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Syllabus Title: 
AP Calculus BC
Syllabus Description: 

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. Prerequisite: Successful completion of Pre-Calculus OR AP Calculus AB OR equivalent.

Collection Semester: 
New Semester Heading: 
SEMESTER 1
New Unit Collection: 
New Unit Heading: 
Unit 1: Review
New Unit Content: 
  • 1.1 Lines
  • 1.2 Functions and Graphs
  • 1.3 Exponential Functions
  • 1.4 Functions and Logarithms
  • 1.5 Trigonometric Functions
New Unit Heading: 
Unit 2: Limits
New Unit Content: 
  • 2.1 Finding Limits Graphically and Numerically
  • 2.2 Evaluating Limits Analytically
  • 2.3 One-sided Limits
  • 2.4 Continuity
  • 2.5 InfiniteLimits
New Unit Heading: 
Unit 3: Derivatives
New Unit Content: 
  • 3.1 The Derivative and the Tangent Line Problem
  • 3.2 Basic Differentiation Rules
  • 3.3 Product and Quotient Rules
  • 3.4 Equations of a Tangent Line
  • 3.5 Velocity and Acceleration
  • 3.6 The Chain Rule
  • 3.7 Implicit Differentiation
  • 3.8 Related Rates - Introduction
  • 3.9 Related Rates - Advanced Examples
New Unit Heading: 
Unit 4: Application of Derivatives
New Unit Content: 
  • 4.1 Extrema on an Interval
  • 4.2 Extrema on a Closed Interval
  • 4.3 Rolle’s Theorem
  • 4.4 Mean Value Theorem
  • 4.5 Increasing and Decreasing Functions and the First Derivative Test
  • 4.6 Concavity and the Second Derivative Test
  • 4.7 Limits at Infinity
  • 4.8 A Summary of Curve Sketching
  • 4.9 Optimization Problems
  • 4.10 Indeterminate Forms and L’Hospital’s Rule
New Semester Heading: 
SEMESTER 2
New Unit Collection: 
New Unit Heading: 
Unit 5: Integration
New Unit Content: 
  • 5.1 Antiderivatives and Indefinite Integration
  • 5.2 Area - Left and Right Side Approximations
  • 5.3 Area - Midpoint and Trapezoidal Approximations
  • 5.4 Riemann Sums and Definite Integrals
  • 5.5 The Fundamental Theorem of Calculus
  • 5.6 Integration by Substitution
New Unit Heading: 
Unit 6: Advanced Functions
New Unit Content: 
  • 6.1 The Natural Logarithmic Functions: Differentiation
  • 6.2 The Natural Logarithmic Functions: Integration
  • 6.3 Inverse Functions
  • 6.4 Exponential Functions: Differentiation and Integration
  • 6.5 Bases Other Than e and Applications
  • 6.6 Inverse Trigonometric Functions and Differentiation
  • 6.7 Inverse Trigonometric Functions and Integration
New Unit Heading: 
Unit 7: Application of Integration
New Unit Content: 
  • 7.1 Slope Fields
  • 7.2 Separation of Variables
  • 7.3 Differential Equations: Growth and Decay
New Unit Heading: 
Unit 8: Area, Volume, and Work
New Unit Content: 
  • 8.1 Area of a Region Between Two Curves
  • 8.2 Area of a Region Between Two Curves - Advanced Examples
  • 8.3 Volume: The Disc Method
  • 8.4 Solids with Known Cross-sections
  • 8.5 Volume: The Shell Method
  • 8.6 Work
New Unit Heading: 
Unit 9: Integration Rules
New Unit Content: 
  • 9.1 Integration by Parts
  • 9.2 Arc Length
  • 9.3 Trigonometric Integrals
  • 9.4 Trigonometric Substitution
  • 9.5 Partial Fractions
  • 9.6 Improper Integrals
New Unit Heading: 
Unit 10: Infinite Series
New Unit Content: 
  • 10.1 Sequences
  • 10.2 Infinite and Geometric Series
  • 10.3 The Integral Test and p-Series
  • 10.4 Comparisons of Series and the Ratio Test
  • 10.5 Alternating Series
  • 10.6 Taylor Polynomials and Approximation
  • 10.7 Power Series
  • 10.8 Representation of Functions by Power Series
  • 10.9 Taylor and Maclaurin Series
New Unit Heading: 
Unit 11: Parametric Equations and Polar Coordinates
New Unit Content: 
  • 11.1 Parametric Equations
  • 11.2 Differentiation of Parametric Equations
  • 11.3 Polar Coordinates and Polar Graphs
  • 11.4 Polar Form of a Derivative
  • 11.5 Areas in Polar Coordinates
New Unit Heading: 
Unit 12: Vector-Valued Functions
New Unit Content: 
  • 12.1 Vector-Valued Functions
  • 12.2 Differentiation and Integration of Vector-Valued Functions
  • 12.3 Velocity and Acceleration