AP® Calculus AB

AP® Calculus AB

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Some basics about AP Calculus AB:

This course provides an in-depth study of differential and integral calculus. Students will explore topics in the AP syllabus such as rules of differentiation, techniques of integration, and applications of the integral. Students should be ready to take the AB Calculus exam at the end of this course.

Topics covered include:

Differential Calculus

  • Techniques for evaluating the limits of a function, including limits at infinity-horizontal asymptotes
  • Continuity
  • Derivative of a function
  • Rules of differentiation: product, quotient, chain, implicit
  • Exponential growth and decay
  • Related rates
  • Linear Approximations and Differentials
  • Applications of the Derivative: MVT, L’Hopital’s Rule, curve sketching, optimization problems

Integral Calculus

  • Summation formulas and area as the limit of the sums of areas of rectangle
  • The definite integral
  • The fundamental theorem of calculus
  • The indefinite integral
  • Substitution rule
  • Applications of the Integral: MVT for integrals, average value of a function, area under a curve, area between curves, volume by disk and washer method, volume by cross-section (or “slicing”)

Typical problem areas include:

  • Derivatives of “special” functions (trig, log, exponential, etc) and how to apply them.
  • Working with the chain rule
  • Substitution method for evaluating an integral

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