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1	CLAST Review Algebra Center of Academic Assistance
2	Real Numbers Real numbers are: Rational numbers either terminating (1.0, -5.2) or repeating decimals (3.17555) Irrational numbers non-terminating and non-repeating decimals (p, ) All the rules that apply to rational numbers in arithmetic also apply to irrational numbers.
3	Addition of Irrational Numbers
4	Multiplication of Irrational Numbers Example: Combine radicands under one radical sign Factor Simplify
5	Division of Irrational Numbers Example: Combine radicands under one radical sign Factor Simplify
6	Rationalize the Denominator Do not leave a radical in the denominator Example: Multiply the radical denominator by itself to form a perfect square. Multiply the numerator by the same term, to keep the value of the fraction (this is actually multiplying by 1) Simplify
7	apply the Order of Operations Agreement By convention, there is a specific order of operations. This mnemonic will help you to remember the order: Please Excuse My Dear Aunt Sally Parentheses solve the terms inside parentheses first Exponents evaluate exponents Multiply and/or Divide from left to right Add and/or Subtract from left to right
8	use Properties of Operations Associative (grouping) a + (b + c) = (a + b) + c a(bc) = (ab)c Commutative (order) a + b = b + a ab = ba Distributive a(b + c) = ab + ac Inverse a + (-a) = 0 a ( ) = 1 if a 0 Identity a + 0 = a
9	use Scientific Notation Scientific notation always appears as a factor (one non-zero integer before the decimal portion) multiplied by a power of 10 Decimal Form Scientific Notation 0.0034 3.4 x 10^-35.46 5.46 x 10⁰ 21,500 2.15 x 10⁴
10	Determine if a Number is a Solution to an Inequality
11	Properties of Equality and Inequality i. If a = b, then a + c = b + c ii. If a > b, then a + c > b + c iii. If a = b, then ac = bc iv. For c > 0, if a > b, then ac > bc v. For c < 0, if a > b, then ac < bc vi. If a > b and b > c, then a > c
12	Use Properties to Identify Equivalent Equations and Inequalities
13	Solve Linear Equations and Inequalities
14	Steps to Find the Solution for an Equation
15	Use Algebraic Formulas
16	Steps to Evaluating Formulas
17	Functions
18	Examples of Functions
19	Visual Examples of Functions
20	Find Values of Functions
21	Find Factors of Quadratic Expressions
22	Find Factors of Quadratic Expressions page 2
23	The FOIL Technique
24	The FOIL Technique page 2
25	Find Solutions to Quadratic Equations
26	A System of Two Linear Equations
27	Solve a System of Two Linear Equations in Two Unknowns: the Addition Method
28	Example of the Addition Method
29	Addition Method page 2
30	Identify Specified Regions of the Coordinate Plane
31	Regions of the Coordinate Plane page 2
32	Problems Involving the Structure and Logic of Algebra
33	Solve Problems Involving the Structure and Logic of Algebra
34	Identify Statements of Proportionality and Variation
35	Example of Direct Variation When traveling, distance equals rate times time, or d = rt Distance increases if rate or time increases Distance decreases if rate or time decreases
36	Example of Inverse Variation
37	Algebraic Word Problems with Variables