Properties of Real Numbers, Algebra 2

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Carleen Eaton

Grant Fraser

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Properties of Real Numbers

Important subsets of the real numbers are: the natural numbers, the whole numbers, the integers, the rationals, and the irrationals.
The real numbers are commutative and associative under addition and multiplication, have additive and multiplicative identities and inverses, and satisfy the distributive property.
Use these properties to simplify expressions.

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Table of Contents

I. Equations and Inequalities
	Expressions and Formulas	28:56
	Properties of Real Numbers	23:45
	Solving Equations	24:41
	Solving Absolute Value Equations	17:36
	Solving Inequalities	19:27
	Solving Compound and Absolute Value Inequalities	24:08
II. Linear Relations and Functions
	Relations and Functions	38:15
	Linear Equations	12:50
	Slope	20:07
	Writing Linear Functions	27:36
	Special Functions	24:28
	Graphing Inequalities	30:37
III. Systems of Equations and Inequalities
	Solving Systems of Equations by Graphing	21:27
	Solving Systems of Equations Algebraically	31:26
	Solving Systems of Inequalities by Graphing	20:43
	Solving Systems of Equations in 3 Variables	21:27
IV. Matrices
	Basic Matrix Concepts	14:08
	Matrix Operations	16:40
	Matrix Multiplication	22:47
	Determinants	25:47
	Cramer's Rule	25:42
	Identity and Inverse Matrices	27:01
	Solving Systems of Equations with Matrices	28:40
V. Quadratic Functions and Inequalities
	Graphing Quadratic Equations	26:36
	Solving Quadratic Equations by Graphing	19:26
	Solving Quadratic Equations by Factoring	17:46
	Imaginary and Complex Numbers	37:41
	Completing the Square	16:42
	Quadratic Formula and the Discriminant	17:44
	Analyzing the Graphs of Quadratic Functions	23:00
	Graphing and Solving Quadratic Inequalities	34:38
VI. Polynomial Functions
	Properties of Exponents	20:28
	Operations on Polynomials	16:13
	Dividing Polynomials	29:26
	Polynomial Functions	29:34
	Analyzing Graphs of Polynomials	34:36
	Solving Polynomial Equations	19:23
	Remainder and Factor Theorems	27:52
	Roots and Zeros	31:04
	Rational Zero Theorem	29:27
VII. Rational Equations and Inequalities
	Operations on Functions	35:12
	Inverse Functions and Relations	18:12
	Square Root Functions and Inequalities	26:24
	nth Roots	24:06
	Operations with Radical Expressions	34:38
	Rational Exponents	24:36
	Solving Radical Equations and Inequalities	38:46
VIII. Radical Expressions and Equations
	Multiplying and Dividing Rational Expressions	30:11
	Adding and Subtracting Rational Exprsesions	51:53
	Graphing Rational Functions	45:13
	Direct, Joint, and Inverse Variation	21:49
	Solving Rational Equations and Inequalities	53:21
IX. Exponential and Logarithmic Relations
	Exponential Functions	28:22
	Logarithms and Logarithmic Functions	36:31
	Properties of Logarithms	29:50
	Common Logarithms	27:10
	Base 'e' and Natural Logarithms	19:52
	Exponential Growth and Decay	28:10
X. Conic Sections
	Midpoint and Distance Formulas	29:35
	Parabolas	26:11
	Circles	17:33
	Ellipses	38:57
	Hyperbolas	37:59
	Conic Sections	23:10
	Solving Quadratic Systems	28:18
XI. Sequences and Series
	Arithmetic Sequences	27:44
	Arithmetic Series	29:12
	Geometric Sequences	24:52
	Geometric Series	27:02
	Infinite Geometric Series	24:01
	Recursion and Special Sequences	17:11
	Binomial Theorem	38:25
	Proof and Mathematical Induction	19:53

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Properties of Real Numbers

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Properties of Real Numbers

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