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.
Sunday, October 19, 2008
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!
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!
Wednesday, September 17, 2008
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
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
Monday, September 15, 2008
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.
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.
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.
Sunday, September 14, 2008
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
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
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
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