ATaylor's Corner

6th Grade: Comparing Fractions !

2011-11-14T08:18:00.000-08:00

In order to compare fractions, you must learn about equivalent fractions. Go to www.khanacademy.org and click on equivalent fractions under arithmetic and watch the video. It is a nice starter video in learning about comparing fractions.

Transition Summer.

2011-06-29T06:52:00.001-07:00

From the high school to the middle school. Here I come!

Review Time for Algebra !!

2011-05-27T07:42:00.000-07:00

Here is a review video for Solving Systems of Equations and Inequalities. There will be a mini quiz on Tuesday.

Solving System of Equations via Graphing

Solving System of Inequalities via Graphing

Study and Enjoy your Memorial Day Weekend :)

Volume of a Sphere

2011-05-17T11:25:00.001-07:00

Surface Area of a Sphere

2011-05-17T11:24:00.001-07:00

Quadratic and Cubic Functions for Algebra

2011-05-09T13:49:00.002-07:00

Intro to Polynomials - Algebra

2011-05-09T13:49:00.001-07:00

The Big Push Is On!

2011-04-20T15:10:00.000-07:00

This week we are reviewing the quadratic formula in Algebra. In a few weeks it will be time to review for finals.

In Geometry, there is no video for networks. So Google it! Let me know what you find.

Area of Triangles!

2011-04-11T13:57:00.000-07:00

Here is the link to the homework page.

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0Bwm4tDQmJ4k5MzExYTAxMDMtNDQ2YS00MjYxLTk0OTItNjU0MmJkNDc4MTEx&hl=en&authkey=CODIkYkM

Paste this link directly into the URL web browser!

Good Luck!

Here is today

2011-04-11T13:44:00.001-07:00

Hi, Tessellation Gurus!

2011-04-01T13:53:00.001-07:00

Hey Geometry students, here is a site to help you along with tessellating.
http://www.tessellations.org

Enjoy Spring Break!

Some Areas of Quadrilaterals

2011-03-30T12:30:00.000-07:00

A video for Algebra on Quadratic Functions and their ZEROES!

2011-03-30T12:23:00.000-07:00

An Algebra Video on Graphing Quadratics

2011-03-28T14:26:00.001-07:00

Fake Facebook Project Due on Thursday!

2011-03-21T21:59:00.000-07:00

Hey, Everyone!
These are the requirements of your fake facebook page project!
1) Do the research before Wednesday.
2) Be sure to find the following information: picture of the person, vital statistics, formula the mathematician is known for, other mathematicians during their time, etc.
3) Design the page as you want with accurate information.
4) Email the fake face book page to your instructor.

A rubric will be posted tomorrow on the grading criteria.

Online Quiz for Geometry!!

2011-03-17T04:15:00.000-07:00

Hello, Students!
By now you have completed the first half of your quiz. Here is the second half! We are going 'green'! Using Geometer Sketchpad, you have the rest of the period to complete this assignment.

You will email me (taylora@clintondaleschools.net) once with two attachments the following information:
1) Using geometer sketchpad, proof how the measure of angle 1 is the sum of opposing arc measures divided by two (what we learned in class yesterday).
2) Create a picture that involves the following information:
a) a moderate sized circle
b) this circle is labeled with two chords
c) this circle also has two tangent lines meeting an outside point
d) one secant line
e) all intersection points labeled

All of this is due at the end of the hour and worth nearly a third of your grade.

From Tangents to Secants!!

2011-03-15T04:56:00.001-07:00

Here is an involved video on Secants! You may need to watch it over and over to get a handle on it!

Blog Homework for both Mathematics Classes!

2011-03-08T13:21:00.000-08:00

For Geometry, watch the following videos:

Now watch this video:

Geometry Students, answer two of the following three questions:
1. Define tangent, circumscribed polygon, inscribed polygon.
2. In circle P, there is an inscribed angle of (3x + 1) degrees. It's corresponding arc (intercepted arc) is 55 degrees. How much is x?
3. Two tangent segments (with a common endpoint) on a circle form a triangle. If the radius is 10 units and the length of the tangent segment is 14 units, what is the length of the distance from the center of the circle to the common endpoint?

For Algebra, go to www.khanacademy.org. Search for prime factorization. Watch the video.
Answer the following questions:
1. Using exponential notation, was the prime factorization of 100, 144, and 196.
2. What is the GCF of 86 and 90, 12 and 15, 144 and 169, 289 and 324.

Please respond in the Google group by Thursday this week.

A Question for the Google Group in C-Mail

2011-02-28T21:23:00.000-08:00

Geometry Classes

Hey, everyone. Here is a question that is to be answered and posted within 48 hours. You may use the computer in the library, the computer in the room, your phone to connect to the internet, etc. Come up with a solution to two of the following questions and respond in the Google group:
1) Find c, if C=55, a=8, and b=12, use the law of cosines;
2) Define the following terms: circle, center, chord, diameter, radius.
3) In circle T, RG=10 and the measure of angle QRG is 120 degrees. What is the major arc degree of QG?
4) What is the difference between arc length and arc degree?
5) Suppose a chord of a circle is 12 centimeters long and is 10 centimeters from the center of the circle. Find the length of the radius.

