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150 multiple-choice questions and 162 flashcards, organised into 8 chapters, written to the Standard HS Calculus course / AP Calculus AB-aligned blueprint. Every question carries a full rationale.
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Standard HS Calculus course / AP Calculus AB-aligned — covers: limits and continuity, derivatives and their applications (rates of change, optimization, related rates, mean value theorem), integrals (Riemann sums, definite and indefinite integrals, FTC), applications of integration (area, volume, motion), differential equations basics. MCQs reference standard calculus pedagogy.
CoStudy's High School Calculus bank holds 312 items organised into 8 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.
Each chapter follows a domain of the published exam outline. Practise one on its own:
A sample of 12 multiple-choice questions from the bank, with the full rationale shown.
Average value of f on [a,b]:
Answer: C — (1/(b−a)) ∫_a^b f(x) dx
C) Standard. A/B/D) Each is incorrect.
Partial fractions for 1/((x−1)(x+2)):
Answer: A — A/(x−1) + B/(x+2)
A) Standard decomposition. B/C/D) Each is incorrect.
AP Calc BC topic that AB doesn't cover:
Answer: A — Series, parametric/polar/vector functions, advanced integration techniques, improper integrals, Euler's method
A) Standard BC-only content. B/C/D) Common to both.
Speed of particle with v(t) = (−t² + 4t) at t = 1:
Answer: A — 3
A) Speed = |v|. v(1) = −1 + 4 = 3. B/C/D) Each is incorrect.
If f(x) = 3x² + 4x + 1, find f'(x).
Answer: A — 6x + 4 (power rule on each term)
Differentiate term-by-term using power rule. d/dx[3x²] = 6x. d/dx[4x] = 4. d/dx[1] = 0. Sum: 6x + 4. Linearity of derivative.
Critical points of f occur where:
Answer: B — f'(x) = 0 or f'(x) does not exist
B) Definition. A) Zero of f. C) Just max. D) Inflection candidate.
What is a RELATED RATES problem about?
Answer: A — Connecting rates of change of related quantities — e.g., as water fills cone, find rate of depth change given rate of volume change; apply chain rule via implicit differentiation
Related rates: differentiate relationship implicitly w.r.t. time. Set up: identify changing quantities, write relationship, differentiate implicitly using chain rule, substitute, solve. Classic problems: ladder sliding, balloon inflating, shadow lengthening.
Maclaurin series of cos(x):
Answer: B — Σ (−1)^n x^(2n) / (2n)!
B) Standard. A) exp. C) sin. D) Wrong.
If velocity v(t) = 6t² + 4, then position s(t) (s(0) = 0) is:
Answer: A — 2t³ + 4t
A) Antiderivative with s(0) = 0. B/C/D) Each is incorrect.
Find d/dx[sin(x)].
Answer: E — cos(x) (derivative of sine is cosine)
Common derivatives: d/dx[sin(x)] = cos(x), d/dx[cos(x)] = -sin(x), d/dx[tan(x)] = sec²(x), d/dx[eˣ] = eˣ, d/dx[ln(x)] = 1/x. Memorize.
Total distance from t=0 to t=2 with v(t) = t − 1 (changes sign):
Answer: B — ∫₀² |t − 1| dt
B) Total distance uses |velocity|. A) Displacement. C/D) Each is incorrect.
Riemann sum approximates:
Answer: D — Definite integral by summing function values × widths over subintervals — left, right, midpoint, trapezoidal rules
D) Standard. A/B/C) Each is incorrect.
6 sample cards from the 162 in the bank.
What is the sum/difference rule?
d/dx[f ± g] = f' ± g'.
Evaluate lim_{x→∞} 1/x.
0.
What is a differential equation?
An equation involving a function and its derivatives.
Find f''(x) for f(x) = x⁴.
f'(x) = 4x³; f''(x) = 12x².
What is Rolle's Theorem?
If f is continuous on [a,b], differentiable on (a,b), and f(a) = f(b), then there exists c in (a,b) with f'(c) = 0.
What is the chain rule?
d/dx[f(g(x))] = f'(g(x))·g'(x).
These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.
The High School Calculus bank holds 312 items: 150 multiple-choice questions, 162 flashcards. 18 of them are on this page to read free, with no signup.
Yes. Every multiple-choice item carries a written rationale that states the controlling principle behind the correct answer and then addresses each wrong option in turn — why it tempts and precisely where it fails. Knowing why the plausible answer was wrong is worth more than knowing which letter was right.
It is organised into 8 chapters that follow the published exam blueprint: Limits and Continuity; Differentiation: Definition and Basic Rules; Differentiation: Composite, Implicit, and Inverse Functions; Contextual Applications of Differentiation; Analytical Applications of Differentiation; Integration and Accumulation of Change; Differential Equations; Applications of Integration. The number of questions in each chapter is proportional to that domain's published weight, so working through the bank exposes you to roughly the mix the real exam uses.
Standard HS Calculus course / AP Calculus AB-aligned — covers: limits and continuity, derivatives and their applications (rates of change, optimization, related rates, mean value theorem), integrals (Riemann sums, definite and indefinite integrals, FTC), applications of integration (area, volume, motion), differential equations basics. MCQs reference standard calculus pedagogy.
The samples on this page are free to read in full, rationales included, with no account. The complete 312-item bank, the timed mock exams and per-chapter progress tracking are part of CoStudy on the web and in the iOS app.
Last reviewed 2026-08-22. Banks are written against the certifying body's published exam outline and re-checked when that outline changes — exams get renumbered, retired and reweighted, and a bank written to a superseded outline teaches the wrong proportions. Figures that are re-indexed annually are deliberately not asserted as rules; the questions test the governing principle instead.