Announcements
NOTICE: I will be offering "Captivating Calculus" in period 5 on Choice Fridays in 1207. 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 Sep. 22
- Monday, Sep. 22: 6.9-6.11
- Wednesday, Sep. 24: 6.12-6.14
- Friday, Sep. 26: Mini-math (6.4-6.14)
- Week of Sep. 29
- Monday, Sep. 29: Integration Bee
- Wednesday, Oct. 1: Unit 6 Review
- Friday, Oct. 3: Work period
- Week of Oct. 6
- Monday, Oct. 6: Work period
- Wednesday, Oct. 8: Work period
- Friday, Oct. 10: No class
- Week of Oct. 13
- Monday, Oct. 13: No class
- Wednesday, Oct. 15: Unit 6 test
- Friday, Oct. 17: 7.1-7.2
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.
- Monday, September 22: 6.9: Worksheet 1 on substitution and 6.9: Worksheet 2 on substitution
- Friday, September 12: Handout from class (Mind Your P's and Two's, Apply Your Understanding of Summation Notation, Translating Notation and Finding Definite Integral Values
- Monday, September 8: Introduction questionnaire and course outline
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 6 test
Scheduled for Wednesday, October 15 in-class. There will be a calculator portion and a non-calculator portion. You should be proficient in all material contained in Unit 6. More precisely, you should be able to:
- Approximate the area under a curve using right and left Riemann sums, midpoint and trapezoidal rules, both with equal and unequal intervals, from a function, graph, or table of values
- Identify if an area estimate is an overestimate or underestimate
- Interpret or produce an integral given a contextual application
- Utilize the Fundamental Theorem of Calculus I to differentiate an accumulation function
- Includes accumulation functions where the bounds are functions
- Analyze accumulation functions for: where they are increasing or decreasing, locate and classify critical points, determine concavity and points of inflection
- Use integral properties
- Solve indefinite integrals or utilize the Fundamental Theorem of Calculus II to solve definite integrals, including:
- Algebraic techniques to simplify the integrand (splitting, expanding, long division, completing the square)
- Substitution Rule
- Integration by Parts (IBP)
- Partial Fraction Decomposition (PFD)
- Handle improper integrals
Exam weighting: 18.5
NOTE: any material from Units 1 to 5 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
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)
- Mini-maths
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