Barrons AP Calculus

(Marvins-Underground-K-12) #1

Barron’s Essential

As you review the content in this book to work toward earning that 5 on your AP
CALCULUS AB exam, here are five things that you MUST know above
everything else:


Learn   the basic   facts:

  • derivatives and antiderivatives of common functions;

  • the product, quotient, and chain rules for finding derivatives;

  • the midpoint, left and right rectangle, and trapezoid approximations for
    estimating definite integrals;

  • finding antiderivatives by substitution;

  • the important theorems: Rolle’s theorem, the Mean Value theorem, and
    especially the Fundamental Theorem of Calculus.
    (Barron’s AP Calculus Flash Cards are a great way to study these!)


Understand  that    a   derivative  is  an  instantaneous   rate    of  change, and be
able to apply that concept to:

  • using L’Hôpital’s rule to find limits of indeterminate forms (only and );

  • find equations of tangent lines;

  • determine where a function is increasing/decreasing, concave up/down, or
    has maxima, minima, or points of inflection;

  • analyze the speed, velocity, and acceleration of an object in motion;

  • solve related rates problems, using implicit differentiation when necessary.

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