AB Calculus Manual (Revised 12/2019)

This page provides the AB Calculus Manual for the classroom - all chapters of this manual are provided as free downloads! This section is a complete high school course for preparing students to take the AB Calculus exam.


In addition to the Essentials section of the manual that provide complete coverage of all topics for the AB exam, there is a Non-Essentials section as well that givers topics that are relevant to AB calculus but not on the actual AP® exam. There is also a Review section that goes over the most common algebraic concepts that give students trouble.


This manual can easily replace an expensive textbook. Teachers teach right from it and students write in it.


The Solution Manual is exactly the same as the student manual except that the solutions with all important steps are shown. There is a one-to-one relationship between the pages of the student manual and the solution manual. So, for example, page 73 will have a series of problems and blank space for the students to write in the solutions. The solution manual's page 73 will have the same problems but with the solutions shown.


In addition, a set of answer pages (no shown work, just the answer) comes with the solution manual for the homework problems.  It is also available in download form as a stand-alone product.


New!  A new student section has been written called Calculus from 30,000 feet. Borrowed from Steven Strogatz's book Infinite Powers, this addendum is meant to be used after the AP exam and gives students a greater insight into how the Infinity Guideline breaks down comples probems into simper ones and then reassembles them. No homework or problems - just an attempy to see the Calculus forest from the trees.


School administrations are increasingly concerned with standards. This material in this manual is aligned to the AP® standards as defined in the their 2019 document: AP® Calculus AB and BC Course and Exam Description available on the website: www.apcentral.collegeboard.org. Although this is included with purchase of the AB Solutions in any format, you can download information about the standards at: AB Standards:




Because of the devastating impact to our way of life because of COVID-19, schools are in a particularly difficult position. It is still up in the air how safe they can be for the students but, no matter what,  classes have to be taught be adults. And those who teach courses like AP calculus are more likely to have years of experience, may be older and simply have to take fewer risks. For a number of schools and communities, the virtual classroom is the safest for everyone.


With that in mind, I have put together YouTube Videos that will teach your class the basic concepts of AP calculus. What is most exciting is that these will follow the classwork section of the AP Calculus manual. Students can download (for free) and print the AB manual student pages. They can download the video for each section and have thorough explanations of just about all the problems in the classwork section.  They can stop the video and write in solutions in their printed student manual. They can replay any section to better understand the steps. If they have questions, they can write them down and when you "meet" with them, you can help clear up their confusion.


They are narrated by me and the style is the same as if I were teaching a class. I show the thought process involved in solving calculus problems. The solutions are the same that appear in the solution manual, but these are explained audibly as well.  Unlike other math videos, you will not see me taking time to write solutions. They appear on the screen instantly and are legible and professional.   Videos will range from 10 minutes to 45 minutes depending on their complexity. Some of the more involved concepts are split into two videos, similar to what you would do when teaching - take several days to cover a topic.  When you "meet" with the students, you can then concentrate on the homework problems.


This is a huge but very exciting undertaking. These videos took time to construct, usually one every two days. But living in Florida, the COVID-19 capital of the world during the summer, they kept me busy for 7 months. All the videos in the AB Essentials and Non-Essentials sections are complete, as well as the Precalculus Review. There is close to 24 hours of instruction.


I suggest that you first view the introduction video to understand how the YouTube videos coordinate with the manual. Then view several of the videos to get a feel for them. Feel free to direct students to this page so that they can download them directly. Have them feel free to make comments (keeping them clean!) for each video. And of course if there is a mistake or I didn't make something clear enough or if they have a question, they can mention that in the comment or, ask you or me directly.


Here is my YouTube channel:




Purchase the Calc AB Solution Manual!
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Student AB Manual in printed form.
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Calc AB Solution Manual in printed form.

Also includes Answers to HW in download form.
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Calc AB Answers only to HW (no work

shown) in download form.

Only $14.95.



