Everything You Need to Ace AP Calculus AB/BC Exams in One Page!

This page features a comprehensive collection of AP Calculus AB/BC tutorial videos aligned with the full curriculum by Tony Record, enriched with supplemental lessons from my YouTube channel. These videos are crafted to help you not only succeed on the AP Calculus AB/BC exam but also deepen your mathematical understanding and sharpen your analytical thinking - skills essential for future coursework in linear algebra, differential equations, and multivariable calculus (Calculus III). I hope these tutorials support you on your path to earning a 5 on the AP exam. 

Note: For the digital AP exams, an embedded Desmos graphing calculator will be available within the exam platform for sections where calculator use is permitted. However, it's still recommended that you bring your own approved calculators, such as TI-84 Plus CE or TI-Nspire calculator, which I used most in the videos, to the exam and ensure that you learn how to use them. If you don't have a TI-84 Plus CE calculator to practice at home, try the online version here. Please check out and bookmark the following link for the Desmos version on the Digital PSAT, NMSQT, SAT, and AP Exams.

AP Calculus Exam Date: May 11th.

Unit O: AP Calculus Prerequisites 

Summer Packet

Unit 1: Limits & Continuity (AB & BC)

Topic 1.1 Can Change Occur at an Instant?

Video 1: Topic 1.1 Can Change Occur at an Instant?

Topic 1.2 Defining Limits and Using Limit Notation

Topic 1.4 Estimating Limit Values from Tables

Video 2: Topic 1.2 & 1.4 Defining Limits + Estimating from Tables 

Topic 1.3 Estimating Limit Values from Graphs

Video 3: Topic 1.3  Estimating Limit Values from Graphs

Topic 1.5 Determining Limits Using Algebraic Properties

Video 4: Topic 1.5(A) Mastering Limits with Algebra & Composite Functions

Video 5: Topic 1.5(B) Non-Traditional Composite/Operation Limits

Topic 1.6 Determining Limits Using Algebraic Manipulation

Topic 1.7 Selecting Procedures for Determining Limits

Video 6: Topic 1.6 & 1.7 Mastering Limit Techniques: Algebraic Manipulation & Strategic Selection 

Topic 1.8 Determining Limits Using the Squeeze Theorem

Video 7: Topic 1.8(A) Proof of lim (sin x)/x = 1 — Geometry, Squeeze Theorem, and Beyond!

Video 8: Topic 1.8(B) Proof of the Limit of (1 - cos x)/x = 0

Video 9: Topic 1.8(C) Proof of lim (tan x)/x = 1

Video 10: Topic 1.8(D) Crushing Limits with the Squeeze Theorem

Topic 1.9 Connecting Multiple Representations of Limits

Video 11: Topic 1.9 Visualize It All: Mastering Limits with Multiple Representations 

Topic 1.10 Exploring Types of Discontinuities

Topic 1.11 Defining Continuity at a Point

Topic 1.12 Confirming Continuity Over an Interval

Topic 1.13 Removing Discontinuities

Video 12: Topic 1.10-1.13 A Deep Dive into Discontinuities & Continuity of Functions

Topic 1.14 Infinite Limits and Vertical Asymptotes

Video 13: Topic 1.14 Crash Course: Infinite Limits & Vertical Asymptotes

Topic 1.15 Limits at Infinity and Horizontal Asymptotes

Video 14: Topic 1.15 Endless Insights: Limits at Infinity & Horizontal Asymptotes

Topic 1.16 Intermediate Value Theorem (IVT)

Video 15: Topic 1.16 Intermediate Value Theorem Demystified

Video 16: Unit 1 Crash Course Everything You Need to Know About the Limits, Continuity, and Intermediate Value Theorem (IVT) for the AP Exam

If you're looking to deepen your understanding of advanced concepts, give this a read.

