The Readable Calculus Project (AB version)
Table of Contents
Introduction: General Overview of Calculus [Intro pdf]
Chapter 1: Derivatives [2023-24 Chapter 1 pdf]
Overview: Review of Derivatives Rules
1.1: The Power and Exponential Rules
1.2: Composite Functions and the Chain Rule
1.3: Trig, Trig Inverse, and Log Rules
1.4: Derivatives in Context: Local Linearity and Motion
1.5: The Product Rule
1.6: The Quotient Rule
1.7: Higher Order Derivatives
1.8: Intro to AP: Basic Derivatives Numerically and Graphically
Chapter 1 Practice Test
Chapter 1 Answer Key
Chapter 2: Indefinite Integrals [2023-24 Chapter 2 pdf]
Overview: The Operations of Calculus
2.1: The Power and Transcendental Rules
2.2: Initial Conditions
2.3: Rectilinear Motion
2.4: Integration by Substitution: Reversing the Chain Rule
2.5: Integration by Substitution: Transcendental Functions
2.6: Separable Differential Equations
2.7: Intro to AP: Slope Fields
Chapter 2 Practice Test
Chapter 2 Answer Key
Chapter 3: Definite Integrals [2023-24Chapter 3 pdf]
Overview:
3.1: Definite Integrals and the Fundamental Theorem of Calculus
3.2: Integration by U-Substitution
3.3: Context: Area, Displacement, and Net Change
3.4: Intro to AP: Accumulation of Rates
3.5: Approximate Integration – Riemann Sums
3.6: Intro to AP: Table Problems
Chapter 3Practice Test
Chapter 3 Answer Key
Chapter 4 Applications of the Derivative I--Graphing [2023-24 Chapter 4 pdf]
Overview:
4.1: Extremes and the Derivative Tests
4.2: Optimization
4.3 The Mean Value Theorem
4.4 Intro to AP: Input-Output Problems
4.5: The Second Derivative, Points of Inflection, and Concavity
4.6: Graphing with Derivatives
4.7: Graphical Analysis I
4.8: Intro to AP: Graphical Analysis II
Chapter 4 Practice Test
Chapter 4 Answer Key
Chapter 5: Applications of the Derivative II—Rates of Change [2023-24 Chapter 5 pdf]
Overview:
5.1: Motion
5.2: Implicit Differentiation
5.3: Related Rates
5.4: Logistic Growth
Chapter 5 Practice Test
Chapter 5 Answer Key
Chapter 6: Applications of Integrals [2023-24 Chapter 6 pdf]
Overview:
6.1: Area between Two Curves
6.2: Arc Length
6.3: Volume by Rotation about the x-axis
6.3: Volume by Rotation about the y-axis
6.5: Volume by Rotation about a Line not an Axis
6.6: Volume by Cross-section Method
6.7: AP Volume FRQs
6.8: Volume by Shell Method
Chapter 6 Practice Test
Chapter 6 Answer Key
Chapter 7: Limits, Continuity and Differentiability [2023-24 Chapter 7 pdf]
Overview: Introduction to Limits
7.1: Limits and L’Hopital’s Rule
7.2: The Limit Definitions of a Derivative
7.3: One-sided Limits
7.4: Continuity
7.5: Differentiability and Smoothness
7.6: Limits at Infinity and End Behavior
Chapter 7 Practice Test
Chapter 7 Answer Key
Chapter 8: AP Calculus AB Review [2023-24 Chapter 8]
Overview:
8.1: Accumulation of Rates
8.2: Reasoning from Tabular Data
8.3: Graphical Analysis
8.4: Rectilinear Motion
8.5: Differential Equations
8.6: Area & Volume
8.7: Related Rates
8.8: Implicit Differentiation
8.9: Miscellaneous Topics
Appendix A: Reminders from PreCalculus [2023-24 Appendix A]
A.1: PreCalculus Basics
A.2: Important Facts for Calculus
A.3: Factoring Review
A.4: Sign Patterns
Finally, this book was funded, in part with money from a government grant allocated during the COVID pandemic. It was written particularly to address learning loss due to COVID – since much material was cut from curricula due to shutdowns of schools, we wrote this to help students transition to an AP level course while teaching skills that were lost during school shutdowns. It is designed so that a student can read and study the material independently to make up for any deficits due to the COVID pandemic.
