Unit 8: Taylor Polynomials and AP Test Prep

Unit 8: Taylor Polynomials

• Day 28: Intro to Power Series

  • • Video 1: The First Power Series

    • Video 2: A Calculator Activity

    • Video 3: Two New Power Series from an Old Power Series

    • Video 4: Why do we Care?

    • Video 5: Radius of Convergence/Interval of Convergence Example 1

    • Video 6: Radius of Convergence/Interval of Convergence Example 2

    • Video 7: Radius of Convergence/Interval of Convergence Example 3

      • • READ and do 8.5: 3-16

          • • 9 11

        • READ and do 8.6: 3-10

          • • 7 8 9

• Day 29: Time to Finish Day 28

  • • • No New Videos

• FriDay 30: Maclaurin and Taylor

  • • Video 1: Derivation of a Taylor Series Part 1

    • Video 2: Derivation of a Taylor Series Part 2

    • Video 3: Derivation of a Taylor Series Part 3

    • Video 4: The Sine of X

    • Video 5: Calculator Activity

    • Video 6: Interval of Convergence

    • Video 7: Other Popular Maclaurin Series

    • Video 8: On More Example

    • Video 9: An Integration

    • Video 10: Maclaurin Series vs Taylor Series

      • • 8.7: 3-21 odd, 31, 32, 34-36, 38

          • • 5 7 13 19

            • 32 36 38

• TuesDay 31 LaGrange Error Bound

  • • Video 0: An Old Question Gives Birth to my FAVORTIE Identity

    • Video 1: Exact Value Review

    • Video 2: Estimating a New Value (Luckily a TON of these are Alternating)

      • • 8.7: 36 and 38

    • Video 3: What if they Don't Alternate?

      • • Canvas Quizzes

    • Video 4: FRQ Practice Bank and Kahn

    • Video 5: Kahn's Take on LaGrange Error Bound

      • • Proof of the LaGrange Error Bound and why I tend to not teach it in class

        • Search for Taylor problems in the below collection. Timing yourself (no more than 15 minutes per attempt), try all 5 of the FRQ's that involve Taylor, there should be 1 per year. Check your answer, the Q&A document, and the stats to see how you did.

          • • 2015's Free Response Questions

            • Answers and Scoring Guidelines

            • Question and Answer Document

            • Statistics

              • • 1c

                • 2a

                • 3b 3d (final answer should have units of m/min)

                • 4d

                • 5b

                • 6c Part 1 (got a phone call...) 6c Part 2

            • 2016's Free Response Questions

            • Answers and Scoring Guidelines

            • Question and Answer Document

            • Statistics

              • • 2d

                • 3b 3c 3d

                • 6a 6b

                • 4d

            • 2017's Free Response Questions

            • Answers and Scoring Guidelines

            • Question and Answer Document

            • Statistics

              • • 1c 1d

                • 3a part 1 (video cut out) 3a part 2

                • 6b 6d

            • 2018's Free Response Questions

            • Answers and Scoring Guidelines

            • Question and Answer Document

            • Statistics

              • • 1d (Final Answer)

                • 2a 2b 2c 2d

                • 3a 3c 3d

                • 4b

            • 2019's Free Response Questions

            • Answers and Scoring Guidelines

            • Question and Answer Document

            • Statistics

              • • 1d

                • 4c

                • 5c

                • 6a 6b 6c

• Day 32: Time to Practice

  • • No New Videos

      • • Work on the above test bank

        • Work on all things Taylor from your Prep Book

• Day 33: Time to Practice

  • • Video: Some Selected Problems from FRQ 14

      • • Work on the above test bank

        • Work on all things Taylor from your Prep Book

• Day 40: I Suppose we Should Chat About Polar a Bit

  • • Video 1: Converting From Cartesian to Polar

    • Video 2: Converting From Polar to Cartesian

    • Video 3: Sketching Some Polar Graphs

    • Video 4: Sketching More Polar Graphs

    • Video 5: Math 251 in Polar Mode

    • Video 6: A Review of Honors Geometry

    • Video 7: Math 252 in Polar Mode

    • Video 8: One More of Those

FRQ 15: Power Series

(No Calculators)

(Shoot for about 60 minutes)