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AP®︎ Calculus AB (2017 edition)

Unit 1: Limits and continuity

About the course: Limits and continuityAnalyzing limits graphically: Limits and continuityAnalyzing limits numerically: Limits and continuityOne-sided limits: Limits and continuityContinuity: Limits and continuityLimit rules for sums, differences, products, quotients, & composites: Limits and continuityDetermining limits using direct substitution: Limits and continuity
Determining limits by factoring & rationalizing: Limits and continuityTrigonometric limits & squeeze theorem: Limits and continuityInfinite limits intro: Limits and continuityAnalyzing limits at infinity: Limits and continuityAnalyzing functions for discontinuities: Limits and continuityStrategy in finding limits: Limits and continuityOptional videos: Limits and continuity

Unit 2: Derivatives introduction

The derivative: An intuitive introduction: Derivatives introductionEstimating derivatives with secant lines and average rate of change: Derivatives introductionSecant lines & average rate of change with arbitrary points: Derivatives introduction
Formal definition of the derivative as a limit: Derivatives introductionDifferentiability: Derivatives introductionTangent lines and local linearity: Derivatives introductionOptional videos: Derivatives introduction

Unit 3: Derivative rules

Basic differentiation rules: Derivative rulesPower rule: Derivative rulesPolynomial functions differentiation: Derivative rulesDerivatives of negative and fractional powers with power rule: Derivative rulesDerivatives of sin(x) and cos(x): Derivative rulesProduct rule: Derivative rules
Quotient rule: Derivative rulesRational functions differentiation: Derivative rulesChain rule: Derivative rulesRadical functions differentiation: Derivative rulesTrigonometric functions differentiation: Derivative rulesStrategy in differentiating functions: Derivative rulesOptional videos: Derivative rules

Unit 4: Advanced derivatives

Differentiating using multiple rules: Advanced derivatives Second derivatives: Advanced derivatives Implicit differentiation: Advanced derivatives Derivatives of inverse functions: Advanced derivatives
Derivatives of inverse trigonometric functions: Advanced derivatives Derivatives of exponential functions: Advanced derivatives Derivatives of logarithmic functions: Advanced derivatives Optional videos: Advanced derivatives

Unit 5: Existence theorems

Intermediate and extreme value theorems: Existence theoremsMean value theorem: Existence theorems

Unit 6: Using derivatives to analyze functions

L'Hôpital's rule: Using derivatives to analyze functionsJustifying properties of functions using the first derivative: Using derivatives to analyze functionsCritical points & intervals of increase or decrease: Using derivatives to analyze functionsFinding relative extrema (first derivative test): Using derivatives to analyze functionsFinding absolute extrema: Using derivatives to analyze functions
Concavity & inflection points intro: Using derivatives to analyze functionsJustifying properties of functions using the second derivative: Using derivatives to analyze functionsFinding inflection points & analyzing concavity: Using derivatives to analyze functionsConnecting ƒ, ƒ’, and ƒ’’: Using derivatives to analyze functionsOptional videos: Using derivatives to analyze functions

Unit 7: Applications of derivatives

Rates of change in applied contexts: Applications of derivativesRelated rates intro: Applications of derivativesRelated rates problems: Applications of derivatives
Optimization: Applications of derivativesMotion problems: Applications of derivatives

Unit 8: Accumulation and Riemann sums

Definite integrals intro: Accumulation and Riemann sumsLeft & right Riemann sums: Accumulation and Riemann sumsMidpoint & trapezoidal sums: Accumulation and Riemann sumsSummation notation: Accumulation and Riemann sums
Riemann sums in summation notation: Accumulation and Riemann sumsDefinite integral as the limit of a Riemann sum: Accumulation and Riemann sumsDefinite integrals properties: Accumulation and Riemann sumsFunctions defined by integrals: Accumulation and Riemann sums

Unit 9: Antiderivatives and the fundamental theorem of calculus

Antiderivatives and indefinite integrals intro: Antiderivatives and the fundamental theorem of calculusFundamental theorem of calculus: Antiderivatives and the fundamental theorem of calculusIndefinite integrals: reverse power rule: Antiderivatives and the fundamental theorem of calculusIndefinite integrals of sin(x), cos(x), eˣ, and 1/x: Antiderivatives and the fundamental theorem of calculus
Finding definite integrals: Antiderivatives and the fundamental theorem of calculus𝘶-substitution: Antiderivatives and the fundamental theorem of calculusAverage value of a function: Antiderivatives and the fundamental theorem of calculusInterpreting behavior of 𝑔 from graph of 𝑔'=ƒ: Antiderivatives and the fundamental theorem of calculusOptional videos: Antiderivatives and the fundamental theorem of calculus

Unit 10: Differential equations

Differential equations intro: Differential equationsSeparable differential equations: Differential equationsDifferential equations: specific solutions: Differential equations
Slope fields: Differential equationsExponential models: Differential equations

Unit 11: Applications of definite integrals

Word problems involving definite integrals: Applications of definite integralsMotion problems (with integrals): Applications of definite integralsArea: vertical areas between curves: Applications of definite integralsArea: horizontal areas between curves: Applications of definite integrals
Volume: known cross sections: Applications of definite integralsVolume: disc method: Applications of definite integralsVolume: washer method: Applications of definite integralsVolume: shell method (optional): Applications of definite integrals

Unit 12: AP Calculus AB solved free response questions from past exams

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Course challenge

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.
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