AP Calculus AB

Advanced Placement Calculus AB covering limits, derivatives, and integrals.

Understanding LimitsIntroduction to DerivativesIntroduction to Integrals
Continuity and Types of DiscontinuitiesThe Chain Rule and Implicit DifferentiationFundamental Theorem of Calculus
Modeling Motion and VelocityApplications in Economics and BiologyEngineering and Technology Applications
Multiple Choice MasteryFree Response SuccessTime Management for the Exam
Understanding LimitsIntroduction to Deri...Introduction to Inte...Continuity and Types...The Chain Rule and I...Fundamental Theorem ...Modeling Motion and ...Applications in Econ...Engineering and Tech...Multiple Choice Mast...Free Response Succes...Time Management for ...
Practical Applications

Applications in Economics and Biology

Calculus in the Real World

Calculus models everything from profits in business to populations in nature!

Economics

  • Marginal Cost/Revenue: Derivatives show how cost or revenue changes with each additional item made or sold.
  • Optimization: Use derivatives to maximize profit or minimize loss.

Biology

  • Population Growth: Integrals predict total population over time, even with changing growth rates.
  • Medicine: Derivatives track how quickly medicine concentration changes in the bloodstream.

Why It Matters

Calculus helps industries make better decisions and scientists understand living systems' behaviors.

Examples

  • Marginal cost, the derivative of the cost function, tells a company whether to make more products.

  • Biologists use integrals to estimate fish populations in a lake over a year.

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Engineering and Technology Applications