PAPPC Polar Relations Unit 8.1, 8.2, 8.3

Hello,
Today is Thursday, Dec. 4, 2008. I am in Montgomery today and tomorrow working on the new Alabama Math Course of Study. If you need help with your work while I am away, please leave a comment and I will respond. You can also e-mail me at tsnipes@mscs.k12.al.us

To the cast and crew of SCROOGE, "break a leg"
Mrs. S

Adv. Alg./Trig Lessons 2.2, 2.3, 2.4

Greetings,
Today is Thursday, Dec. 4, 2008. I am in Montgomery today and tomorrow working on the new Alabama Math Course of Study. If you need help with your work while I am away, please leave a comment and I will respond. You can also e-mail me at tsnipes@mscs.k12.al.us

To the cast and crew of SCROOGE, "break a leg"
Mrs. S

ADV. ALG./TRIG & PAPPC

Both classes have a quiz Thursday and a test on Friday, Nov. 21.
AAT (1st and 4th)
AAT Quiz and Test will cover Trig lessons 1.5 - 1.8 with review problems from 1.1 - 1.4.
Don't forget to bring your completed "BINGO" REVIEW Assignment on Thursday. After discussion of the review we will take our quiz using the SENTEO response system.
You may use the remainder of the class to study for Friday's test in your groups...

PAPPC (3rd block)
Thursday, you will complete the 2.2 - 3.2 quiz. After discussing the quiz, we will review bearings and do the 'ON THE WALL' review problems in the yellow hall.

If time permits, we will also discuss the first lesson in our next unit on Polar Functions. (Bring your Precal Book to class)
Your test FRiday will have 15 problems from chap. 3 and two review problems from chap 2. (Go to first lunch Friday). After FRiday's test, you will do the chapter 3 homework check and begin working the first assignment from the Polar Functions unit.

If you have any questions, post a comment.
Mrs. S

Advanced Algebra/Trig Lesson 1.7
Inverse trig functions
Y = Arcsin X
range [-pi/2, pi/2]
If x is a negative number, the angle y is a positive Quad I angle.
If x is a positive number, the angle y is a negative Quad IV angle.
Y can also equal -pi/2, 0, and pi/2

Y = Arctan X
range (-pi/2, pi/2)
If x is a positive number, the angle y is a positive Quad I angle.
If x is a negative number, the angle y is a negative Quad IV angle.
Y can also equal 0. Note that the range excludes -pi/2 an pi/2 as values for y.

Y = Arccos X
range [0,pi]
If x is a positive number, the angle y is a positive Quad I angle.
If x is a negative number, the angle y is a positive Quad Ii angle.

PROBLEM SOLVING TIPS :)
1. KNOW YOUR UNIT CIRCLE.
2. For problems such as sin(arcsin 1/2) the answer is 1/2. Rationale: If the trig function is outside the parenthesis, the trig function and the inverse cancel one another out.
3. for problems such as arcsin (sin 3pi) YOU CANNOT CANCEL
Work inside the parenthesis first to get 0. Next find arcsin 0.
Solution: Y = 0.

I will be online between 7 and 9 pm tonight. The time on this blog is not set correctly, so you will need to look at you clock to know if I will be online.

Important stuff: Quiz Thursday on 1.5 - 1.8
Test Friday on 1.5 - 1.8 with major review problems from 1.1 - 1.4

See ya'll tomorrow
Mrs. S

AP CALCULUS 2009

Do you need help with your Calculus Fall work? Leave a comment with specific details regarding what your understand and what you need help with.
Students may help one another online and occasionally I will give online help. If you help another student online, you will receive bonus credit in AP next spring. (of course, all information you share must be accurate)

Thanks for all of your hard work.
:) Mrs. S.

