AP Calculus AB

Overview:

The AP Calculus AB course is designed to provide students with a solid foundation in differential and integral calculus. This course explores the concepts of limits, derivatives, integrals, and their applications. Students will develop critical thinking skills through problem-solving and analytical reasoning, preparing them for success in college-level mathematics.

Skills to Learn:

• Analytical reasoning and problem-solving skills
• Critical thinking and mathematical modeling abilities
• Proficiency in calculus techniques such as differentiation and integration
• Interpretation and analysis of mathematical functions and their graphs

Prerequisites:

• Strong algebraic skills, including proficiency in manipulating equations and understanding functions
• Familiarity with basic trigonometric functions and their properties
• Previous exposure to pre-calculus topics such as limits, continuity, and polynomial functions is recommended but not required.

Curriculum:

1- Limits and Continuity:

• Definition and properties of limits
• Techniques for evaluating limits
• Continuity of functions

2- Differentiation:

• Definition and properties of derivatives
• Rules of differentiation (power, product, quotient, chain rules)
• Applications of derivatives (related rates, optimization, curve sketching)

3- Applications of Integration:

• Definite and indefinite integrals
• Techniques of integration (substitution, integration by parts)
• Applications of integrals (area under a curve, volumes of solids)

4- The Fundamental Theorem of Calculus:

• Statement and applications of the Fundamental Theorem of Calculus
• Accumulation functions and definite integrals

5- Differential Equations:

• Solutions of first-order differential equations
• Separation of variables and slope fields
• Applications of differential equations

6- Graphical Analysis:

• Analysis of functions and their graphs
• Behavior of functions near asymptotes and critical points
• Interpretation of graphs in calculus contexts

7- Exam Preparation:

• Practice with multiple-choice and free-response questions
• Test-taking strategies and tips for success on the AP Calculus AB exam
  
  
  Throughout the course, students will engage in interactive activities, problem-solving exercises, and real-world applications to deepen their understanding of calculus concepts and their practical significance.

Who:  10,11 and 12th Grades

Duration: 40-60 hours

Fee: $1500