Circle Properties

2011-02-24T08:54:00.000-08:00

Here is a video on Chords and the Circle. Watch it. You may need it for tomorrow.

Law of Exponents This Week in Algebra.

2011-02-17T08:07:00.000-08:00

Here is a video on Multiplying Monomials and Dividing them!

Look it over.

Here is the Law of Sines.

2011-02-16T08:41:00.000-08:00

Please watch the video.

Using The GOOGLE in Geometry!

2011-02-14T13:13:00.000-08:00

Please watch the video.

Now, do a write up of two problems off of the 8-4 Practice Sheet. Post the solutions in the google group. Type out the answers, no short answers. Explain it like I did in class.

Here is the Discussion Questions for Algebra and Geometry!

2011-02-11T11:17:00.000-08:00

For GEOMETRY....if given a right triangle and you are told the following information:
The SIN of the angle is (9/41). Can you find the missing side? Please work out the problem on scrap paper and type out the solution/explanation in the discussion group in www.ATaylorsCorner.googlegroup.com

Here is a video related to the topic at hand:

Here is a video on the 2 Special Triangles!

2011-02-09T15:01:00.000-08:00

45-90-45 Triangle!

30-60-90 Triangle!

There will be a blog question on this stuff coming soon. You will have to respond via the Google group!

Let The Discussion Begin!

2011-02-01T13:19:00.001-08:00

Hi, Everyone in Geometry Class.
Can anyone solve the following problem? Give a clear explanation of the problem.

Triangle ABC is similar to triangle DEF. BY is the altitude of triangle ABC, and is 10 units long. EZ is the altitude of triangle DEF, and is 25 units long. Find DE, if DE is 5k + 10, and AB is 6.

All who participate in the discussion, could earn 5 participation points (the equivalent of homework) one time for the day. This discussion ends on Friday.

Graphing Inequalitites: Algebra

2011-02-01T12:51:00.000-08:00

Google Group to Come This Week

2011-01-31T13:40:00.000-08:00

Hi.
My class will have a google group soon, ATaylorsCorner google group. On it, there will be discussions of class problems and various solutions to many equations.

In the meantime, here is a video on Pythagorean Theorem:

Parallel Lines and Proportional Parts

2011-01-25T09:31:00.001-08:00

Here is a useful video for Section 7.4! It is similar to the homework and tomorrow's assignment:

More Triangle Stuff

2011-01-05T07:08:00.000-08:00

Here is a video on ratios and proportions as it relates to the similar triangles:

This Week in Mathematics!!

2011-01-04T12:26:00.001-08:00

It's a new year in Clintondale, not school year. Mid-Terms are fast approaching!
In Geometry, we are discussing this that are similar. Here is a video to discuss similar polygons:

Here is a video on solving a system of linear equations:

Here is a plant problem. It is similar to how we solved the Marker and T-Shirt problem in class.

Here are Mid Term Reviews!

2010-12-22T04:54:00.000-08:00

Here is the Algebra Review.

Here is the Geometry Review.

Unfortunately, this review doesn't cover Chapter 2. We will go more in depth on it when we come back.

Please be safe!

Also for Geometry...your Mid-Term Project is as follows:

Video on Trapezoids!

2010-12-17T05:05:00.000-08:00

Here is a video on Trapezoids: Irregular & Isosceles.

Here is a video on scatter plots for next week in algebra.

See you next week!

Difference between Parallel and Perpendicular Lines

2010-12-09T08:05:00.000-08:00

For my Algebra students,

Here is the review sheet for Geometry!

2010-12-08T09:57:00.000-08:00

I just found out...focus on 5.4, 5.5, 6.1, 6.2, and 6.3 only. If you do more the better for you.

The answers are as follows:
1. square, 2. rectangle, 3. parallelogram, 4. parallelogram, 5. square, 6. square,
7. rhombus, 8. parallelogram, 9. rhombus, 10. rectangle, 11.9, 12. 8, 13. 1, 14. 28, 15. 7, 16. 21, 17. 72, 18. 94, and 19. 78

Study well, be safe!

Geometry Videoes on Special Quadrilaterals!

2010-12-07T10:28:00.001-08:00

Parallelograms:

Rectangle & Square Video:

Rhombus Video:

Be Safe!

Videos for this week in Algebra and Geometry!

2010-11-30T04:42:00.000-08:00

Here's a vid on slope.

Here's a vid on finding slope with two points.

Here's a vid on Triangle Inequalities.

Here's a vid on Parallelograms.

More to come!

This Short Week Was Review and More in Geometry Too!

2010-11-24T10:59:00.000-08:00

Here is a video on what we covered in class this week. There will be a warmup of this on Monday. Watch the video a couple of times.

Happy Thanksgiving!

This Short Week Was Review and More!

2010-11-24T10:49:00.000-08:00

For Algebra we talked about finding patterns. We will do more of that next week. For instance, the sand pile problem. The equation is y = 2500-5x, where x stands for buckets of sand being moved to the barge and y stands for the remaining sand on the river bank.

Next week we will open up with the bowling problem. The cost of renting shoes and bowling games. There is a linear relationship between the two. Look at this video on patterns and the connections between graphs, tables, and numeric symbols in linear relationships.

Happy Thanksgiving!!

Videos for Algebra on Functions!

