terminal side of angle back to its starting point measures  360⁰ (make a circle).

Degree measurements :

• 90⁰ (right angle) = ¼ revolution
• 180⁰ (straight angle)

There are two units in angle, degree and radian.

360˚ = single revolution
1 full revolution = 2π radians

So,

360˚ = 2π radian

360˚/2 = 2π/2 radian
180˚ = π radian
180˚/180 = π/180 radian
1˚= π/180 radian

1 radian = 180/π

And how to convert degree into radian and radian into degree?

For example:

a. 120˚ Convert  to radian.

1˚ = π/180
120×1˚ = 120x(π/180 radian)
120˚=120π/180 radian (all number is divided by 60)
120˚=2π/3 radian

b. 11π/12 radian convert into degrees!

11π/12 x 1 radian = 180/π. 11π/12 = 165˚

Special angle, there are some angle that are called special angle, that are 0˚, 30˚, 45˚, 60˚, 90˚.

Multiplying Exponent

There are some rules when we learn about exponent.

Rule I

Some both base and multiply base
aⁿbⁿ = (ab)ⁿ

Example :

3⁵x4⁵

= (3.4)⁵

=12⁵

Rule II

Divide instead multiply

aⁿ/bⁿ= (a/b)ⁿ

example :

6³/2³

= (6/2)³

= 3x3x3

= 27

Rule III

Base number base power

(aⁿ)^m =a^n.m

Example: 

(2³)²

= 8²

= 64

Rule IV

Differential exponent, same number base

aⁿa^m = a^(n+m)

example :

2³x2⁵

= 2⁽³⁺⁵⁾

= 2⁸

Rule V

aⁿ/a^m = a^(n-m)

Example :

4⁵/4³

= 4^(5-3)

=4²

= 16

MULTI DIVISION MATH

Standard algorithm for multiplying

26×31= …

It can be solved by different methods

First method, 

 

Then, products method

 

Then, Latice Solution

 

Standard algorithm for division

By long division 133 : 6 =22 R.1 or 22 1/6

This division can be solved by different method

First method,

133:6=…

6×10=60
6×20=120
6×1=6
6×21=126
6×1=6
6×22=132
6×22+1=133
so, 133:6 = 22 R.1

Second method,

133:6= …

6×10=60
6×10=60
6×1=6
6×1=6
(10+10+1+1)=22
So, 133:6 = 22 R.1

QUADRATIC FORM

(3x-1)(x+2) = 3x²+6x-x-2 = 3x²+5x-2 (it is basic quadratic form)

y=3x²+5x-2

Standard quadratic form : y=ax²+bx+c

Linear equation

y=mx+b

m is slope and y b is y-intercept

Rate of change for quadratic equation is not constant

 

Slope changing over times

y=100-16x

at x=0 → y=100

at x=1→y=100-16=84

at x=2→ y=100-2.16=68

different point → different slope.