Cool Math Guy – Algebra I

Cool Math Guy – Algebra I

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Size: 6.14 GB | Genre: MathCore topics include solving linear equations and inequalities, graphing equations and inequalities with some use of the graphing calculator, exponents, polynomials, factoring, rational expressions and equations, systems of linear equations and inequalities, radical expressions and equations, and solving quadratic equations. Algebra I follows Prealgebra in the sequence of math courses and is often used as a developmental course at the college level under the name Elementary Algebra.

Chapter 1 – THE REAL NUMBER SYSTEM

1.1 Real Numbers: Order and Absolute Value

1.2 Adding and Subtracting Integers

1.3 Multiplying and Dividing Integers

1.4 Operations with Rational Numbers

1.5 Exponents, Order of Operations, and Properties of Real NumbersChapter 2 – FUNDAMENTALS OF ALGEBRA

2.1 Writing and Evaluating Algebraic Expressions

2.2 Simplifying Algebraic Expressions

2.3 Algebra and Problem Solving

2.4 Introduction to EquationsChapter 3 – LINEAR EQUATIONS AND PROBLEM SOLVING

3.1 Solving Linear Equations

3.2 Equations that Reduce to Linear Form

3.3 Problem Solving with Percents

3.4 Ratios and Proportions

3.5 Geometric and Scientific Applications

3.6 Linear InequalitiesChapter 4 – EQUATIONS AND INEQUALITIES IN TWO VARIABLES

4.1 Ordered Pairs and Graphs

4.2 Graphs of Equations in Two Variables

4.3 Slope and Graphs of Linear Equations

4.4 Equations of Lines

4.5 Graphs of Linear Inequalities

Chapter 5 – EXPONENTS AND POLYNOMIALS5.1 Negative Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Multiplying Polynomials: Special Products

5.4 Dividing PolynomialsChapter 6 – FACTORING AND SOLVING EQUATIONS

6.1 Factoring Polynomials with Common Factors

6.2 Factoring Trinomials

6.3 More About Factoring Trinomials

6.4 Factoring Polynomials with Special Forms

6.5 Solving Quadratic Equations by FactoringChapter 7 – RATIONAL EXPRESSIONS AND EQUATIONS

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions

7.4 Complex Fractions

7.5 Rational Equations and ApplicationsChapter 8 – SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES

8.1 Solving Systems of Equations by Graphing

8.2 Solving Systems of Equations by Substitution

8.3 Solving Systems of Equations by Elimination

8.4 Applications of Systems of Linear Equations

8.5 Systems of Linear InequalitiesChapter 9 – RADICAL EXPRESSIONS AND EQUATIONS

9.1 Roots and Radicals

9.2 Simplifying Radicals

9.3 Operations with Radical Expressions

9.4 Radical Equations and ApplicationsChapter 10 – QUADRATIC EQUATIONS AND FUNCTIONS

10.1 Solution by the Square Root Property

10.2 Solution by Completing the Square

10.3 Solution by the Quadratic Formula

10.4 Graphing Quadratic Equations

10.5 Applications of Quadratic Equations

10.6 Complex Numbers

10.7 Relations, Functions, and Graphs

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Cool Math Guy – Algebra II

Topics in Algebra II primarily extend concepts learned in Algebra I and also include functions, complex numbers, exponential and logarithmic functions, use of the graphing calculator, matrices, conics, sequences and series. Algebra II follows either Algebra I or Geometry in the sequence of math courses and is often used as a developmental course at the college level under the name Intermediate Algebra.

Chapter 1 – FUNDAMENTALS OF ALGEBRA

1.1 The Real Number System

1.2 Operations with Real Numbers

1.3 Properties of Real Numbers

1.4 Algebraic Expressions

1.5 Constructing Algebraic ExpressionsChapter 2 – LINEAR EQUATIONS AND INEQUALITIES

2.1 Linear Equations

2.2 Linear Equations and Problem Solving

2.3 Business and Scientific Problems

2.4 Linear Inequalities

2.5 Absolute Value Equations and InequalitiesChapter 3 – GRAPHS AND FUNCTIONS

3.1 The Rectangular Coordinate System

3.2 Graphs of Equations

3.3 Slope and Graphs of Linear Equations

3.4 Equations of Lines

3.5 Graphs of Linear Inequalities

3.6 Relations and Functions

3.7 Graphs of FunctionsChapter 4 – SYSTEMS OF EQUATIONS AND INEQUALITIES

4.1 Systems of Equations

4.2 Linear Systems in Two Variables

4.3 Linear Systems in Three Variables

4.4 Matrices and Linear Systems

4.5 Determinants and Linear Systems

4.6 Systems of Linear InequalitiesChapter 5 – POLYNOMIALS AND FACTORING

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Multiplying Polynomials

5.4 Factoring by Grouping and Special Forms

5.5 Factoring Trinomials

5.6 Solving Polynomial Equations by FactoringChapter 6 – RATIONAL EXPRESSIONS, EQUATIONS, AND FUNCTIONS

6.1 Rational Expressions and Functions

6.2 Multiplying and Dividing Rational Expressions

6.3 Adding and Subtracting Rational Expressions

6.4 Complex Fractions

6.5 Dividing Polynomials and Synthetic Division

6.6 Solving Rational Equations

6.7 Applications and VariationChapter 7 – RADICALS AND COMPLEX NUMBERS

7.1 Radicals and Rational Exponents

7.2 Simplifying Radical Expressions

7.3 Adding and Subtracting Radical Expressions

7.4 Multiplying and Dividing Radical Expressions

7.5 Radical Equations and Applications

7.6 Complex NumbersChapter 8 – QUADRATIC EQUATIONS, FUNCTIONS, AND INEQUALITIES

8.1 Solving Quadratic Equations: Factoring and Special Forms

8.2 Completing the Square

8.3 The Quadratic Formula

8.4 Graphs of Quadratic Functions

8.5 Applications of Quadratic Equations

8.6 Quadratic and Rational InequalitiesChapter 9 – EXPONENTIAL AND LOGARITHMIC FUNCTIONS

9.1 Exponential Functions

9.2 Composite and Inverse Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Solving Exponential and Logarithmic Equations

9.6 ApplicationsChapter 10 – CONICS

10.1 Circles and Parabolas

10.2 Ellipses

10.3 Hyperbolas

10.4 Solving Nonlinear Systems of EquationsChapter 11 – SEQUENCES, SERIES, AND THE BINOMIAL THEOREM

11.1 Sequences and Series

11.2 Arithmetic Sequences

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

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