2010-11-19T07:35:00.000-08:00

A video on function notation.

Understanding of graphs.

Remember to study for Wednesday!!

The Videos are here!!

2010-11-18T06:23:00.000-08:00

Here is the vid on HL,LL,LA, and HA for GEOMETRY.

Here is the video on Coordinate Planes and Graphing Linear Equations for ALGEBRA.

Ask questions in class.

This week we are reviewing for next week's test on Wednesday!

2010-11-17T21:33:00.000-08:00

In Geometry, we are discussing Right Triangle Congruences and Special Segments in Triangles.
Remember that HL is similar to SSS. Also, LL is similar to SAS. LA is similar to AAS. And lastly, HA is similar to ASA. The special segments are perpendicular bisector, angle bisector, median, and altitude.

In Algebra, we are discussing graphing coordinates and linear equations on a coordinate plane. The key words to remember are domain, range, relation and linear relation.

I will post the videos later.

The Final Push Before The Cardmarking!

2010-10-29T08:13:00.000-07:00

Geometry students here is an extra credit assignment due by next Thursday.

Check my google group: ATaylorsCorner. You need a gmail account to get access.

Algebra students here is a video of what we will be covering next week, compound inequalities and absolute value inequalities.

Algebra Update

2010-10-19T09:36:00.000-07:00

Hi, everyone. Here is a video on solving inequalities:

Tomorrow, I will put up solving inequalities by multiplication and division.

Geometry Class

2010-10-19T09:35:00.000-07:00

Here's a video on Section 3-4 and 3-5 stuff:

Algebra Review

2010-10-04T09:15:00.000-07:00

This week, we are covering addition and multiplication linear equations. Here are some vids on the matter:

Single Step Equation

Two Step Equation

Multi-Step Equation

Study for the MEAP!

Geometry Update.

2010-10-04T09:12:00.000-07:00

Here are some vids for geometry this week:

Corresponding Angles

Alternate Interior and Exterior Angles:

Study well!

Here are some vids to help you out!!

2010-09-22T04:55:00.000-07:00

Algebra Videos on Order of Operations on Integers:

Geometry Videos on Midpoints, Angle Bisector, and 90/180 angles:

Any questions...email me at taylora@clintondaleschools.net

BE SAFE!!

Several Days Left! Prom is over.

2010-05-11T15:11:00.000-07:00

Hi. Life in the district is a flurry.

In the Elementary School, we are getting ready to celebrate Blue Ribbon Day with Blue Moon ice cream.

In the Middle School, we are continuing are lessons on Astronomy.

In the High School, STUCO is preparing to schedule next years events.

The end of year is always interesting and scary at the same time.

Be Safe, people!

Six Weeks Remain

2010-04-26T14:00:00.001-07:00

The end of 2009-2010 school year is coming to a slow close.

In the middle school, we are continuing our discussion of the universe focusing on Stellar Parallax.

Also, we are beginning our discussion of Monsoon Asia.

In the elementary school, we are beginning order of operations and fractions with 2 thru 5 graders.

In the high school, we have wrapped up All Star Sports Week. The Sophomores have the School Spirit this year. Next up are elections and the car wash.

See ya soon, Be Safe!

Less than four months to go!

2010-03-03T06:38:00.000-08:00

Hi, Everyone.

Life in the district is interesting as usual. The high school is preparing for ACT testing and All Star Sports Week via Student Congress. STUCO just came back front Regional Conference in Clinton Twp. at the MISD. We learned about reinventing ourselves as leaders of our high school community.

The middle school is preparing for cardboard races. In science, we are learning the last of weather and climate. We will be moving on to Astronomy in two weeks. In geography, we are learning about South Africa and apartheid.

Parker Elementary has just completed "Reading Camp", that was interesting. The kids, I have, are moving on to multiplication tables and harder words for spelling.

Be Safe!

A Journal To Help Through The Year!

2010-01-07T13:41:00.000-08:00

It's a brand new year in Michigan.

I ahve decide to begin a journal to help with the new role I am in with the district.

I am working in the Middle School and Parker Elementary, working with good kids.

If anyone needs help with mathematics, drop a line.

Be safe this snowy season!

Homecoming Week Is One Day Away From Ending!

2009-10-23T14:25:00.000-07:00

Today, a sub was in class.

There will be a test in each hour next week Thrusday, October 29, 2009. There will be a notebook check on Friday, October 30, 2009.

In Advanced Algebra, the test will cover Relations/Functions, Linear Equations, Slopes of Linear Equations, and Writing Linear Equations.

In Algebra, the test will cover Solving Equations by Addition (and subtraction), Solving Equations by Multiplication (and division), Multi-Step Equations, and Solving Equations on Both Sides.

In Geometry, the test will cover Inductive Reasoning and Conjecturing (Drawing Conclusions), If/Then Statements, Deductive Reasoning, Using Proof in Algebra, and Verifying Segment and Angle Relationships.

I will have review sheets on Tuesday.

Be Safe...Mr. Taylor

It's Tuesday of Spirit Week!

