Investigating College Algebra and Trigonometry with Technology
June 2008, ©2006
The American Mathematical Association of Two-Year Colleges (AMATYC) and the Mathematical Association of America’s Committee on Undergraduate Programs in Mathematics (CUPM) set standards for meaningful and relevant mathematics and the refocusing of the College Algebra and Trigonometry course. This text follows their recommendations for using technology, experiencing varied applications of mathematics, and having opportunities to solve problems, reason critically, exhibit persistence, and test conjectures through investigations and data analysis.
To the Student.
To the Instructor.
Chapter 1. Problem Solving.
1.1 Pictures, Graphs, and Diagrams.
1.2 Symbolic Representation.
1.3 Organizing Information.
1.4 Measures of Central Tendency and Box Plots.
1.5 Measures of Spread.
Chapter 1 Review.
Chapter 2. Patterns and Recursion.
2.1 Recursively Defined Sequences.
2.2 Modeling Growth and Decay.
2.3 A First Look at Limits.
2.4 Graphing and Sequences.
2.5 Loans and Investments.
Chapter 2 Review.
Chapter 3. Linear Models and Systems.
3.1 Linear Equations.
3.2 Revisiting Slope.
3.3 Fitting a Line to Data.
3.4 Linear Systems.
3.5 Substitution and Elimination.
Chapter 3 Review.
Chapter 4. Functions, Relations, and Transformations.
4.1 Interpreting Graphs.
4.2 Function Notation.
4.3 Lines in Motion.
4.4 Translations and the Quadratic Family.
4.5 Reflections and the Square Root Family.
4.6 Stretches and Shrinks and the Absolute Value Family.
4.7 Transformations and the Circle Family.
4.8 Compositions of Functions.
Chapter 4 Review.
Chapter 5. Exponential, Power, and Logarithmic Functions.
5.1 The Exponential Function.
5.2 Properties of Exponents.
5.3 Fractional Exponents and Roots.
5.4 Applications of Power Equations.
5.5 Building Inverses of Functions.
5.6 The Logarithmic Function.
5.7 Properties of Logarithms.
5.8 Applications of Logarithms.
Chapter 5 Review.
Chapter 6. Quadratic and Other Polynomial Functions.
6.1 Polynomial Degree and Finite Differences.
6.2 Equivalent Quadratic Forms.
6.3 Completing the Square.
6.4 The Quadratic Formula.
6.5 Complex Numbers.
6.6 Factoring Polynomials.
6.7 Higher-Degree Polynomials.
6.8 More about Finding Solutions.
Chapter 6 Review.
Chapter 7. Matrices and Linear Systems.
7.1 Matrix Representations.
7.2 Matrix Operations.
7.3 The Row Reduction Method.
7.4 Solving Systems with Inverse Matrices.
7.5 Systems of Linear Inequalities.
7.6 Linear Programming.
Chapter 7 Review.
Chapter 8. Parametric Equations and Trigonometry.
8.1 Graphing Parametric Equations.
8.2 Converting Parametric to Nonparametric Equations.
8.3 Right Triangle Trigonometry.
8.4 Using Trigonometry to Set a Course.
8.5 Projectile Motion.
8.6 The Law of Sines.
8.7 The Law of Cosines.
Chapter 8 Review.
Chapter 9. Conic Sections and Rational Functions.
9.1 Using the Distance Formula.
9.2 Circles and Ellipses.
9.4 The Hyperbola.
9.5 Nonlinear Systems of Equations.
9.6 Introduction to Rational Functions.
9.7 Graphs of Rational Functions.
9.8 Operations with Rational Expressions.
Chapter 9 Review.
Chapter 10. Series.
10.1 Arithmetic Series.
10.2 Infinite Geometric Series.
10.3 Partial Sums of Geometric Series.
Chapter 10 Review.
Chapter 11. Probability.
11.1 Randomness and Probability.
11.2 Counting Outcomes and Tree Diagrams.
11.3 Mutually Exclusive Events and Venn Diagrams.
11.4 Random Variables and Expected Value.
11.5 Permutations and Probability.
11.6 Combinations and Probability.
11.7 The Binomial Theorem and Pascal’s Triangle.
Chapter 11 Review.
Chapter 12. Trigonometric Functions (on the Student CD).
12.1 Defining the Circular Function.
12.2 Radian Measure and Arc Length.
12.3 Graphing Trigonometric Functions.
12.4 Inverses of Trigonometric Functions.
12.5 Polar Coordinates.
Chapter 12 Review.
Chapter 13. Trigonometric Identities (on the Student CD).
13.1 Fundamental Trigonometric Identities.
13.2 Sum and Difference Identities.
13.3 Double- and Half-Angle Identities.
13.4 Modeling with Trigonometric Equations.
13.5 Solving Trigonometric Equations.
Chapter 13 Review.
Resources on the Student CD.
Prerequisite Review: Numbers and Figures • Operations on Numbers •
The Ideas that Motivate Algebra • Exponents • Radicals • Polynomials •
Factoring Polynomials • Rational Expressions.
Chapter 12 Trigonometric Functions.
Chapter 13 Trigonometric Identities.
Microsoft® Excel Notes.
Interactive Spreadsheets for Excel Explorations.
- Discovery-based Investigations provide in-depth contextual content, real-life data, and the integration of technology to let students explore a problem before solving it
Students analyze data, which they are given or gather themselves, to make sense of the mathematical relationships they observe
Examples are fully worked out and include reasons that justify the process
Support the use of graphing calculators, which let students easily manipulate large amounts of data and see the “big picture” of the math being used
Optional interactive Explorations, included on the Student CD, use Microsoft® Excel to build spreadsheets for Activities in which students investigate algebra concepts