Let's+Tie+the+Knott+(Algebra)

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Rational vs. Irrational Numbers Is pi an irrational number? ﻿Yes pi is an irrational number! Are non-perfect squares irrational?

__**﻿-Rational**__ ex: 2/3, 6/1 __**-Irrational**__ ex: pi __**-Whole**__ ex: 0, 1, 2, 3.. __**-Integer**__ ex: ... -2, -1, 0. 1, 2, ... __**-Natural (counting)**__ ex: 1, 2, 3, ... -CS4A
 * Real #'s: **

Commutative Property Associative Property Identity Property Inverse Property Distribution Property
 * Real Number Properties:**

P erenthisis E exponents M ultiplication D ivision A ddition S ubtraction <span style="color: #808000; font-family: 'Comic Sans MS',cursive;">CA 4A
 * <span style="font-family: 'Comic Sans MS',cursive;">Order of Operations: **

What is anything raised to the ZERO power? When do you add the exponents? When do you subtract exponents? What does is the power rule for exponents?
 * <span style="font-family: 'Comic Sans MS',cursive;">Exponents: **

<span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">Steps for scientific notation: <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">1st number is between 1-10 <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">2nd number is raised to the number of decimal places moved. (exponent). <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">-CS4A
 * <span style="font-family: 'Comic Sans MS',cursive;">Scientific Notation: **<span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">﻿is used to write extremely large and extremely small numbers. In scientific notations, a number is written as the product of 2 numbers.
 * <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">Remember if you... move to the right --> + exponent **
 * <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">move to the left --> - exponent **

<span style="font-family: 'Comic Sans MS',cursive;">**Absolute Value:** the distance of a quantity from zero -- MD2b

<span style="font-family: 'Comic Sans MS',cursive;">**Radicals (+, -, *, /):** when you multiply and divide radicals you can just multiply/divide them as you normally would. then simplify! but if there is a "rat in the basement", then you gotta multiply the radical by the "rat's" reciprocal until it cannot be simplified anymore. However when you are adding or subtracting radicals it is slightly more complicated. you need to make sure that the radicals have the same "doghouse", aka make sure that both radicals match (on the inside of the radical sign). <span style="font-family: 'Comic Sans MS',cursive;">--MD2b

<span style="font-family: 'Comic Sans MS',cursive;">**Sets** (union, intersection, complement, Venns, etc): union is all of the variables/numbers in the sets put together, intersection is what selected sets have in common, complement is what one specific set does have that another one doesnt. A Venn Diagram is a type of chart that represents data from number sets. the venn diagram compares union, intersection and complement. <span style="font-family: 'Comic Sans MS',cursive;">--MD2b

<span style="font-family: 'Comic Sans MS',cursive;">ex: sum means addition <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">﻿﻿__**product-**__ answer to a multiplication problem <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">__**less than-**__ subtraction and switch order <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">__**the difference-**__ subtraction <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">__**quotient-**__ answer to a division problem <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">__**total, increase, add, gain, plus, put together-**__ addition <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">__**minus, take away, remove, subtracted from, loose, less than, whats left-**__ subtraction <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">__**divided by, dividend, fraction, goes into**__- division <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">__**multiplied by, times, double and twice, squared-**__ multiplication <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">-CS4A
 * <span style="font-family: 'Comic Sans MS',cursive;">Translating English---> Math **

<span style="font-family: 'Comic Sans MS',cursive;">**Combining Like Terms** (adding polynomials) So lets jus say that there is... x^2 and a regular x. You can not add them because the exponent is notthe same. But if there was...x^3 plus x^3 you could add them because they have the same exponent! -CA4A

<span style="font-family: 'Comic Sans MS',cursive;">**Subtracting Polynomials**: re-write the first polynomial term, change the subtraction sign to an addition sign, and change all of the integers in the following polynomial term to it's opposite. BTW if the problem says "subtracted from" or "less than" your first step is to reverse the first and second polynomial terms you see. --MD2b


