AP Calculus AB: The 18-Hour Fast Track to a Perfect Score

From Limits to Integrals—Complete Exam Prep with Lectures and Walkthroughs

What you’ll learn

• Define and evaluate limits algebraically and graphically
• Identify types of discontinuities and determine continuity of functions
• Compute derivatives using fundamental differentiation rules
• Apply implicit differentiation to solve complex equations
• Differentiate trigonometric, exponential, and logarithmic functions
• Use derivatives to analyze and graph functions (increasing/decreasing, concavity, extrema)
• Solve optimization and related rates problems
• Interpret the derivative in motion problems (velocity and acceleration)
• Compute definite and indefinite integrals using basic techniques
• Apply the Fundamental Theorem of Calculus to evaluate integrals
• Use u-substitution for integration
• Calculate areas under curves and between functions
• Solve accumulation and net change problems
• Analyze motion using integrals (position, velocity, displacement)
• Solve basic separable differential equations
• Interpret slope fields and their connections to differential equations
• Develop problem-solving strategies for multiple-choice and free-response questions
• Improve time management and test-taking skills
• Complete practice exams to build confidence and readiness

Requirements

• You should have successfully completed courses in which you studied algebra, geometry, trigonometry, analytic geometry, and elementary functions.
• You should understand the properties of linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions and know how to graph these functions and solve equations involving them.
• You should also be familiar with algebraic transformations, combinations, compositions, and inverses for general functions.

Description

How This Course Works:

This course is designed to give you everything you need to ace the AP Calculus AB exam. You’ll get concise, clear video lessons, downloadable lecture notes, and plenty of practice problems—with fully worked solutions. Every concept is broken down step-by-step, including all derivations, examples, and rules, so nothing is left unexplained.

What are AP Exams and Who Should Take This Course?
AP (Advanced Placement) exams are standardized college-level assessments administered by the College Board. Scoring well can earn you college credit, advanced placement in university courses, or simply a stronger math foundation. This course is ideal for high school students currently enrolled in AP Calculus AB or anyone preparing to take the exam independently.

Course Structure:

The course is organized into easy-to-follow sections that align with the official College Board AP Calculus AB curriculum:

• Precalculus Review – Brush up on the essential algebra and trigonometry skills.
• Unit 1: Limits and Continuity – Learn how limits work and why continuity matters.
• Unit 2: Differentiation – Definition and Basic Rules – Explore the derivative and how to apply it.
• Unit 3: Differentiation – Advanced Techniques – Master the chain rule, implicit differentiation, and inverse functions.
• Unit 4: Applications of Derivatives – Analyze motion, optimize functions, and solve related rates problems.
• Unit 5: Analytical Applications of Derivatives – Dive into curve sketching, concavity, and the Mean Value Theorem.
• Unit 6: Integration and the Accumulation of Change – Understand area under a curve, definite and indefinite integrals, and the Fundamental Theorem of Calculus.
• Unit 7: Differential Equations – Learn how to solve and interpret basic differential equations.
• Unit 8: Applications of Integration – Calculate area between curves, volumes of solids, and more.
• Past AP Exam Walk-throughs – Study real exam problems with full, step-by-step solutions.

What You’ll Get in Each Section:

• Videos – I break down each topic with clear explanations and real examples. You’ll learn how to approach different types of problems and develop confidence solving them on your own.
• Lecture Notes – These are the notes I write during the videos. You can download them and study offline—but I still recommend taking your own notes too!
• Extra Resources – Helpful tools like formula sheets and study tips to boost your preparation.
• Assignments – Practice problems for each topic. Try them yourself before looking at the solutions! If you’re stuck, revisit the videos or ask for help in the Q&A section.

Included in the Course:

• An instructor (that’s me!) who genuinely cares about your success
• Lifetime access to all course materials
• Friendly support in the Q&A section
• A downloadable Certificate of Completion from Udemy

To Boost Your Learning, You’ll Also Get:

• Downloadable lectures for studying anytime, anywhere
• All lecture notes and extra study resources
• 14 problem sets with fully explained solutions
• 3 complete past exam walk-throughs

Let’s get started—I’ll see you inside!

– Gina 🙂

Who this course is for:

• High school students aiming to earn college credit or prepare for university-level math.
• Students who have completed Precalculus and have a strong foundation in algebra, functions, and trigonometry.
• STEM-focused students planning to pursue degrees in mathematics, engineering, physics, computer science, economics, or other quantitative fields.
• Students who enjoy problem-solving and logical reasoning.
• Those looking to strengthen their college applications with a challenging course.
• Students who want to save time and money in college by earning AP credit for calculus.
• High-achieving students who want to challenge themselves with a rigorous math course.
• Students preparing for standardized tests such as the SAT, ACT, or college entrance exams that include calculus-based questions.