2009-10-20T12:48:00.000-07:00

Hi, Everyone.
Today was Twin Day. Tomorrow is Wacky Wednesday.
In Advanced Algebra we wrapped up our discussion of solving word problems and linear equations in the slope intercept form, y = mx + b. We shall continue our discussion of slopes of linear functions.

m = (y2 - y1)/(x2 - x1)

Linear functions have positive, negative or zero slopes. Vertical lines have an undefined slope. Slopes of two lines can be parallel, non parallel or perpendicular. Perpendicular slopes are slopes of two different lines in which the slopes are opposite reciprocals of one another. For example, 5 and -1/5.

In Algebra, we began talking about Multi Step Linear Equations. For example:

5x - 6 = 14

5x -6 + 6 = 14 + 6

5x + 0 = 20

(1/5) 5x = 20 (1/5)

x = 4

In Geometry, we are proving segment and angle relationships. I will put up a proof tomorrow.

Not much homework due to Homecoming Week.

Be Safe, Mr. Taylor.

Advanced Algebra

2009-10-13T13:19:00.001-07:00

Hi, Gang!
Here is the homework:

Lesson 10: On a bike

George rode his bike from the basketball court at a speed of 5 feet per second.

1. Fill in the table below giving George's distance from the court after each second. Continue for 12 seconds.

Time (in seconds) : 0 1 2 ......
Distance (in feet) : ................

2. How far is George from the court after 4 seconds? After 4.5 seconds?
3. When is George 15 feet from the court? When is he 17.5 feet from the court?
4. Write an equation for George's distance from the court as a function of time. Use y for his distance in feet and x for the number of seconds elapsed.
5. What do you think the graph will look like? Draw a sketch.
6. Graph the table values yopu found in Question 1. (Scale your axes.) This should match the graph of the equation. Was your sketch right?
7. In terms of George's bike ride, what does the slope represent?
8. In terms of George's bike ride, what would an increase in the y-intercept mean? How about a gentler slope?

Remember to at least try these problems, show some work!

Mr. Taylor-Be Safe!

Some Sample Problems!

2009-10-11T20:38:00.000-07:00

I couldn't find any appropiate videos yet!

But here are some sample problems for each class. This is what we will concentrating on this week and of course word problems.

Advanced Algebra Sample Problem:

Using the standard form of linear equations, Ax + By = C, it is easy to find x and y intercepts. It is important to remember that A and B must be integers and not zeroes.

For instance - x intercept: 5x - 6y = 30. Let y be zero. So 5x - 6(0) = 30.
That is, 5x = 30. So, x = 6. The x intercept is (6,0).

For instance - y intercept: 5x - 6y = 30. Let x be zero. So 5(0) - 6y = 30.
That is, -6y = 30. So, y = -5. The y intercept is (0,-5).

To find slope, solve the equation for y, into y = mx + b (slope intercept form).
So, 5x - 6y = 30
5x - 5x - 6y = 30 - 5x
- 6y = 30 - 5x
y = -5 + (5/6)x
The slope of the line is (5/6).

What is the slope of 7x + 6y = 84?

Algebra Sample Problem:

Solving Equations involves finding the missing number to make the statement true.

For instance, x + 2 = 4. To solve this problem remember that the additive inverse of a number is the opposite of the number. The additive inverse of 5 is -5. When you add opposites, you get zero.

So, x + 2 = 4.
Then, x + 2 + (-2) = 4 + (-2)
Then, x + 0 = 2
Then, x = 2.

It’s all a balancing act.

Geometry Sample Problem:

Statement: The Governor of Michigan is Jennifer Granholm.

Conditional: If a person is governor of Michigan, then that person is Jennifer Granholm.

Converse: If there is a person called Jennifer Granholm, then that person is governor of Michigan.

Inverse: If a person is not governor of Michigan, then the person is not Jennifer Granholm.

Contrapositive: If there is not a person called Jennifer Granholm, then that person is not governor of Michigan.

Create the four conditional statements for:
1) Detroit is a city in Michigan. 2) Perpendicular lines make four right angles.

It's the weekend! Two weeks left 'til HOMECOMING!

2009-10-09T12:31:00.000-07:00

Hi, Everyone.

In Advanced Algebra, we are learning about linear equations in Standard Form. This form works best in solving for x & y intercepts, manually. On Monday, we will use the graphing calculator. For 1st hour, the homework is pg.77 #6-10,18-27. For 6th hour, the homework is pg.76-77 #8-10,22-27. We will continue with that and finding the slope of a line next week. There will be a regular quiz on Monday.

In Algebra, due to a 9th grade meeting, the retake test is Monday. On Tuesday, we will begin solving linear equations.

In Geometry, we are continuing our discussion of conditional statements. The homework over the weekend will be pg. 81 #19-30. Next week, we will discuss the four conditional statements: conditional, inverse, converse, and contrapositive. There will be a regular group quiz on Monday.

This weekend I will put up sample problems for each class. Maybe some vids, if I can find some.

Enjoy the weekend! Mr. Taylor

It's Post Mosaic Day!

2009-10-07T21:46:00.000-07:00

This week in Mathematics....

In Advanced Algebra, we are discussing Relations and Functions. We are exploring domain and range with the graphing calculator. Today we will look at the differences between relations and functions more.

