# Modules

The segments of each module are as follows.

**Module A: Basics of Algebra and Solving Equations**

Solving Polynomial Equations; Solving Equations with Rational Expressions; Solving Equations with Radical Expressions; Solving Inequalities; Solving a System of Equations

** Module 1: Basics of Calculus Readiness**

Algebraic Readiness for Calculus; Understanding of Functions; Composition of Functions; Graphs of Typical Functions; Transformations of Functions

** Module 2: Fundamentals of Trigonometry **

Circular Definition of the Trig Functions; Trigonometric Identities and Relationships*; Graphs of Sine, Cosine, and Tangent Functions; Transformations of the Graphs of Trigonometric Functions; The Graphs of Reciprocal Trigonometric Functions; Use of Inverse Trigonometric Functions*; Applications of Right Triangle Trigonometry; Areas of Triangles and the Laws of Sines and Cosines; Solving Trigonometric Equations*

** Module 3: Modeling with Mathematics **

Translating Common Situations to Mathematical Equations or Inequalities to Solve; Creating Functions That Model a Situation and Interpreting Their Graphs; Identifying Extreme Values of a Situation Based on the Graph of a Modeling Function; Translating Problems Involving Rates into Mathematical Models

** Module 4: The Foothills of Calculus **

The Limit of a Function as x Approaches a Constant; The Limit of a Function as x Approaches Infinity; Recognizing the Continuity of a Function at a Point or Over an Interval: Identifying Vertical and Horizontal Asymptotes; Average versus Instantaneous Rate of Change of a Function; The Definition of the Derivative of a Function including Sine and Cosine*; Tangent Lines*

** Module 5*: Beyond Calculus Readiness **

The Power Rule, Product Rule, and Quotient Rules for Derivatives; The Chain Rule for Differentiating a Composition of Functions; Finding Extreme Values of a Function; The Mean Value Theorem; Implicit Differentiation; Solving Related Rate Problems

** Module 6*: Getting Ahead in Calculus **

Finding Antiderivatives; U-substitution; The Fundamental Theorem of Calculus; Applications Making Use of Definite Integrals; Approximating the Area under a Curve; Finding the Exact Value of the Area Bounded by Two Curves;

** Module 7: The Foothills of Calculus II **

Working with Expressions & Equations Involving Exponential Functions; Inverse Functions; Understanding the Logarithm as an Inverse to Use When Solving an Exponential Equation; Understanding Exponential Functions; The Logarithm Function as an Inverse Function

** Module 8: Getting Ahead in Calculus II **

Derivatives & Integrals including Exponential Functions; Derivatives & Integrals including Logarithmic Functions; Derivatives & Integrals including Inverse Trigonometric Functions; Sigma Notation; Geometric Sequences & Series