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AB Calculus Manual (Revised 12/2019)

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 :

LET ME HELP YOU TEACH YOUR CLASS!

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.  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:

https://www.youtube.com/channel/UC-y4_ldufRdVd5r_CuCzDCQ

AB Calc Cover Pages
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
Pages 27-46 - Revised 12/01/20 06. Derivative definition 07. Derivatives w/ technology 08. Differentiation techniques 09. Chain Rule
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
Pages 70-93 - Revised 12/02/20 15. Continuity/differentiability 16. Related rates
Pages 94-121 - Revised 12/02/20 17. Straight-line motion   18. 3 important theorems 19. Function analysis
Pages 122-151 - Revised 12/04/20 20. Curve sketching 21. Absolute extrema 22. Optimization 23. Economic optimization 24. L'Hospital's rule
Pages 152-174 - Revised 12/05/20 25. Indefinite integration 26. -substitution 27. Definite Integral and Area 28. The Accumulation Function MB
Pages 175-198 - Revised 12/06/20 29. Riemann Sums   30. Fundamental Theorem 31. Definite integrals -sub 32. Integrating transcendentals 33. Motion revisited
Pages 199-212 - Revised 12/06/20 34. Average value, 2nd FTC 35. Inverse Trig 36. Area between curves
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
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
Pages 268-278 Complex fractions Inverses Exponentials/logs Graphical solutions Sigma notation
Limits and the Infinity Guideline: Addendum 1                 Derivatives as a Measure of Change: Addendum 2         Infinitesimals and Differentials:                          Integrals - an Accumulation of Change: Addendum 3
Calc Review page:

• AB Multiple Choice Exam Prep
• AB Free Response Exam Prep
• BC Multiple Choice Exam Prep
• BC Free Response Exam Prep
• Diving In to AP ® Calculus
• AB Step by Step
• BC Step by Step
• AB Calculus Exams & Quizzes
• BC Calculus Exams & Quizzes
• Calc AB Manual
• Calc BC Manual
• Combined AB/BC Calc Manual
• AB Calculus Powerpoints
• BC Calculus Powerpoints
• Calculus OnTheWall Intro Video
• Calculus Jeopardy
• Calculus Across & Down
• Word Search Poster
• Test Your Strength: AB Version
• Test Your Strength: BC Version
• Test Your Strength: Precalc
• Math Wars AB
• Math Wars BC

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AP® Calculus AB Homework Help

The fast pace of an AP class paired with the difficulty of calculus can make Advanced Placement Calculus AB a real challenge for students. Our tutoring community can help you conquer complex calculus topics. Let us connect you with an expert tutor that knows how to explain asymptotic and unbounded behavior, and can help you learn the methods for cracking the AP Calc AB exam in May. Don't stress. AP Calculus AB homework help is available 24/7. 

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AP Calculus AB Class Schedule and Homework Assignments

* Lesson recordings are from 2020-21, so they may not completely match the lessons from this year.