In Algebra, we are discussing square roots and reviewing for the retake of last week's test. Here is the review:

Know who to do the following....
1) There will be several questions regarding the real numbers; can you give examples of them?
2) There will be several questiosn regarding the comparison of numbers; what number is greater/less than the other? Which ways can you compare two fractions?
3) There will be several questions regarding the addition of real numbers; subtraction is addition of the opposite.
4) There will be several questions regarding the multiplication of real numbers; division is multiplication of the reciprocal.
5) There will be several order of operation problems; PEMDAS.
6) There will be several real number property problems; can you give examples of the properties.
7) There will be several distributive property problems. Can you distribute and add like terms?

The retake is Friday.

In Geometry, we are talking about "Drawing Conclusions". What conjectures can be made based on given information. Given a conjecture, can you determine if it is true or false? If false... with a counterexample?

For instance...
1)Billy has attended school for seven hours and ate two large meals. Billy went to football practice for two hours and ate one large sub sandwich. Billy drove home on the freeway for 65 minutes, while drinking coffee. Ten hours later, Billy wakes up in the hospital. What could have happened to Billy?
2) Given:Segments AS and SD are congruent. Conjecture:S is the midpoint of AD.

See you soon, Mr. T.

By Popluar Demand!

2009-10-03T08:44:00.000-07:00

Here is the answer key.

Answer Key for Review of Advanced Algebra Chapter 1 Test

1. Rational and Irrational

2. Look in the text

3. Additive Inverses { -3, -.66, -(2/5), 9}
Multiplicative Inverses {(1/3), (100/66), (5/2), (-1/9)}
4. 85, 6

5. The principle is $3333.33.

6. The length is 175 feet. The width is 25 feet.

7. a) (-1/9) b) (354/7)

8. a) 4(h -17) b) (g^2 + h^3)/4 c) 100 = 4 + 6p d) 35 > y + .5

9. j = (-6/5)

10. g = (-44/29)

11. 1 > k

12. r > -5

13. q = {(-16/3), 4}

14. w = { no solution}

15. -4 < r < 3

16. -6 > t or 18 < t

By popular demand!

2009-10-03T08:32:00.000-07:00

Here is the review sheet. I apologize the computer program wouldn't copy it like I wanted.

Review for Advanced Algebra Chapter 1 Test

A. Real Numbers
1. List the two types of real numbers.
2. Give specific examples of whole numbers, natural numbers, and integers.
3. List the additive inverse and multiplicative inverse for each number:

B. Order of Operations
4. Evaluate the following: (4[5-3^2(6+4)])/(4-8)
((9+3)/(6^2-30))- (10(3-4)-6)
[ ] are absolute value.

C. Word Problem
5. Mr. Green has earned $500 after investing a certain amount into an investment company. The company gained this amount after 18 months at a rate of 10%. How much did Mr. Green invest?
6. The perimeter of the new CHS rectangular pool is 400 feet. If the pool’s length is 7 more than the width, what is the length and width of the pool?

D. Expressions
7. If a = 2, b = 5, and c = -3, then what is the following:
a) (ab + 4c)/ac^2
b) 12 + abc((20-a)/(bc + 1))
8. Translate into an algebraic expression:
a) four times the quantity of a number minus 17
b) the square of a number plus the cube of another number, all divided by four
c) 100 is four more than 6 times a number
d) 35 is greater than a number plus one half.

E. Solving Equations
9. 10 - 4j = 22 + 6j
10. .5 +8g = .75g - 5

F. Solving Inequalities
11. 12 > 3k + 9
12. 6r < 10r + 20

G. Solving Absolute Value Equations
13. [2+3q] + 9 = 23
14. 3 - [5w + 4] = 10

H. Solving Absolute Value Inequalities
15. [2 + 4r] < 14
16. 36 < [3f -18]

It's Friday Eve. Tomorrow and Monday is Test Day.

2009-10-01T14:17:00.000-07:00

In Advanced Algebra, we are in the final stretch of preparing for our CH Test Exam on Monday. Tomorrow we will play Jeopardy - the questions will come from the Chapter One Review Test. The following is due tomorrow pg. 56-57 #13-28, 33-60. The test will cover Real Numbers, Order of Operations, Evaluating Expressions, Solving Equations and Inequalities, and
Absolute Value Equations and Inequalities.
Tomorrow I will place a review sheet on this blog with the answer key. Work out the problems and check yourself. If you can pass it, you will be ready.

In Algebra, we have reviewed for the CH test on Friday. It will cover real numbers, comparing real numbers, order of operations, adding and mulitiplying real numbers, and the properties of real numbers.

In Geometry, we have reviewed for the CH 1 test. It is in two parts: part one is from 1-1 to 1-4 on Friday, part two is from 1-5 to 1-6/1-7 on Monday. It has been suggested to bring the Definition Sheet to the test. IT WILL BE USEFUL!

It's A Brand New Week-Week of Progress!

2009-09-28T14:37:00.000-07:00

Hi, everyone.
This week is review week. Advanced Algebra & Geometry test is pushed back to October 5, 2009. Algebra 1 test is October 2, 2009. Everyone should start studying, do not procrastinate!

The homework for Advanced Algebra this week is pg. 56-57 #13-28, 33-40, 45-60. It is due Friday. We continued are discussion of Solving Inequalities. Tomorrow we'll discuss solving absolute value inequalities.

In Algebra, we discussed the Distributive Property. We will continue that discussion tomorrow with combining like terms through this property.

