AP Calculus AB is a college-level course covering the first semester of university calculus. It focuses on limits, derivatives, integrals, and the Fundamental Theorem of Calculus, with applications in motion, area, and accumulation.
Eight units covering: limits and continuity, differentiation (definition, basic rules, chain rule, implicit differentiation), applications of derivatives (related rates, optimisation, curve sketching, L'Hôpital's Rule), integration (Riemann sums, definite/indefinite integrals, FTC), differential equations (slope fields, separation of variables), and applications of integration (area between curves, volume, accumulation functions).
Section I: 45 MCQs in 1h 45min (Part A: 30Q no calculator, Part B: 15Q calculator). Section II: 6 FRQs in 1h 30min (Part A: 2Q calculator, Part B: 4Q no calculator). Score: 1–5, with 3+ considered passing. A score of 4 or 5 earns college credit at most US universities. Approximately 60% of students score 3+ annually.
Limit definition of derivative: f'(x) = lim(h→0) [f(x+h)−f(x)]/h. Power Rule: d/dx[xⁿ] = nxⁿ⁻¹. Chain Rule: d/dx[f(g(x))] = f'(g(x))·g'(x). FTC Part 1: d/dx[∫ₐˣ f(t)dt] = f(x). FTC Part 2: ∫ₐᵇ f(x)dx = F(b)−F(a). Students must understand these conceptually and procedurally.
AP Calculus AB covers approximately the first semester of college calculus. AP Calculus BC covers the full year (both first and second semesters). BC includes everything in AB plus: parametric/polar/vector functions, Euler's method, logistic differential equations, integration techniques (by parts, partial fractions), improper integrals, and infinite series (Taylor/Maclaurin). BC students receive an AB sub-score even if they don't take the AB exam separately.
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