Notes APCalculus AB

Calculus AB Study Notes

AP · Free revision notes covering the complete syllabus

8 Units30 Notes Available

Unit 1: Limits and Continuity

Study materials and practice for Unit 1: Limits and Continuity

Limits from graphs/tables/algebra

Limit properties and algebraic techniques

Continuity and discontinuities

Intermediate Value Theorem

Unit 2: Differentiation: Definition & Fundamental Properties

Study materials and practice for Unit 2: Differentiation: Definition & Fundamental Properties

Derivative definition (limit)

Derivative rules (power/product/quotient/chain)

Derivatives of trig/exp/log functions

Implicit differentiation intro

Unit 3: Differentiation: Composite/Implicit/Inverse

Study materials and practice for Unit 3: Differentiation: Composite/Implicit/Inverse

Chain rule applications

Implicit differentiation

Related rates

Motion interpretation

Unit 4: Contextual Applications of Differentiation

Study materials and practice for Unit 4: Contextual Applications of Differentiation

Local linearization/differentials

Optimization

Mean Value Theorem applications

Unit 5: Analytical Applications of Differentiation

Study materials and practice for Unit 5: Analytical Applications of Differentiation

Monotonicity and concavity

First/second derivative tests

Curve sketching

Motion analysis

Unit 6: Integration and Accumulation of Change

Study materials and practice for Unit 6: Integration and Accumulation of Change

Riemann sums and definite integral

FTC and accumulation functions

Numerical integration

Unit 7: Differential Equations

Study materials and practice for Unit 7: Differential Equations

Slope fields

Separable differential equations

Exponential models

Euler’s method (as applicable)

Unit 8: Applications of Integration

Study materials and practice for Unit 8: Applications of Integration

Area between curves

Volume (disk/washer)

Average value

Applications in context

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