Scribe Post 1/8/10

At the beginning of class people had questions with the homework problems at the end of the assignment using the sum of the first n terms of any arithmetic sequence formula, #67, 69, 71, 85. We started with the warm-up which was doing the half-sheet of arithmetic sequences and series which was passed out to us last class. Mr. Obrien explained how make a table with arithmetic sequences to find the common difference. The graph of a arithmetic sequence has a linear graph, y = mx + b. He also reminded us to always check our answers for n by simply testing it.

Mr. Obrien showed how to solve the nth term without using the formulas, which was much quicker. For example:,, 9d + = , 9d + 16 = 43, 9d = 27, d = 3. So instead of using formulas you can find without them. = 3n + 4. Because 3 is the difference so it is the nth term, then since you know = 16, 4 x 3 = 12 + 4 = 16, so you found the nth term without using the formula.

We learned about Gauss's formula of finding how to find the sum of numbers 1 through 1000. So 1001 x 500 = 500500. The formula for this is: .

Next students put up the answers to the questions from the homework that students had questions on. Mr. Obrien explained that there are three numbers between 10 and 12, 10, 11, 12. This sounds simply, but it is helpful to understand when doing problems such as #69 on the homework. Next he passed out a yellow half-sheet. We started by defining a geometric sequence:
= r x
To finish class we filled in the formulas on the yellow sheet which we will use for tonights homework.

HW

HW:

• p. 669/5, 11, 19, 25, 29, 35, 41, 53, 57, 63, 73, 77, 79, 83, 89

HW for Fri

HW:

• p. 659/1, 9, 11, 16, 19, 21, 27, 37, 39, 41, 45, 67, 69, 71, 85

HW

HW:

• Check out this link for a revision of function and sequence mode on your calculator and this link for a revision of finding summations on your calculator.
• p. 649/1, 3, 5, 7, 23, 25, 37, 43, 51, 53, 54, 57, 73, 77, 81, 93, 97
  

Unit 3 test

Here's a blank copy of the Unit 3 test to use as practice before Tuesday's follow-up test:

Unit 3 test

Wednesday and Friday

You have all class to work on Supercorrections and prepare for the follow-up test next Tuesday. Please feel free to use this document to discuss problems:

http://etherpad.com/HwRSczyOkJ

If you'd like me to jump into a discussion, just let me know with an email.

Although I will be in London for the rest of the week, I am available via email. Just shoot me your questions!

Update: I'm now in the UK (Wednesday)- if you use the Etherpad link above, I can contribute to your discussion.

Scribe Post for 10/10/09

Mr. O'Brien passed the Unit 3 Quiz #2 tests back today, and we went over them for the first part of class. While going over the test, Mr. O'Brien stressed the importance of considering the order of operations while condensing logarithms. He also explained some of the simplifying, and explained why an expression such as

is not fully simplified, and should be further simplified to:



Mr. O'Brien also emphasized that we should use "=" only when the equation is completely equal, and "≈" if the equation is approximately equal. For example, if you have the equation x = 12/13, the equals sign is appropriate. But if you make 12/13 a decimal, it should be written as x ≈ .923 because the decimal is being rounded. He also pointed out that people were losing points for not following directions (for example, rounding to four decimal places when the problem specified to round to three decimal places).

He also explained problem #9 in detail, as follows:
ln 4x = 14/13 can be rewritten as




either by thinking of it as just directly translating it into this form, or by making each side of the equation raised to a power of e, like this:




He then explained checking it without a calculator. He also said to beware of extraneous solutions for our test. A problem can be done perfectly correctly, but then the solutions can be extraneous. This means we should be careful to check our answers by substituting the values back into the equations. He later said how we need to use common sense in checking our answers. For example, if we're doing a carbon dating problem and we get a negative answer for the time, there's obviously a problem with our math.

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We then went to p. 270 of the textbook, which went over all of the things we're expected to know for the test. The themes of the test are the basics, as well as real-life problems. Note: we do not have to "recognize the five most common types of models involving exponential and logarithmic functions". We have to be able to use things from section 3.5, but we don't have to have them memorized.

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After this, we reviewed homework questions. Mr. O'Brien talked about how, in order to minimize the amount of time we spent on problems during math tests, we should go through the problems to see if there are things we can recognize. For example, repeated calculations can use the "function machine" on our calculators. (Enter the function into the y= on our calculator, and then use a table that's set to ask for the independent variables.)

He also reviewed the correlation between




with the first equation being used for daily, monthly, yearly, etc. compounding, and the Pert equation being used for continuous compounding. (We will not need to have these equations memorized for the test).

Then we reviewed using the [STO→] key to store long values to letters in our calculators. To store a value (for example .56273) to a letter (or example A), type [.56273][STO→][ALPHA][A]. Then to recall the value, simply type [ALPHA][A].

Remember that % decrease is (amount of decrease/total amount). The amount of decrease is the difference of the two values.

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For homework, we have to correct all our homework to turn in next class, do 8 problems from the Chapter 3 Review Test to include with our homework packet, and revise for the test next class. Mr. O'Brien said that the test will have a lot of word problems.

Scribe for next class is Andy.