Most concepts in AB Calculus AB are covered in Calculus 30 course. For videos pertaining to Calculus 30 please see the Calculus 30 Course page
AP Calculus AB concepts (beyond Calc 30)
Some concepts can be found in “Calculus Graphical, Numerical, Algebraic” Third Edition by Finney, Demana, Waits, and Kennedy
“The only way to learn mathematics is to do mathematics”
Paul Halmos
Online calculator (Mathway Calculator Widget)
- Derivative Calculator – with steps!
- Implicit Differentiation Calculator – with steps
- Integral Calculator – with steps!
Mr. Maxwell’s Syllabus and Outline
Unit 1
AP Calculus (30L) – 7.5 / 7.6 Inverse Trig Functions and their Derivatives
Stewart Calculus Text
7.5 p. 334 #1ace, 2ace
7.6 p.339 #1acegi, 2
AP Calculus (30L) – Derivatives of Inverses
Finney Text p 170 #27-29
AP Calculus (30L) – Intermediate Value / Rolle’s / Mean Value / Extreme Value Theorems
Rolle’s / MVT (Finney text) p.202 #1, 4, 7, 9, 11, 12, 14, 47-49 ,51 , 53, 56
AP Calculus (30L)-Linear Approximation
p. 242 #1-7, 11-14, 59
Unit 1 Exam – Mar 6 / 23
Unit 2
AP Calculus (30L)-Average Value of a function
Finney text: P. 291 #11-14, 31-36, 49,50
AP Calc 30L: Fundamental theorem Part 1 and 2
Finney p 302 #1-16
- AP Calculus 30L- Fundamental Theorem of Calculus (Part 1 & 2 – 2021)
- AP Calculus 30L Fundamental Theorem of Calculus (Part 2- 2019)
Calc 30L Ave Value Fundamental Theorem QUIZ
AP Calculus (30L) – Riemann Sums
Finney Text
p. 270 #5, 6, 18
p. 282 Quick Rev. #1-6, Ex. #1,3,5,41-45
Squeeze Theorem
Homework: Finney p. 68 #59-61
Unit 2 Exam: Mar 21 / 23
Unit 3
Differential Equations and Slope Fields
- Diff Equations part one Stewart Text 9.2 # 1ac,2bc,3ac,4ac
- Finney p.327 #11-16
Slope Fields - Finney Text P. 328 #29-40, 51, 59, 61, 64
Separable Differential Equations - Finney P.357 #1-9 (first order)
- Finney P.330 #68 (second order)
- AP Calculus 30L – Introduction to Differential equations with Initial Conditions
- AP Calculus 30L – Introduction to SLOPE FIELDS
- AP Calculus 30L – Slope Fields (Lesson #1of2)
- AP Calculus 30L- Slope Fields (Lesson #2of2)
- AP Calculus 30L – Solving Separable Differential Equations First Order
- AP Calculus 30L Solving Separable Differential Equations #2
- AP Calclulus 30L – Solving Separable Differential Equations #3
- AP Calculus 30L – Second Order Differential Equations with Initial Conditions
-Calc 30L Quiz Slope Fields and Diff Eq
L’Hopital’s Rule
L’Hopitals rule
Finney P. 450 (8.2) #1-8, 16, 27, 28, 33, 49, 58, 62, 63 (optional), 68
Euler’s Method
Euler’s Method (Finney p. 325)
P. 328 #41, 43, 45, 47, 49, 50, 53
Unit 3 Exam: Apr 19 / 23
Unit 4
AP Calculus AB: Cross Sectional Solids and Volumes of Solids of Revolution
- AP Calculus 30L Volumes of solids with known cross sections (part 1) INTRO
- AP Calculus 30L Cross Sectional Volumes 2021 (part 2)
- Blooper INTRO video…
- AP Calculus Integrals as Volumes – cross sectional areas example
Solids of Revolution
Disc method (Finney) p. 406 #7, 10-14
Washer Method (Finney) p. 407 #8, 9, 15, 16, 17, 19
- AP Calculus AB Volumes of Solids of Revolution Disk and Washer Method (Part 1of2 – (2022 horizontal axis of rotation)
- AP Calculus AB – Washer Method – rotation about VERTICAL axis (Part 2of2 -2021)
- AP Calculus AB – Volumes of Revolution (Disk Method) (2017 lesson) Introduction
- AP Calculus AB – Volume of Solid of Revolution (Disk Method) Example – Volume of Sphere
- AP Calculus AB Solid of Revolution Example (Disc Method-HARD!)
