Reason 4

They believe grades are everything

Yes, grades are very important. Yes, better grades can make your life now AND in the future better and more enriched and open more doors. BUT ... it's not everything. Students place a ton of pressure on themselves for those high grades and spend tons of time cramming and stressing and not sleeping. Instead, focus your attention when you can online ... not when you're made to according to your class schedule. 

Module 2

Polynomials

Polynomials is another basic foundation for Calculus but also of what you have previously studied.  We will expand on our understanding of polynomials to refine the meaning for complex numbers, zeros, extrema, and theorems such as the fundamental theorem of Algebra.  Our understanding of polynomials will help us later by making  connections to other continuous functions in Pre-Calculus and Calculus.

Module Highlights:

• Characteristics of Polynomials  - Explain the importance of knowing we have a polynomial and the properties that make polynomials so unique
• Binomial expansion - Investigate the different ways we can represent polynomials and their forms by using binomial expansion as well as completing the square
• Real Zeros of Polynomials - Make clear what is a zero, solution and root to a polynomials and what does that tell us about the polynomial
• Irrational Zeros of Polynomials - Use our understanding of irrational numbers to apply to the zeros of polynomials by using division and factoring
• Complex Zeros of Polynomials - Learn how complex numbers fit inside of our understanding with polynomials functions and how we can apply them to understand important theorems

Module 3

Rational Functions

Nobody really likes fractions but then when you add polynomials into the mix it gets even more confusing.  Fortunately we have an understanding of functions and polynomials to this point so understanding the graph, domain and operations of functions makes everything just a little bit easier. Rational functions also help us redefine our understanding for asymptotes which will be used throughout the curriculum.

Module Highlights:

• Simplify Rational Expressions - Learn the difference between an asymptote and a hole and how to identify them with simplifying rational expressions including complex fractions
• Graph Rational Functions - Graph rational expressions using your understanding of asymptotes, holes, zeros and intercepts
• Solve Rational Expressions - Find the values that make a rational expression true but using what we know about solutions and the graph of a rational equation

Module 4

Trigonometry

Trigonometry is like no other topic we have covered up to this point but we can apply what we previously learned in our unit studying triangles and the relationships of their sides and angles.  In this chapter we will focus on right triangles and how to understand and apply the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent.

Module Highlights:

Curiosity-driven fascinations breaking down the process of how they’ll achieve the promise of the module.

• Right Triangles - Find the missing sides of Right Triangles using the Pythagorean Theorem as well as trigonometric identities SOHCAHTOA
• Angles in Trigonometry - Develop the understanding of an angle in standard form and how the idea of radians, degrees minutes and seconds can be applied
• Angles and Constraints - Understand how constraints can affect the trigonometric ratios when being applied on a coordinate grid
• The Unit Circle - Use your understanding of right triangles, trigonometric ratios and constraints to develop and apply the unit circle
• Graph Sine, Cosine and Tangent - Identify the key components of what makes a trigonometric graph and how those relate to the values on a coordinate grid and unit circle
• Graph Cosecant, Secant, and Cotangent - Make clear the relationship between the graphs of trigonometric functions and their reciprocal counterpart
• Trigonometric Inverses - Apply constraints of functions to understand when to evaluate the inverse of a trigonometric function as well as the properties of its graph

Module 5

Analytic Trigonometry

Analytic Trigonometry takes everything that we have learned in our last chapter and begins to apply our understanding to dive deeper into how the six trigonometric functions are related to one another and with algebra.  Throughout this chapter students will be required to refresh their algebra skills and apply them with trigonometric terms.

Module Highlights: 

• Simplify Identities - Simplify trigonometric expressions to a single number or function by using basic trigonometric identities and algebraic techniques
• Verify Identities - Apply trigonometric identities as well as algebraic techniques to simplify one side of an identity to verify it is the same as the other
• Solve Trigonometric Equations - Find the solutions to a trigonometric equation using algebraic techniques, trigonometric identities and our understanding of the unit circle as well as the graphs of each trigonometric function
• Sum and Difference Formulas - Learn how to simplify, verify, solve and evaluate using the sum and difference formulas for sine, cosine and tangent

• Double and Half Angle Formulas - Learn how to simplify, verify, solve and evaluate using the sum and difference formulas for sine, cosine and tangent

Module 6

Applications of Trigonometry

Applications of trigonometry moves our understanding of trigonometry into the real word with applications that will help students explore the possibilities of what they have been learning through multiple word problems in each chapter.

Module Highlights:

• Word Problems in Trigonometry - Apply basic evaluating trigonometric functions and their inverse functions to find the missing side of a right triangle given a word problem
• Law of Sines - Explore how to find the missing sides of a triangle when given an oblique triangle and when the information provided gives the ambiguous case
• Law of Cosines - Use the law of sines and cosines to find all the missing sides of an oblique triangle as well as determine the area of an oblique triangle
• Vectors on a Plane - Learn the basics of vector operations such as graphing, magnitude, and the unit vector to better understand the importance of vectors
• Applications of Vectors - Apply your understanding of vectors and their different forms to solve word problems using vectors as well as apply the dot product
• Parametric Equations - Take previously understood functions and describe them as separate functions based on a variable called the parameter
• Polar Equations - Develop a new understanding for points and equations on a coordinate grid using the angle and distance from the origin

Module 7

Conic Sections

Conic sections expand on the lessons from parametric and polar equations to understand equations that are not functions.  We do this by understanding the graphs of conic sections and different ways we can slice a cone.

Module Highlights: 

• Classifying Conic Sections - Classify the type of conic sections given the equation in standard and general form by completing the square and inspection
• The Parabola - Determine the parts of a parabola to help sketch its graph as well as write the equation in standard and general form
• The Ellipse - Determine the parts of an ellipse to help sketch its graph as well as write the equation in standard and general form
• The Hyperbola - Determine the parts of a hyperbola to help sketch its graph as well as write the equation in standard and general form

Module 8

The Limit

The limit is our introduction into Calculus.  We will spend a little bit of time understanding the idea and purpose of the limit but mainly focus our attention on the different methods to evaluate the limit based on the techniques we have learned in this course.

Module Highlights:

• The General Limit - Develop your understanding of the general limit by using a table of values, direct substitution and a graph
• Left and Right Hand Limits - Use your understanding of the general limit to further evaluate the left and right hand limits algebraically and from a graph
• Limits at Infinity - Apply your understanding of vertical and horizontal asymptotes and end behavior to evaluate the limit at positive and negative infinity