AP Calculus AB is an advanced mathematics course designed to prepare students for college-level calculus. This course covers fundamental concepts of differential and integral calculus, including limits, derivatives, definite and indefinite integrals, and their real-world applications. Students will develop problem-solving skills, mathematical reasoning, and an analytical approach to solving complex calculus problems.
What You’ll Learn:
•Limits & Continuity – Understanding the foundation of calculus, including limit laws and asymptotic behavior.
•Derivatives – Learning differentiation techniques, applications in motion, optimization, and related rates.
•Integrals & The Fundamental Theorem of Calculus – Exploring antiderivatives, definite and indefinite integrals, and their applications in area and volume calculations.
•Applications of Calculus – Applying calculus concepts to physics, economics, and engineering scenarios.
•Graphical, Analytical, and Numerical Approaches – Mastering multiple methods for solving calculus problems using technology and real-world examples.
Who Should Take This Course?
This course is ideal for high school students with a strong background in algebra, trigonometry, and pre-calculus who want to:
✔️ Challenge themselves with college-level math
✔️ Earn college credit through the AP Calculus AB Exam
✔️ Improve problem-solving skills for STEM-related fields
Course Features:
Interactive lessons with real-world applications
Video tutorials, step-by-step solutions, and guided practice problems
Exam-style questions to prepare for the AP test
Personalized feedback and instructor support
Enroll today and take the first step toward mastering calculus!
Eğitim Özellikleri
- Dersler 50
- Sınav 0
- Süre 25 weeks
- Yetenek seviyesi Expert
- Dil English
- Öğrenciler 46
- Başarı Belgesi Hayır
- Değerlendirme Evet
- 8 Sections
- 50 Lessons
- 25 Weeks
- Limits and Continuity- Master the concept of limits using graphical, numerical, and algebraic approaches - Apply limit properties to evaluate one-sided and two-sided limits - Determine continuity of functions and identify types of discontinuities6
- 1.11.1 Understanding Limits: Graphical and Numerical Approaches
- 1.21.2 Finding Limits Algebraically and Limit Properties
- 1.31.3 One-Sided Limits and Infinite Limits
- 1.41.4 Limits at Infinity and Horizontal Asymptotes
- 1.51.5 Continuity: Definition and Types of Discontinuities
- 1.61.6 Intermediate Value Theorem and Applications
- Differentiation - Definition and Fundamental Properties- Understand the derivative as a limit and interpret it as instantaneous rate of change - Apply differentiation rules to polynomial, trigonometric, exponential, and logarithmic functions - Master the chain rule, product rule, and quotient rule for composite functions9
- 2.12.1 The Derivative as a Limit: Definition and Interpretation
- 2.22.2 Differentiability and the Relationship Between Continuity and Differentiability
- 2.32.3 Basic Differentiation Rules: Power, Sum, and Constant Rules
- 2.42.4 Product Rule and Quotient Rule
- 2.52.5 Chain Rule and Composite Functions
- 2.62.6 Derivatives of Trigonometric Functions
- 2.72.7 Derivatives of Exponential and Logarithmic Functions
- 2.82.8 Implicit Differentiation
- 2.92.9 Derivatives of Inverse Trigonometric Functions
- Differentiation - Composite, Implicit, and Inverse Functions- Apply advanced differentiation techniques including implicit differentiation and related rates - Solve optimization problems using derivatives - Use L'Hôpital's Rule to evaluate indeterminate forms4
- Contextual Applications of Differentiation- Analyze functions using first and second derivatives to determine critical points, extrema, and concavity - Model real-world scenarios with position, velocity, and acceleration functions - Apply optimization techniques to solve practical problems8
- 4.14.1 Mean Value Theorem and Rolle’s Theorem
- 4.24.2 Extreme Value Theorem and Critical Points
- 4.34.3 First Derivative Test: Increasing and Decreasing Functions
- 4.44.4 Second Derivative Test: Concavity and Points of Inflection
- 4.54.5 Curve Sketching Using Derivatives
- 4.64.6 Optimization Problems: Maximum and Minimum Values
- 4.74.7 Position, Velocity, and Acceleration in Motion Problems
- 4.84.8 Related Rates in Real-World Applications
- Analytical Applications of Differentiation- Use derivatives to analyze and sketch graphs of functions comprehensively - Solve practical optimization and related rates problems across various contexts - Connect graphical, numerical, and analytical representations of derivatives4
- Integration and Accumulation of Change- Understand the definite integral as accumulation and area under a curve - Apply the Fundamental Theorem of Calculus to evaluate definite integrals - Master integration techniques including substitution and integration by parts8
- 6.16.1 Antiderivatives and Indefinite Integrals
- 6.26.2 Riemann Sums: Approximating Area Under a Curve
- 6.36.3 The Definite Integral: Definition and Properties
- 6.46.4 Fundamental Theorem of Calculus (Part 1 and Part 2)
- 6.56.5 Integration Using U-Substitution
- 6.66.6 Integration by Parts
- 6.76.7 Accumulation Functions and Net Change
- 6.86.8 Average Value of a Function
- Differential Equations and Mathematical Modeling- Solve separable differential equations and apply initial conditions - Use slope fields to visualize solutions to differential equations - Model exponential growth and decay using differential equations5
- Applications of Integration- Calculate areas between curves using definite integrals - Find volumes of solids of revolution using disk, washer, and shell methods - Apply integration to solve practical problems involving accumulation and motion6
Target audiences
- High School Students