AB Calc Cover Pages
ABSolutionsp000Cover.pdf  0.5MB
Intro Video

Free YouTube


Pages 1-26 - Revised 11/30/20

01. Introduction

02. Tangent Lines

03. Average and Instanteous Rate of Change

04. Limits graphical

05. Limits Algebraic

ABStudentsp001-026.pdf  4.4MB

Download Free




Video 01/02


Video 03

Video 04

Video 05

Pages 27-46 - Revised 12/01/20

06. Derivative definition

07. Derivatives w/ technology

08. Differentiation techniques

09. Chain Rule

ABStudentsp027-046.pdf  4.6MB
Download Free


Video 06/07

Video 08a

Video 08b

Video 09

Pages 47-69 - Revised 12/01/20
10. Derivatives of trig functions
11. Implicit differentiation
12. Derivatives transcendentals


13. Derivatives of inverses
14. Linear approximations

ABStudentsp047-069.pdf  4.4MB
Download Free


Video 10

Video 11

Video 12a

Video 12b

Video 13

Video 14

Pages 70-93 - Revised 12/02/20
15. Continuity/differentiability
16. Related rates
ABStudentsp070-093.pdf  2.5MB


Video 15

Video 16a

Video 16b

Pages 94-121 - Revised 12/02/20
17. Straight-line motion


18. 3 important theorems
19. Function analysis

ABStudentsp094-121.pdf  4.5MB


Video 17a

Video 17b

Video 18

Video 19a

Video 19b

Pages 122-151 - Revised 12/04/20
20. Curve sketching
21. Absolute extrema
22. Optimization
23. Economic optimization
24. L'Hospital's rule
ABStudentsp122-151.pdf  3.3MB


Video 20

Video 21

Video 22

Video 23

Video 24

Pages 152-174 - Revised 12/05/20
25. Indefinite integration
26. u-substitution
27. Definite Integral and Area

28. The Accumulation Function

ABStudentsp152-174.pdf  5.7MB


Video 25

Video 26

Video 27

Video 28

Pages 175-198 - Revised 12/06/20
29. Riemann Sums


30. Fundamental Theorem

31. Definite integrals u-sub
32. Integrating transcendentals
33. Motion revisited

ABStudentsp175-198.pdf  4.6MB


Video 29a

Video 29b

Video 30

Video 31

Video 32

Video 33

Pages 199-212 - Revised 12/06/20
34. Average value, 2nd FTC
35. Inverse Trig
36. Area between curves
ABStudentsp199-212.pdf  3.2MB


Video 34

Video 35

Video 36

Pages 213-240 - Revised 12/06/20
37. Volumes


38. Integral Applications
39. Slope fields
40. DEQ's
41. Exponential growth
42. Other growth models

ABStudentsp213-240.pdf  3.6MB


Video 37a

Video 37b

Video 38

Video 39

Video 40

Video 41

Video 42

Pages 241-267 - Revised 1/010/21
1a. Introduction
12a. Logarithmic differentiation
14a. Differentials
26a. L'Hospital advanced
24b. Newton's Method
29a. Exact area w/limits
37a. Volume shells
ABStudentsp241-267NonEss.pdf  5.1MB



Video N12a

Video N14a

Video N24a

Video N24b

Video N27a

Video N37a

Pages 268-278
Complex fractions
Graphical solutions
Sigma notation
ABStudentsp268-278Review.pdf  3.4MB


Video R1

Video R2

Video R3

Video R4

Video R5

Calculus From 30,000 Feet  

Limits and the Infinity Guideline: p 279-284                      Download

Derivatives as a Measure of Change: p 285-294             Download

Infinitesimals and Differentials: p 295-300                        Download

Integrals - an Accumulation of Change: p 301-307          Download



Calculus Review questions are available on the
AP® Calc Review page: click here

(Previously items 49 and 50.)





Purchase the Calc AB Solution Manual!
Only $99.95
(for download)
Full Calc AB Manual in printed form.
Only $54.95
(plus $12 shipping)
Calc AB Solution Manual in printed form.
Only $129.95
(plus $12 shipping)

Calc AB Answers only to HW (no work

shown) in download form.

Only $14.95.




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