Debbie Poss's Blog

Accelerated Math II - We Love Logs! - October 28, 2011

Today we discovered that a logarithm was just an exponent, because if b^p= N, then log_bN = p.  The assignment for the weekend is from the Green Math III book - work the odd problems on pg 147 and 148.

If you are planning ahead, I'm planning on testing over logs on Monday, November 14.  That should give us enough time to complete statistics and be ready for the EOCT in Math II on December 13, 14. 

Accelerated Math II - Test Tomorrow - October 26, 2011

In order to prepare for the test tomorrow, students received a review sheet.  Here is that sheet with answers. Download Standards for tomorrow 

We also planned to take an IRespond test, but didn't have time to complete it after answering questions in class.  Students did get this test, though and I recommend that students give themselves 20 minutes to complete it.  (That might help simulate the pressure you feel in class.) Here are the answers to that practice test:

1.E   2.D   3.D   4.C   5.E   6.C   7.D   8.E   9.B   10.B    11.B    12.B    13.D    14.D

Students in 6th and 7th period also received an ASE practice test.  Answers to it are: 

1.E   2.D   *3.This question has a typo.  If h(x) = 4x³ - 12x², then the answer is C.  4.D    5.B    6.E  

 

Accelerated Math III - Other Trig Functions - October 26, 2011

Today we looked at graphing trig functions again.  The first time we looked at the "size and shape" of the graph and then translated the graph to the correct "location".  Today we analyzed the graph by looking at corresponding points on the unit circle.  That meant we looked at 1/4 the period to locate points on the curve.   Clearly both methods work, but students need to find out which way works best for them. 

Then we started to graph the other trig functions, but didn't complete that task.  Therefore the assignment for tonight is A) Using the worksheet we started in class, sketch a very good graph of y = tan x.  (Most students have already done this.)  B)  Using the graph of y = tan x and properties of reciprocals of numbers, sketch a good graph of y = cot x.  C)  Sketch y = cos x and using this and the properties of reciprocals, sketch an excellent graph of y = sec x.  (Many students have done this, too.)  D)  Use your experience to sketch an excellent graph of y = csc x.  E)  Write down the domains and ranges of all of these 4 functions. 

Then, go to your text and read pages 105 - 107.  On page 108-109, work Q1  - Q10 and problems 1-14.  Yes, I know the questions in your book are some of the same you've already answered, but seeing them again will help you remember these functions!

Accelerated Math II - Sequences and Series - October 25, 2011

Here are questions about sequences and series:  Pg. 136: 1-21 odd, and Pg. 141:  1 - 27 odd 

Accelerated Math III - More graphs of sines and cosines - October 25, 2011

Tonight's assignment is Pg. 103, 13 - 27 odd and Pg. 122: 26, 28, 34, 36, 42

Accelerated Math II - Inverses of Non-Linear Functions - October 24, 2011

Complete the back of the "Inverses of Non-Linear Functions"  worksheet that we started in class.  Attached are partial answers, however, I believe that there is at least 1 typo on this page.  Let me know if you find it.:-)

Download Answers to nonlinear inverses

Accelerated Math III - Graphs of Sines and Cosines - October 24, 2011

The assignment is page 102 problems Q1 - Q10 and 1-11 odd.  Also page 121 - 122, problems Q1 - Q10 and 25 - 41 odd.  Remember that the answers are in the back of the book.

Accelerated Math II - Compositions of Functions - October 12, 2011

The homework for 6th and 7th period was a "More on Compositions" worksheet and the answers are as follows:

1.  (8x + 5)/(4x + 3)     2.  16x² + 16x + 3      3.  2^x+2 + 7      4. (2x² - 4x - 1)/(x² - 2x)   5.  (-2x + 1)/x²    6. 2^2x - 1   7.  x⁴ - 4x³ + 2x² + 4x    8.  (3x - 2)/(2x - 1)

Back page:  1.  a)  {1, 2, 3, 4}  b) {1, 2, 3, 5}   2.  a) {0, 1, 2, 4}  b)  {1, 3, 4, 5}  3.  {(0, 1), (1, 2), (2, 3)}  Although g maps 4 to 5, 5 is not in the domain of f.   4.  {0, 1, 2} is a subset of the domain of g(x) because g provides the initial x values for f(g(x)).  The range is {1, 2, 3} which is a subset of the range of f(x) because f provides the final y values.   5.  {(3, 4), (4, 1)}  Other points of f don't have y values that are in the domain of g.  The domain of g(f(x)) is {3, 4} which is a subset of the domain of f(x) because f(x) provides the initial x values (since it's the "inside function").  The range of g(f(x)) = {4, 1}.

First period is working on more Practice (Operations with Functions) and this worksheet was given to 6th and 7th as additional problems for review.  Answers to this worksheet are:

1.  (f+g)(x) = 8x² + 5x - 13   and (f-g)(x) = 6x² + 5x + 13

2.  (f+g)(x) = 13x² - 5x + 41  and (f-g)(x) = -13x² - 5x + 41

3.  (f+g)(x) = x² - 20x/3 + 2   and (f-g)(x) = x² + 22x/3 + 16

4.  (f+g)(x) = 4x² + 6  and (f-g)(x) = -21x² + 6

5.  (f*g)(x) = 105x + 25   and (f/g)(x) = 7x + 1

6. (f*g)(x) = 3x³ + 17x² + 75x + 425   and (f/g)(x) = (x² + 25)/(3x + 17)  Where x doesn't equal -17/3

7.  (f*g)(x) = x⁴ - 256   and (f/g)(x) = (x² + 16)/(x² - 16) where x doesn't equal 4 or -4

8.  (f+g)(x) = -x + 8            9.  (f-g)(x) = -3x - 12

10.  (g-f)(x) = 3x + 12        11.  (f*g)(x) = -2x² - 22x  - 20

12.  (f/g)(x) = (-2x - 2)/(x + 10) for x not equal to -10

13.  (g/f)(x) = (x+10)/(-2x - 2) for x not equal to -1

14.  f(g(x)) = x   and g(f(x)) = x

15.  f(g(x)) = 4x² - 4   and g(f(x) = 16x² - 1

16.  f(g(x)) = -x² + 1  and g(f(x)) = -x² + 1

17.  -44       18. -52       19.  -10 

 20.  -5       21.  -5         22.  22

23.  -55       24.  -28        25.  242

 

 

 

Advisement - Bring calculators and pencils for the PSAT tomorrow!

This is just a reminder that we are giving the PSAT tomorrow, October 12, 2011 and that all students grades 9-11 need to bring their calculator and several #2 pencils.  It would be advisable NOT to bring your cell phone, but if you do, I'll keep in in a box for you while you are taking this nationally recognized test.

Accelerated Math III - Quiz and Rotary Motion - October 11, 2011

Today we took a quiz on beginning trig concepts.  The assignment for the night is to read pages 138-142 about rotary motion and to work problems 1-9 on pg. 143.