- Project Manager/Lead Writer: Kevin Quattrin
- Associate Writer: Paul Maychrowitz
- Associate Writer: Najla (nee Fawal) Abrao
- Chief Editor: Elizabeth Regalia
Table of Contents
Introduction: General Overview of Calculus [Intro pdf]
Chapter 1: Derivatives [2023-24 Chapter 1 pdf]
Overview: Review of Derivatives Rules
1.1: The Power and Exponential Rules
1.2: Composite Functions and the Chain Rule
1.3: Trig, Trig Inverse, and Log Rules
1.4: Derivatives in Context: Local Linearity and Motion
1.5: The Product Rule
1.6: The Quotient Rule
1.7: Higher Order Derivatives
1.8: Intro to AP: Basic Derivatives Numerically and Graphically
Chapter 1 Practice Test
Chapter 1 Answer Key
Chapter 2: Indefinite Integrals [2023-24 Chapter 2 pdf]
Overview: The Operations of Calculus
2.1: The Power and Transcendental Rules
2.2: Initial Conditions
2.3: Rectilinear Motion
2.4: Integration by Substitution: Reversing the Chain Rule
2.5: Integration by Substitution: Transcendental Functions
2.6: Separable Differential Equations
2.7: Intro to AP: Slope Fields
Chapter 2 Practice Test
Chapter 2 Answer Key
Chapter 3: Definite Integrals [2023-24Chapter 3 pdf]
Overview:
3.1: Definite Integrals and the Fundamental Theorem of Calculus
3.2: Integration by U-Substitution
3.3: Context: Area, Displacement, and Net Change
3.4: Intro to AP: Accumulation of Rates
3.5: Approximate Integration – Riemann Sums
3.6: Intro to AP: Table Problems
Chapter 3Practice Test
Chapter 3 Answer Key
Chapter 4 Applications of the Derivative I--Graphing [2023-24 Chapter 4 pdf]
Overview:
4.1: Extremes and the Derivative Tests
4.2: Optimization
4.3 The Mean Value Theorem
4.4 Intro to AP: Input-Output Problems
4.5: The Second Derivative, Points of Inflection, and Concavity
4.6: Graphing with Derivatives
4.7: Graphical Analysis I
4.8: Intro to AP: Graphical Analysis II
Chapter 4 Practice Test
Chapter 4 Answer Key
Chapter 5: Applications of the Derivative II—Rates of Change [2023-24 Chapter 5 pdf]
Overview:
5.1: Motion
5.2: Implicit Differentiation
5.3: Related Rates
5.4: Logistic Growth
Chapter 5 Practice Test
Chapter 5 Answer Key
Chapter 6: Applications of Integrals [2023-24 Chapter 6 pdf]
Overview:
6.1: Area between Two Curves
6.2: Arc Length
6.3: Volume by Rotation about the x-axis
6.3: Volume by Rotation about the y-axis
6.5: Volume by Rotation about a Line not an Axis
6.6: Volume by Cross-section Method
6.7: AP Volume FRQs
6.8: Volume by Shell Method
Chapter 6 Practice Test
Chapter 6 Answer Key
Chapter 7: Limits, Continuity and Differentiability [2023-24 Chapter 7 pdf]
Overview: Introduction to Limits
7.1: Limits and L’Hopital’s Rule
7.2: The Limit Definitions of a Derivative
7.3: One-sided Limits
7.4: Continuity
7.5: Differentiability and Smoothness
7.6: Limits at Infinity and End Behavior
Chapter 7 Practice Test
Chapter 7 Answer Key
Chapter 8: AP Calculus AB Review [2023-24 Chapter 8]
Overview:
8.1: Accumulation of Rates
8.2: Reasoning from Tabular Data
8.3: Graphical Analysis
8.4: Rectilinear Motion
8.5: Differential Equations
8.6: Area & Volume
8.7: Related Rates
8.8: Implicit Differentiation
8.9: Miscellaneous Topics
Appendix A: Reminders from PreCalculus [2023-24 Appendix A]
A.1: PreCalculus Basics
A.2: Important Facts for Calculus
A.3: Factoring Review
A.4: Sign Patterns
Finally, this book was funded, in part with money from a government grant allocated during the COVID pandemic. It was written particularly to address learning loss due to COVID – since much material was cut from curricula due to shutdowns of schools, we wrote this to help students transition to an AP level course while teaching skills that were lost during school shutdowns. It is designed so that a student can read and study the material independently to make up for any deficits due to the COVID pandemic.