• Limits of Functions

Unit 2: Differentiation: Definition & Fundamental Properties (AB & BC)

Topic 2.1 Defining Average and Instantaneous Rate of Change at a Point

Video 17: Topic 2.1 From Average to Instant: Mastering Instantaneous Rate of Change

Topic 2.2 Defining the Derivative of a Function and Using Derivative Notation

Topic 2.3 Estimating Derivatives of a Function at a Point

Topic 2.4 Connecting Differentiability and Continuity

Video 18: Topic 2.2-2.4 Sharp Corners, Gaps & Tangents: When Derivatives Don’t Exist! 

Topic 2.5 Applying the Power Rule

Topic 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple

Video 19: Topic 2.5-2.6 Derivatives in Seconds: The Power Rule and Beyond

Topic 2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)

Video 20: Topic 2.7(A) Proof of d/dx[sin(x)] = cos(x) and d/dx[cos(x)] = -sin(x)

Video 21: Topic 2.7(B) Derivatives of sin, cos, eˣ, and ln(x) – No Memorizing, Just Mastery

Topic 2.8 The Product Rule

Video 22: Topic 2.8(A) Proof of the Product Rule (fg)' = f·g' + f'·g

Video 23: Topic 2.8(B) Don’t FOIL It! Use the Product Rule Like a Calculus Pro

Topic 2.9 The Quotient Rule

Video 24: Topic 2.9(A) Proof of the Quotient Rule Why (f/g)’ Isn’t Just f’/g’ 

Video 25: Topic 2.9(B) Derivatives of Rational Functions? Use the Quotient Rule!

Topic 2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x) 

Video 26: Topic 2.10(A) Proving the Big Four: tan, cot, sec, and csc Derivatives Made Easy

Video 27: Topic 2.10(B) Mastering Trig Derivatives: tan(x), cot(x), sec(x), and csc(x) with examples

Video 28: Unit 2 Crash Course Everything You Need to Know About the Differentiation for the AP Exam

Unit 3: Differentiation: Composite, Implicit, & Inverse Functions (AB & BC)

Topic 3.1 The Chain Rule

Video 29: Topic 3.1 Chain Rule Hacks to Boost Your AP Calculus Scores

Topic 3.2 Implicit Differentiation

Video 30: Topic 3.2 Implicit Differentiation Demystified – Must-Know for the AP Exam 

Topic 3.3 Differentiating Inverse Functions

Video 31: Topic 3.3 Differentiating Inverse Functions with Confidence!

Topic 3.4 Differentiating Inverse Trigonometric Functions

Video 32: Topic 3.4 Arc-attack! Mastering Derivatives of Inverse Trig Functions

Topic 3.5 Selecting Procedures for Calculating Derivatives

Video 33: Topic 3.5 Selecting Procedures for Calculating Derivatives

Topic 3.6 Calculating Higher-Order Derivatives

Video 34: Topic 3.6 Beyond the First Derivative: Mastering Higher-Order Derivatives!

Video 35: Unit 3 Crash Course Everything You Need to Know About the Differentiation of Composite, Implicit, & Inverse Function for the AP Exam 

Unit 4: Contextual Applications of Differentiation (AB & BC)

Topic 4.1 Interpreting the Meaning of the Derivative in Context

Video 36: Topic 4.1 Interpreting Derivatives in Context with AP Style Examples! 

Topic 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

Video 37: Topic 4.2 Position, Velocity & Acceleration—The Ultimate Motion Breakdown with AP-Style Examples!

Topic 4.3 Rates of Change in Applied Contexts Other Than Motion

Video 38: Topic 4.3 Rates of Change in Applied Contexts Other Than Motion

Topic 4.4 Introduction to Related Rates

Topic 4.5 Solving Related Rates Problems

Video 39: Topic 4.4-4.5(A) The #1 Related Rates Video You Need for the AP Calc Exam! (Part 1)

Video 40: Topic 4.4-4.5(B) Master Related Rates with These Real AP Calc Problems! (Part 2)

Topic 4.6 Approximating Values of a Function Using Local Linearity and Linearization

Video 41: Topic 4.6 Linear Approximations | Master Linearization & Local Linearity

Topic 4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms

Video 42: Topic 4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms

Video 43: Unit 4 Crash Course Everything You Need to Know About the Contextual Applications of Differentiation for the AP Exam 