PAPPC 1.1 - 1.8 TEST HELP

Greetings everyone,
How was class today? I'm sure that all of you worked hard in your groups and helped one another. If you have any questions, feel free to post a comment. I will be online until around 10 pm to help you. Be sure to read the notes I left on the board regarding pacing yourself on the test. If you know the objectives and how to work all types of problems you will do fine. You have 45 minutes for part I (no calc.) and 45 minutes for part II (Calculator, 9 application problems).
Part I is the basics: simple stuff like graphs of sinusoids, coterminal angles, and inverse trig function problems like arcsin (sin PI). On part II, you may see a bearing problem and a harmonic motion problem in addition to the "basic" triangle trig word problems.
Good Luck! I'd love to hear from you:)

Advanced Algebra/Trig 1.1 - 1.4 Test Help

Hello everyone,
I have spent today in Montgomery at the State Dept. of Education. We are working on the new Math Course of Study for the state of Alabama. I hope your review time in class today went well and that you are using the Study Guide I gave you on Monday. If you are unsure how to do a problem, read the tips on the study guide for that objective.
I will be online until 10 pm tonight. If you have any questions, leave a comment and I will help you. Study well and do your bet tomorrow!
Mrs. S

NEW LINKS

CHECK OUT "TOPICS RELATED TO CURRENT LESSONS"
There are two new links: One is to the "MATH FORUM". This site offers online help as well as a lot of interesting math stuff. The other link is to various latitude maps and relevant information.

TRIG LESSON 1.1 Adv. Alg. Trig and PAPPC

Hello everyone,

The BLOG is BACK !:)!

Thanks for your kind words, cards, and expressions of sympathy during the loss of my mother. You are a wonderful group of students and I am so honored to be your teacher.

Let's review what we have learned since beginning our study of Trig.
1. There are two ways to measure an angle: DEGREES & RADIANS
We have learned how to convert from degrees to radians and vice versa.
30 degrees X pi/180degrees converts to pi/6 radians.
Degrees and Radians are two ways to measure the same angle, just like fahrenheit
and celsius are two ways to measure the same temperature.
2. We did an exploration in which we discovered the true meaning of 1 radian:
ONE RADIAN is the measure of an ANGLE that intercepts an ARC EQUAL TO THE
RADIUS OF THE CIRCLE.
3. Another exploration involved complementary and supplementary angles. We reviewed
that an angle has no complement if greater than 90 deg., and no supplement if
greater than 180 deg.
4. Coterminal angles are found by adding or subtracting any multiple
of pi to the given angle.
5. All of you need to know the quadrant angles in both degree
and radian measure. It is also useful to be familiar with the radian measure
as a decimal value rounded to two places. This knowledge is useful when a
problem tells you to determine the quadrant in which an angle
lies. You will use this strategy of determining the
quadrant when told to sketch an angle in standard position.
6. Convertions between decimal degrees and degrees/minutes/seconds were practiced
so that we could work application problems involving latitude.
7. There are three important formulas in Lesson 1.1:
Arc Length - used in latitude applications involving distance between cities and
difference in latitude between two cities.
Linear Velocity - (distance)/(time) or (radius)X(angular velocity)
Angular Velocity- (radians)/(time)
The # of revolutions can be changed to angular velocity:
Just multiply (rev.)/(time) X (2pi rad)/(1rev.)

STAY TUNED THE UNIT CIRCLE IS OUR NEXT LESSON!

PAPPC LESSON 3.6

Hi everyone,
Lesson 3.6 concludes the material that will be covered on the 3.1 - 3.6 Test (The test is Friday, Sept. 19) In this lesson, we solved rational inequalities. The solution process utilizes the following steps:
Find the zeros and the excluded domain values. These numbers divide the real number line into intervals. Pick a "test point" in each interval and test it in the original function. If the "test point" produces a true inequality, then the interval is in the solution set. If the "test point" produces a false inequality, then the interval is not in the solution set.
This lesson uses the term "strict" for an inequality such as < or >.

I want each of you to know that I am pleased with your progress in this class. I realize that the transition into a Pre AP class has been difficult for many of you. You are a hard working group and I commend you :)
Mrs. S

TEST BONUS OPPORTUNITY: Check out the link to Plus magazine

How long will you live? Who will win the Presidential election? How should you write down numbers? Who's your ideal partner? How good is our voting system? What is a differential equation? These are difficult and momentous questions. This issue of Plus has some answers, along with a tour of digital art and the usual range of podcasts, news and reviews.

