Solutions for Area and Volume Problem Sets

Area and Volume Problem Set 1 and Area and Volume Problem Set 2 can be downloaded here.

The solutions for Problem Set 1 and Problem Set 2 are complete as well.

Problem Set 1



1971 AB5 Video


1969 AB5 Video



1975 AB6 Video



1976 AB3 Video


1977 AB3 Video



1969 AB4 Video 1
1969 AB4 Video 2


1970 AB1 Video


1971 AB2 Video

Problem Set 2


1980 AB1 Video
1980 AB1 Video 2 (Calculator Pt.1)
1980 AB1 Video 2 (Calculator Pt.2)


1981 AB2 Video



1985 AB3 Video



1987 AB3 Video
1987 AB3 Video (Calculator)



1988 AB3 Video

Some solutions

In response to the questions asked:

1969 BC 10


1969 BC 23


1969 BC 10 and BC 23 Video

1969 BC 23 continued and 1973 AB 31 and 1973 AB 37 Video

1973 AB 31


1973 AB 37


1985 BC 28


Actually, the answer is E to 28 above. I did the right work and had the right answer, but wrote D. Sorry.

1985 BC 33


1985 BC 28 and 1985 BC 33 Video

Answers to Multiple Choice Practice Problem Set

The answers to the multiple choice practice problem set are below:



Let me know if you have any questions on these, and I can post explanation videos. If there are no questions, I assume you get it. :)

Solution to class problem

I have worked out a few ways to get the correct answer to the problem we were working on at the end of class. They are contained in the video here. Please print out a copy of the problem set and bring it with you to class tomorrow.

I have uploaded a practice worksheet with AP multiple choice questions on the material in chapter 5. You can download it here.

I am also listing hw problems from the text. There are lots of examples of how these types of problems work and corresponding solutions. You do not need to do them all, but these are problems that you will be responsible for.

Larson 7.0 Chapter 5
Section 1 #45-69 odds,
Section 2 #1-39 odds,
Section 3 #47-53, #71-79 odds,
Section 4 #39-71, #87-107 odds,
Section 5 #41-55, #61-67 odds,
Section 6 #1-9, 17-19 odds,
Section 7 #31-63 odds,
Section 8 #41-59 odds,
Section 9 #1-41 odds

That's alot. There are a few formulas to remember, but the process is the same as what we have been doing all along.

I am out Friday, but you should now have plenty to work on. :)

Remember to email me with questions!!!! Don't wait till Tuesday. Thanks!!!
On Tuesday and Wednesday we will finalize the AB material!!!!

Integration Review

Integration Review all evens. These are from the Chapter Review exercises at the end of Chapter 4. Solutions to odd problems are online. Bring final questions on Monday and test Tuesday. If I am out Monday, then final questions on Tuesday and test Wednesday. If you have questions, let me know before then!!!!

Solution to #12 using geometric formulas:



And video solutions (not sure why I keep calling this problem 14, it is really problem 12):

Part 1:



Part 2:



Part 3 (Using integration - I think this is much more complicated, but you should follow it through and learn from the techniques used):



Part 4 (Finishing up with the integration and then taking a short cut or two)



I hope you spend some time going over these videos. The problem is not trivial and I can't say that I have ever solved or even seen a similar one, but hopefully we can learn something from it. I think it is a great problem and definitely a challenging one. :) Below is a printable copy of the solution.

Integration by Substitution and Trapezoidal Rule

Integration by Substitution: Larson 7.0, Chapter 4, Section 5 #7-39 odd, 41-53 odd, 57-81 odd.
Trapezoidal Rule: Larson 7.0, Chapter 4, Section 5 #1-19 odd

Fundamental Theorem

This is the bread and butter of integration. Please practice, practice, practice!
Homework assignment: Larson Ch. 4 Section 4 5-31 odd, 35-51 odd, 53-60 all, 69-91 odd

Fundamental Theorem of Calculus Part 2

The assignment here on Definite Integrals and the Fundamental Theorem is related to the ideas that we have talked about below. This should carry you over until we return next Monday. Please let me know if you have any questions on these before we return. Don't wait till that time to ask! You can comment here or reach me by email.