Unit 5: Analytical Applications of Differentiation (AB & BC)

Topic 5.1 Using the Mean Value Theorem (IVT)

Video 44: Topic 5.1 Mastering the Mean Value Theorem (IVT) & the Rolle's Theorem

Topic 5.2 Extreme Value Theorem (EVT), Global Versus Local Extrema, and Critical Points

Video 45: Topic 5.2 Extreme Value Theorem (EVT), Global vs. Local Extrema, and Critical Points

Topic 5.3 Determining Intervals on Which a Function is Increasing or Decreasing

Video 46: Topic 5.3 Determine Intervals on Which a Function is Increasing or Decreasing

Topic 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema

Video 47: Topic 5.4 First Derivative Test | Relative Maximum | Relative Minimum

Topic 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema

Video 48: Topic 5.5 Master the Candidates Test | Global Maximum & Minimum

Topic 5.6 Determining Concavity of Functions over Their Domains

Video 49: Topic 5.6 Determining Concavity of Functions over Their Domains | Inflection Points | Second Derivative

Topic 5.7 Using the Second Derivative Test (SDT) to Determine Extrema

Video 50: Topic 5.7 Using the Second Derivative Test (SDT) to Determine Extrema

Topic 5.8 Sketching Graphs of Functions and Their Derivatives

Topic 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative

Video 51: Topic 5.8-5.9(A) Sketching f′(x) from f(x) — A Visual Guide to Derivatives

Video 52: Topic 5.8-5.9(B) Graphing f(x) from f′(x) — The Reverse Engineering of Calculus!

Topic 5.10 Introduction to Optimization Problems

Topic 5.11 Solving Optimization Problems

Video 53: Topic 5.10-5.11 Master Optimization Problems in Minutes!

Topic 5.12 Exploring Behaviors of Implicit Relations

Video 54: Topic 5.12 Exploring Behaviors of Implicit Relations

Video 55: Unit 5 Crash Course Everything You Need to Know About the Analytical Applications of Differentiation for the AP Exam

If you're looking to deepen your understanding of advanced concepts, give this a read.

• Applications of Differentiation in Solving Equations & Systems of Equations

• Applications of Differentiation in Solving Equations with Parameters

Unit 6: Integration & Accumulation of Change (AB & BC)

Topic 6.1 Exploring Accumulation of Change

Video 56: Topic 6.1 From Rate to Total: Mastering Accumulations of Change

Topic 6.2 Approximating Areas with Riemann Sums

Video 57: Topic 6.2 Approximating Areas with Left, Right, and Midpoint Riemann Sums as well as Trapezoidal Rules

Topic 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation

Video 58: Topic 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation

Topic 6.4 The Fundamental Theorem of Calculus (FTC) and Accumulation Functions

Topic 6.5 Interpreting the Behavior of Accumulation Functions Involving Area

Video 59: Topic 6.4-6.5A Unlocking the Fundamental Theorem of Calculus (FTC) & Net Change 

Video 60: Topic 6.4-6.5B Mastering Rate In–Rate Out Problems

Topic 6.6 Applying Properties of Definite Integrals

Video 61: Topic 6.6 Applying Properties of Definite Integrals 

Topic 6.7 The Fundamental Theorem of Calculus (FTC) and Definite Integrals

Topic 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

Video 62: Topic 6.7-6.8 The Fundamental Theorem of Calculus (FTC), Definite Integrals, and Indefinite Integrals

Topic 6.9 Integrating Using Substitution

Video 63: Topic 6.9 The Secret to Solving Tricky Integrals: u-Substitution Explained

Topic 6.10 Integrating Functions Using Long Division and Completing the Square

Must watch Videos 64 - 67 since they are prerequisites for Topic 6.10.

Video 64: Long Division & Synthetic Division with 8 Specific Examples - The easy way!

Video 65: Dividing Polynomials using 3 methods: Factoring - Long Division - Synthetic Division.

Video 66: Factoring Special Cases of polynomials.

