Calculus
High school · Math
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Topics typically covered
Click a topic for the full text and related unit practice.
High school calculus scope aligned to typical non-AP calculus syllabi and AP Calculus AB topics at standard depth (limits, derivatives, integrals, and applications).
Limits and continuity
- Limit concept — Estimate limits from graphs and tables; interpret limiting behavior
- Limit laws — Evaluate limits using algebraic techniques and limit laws
- Continuity — Determine continuity at a point and on intervals; classify discontinuities
- Limits at infinity — Analyze end behavior and horizontal asymptotes using limits
Derivatives
- Definition of the derivative — Define derivative as a limit; interpret as instantaneous rate of change
- Differentiation rules — Apply power, product, quotient, and chain rules
- Implicit differentiation — Differentiate implicitly defined relations
- Derivatives of transcendentals — Differentiate exponential, logarithmic, and trigonometric functions
Applications of derivatives
- Related rates — Solve related rates problems in geometry and physics contexts
- Curve sketching — Use first and second derivatives to analyze increasing/decreasing and concavity
- Optimization — Solve applied maximum and minimum problems
- Linear approximation — Use differentials and tangent-line approximations
Integration
- Antiderivatives — Find indefinite integrals using basic rules and substitution
- Definite integrals — Interpret definite integrals as area; apply the Fundamental Theorem of Calculus
- Riemann sums — Approximate area with left, right, and midpoint sums
- Integration by substitution — Evaluate integrals using u-substitution
Applications of integration
- Area between curves — Find area between two curves on an interval
- Volume of revolution — Compute volumes using disk and washer methods (intro)
- Average value — Find average value of a function on an interval
- Accumulation functions — Interpret integrals as net change in applied settings