AP Calc BC Homework - Block E

AMC 12 (grades 11 and 12): Tuesday November 14, 2023

AMC 10 (grades 9 and 10): Tuesday November 14, 2023

Top 5 of each represent St Francis in this national competition.

AMC 12 at AoPS

1. Watch Video and Do 4 Exercises at Khan-Academy. (Class join code 6QVDHSD3)
2. Do 9.1 Sequence WS (Substitute has paper copies and the the key.. Upload to CW 2-1 in Portals)

1. Why study series?
2. 9.2 Series and Convergence
   1. Geometric Series
   2. Limit of nth term of a Convergent Series Th,
   3. nth term test for Divergence
3. ∆Math Lab 2-1 (9.1-9.2)

1. Orders of Growth Poster

2. Order of Magnitude WS

3. Cesàro Summation and Analytic Continuation Video

4. Divergent Infinite Sums BriTheMathGuy Video

1. Orders of Growth Poster
   

2. Order of Magnitude WS

1. Proofs that the Harmonic Series Diverges:
   1. Goldmakher's Short Proof
   2. Proofs part 1
   3. Proofs 2
   4. ∆Math HW Q 2-3 (ch 9.1-9,2)
2. Slides :Geometric, nth term, Integral Test, p test (92.-9.3 pdf) (keynote)

For HW

1. Textbook Problems
2. ∆Math Lab 2-2: Integral Tests

1. Convergence Test Table 1

2. Convergence Table 2

3. n-term Div wikibooks on nth Term Test for Divergence
4. Geometric Series from Ximera
5. p-series @17Calc
6. Integral Test from former 17Calc

1. FRQ Quiz on sequences, n-th term, p-series, geometric, and Integral tests.
2. Direct Comparison Test (DCT)
3. Limit Comparison Test (LCT)
4. DCT from former@ 17Calc
5. LCT from former 17Calc

1. Convergence Test Table 1
   
2. Convergence Table 2
   
3. Convergence WS
4. Video: LCT Proof

1. Q 2-5 (9.1-9.4)
2. Intro to AST Alternating Series WS
3. AST Slides
4. AST Practice
5. Exercises from former 17Calculus

1. Textbook Exercises
2. ∆Math Lab: LCT/AST (Lab 2-4 and 2-5)

1. AST Examples

2. AST Remainder/Error Estimation

3. Alternating Series Test Practice

4. Cool Fact about conditionally convergent series
   

In class

1. 11:20- Seniors to the Theater - Academic Awards Assembly
2. page 9-13
3. Seq and Seiries - formerly @ 17 Calc

1. Textbook problems
2. Lab 2-6: Ratio Test

1. Review of Convergence Tests - How to pick the right one
2. Absolute vs Conditional Convergence
3. Which Test is Best #1
4. Which Test is Best #2?
5. Flowchart 1
6. Flowchart 2
7. Flowchart 3
8. HWQ on Ratio/Root Tests
9. Ch 9 MC Practice with answers

1. Convergence Test Strategy Video

2. Series Test Practice WS

3. Summary by Cal-Tech student Laura Shou

4. David Mao Examples of comparison Tests

5. Calc 13 Summary

1. Get the KhanApp

2. Chapter 9 Stuff at Khan

3. Sequences from Ximera
4. n-th Term Test

5. Geometric Series from Ximera

6. Telescoping Series

7. Integral Test

8. DCT

9. LCT

10. AST

11. Ratio Rest

12. Root Test

13. Interval of Convergence

1. Convergence WS
   
2. Ratio Test Practice
   

1. Series Test Practice WS

2. Summary

3. David Mao Examples of comparison Tests

4. Sequence and Series Exercises from Wikibooks Has hints, answers, and Full Solutions

• 9th and 10th grade Student SFHS Registration

• Sign Up for AMC 10 Practice Contest

• Past AMC 10 Questions and Solutions

1. Go over Test 9A
2. Examples of Taylor Series Questions (∆Math)
3. Taylor Series Practice (∆Math)
4. Taylor WS 1
5. Taylor Polynomials 2 WS.pdf
   
6. Legrange Error (Taylor Theorem)

• Does the Alternating series ever fail? (ppt)

• Does the Alt Series Remaider ever Fail? (video)
• Error Bounds In Power Series WS

For HW

• Textbook Problems
• Lab 2-7 Practice Taylor Series (∆Math)

1. TaylorPolynomials1WS.pdf
   
2. Taylor Polynomials 2 WS.pdf
   
3. Lagrange Remainder WS.pdf
   

• 11th and 12th grade SFHS Registration (Must be completed before the Contest Day)

• Sign Up for AMC 12 Practice Contest
• Past AMC 12 Questions and Solutions

1. ∆Math Lab 2-8: Lagrange and Alt Series Error Bound
2. Get caught on late ∆Math Qtr 2 Labs

In class

1. HWQ 2-13(∆Math)
2. 9.8 Power Series: Intervals of Convergence
3. 9.9 Representation of Functions by Power Series

Textbook exercises
2. BC Lab: Power Series (∆ Math)

1. Collaborative Proof of Euler's Equation e^πi+1 = 0
2. HWQ 2-14 (Paper)
3. Remainder Quiz Correction
4. Worksheet 3 on Series
   (Here are answers to check your work)
5. Error Bounds WS ( filled in)

1. Finish Remainder Quiz Correction
2. p 680 from Text Book
3. Finish Worksheet 3 on Series
   (Here are answers to check your work)

1. Gotta No
2. Fill in version
3. Ch 9 MC Practice with answers

1. Get the KhanApp

2. Chapter 9 Stuff at Khan

3. Sequences from Ximera
4. n-th Term Test

5. Sequences from Ximera
6. Geometric Series from Ximera

1. Review
2. Q 2-16 on 9B
3. Unit 10 Progress Check: MCQ Part A, B, C (AP Classroom)

1. Class 2-18 at AP Classroom
2. Sem 1 FRQ
3. Unit 10 Progress Check: MCQ Part A
4. Unit 10 Progress Check: MCQ Part B
5. Unit 10 Progress Check: MCQ Part C