Video 67: Solving Quadratic Equations by Taking Square Root and Completing Squares.

Video 68: Topic 6.10 Tame the Toughest Integrals: Long Division & Completing the Square Explained!

Topic 6.11 Integrating Using Integration by Parts (BC only)

Video 69: Topic 6.11 Master Integration by Parts Step-by-Step

Topic 6.12 Integrating Using Linear Partial Fractions (BC only)

Video 70: Topic 6.12 Integrating Using Partial Fraction Decomposition

Topic 6.13 Evaluating Improper Integrals (BC only)

Video 71: Topic 6.13 Infinite Limits? No Problem! Evaluating Improper Integrals

Topic 6.14 Selecting Techniques for Antidifferentiation

Video 72: Topic 6.14 Selecting the Best Techniques for Antidifferentiation

Video 73: Unit 6 Crash Course Everything You Need to Know About Integration for the AP exam

If you're looking to deepen your understanding of advanced concepts, give this a read.

• Advanced Integration of Rational Functions

• Integration of Composite Functions

• Integration of Trigonometric Functions in Math Olympiad

• Video 74: MIT Integration Bee 2025 The Improper Integral That Raised Eyebrows

• Video 75: Proof of the Most Mysterious Limit in Calculus lim(1+1/n)^n = e!

Unit 7: Differential Equations (AB & BC)

Topic 7.1 Modeling Situations with Differential Equations

Video 76: Topic 7.1

Topic 7.2 Verifying Solutions for Differential Equations

Video 77: Topic 7.2

Topic 7.3 Sketching Slope Fields

Topic 7.4 Reasoning Using Slope Fields

Video 78: Topic 7.3-7.4

Topic 7.5 Euler's Method (BC only)

Video 79: Topic 7.5

Topic 7.6 General Solutions Using Separation of Variables

Video 80: Topic 7.6

Topic 7.7 Particular Solutions using Initial Conditions and Separation of Variables

Video 81: Topic 7.7

Topic 7.8 Exponential Models with Differential Equations

Video 82: Topic 7.8

Topic 7.9 Logistic Models with Differential Equations (BC only)

Video 83: Topic 7.9

Video 84: Unit 7 Crash Course

If you're looking to deepen your understanding of advanced concepts, give this a watch.

Video 85: Introduction to Differential Equations - Order - ODE - PDE - Solutions.

Video 86: Find n-Parameter Family of Solutions, General Solution, Particular Solution.

Unit 8: Applications of Integration (AB & BC)

Topic 8.1 Average Value of a Function on an Interval

Video 83: Topic 8.1

Topic 8.2 Position, Velocity, and Acceleration Using Integrals

Video 84: Topic 8.2

Topic 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

Video 85: Topic 8.3

Topic 8.4 Area Between Curves (with respect to x)

Video 86: Topic 8.4

Topic 8.5 Area Between Curves (with respect to y)

Video 87: Topic 8.5

Topic 8.6 Area Between Curves - More than Two Intersections

Video 88: Topic 8.6

Topic 8.7 Cross Sections: Squares and Rectangles

Topic 8.8 Cross Sections: Triangles and Semicircles

Video 89: Topic 8.7-8.8

Topic 8.9 Disc Method: Revolving Around the x- or y- Axis

Video 90: Topic 8.9

Topic 8.10 Disc Method: Revolving Around Other Axes

Video 91: Topic 8.10

Topic 8.11 Washer Method: Revolving Around the x- or y-Axis

Video 92: Topic 8.11

Topic 8.12 Washer Method: Revolving Around Other Axes

Video 93: Topic 8.12

Topic 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC only)

Video 94: Topic 8.13

Video 95: Unit 8 Crash Course

Unit 9: Parametric Equations, Polar Coordinates, & Vector-Valued Functions  (BC only)

Topic 9.1 Defining and Differentiating Parametric Equations

Video 96: Topic 9.1

Topic 9.2 Second Derivatives of Parametric Equations

Video 97: Topic 9.2

Topic 9.3 Arc Lengths of Curves (Parametric Equations)

Video 98: Topic 9.3

Topic 9.4 Defining and Differentiating Vector-Valued Functions

Video 99: Topic 9.4

Topic 9.5 Integrating Vector-Valued Functions

Video 100: Topic 9.5

Topic 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions

Video 101: Topic 9.6

Topic 9.7 Defining Polar Coordinates and Differentiating in Polar Form

Must watch Videos 102 - 109 since they are prerequisites for Topic 9.7.

