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Updates
NOTICE: I will be offering “Calculus help” in period 5 on Choice Fridays in 2407. This class is mandatory for those who scored below 80% on a unit test, but highly encouraged for anyone who is struggling or unsure about any of the material. Otherwise, please use this as an additional opportunity to get help with calculus, or to come ask deeper questions that we don’t have time for in class. If you don’t have any questions, feel free to come by anyway for your lunch hour to hang out in case any questions arise from others. Please let me know in advance if you intend to come; I will typically come for the first few minutes to see if anyone shows up.
As I mentioned in class earlier this year, the AP exam will be hybrid - meaning the MCQ will be done online, and the FRQ will be viewed online (while the responses are still on paper). When I say online, I mean you will be using Bluebook to access everything. There are test previews available on Bluebook as of today, so I encourage you to download Bluebook on your own (Windows) device to familiarize yourself with the system. For the actual test, you will not need your devices as Bluebook will be loaded onto secure devices for your use. Please note you will also need your CollegeBoard login information to access the app for the exam.
Schedule
Tentative schedule for upcoming classes:
- Week of Feb. 24
- Monday, Feb. 24: Unit 10 mid-unit test (10.1-10.9)
- Wednesday, Feb. 26: No class - PCF contests
- Friday, Feb. 28: 10.10
- Week of Mar. 3
- Monday, Mar. 3: 10.11
- Wednesday, Mar. 5: 10.12-10.13
- Friday, Mar. 7: 10.13
- Week of Mar. 10
- Monday, Mar. 10: 10.14-10.15
- Wednesday, Mar. 12: pi is irrational (tentative)
- Friday, Mar. 14: pi day
- Week of Mar. 17
- Monday, Mar. 17: Unit 10 review
- Wednesday, Mar. 19: Mini-math (10.10-10.15)
- Friday, Mar. 21: Unit 10 review
- Week of Mar. 24
- Monday, Mar. 24: Unit 10 test
- Wednesday, Mar. 26:
- Friday, Mar. 28: Good Friday
Homework
If you are consistently spending more than 1 hour per day on homework, please see me. (Nearly) Every section we cover will have an associated AP Classroom online homework for you to complete by a certain deadline, typically before the next class (or in the case of a test, the class after that). You will also receive paper assignments from Flipped Math to work on. Any additional homework outside of these two will be posted here.
Homework for Friday, December 13:
- 10.1 Q1-37 (odd only, skip 17)
Homework for Monday, September 9:
- Introduction Questionnaire
Exams
Unit 10 mid-unit test scheduled for Monday, February 24 in-class. You should be proficient in all material contained in 10.1 through 10.9. More precisely, you should be able to:
- Determine convergence or divergence of a series using:
- its partial sums (e.g. telescoping series)
- geometric series (and know the value of the sum if it converges)
- nth term test
- p-series
- comparison tests
- alternating series test
- ratio test
- absolute convergence
- Determine if a series converges absolutely or conditionally (or neither)
Exam weighting: 8.75
NOTE: any material from Units 1 to 9 is also fair game and may be useful/necessary.
Final exam information: 8:00AM, Monday, May 12, 5th floor
Part I tests are MCQ and Part II tests are FRQ
Online resources
- The Essence of Calculus YouTube series (brought to you by 3 Blue 1 Brown)
- AP Calculus BC course (Khan Academy)
- Online calculator (WolframAlpha)
- Brachistochrone curve
- Interactive visualization of the Chain Rule
- Optimization problems
- Concavity
- Trigonometry
- DE
- Integration
Practice problems
- Unit 1
- Unit 3-5
- Derivative practice (not comprehensive, answers included)
- Unit 6
- Unit 7
- Unit 8
- Unit 10
- Mini-maths
- Mini-math for September 13 (6.1-6.3) (Solutions)
- Mini-math for September 27 (6.4-6.14) (Solutions)
- Mini-math for October 25 (7.1-7.5) (Solutions)
- Mini-math for October 30 (7.6-7.9) (Solutions)
- Mini-math for November 22 (8.1-8.6) (Solutions)
- Mini-math for December 4 (8.7-8.13) (Solutions)
- Mini-math for January 10 (9.1-9.6) (Solutions)
- Mini-math for January 22 (9.6-9.9) (Solutions)
- Mini-math for February 14 (10.1-10.9) (Solutions)
Challenges
Calculus-based:
- Unit 1: A weird limit - Find an example of a function whose limit at 0 from the right DNE.
- Unit 1: Continuous nowhere - Does there exist a function which is continuous nowhere?
- Unit 1: Continuous on the irrationals - Does there exist a function which is continuous only on the irrationals?
- Unit 1: Continuous on the rationals - Does there exist a function which is continuous only on the rationals?
- Unit 2: Continuous but not differentiable - Does there exist a function which is continuous everywhere but not differentiable infinitely often?
- Unit 2: Differentiability for piecewise - Prove you can use derivatives from the left and right to determine differentiability for piecewise functions.
- Unit 3: Continuous but nowhere differentiable - Does there exist a function which is continuous everywhere but differentiable nowhere?
- Unit 6: An integral - Evaluate this integral.
- Unit 6: Integration by parts - Evaluate this integral using integration by parts.
- Unit 6: Coefficients in a partial fraction decomposition - Why are we allowed to use values of x for which the original expression is undefined?
- Unit 6: An improper integral - Evaluate this improper integral.
- Unit 7: division by 0 in separation of variables - Find an example where you have to be more careful about separation of variables
- Unit 9: bat curve - Find a function whose graph matches mine
- Unit 10: A Challenging Series - Find the exact value of this non-geometric series
- Unit 10: Sparse Harmonic Series - Show that if we remove certain terms from the harmonic series, we get convergence
- Unit 10: Divergence Test II - Prove that even if n times the summands do not converge to 0, then the series divereges
- Unit 10: Sum of Product - Prove that the product of summands from convergent series is convergent
Assorted: