Catholic Tech

Calculus I

Course Topics

  1. Limits and Continuity
    • Introduction to limits
    • Evaluating limits algebraically and graphically
    • One-sided limits and infinite limits
    • Continuity and discontinuity
    • Intermediate Value Theorem
  2. Differentiation: Definition and Basic Techniques
    • Definition of the derivative
    • Interpretation of the derivative as a rate of change
    • Differentiation rules for polynomials, exponentials, logarithms, and trigonometric functions
    • Implicit differentiation
    • Related rates problems
  3. Applications of Derivatives
    • Analysis of graphs using derivatives
    • Optimization problems
    • Modeling rates of change
    • Derivatives of inverse functions
    • Linear approximation and differentials
  4. Integration and Accumulation
    • Antiderivatives and indefinite integrals
    • Integration by substitution
    • Definite integrals and areas under curves
    • The Fundamental Theorem of Calculus
    • Average value of a function
  5. Applications of Integration
    • Area between curves
    • Volumes of solids of revolution
    • Work, average value, and accumulation
    • Differential equations and slope fields
    • Applications to physics and economics
  6. Exam Preparation
    • Review of all topics covered in the course
    • Practice with AP-style multiple-choice and free-response questions
    • Test-taking strategies and time management tips


The course syllabus is subject to change at the discretion of the instructor. Any modifications or updates will be communicated in advance.