Quick links
Updates
NOTICE: AP Daily: Practice Sessions will be available on AP Classroom and Youtube starting Monday, April 22. These are 15-minute videos are designed to be quick reviews and a look into AP-style questions.
NOTICE: I am no longer running a calculus tutorial on Fridays. However, please reach out to me directly if you ever have any questions and we will find a time to go over your questions.
Schedule
Tentative schedule for upcoming classes:
- Week of Apr. 1
- Monday, Apr. 1: AP Calculus practice/review (Social 30 pull-out) - Test 3 Part I Part A
- Wednesday, Apr. 3: AP Calculus practice/review - Test 3 Part I Part B, Part II Part A
- Friday, Apr. 5: AP Calculus practice/review (Social 30 diploma) - Test 3 Part II Part B (start at 8:15)
- Week of Apr. 8
- Monday, Apr. 8: AP Calculus practice/review (Social 30 pull-out) - Test 4 Part I (Part II at home) and review Test 4 (until 4:30PM)
- Wednesday, Apr. 10: AP Calculus practice/review - Test 5 Part I (Part II at home) and review Test 5 (period 4-6)
- Friday, Apr. 12: AP Calculus practice/review (Social 30 diploma) - COL Fine Arts, no class
- Week of Apr. 15
- Monday, Apr. 15: AP Calculus practice/review - Test 6 Part I (Part II at home) until 3:45PM
- Wednesday, Apr. 17: AP Calculus practice/review - Review Test 6, any FRQ
- Friday, Apr. 19: PTC
- Week of Apr. 22
- Monday, Apr. 22:
- Wednesday, Apr. 24: Spring break
- Friday, Apr. 26: Spring break
- Week of Apr. 29
- Monday, Apr. 29: AP Calculus practice/review - Test 7 Part I (Part II at home) until 3:45PM
- Wednesday, May. 1: AP Calculus FRQ practice/review - Review Test 7, any FRQ
- Friday, May. 3: AP Calculus FRQ practice/review
- Week of May. 6
- Monday, May. 6: AP Calculus practice/review - Test 8 Part I (Part II at home) until 3:45PM
- Wednesday, May. 8: AP Calculus FRQ practice/review - Review Test 8, any FRQ
- Friday, May. 10: AP Calculus FRQ practice/review
- Week of May. 13
- Monday, May. 13: AP test
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 Wednesday, December 20:
- Send me the link to your Desmos parametric/polar painting
Homework for Monday, December 18:
- Odd questions from 1 to 55(a) (51, 53 are optional) from 10.3 of the handout packet
Homework for Wednesday, December 13:
- Odd questions from 1 to 37 (except 17) from 10.1 of the handout packet
Homework for Monday, November 26:
- Desmos activity (Volume of Solid of Revolution)
Homework for Monday, September 18:
Homework for Friday, September 8:
- Introduction Questionnaire
Exams
Unit 10 final unit test scheduled for Monday, April 10 in-class. You should be proficient in all material contained in Unit 10, though the majority of questions will focus on 10.10-10.15. More precisely, you should be able to:
- Determine convergence or divergence of a series using:
- its partial sums
- 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
- Apply the AST error bound
- Find and use the Taylor or Maclaurin polynomial of a function
- Apply the Lagrange error bound
- Find the radius and interval of convergence of a power series
- Find Taylor and Maclaurin series of a function
- this includes using known series to generate new series via substitution, addition/subtraction/multiplication/division, differentiation, or integration
Exam weighting: 17.5
NOTE: any material from Units 1 to 9 is also fair game and may be useful/necessary.
Final exam information: 8:00AM, Monday, May 13, 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)
- Online graphing program (Desmos)
Brachistochrone curve
- Short by ActionLab
- Interactive visualization of the Chain Rule
- Optimization problems
- Concavity
- Trigonometry
- DE
- Integration
- Parametric/Polar
- Series
Practice problems
- Calculus readiness test (Answers)
- Unit 1
- Unit 6
- Unit 7
- Unit 8
- Unit 10
- Mini-maths
- Mini-math for September 15 (6.1-6.4) (Solutions)
- Mini-math for September 29 (6.5-6.14) (Solutions)
- Mini-math for October 18 (7.1-7.5) (Solutions)
- Mini-math for October 23 (7.6-7.9) (Solutions)
- Mini-math for November 20 (8.1-8.6) (Solutions)
- Mini-math for December 4 (8.7-8.13) (Solutions)
- Mini-math for January 12 (9.1-9.6) (Solutions)
- Mini-math for January 19 (9.6-9.9) (Solutions)
- Mini-math for February 9 (10.1-10.9) (Solutions)
- Mini-math for March 20 (10.10-10.15) (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
- Unit 10: Rearrangement of conditionally convergent series - Prove that the terms of a conditionally convergent series can be rearranged so that the new series will converge to any given real number
- Unit 10: Basel problem - Find the exact value of the sum of the reciprocals of the squares of the positive integers
- Unit 10: Euler’s Constant - Explore the harmonic series
- Unit 10: Function that is not equal to its Taylor series - Find a function that does equal its Taylor series
Assorted: