Last bit of Calculus

Post AP but pre-end-of-school, we work on a few more things.

Taylor Series:
Work through handout Thursday, May 5th through Monday, May 16th.
Quiz on Tuesday, May 17th.

AP Question Rubrics:
You will work in groups of three to prepare answer keys and rubrics for some of the open response questions from the AP exam. Due by Friday, May 27th.

During Finals Days:
Makeup work can be done during H-Block on the 25th through the 27th. After that I have to do your grades and cannot accept anything else.

I will see you at graduation!

Review Schedule for the Final and AP Exam

Below is the plan for the review. If you have other topics/questions, please bring them to my attention.

4/07   FTC, Integration Techniques, Differential Equations, give out the 2003 AP Exam
4/08   Area and Volume

4/12   Numerical Techniques
4/13   Rates in the real world
4/14   Score the 2003 exam, Moving Particles
4/15   Min/Max, Inc/Dec, Curve Sketching, Optimization, give out the 2008 AP Exam

4/26   Score the 2008 exam, do the hard 1998 multiple choice
4/27   Miscellaneous AP Problems
4/28   Final, Day 1
4/29   Final, Day 2

5/03   go over Final
5/04   AP Exam at 8am

AP Exam Day info

Here is a document with info exam day: what you can bring, what you should bring, what you shouldn't bring, etc.

Quick Polar Unit

Here is the schedule of our foray into polar coordinates and polar equations. The graphs are fun and the calculus of polar is really cool. Note the Cumulative Exam that is also part of the schedule.

3/24  Intro to Polar Coordinates and Polar Equations
            HW p.557/1-4, 21-29 odd
3/25  Graphing Polar Equations by Hand
            HW p.557-558/5-19 odd, 31-37 odd

3/29  Slope and Area (single curves)
            HW p.558/39-49 odd, 59
3/30  Area between curves, Lengths of Polar Curves
            HW p.558/51-57 odd, 60, 72 and you derive length formula
3/31  More Practice of all polar skills
            HW Lengths of p.558/43-49 odd and any other helpful problems on p.557-558
4/01  Review of polar as well as a general review of all topics

4/05  Cumulative Exam
4/06  Polar Quiz
4/07  Start Review of year (based on results of Cumulative Exam)

Ch 7: Area and Volume using Calculus

We start our last AP topic, Area and Volume. This is the most concrete of the topics we study where every result comes from a visualizable problem.

3/01  Area between Curves
        HW p.395-397/3-48 by 3's
3/02  Volume of "Mathematicians Paperweights"
        HW p.406-407/1-6
3/03  Volumes using Discs
        HW p.407-410/7-14,23,24,39,40,49,70
3/04  Volumes using Washers
        HW p.407-408/15-20,25-28,41,42

3/08  Rotating around other lines than the axes
        HW p.407-409/21,22,43-47a,50-53
3/09  Length of a Curve
        HW p.416-417/1-17 odd,23-29 odd
3/10  Surface Area; Half Day (C B H F)
        HW p.409/55-62
3/11  Quiz; Integration as net change
        HW p.386-387/1-25 odd, 26

3/15  Application Problems
        HW p.425/1-6, 8, 10, 11
3/16  More Application Problems
        HW p.426-427/17, 18, 20, 21-23, 25
3/17  Review
        HW p.430-433/3-21 by 3',22-24,26-29,32,38
3/18  More Review
        HW Worksheet of Problems

3/22  Test of Ch 7

The solution manual for Chapter 7 is available here.

Finishing Chapter 6

2/08  Quiz #4, Extra Practice of Integration by Parts
          HW Finish handout
2/09  Separation of Variables
          HW p.357-359/1-10,21,23,41,43,54
2/10  Exponential Growth and Decay, Partial Fraction Decomposition; Quiz #5
          HW p.358-361/35,40,42,58 and p.369/1-17 odd
2/11  Logistic Function (Mixed Integration due)
          HW p.369-371/19-35 odd, 42-45

2/15  Review day 1; Quiz #6
          HW p.373-376/24-63 by 3's, 67-69
2/16  Review day 2
2/17  Test of Chapter 6
2/18  Area Exploration; Last day for quiz makeup

2/19-2/27  February Vacation

Optional Quarter Test

The Optional Quarter Test will be after school on Tuesday. It is cumulative for the year which means it covers limits, derivative, applications of derivatives, the fundamental theorem of calculus and some antiderivatives/integrals. If nothing else, be able to write the tangent line to any function.

If you cannot take it after school on Tuesday, you must tell me and arrange when you will take it before that time.

Ch 6 - Differential Equations

Differential equations is a large topic in science and engineering. It comes up in many applications and you can take a whole semester course on it in college. We will be doing an intro that utilizes many of the skills that we have already learned, plus some new ones. We will be working to solve them three ways: Numerically, Graphically and Analytically.

As we go through the analytic methods there will be frequent (maybe daily) short quizzes to assess how you are doing on learning the analytic skills and when to apply them.

1/19  6.1  Numerical Solutions: Euler's Method
           HW p.328-330/41-48,53,68 also enter the Slope Field Program in your calculator
1/20  6.1  Graphical Solutions: Slope Fields
           HW p.328-330/25-40,49-51,59,61,62,67
1/21  Snow Day

1/25  6.1  Analytical Solutions: Antiderivatives (technique 1)
           HW p.327,330/1-23 odd,65,69,70
1/26  6.2  Integration by Substitution (analytic technique 2)
           HW p.338-340/18-66 by 3's,78,79,81
1/27  Snow Day
1/28  6.3  Integration by Parts (analytic technique 3)
           HW p.346/1-16

2/01  Early Release, half block class, Integration Quiz 2
2/02  Snow Day
2/03  Discuss substitution, Integration Quiz 3, start Mixed Integration handout
2/04  6.3  More Integration by Parts (repeated, circular, tricky)
           HW p.347-348/17-32,42,45,49

2/11  Mixed Integration handout due

Here are the solutions for the Chapter 6 questions.

Finishing Ch 5 and Second Term

We are back from vacation but in the middle of Ch 5. Here is the proposed syllabus for the rest of the chapter:

1/04 Review what we know so far.  CW p.293/4
         HW p.315-317/1-4,6-9,1,13,35-38,46
1/05 More with the Fundamental Theorem of Calculus (5.4)
         HW p.302-305/10,11,16,17,19,20,29-31,35,43,46,58-61,73,75
1/06 Trapezoidal Rule (5.5)
         HW p.312-314/1-9 odd,10-12,20,39
1/07 Simpson's Rule and Review
         HW finish handout

1/11 Review Day 1
         HW p.316-319/15-30 by 5's,33,54,56,58-60
1/12 Snow Day
1/13 Half-day, no class
1/14 Review Day 2 - Extension Problems
         HW finish handout solutions

1/17 Martin Luther King Day, no school
1/18 Test of Ch 5
1/21 End of Term 2