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AP Calculus AB

AP · College BoardCalculus AB509 cards

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Flashcards for the College Board AP Calculus AB course, split into the eight units of the Course and Exam Description and then by topic, in that order. Worked examples use their own numbers rather than a released free-response question.

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What is inside (40 subdecks)

  • Unit 1 Limits and Continuity73 cards
    • 1.1-1.4 Defining and estimating limits17 cards
    • 1.5-1.8 Determining limits algebraically22 cards
    • 1.10-1.13 Continuity13 cards
    • 1.14-1.16 Infinite limits, asymptotes and the Intermediate Value Theorem21 cards
  • Unit 2 Differentiation: Definition and Fundamental Properties64 cards
    • 2.1-2.4 Defining the derivative24 cards
    • 2.5-2.7 Basic derivative rules24 cards
    • 2.8-2.10 The product rule, the quotient rule and trigonometric derivatives16 cards
  • Unit 3 Differentiation: Composite, Implicit and Inverse Functions51 cards
    • 3.1-3.2 The chain rule and implicit differentiation22 cards
    • 3.3-3.4 Derivatives of inverse and inverse trigonometric functions17 cards
    • 3.6 Higher-order derivatives12 cards
  • Unit 4 Contextual Applications of Differentiation52 cards
    • 4.1-4.2 Rates of change in context and straight-line motion16 cards
    • 4.3-4.5 Related rates16 cards
    • 4.6-4.7 Linearisation and L'Hospital's rule20 cards
  • Unit 5 Analytical Applications of Differentiation84 cards
    • 5.1-5.2 The Mean Value Theorem, the Extreme Value Theorem and critical points14 cards
    • 5.3-5.5 Increasing, decreasing and relative or absolute extrema17 cards
    • 5.6-5.7 Concavity and the second derivative test19 cards
    • 5.8-5.9 Connecting a function to its first and second derivatives11 cards
    • 5.10-5.11 Optimisation15 cards
    • 5.12 Implicit relations8 cards
  • Unit 6 Integration and Accumulation of Change81 cards
    • 6.1-6.3 Accumulation of change and Riemann sums27 cards
    • 6.4-6.5 The Fundamental Theorem of Calculus and accumulation functions11 cards
    • 6.6-6.7 Properties of definite integrals13 cards
    • 6.8 Antiderivatives and indefinite integrals16 cards
    • 6.9-6.10 Integration by substitution, long division and completing the square14 cards
  • Unit 7 Differential Equations46 cards
    • 7.1-7.2 Setting up and verifying differential equations11 cards
    • 7.3-7.4 Slope fields11 cards
    • 7.6-7.7 Separation of variables12 cards
    • 7.8 Exponential growth and decay models12 cards
  • Unit 8 Applications of Integration58 cards
    • 8.1-8.3 Average value, motion and accumulation in context16 cards
    • 8.4-8.6 The area between curves11 cards
    • 8.7-8.8 Volumes with known cross sections13 cards
    • 8.9-8.12 Volumes of revolution: the disc and washer methods18 cards

Some of its cards

  • How is the derivative of a function interpreted in context?
    As the instantaneous rate of change of the function with respect to its independent variable
  • How is the volume of a solid with known cross sections calculated?
    By integrating the cross-sectional area function along the axis perpendicular to the cross sections
  • What is the power rule for derivatives?
    ddx[xr]=rxr−1\dfrac{d}{dx}\left[x^r\right] = rx^{r-1}
  • What does it mean for ff to be increasing on an interval?
    As xx increases on the interval, f(x)f(x) also increases
  • How is the average rate of change of ff over [a,a+h][a, a+h] written as a difference quotient?
    f(a+h)−f(a)h\dfrac{f(a+h) - f(a)}{h}
  • If a quantity's rate of change is always proportional to how large the quantity currently is, what differential equation describes it?
    dydt=ky\dfrac{dy}{dt} = ky
  • How is the second derivative f′′f'' of a function ff obtained?
    By differentiating f′f', provided that derivative exists
  • What does it mean to say lim⁡x→cf(x)=∞\lim_{x \to c} f(x) = \infty?
    As xx approaches cc, the values of f(x)f(x) grow without bound
  • To solve a separable differential equation: separate the variables, then antidifferentiate both sides, then add [...].
    To solve a separable differential equation: separate the variables, then antidifferentiate both sides, then add a constant of integration.
  • What is a differential equation?
    An equation that relates a function of an independent variable to the function's derivatives

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