In Geometry, we began a discussion of Exploring Angles, after retaking the quiz in a group setting. In the lab, we did the same thing.

There is more to come.

Be Safe! -Mr. Taylor

Here are some examples!

2009-09-24T20:51:00.000-07:00

Order of Operations

Go to: http://www.youtube.com/watch?v=pEz_Wn35098

Solving Equations and Absolute Value

Go to: http://www.youtube.com/watch?v=ZouQdHSyelg

Friday is tomorrow; Thank You, __________ !

2009-09-24T16:40:00.000-07:00

Hi, folks.
It's close to the weekend. Tomorrow is the Homework Quiz in all classes.

In Advanced Algebra, it will cover Solving Equations, Translation of Algebraic Expressions, and Solving Absolute Value Equations. I will post an example of each in an hour. We will wrap up our discussion of Solving Inequalities, but we will use the graphing calculator.

In Algebra, it will cover Order of Operations, Multiplying and Dividing Real Numbers. I will post an example of each in an hour. We will do a quick review of the last three weeks in preparation for the test on October 2, thru Jeopardy.

In Geometry, it will cover Measuring Segments, Distance Formula, and Midpoint of Segments. We will practice drawing angles with the protractor and compass.

In Geometry Lab, we will do an exercise in the lab practicing angle bisecting.

See you in an hour or two, Grey's Anatomy is coming on.
-A. Taylor

It's Tuesday. Here is the week's lesson.

2009-09-22T07:45:00.000-07:00

This week we are covering many topics.

In Advanced Algebra, we are reviewing Solving Equations and Absolute Value Equations. The homework thus far is-a Kuta Software Sheet on Solving Linear Equations and a Kuta Software Sheet on Solving Absolute Value Equations.

In Algebra, we are reviewing Multiplying and Dividing Real Numbers. The homework thus far is a worksheet on multiplying numbers.

In Geometry, we are discussing measuring segments and midpoints of segments. The homework thus far is a worksheet on midpoints.

There is an exam in all class on October 2, 2009-in addition to a notebook check.

See ya, Mr. Taylor.

Thursday has arrived; I behind :)

2009-09-16T16:18:00.000-07:00

So, this week is crazy. We are covering some simple things.

In Advanced Algebra, we are covering Order of Operations, Expressions and Formulas, Word Problems, and Solving Linear Equations. On Monday the homework covered Order of Operations on pg. 11 #30-41. On Tuesday the sub gave a work sheet on Order of Operations and Expressions. On Wednesday the homework covered word problems. Tomorrow we will review the week events and move into solving equations.

In Geometry, we are covering how to draw figures with planes, lines, and points; also we are discussing segement postulates, pythagorean theorem, and distance formula. On Monday we continued are discussion on drawing figures. On Tuesday the sub had an assignment to practice Monday's work: pg. 17 #43-56. On Wednesday we moved on to segment postulates: the ruler postulate-The points on any line can be paired with real numbers so that, given any two points P and Q on the line, P corresponds to zero, and Q corresponds to a positive number. Google it!

In Algebra, we are covering comparing rational numbers and adding/multiplying them. The worksheets for classwork and homework will be put online tomorrow.

The homework quiz is coming up soon (like Friday). Get ready for it.

Bye, Mr. Taylor.

Here is some stuff from last week!!

2009-09-13T19:45:00.000-07:00

Here is the worksheet from the Geometer Sketchpad Lesson. It can be done by hand!
Geo1.2

More later...

The Week Is Over! A lot has happened!

2009-09-11T12:19:00.001-07:00

Hello, Everyone.
The first week has been so busy!
On Wednesday, Advanced Algebra worked on 1-2: Properties of Real Numbers. We talked about rational numbers-a number that can be written as a fraction and irrational numbers-a decimal that doesn't repeat or end like e or pi. Also we mentioned, adding integers. The homework was a worksheet.
On Thursday, Advanced Algebra worked on a worksheet concerning real numbers. I will post it online tomorrow.
On Friday, Advanced Algebra took a pre assessment test on Chapters 1 thru 2; it was just to see what is going on.

On Wednesday, Algebra worked on 2-1: Integers and Number Line. We talked about rational numbers-a number that can be written as a fraction and irrational numbers-a decimal that doesn't repeat or end like e or pi. Also we mentioned, adding integers.
On Thursday, Algebra took a pre assessment test on Chapters 1 thru 2; it was just to see what is going on.
On Friday, Algebra discussed 2-1 and moved to 2-4: Rational Numbers. We discuss the comparison of fractions and decimals. I will post an example of this tomorrow.

On Wednesday, Geometry worked on 1-1: Coordinate Plane. I will post the information that we discussed tomorrow.
On Thursday, Geometry took a pre assessment test on Chapters 1 thru 2; it was just to see what is going on.
On Friday, Geometry worked on 1-2: Points, Lines, And Planes. I will post the information tomorrow.

On Wednesday and Friday, Geometry Lab worked on two logic puzzles. These puzzles are designed to engage the student's ability to problem solve.
On Thursday, Geometry Lab used Geometer Sketchpad to explore the program construct various figures. I will post the sheet online tomorrow.

Next week will be a hectic one with Student Congress-Lock In and other such things!
See ya soon!

Mr. Taylor

First Day Of School !

