AP Calculus AB

AP Calculus AB Curriculum Map 

Unit 1: Limits and Continuity 

• Key Topics:

  • Concept of a limit

  • One-sided limits

  • Limits at infinity

  • Infinite limits

  • Continuity and types of discontinuities

  • Intermediate Value Theorem

• Skills:

  • Evaluate limits algebraically, graphically, numerically

  • Understand limits leading to derivative definition

Unit 2: Derivatives – Definition and Basic Rules 

• Key Topics:

  • Derivative as a limit

  • Power, constant, sum, difference rules

  • Constant multiple rule

  • Product and quotient rules

  • Chain rule (intro)

• Skills:

  • Differentiate polynomial, exponential, trigonometric functions

  • Apply derivative rules to various functions

Unit 3: Applications of Derivatives 

• Key Topics:

  • Tangent lines and rates of change

  • Increasing/decreasing functions

  • First and second derivative tests

  • Concavity and inflection points

  • Optimization problems

  • Related rates

  • Linear approximation

• Skills:

  • Analyze function behavior using derivatives

  • Solve real-world problems using derivatives
    
    

Unit 4: Integrals 

• Key Topics:

  • Antiderivatives and indefinite integrals

  • Definite integrals and Riemann sums

  • Fundamental Theorem of Calculus (parts 1 & 2)

  • Area under curves

  • Net change theorem

• Skills:

  • Compute definite and indefinite integrals

  • Apply integrals to area and accumulation problems
    
    

Unit 5: Applications of Integrals 

• Key Topics:

  • Area between curves

  • Volume using disks and washers

  • Average value of a function

  • Solids of revolution

• Skills:

  • Solve real-world applications using definite integrals

  • Set up integrals from word problems
    
    

Unit 6: Differential Equations and Slope Fields 

• Key Topics:

  • Solving basic differential equations (separable)

  • Slope fields

  • Growth and decay applications

  • Motion problems (position, velocity, acceleration)

• Skills:

  • Interpret slope fields and differential equations

  • Apply differential equations to real-world contexts
    
    

Unit 7: Advanced Derivatives and Integrals 

• Key Topics:

  • Implicit differentiation

  • Higher-order derivatives

  • Integrals involving substitution

  • Integrals for motion applications (position, velocity, acceleration)

• Skills:

  • Differentiate implicitly

  • Solve advanced integration problems

  • Connect derivatives and integrals in applied contexts
    
    

Unit 8: Review and AP Exam Preparation 

• Key Topics:

  • Comprehensive review of limits, derivatives, integrals

  • AP-style multiple choice and free-response practice

  • Time management strategies for the exam

• Skills:

  • Apply all calculus concepts efficiently under exam conditions

  • Identify and correct common mistakes