Today we discussed the Properties of Definite Integrals. A list is posted here:



Also, we started with a justification of the Fundamental Theorem of Calculus Pt. 1. This is portrayed in the diagram below:



This leads to the gray box at the top. We call the Fundamental Theorem of Calculus Pt 1. Please follow the logic



This then leads to the Fundamental Theorem Pt 2.



The following is an example that may help with some of the problems on the FTC part 1. I will also put some videos out regarding these problems over the weekend.

Integrals

Integrals from Known Geometric Formulas HW assignment can be downloaded here.



Rectangular Approximation HW assignment can be downloaded here.

Solutions and HW

Solutions and HW for tonight is Chapter 4.1 Section 1-70 odds.

Derivatives Review Free Response Questions

Free Response Question problem set due 11/18/09.

Take Home Assignment

I have decided that we will follow the progression of the book we have been using to deal with the following topics:

Derivatives of Inverse Functions
Derivatives of logarithmic functions with base b
Derivatives of exponential functions with base b
Logarithmic differentiation
Derivatives of Inverse Trig Functions

These are all covered in chapter 5 after basic integration. We can cover more of Linear Approximation through examples over time. It is not a difficult topic at all and with a little practice you will be great at it.

Instead, for this evening I would like you to complete the 4 problems on the attached Take Home Assignment. The problems are challenging, but definitely within the scope of your capability. You may discuss them, but I would like you to complete them tonight.

Solution for #3 on new group test

Below is a solution for #3. There are two graphics and three videos.

Solutions to Problem Set 3 and a new group test!!!

The solutions to the Problem Set 3 are here! The new group test is here as well. Enjoy! This basically concludes out study of derivatives. We will continue to practice, but starting next week, we move on to bigger and badder things - integration.

Motion Problems

Motion Problems

This is an explanation of Applications of Derivatives problem set #65



Here are the videos that show the detail



And continued



Finally

Test on Applications of Derivatives Wednesday 11/4

Derivatives Problem Set #3 and Applications of Derivatives Problem Set #1 and Solutions are attached here.

Derivative Problem Sets and Test on Friday

I have attached two derivative problem sets. The first is a general set of problems that covers all the work we have done to date. The second covers only the topics of Chain Rule, Implicit Differentiation and Related Rates.

The problem sets are not due until Monday 10/26, but will be useful in preparing for the upcoming test on Friday - especially the second one, so try to concentrate on that one. Good luck!

New Video Resources

I have found some new calculus tutorial videos on the web that may be helpful for some. You can find them here. I have also added a list called "Blogging Tutorials" that might be helpful in doing various things in your blogs. Today I added a tutorial on how to create a link to a resource in your blog posts. The video is also embedded here for your convenience.



If you have any other suggestions for topics, let me know.

Limits Problem Sets

I have posted limits problem set #1 for your practice. These are all multiple choice questions. Good AP practice.

Test Tomorrow!

Don't forget (and I'm sure you haven't) that we have a test tomorrow. If you think you need extra time, you can start the test any time during the lunch period. Hint: My tests may not be difficult, but you may find them lengthy.

You should know:
1) Finding limits using your calculator
2) Finding limits from graphs of piecewise functions
3) Finding limits by applying the properties of limits
4) Finding limits of functions algebraically using:
a. Factor and cancel
b. Rationalizing
c. Simplifying fractions
5) Graphing piecewise defined functions and finding limits using the graphs
6) Finding limits of trig functions using the two basic trig limits

You should have the Point Point presentation and Larson Calculus 7.0 Sections 1.2 and 1.3.

Please let me know if you have any questions. See you tomorrow!

Limits Power Point Presentation

Please let me know if you have any problems downloading it.

Welcome to the new school year. I look forward to working with you all. It is going to be a great year and we are all going to learn a lot. Better still, it will be over before you know it and you all will be heading off to college. Let's all value the little time we have together and make it a successful year for everyone!

The AB class now has it's own blog site. It can be found here.