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Mathematics & Statistics

**Prerequisites:** C (2.0) or better in MAC 1105, * or* SAT Math score of 570 or better,

**Course Description:** The course follows the Math Emporium model: Students meet twice a week for 75-minute lectures and must spend 2 hours per week in the SMART Lab. Successful completion of the course merits 4 semester hours of credit and provides sufficient background for the calculus sequences MAC 2281, 2282, 2283 and MAC 2311, 2312, 2313. There are four tests plus a final exam. The final exam is cumulative and all multiple choice.

**Foundations of Knowledge & Learning:** This course is part of the University of South Floridaâ€™s Foundations of Knowledge and Learning (FKL) Core Curriculum. It is certified for Mathematics and Quantitative Reasoning and will meet the following four dimensions: Critical Thinking, Inquiry-based Learning, Scientific Processes, and Quantitative Literacy. Students enrolled in this course will be expected to participate in the USF General Education assessment effort. This might involve answering questions that measure quantitative reasoning skills (but are not directly related to the course), responding to surveys, or participating in other measurements designed to assess the FKL Core Curriculum learning outcomes.

**Text:** *Precalculus: A Unit Circle Approach*, 3rd Edition,

by Ratti, McWaters, and Skrzypek

**Course Content**

**4. Trigonometric Functions** (2.5 weeks)

4.1 Angles and Their Measure

4.2 The Unit Circle: Trigonometric Functions of Real Numbers

4.3 Trigonometric Functions of Angles

4.4 Graphs of the Sine and Cosine Functions

4.5 Graphs of the Other Trigonometric Functions

4.6 Inverse Trigonometric Functions

**5. Analytic Trigonometry** (2 weeks)

5.1 Trigonometric Identities

5.2 Sum and Difference Formulas

5.3 Double-Angle and Half-Angle Formulas

5.4 Product-to-Sum and Sum-to-Product Formulas (omit)

5.5 Trigonometric Equations

**6. Applications of Trigonometric Functions** (2 weeks)

6.1 Right-Triangle Trigonometry

6.2 The Law of Sines

6.3 The Law of Cosines

6.4 Vectors (omit)

6.5 The Dot Product (omit)

6.6 Polar Coordinates

6.7 Polar Form of Complex Numbers: DeMoivre's Theorem (omit)

**7. Systems of Equations and Inequalities** (1 week)

7.1 Systems of Equations in Two Variables

7.2 Systems of Linear Equations in Three Variables

7.3 Systems of Inequalities (omit)

7.4 Matrices and Systems of Equations (omit)

7.5 Determinants and Cramer's Rule (omit)

7.6 Partial-Fraction Decomposition

7.7 Matrix Algebra (omit)

7.8 The Matrix Inverse (omit)

**8. Analytic Geometry** (1.5 weeks)

8.1 Conic Sections: Overview

8.2 The Parabola

8.3 The Ellipse

8.4 The Hyperbola

8.5 Rotation of Axes (omit)

8.6 Polar Equations of Conics (omit)

8.7 Parametric Equations (omit)

**9. Further Topics in Algebra** (2 weeks)

9.1 Sequences and Series

9.2 Arithmetic Sequences: Partial Sums

9.3 Geometric Sequences and Series

9.4 Mathematical Induction (omit)

9.5 The Binomial Theorem

9.6 Counting Principles (omit)

9.7 Probability (omit)

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