If f(2)=99 but f(x)=x+4 for x≠2, what is lim x→2 f(x)?
Answer & explanation
Learn: Limits without guessing6; a value assigned at one point does not change nearby behavior.
All examsAP Calculus ABFoundation path
View coverage AP Calculus AB Flashcards & Study Review
Read 12 sample cards from the 80-card AP Calculus AB foundation collection. Try recalling each answer before checking the explanation.
Version 2026-10-27 · Original foundation materials · No sign-up
What this collection covers
Calculus AB foundation practice.
The cards preview selected ideas; they do not measure readiness for the whole examination. Your personal review schedule is available in the review tool.
Author-reviewed learning materials. Independent educator review is pending; question difficulty has not been calibrated with learner results. Check coverage and gaps before planning your preparation.
Sample flashcards, with answers
What is d(4x³)/dx?
Answer & explanation
Learn: Derivative rules and meaning12x².
Can displacement be zero while distance is positive?
Answer & explanation
Learn: Position, velocity and accelerationYes; returning to the starting position is an example.
What is ∫₀² 3x² dx?
Answer & explanation
Learn: Integrals and numerical accumulation8.
Does checking a differential equation alone verify an initial-value solution?
Answer & explanation
Learn: Differential equations and initial valuesNo. Also check the initial condition.
How do you obtain average value from a definite integral?
Answer & explanation
Learn: Area, average value and volumeDivide ∫ₐᵇf(x)dx by b−a, with a<b.
What interval conditions does the derivative Mean Value Theorem require?
Answer & explanation
Learn: Choose and justify a theoremContinuity on the closed interval and differentiability on its interior.
For horizontal area slices, which boundary difference is integrated?
Answer & explanation
Learn: Areas across intersections and sideways slicesRight x-boundary minus left x-boundary, with respect to y.
Is |x| differentiable at zero?
Answer & explanation
Learn: Continuity and local changeNo; its left derivative is −1 and right derivative is 1.
Which factor is missing from d(sin(3x))/dx=cos(3x)?
Answer & explanation
Learn: Products, quotients and chains3, the derivative of the inner function 3x.
Does f′(a)=0 guarantee a local extremum?
Answer & explanation
Learn: Tangents and derivative testsNo; f(x)=x³ at zero is a counterexample.
For F(x)=∫₀ˣ t² dt, what is F′(x)?
Answer & explanation
Learn: The fundamental theoremx².
Use the cards as a recall routine
- Read the prompt and explain your answer before looking below it.
- Compare your reasoning with the saved answer, then revisit the linked lesson if a distinction is unclear.
- Use the spaced-review tool to schedule another attempt; its personal state stays in your browser.
Sources and preparation route
These prompts and explanations are the site's original learning materials. The reference links below support the selected skills; they are not endorsements or official examination questions.