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High School Pre-Calculus Honors

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Suggested Prerequisites

Algebra 1, Algebra 2, Geometry

Description

Explore new concepts that will take your math knowledge to new heights. Dive deeper into your knowledge of functions by analyzing their key features and combining them to solve real-world problems. Learn about trigonometric functions and their applications, along with new ways to use the coordinate plane to represent different types of functions. Apply these skills to discover the power mathematics has in everyday life and to prepare for advanced mathematical studies in college or your future career.

Module One: Functions

-Determine key features of different function types

-Interpret key features of different function types

-Solve problems modeled with different function types

-Graph different function types

-Apply functions to real-world contexts

-Determine the constraints from real-world contexts


Module Two: Applications of Functions

-Compare key features of functions

-Solve systems of equations

-Combine functions

-Compose functions

-Determine inverse functions

-Find and apply the difference quotient

-Analyze real-world applications of function combinations


Module Three: Conics

-Derive equations of conic sections

-Determine equations of conic sections

-Determine key features of conic sections

-Interpret key features of conic sections

-Analyze real-world applications of conic sections


Module Four: Sequences and Series

-Determine arithmetic and geometric sequences

-Differentiate between arithmetic and geometric sequences

-Solve problems using formulas for sequences and series

-Solve problems using summation notation

-Analyze real-world applications of sequences and series

Module Five: Trigonometry

-Define trigonometric functions

-Convert angle measures between degrees and radians

-Differentiate between reference angles and coterminal angles

-Apply the Laws of Sines and Cosines

-Determine the values on the unit circle

-Verify trigonometric functions using the unit circle

-Apply technology with trigonometric functions

-Graph trigonometric functions

-Determine key features of trigonometric functions

-Analyze real-world applications of trigonometric functions


Module Six: Trigonometric Identities and Formulas

-Prove and apply Pythagorean identities

-Simplify expressions using trigonometric identities

-Prove angle formulas for sine, cosine, and tangent

-Apply angle formulas for sine, cosine, and tangent

-Solve trigonometric equations

-Analyze real-world applications of trigonometric equations


Module Seven: Vectors

-Define vectors using magnitude and direction

-Represent vectors in different forms

-Perform operations on vectors algebraically and graphically

-Apply the dot product to solve problems

-Apply vector projections to solve problems

-Analyze properties of vector scalar multiples

-Analyze real-world applications of vectors


Module Eight: Analyzing the Coordinate Plane

-Define and plot polar coordinates

-Convert coordinates between polar and rectangular forms

-Graph polar equations

-Represent complex numbers using polar and rectangular coordinates

-Calculate distance on the complex coordinate plane

-Multiply complex numbers in trigonometric form

-Analyze real-world applications of complex numbers

-Graph parametric equations

-Convert between parametric and rectangular equations

-Analyze real-world applications of parametric equationsÂ