The AP Calculus AB Tutor in CALIFORNIA course is designed to provide high school students with a strong foundation in differential and integral calculus, equivalent to a first-semester college calculus class. This course develops students’ skills in problem-solving, analytical thinking, and mathematical modeling while preparing them for the AP Calculus AB Exam conducted by the College Board.

Course Goals

By the end of the course, students will:

• Understand limits and their role in defining derivatives and integrals.
• Apply derivatives to solve problems involving rates of change, motion, and optimization.
• Use integrals for finding areas, volumes, and accumulated change.
• Interpret and communicate calculus concepts graphically, numerically, analytically, and verbally.

AP CALCULUS AB TUTOR IN CALIFORNIA

Main Topics Covered

1. Limits and Continuity

• Understanding the concept of a limit.
• One-sided limits and infinite limits.
• Continuity and the Intermediate Value Theorem.

2. Derivatives

• Definition of the derivative as a limit.
• Differentiation rules (power, product, quotient, chain).
• Implicit differentiation.
• Applications: related rates, motion problems, slope of tangent lines.

3. Applications of Derivatives

• Increasing/decreasing functions and extrema.
• Concavity and points of inflection.
• Curve sketching.
• Optimization problems.
• Mean Value Theorem.

AP CALCULUS AB TUTOR IN CALIFORNIA

4. Integrals

• Antiderivatives and indefinite integrals.
• Definite integrals and the Fundamental Theorem of Calculus.
• Riemann sums and trapezoidal rule.
• Applications: area under curves, net change theorem, accumulation functions.

5. Differential Equations & Slope Fields

• Solving basic differential equations.
• Slope fields and Euler’s method.
• Modeling exponential growth and decay.

6. Applications of Integration

• Finding area between curves.
• Volume of solids of revolution (disk/washer methods).

Assessment and Exam Preparation

• Multiple-Choice Questions (MCQs): Testing conceptual understanding and problem-solving speed.
• Free Response Questions (FRQs): Requiring clear, logical explanations with correct mathematical notation.
• Practice with graphing calculators for problem-solving and verification.

AP CALCULUS AB TUTOR IN CALIFORNIA

Who Should Take AP Calculus AB?

This course is ideal for students aiming to pursue STEM fields such as engineering, physics, computer science, or economics, or anyone seeking college credit for calculus before entering university.