Video 102: How to Find Multiple Representations of Polar Coordinates.

Video 103: How to Convert between Polar and Rectangular Coordinates.

Video 104: Tests for Symmetry.

Video 105: Graphs of Polar Equations of Circles.

Video 106: Graphs of Limacon Curves.

Video 107: Graphs of Rose Curves.

Video 108: Graphs of Lemniscate Curves.

Video 109: Graphs of Archimedean Spirals: TI-Nspire, TI-84, & Desmos Made Easy! 

After learning how to graph polar functions by hand from Videos 105–108, use the following link to practice graphing them on Desmos. 

Video 110: Polar Function Graph Related Problems.

Here's a link to a Desmos demonstration that beautifully illustrates the relationship between polar and rectangular graphs on the same xy-coordinate plane - definitely worth exploring!

 Topic 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

Video 111: Topic 9.8

Topic 9.9 Finding the Area of the Region Bounded by Two Polar Curves

Video 112: Topic 9.9

Video 113: Unit 9 Crash Course

Unit 10: Infinite Sequences & Series (BC only)

Must watch Videos 113 since it is a prerequisite for Topic 10.1-10.2.

Video 114: Change in Arithmetic and Geometric Sequences.

Topic 10.1 Defining Convergent and Divergent Infinite Series

Video 115: Topic 10.1

Topic 10.2 Working with Geometric Series

Video 116: Topic 10.2

Topic 10.3 The nth Term Test for Divergence

Video 117: Topic 10.3

Topic 10.4 Integral Test for Convergence

Video 118: Topic 10.4

Topic 10.5 Harmonic Series and p-Series

Video 119: Topic 10.5

Topic 10.6 Comparison Tests for Convergence

Video 120: Topic 10.6

Topic 10.7 Alternating Series Test for Convergence

Video 121: Topic 10.7

Topic 10.8 Ratio Test for Convergence

Video 122: Topic 10.8

Topic 10.9 Determining Absolute or Conditional Convergence

Video 123: Topic 10.9

Topic 10.10 Alternating Series Error Bound

Video 124: Topic 10.10

Topic 10.11 Finding Taylor Polynomial Approximations of Functions

Video 125: Topic 10.11

Topic 10.12 Lagrange Error Bound

Video 126: Topic 10.12

Topic 10.13 Radius and Interval of Convergence of Power Series

Video 127: Topic 10.13

Topic 10.14 Finding Taylor Maclaurin Series for a Function

Video 128: Topic 10.14

Topic 10.15 Representing Functions as a Power Series

Video 129: Topic 10.15

Video 130: Unit 10 Crash Course

If you're looking to deepen your understanding of advanced concepts, give this a read.

• Techniques in Solving Sequences & Series

AP Calculus Exam Prep - Road to a 5!

Past AP Calculus AB/BC Exams

Use the past AP Calculus AB/BC exams below to sharpen your skills and get familiar with the test format. Reviewing real exam questions helps build familiarity with the format, reinforce key concepts, and boost confidence. Practicing with these resources is one of the best ways to identify strengths and target areas for growth - use them to your full advantage! If there's any concept you've missed or want to strengthen your understanding of, be sure to check out the corresponding videos above.

Video 1: Full Solutions to the AP Calculus AB FRQ 2023.

Video 2: Full Solutions to the AP Calculus BC FRQ 2023.

Video 3: Full Solutions to the AP Calculus AB FRQ 2024.

Video 4: Full Solutions to the AP Calculus BC FRQ 2024.

Video 5: Full Solutions to the AP Calculus AB FRQ 2025.

Video 6: Full Solutions to the AP Calculus BC FRQ 2025.

