**Pre-Calculus/Pre-CalculusDownload PDF Honors**

**Credit Hours: 1.0**

**Course Length: 2 Semesters**

**Course Description**

The purpose of this course is to investigate the major topics in Precalculus and to prepare students to continue on to Calculus. After completing this course, students will understand polynomial functions, polar coordinates, complex numbers, conic sections, exponential functions, logarithmic functions, sequences, and series. The second semester introduces students to the concepts of trigonometry. Students will learn about the basic trigonometric functions and how to graph these functions. Students will also learn how to solve right triangles and how to use Law of Sines and Law of Cosines. Students will also explore how these concepts connect to real-world applications.

The honors level course requires students to utilize higher order thinking skills such as analysis and synthesis while completing more rigorous assignments. In addition, more emphasis is placed on research mastery and project based learning.

**Course Objectives**

- Understand the major topics in Precalculus.
- Identify how the Precalculus topics relate to real-world situations.
- Apply the topics in Precalculus to solve problems.
- Explain how Precalculus is used within the greater study of mathematics.
- Identify properties of and perform operations on polynomial and rational functions.
- Analyze graphs, determine inverse functions, and solve systems of inequalities.
- Graph, analyze, and apply trigonometric functions.
- Identify and apply trigonometric identities to solve equations and inequalities.

**Course Prerequisites**

Algebra II

**Required Textbook(s) and/or Materials**

None

**Course Outline**

**Module I: Introduction to Precalculus and Polynomial Functions**

- Section 1 – Introduction to Precalculus
- Section 2 – Polynomial Functions: Introduction
- Section 3 – Polynomial Functions
- Section 4 – Quadratic Functions
- Section 5 – Roots of Polynomial Equations
- Section 6 – Rational Equations and Radical Equations
- Section 7 – Introduction to Precalculus and Polynomial Functions Unit Review

**Module II: Polar Form of Complex Numbers**

- Section 1 – Polar Form of Complex Numbers: Introduction
- Section 2 – The Polar Coordinate System
- Section 3 – Polar and Rectangular Form
- Section 4 – Operations with Complex Numbers
- Section 5 – Polar Form of Complex Numbers
- Section 6 – Polar Form of Complex Numbers Unit Review

**Module III: Conic Sections**

- Section 1 – Conic Sections: Introduction
- Section 2 – Conic Sections
- Section 3 – Circles
- Section 4 – Ellipses
- Section 5 – Hyperbolas
- Section 6 – Parabolas
- Section 7 – Conic Sections Unit Review

**Module IV: Exponents and Logarithms**

- Section 1 – Exponents and Logarithms: Introduction
- Section 2 – Exponential Functions
- Section 3 – Logarithmic Functions
- Section 4 – Exponents and Logarithms Unit Review

**Module V: Discrete Mathematics**

- Section 1 – Discrete Mathematics: Introduction
- Section 2 – Discrete Mathematics
- Section 3 – Sequences and Series: Terms, Sums, and Limits
- Section 4 – Sequences and Series: Convergence, Divergence, and Applications
- Section 5 – Discrete Mathematics Unit Review

**Semester 1 Exam**

**Module VI: Introduction to Trigonometry – Linear Relationships and Functions**

- Section 1 – Introduction to Trigonometry
- Section 2 – Introduction to Trigonometry: Linear Relationships and Functions
- Section 3 – Relations, Functions, and Graphs
- Section 4 – Slope, Linear Relations, Scatter Plots, and Piecewise Functions
- Section 4 – Introduction to Trigonometry: Linear Relationships and Functions Unit Review

**Module VII: Trigonometric Ratios**

- Section 1 – Trigonometric Ratios
- Section 2 – Angles and Angle Measures
- Section 3 – Right Triangles and Trigonometric Ratios
- Section 4 – The Unit Circle
- Section 5 – Trigonometric Ratios Unit Review

**Module VIII: Graphing Trigonometric Functions**

- Section 1 – Introduction to Graphing Trigonometric Functions
- Section 2 – Graphing Trigonometric Functions
- Section 3 – Transformations of Trigonometric Functions
- Section 4 – Real-world Applications of Trigonometric Functions
- Section 5 – Vectors
- Section 6 – Graphing Trigonometric Functions Unit Review

**Module IX: Trigonometric Laws and Identities**

- Section 1 – Trigonometric Laws and Identities
- Section 2 – Law of Sines and Law of Cosines
- Section 3 – Trigonometric Identities and Equations
- Section 4 – Area of Triangles
- Section 5 – Angular and Linear Velocities
- Section 6 – Trigonometric Laws and Identities Unit Review