PRE-CALCULUS

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Course Code:
Honors Course Code: 1202340
AP Course Code:
Description:

This is a serious course for serious students. The kind of students who want to develop the skills needed for advancing to calculus. Although many things in life involve relatively simple systems, there are many complex and nonlinear processes that reveal a more complete picture of our world. That is what you’ll find here.

We’ll use our national parks as the setting for examining these complex processes. Plotting and projecting the population of park wolves is typical of the complexities encountered when park administrators make policy decisions. Fortunately, the kind of tools presented in this course can help. You’ll learn about functions, matrix algebra, and sequences and series. You’ll also acquire the confidence to think like a mathematician, finding logic and order in a complex world.

This course will require motivation, dedication and lots of hard work. You’ll be joined in this endeavor by your instructor and fellow students. If you are a serious student, you have come to the right place.

Prerequisites: Algebra I, Geometry, and Algebra II.

Estimated Completion Time: 2 segments / 32-36 weeks or 1 block/18 weeks

Major Topics and Concepts:

Segment 1

* Functions
* Domain and range
* Rigid and non-rigid transformations
* Composition and arithmetic of functions
* Function inverses
* Linear regression
* Solve and graph quadratic functions
* Characteristics of a polynomial function
* Rational Root Theorem, long and synthetic division, Fundamental Theorem of Algebra
* Complex numbers as solutions to polynomial equations
* Domain and the asymptotes of a rational function
* Analyze and graph a rational function
* Analyze and graph the exponential function
* Analyze and graph the logarithmic function
* Properties of logarithms
* Exponential and logarithmic equations
* Regression equations of non-linear data
* Angles in radians and degrees
* Define the trigonometric functions using the coordinates of a unit circle and using a right triangle
* Evaluate the trigonometric function values of any angle measure
* Analyze and graph sine, cosine and tangent functions
* Inverse trigonometric values
* Solve right-triangle real-world problems
* Evaluate trigonometric values using identities
* Prove that a given equation is an identity
* Solve equations that contain trigonometric functions
* Use argument identities

Segment 2

* Use the Law of Sines and Law of Cosines to solve a triangle, including the ambiguous case
* Find the area of the triangle including Hero’s formula
* Vector arithmetic including the dot product
* Arithmetic of Complex numbers using Vectors and DeMoivre’s Theorem
* Gauss-Jordan elimination to solve systems of equations
* Add, subtract and multiply matrices
* Inverse of a matrix to solve a system of equations
* Determinant of a matrix and Cramer's Rule to solve a system of equations
* Terms of a sequence, sigma notation
* Arithmetic sequences and series
* Geometric sequences and series
* Proof by Mathematical Induction
* Analyze and graph equations that produce parabolas, ellipses and hyperbolas
* Analyze degenerate conic sections
* Solve systems of quadratics
* Parametric equations and graphs and conversion to rectangular form
* Domain and range of parametric equations
* Plotting points in the polar system
* Graphing polar equations
* Find limits graphically and numerically

Course Assessment and
Participation Requirements:

Besides engaging students in challenging curriculum, VLACS guides students to reflect on their learning and to evaluate their progress through a variety of assessments. Assessments can be in the form of self-checks, practice lessons, multiple choice questions, writing assignments, graphing calculator labs, oral assessments, and discussions. Instructors evaluate progress and provide interventions through the variety of assessments built into a course, as well as through contact with the student in other venues.