about

AP Calculus AB follows the curriculum set forth by the College Board. It is worth the equivalent of one semester of college credit upon successful completion of the AP examination offered in May. Students enrolled in this course are required to take this test. Topics covered include library of functions, limits, the derivative, applications of the derivative, definite and indefinite integrals, applications of integration, etc.

notes / updates

April 3, 2025 | Feedback on today's quiz
a)
Draw the region neatly. Label the x and y-intercepts: (2,0) and (0,2).

b)
We are revolving about the x-axis. Use the Disk Method:

V_{d i s k} = π 2 \int 0 (2 - x)^{2} d x = . . . = \frac{8 π}{3}

$V_{disk} = \pi \int\limits_0^2 (2-x)^2 dx = ... = \frac{8 \pi}{3}$ cubic units.

There is a gap, so we use the Washer method with respect to y. First find the outer and inner radii:

R = 2 - 0 = 2. r = 2 - x = 2 - (2 - y) = y

$R = 2- 0 = 2. r = 2-x = 2 - (2-y) = y$

V_{w a s h e r} = π 2 \int 0 (2^{2} - y^{2}) d y

$V_{washer} = \pi \int\limits_0^2 (2^2-y^2) dy$
Note: do NOT evaluate.

d)
Draw a typical cross-section and set up the area:

A (x) = y * y = (2 - x)^{2}

$A(x) = y*y = (2-x)^2$
The volume calculation is nearly identical to the calculation in part b).

V = 2 \int 0 (2 - x)^{2} d x = . . . = \frac{8}{3}

$V = \int\limits_0^2 (2-x)^2 dx = ... = \frac{8}{3}$ cubic units.

April 2, 2025 | Visualizing Solids of Known Cross-Sections
https://www.geogebra.org/m/XFgMaKTy

February 27, 2025 | Study Guide
As we get closer to the end of the curriculum, now is a good time to invest in a study guide for AP Calculus AB. The Princeton Review at the link below is recommended. Older editions of the same series should be fine, too. If you don't like Amazon, buy elsewhere after searching by title or ISBN. Purchasing the study guide is NOT required.
Publisher: Princeton Review; Premium edition
ISBN-10: 0593516737
ISBN-13: 978-0593516737
https://www.amazon.com/Princeton-Review-Calculus-Premium-Prep/dp/0593516737

January 13, 2025 | Thoughts on recent quiz
If there are typos or mistakes, let me know so I can fix them here.

P1.

s (t) = t^{3} - 9 t^{2} + 24 t

$s(t) = t^3-9t^2+24t$

v (t) = 3 t^{2} - 18 t + 24 = 3 (t - 2) (t - 4)

$v(t) = 3t^2-18t+24 = 3 (t-2)(t-4)$

a (t) = 6 t - 18 = 6 (t - 3)

$a(t) = 6t-18 = 6(t-3)$
Study the sign behavior of velocity and acceleration, to conclude that that particle is slowing down on the intervals (0, 2) and (3,4) and speeding up on the intervals (2, 3) and

(4, \infty)

$(4, \infty)$ .
Be sure to include a neat schematic drawing with domain

t \geq 0

$t\geq 0$ and s(0) = 0, s(2)=20, s(3)=18, s(4)=16.

links

expectations

grading

Fall Semester
Homework and Participation: 0%
Quizzes/Assessments/Labs: 80%
Comprehensive Fall Final Exam: 20%

Spring Semester
Homework and Participation: 0%
Quizzes/Assessments/Labs: 100%
Final Exam: 0% (no spring final exam for AP courses)

learning tools
textbook (issued on first day)
notebook
writing utensils
ap study guide
graphing calculator / bring to class daily (see approved models below)

attendance
If you must be absent and you know ahead of time, then let me know and I will try to refer you to the topic to be covered that day. You are responsible for obtaining missed notes and other class details from your classmates. Given the pace of the curriculum, I must inform you that one missed class meeting can have a big impact on your progress in this course.

smart devices
All smart phones/watches should be stored and remain inside the school bag on mute/vibrate. We will announce ahead of time when we plan to use smart devices for learning purposes.
Note-taking digital devices like the iPad or other tablets are * not allowed * . If you need plain paper, let me know. I recommend a lined paper notebook.

spoken language
We are expected to speak English in the classroom space.

calculators
TI-83/84/89/NSPIRE are recommended graphing calculator models. The in-class demonstrations will focus on the TI-84 features. Be sure to check the calculator policy on the college board website at this link. In addition to the graphing calculator, we will also use a few CAS applications, so be sure to bring your laptop to class daily.

office hours
available by appointment most mornings (8:00am - 8:30am) or during shared "free" block. reach out via email or ask me in person and we'll schedule a time to meet.