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AP Calculus BC

AP · College BoardCalculus BC672 cards

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Flashcards for AP Calculus BC, following the College Board Course and Exam Description (effective Fall 2020, current for exams from 2027), split into the ten course units and then by topic. Cards cover the content Calculus AB and BC share as well as the BC-only topics: Euler's method, logistic models, parametric and polar curves, vector-valued functions and infinite series.

Adding it gives you your own copy, with every subdeck below. Each card then comes back just before you would forget it, and every one you get right or wrong counts towards your mastery of its topic. You can delete or suspend the parts you are not studying once it is yours.

What is inside (74 subdecks)

  • Unit 1 Limits and Continuity72 cards
    • 1.1 to 1.4 Defining and estimating limits16 cards
    • 1.5 to 1.9 Limit laws and techniques21 cards
    • 1.10 to 1.13 Continuity15 cards
    • 1.14 to 1.16 Infinite limits, asymptotes and the Intermediate Value Theorem20 cards
  • Unit 2 Differentiation: Definition and Fundamental Properties66 cards
    • 2.1 to 2.4 The derivative as a limit18 cards
    • 2.5 to 2.7 The power, sum and standard function rules26 cards
    • 2.8 to 2.10 Product, quotient and the other trig derivatives22 cards
  • Unit 3 Differentiation: Composite, Implicit, and Inverse Functions50 cards
    • 3.1 The chain rule17 cards
    • 3.2 Implicit differentiation10 cards
    • 3.3 and 3.4 Derivatives of inverse and inverse trigonometric functions15 cards
    • 3.6 Higher-order derivatives8 cards
  • Unit 4 Contextual Applications of Differentiation46 cards
    • 4.1 to 4.3 Interpreting derivatives and rates of change in context15 cards
    • 4.4 and 4.5 Related rates12 cards
    • 4.6 Local linearity and linearization6 cards
    • 4.7 L'Hospital's rule13 cards
  • Unit 5 Analytical Applications of Differentiation59 cards
    • 5.1 and 5.2 The Mean Value Theorem and the Extreme Value Theorem12 cards
    • 5.3 and 5.4 Increasing, decreasing and the first derivative test10 cards
    • 5.5 The candidates test for absolute extrema5 cards
    • 5.6 and 5.7 Concavity and the second derivative test11 cards
    • 5.8 and 5.9 Connecting a function to its first and second derivatives5 cards
    • 5.10 and 5.11 Optimization8 cards
    • 5.12 Behaviour of implicitly defined functions8 cards
  • Unit 6 Integration and Accumulation of Change98 cards
    • 6.1 Accumulation of change4 cards
    • 6.2 and 6.3 Riemann sums and definite integral notation14 cards
    • 6.4 and 6.5 The Fundamental Theorem of Calculus and accumulation functions7 cards
    • 6.6 and 6.7 Properties of definite integrals and evaluating them15 cards
    • 6.8 Finding antiderivatives21 cards
    • 6.9 Integration by substitution8 cards
    • 6.10 Long division and completing the square4 cards
    • 6.11 Integration by parts9 cards
    • 6.12 Integration by linear partial fractions4 cards
    • 6.13 Improper integrals12 cards
  • Unit 7 Differential Equations49 cards
    • 7.1 and 7.2 Modelling with and verifying differential equations7 cards
    • 7.3 and 7.4 Slope fields8 cards
    • 7.5 Euler's method6 cards
    • 7.6 and 7.7 Separation of variables9 cards
    • 7.8 Exponential growth and decay models7 cards
    • 7.9 Logistic models12 cards
  • Unit 8 Applications of Integration59 cards
    • 8.1 Average value of a function7 cards
    • 8.2 and 8.3 Motion and accumulation in applied contexts11 cards
    • 8.4 to 8.6 Area between curves9 cards
    • 8.7 and 8.8 Volumes with known cross sections8 cards
    • 8.9 to 8.12 Volumes of revolution: disc and washer methods17 cards
    • 8.13 Arc length7 cards
  • Unit 9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions51 cards
    • 9.1 and 9.2 Derivatives of parametric equations12 cards
    • 9.3 Arc length of parametric curves6 cards
    • 9.4 to 9.6 Vector-valued functions and planar motion14 cards
    • 9.7 Polar coordinates and differentiation in polar form11 cards
    • 9.8 and 9.9 Area in polar coordinates8 cards
  • Unit 10 Infinite Sequences and Series122 cards
    • 10.1 Convergence and divergence of infinite series10 cards
    • 10.2 Geometric series8 cards
    • 10.3 The nth term test for divergence5 cards
    • 10.4 The integral test6 cards
    • 10.5 The harmonic series and p-series7 cards
    • 10.6 Comparison tests10 cards
    • 10.7 The alternating series test5 cards
    • 10.8 The ratio test10 cards
    • 10.9 Absolute and conditional convergence7 cards
    • 10.10 The alternating series error bound5 cards
    • 10.11 Taylor polynomial approximations10 cards
    • 10.12 The Lagrange error bound7 cards
    • 10.13 Radius and interval of convergence13 cards
    • 10.14 Taylor and Maclaurin series of standard functions12 cards
    • 10.15 Representing functions as power series7 cards

Some of its cards

  • ∫abc f(x) dx\displaystyle\int_a^b c\,f(x)\,dx, for a constant cc
    c∫abf(x) dxc\displaystyle\int_a^b f(x)\,dx
  • What shape do the cross sections of a solid of revolution have when a region touching the axis of revolution is revolved around it?
    Discs (solid circles).
  • How is the instantaneous rate of change of ff at x=ax=a defined using a difference quotient?
    f′(a)=lim⁡h→0f(a+h)−f(a)hf'(a) = \lim_{h \to 0} \dfrac{f(a+h)-f(a)}{h}, provided the limit exists.
  • How is the area between two curves y=f(x)y=f(x) and y=g(x)y=g(x) found on [a,b][a,b], where f(x)≥g(x)f(x) \ge g(x)?
    ∫ab[f(x)−g(x)] dx\displaystyle\int_a^b [f(x)-g(x)]\,dx
  • What does the nnth term test check?
    Whether the terms of a series tend to 00 as n→∞n \to \infty.
  • What is a Maclaurin series?
    A Taylor series centred at x=0x=0.
  • lim⁡x→cf(x)+lim⁡x→cg(x)\lim_{x \to c} f(x) + \lim_{x \to c} g(x)
    lim⁡x→c[f(x)+g(x)]\lim_{x \to c}[f(x)+g(x)], given both limits exist
  • What is a slope field?
    A graphical representation of a differential equation, showing a short line segment at each of a set of points with the slope dydx\frac{dy}{dx} given by the equation there.
  • What does the ratio test examine?
    The limit of the absolute value of the ratio of consecutive terms, lim⁡n→∞∣an+1an∣\lim_{n \to \infty} \left|\dfrac{a_{n+1}}{a_n}\right|.
  • The length of a curve given parametrically by x(t)x(t) and y(t)y(t) for α≤t≤β\alpha \le t \le \beta is ∫αβ[...] dt\displaystyle\int_\alpha^\beta [...]\,dt.
    The length of a curve given parametrically by x(t)x(t) and y(t)y(t) for α≤t≤β\alpha \le t \le \beta is ∫αβ(dxdt)2+(dydt)2 dt\displaystyle\int_\alpha^\beta \sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2} \,dt.

And 662 more once you add the deck.