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about

AP Calculus BC follows the curriculum set forth by the College Board. It is worth the equivalent of two semesters of college credit upon successful completion of the AP examination 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, techniques of integration, infinite series and sequences, etc.

notes / updates

April 3, 2025 | Common Maclaurin Series with Desmos


February 24, 2025 | Feedback on today's quiz.
P1.
Be sure to draw and shade the region. When drawing the graph, give a little more detail (for example, the vertical asymptotes).
A=24x21dx=limtt2(Ax1+Bx+1)dx=...=2ln3
Show work when calculating A=2,B=2.

P2.
Recognize the integral as improper due to the discontinuity. This means we NEED to use limits. Use u-substitution.
24x16x2dx=limb4+122b2x16x2dx=...=23

P3.
Rewrite the integral by completing the square:
1(2y1)24dy
Use trigonometric substitution with: 2y1=2secθ.
Be sure to draw a right triangle. The final answer comes out to:
12ln|2y1+4y24y32|+C

P4.
10 x21x2dx

Option 1: Use u-substitution with u=1x2, then w-substitution with w=2u.
Option 2: Use trigonometric substitution with x=sinθ.
No matter which option you choose, be sure to update the bounds carefully whenever you switch variables. The final answer is: 2(827)15
February 17, 2025 | Feedback on today's quiz.
P1.
1x2a2dx
Use trigonometric substitution with: x=asecθ.
Be sure to draw a right triangle with all three sides labeled.
dx=asecθtanθdθ
After the substitution of the expressions for x and dx, the integral reduces to:
secθdθ=ln|secθ+tanθ|+C=ln|x+x2a2a|+C

P2.
One of your classmates pointed out that I was missing a dx at the end of the integral for this problem.
33/20(x3(4x2+9)3/2)dx
Option 1: u=4x2+9,du=8xdx,x3=x2x=u94x
Remember to switch the bounds of integration to 9u36 when switching from dx to du.


Option 2: Use trigonometric substitution with x=32tanθ
Be sure to draw a right triangle and update the bounds: 0θπ3
The final answer with either approach comes out to 3/32.
January 15, 2025 | Problem 59 (Section 4.1)
The initial velocity is v(0)=16 ft/s (positive because the object is moving up).
The initial position is s(0)=64 ft.
a)
Find the velocity function: v(t)=32t+16 by taking the anti-derivative of acceleration and using the initial value.
Find the position function s(t)=16t2+16t+64 by taking the anti-derivative of velocity and using the initial value.
To find the time when the object hits the ground, set the position expression equal to zero, then solve.
b) Plug the t-value into the velocity function.

January 13, 2025 | Feedback on Today's Quiz
P1.
We know for all four parts that f(x)=v(x).
a) 2v(x)dx=2v(x)dx=2f(x)+C, so statement 1 is true.
b) The derivative of f(2x) is 2f(2x)=2v(2x), so the second statement is false.
f(x)=sin(x),v(x)=cos(x) should work as an example.
c) (v(x)+1)dx=f(x)+x+K, so the third statement is false.
d) If we use the same example as the one in part b), we can see that (sinx)2 is not an anti-derivative of (cosx)2. Therefore the fourth statement is false.

P2.
a(t)=32(32)dt=32t+C=v(t)
Since the initial velocity is zero, it follows that C=0.
The velocity when the stone hits the ground is -120. The time at which this happens can be determined by solving:
v(t)=32t=120t=154.
the position function is: s(t)=v(t)dt=(32t)dt=16t2+K.
The position is zero when t=154, so find K=225 feet.
The is also the height of the cliff since it is the value of the position function s(t)=16t2+225 when t=0

P3.
a. [121x231+x2]dx=arcsinx23arctanx+C

b. secx+cosx2cosxdx=(12sec2x+12)dx=12tanx+12x+C

ap classroom

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.