Plus is an online magazine that has some really neat stuff! See how you can use this site to
a. Find real life stuff that uses the math we are learning.
b. Find neat ideas and connections that you've never heard of before

Bonus opportunity: Read any issue of Plus Magazine. Create a 5 minute power point presentation telling a story about what you learned. (Your power point should just be an outline...most of the story will be told by you.) Present your story to the class and receive from 1 to 5 bonus points on a test.

Lesson 8.6 Adv. Alg./Trig

Natural logs are base e logarithms. Example: ln 3
All log properties for common logs apply to natural logs.
* e is approximately equal to the irrational number 2.71828182845904523....
* To write a natural log as a single logarithm, use the product,
quotient, and power rules.
* To solve a natural log equation, simplify then change to
exponential form and solve for the variable.
* To solve an exponential equation in base e, simplify,
take the natural log of both sides of the equation, use the
power rule, then solve for the variable.
Tomorrow we will work the application problems in 8.6 and review
8.5 and 8.6 by working group problems.

PAPPC Lesson 3.5

Lesson 3.5 is all about graphing rational functions. Make sure that you know the difference between a rational function and a polynomial function. Here are the hi-lites of the lesson: Before sketching the graph, find the Domain, Hole(s), Vertical Asymptotes, Horizontal or Oblique Asymptotes, and Zeros and y-intercept. After graphing, determine the range of the function.

Graphing Tips: 1. Sketch hole(s), zero(s), and y-intercept of the graph.
2. Sketch vertical, horizontal or oblique asymptote(s)
3. Note if the ratio of the leading coefficients is
positive or negative.
a. If positive, the graph begins on the right of and above
the x-axis.
b. If negative, the graph begins on the right of and below
the x-axis.
4. Sketch the first branch of the graph in the appropriate region.
5. Use the multiplicity of the vertical asymptote to determine from
which infininty to begin the next branch of the graph.
6. Repeat steps 4 and 5 until the graph is complete.

Please help one another by commenting with your own tips and helps for graphing. See you Monday.
Mrs. S

Lesson 8.5 Adv. Alg./Trig

Lesson 8.5
This lesson has 3 objectives. On Friday, Sept. 12, we learned how to solve exponential equations using four easy steps. You have a copy of these steps on your "footprints" graphic organizer. We also learned the second objective which is to solve logarithmic equations using two easy steps which are also on your "footprints" graphic organizer.

On Monday, Sept. 15, we will learn how to use the "change of base formula" for logarithms. This is the third and final objective of lesson 8.5

Advanced Algebra/Trig Lesson 8.4

Lesson 8.4 is all about the three logarithm properties.
The product rule changes the product of a single log to the sum of two logs.
The quotient rule changes the quotient of a single log to the difference of two logs.
The power rule allows us to move an exponent down and multiple it times the log of the given number.

Bonus Question: You will receive a bonus point on the next quiz if you e-mail me the correct answer before 8 am on Thurs., Sept. 11, 2008

Write (logX - logY + logZ) as a single logarithm.

e-mail your answer to tsnipes@mscs.k12.al.us. Do not post your answer as a comment to this posting.

PAPPC LESSON 3.4

Your task today is to find the domain of a rational function.
You must also know how to find the vertical, horizontal, and slant asymptotes of a rational function.

To determine the domain, you must find the values that cause the denominator to = zero. These values are NOT in the domain. It may help you to "see" the domain if you sketch a number line, put open circles for undefined values, and shade the line for values that are in the domain. Use your number line as an aid in writing the interval(s) that make up the domain.

Use you class notes to study vertical, horiz., and slant asymptotes. If you have any questions, please ask for help online.

Bonus Question: Worth 2 point on Friday's quiz. e-mail your answer to tsnipes@mscs.k12.al.us Your e-mail must be posted before 8 am on Thurs. Sept. 11, 2008

1. Explain how to find the holes and vertical asymptotes of a rational function.
2. Explain why a polynomial function will never have any vertical asymptotes or
holes."
Mrs. S

Advanced Algebra/Trig Lesson 8.3

Logarithmic functions as Inverses

You may wonder about the title of this lesson and what it means. The logarithmic function (log function) has an inverse relationship with the exponential function we studied in lesson 8.1

Think about the graph for y = 2^x.
Now, look on page 440 of your text and look at the graph under objective 2.
Notice the exponential funtion is sketched in red ink and the logarithmic function is sketched in blue ink.
Now look at the graph in example 5. What other equation has been graphed in green?