Assorted Advanced Concepts

Dive into a collection of advanced math concepts!

This series of videos covers a variety of challenging topics designed to deepen your understanding and sharpen your problem-solving skills. Whether you’re preparing for competitions, exams, or just love advanced math, these concepts will push your thinking and expand your toolkit. Ready to level up? Let’s get started! 

Video 1: Crack the Code: Solve the Integral, Get the Wi-Fi 

Video 2: This Trig Integral Broke My Brain… 

Video 3: The Most Satisfying Integral You’ll See Today – Putnam Challenge 

Video 4: Only True Math Nerds Can Solve This MIT Integral. 

Video 5: Crack the Code: Evaluating a Hard Trigonometric Integral! 

Video 6: Oxford MAT 1998’s Toughest Integral — Can You Solve It? 

Video 7: A Stunning Definite Integral from Vietnam – Can You Solve It? 

Video 8: Can You Solve This Tough JEE Advanced Limit? 

Video 9: Dare to Solve This Radical Trig Integral? 

Video 10: Double Your Skills: 2 Ways to Find Tough Limits 

Video 11: This Integral Stumped Math Olympiad Students — Can You Solve It? 

Video 12: Can You Crack This Putnam-Level Integral? 

Video 13: This Trick Makes Integrating cos⁶xdx Simple! 

Video 14: Level Up Your Integration Skills with Square Root of tanxdx 

Video 15: This Rational Function Looks Scary… But You’ve Got This! Integrate 1/(x^6 - 1) 

Video 16: How to Integrate cosⁿx Like a Math Pro! 

Video 17: How to Integrate (3 + cos⁵x)dx — The Smart Way! 

Video 18: Solve This Rational Integral FAST or Lose the Challenge! ⏳ 

Video 19: Mind-Blowing Integral Trick! 🔥 Solving a Tough Cos² Integral Step-by-Step

Video 20: This Rational Integral Stumps Most Calculus Students! 

Video 21: Disk & Washer Methods Made Easy — AP Calc Must-Know! 

Video 22: JEE Advanced Killer Integral – Only the Best Can Solve It! 

Video 23: 2024 JEE Advanced: The Insane Integral Everyone's Talking About! 

Video 24: The Integral That Scares Students — Integral of ln(tanx)/sinxcosxdx 

Video 25: This Tough Composite Integral Stumped Students!  

Video 26: This Radical Integral Looks Scary… But Watch How Easy It Gets! 😲 

Video 27: MIT Integration Bee 2025: Can You Solve This Before Me? 

Video 28: MIT Bee Final Boss: Insane Trig Integral DECODED! 

Video 29: How to Tackle Hard Trig Integrals — Integration Bee Strategy 

Video 30: Stop Struggling! Integrate Composite Functions Like a Pro! 

Video 31: This Tricky Integral Stumped the MIT Semifinals | MIT Integration Bee 2025 

Video 32: Cracking an MIT Final Round Integral with Just One Clever Trick

Video 33: MIT Integration Bee 2022: Tough Integral, Tougher Competition! 

Video 34: MIT’s “Impossible” Integral Cracked with One Simple Trick! MIT Integration Bee 2022

Video 35: Mastering 20 Advanced Integrals from Olympiads & MIT Integration Bee 

Video 36: JEE Advanced Trig Integral That Stumps Everyone 🤯 

Video 37: 20 Hard Integrals from the 2025 MIT Integration Bee (Can You Survive?)

Video 38: MIT Integration Bee 2025: Infinite Series Meets Calculus

Video 39: A Deep Dive into a Brutal Trig Integral from the MIT Integration Bee 2025

Video 40: MIT Integration Bee Meets Math Olympiad: TOP 20 Killer Integrals

...and many more. Explore my playlist of nearly 1000 Math Olympiad problem videos, with new content added regularly. Dive in and challenge yourself! 

Full Solutions to the AP Calculus AB/BC FRQ 2025

Full Solutions to the AP Calculus AB/BC FRQ 2024

Full Solutions to the AP Calculus AB/BC FRQ 2023

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