pre-calculus ONLINE 

COURSE OVERVIEW
Course Length: 2 semesters
Course Credit: 1 
​Program: Homeschool Advantage, NFC Academy Teachers
NCAA Approved 
High School Grade: 11-12 
Accredited: Cognia-SACS/CASI, Middle States, FACCS
Pre-Calculus prepares students for calculus and college level math with interactive online lessons and advanced problem solving. Students will explore the purpose of calculus and mathematical analysis while they expand their algebraic knowledge through the realm of trigonometry. With a clear, step-by-step delivery, this online course covers a wide range of mathematical concepts including an in-depth observation of math functions, quadratic inequalities, logarithms, probabilities, and permutation. Lessons are interactive to encourage retention of complex information and provide learning tools to clarify complicated mathematic operations.
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Pre-calculus is a full-year, high school credit course that is intended for the student who has successfully mastered the core algebraic and conceptual geometric concepts covered in the prerequisite courses: Algebra I, Geometry, and Algebra II. The course primarily focuses on the skills and methods of analytic geometry and trigonometry while investigating further relationships in functions, probability, number theory, limits, and the introduction of derivatives.
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Throughout the course, students will explore the following topics: Relations and Functions; Special Functions; Trigonometric Functions; Circular Functions and Graphs; Identities and Functions of Multiple Angles; Application of Trigonometric Functions; Inverse Trigonometric Functions and Polar Coordinates; Quadratic Equations; Probability; Calculus Basics.
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COURSE CONCEPTS & SAMPLES
            Curriculum Focus
  • Relations and Functions: Student Will Examine Functions, Inverses of Functions and Combine Functions to Verify Inverses, as well as Distinguish Between Linear and Quadratic Functions.
  • Functions: Student Will Solve Polynomials Using the Quadratic Theorem, Remainder Theorem and Factor Theorem, Identify Graphs Of Different Polynomial Equations and Inequalities, and Understand Complex Numbers.
  • Trigonometric Functions: Student Will Identify and Solve for Missing Components of Trigonometric Functions, Calculating Trigonometric Values for Different Angles and Relate Degrees to Radians, and Radians to Degrees.
  • Circular Functions and Their Graphs: Student Will Use Parametric Equations With Trigonometric Operations to Model and Solve Problems, and Calculate Amplitude, Period, and Phase Shift for Graphed Trigonometric Functions.
  • Identities and Functions of Multiple Angles: Student Will Simplify Trigonometric Expressions Utilizing Trigonometric Identities, and Double and Half-Angel Formulas, and Combine the Identities and Angle Formulas Learned n this Unit to Prove Trigonometric Relationships.
  • Application of Trigonometric Functions: Student Will Solve Problems Using Trigonometric Functions, and Combine Trigonometric Functions and Vectors to Solve Incline Plane Problems and Navigation Problems.
  • Inverse Trigonometric Functions and Polar Coordinates: Student Will Solve for Unknowns Using Inverse Trigonometric Functions, Recognize Their Graphs, and Convert Equations from Cartesian to Polar Coordinates, and from polar to Cartesian Coordinates.
  • Quadratic Equations: Student Will Identify Properties and Equations of Circles, Ellipses, Parabolas and Hyperbolas, and Calculate Point Rotations and Apply them to Equations.
  • Counting Principles: Student Will Distinguish between Mutually Exclusive, Independent and Dependent Events, and Between Combination and Permutation, and Use the Explicit Formula and the Recursive Formula to Find the Nth Term as well as the General Term of an Arithmetic Sequence, rr Geometric Sequence.
  • Calculus: Student Will Solve Functions Involving Numbers and Conditions, Understand Limit Notation, and Evaluate Limits Using the Limit Theorems, and Find the Slope of Curves, and Calculate the Angle Between Two Curves.
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