AP Calculus AB Math Lessons
The AP Calculus AB course in 22 lessons, from Introducing Limits to Average Value, Area and Volume, each one with its Key facts and a closing set of questions and answers.
- 87 US Letter pages
- 22 chapters
- 117 lesson sections
- PDF to print
- Cards accepted without a PayPal account
- Instant download, up to 3 devices
About this book
AP Calculus AB starts with limits and continuity and moves quickly to the derivative. The lessons cover the derivative rules, the chain rule, implicit differentiation, related rates, the Mean Value Theorem and optimization, then Riemann sums and the definite integral.
Every chapter opens with the skills it builds; in Increasing, Decreasing and the First Derivative Test, for instance: build a sign chart, understand the First Derivative Test, read a graph of f′. A Key facts box sums up what to remember. Most of the 117 lesson sections of the book are written as questions a student would ask, such as How does the derivative show increasing and decreasing?
For a student taking AP Calculus AB, a parent, or a teacher who wants chapter tests ready to print. Pair it with the AP Calculus AB Math Worksheets with Answers to practice each chapter right after reading it.
Detailed contents
The 22 chapters of the AP Calculus AB lesson book, the sections of each lesson and the page where each chapter starts.
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1
Introducing Limits
- What is a limit?
- How do you estimate a limit from a table?
- What are one-sided limits?
- When does a limit fail to exist?
- What is a reliable method?
- Limits intro lesson: questions and answers
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2
Evaluating Limits Algebraically
- What are the limit laws?
- What if substitution gives 0/0?
- How do you handle square roots?
- Which trig limits must you know?
- What is the Squeeze Theorem?
- What is a clean written method?
- Limit algebra lesson: questions and answers
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3
Continuity and the Intermediate Value Theorem
- What does it mean to be continuous?
- What kinds of discontinuity are there?
- How do you make a piecewise function continuous?
- What is the Intermediate Value Theorem?
- Continuity lesson: questions and answers
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4
Infinite Limits and Asymptotes
- What is an infinite limit?
- What are limits at infinity?
- How do you find limits at infinity of rational functions?
- What about exponential and logarithmic functions?
- How do you find every asymptote of a rational function?
- Asymptotes lesson: questions and answers
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5
The Derivative as a Limit
- What is the derivative?
- How do secant slopes become a tangent slope?
- How do you compute a derivative from the definition?
- What does a derivative tell you in a real situation?
- When is a function not differentiable?
- Derivative definition lesson: questions and answers
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6
Power, Sum and Basic Function Derivative Rules
- What are the basic derivative rules?
- How do you differentiate roots and fractions?
- What are the derivatives of sine, cosine, e^x and ln x?
- What is a good order of work?
- How do you find tangent and normal lines?
- Derivative rules lesson: questions and answers
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7
Product Rule, Quotient Rule and Trig Derivatives
- What is the product rule?
- u · v
- What is the quotient rule?
- What are the derivatives of the other trig functions?
- How do you use the rules together?
- What mistakes should you avoid?
- Product quotient lesson: questions and answers
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8
The Chain Rule
- What is the chain rule?
- How do you apply the chain rule step by step?
- What are the most common chain rule patterns?
- How do you use the chain rule with a table of values?
- Chain rule lesson: questions and answers
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9
Implicit Differentiation
- What is implicit differentiation?
- How do you do it step by step?
- How do products and other terms work?
- When are tangents horizontal or vertical?
- Implicit lesson: questions and answers
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10
Derivatives of Inverse Functions
- How do you differentiate an inverse function?
- What are the derivatives of inverse trig functions?
- What are higher-order derivatives?
- How do you choose a method?
- Inverse derivatives lesson: questions and answers
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11
Rates of Change in Context and Straight-Line Motion
- What does a derivative mean in context?
- How do position, velocity and acceleration connect?
- When is a particle speeding up or slowing down?
- What other rates of change appear in problems?
