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 Jan. 26
- Monday, Jan. 26: 10.2-10.3
- Wednesday, Jan. 28: 10.4-10.5
- Friday, Jan. 30: BLOCK WEEK
- Week of Feb. 2
- Monday, Feb. 2: 10.6-10.7
- Wednesday, Feb. 4: 10.8-10.9
- Friday, Feb. 6: Mini-math (10.1-10.9)
- Week of Feb. 9
- Monday, Feb. 9: Series Bee
- Wednesday, Feb. 11: Unit 10 mid-unit test (10.1-10.9)
- Friday, Feb. 13: 10.10?
- Week of Feb. 16
- Monday, Feb. 16: February break
- Wednesday, Feb. 18: February break
- Friday, Feb. 20: February break
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 9 test
Scheduled for Wednesday, January 21 in-class. You should be proficient in all material contained in Unit 9. More precisely, you should be able to:
- Convert between parametric form and Cartesian form
- Calculate the first and second derivatives in parametric form
- Determine where a graph (in parametric or polar) has a horizontal or vertical tangent
- Find derivatives and integrals of vector-valued functions
- Be able to find the distance, displacement, speed, velocity, and acceleration of a particle given relevant information
- Find the arc length of a parametric curve
- Convert between polar form and Cartesian form
- Find the first and second derivatives in polar form (special case of parametric)
- Find the area of polar curves
- Find the area between polar curves
Exam weighting: 11.5
NOTE: any material from Units 1 to 8 is also fair game and may be useful/necessary.
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
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
- 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)
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