Udemy – Ap Calculus Ab The 16-Hour Fast Track To A Perfect Score

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.

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