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Stuff you MUST know Cold for the AP Calculus Exam

Prepare for the AP Calculus Exam with these essential concepts! Understand curve sketching techniques, including analyzing critical points, local extrema, and points of inflection. Learn about the Fundamental Theorem of Calculus, Mean Value Theorem, and various differentiation rules. This guide covers derivatives, integrals, and methods for approximation using the Trapezoidal Rule. Additionally, master the basics of trigonometric functions and their values at common angles. Don't miss out on key information to excel in your exam!

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Stuff you MUST know Cold for the AP Calculus Exam

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  1. Stuff you MUST know Cold for the AP Calculus Exam

  2. Curve sketching and analysis y = f(x) must be continuous at each: • critical point: = 0 or undefined. And don’t forget endpoints • local minimum: goes (–,0,+) or (–,und,+) or > 0 • local maximum: goes (+,0,–) or (+,und,–) or < 0 • point of inflection: concavity changes goes from (+,0,–), (–,0,+), (+,und,–), or (–,und,+)

  3. Basic Derivatives

  4. Basic Integrals Plus a CONSTANT

  5. Some more handy integrals

  6. More Derivatives Recall “change of base”

  7. Differentiation Rules Chain Rule Product Rule Quotient Rule

  8. The Fundamental Theorem of Calculus Corollary to FTC

  9. Intermediate Value Theorem • If the function f(x) is continuous on [a, b], and y is a number between f(a) and f(b), then there exists at least one number x = c in the open interval (a, b) such that f(c) = y. Mean Value Theorem . . • If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), then there is at least one number x = c in (a, b) such that

  10. Mean Value Theorem & Rolle’s Theorem If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), then there is at least one number x = c in (a, b) such that If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), AND f(a) = f(b), then there is at least one number x = c in (a, b) such that f '(c) = 0.

  11. Approximation Methods for Integration Trapezoidal Rule Also remember LRAM, RRAM, MRAM

  12. Theorem of the Mean Valuei.e. AVERAGE VALUE • If the function f(x) is continuous on [a, b] and the first derivative exists on the interval (a, b), then there exists a number x = c on (a, b) such that • This value f(c) is the “average value” of the function on the interval [a, b].

  13. Solids of Revolution and friends • Disk Method • WasherMethod • General volume equation (not rotated) Does not necessarily include a π

  14. Distance, Velocity, and Acceleration velocity = (position) average velocity = (velocity) acceleration = speed = displacement =

  15. Values of Trigonometric Functions for Common Angles π/3 = 60° π/6 = 30° θ sin θ cos θ tan θ 0° 0 1 0 sine ,30° cosine 37° 3/5 4/5 3/4 ,45° 1 53° 4/5 3/5 4/3 ,60° ,90° 1 0 ∞ π,180° 0 –1 0

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