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Course Objectives

Students will:

  • Develop conceptual understanding of limits, derivatives, and integrals.
  • Apply calculus concepts to real-world situations.
  • Analyze functions using graphical, numerical, analytical, and verbal representations.
  • Construct mathematical arguments and justify solutions.
  • Prepare for success on the AP Calculus AB Examination.

Prerequisites

Students should have successfully completed:

  • Algebra I
  • Geometry
  • Algebra II
  • Precalculus (or equivalent)

Required Materials

  • Graphing Calculator (TI-84 Plus CE or equivalent)
  • Spiral notebook or binder
  • Pencils and erasers
  • Ruler
  • College-ruled notebook paper
  • Access to AP Classroom and school learning management system

Course Units

Unit 1: Limits and Continuity

  • Limits
  • Continuity
  • Intermediate Value Theorem
  • Limits at Infinity
  • Asymptotes

Unit 2: Differentiation: Definition and Fundamental Properties

  • Definition of the derivative
  • Basic differentiation rules
  • Tangent lines
  • Rates of change

Unit 3: Composite, Implicit, and Inverse Functions

  • Chain Rule
  • Implicit differentiation
  • Inverse functions
  • Higher-order derivatives

Unit 4: Contextual Applications of Differentiation

  • Related rates
  • Motion problems
  • Linear approximation
  • L'Hospital's Rule

Unit 5: Analytical Applications of Differentiation

  • Mean Value Theorem
  • Extreme Value Theorem
  • Curve sketching
  • Optimization
  • First and Second Derivative Tests

Unit 6: Integration and Accumulation of Change

  • Riemann sums
  • Definite integrals
  • Fundamental Theorem of Calculus
  • Antiderivatives

Unit 7: Differential Equations

  • Slope fields
  • Separation of variables
  • Exponential growth and decay

Unit 8: Applications of Integration

  • Area between curves
  • Volumes
  • Average value of a function
  • Particle motion
  • Accumulation functions

These eight units follow the College Board AP Calculus AB framework.

Grading Policy

  • Tests and Major Assessments ............ 40%
  • Quizzes ............................................. 25%
  • Homework and Classwork ............... 20%
  • AP Classroom Assignments ............ 10%
  • Participation ...................................... 5%

Homework Policy

  • Homework is assigned regularly.
  • Show all mathematical work.
  • Homework is due at the beginning of class.
  • Late assignments receive reduced credit according to classroom policy.
  • Assignments more than one day late may not be accepted unless prior approval is given.

Classroom Expectations

Students are expected to:

  • Arrive on time and prepared.
  • Bring all required materials.
  • Participate actively in class discussions.
  • Respect classmates and the learning environment.
  • Maintain academic integrity.
  • Use electronic devices only when authorized.

Study Expectations

Students should:

  • Study 45–60 minutes daily.
  • Review notes after every class.
  • Complete all assigned practice.
  • Memorize important derivative and integral formulas.
  • Practice AP-style multiple-choice and free-response questions weekly.
  • Attend extra help sessions when needed.

Assessments

Students will complete:

  • Unit Tests
  • Quizzes
  • AP Classroom Assignments
  • Multiple Choice Practice
  • Free Response Practice (FRQs)
  • Midterm Examination
  • Final Examination
  • Mock AP Examination

Academic Integrity

Students must complete all assessments independently unless collaboration is specifically permitted. Unauthorized assistance, plagiarism, or misuse of artificial intelligence or online resources may result in disciplinary action according to school policy.

AP Examination

Students are encouraged to take the AP Calculus AB Exam in May. The exam consists of:

  • Multiple-Choice Section (50%)
  • Free-Response Section (50%)

The College Board has announced updates to exam timing and multiple-choice structure beginning with the May 2027 administration while maintaining the same course content.

Extra Help

Additional help is available by appointment or during scheduled tutoring sessions.

Success in AP Calculus

Students who are successful:

  • Attend class every day.
  • Complete homework consistently.
  • Ask questions.
  • Learn from mistakes.
  • Practice mathematics daily.
  • Stay organized.
  • Maintain a positive work ethic.

Welcome to AP Calculus AB! This course is rigorous, challenging, and rewarding. Through dedication, perseverance, and consistent practice, you will develop the mathematical skills needed for college-level calculus and success on the AP Examination.