Course Description

Pre-requisite: Pre-Calculus

AP Calculus AB is a college-level course for high school students that covers the foundational concepts of calculus. The course focuses on differential and integral calculus, exploring limits, derivatives, integrals, and the Fundamental Theorem of Calculus. Students will develop strong analytical skills as they learn to apply calculus concepts to solve real-world problems and mathematical challenges.

Through a combination of lectures, problem sets, and hands-on activities, students will gain a deep understanding of calculus principles and their applications in various fields, such as physics, engineering, and economics. The course includes preparation for the AP Calculus AB exam, with practice exams and exam-specific strategies.

By the end of the course, students will have a solid grasp of key calculus topics and be well-prepared for the AP exam and further studies in mathematics or related disciplines. This course is ideal for students with a strong interest in mathematics who are ready for an advanced and challenging curriculum.

Course Details

AP Calculus AB

Eleventh Grade
Twelfth Grade

Course Objectives

  • Understand the fundamental concepts of calculus, including limits, derivatives, and integrals.
  • Develop skills in applying calculus to solve real-world problems.
  • Learn to analyze functions and their behaviors.
  • Gain experience in solving differential equations.
  • Prepare for the AP Calculus AB exam through practice exams and targeted review.

Course Outline

Unit 1: Limits and Continuity

  • Introduction to Limits
    • Understanding the concept of a limit and its notation.
    • Finding limits using algebraic techniques.
  • Continuity
    • Exploring the concept of continuity and its importance in calculus.
    • Identifying points of discontinuity and types of discontinuities.
  • Limits at Infinity
    • Understanding limits at infinity and horizontal asymptotes.
    • Applying limits at infinity to real-world scenarios.

Unit 2: Derivatives

  • Definition of the Derivative
    • Understanding derivatives as rates of change and slopes of tangent lines.
    • Finding derivatives using the limit definition.
  • Basic Differentiation Rules
    • Learning the power rule, product rule, and quotient rule.
    • Applying basic differentiation rules to various functions.
  • Derivatives of Trigonometric Functions
    • Finding derivatives of sine, cosine, and other trigonometric functions.
    • Applying differentiation rules to trigonometric problems.

Unit 3: Applications of Derivatives

  • Implicit Differentiation and Related Rates
    • Understanding implicit differentiation and its applications.
    • Solving related rates problems using derivatives.
  • Curve Sketching and Function Analysis
    • Analyzing functions using derivatives (critical points, inflection points, and concavity).
    • Sketching curves based on derivative information.
  • Optimization
    • Applying derivatives to solve optimization problems.
    • Identifying maxima and minima in real-world contexts.

Unit 4: Integrals

  • Antiderivatives and Indefinite Integrals
    • Understanding antiderivatives and basic integration rules.
    • Finding indefinite integrals of various functions.
  • Definite Integrals and Area Under a Curve
    • Using definite integrals to find areas under curves.
    • Applying definite integrals to real-world scenarios.
  • The Fundamental Theorem of Calculus
    • Exploring the connection between derivatives and integrals.
    • Understanding and applying the Fundamental Theorem of Calculus.

Unit 5: Applications of Integrals

  • Area and Volume Applications
    • Using integrals to find areas between curves.
    • Applying integrals to calculate volumes of solids of revolution.
  • Differential Equations
    • Solving basic differential equations using separation of variables.
    • Applying differential equations to model real-world problems.

Unit 6: Review and AP Exam Preparation

  • AP Exam Review
    • Comprehensive review of key calculus concepts.
    • Practice with multiple-choice and free-response questions.
  • Full-Length Practice Exam
    • Administering a full-length AP Calculus AB practice exam.
    • Reviewing challenging concepts and discussing exam strategies.

Expected Outcomes

By the end of this course, students will have a comprehensive understanding of calculus concepts, including derivatives, integrals, and the Fundamental Theorem of Calculus. They will have developed strong problem-solving skills and be well-prepared for the AP Calculus AB exam and further studies in mathematics or related fields.

Syllabus for upcoming year coming soon. 

Coming soon.