2009-09-07T21:31:00.000-07:00

Hello, everyone. This is my blog for the new school year! Here is where information for the day will be posted after 3:30 pm. Classwork, homework assignments, etc. Videos will be posted as well as websites designed to help you learn the material at home.

Here is the syllabus for all my classes:
CHS ADVA SY2

Enjoy the new year! Remember if you want an A, do the math!

The Halfway Mark of Summer

2009-07-19T09:29:00.001-07:00

The halfway mark has reared its head. In a little over a month school will be back in session. Homecoming.... The cycle repeats again!

See you soon.

The Seniors have left the building!

2009-05-29T12:49:00.000-07:00

This week quite a few things have happened:

In Advanced Algebra, we discussed the last of Chapter 10: Exponents and Logs. Yesterdays homework was pg. 634 #6-10.
As for the Special Project, it is due on Tuesday, June 2, 2009. The next problem is #6: Based on your data (from #1 thru #4) and modeling #5, what would be the half life of "your C-14"? What did you learn from this project? Be detailed.

In Geometry, we discussed Chapter 11. Yesterday, we discussed Euler's Formula: F+V=S whereas S-2=3. There are five platonic solids: tertahedron (fire), octagedron (earth), hexahedron(air), dodecahedron (ether and/or heaven), and icosahedron (water). Today we generated several formulas for the surface area of various solids:
a square pyramid, a cube, a triangluar prism, square prism, cylinder, and hexahedron.
The homework from Thrusday was to do pg, 570 #1-20.

Here is an adjustment to the schedule from Tuesday. Next week we'll wrap up 11-2 and begin reviewing each chapter until the final.

Be safe!

It's Week 38, post-Memorial Day!

2009-05-26T14:17:00.000-07:00

Hi, everyone.

In Advanced Algebra, we discussed 10-6: Solving Exponential Equations. We also worked on our special project for fifteen minutes. We will continue to work on it tomorrow after I introduce 10-7: Exponential Growth and Decay. The homework is pg. 629 #13-30.

In Geometry, we reviewed Chapter 10 by playing Math Jeopardy. Questions from the game will be similar to the test questions. Also, today the tessellation project is due. Every other day it is late is five points less.

Be Safe! It is near the end. Please don't lose focus!

It's WK 38. Here is your calendar of the Final School Days!

2009-05-24T20:33:00.000-07:00

Sunday

Publish at Scribd or explore others: Study Guides, Notes, School Work

Next week is around the corner!

2009-05-21T12:28:00.000-07:00

Tomorrow, I will put up a calendar for the final few weeks of school.

In Advanced Algebra, we discussed 10-5. The homework is pg. 624 #29-32,34.

In Geometry, we discussed 10-5. The homework is pg. 545 #Exploration: Scientific Calculator-complete the chart.

Be Safe!

As promised. Here are some samples for the quiz!

2009-05-17T23:07:00.000-07:00

Advanced Algebra, here you go!

A as Can

Publish at Scribd or explore others: Study Guides, Notes, School Work

Geometry here you go!

GScan

Publish at Scribd or explore others: Study Guides, Notes, School Work

Be Safe!

The end is coming. Several Weeks remain!

2009-05-15T13:36:00.000-07:00

Hi, everyone.

In Advanced Algebra, we reviewed 10-3: Logs and Their Properties. There was an extra credit assignment that will be placed on-line tomorrow. There will be a quiz on 10-1 thru 10-3. An example of generating an exponential function will also be placed
on-line tomorrow. You will receive the special project on Wednesday.

In Geometry, we discussed 10-4: Area of Rhombi, Triangles, and Trapezoids. An example of each will be placed on-line tomorrow. There will be a quiz on 10-1 thru 10-4. On Thursday you will have a chance to work on the special project.

Be Safe!

It's Friday Eve. Homework is due tomorrow!

2009-05-14T13:14:00.001-07:00

Hi, everyone.

Today in Advanced Algebra, we discussed 10-3 Logs and Their Properities. That is,
x = log (base b) of y - log (base b) of v is x = log (base b) of (y/v).
Another property is that, x = log (base b) of y + log (base b) of v is x = log (base b) of (y(v)). Another property is that x = log (base b) of b = 1. The other property is that x = log (base b) of b^2 is equivalent to x = 2 log (base b) of b.
The homework is the following pg. 615 #26-34.

Today in Geometry, we discussed 10-3 Area of Parallelograms. That is, the A = L(W) or A = B(H), for any parallelogram. We did an in class assignment on it.

Be Safe.

It's Wednesday; so little time, so much to do!

2009-05-13T12:18:00.000-07:00

Hi y'all.
In Advanced Algebra, we discussed a new section 10-2: Logs and Log Functions. This lesson follows from exponential functions. That is, y =(b)^x can be translated to
x = log (base b) of y. For example, 9 = 3^2 is also 2 = log (base 3) of 9. Also, we talked about 3^(2x) = 9^(4x-1). It is the same as 3^(2x) = 3^2(4x-1), because 9 = 3^2. This sentence translates into 3^(2x) = 3^(8x-2). Since that have the same base, work with the exponents. 2x = 8x-2. Solve for 'x'. x = (1/3). We mentioned that log (base b) of y - log (base b) of v = log (base b) of (y/v). Tomorrow we will talk about the addition of logs with the same bases. The homework is pg. 608-609 #18-20,31-39.