 * <span style="font-family: 'Comic Sans MS',cursive;">Multiplying Polynomials **

<span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">**F**irsts <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">**O**utters <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">**I**nners <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">**L**asts <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">-CS4A
 * <span style="font-family: 'Comic Sans MS',cursive;">FOIL (double distribution): **

Ps- __NEVER__ forget to expand (x - 4)^2 which is (x - 4) ( x - 4)

<span style="font-family: 'Comic Sans MS',cursive;">1. GCF 2. <span style="color: #ff0039; font-family: 'Comic Sans MS',cursive;"> DOPS <span style="font-family: 'Comic Sans MS',cursive;">3. reverse foil -MD 2B
 * <span style="font-family: 'Comic Sans MS',cursive;">Factoring: **


 * <span style="font-family: 'Comic Sans MS',cursive;">Solving Equations **


 * <span style="font-family: 'Comic Sans MS',cursive;">Solving Inequalities **

**when solving inequalities, the rule that you absolutely MUST remember is that when you divide by a negative number, you have to switch the sign. -md 2B**
====**percents are a way to represent parts of a whole. percents are easy because you know that they are out of one hundred, which is helpful when solving proportions, dealing with money problems, statistics and more! -md 2B**====
 * <span style="font-family: 'Comic Sans MS',cursive;">All about Percents: **

<span style="font-family: 'Comic Sans MS',cursive;">1. Motion: Remember...distance = __X__ __ <span style="font-family: 'Comic Sans MS',cursive;">When do you set the two distances equal to each other? <span style="font-family: 'Comic Sans MS',cursive;">How do you know when to "add up" the two distances?
 * <span style="font-family: 'Comic Sans MS',cursive;">Word Problems **

<span style="font-family: 'Comic Sans MS',cursive;">2. Consecutive integers <span style="font-family: 'Comic Sans MS',cursive;">How do you set up your let statements for <span style="font-family: 'Comic Sans MS',cursive;">a) consecutive inegers? n, n+1, n+2, n+3, etc. <span style="font-family: 'Comic Sans MS',cursive;">b) consecutive even or odd integers? n+2, n+4, n+6, etc, OR n+3, n+5, n+7 -md 2b

<span style="font-family: 'Comic Sans MS',cursive;">Empirical vs. Theoretical Probability <span style="font-family: 'Comic Sans MS',cursive;">- emp = done by experiment; actually proven to work out a certain way. - md 2B <span style="font-family: 'Comic Sans MS',cursive;">- theor = "theoretically speaking", as if it had really happened, finding the likeliness of what would happen. - md 2B <span style="font-family: 'Comic Sans MS',cursive;">"or" vs. "and" - use additon for the word "or", and multiplication for the word "and". -md 2B <span style="font-family: 'Comic Sans MS',cursive;">Mutually Exclusive Events - <span style="font-family: 'Comic Sans MS',cursive;">Conditional Probability - <span style="font-family: 'Comic Sans MS',cursive;">Factorials - multiplying the number times every consecutive numer below it. - md 2B <span style="font-family: 'Comic Sans MS',cursive;">Permutations - rearranging/changing the order of events/variables in a specific sequence. -md 2B
 * <span style="font-family: 'Comic Sans MS',cursive;">Probability **

<span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">3 Measures of Central Tendencies - mean, median, and mode :)
 * <span style="font-family: 'Comic Sans MS',cursive;">Statistics **

<span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">Range - the difference between the largest and smallest values in a group of data.

<span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">Outlier - a value in a set of data that completely stands out from everything else... it usually throws off the mean/average of the group and affects the range as well.

<span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">Ti-83/84 w/ Stats?! <span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">ok... go to:

<span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">1) STAT <span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">2) edit <span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">3) L1 (clear it if theres previous work in there) <span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">4) enter each number in the set of data and press ENTER after each number is typed in. <span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">5) then press STAT again <span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">6) choose the first option and press enter. <span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">THERE YA GO!

<span style="color: #ff5600; font-family: Arial,Helvetica,sans-serif;">- md 2b