Ap Calculus Ab: The 16-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 successLifetime access to all course materialsFriendly support in the Q&A sectionA downloadable Certificate of Completion from UdemyTo Boost Your Learning, You’ll Also Get:Downloadable lectures for studying anytime, anywhereAll lecture notes and extra study resources14 problem sets with fully explained solutions3 complete past exam walk-throughsLet’s get started—I'll see you inside!– Gina :)

Overview

Section 1: Introduction

Lecture 1 Overview

Lecture 2 Welcome and How It Works

Lecture 3 About the Exam

Lecture 4 Tips to Maximize Your Learning

Section 2: Precalculus Review

Lecture 5 Downloadable Notes

Section 3: Unit 1: Limits and Continuity

Lecture 6 Downloadable Notes

Lecture 7 Overview of Unit 1

Section 4: Unit 2 (Part I): Differentiation: Definition and Fundamental Properties

Lecture 8 Downloadable Notes

Lecture 9 Overview of Unit 2

Lecture 10 Secant and Tangent Lines (graphically and algebraically)

Lecture 11 Derivative Function

Lecture 12 Power Rule

Lecture 13 Different Derivative Notations

Lecture 14 Constant Multiple Rule

Lecture 15 Sum and Difference Rules

Lecture 16 Product Rule

Lecture 17 Quotient Rule

Lecture 18 Differentiability

Lecture 19 Normal Line

Section 5: Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

Lecture 20 Overview of Unit 3

Lecture 21 Higher-Order Derivatives

Lecture 22 Chain Rule

Lecture 23 Implicit Differentiation

Lecture 24 Example: Implicit Differentiation

Section 6: Unit 2 (Part II): Differentiation: Derivatives of Transcendental Functions

Lecture 25 Downloadable Notes

Lecture 26 Review on Trigonometric Functions

Lecture 27 Derivatives of Trigonometric Functions

Lecture 28 Examples: Derivatives of Trigonometric Functions

Lecture 29 Inverse Trigonometric Functions

Lecture 30 Derivatives of Inverse Trigonometric Functions

Lecture 31 Review on Exponential and Logarithmic Rules

Lecture 32 Derivatives of Exponential and Logarithmic Functions

Section 7: Unit 4: Contextual Applications of Differentiation

Lecture 33 Downloadable Notes

Lecture 34 Overview of Unit 4

Lecture 35 L’Hôpital’s Rule

Lecture 36 More Indeterminate Type

Lecture 37 Rates of Change

Lecture 38 Examples: Rectilinear Motion

Lecture 39 Calculus in Physics (Kinematic Equations)

Lecture 40 Introduction to Differential Equations

Lecture 41 Simple Harmonic Motion

Lecture 42 Example: Simple Harmonic Motion

Lecture 43 Differentials

Lecture 44 Examples: Linear Approximation

Section 8: Unit 5: Analytical Applications of Differentiation

Lecture 45 Downloadable Notes

Lecture 46 Overview of Unit 5

Lecture 47 The Mean Value Theorem (MVT)

Lecture 48 Rolle's Theorem (A Special Case of MVT)

Lecture 49 Orthogonality

Lecture 50 Increasing and Decreasing

Lecture 51 Local Max/Min and Critical Points

Lecture 52 Examples: Critical Values

Lecture 53 First Derivative Test

Lecture 54 Concavity and Inflection Points

Lecture 55 Second Derivative Test

Lecture 56 Extreme Value Theorem (EVT)

Lecture 57 Curve Sketching

Lecture 58 Example 1: Curve Sketching

Lecture 59 Example 2: Curve Sketching

Lecture 60 Optimization Problems

Lecture 61 Examples: Optimization Problems

Section 9: Unit 6: Integration and Accumulation of Change

Lecture 62 Downloadable Notes

Lecture 63 Overview of Unit 6

Lecture 64 Area Estimation

Lecture 65 Example 2: Area Estimation of Sine Function

Lecture 66 Example 3: Area Estimation Physical Context

Lecture 67 Sigma Notation

Lecture 68 Summation Rules and Formulas

Lecture 69 Examples: Evaluate Summation

Lecture 70 Limit of a Riemann Sum

Lecture 71 Example 1: Evaluate Signed Area

Lecture 72 Example 2: Evaluate Signed Area

Lecture 73 Example 3: Evaluate Signed Area

Lecture 74 Example 4: Evaluate Signed Area

Lecture 75 Fundamental Theorem of Calculus (Part II)

Lecture 76 Basic Antiderivatives

Lecture 77 Proof of FTC (Part II)

Lecture 78 Properties of the Definite Integral

Lecture 79 Examples: Evaluate Definite Integral

Lecture 80 Fundamental Theorem of Calculus (Part I)

Lecture 81 Proof of FTC (Part I)

Lecture 82 Examples: FTC (Part I)

Lecture 83 Antiderivatives

Lecture 84 Examples: Antiderivatives in Physics

Lecture 85 Solving Non Basic Antiderivatives

Lecture 86 Substitution Method

Lecture 87 More Examples of u-Sub

Lecture 88 Algebraic Method

Lecture 89 Three "New" Basic Rules

Lecture 90 Algebraic Method: Completion of Square

Lecture 91 Long Division

Section 10: Unit 7: Differential Equations

Lecture 92 Downloadable Notes

Lecture 93 Overview of Unit 7

Lecture 94 Differential Equation (DE)

Lecture 95 Separable Differential Equations

Lecture 96 Examples: Separable DE

Lecture 97 Recap and More Examples: Separable DE

Section 11: Unit 8: Applications of Integration

Lecture 98 Downloadable Notes

Lecture 99 Overview of Unit 8

Lecture 100 Applications of Integration

Lecture 101 Average Value of a Function

Lecture 102 Mean Value Theorem for Integrals

Lecture 103 Proof of the MVT

Lecture 104 Revisited Examples: MVT

Lecture 105 Examples: MVT

Lecture 106 Area Between Curves

Lecture 107 Examples: Area Between Curves

Lecture 108 Example: Area Between Curves (Physics)

Lecture 109 Antoinette's Theorem

Lecture 110 Area Bounded by More Than 2 Curves

Lecture 111 Horizontal Rectangle Representation

Lecture 112 Examples: Horizontal Rectangle Representation

Lecture 113 Volume of Rotation

Lecture 114 Examples: Volume of Rotation

Lecture 115 Washer Method Involving Horizontal Rectangles

Lecture 116 The Shell Method

Lecture 117 Examples: The Shell Method

Section 12: Past AP Calculus AB Exams

Lecture 118 Past AP Calculus AB Exams

Lecture 119 Free-Response Questions 2024

Lecture 120 2024 Part A Solutions

Lecture 121 2024 Part B Solutions - 1

Lecture 122 2024 Part B Solutions - 2

Lecture 123 Free-Response Questions 2023

Lecture 124 2023 Part A Solutions

Lecture 125 2023 Part B Solutions - 1

Lecture 126 2023 Part B Solutions - 2

Lecture 127 Free-Response Questions 2022

Lecture 128 2022 Part A Solutions

Lecture 129 2022 Part B Solutions - 1

Lecture 130 2022 Part B Solutions - 2

Section 13: Conclusion

Lecture 131 Thank You & Good Luck & Next Step

Lecture 132 BONUS

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.