Foundations of Mathematics Book

(All chapters begin with a Pretest and end with a Summary and Review, and Chapter Test.)

1. Whole Numbers

Standard Notation; Order.

Addition and Subtraction.

Multiplication and Division; Rounding and Estimating.

Solving Equations.

Applications and Problem Solving.

Exponential Notation and Order of Operations.

Factorizations.

Divisibility.

Least Common Multiples.

2. Fraction Notation.

Fraction Notation and Simplifying.

Multiplication and Division.

Addition and Subtraction; Order.

Mixed Numerals.

Applications and Problem Solving.

Order of Operations; Estimation.

3. Decimal Notation.

Decimal Notation, Order, and Rounding.

Addition and Subtraction.

Multiplication.

Division.

Converting from Fraction Notation to Decimal Notation.

Estimating.

Applications and Problem Solving.

4. Percent Notation.

Ratio and Proportion.

Percent Notation.

Percent and Fraction Notation.

Solving Percent Problems Using Percent Equations.

Solving Percent Problems Using Proportions.

Applications of Percent.

Sales Tax, Commission, Discount, and Interest.

Interest Rates on Credit Cards and Loans.

5. Geometry.

Basic Geometric Figures.

Perimeter.

Area.

Circles.

Volume and Surface Area.

Relationships Between Angle Measures.

Congruent Triangles and Properties of Parallelograms.

Similar Triangles.

6. Introduction to Real Numbers and Algebraic Expressions.

Introduction to Algebra.

The Real Numbers.

Addition of Real Numbers.

Subtraction of Real Numbers.

Multiplication of Real Numbers.

Division of Real Numbers.

Properties of Real Numbers.

Simplifying Expressions; Order of Operations.

7. Solving Equations and Inequalities.

Solving Equations: The Addition Principle.

Solving Equations: The Multiplication Principle.

Using the Principles Together.

Formulas.

Applications of Percent.

Applications and Problem Solving.

Solving Inequalities.

Applications and Problem Solving with Inequalities.

8. Graphs of Linear Equations.

Graphs and Applications.

Graphing Linear Equations.

More with Graphing and Intercepts.

Slope and Applications.

9. Polynomials: Operations.

Integers as Exponents.

Exponents and Scientific Notation.

Introduction to Polynomials.

Addition and Subtraction of Polynomials.

Multiplication of Polynomials.

Special Products.

Operations with Polynomials in Several Variables.

Division of Polynomials.

10. Polynomials: Factoring.

Introduction to Factoring.

Factoring Trinomials of the Type x² + bx + c.

Factoring ax² + bx + c, a 1, FOIL Method.

Factoring ax² + bx + c, a 1, ac-Method.

Factoring Trinomial Squares and Differences of Squares.

Factoring Sums or Differences of Cubes.

Factoring: A General Strategy.

Solving Quadratic Equations by Factoring.

Applications of Quadratic Equations.

11. Rational Expressions and Equations.

Multiplying and Simplifying Rational Expressions.

Division and Reciprocals.

Least Common Multiples and Denominators.

Adding Rational Expressions.

Subtracting Rational Expressions.

Complex Rational Expressions.

Solving Rational Equations.

Applications Using Rational Equations and Proportions.

Variation and Applications.

12. Graphs, Functions, and Applications.

Functions and Graphs.

Finding Domain and Range.

Linear Functions: Graphs and Slope.

More on Graphing Linear Equations.

Finding Equations of Lines; Applications.

13. Systems of Equations.

Systems of Equations in Two Variables.

Solving by Substitution.

Solving by Elimination.

Solving Applied Problems: Two Equations.

Systems of Equations in Three Variables.

Solving Applied Problems: Three Equations.

Business and Economics Applications.

14. More on Inequalities.

Sets, Inequalities, and Interval Notation.

Intersections, Unions, and Compound Inequalities.

Absolute-Value Equations and Inequalities.

Systems of Inequalities in Two Variables.

15. Radical Expressions, Equations, and Functions.

Radical Expressions and Functions.

Rational Numbers as Exponents.

Simplifying Radical Expressions.

Addition, Subtraction, and More Multiplication.

More on Division of Radical Expressions.

Solving Radical Equations.

Applications Involving Powers and Roots.

The Complex Numbers.

16. Quadratic Equations and Functions.

The Basics of Solving Quadratic Equations.

The Quadratic Formula.

Applications Involving Quadratic Equations.

More on Quadratic Equations.

Graphing Quadratic Equations: f(x) = a(x - h)² + k.

Graphing Mathematical Quadratic Equations: f(x) = ax² + bx + c.

Modeling with Quadratic Functions.

Polynomial and Rational Inequalities.

17. Exponential and Logarithmic Functions.

Exponential Functions.

Inverse and Composite Functions.

Logarithmic Functions.

Properties of Logarithmic Functions.

Natural Logarithmic Functions.

Solving Exponential and Logarithmic Equations.

Mathematical Modeling with Exponential and Logarithmic Functions.

Appendixes.

American Units of Measure.

Metric Units of Measure.

Mean, Median, and Mode.

Tables and Pictographs.

The Distance and Midpoint Formulas.

Nonlinear Inequalities.

Sequences and Series.

Applying Reasoning Skills.

TASP Correlation and Practice Test.