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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:
SEMESTER 1
New Unit Collection:
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
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
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
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
SEMESTER 2
New Unit Collection:
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 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
Unit 7: Application of Integration
New Unit Content:
• 7.1 Slope Fields
• 7.2 Separation of Variables
• 7.3 Differential Equations: Growth and Decay
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
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
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