🇺🇸 United States • College Board100% Free & OpenCollege-Level Courses for High School Students
Advanced Placement (AP®) Suite
Earn University College Credits with AP Calculus, Physics, Chemistry, Biology, U.S. History & Computer Science A
Exam Duration
3 Hours to 3 Hours 15 Minutes per AP Exam
Score / Scale
Scores 1 to 5 (Score of 3+ qualifies for college credit at most universities)
Exam Format
Standardized End-of-Course Examination (Paper & Digital Hybrid)
Subjects in Suite:
Units & Modules
Unit 1 • 10–12% of AP Calculus Exam
AP Calculus: Limits, Continuity & Derivative Foundations
Defining limits analytically and graphically, indeterminate forms, L’Hôpital’s Rule, the Squeeze Theorem, and the formal definition of derivative as a limit.
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Runtime: 17 MinsThe essence of calculus
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🔑 High-Yield Concepts & Formulas for this Unit
- Definition of Derivative: f’(x) = lim(h→0) [f(x+h) - f(x)] / h
- Intermediate Value Theorem (IVT) and Extreme Value Theorem (EVT)
- Evaluating indeterminate forms (0/0, ∞/∞) using L’Hôpital’s Rule: lim f(x)/g(x) = lim f’(x)/g’(x)
- Continuity condition: f(a) is defined, lim(x→a) f(x) exists, and lim(x→a) f(x) = f(a)
Topics & Learning Objectives
Limit Laws & Asymptotic Behavior
Evaluating one-sided and two-sided limits algebraically.
Instantaneous Rate of Change & Derivative Definition
Connecting secant line slope to tangent line slope.