- AP Calculus AB – Washer Method – Volumes of Solids of Revolution
Unit 4 Exam: April 26 / 23
AP Calculus AB Exam Practice (Apr 26 – May 8)
- AP Calculus Exam Reader TIPS (full video by Mr. MathWell)
- AP Central Review Videos Playlist – AP Calculus AB
- AP Calculus AB Practice Tests | High School Test Prep
- AP Calculus Exam Free Response Question (bees entering and leaving the hive)
- AP Central multiple choice review for AP Exam
- AP practice Exam with Solutions – 2006
- 2012 Public Practice Exam: AP Calculus AB
- AP Central multiple choice review for AP Exam
- 3Blue 1Brown – Essence of Calculus Videos YouTube
AP Exam Date: Monday May 8, 2023; 8am
PROJECT
Independent Student Project – approx 5 hours class time will be given. Project and presentations Due ______TBA________. Presentations options to be discussed with Mr. Maxwell. See document for ideas and instructions. Ideas must be from approved list in document.
Advanced Topics – not included in AP Calculus AB
Unit 5 – Cylindrical Shells
AP Calc 30L: Cylindrical Shell Method – Volumes of Solids of Revolution
Homework:
Part 1 -Online text #1-7, 15-18 (even questions for hand in)
Part 2 -Online text #9-14, 21-26, 29-32 (even questions for hand in)
Additional text Questions
Finney p. 407 #7-10 Solve using Cylindrical Shell Method – compare with Disc / Washer Method from previous asn’t
Finney p. 407 #33-38
- AP Calculus 30L Cylindrical Shell Method (Full Lesson 2021)
- AP Calculus 30L Cylindrical Shell Method (around vertical axis 2023 – part 1of2)
- AP Calculus 30L Cylindrical Shell Method (around horizontal axis 2023-part 2of2)
- AP Calculus 30L Washer Method vs Shell Method (Brief Intro)
- AP Calculus 30L Cylindrical Shell Method Example 1b
- AP Calculus 30L Shell Method Example #4
- AP Calculus 30L Shell method example #2
- AP Calculus 30L Cylindrical Shell Method (dy version)
Unit 6 – Advanced Integration Techniques
Calculus 30L: Integration By Parts – DI Method
Stewart Text – 11.4 #1, 2, 7
Finney Text p. 346 #1-10, 17-20, 38-40
- AP Calculus 30 L – Integration By Parts INTRO and D.I. Method Type 1 and 2) 2018
- AP Calculus 30 L – D. I. (Tabular Integration) Method introduction (2021)
- AP Calculus 30L – DI method (type 2) Integrating By Parts (2021)
- AP Calculus 30 L – Integration By Parts – DI Method Type 2&3 (2021)
- AP Calculus 30 L – DI Method Type 3 Repeated Integral Row – Example 1
- AP Calculus 30 L – DI method Type 3 – Repeated Integral Example 2
Calculus 30L: Integrating using Partial Fractions
Finney Text Homework: p369 #1-14, p.371 #43, 47, 48
Calculus 30 L: Integrating Using Trigonometric Substitution
- Integration: Trigonometric Substitution – mrmathwell
- Integration: Trig sub Examples – mrmathwell
- Integrating by Trig Substitution (2022 Examples)
- Trig Sub Example 2 – mrmathwell
- Calculus 30L – Mr. Liu – Trigonometric Substitution Indefinite Integrals
- Introduction to trigonometric substitution – Kahn
- Integrals: Trig Substitution 1 – Kahn
- Integrals: Trig Substitution 2 – Kahn
- Trig and U substitution together (part 1) – Kahn
- Trig and U substitution together (part 2) – Kahn
Unit 6 Exam: June 14 / 23
Projects
Over the years students have created some incredible final projects, here are a few of them;)
L’Hopital’s Rule Lesson – Ms. Sandstra
Calculus 30L – Mr. Liu – Trigonometric Substitution Indefinite Integrals
University Calculus
If you have taken this class, I am assuming you will be taking University Calculus at some point… please feel free to explore the videos and the lab manual exercises below for practice and preparation.