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 Notation 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. Data, Graphs, and Statistics.
Averages, Medians, and Modes.
Tables and Pictographs.
Bar Graphs and Line Graphs.
Circle Graphs.
6. Geometry.
Basic Geometric Figures.
Perimeter.
Area.
Circles.
Volume and Surface Area.
Relationships Between Angle Measures.
Congruent Triangles and Properties of Parallelograms.
Similar Triangles.
7. 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.
8. 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.
9. Graphs of Linear Equations.
Graphs and Applications.
Graphing Linear Equations.
More with Graphing and Intercepts.
Slope and Applications.
10. 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.
11. Polynomials: Factoring.
Introduction to Factoring.
Factoring Trinomials of the Type x2 + bx + c.
Factoring ax2 + bx + c, a 1, The FOIL Method.
Factoring ax2 + bx + c, a 1, The ac-Method.
Factoring Trinomial Squares and Differences of Squares.
Factoring: A General Strategy.
Solving Quadratic Equations by Factoring.
Applications of Quadratic Equations.
12. Rational Expressions and Equations.
Multiplying and Simplifying Rational Expressions.
Division and Reciprocals.
Least Common Multiples and Denominators.
Adding Rational Expressions.
Subtracting Rational Expressions.
Solving Rational Equations.
Applications Using Rational Equations and Proportions.
Complex Rational Expressions.
13. Graphs, Slope, and Applications.
The Slope-Intercept Equation.
Graphing Using the Slope and the y-Intercept.
Parallel and Perpendicular Lines.
Graphing Inequalities in Two Variables.
Direct and Inverse Variation.
14. Systems of Equations.
Systems of Equations in Two Variables.
The Substitution Method.
The Elimination Method.
Applications and Problem Solving.
Applications with Motion.
15. Radical Expressions and Equations.
Introduction to Radical Expressions.
Multiplying and Simplifying with Radical Expressions.
Quotients Involving Radical Expressions.
Addition, Subtraction, and More Multiplication.
Radical Equations.
Applications with Right Triangles.
16. Quadratic Equations.
Introduction to Quadratic Equations.
Solving Quadratic Equations by Completing the Square.
The Quadratic Formula.
Formulas.
Applications and Problem Solving.
Graphs of Quadratic Equations.
Functions.
Appendix A. Linear Measures: American and Metric.
Appendix B. Weight and Mass; Medical Applications.
Appendix C. Capacity; Medical Applications.
Appendix D. Time and Temperature.
Appendix E. Sets.
Appendix F. Factoring Sums or Differences of Cubes.
Appendix G. Equations Involving Absolute Value.
Appendix H. The Distance Formula and Midpoints.
Appendix I. Higher Roots, and Rational Numbers as Exponents.
Appendix J. Nonlinear Inequalities.
Appendix K. Systems of Linear Inequalities.
Appendix L. Probability.
Appendix M. Applying Reasoning Skills.
Appendix N. Multi-step Applied Problems.
Appendix O. TASP Practice Test.
