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# AP Calculus BC

Want a future in video game engineering, economics, or science? Then this AP Calculus course is for you. Calculus is the mathematical study of change. After taking this course you’ll be able to work with functions in a variety of ways, and be able to use derivatives to solve a variety of problems, which is math-speak for having the skills to build the future of technology. This course features a wide range of readings, simulations, assessments, and more to ensure successful course completion. RECOMMENDED PREREQUISITE: Successful completion of math through Algebra II, Math III and/or Pre-Calculus equivalent.

Basic and On Demand are always open for registration.

Plus courses are created upon request.

## SEMESTER 1

**Unit 1: Review**

- Lines
- Functions and Graphs
- Exponential Functions
- Functions and Logarithms
- Trigonometric Functions

**Unit 2: Limits**

- Finding Limits Graphically and Numerically
- Evaluating Limits Analytically
- One-sided Limits
- Continuity
- InfiniteLimits

**Unit 3: Derivatives**

- The Derivative and the Tangent Line Problem
- Basic Differentiation Rules
- Product and Quotient Rules
- Equations of a Tangent Line
- Velocity and Acceleration
- The Chain Rule
- Implicit Differentiation
- Related Rates - Introduction
- Related Rates - Advanced Examples

**Unit 4: Application of Derivatives**

- Extrema on an Interval
- Extrema on a Closed Interval
- Rolle’s Theorem
- Mean Value Theorem
- Increasing and Decreasing Functions and the First Derivative Test
- Concavity and the Second Derivative Test
- Limits at Infinity
- A Summary of Curve Sketching
- Optimization Problems
- Indeterminate Forms and L’Hospital’s Rule

**Unit 5: Integration**

- Antiderivatives and Indefinite Integration
- Area - Left and Right Side Approximations
- Area - Midpoint and Trapezoidal Approximations
- Riemann Sums and Definite Integrals
- The Fundamental Theorem of Calculus
- Integration by Substitution

**Unit 6: Advanced Functions**

- The Natural Logarithmic Functions: Differentiation
- The Natural Logarithmic Functions: Integration
- Inverse Functions
- Exponential Functions: Differentiation and Integration
- Bases Other Than e and Applications
- Inverse Trigonometric Functions and Differentiation
- Inverse Trigonometric Functions and Integration

## SEMESTER 2

**Unit 7: Application of Integration**

- Slope Fields
- Separation of Variables
- Differential Equations: Growth and Decay

**Unit 8: Area, Volume, and Work**

- Area of a Region Between Two Curves
- Area of a Region Between Two Curves - Advanced Examples
- Volume: The Disc Method
- Solids with Known Cross-sections
- Volume: The Shell Method
- Work

**Unit 9: Integration Rules**

- Integration by Parts
- Arc Length
- Trigonometric Integrals
- Trigonometric Substitution
- Partial Fractions
- Improper Integrals

**Unit 10: Infinite Series**

- Sequences
- Infinite and Geometric Series
- The Integral Test and p-Series
- Comparisons of Series and the Ratio Test
- Alternating Series
- Taylor Polynomials and Approximation
- Power Series
- Representation of Functions by Power Series
- Taylor and Maclaurin Series

**Unit 11: Parametric Equations and Polar Coordinates**

- Parametric Equations
- Differentiation of Parametric Equations
- Polar Coordinates and Polar Graphs
- Polar Form of a Derivative
- Areas in Polar Coordinates

**Unit 12: Vector-Valued Functions**

- Vector-Valued Functions
- Differentiation and Integration of Vector-Valued Functions
- Velocity and Acceleration