video probability "Basic Probability"

INTRODUCTION PROBABLITY

WHAT IS PROBABILITY???

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty).The higher the probability of an event, the more certain we are that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is unbiased, the two outcomes ("head" and "tail") are equally probable; the probability of "head" equals the probability of "tail." Since no other outcome is possible, the probability is 1/2 (or 50%) of either "head" or "tail". In other words, the probability of "head" is 1 out of 2 outcomes and the probability of "tail" is also, 1 out of 2 outcomes, expressed as 0.5 using the above mentioned quantification system.

Video Algebra

HOW TO DO ALGEBRA “SIMPLIFYING 

FRACTION ALGEBRA” ?????

Here is the video 

Algebra

Introduction of Algebra

Algebra  is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols it is a unifying thread of almost all of mathematics.

ALGEBRA EXAMPLE

Solving an equation:

2x+3=x+15

Why Use a Letter?

	Because:
	it is easier to write "x" than drawing empty boxes (and easier to say "x" than "the empty box").
	if there are several empty boxes (several "unknowns") we can use a different letter for each one.

So x is simply better than having an empty box. We aren't trying to make words with it!

And it doesn't have to be x, it could be y or w ... or any letter or symbol we like.

How to Solve

Algebra is just like a puzzle where we start with something like "x − 2 = 4" and we want to end up with something like "x = 6".

But instead of saying "obviously x=6", use this neat step-by-step approach:

• Work out what to remove to get "x = ..."
• Remove it by doing the opposite (adding is the opposite of subtracting)
• Do that to both sides

Here is an example:

We want to remove the "-2"	To remove it, do the opposite, in this case add 2:	Do it to both sides:	Which is ...	Solved!

Video of Quadratic Equation

Introduction to Quadratic Equations.

Definition of a quadratic equation 

A quadratic equation in x is an equation that can be written in the

 form 2 0, , , 0. ax bx c where a b and c are 

real numbers with a + += ≠ 

A quadratic equation in x also called a second degree polynomial equation in x. 

Quadratic formula and its derivation 

Completing the square can be used to derive a general formula for solving quadratic equations, called the quadratic formula.^[5] The mathematical proof will now be briefly summarized.^[6] It can easily be seen, by polynomial expansion, that the following equation is equivalent to the quadratic equation:

${\displaystyle \left(x+{\frac {b}{2a}}\right)^{2}={\frac {b^{2}-4ac}{4a^{2}}}.}$

Taking the square root of both sides, and isolating x, gives:

${\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac\ }}}{2a}}.}$

Some sources, particularly older ones, use alternative parameterizations of the quadratic equation such as ax² + 2bx + c = 0 or ax² − 2bx + c = 0 ,^[7] where b has a magnitude one half of the more common one, possibly with opposite sign. These result in slightly different forms for the solution, but are otherwise equivalent.

A number of alternative derivations can be found in the literature. These proofs are simpler than the standard completing the square method, represent interesting applications of other frequently used techniques in algebra, or offer insight into other areas of mathematics.

A lesser known quadratic formula, as used in Muller's method, and which can be found from Vieta's formulas, provides the same roots via the equation:

${\displaystyle x={\frac {-2c}{b\pm {\sqrt {b^{2}-4ac}}}}.}$

One property of this form is that it yields one valid root when a = 0, while the other root contains division by zero, because when a = 0, the quadratic equation becomes a linear equation, which has one root. By contrast, in this case the more common formula has division by zero in both cases.

Video Tutorial on How to Use the Pythagorean Theorem

Pythagoras Theorem

Conceptual Animation of Pythagorean Theorem

The Formula

The picture below shows the formula for the Pythagorean theorem. In the pictures below, side C is always thehypotenuse. Remember that this formula only applies to right triangles.

Examples of the Pythagorean Theorem

When you use the Pythagorean theorem, just remember that the hypotenuse is always 'C' in the formula above . Look at the following examples to see pictures of the formula.

RATIO INTRODUCTION AND WORD PROBLEMS

RATIO

              

A ratio compares values.

A ratio says how much of one thing there is compared to another thing.

There are 3 blue squares to 1 yellow square

Ratios can be shown in different ways:

Using the ":" to separate the values:		3 : 1
Instead of the ":" we can use the word "to":		3 to 1
Or write it like a fraction:		31

A ratio can be scaled up:

Here the ratio is also 3 blue squares to 1 yellow square,
even though there are more squares.

Using Ratios

The trick with ratios is to always multiply or divide the numbers by the same value.

Example:

4 : 5 is the same as 4×2 : 5×2 = 8 : 10

Recipes

Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.

So the ratio of flour to milk is 3 : 2

To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:

3×4 : 2×4 = 12 : 8

In other words, 12 cups of flour and 8 cups of milk.

The ratio is still the same, so the pancakes should be just as yummy.