8/21	Policy Sheet First Day Survey Linear, Polynomial, and Exponential Functions (1.1, 1.2, 1.5)		p. 12:  17-18, 23-27, 39-42, 74, 76-77, 79, 82 p. 25:  32-33, 35, 43a p. 58:  33, 39-43 odd, 56-57, 61-62
8/23	Trigonometry and Combining Functions (1.3, 1.4)	Video	p. 37:  23-33 odd, 77-87 odd p. 46:  16, 57-71 odd, 76-78
8/27	Inverse Functions and Logarithms (1.6, 1.7)	Video	p. 73:  21-29 odd, 34-36, 39-43 odd, 53-63, 70-72, 77-79 odd, 94, 101-113 odd p. 78:  5-10, 13
8/29	Limits		p. 103:  25-36 p. 129:  17 (a-d), 25, 27, 29-35, 45-52
9/3	Limits, Asymptotes, and Continuity		p: 102:  7-8, 10, 11-12 (skip f), 14-15, 39-51 p. 130:  63-68, 80-82 p. 143:  17-18, 27-32, 35 (use calculator), 44-45, 50-51, 57-60
9/5	Review Chapter 1/2		Sample Test (answers)
	Test Chapter 1/2
9/11	Velocity and Tangents		p. 89:  8, 13-15 p. 174:  30-33, 63
9/13	The Derivative (3.1)		p. 173:  14-17 (NC on 16), 22-25 (NC on 22), 34-37, 41-42, 47-48 (NC), 57-58, 68-71
9/17	The Derivative Function (3.2)		p. 188:  7-9, 11-19, 25-27, 30-34, 53-56, 67-70, 74-76
9/19	Interpreting Derivatives and Higher Order Derivatives		p. 176:  73-78 p. 189:  20-24, 47-48, 52 p. 190: 41-42, 59-61, 63, 65-66
9/23	Derivatives of Polynomials and Exponents (3.3)		p. 203: 11-39 odd, 45-49 odd, 61-65, 70-76, 86-87, 91-92
9/25	Review Chapter 3A		Sample Test (answers)
9/27	Test Chapter 3A
10/1	Product and Quotient Rules (3.4)	Video	p. 213: 6-7, 11-41 odd, 42-45, 47-51 odd (only part a), 54-66, 75
10/3	Derivatives of Trig Functions (3.5)		p. 223:  5, 9-25 odd, 45-51 odd, 59-62, 67-68 p. 206:  96-102
10/8	Chain Rule (3.6)		p. 234: 7-8, 17-41 odd (skip 35), 61, 63, 68-78, 82-85, 87
10/10	Derivatives of Logs and Inverse Functions (3.7, 3.8)		p. 248:  41-51 odd p. 259:  7-31 odd, 44, 56-59, 62-66, 68-71
	Implicit Differentiation		p. 248: 9-16, 19-35 odd, 36-37, 55-61 odd, 63-70, 79-80, 106-112
	Derivative Quiz Motion Problems (3.9)	Video	p. 270: 1-10
10/18	Linear Approximation (3.11)		p. 285: 1-4, 7-15, 17-19, 21-22
10/22	Review Chapter 3B		Sample Test (answers)
10/24	Test Chapter 3B
	L’Hopital’s Rule		p. 347: 5, 12, 13-39 odd (skip 33), 43, 73, 81
10/30	Related Rates		p. 279: 1-11, 13-19
11/1	Practice Related Rates		p. 280: 20-21, 23-29, 31-32, 34-35, 38
11/5	Graphing		p. 304:  35-49 odd p. 331:  11-12, 14-15, 17-25 odd, 26-29, 45-53
11/7	Graphing, Part 2		p. 304:  21-33 odd, 53-67 odd, 69-72, 79-80 p. 334:  66, 70-71, 82, 89, 98 p. 363:  69-73
11/12	Optimization		p. 374: 6-8, 11-14, 20, 24, 48
11/14	Practice Optimization		p. 374: 18, 22, 23, 27, 34, 42, 49
	MVT, IVT, EVT		MVT, IVT, EVT Worksheet (solutions)
11/20	Review Chapter 4 Assign Mathematician Report		Sample Test (answers)
11/22	Test Chapter 4
12/3	Riemann Sums (5.2)		p. 411: 8-9, 11-12, 15-16, 21, 23, 32-33, 41-42
12/5	The Definite Integral (5.3)		p. 428:  10-17, 32, 34, 40-41, 43-53 odd, 58-62, 64-65, 67-68 p. 456:  68-69, 72-73, 76
	FTOC		p. 455:  58-66, 75-81 odd, 82 p. 506:  17-27
12/11	Review Chapter 5A		Sample Test (answers)
12/13	Test Chapter 5A
12/17	Mathematician Reports Due
12/19	Review		Semester 1 Final Review (answers)
	Review
1/8	Review
1/10	Review		Sample Final (answers)
1/14 1/16	Final Exam		Mathematician Reports Due

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