- Rates motion lesson: questions and answers
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12
Related Rates
- What is a related rates problem?
- How do you set up a ladder problem?
- What about volumes?
- Related rates lesson: questions and answers
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13
Linearization and L'Hopital's Rule
- What is a local linear approximation?
- When is the estimate too high or too low?
- What is L'Hôpital's Rule?
- Linearization lesson: questions and answers
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14
Mean Value Theorem and Extreme Value Theorem
- What is the Mean Value Theorem?
- What is the Extreme Value Theorem?
- What are critical numbers?
- How do you find absolute extrema on a closed interval?
- Mvt evt lesson: questions and answers
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15
Increasing, Decreasing and the First Derivative Test
- How does the derivative show increasing and decreasing?
- How do you build a sign chart?
- What is the First Derivative Test?
- How do you read a graph of f′?
- First derivative lesson: questions and answers
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16
Concavity and the Second Derivative
- What does the second derivative tell you?
- What is the second derivative test?
- How do f, f′ and f″ connect?
- Concavity lesson: questions and answers
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17
Optimization
- What is an optimization problem?
- How do you set up and solve one?
- How do you justify a maximum or minimum?
- What other models appear?
- Optimization lesson: questions and answers
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18
Riemann Sums and the Definite Integral
- What is accumulation of change?
- What is a Riemann sum?
- What is the trapezoidal sum?
- What is a definite integral?
- Riemann sums lesson: questions and answers
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19
Fundamental Theorem of Calculus and Antiderivatives
- What is an accumulation function?
- What is an antiderivative?
- How do you evaluate a definite integral?
- What is an initial value problem?
- Ftc lesson: questions and answers
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20
Integration by Substitution
- What is integration by substitution?
- How do you choose u?
- How do definite integrals change?
- What if substitution is not enough?
- U substitution lesson: questions and answers
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21
Differential Equations and Slope Fields
- What is a differential equation?
- What is a slope field?
- What is Euler's method?
- How do you solve by separation of variables?
- What are exponential growth and decay models?
- Differential equations lesson: questions and answers
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22
Average Value, Area and Volume
- How is the average value of a function defined?
- What do integrals say about moving objects?
- How is the area between two curves computed?
- How are volumes built from cross sections?
- How do discs and washers work?
- Ap calculus area volume lesson: questions and answers
Sample pages
Three pages from the AP Calculus AB Math Lessons, exactly as you will print them. Click to enlarge.
How to use this lesson book
Read one chapter at a time
The 22 chapters follow the order of the AP Calculus AB course; at about 4 pages each, a chapter is one short sitting.
Copy the key facts
Write the Key facts of Riemann Sums and the Definite Integral on an index card: a ready-made summary for the night before a quiz.
Try the closing questions
Cover the answers at the end of Average Value, Area and Volume and answer first: the best way to check understanding.
Frequently asked questions
What is in the AP Calculus AB lesson book?
87 US Letter pages and 22 chapters, one lesson per chapter, with 117 lesson sections in all. The full contents are listed above on this page.
Does the AP Calculus AB lesson book include exercises?
Each chapter ends with a short set of questions and answers. For full practice, the AP Calculus AB Math Worksheets with Answers follows the same 22 chapters.
Do I need the AP Calculus AB Math Worksheets with Answers along with the lesson book?
No, the AP Calculus AB Math Lessons stands on its own. But both books follow the same 22 chapters of AP Calculus AB; together they make a complete course, lesson then practice.
How do I receive the AP Calculus AB Math Lessons?
Right after paying with PayPal or a card, you reach your download page, where the AP Calculus AB Math Lessons is waiting. An email with the link is sent too.
Can I print the AP Calculus AB lesson book and open it on several devices?
Yes: the 87-page PDF of the AP Calculus AB Math Lessons prints as often as you need and opens on three devices (computer, tablet, phone). It carries your name at the bottom of the pages.
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