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Calculus Bookshelf

Courses: AP Calculus BC

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AP Calculus BC Overview

This course prepares high school students planning to take the Calculus BC Advanced Placement exam. For more information about this exam, please click here.  Students will study the main ideas found in differential calculus: limits, derivatives, and basic integration. By the end of the course, students will be able to demonstrate an adequate understanding of these topics.

 

To be successful in this course, students must be proficient in precalculus. Students may forgo enrolling in a precalculus course provided they have a strong background in algebra 2  and trigonometry. Please review the prerequisite before enrolling in this course. Students will not be able to complete the course without having a strong background in these subjects.

 

The topics discussed in AP Calculus BC are equivalent to the topics discussed at the college level: calculus 1 course and calculus 2. Consequently, this course moves at a faster rate than Calculus AB. Students who take the AP Calculus BC exam will also receive a subscore for the AP Calculus AB exam. When you take the BC exam you will receive AB Calculus subscore. Those who score a 3 on the exam may qualify for college credit for Calculus 1 and Calculus 2, whereas some colleges require at least a 4 on the exam.

Course Description: 

This course prepares high school students planning to take the Calculus BC Advanced Placement exam. For more information about this exam please click here.  Students will study the main ideas found in differential calculus: limits, derivatives, and basic integration. By the end of the course, students will be able to demonstrate an adequate understanding of these topics.


To be successful in this course students must be proficient in precalculus. Students may forgo enrolling in a precalculus course provided they have a strong background in algebra 2  and trigonometry. Please review the prerequisite before enrolling in this course. Students will not be able to complete the course without having a strong background in these subjects.


The topics discussed in AP Calculus BC are equivalent to the topics discussed at the college level: calculus 1 course and calculus 2. Consequently, this course moves at a faster rate than Calculus AB. Students who take the AP Calculus BC exam will also receive a subscore for the AP Calculus AB exam. When you take the BC exam you will receive AB Calculus subscore. Those who score a 3 on the exam may qualify for college credit for Calculus 1 and Calculus 2, whereas some colleges require at least a 4 on the exam.


Prerequisite: Precalculus (Honors) or AP Calculus AB.

Course Topics

  • The idea of a limit
  • Calculating limits
  • Squeeze Theorem
  • Infinite Limits
  • Indeterminate Forms
  • L’Hospital’s Rule
  • Continuity
  • Average Rate of Change
  • Instantaneous Rate of Change
  • Properties of Derivatives
  • Derivatives of Special Functions
    • Trigonometric Functions
    • Exponential Functions
    • Logarithmic Functions
  • The Power Rule
  • The Product Rule
  • The Quotient Rule
  • The Chain Rule
  • Implicit Differentiation
  • Logarithmic Differentiation
  • Inverse Trigonometric Functions
  • Optimization
  • Related Rates, I
  • Related Rates, II
  • Motion
    • Position
    • Velocity
    • Acceleration
  • Linear Approximation
  • Critical Points
  • Monotonicity of Functions
    • Increasing, Decreasing 
  • Inflection Points
  • Concavity
  • Relative and Absolute Extrema
    • First Derivative Test
    • Second Derivative Test
  • Graphing Functions
  • Interpreting Graphs 
  • Antiderivatives
    • Indefinite Integrals
  • Fundamental Theorem of Calculus
    • Definite Integrals 
  • Basic Properties of Integrals
  • Integrals of Basic Functions
  • Integration by substitution
  • Numerical Integration
    • Left-Hand Rule
    • Right-Hand Rule
    • Midpoint Rule
    • Trapezoidal Rule
    • Simpson’s Rule
  • The Area of an Enclosed Region
    • Vertical Simple Regions
    • Horizontal Simple Regions
  • The Average Value of a Function
  • Volumes
    • Disk/Washer Method
    • Shell Method
    • Non-rotational Symmetries
      • Cross-sections
  • Separable Differential Equations
  • Graphing and Understanding Slope Fields
  • Growth and Decay Problems
  • U-Substitution
  • Integration By Parts
  • Trigonometric Integrals
  • Trigonometric Substitution
  • Partial Fractions
  • Improper Integrals
  • Numerical Integration
    • Left-Hand Rule
    • Right-Hand Rule
    • Midpoint Rule
    • Trapezoidal Rule
    • Simpson’s Rule
  • Area Under a Curve
  • Volume
    • Disk/Washer Method
    • Shell Method
    • Non-rotational symmetries
  • Arc Length
  • Surface Area
  • Applications to Physics
    • Work
    • Hydrostatic Pressure
    • Centers of Mass
  • Probability
  • Economics
  • Sequences
    • Monotone and Bounded
    • Sequences
  • Series Structures
    • Geometric Series
    • Telescopic Series
  • Convergence Tests
    • Divergence Theorem
    • Direct Comparision Test
    • Limit Comparision Test
    • Integral Test
    • Ratio and Root Test
    • Alternating Series
  • Radius of Convergence
  • Interval of Convergence
  • Taylor Polynomials
  • Taylor Series
  • Function Representations
  • Power Series Operations
  • Parametric Descriptions
    • Graphing Curves
    • Eliminating Variables
  • Calculus of Parametric Equations
    • Tangent Lines
    • Parametric Areas
    • Parametric Arc Length
    • Parametric Surface Area
  • Polar Curves
  • Graphing 
  • Symmetry
  • Tangent Lines
  • Polar Area
  • Polar Arc Length

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