AP Calculus AB
AP Calculus AB: Your Gateway to Higher Mathematics at mathaversity.com
Welcome to mathaversity.com's best AP Calculus AB course. We make hard ideas easy to understand by breaking them down into simple lessons. This class is for motivated students who are ready to take on a college-level curriculum and get college credit by doing well on the AP® Calculus AB Exam.
What is the AP Calculus AB exam?
AP Calculus AB is a college-level math class that teaches the basics of differential and integral calculus. It is a year-long, in-depth study that looks into the "why" and "how" of change. The course is the same as a first-semester college calculus class and gives anyone who wants to get a degree in science, technology, engineering, mathematics, or economics a strong base.
Our program at mathaversity.com isn't just about memorising math rules. We stress a deep understanding of concepts, which will help you learn the math skills you need to do well on the AP exam and in your future academic career.
Why should you choose mathaversity.com for AP Calculus AB?
Aligned with the College Board's curriculum
We have carefully planned our course structure, content, and practice materials to match the official AP Calculus AB Course and Exam Description. This will make sure you are ready for the test.
Tutors with experience
Our tutors are all certified and know a lot about AP. Not only do they teach the material, but they also give you proven ways to answer multiple-choice and free-response questions, which will help you get that high score.
A lot of practice materials
We have a huge library of resources, such as
- Worksheets for each unit that are specific to the topic.
- Full-length practice AP tests to help you get ready for the real thing.
- Step-by-step solutions for every problem, so you can learn from what you did wrong.
Downloadable Worksheets
We also have a huge library of practice worksheets for every subject that you can download, along with answer keys that explain how to do each one. These are great for helping you remember what you've learnt and getting better at solving problems.
You can get to them here: Worksheet
Interactive Learning Platform
Our platform has fun video lessons, quizzes that you can take, and a progress tracker to help you keep track of how well you know each topic.
Flexible Learning
Our self-paced modules and one-on-one tutoring sessions can fit into your busy schedule, whether you have other AP classes, sports, or other activities to do.
Key Topics Covered in Our AP Calculus AB Course
Our curriculum is meticulously structured into the eight units defined by the College Board, ensuring complete coverage and a logical progression of skills.
Unit 1: Limits and Continuity
- Fundamental Concepts: Introduction to the core idea of calculus—the limit. Learn to evaluate limits graphically, numerically, and analytically.
- Theorems: Understand and apply key theorems like the Squeeze Theorem and the Intermediate Value Theorem to analyze function behavior.
- Continuity: Explore the concept of continuity and types of discontinuities, connecting limits to the behavior of a function.
Unit 2: Differentiation: Definition and Fundamental Rules
- The Derivative: Define the derivative as a limit and understand its meaning as an instantaneous rate of change and the slope of a tangent line.
- Basic Rules: Master the fundamental rules of differentiation, including the Power Rule, Product Rule, Quotient Rule, and derivatives of trigonometric and exponential functions.
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- The Chain Rule: Learn how to apply the powerful Chain Rule to find derivatives of composite functions.
- Advanced Techniques: Master implicit differentiation to find derivatives of equations that are not explicitly functions, and learn to differentiate inverse and inverse trigonometric functions.
Unit 4: Contextual Applications of Differentiation
- Real-World Problems: Apply derivatives to model and solve real-world problems.
- Rates of Change: Interpret the derivative in various contexts, including rates of change in physics (position, velocity, acceleration), economics, and more.
- Related Rates: Solve complex problems where multiple rates of change are related to each other.
Unit 5: Analytical Applications of Differentiation
- Function Analysis: Use derivatives to analyze the properties of a function, including finding extrema (maxima and minima), intervals of increasing and decreasing, and concavity.
- Theorems: Apply the Mean Value Theorem and the Extreme Value Theorem to justify your reasoning about function behavior.
- Optimization: Learn to solve optimization problems, finding the maximum or minimum value in a given scenario.
Unit 6: Integration and Accumulation of Change
- The Indefinite Integral: Learn to find antiderivatives and use the indefinite integral.
- Riemann Sums and Definite Integrals: Introduce the concept of a definite integral as the limit of a Riemann sum, representing the accumulation of a rate of change.
- The Fundamental Theorem of Calculus: Understand this cornerstone of calculus, which connects differentiation and integration.
Unit 7: Differential Equations
- Modeling Change: Model real-world phenomena using differential equations
- Solving Equations: Learn to solve separable differential equations and interpret solutions in the context of slope fields.
Unit 8: Applications of Integration
- Area and Volume: Use definite integrals to find the area of a region between two curves and the volume of solids generated by cross-sections.
- Accumulation: Apply integrals to solve accumulation problems related to motion, total change, and average value.
Who Should Take This Class?
Students in High School: Trying to get a 3, 4, or 5 on the AP Calculus AB Exam so you can get college credit and stand out in college admissions.
College students who need to review or improve their calculus skills for a required course or a STEM major.
Adult Learners: Want to get better at calculus for personal or professional reasons.
Are you ready to learn calculus and get college credit?
Sign up for our AP Calculus AB course at mathaversity.com today and open the door to your academic success.
