Algebra Foundations Basic Math, Introductory and Intermediate Algebra

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1. Whole Numbers

1.1 Standard Notation

1.2 Addition

1.3 Subtraction

1.4 Multiplication

1.5 Division

1.6 Rounding and Estimating; Order

1.7 Solving Equations

1.8 Applications and Problem Solving

1.9 Exponential Notation and Order of Operations

2. Fraction Notation: Multiplication and Division

2.1 Factorizations

2.2 Divisibility

2.3 Fractions and Fraction Notation

2.4 Multiplication and Applications

2.5 Simplifying

2.6 Multiplying, Simplifying, and Applications.

2.7 Division and Applications

3. Fraction Notation and Mixed Numerals

3.1 Least Common Multiples

3.2 Addition and Applications

3.3 Subtraction, Order, and Applications

3.4 Mixed Numerals

3.5 Addition and Subtraction Using Mixed Numerals; Applications

3.6 Multiplication and Division Using Mixed Numerals; Applications

3.7 Order of Operations, Complex Fractions, and Estimation.

4. Decimal Notation

4.1 Decimal Notation, Order, and Rounding

4.2 Addition and Subtraction

4.3 Multiplication

4.4 Division

4.5 Converting from Fraction Notation to Decimal Notation

4.6 Estimating

4.7 Applications and Problem Solving

5. Ratio and Proportion

5.1 Introduction to Ratios

5.2 Rates and Unit Prices

5.3 Proportions

5.4 Applications of Proportions

5.5 Geometric Applications

6. Percent Notation

6.1 Percent Notation

6.2 Percent Notation and Fraction Notation

6.3 Solving Percent Problems Using Percent Equations

6.4 Solving Percent Problems Using Proportions

6.5 Applications of Percent

6.6 Sales Tax, Commission, and Discount

6.7 Simple Interest and Compound Interest; Credit Cards

7. Data, Graphs, and Statistics

7.1 Averages, Medians, and Modes

7.2 Interpreting Data from Tables and Graphs

7.3 Interpreting and Drawing Bar Graphs and Line Graphs

7.4 Interpreting and Drawing Circle Graphs

8. Measurement

8.1 Linear Measures: American Units

8.2 Linear Measures: Metric Units

8.3 Converting Between American Units and Metric Units

8.4 Weight and Mass; Medical Applications

8.5 Capacity; Medical Applications

8.6 Time and Temperature

8.7 Converting Units of Area

9. Geometry

9.1 Perimeter

9.2 Area

9.3 Circles

9.4 Volume

9.5 Angles and Triangles

9.6 Square Roots and the Pythagorean Theorem

10. Introduction to Real Numbers and Algebraic Expressions

10.1 Introduction to Algebra

10.2 The Real Numbers

10.3 Addition of Real Numbers

10.4 Subtraction of Real Numbers

10.5 Multiplication of Real Numbers

10.6 Division of Real Numbers

10.7 Properties of Real Numbers

10.8 Simplifying Expressions; Order of Operations

11. Solving Equations and Inequalities

11.1 Solving Equations: The Addition Principle

11.2 Solving Equations: The Multiplication Principle

11.3 Using the Principles Together

11.4 Formulas

11.5 Applications of Percent

11.6 Applications and Problem Solving with Inequalities

12. Graphs of Linear Equations

12.1 Graphs of Linear Equations

12.2 Graphing Linear Equations

12.3 More with Graphing and Intercepts

12.4 Slope and Applications

13. Polynomials: Operations

13.1 Integers as Exponents

13.2 Exponents and Scientific Notation

13.3 Introduction to Polynomials

13.4 Addition and Subtraction od Polynomials

13.5 Multiplication of Polynomials

13.6 Special Products

13.7 Operations with Polynomials in Several Variables

13.8 Division of Polynomials

14. Polynomials: Factoring

14.1 Factoring Sums or Differences of Cubes

14.2 Factoring: A General Strategy

14.3 Solving Quadratic Equations by Factoring

14.4 Applications of Quadratic Equations

14.5 Introduction to Factoring

14.6 Factoring Trinomials of the Type x² + bx + c

14.7 Factoring ax² + bx + c, a≠ 1: The FOIL Method

14.8 Factoring ax² + bx + c, a ≠ 1: The ac-Method

14.9 Factoring Trinomial Squares and Difference of Squares

15. Rational Expressions and Equations

15.1 Multiplying and Simplifying Rational Expressions

15.2 Division and Reciprocals

15.3 Least Common Multiples and Denominators

15.4 Adding Rational Expressions

15.5 Subtracting Rational Expressions

15.6 Complex Rational Expressions

15.7 Solving Rational Equations

15.8 Applications Using Rational Equations and Proportions

15.9 Variation and Applications

16. Graphs, Functions, and Applications

16.1 Functions and Graphs

16.2 Finding Domain and Range

16.3 Linear Functions: Graphs and Slope

16.4 More on Graphing Linear Equations

16.5 Finding Equations of Lines; Applications

17. Systems of Equations

17.1 Systems of Equations in Two Variables

17.2 Solving by Substitution

17.3 Solving by Elimination

17.4 Solving Applied Problems: Two Equations

17.5 Systems of Equations in Three Variables

17.6 Solving Applied Problems: Three Equations

18. More on Inequalities

18.1 Sets, Inequalities, and Interval Notation

18.2 Intersections, Unions, and Compound Inequalities

18.3 Absolute-Value Equations and inequalities

18.4 Systems of Inequalities in Two Variables

19. Radical Expressions, Equations, and Functions

19.1 Radical Expressions and Functions

19.2 Rational Numbers as Exponents

19.3 Simplifying Radical Expressions

19.4 Addition, Subtraction, and More Multiplication

19.5 More on Division of Radical Expressions

19.6 Solving Radical Equations

19.7 Applications Involving Powers and Roots

19.8 The Complex Numbers

20. Quadratic Equations and Functions

20.1 The Basics of Solving Quadratic Equations

20.2 The Quadratic Formula

20.3 Applications Involving Quadratic Equations

20.4 More on Quadratic Equations

20.5 Graphing f(x) = a(x - h)2 + k

20.6 Graphing f(x) = ax2 + bx + c

20.7 Mathematical Modeling with Quadratic functions

20.8 Polynomial Inequalities and Rational lnequalities

21. Exponential Functions and Logarithmic Functions

21.1 Exponential Functions

21.2 Composite Functions and Inverse Functions

21.3 Logarithmic Functions

21.4 Properties of Logarithmic Functions

21.5 Natural Logarithmic Functions

21.6 Solving Exponential Equations and Logarithmic Equations

21.7 Mathematical Modeling with Exponential Functions and Logarithmic Functions

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