BC Calculus Manual (Revised 12/2019)

This page provides the BC 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 BC Calculus exam.


In addition to the Essentials section of the manual that provide complete coverage of all topics for the BC exam, there is a Non-Essentials section as well that teaches topics that are relevant to BC calculus but not on the actual AP® exam. There is also a Review section that goes over the most important concepts from AB Calculus.


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) to homework is included with the solution manual.  It is also available in download form as a stand-alone product.


New: 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 BC Solutions in any format, you can download information about the standards at: BC 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 BC 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 15 minutes to 35 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 BC Essentials and Non-Essential sections are complete taking up over 17 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 BC Solution Manual.
Only $99.95
(for download) 



Student BC Manual (no solutions) in printed form.
Only $54.95
(plus $10 shipping)



Calc BC Solution Manual in printed form.
Only $129.95
(plus $10 shipping)



Calc BC Answers only to HW (no work

shown) in download form.

Only $14.95.





1. BC First Pages
Intro Video
Essentials   YouTube Videos free

Pages 1-30 - Revised 12/6/20
 01. Indeterminate Forms/L'Hospital's Rule
 02. Integration by Parts
 03. Integration by Partial Fractions
 04. Improper Integrals
 05. Arc Length/Surface of Revolutions

BCStudentsp001-030.pdf  (4.5 meg) 



Video BC 01

Video BC 02

Video BC 03

Video BC 04

Video BC 05


Pages 31-55 - Revised 12/7/20
 06. Euler's Method
 07. Logistic Growth
 08. Curves Defined by Parametric Equations
 09. Calculus and Parametric Equations

BCStudentsp031-055.pdf  (4.2 meg) 



Video BC 06

Video BC 07

Video BC 08

Video BC 09


Pages 56-76 - Revised 12/7/20
 10. Polar Coordinates and Graphs

 11. Polar Coordinates - Area & Arc Length
 12. Vectors in the Plane
 13. Vector-Valued Functions
 14. Velocity & Acceleration of Vectors

BCStudentsp056-076.pdf  (5.5 meg) 



Video BC 10

Video BC 11

Video BC 12

Video BC 13

Video BC 14


Pages 77-102 - Revised 12/8/20
 15. Taylor Polynomials

 16. Sequences

 17. Infinite Series

 18. Geometric and p-Series

 19. The Integral Test

BCStudentsp077-102.pdf  (5.3 meg) 



Video BC 15a

Video BC 15b

Video BC 16

Video BC 17

Video BC 18

Video BC 19


Pages 103-133 - Revised 12/8/20
 20. Comparison of Series
 21. Alternating Series
 22. Ratio and Root Tests
 23. Convergence/Divergence Review
 24  Power Series

 25. Taylor and Maclaurin Series

 26. Manipulation of Series

BCStudentsp103-133.pdf  (4.7 meg) 



Video BC 20

Video BC 21

Video BC 22

Video BC 23

Video BC 24

Video BC 25

Video BC 26a

Video BC 26b


Pages 134-156 - Revised 1/31/21
 0a. Marginal Analysis & Demand Elasticity
 1a. Epsilon-Delta Definition of Limit
 2a. Powers of Sines and Cosines
 3a. Partial Fractions Advanced
 5a. Simpson's Method

BCStudentsp134-156NonEss.pdf  (3.8 meg) 



Video BC 0a


Video BC 01a

Video BC 02a

Video BC 03a

Video BC 05a


Pages 157-180 - Revised 12/24/20
 7a. Work
 7b. Fluid Force
 7c. Center of Mass

 27. First Order Differential Equations -

BCStudentsp157-180NonEss2.pdf  (2.4 meg) 



Video BC 07a

Video BC 07b

Video BC 07c

Video BC 27


Pages 181 - 204 - AB Review -
 R1. Basic Differentiation
 R2. Linear Approximations
 R3. Limits, Continuity, and Differentiability

 R4. Related Rates

 R5. Function Analysis

 R6. Integration Techniques

 R7. Definite Integral & Accumulation Function

 R8. Riemann Sums

 R9. Fundamental Theorem of Calculus

 R10. Straight-Line Motion

 R11. Area and Volume

 R12. Differential Equations and Growth/Decay


BCStudentsp181-204Review.pdf  (4.7meg) 



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

(Previously items 52 and 53.)





Purchase the Calc BC Solution Manual.
Only $99.95
(for download) 



Student BC Manual (no solutions) in printed form.
Only $54.95
(plus $10 shipping)



Calc BC Solution Manual in printed form.
Only $129.95
(plus $10 shipping)



Calc BC Answers only to HW (no work

shown) in download form.

Only $14.95.




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