Announcements
NOTICE: I will be offering "Captivating Calculus" in period 5 on Choice Fridays in 1209 (if you come late and I'm not there, try to find me in the math lab or jr. dojo). 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. Please let me know in advance if you are coming, as I normally teach during this period and need to get coverage in order to run Captivating Calculus. If you score below 80% on a test, this period of help is mandatory.
Schedule
- Week of Feb. 23
- Monday, Feb. 23: 10.10-10.11
- Wednesday, Feb. 25: No class - PCF contests
- Friday, Feb. 27: 10.12
- Week of Mar. 2
- Monday, Mar. 2: 10.13-10.14
- Wednesday, Mar. 4: 10.15
- Friday, Mar. 6: Mini-math (10.10-10.15)
Homework
If you are consistently spending more than 1 hour per day on homework, please see me. Nearly every section has an AP Classroom homework with a deadline (usually the next class). Paper assignments from Flipped Math will also be assigned, also due for the next class. Any additional homework will be listed here.
Exams
For MCQ, selecting the correct option gives you full points (as it would on the AP exam). Unlike the AP exam, you can earn partial marks if you show work and make significant progress. For the FRQ, you should make attempts to reasonably simplify (e.g. combine your integers into a single integer). This is different from the actual AP exam, where you only need to leave it in a form that a scientific calculator can evaluate. As for showing work, you should think about key steps; most of the FRQ can be solved in a few lines. Finally, keep in mind that every test in this course is partly cumulative, in the sense that I will be adding questions from previous units on each test, though they will make up a tiny portion. Math is not meant to be "siloed", and you need to be able to answer questions without having to cram for a specific unit.Unit 10 mid-unit test
Scheduled for Wednesday, February 18 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)
- Determine values of x for which a series converges (or is absolutely convergent)
Final exam information: 8:00 AM, Monday, May 12, 5th floor
| Part I - MC | Part II - FRQ | ||
|---|---|---|---|
| Part A | Part B | Part A | Part B |
| 30 | 15 | 2 | 4 |
| 60 minutes | 45 minutes | 30 minutes | 60 minutes |
| No Calculator | Calculator Required | Calculator Required | No Calculator |
| 33.3% | 16.7% | 16.7% | 33.3% |
Online Resources
- Shared Google Drive for AP Calculus BC
- RTC information
- Flipped Math – AP Calculus
- The Essence of Calculus (3Blue1Brown)
- Khan Academy: AP Calculus BC
- WolframAlpha – Online calculator
- Desmos – Graphing calculator
- Interactive Chain Rule
- Concavity visual: Curve, tangent, and f''
- Trig: Etymology of trig functions · Proofs of trig derivatives
- DE: Slope field plotter · Logistic model derivation
- Integration: 8.2 example · Volume: cross sections · Volume (GeoGebra) · Volumes of revolution
- Polar: 9.7 example · 9.9 example 1 · 9.9 example 2 · 9.9 example 5
- Series: Series quick reference sheet
Practice Problems
- Unit 1
- Units 3–5
- Derivative practice (answers included)
- Unit 6
- 6.1–6.3 handout (Solutions)
- Numerical Integration worksheet (Solutions)
- Worksheet 1 on substitution
- Worksheet 2 on substitution
- Interactive practice on completing the square
- Practice on polynomial division (focus on linear divisors, then quadratic divisors)
- Worksheet on long division & completing the square
- Practice with various integration techniques (Solutions)
- Integration Bee (Solutions)
- Unit 7
- Unit 8
- Unit 10
- Mini-maths
- Mini-math Sep 13 (6.1–6.3) (Solutions)
- Mini-math Sep 26 (6.4–6.14) (Solutions)
- Mini-math Oct 24 (7.1–7.5) (Solutions)
- Mini-math Oct 29 (7.6–7.9) (Solutions)
- Mini-math Nov 21 (8.1–8.6) (Solutions)
- Mini-math Dec 3 (8.7–8.13) (Solutions)
- Mini-math Jan 9 (9.1–9.6) (Solutions)
- Mini-math Jan 16 (9.6–9.9) (Solutions)
- Mini-math Feb 6 (10.1–10.9) (Solutions)
Challenges
- Unit 1: A weird limit – limit at 0⁺ DNE example.
- Unit 1: Continuous nowhere
- Unit 1: Continuous on irrationals
- Unit 1: Continuous on rationals
- Unit 2: Continuous but not differentiable
- Unit 2: Differentiability for piecewise
- Unit 3: Continuous but nowhere differentiable
- Unit 6: An integral
- Unit 6: Integration by parts
- Unit 6: Integration by parts II
- Unit 6: Integration by parts III
- Unit 6: Coefficients in PFD
- Unit 6: An improper integral
- Unit 7: SOV & division by 0
- Unit 9: Bat curve
- Unit 9: Area of lemniscate
- Unit 10: Challenging series
- Unit 10: Sparse Harmonic Series
- Unit 10: Divergence Test II
- Unit 10: Sum of product