In Alg. 2, you learned that a function and its inverse are "SYMMETRIC" about the line y = x. This means that if you fold the graph on the line y = x, the exponential function and the log function fold on top of each other.

ISN'T MATH NEAT... Again, looking at the graph in example 5, look
at the asymptote for y = log (base 2) of x.
The asymptote for the logarithmic function is the y axis or the line x = 0.
As you remember, the asymptote for the exponential function is the line y = 0.

Tonight's assignment: Post a comment and answer the following QUESTIONS?????????????????????????????????????????
1. In this lesson, what did you learn about a common log?
2. How do you change an exponential equation (y=b^x) to a log equation?
3. How do you change a log equation to an exponential equation?

Lesson 3.3 PAPPC

3.3 POLYNOMIAL FUNCTIONS AND MODELS
This lesson has THREE BIG OBJECTIVES :)
A. Identify polynomial functions and their degrees (See ex. 1 page 201
B. Identify the zeros of a polynomial function and their multiplicity. Know how to obtain the degree of a function by adding the multiplicities of the function.
Know when the graph crosses the x-axis and when the graph touches(is tangent to) the x-axis. See pages 204-205
C. analyze the graph of a polynomial function. Know the 4 "End Behavior" rules See pages 206 - 208. Work examples 5 and 6.

I will be online tonight(Sept. 8) from 7 to 9 pm. Leave me a question, comment, or tell me something GOOD that you have learned in lesson 3.3!

Lesson 3.2 PAPPC

POWER FUNTIONS AND MODELS

Lesson 3.2 is all about the properties of power functions of even and odd degrees. The most important concept for 3.2 is this: You should be able to sketch the graph of a power function, by looking at its degree and determining the end behavior of the graph.
The properties of power functions are discussed on pages 196 and 197. Here is an example: y = x^4 flattens at the vertex and gets more vertical as -1 < x < 1.
Read about these properties, and play with graphs on your TI-84 to learn more.
TI-84 exercises:
Graph y = x^2, y = x^2 + 1, and y = (x - 4)^2 + 1. What do you notice about the "end behavior" of all graphs. Now graph y = (x-1)(x-4). How is this graph different from the first three?

Leave me a comment with your observations and your questions on 3.2 :)

Lesson 3.1 PAPPC

Many real life applications are modeled by quadratic functions. Think about some of the application problems in this lesson. What real life applications did you model using a quadratic function? It is important that you can name some of these applications. In particular, know that a revenue equation = xp where x is the number of goods sold and p is the price.

Other important objectives from 3.1 are.....
1. Write quadratic equations in quadratic form, or in vertex form, when given the graph with vertex and y-intercept.
2. Graph quadratic functions by hand by determining and labeling the vertex, axis of symmetry, y-intercept, vertical compression/stretch.
3. Given an equation in quadratic form, know the equation of the axis of symmetry, and know at first glance the y-intercept.
4. Know how the value of a determines if there is a vertical stretch, or a vertical compression.
5. EXTRA EXTRA EXTRA!! (required info that is not in our text)
The focus of the parabola (in vertex form) is k + 1/(4a) OR K - 1/(4a)
The LATUS RECTUM = 1/a (THE L.R. IS the line passing thru the focus.)


Please leave a comment if you have questions re. problems in this lesson.
Mrs. S

Adv. Alg./Trig Lesson 8.1

Advanced Algebra Trig Lesson 8.1 EXPONENTIAL FUNCTIONS

This lesson introduces us to the exponential function: y = ab^x.
If b > 1, the equation represents exponential growth.
if 0 < b < 1, the equation represents exponential decay (also known as depreciation)

In this equation, b is called the "growth factor", or the "decay factor". In real world applications b = 1 + r (where r is the rate as a decimal). In depreciation problems, r is negative. In growth problems, r is positive.

a represents the y-intercept of the graph. (0,a).
draft 1/24/09 by Mrs. S.