AP Calculus BC

Summer Courses:

Advanced Courses

AP Calculus BC

Grade Level:
Grade 9-12
Course Dates:
July 17-28
Course Pricing:
  • $810
Course Logistics:
Duration: 180 minutes (3 hours)
Number of Classes : 10 Classes
Occurs: Weekdays (1:30pm-4:30pm)
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Course Topics:

Course Topics are organized as six modules with five granular topics covered under each module. If a summer course offers sessions A and B, please note both sessions will cover the same content as described below. Click through below to see all modules/topics for this course.

01 - Limits/Derivatives

  • Limit and Derivative Rules (multiplication/division)
  • Continuity, Limits with infinity, L'Hôpital's Rule
  • Derivatives of Trigonometric and Exponential/Logarithmic Functions
  • The Chain Rule, Related Rates, Higher Order Derivatives
  • Implicit and Logarithmic Differentiation

02 - Evaluating Integrals

  • Riemann Sums
  • Integration by Substitution, Trigonometric Substitutions
  • Integration by Parts
  • Partial Fraction Decomposition
  • Improper Integrals and Definite Integral Manipulations

03 - Applications of Integration

  • Average Value of a function, Mean Value Theorem, Intermediate Value Theorem
  • Areas of Bounded Regions
  • Solids of Revolution, Solids with Cross Sections
  • Arc Length
  • Moment of Inertia

04 - Differential Equations

  • Introducing Differential Equations
  • Euler's Method of Approximations and Slope Fields
  • Solving Separable Differential Equations
  • Logistic and Exponential Functions
  • Modeling / Population Growth

05 - Parametric and Polar

  • Derivatives of Parametric and Vector Valued Functions
  • Accumulation of Change with Definite Integrals, Integration to find position of a particle
  • Speed, Velocity Vectors, and Acceleration Vectors of a particle
  • Derivatives of Polar Functions, Introduction to finding areas bounded by polar functions
  • Areas of regions bounded by polar curves

06 - Sequences and Series

  • Definition of Convergence, Absolute Convergence, Conditional Convergence with Limits
  • Basis types of series (Geometric, Harmonic, p-series), Convergence and Divergence tests
  • Alternating Series Error Bound, Approximating convergent series
  • Introduction to Taylor and Maclaurin Series, Interval and radius of convergence
  • Taylor's  Theorem, Lagrange Error Bound, Calculating and Manipulating power series with derivatives and integrals
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