Developmental Mathematics/TASP

(Each chapter ends with Summary and Review Exercises and Test.)

1. Operations on the Whole Numbers.


Pretest.



Standard Notation; Order.



Addition and Subtraction; Estimation.



Multiplication and Division.



Solving Equations.



Applications and Problem Solving.



Exponential Notation and Order of Operations.



Factorizations.



Divisibility.



Least Common Multiples.



2. Fractional Notation.


Pretest.



Fractional Notation and Simplifying.



Multiplication, Division, and Applications; Order.



Addition, Subtraction, and Applications; Order.



Mixed Numerals.



Applications and Problem Solving.



Order of Operations; Estimation.



3. Decimal Notation.


Pretest.



Decimal Notation, Order, and Rounding.



Addition and Subtraction with Decimal Notation.



Multiplication with Decimal Notation.



Division with Decimal Notation.



Converting from Fractional Notation to Decimal Notation.



Estimating.



Applications and Problem Solving.



4. Percent Notation.


Pretest.



Ratio and Proportion.



Percent Notation.



Percent Notation and Fractional Notation.



Solving Percent Problems Using Equations.



Solving Percent Problems Using Proportions.



Applications of Percent.



Consumer Applications.



5. Data Analysis, Graphs, and Statistics.


Pretest.



Averages, Medians, and Modes.



Tables and Pictographs.



Bar Graphs and Line Graphs.



Circle Graphs.



Data Analysis and Predictions.



6. Geometry.


Pretest.



Basic Geometric Figures.



Perimeter.



Area: Rectangles and Squares.



Area: Parallelograms, Triangles, and Trapezoids.



Circles.



Volume and Surface Area.



Relationship Between Angle Measures.



Congruent Triangles and Properties of Parallelograms.



Similar Triangles.



7. Introduction to Real Numbers and Algebraic Expressions.


Pretest.



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.


Pretest.



Solving Equations: The Addition Principle.



Solving Equations: The Multiplication Principle.



Using the Principles Together.



Applications and Problem Solving.



Applications with Percents.



Formulas.



Solving Inequalities.



Applications and Problem Solving Inequalities.



9. Graphs of Equations: Data Analysis.


Pretest.



Graphs and Applications.



Graphing Linear Equations.



More with Graphing and Intercepts.



Applications and Data Analysis with Graphs.



10. Polynomials: Operations.


Pretest.



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.


Pretest.



Introduction to Factoring.



Factoring Trinomials of the Type x2 + bx + c.



Factoring ax2 + bx + c, a Ö 1, Using FOIL.



Factoring ax2 + bx + c, a Ö 1, Using Grouping.



Factoring Trinomial Squares and Differences of Squares.



Factoring: A General Strategy.



Solving Quadratic Equations by Factoring.



Applications and Problem Solving.



12. Rational Expressions and Equations.


Pretest.



Multiplying and Simplifying Rational Expressions.



Division and Reciprocals.



Least Common Multiples and Denominators.



Adding Rational Expressions.



Subtracting Rational Expressions.



Solving Rational Expressions.



Applications, Proportions, and Problem Solving.



Formulas and Applications.



Complex Rational Expressions.



13. Graphs, Slope, and Applications.


Pretest.



Slope and Applications.



Equations of Lines.



Parallel and Perpendicular Lines.



Graphing Inequalities in Two Variables.



Direct and Inverse Variation.



14. Systems of Equations.


Pretest.



Systems of Equations in Two Variables.



The Substitution Method.



The Elimination Method.



Applications and Problem Solving.



Applications with Motion.



15. Radical Expressions and Equations.


Pretest.



Introduction to Square Roots and Radical Expressions.



Multiplying and Simplifying with Radical Expressions.



Quotients Involving Square Roots.



Addition, Subtraction, and More Multiplication.



Radical Expressions.



Applications and Right Triangles.



16. Quadratic Equations.


Pretest.



Introduction to Quadratic Equations.



Solving Quadratic Equations by Completing the Square.



The Quadratic Formula.



Formulas.



Applications and Problem Solving.



Graphs of Quadratic Functions.



Functions.



Appendixes.


Appendix A: Linear Measures: American and Metric.



Appendix B: Capacity, Weight, Mass, and Time.



Appendix C: Factoring Sums or Differences of Cubes.



Appendix D: Equations Involving Absolute Value.



Appendix E: The Distance Formula and Midpoints.



Appendix F: Higher Roots, and Rational Numbers as Exponents.



Appendix G: Nonlinear Inequalities.



Appendix H: Systems of Linear Inequalities.



Appendix I: Probability.



Appendix J: Applying Reasoning Skills.



Appendix K: Multi-Step Applications.



Appendix L: Sample TASP Exam.