In Geometry, we discussed the Tessellation (final special project) Project in class. The instructions sheet is self-explanatory.

Tessellations Project

Publish at Scribd or explore others:

It is due on May 26, 2009. Tomorrow we will tackle Area of Parallelograms. The homework is to work on the template and design of your tessellation.

Be Safe!

Week 36! There are 20 teaching days left!

2009-05-11T12:37:00.001-07:00

Hi, everyone.
Today everyone started Chapter 10. In Advanced Algebra, we began are exploration of exponential functions, with the lesson titled Mmm...Eminem's M&Ms. Based on situation we will generate a exponential function. The homework is to create a list of values that shows the decline of stores during a recession.

In Geometry, we began are exploration of polygons. We discovered that the equation for interior angle measures of a n-sided polygon is given by the formula:
I = (180(n - 2))/n, for n is the number of sides in a polygon and I is the interior angle measure for the n-sided polygon. We also derived that I + E = 180, where E is the exterior angle measure of the n-sided polygon. These formulas work for a convex polygon. The homework is pg. 519 #22-44.

BE SAFE!

It's The Friday before Mother's Day!

2009-05-08T11:51:00.001-07:00

Today in class, every hour took their Chapter 9 Test.

Next week, we will start Chapter 10. In Advanced Algebra, we will start Chapter 10 Exponential and Logarithmic functions. In Geometry, we will start Chapter 10 Polygons.

Be Safe!

21 Teaching Days Remaining!

2009-05-07T14:16:00.000-07:00

Hi, everyone.
Tomorrow is test day for Chapter 9 in Advanced Algebra and Geometry. Next Monday we start Chapter 10.

Be Safe!

IT'S HUMP DAY, 22 TEACHING DAYS REMAINING!

2009-05-06T11:34:00.000-07:00

Today in Advanced Algebra, we discussed 9-6: Solving Rational Equations and Inequalities. Review for the test on Friday (Thursday if you are going to prom).

Today in Geometry, we discussed 9-7: Special Segments. There are two new formulas. I will put them up tomorrow. The homework is pg 495 #15, 16, 18-20. Review for the test on Friday (Thursday if you are going to prom).

Study!

From Monday to Tuesday...Week 35!

2009-05-05T05:37:00.000-07:00

On Monday,
Advanced Algebra discussed 9-4: Adding and Subtracting Rational Expressions. The homework was pg. 573 #18-31.
Geometry discussed 9-6: Secants and Tangents. The homework was to review for the test. 6th HR had a worksheet for homework.

On Tuesday,
Advanced Algebra reviewed 9-4 and started 9-5: Solving Rational Equations. The homework is pg. 582 #22-30.
Geometry reviewed 9-6. In class we did pg. 487 #14-32; and a worksheet for practice.
Tomorrow we move on to 9-7.

Be Safe!

Advanced Algebra Students

2009-05-02T22:10:00.000-07:00

Here is the last journal question:
GAP is selling unisex T-Shirts. The store needs to create a box that fits their needs. The dimensions of the box are as follows: the box is to have square ends, the length of the box is to be 24 inches longer than one side of the square end. The volume of the box is to be 512 cubic inches. Find the correct dimensions of the box.

It's 26 Teaching Days Remaining!

2009-05-01T12:10:00.000-07:00

It is a time for urgency. Too many people have developed a bad case of SENIORITIS, and they aren't seniors. Get on the ball and prepare yourselves for what is to come!

In Advanced Algebra, we took a quiz on 9-1 thru 9-3; we also started 9-4: Adding and Subtracting Polynomials. Review this material. The chapter test is on Thrusday for seniors and Friday for non seniors. The homework is to do whatever assignments you got a zero on or a bad grade on. Bring it back by Monday 3:40 pm.

In Geometry, we took did 9-5: pg. 480 #31-36 as classwork. The rest of the hour was devoted to figuring out what assignments needed to be done/redone by Monday 3:40 pm. The chapter test is on Thrusday for seniors and Friday for non seniors.

There will be at least one special project, at most two special project to be done before the close of the card marking.

BE SAFE!

It's Week 34. I am back. And there is a sense of urgency!

2009-04-30T13:50:00.000-07:00

Hi, Ya'll.
It's time to hit the ground running. There is a lot to talk about so here goes.

On Thursday, April 23, 2009- Advanced Algebra did pg. 897 Lesson 9-1 and 9-2. Geometry did pg. 780 Lesson 9-1 thru 9-4.

On Friday, April 24, 2009-Advanced Algebra did pg. 892-896 Lesson 7-1 thru Lesson 8-8 (omit 7-7). Geometry did pg. 774-779 Lesson 6-1 thru 8-6 every multiple of 3.

On Monday, April 27, 2009-all class took an assessment.

On Tuesday, April 28, 2009-Advanced Algebra did pg. 912 #1-30. Geometry did pg. 793 & 794 (omit the proofs). This assignment was worth at most 10 extra credit points towards the final exam.

On Wednesday, April 29, 2009-Advanced Algebra reviewed 9-2 and discussed 9-3: Multiplying and Dividing Rational Expressions. It is based off of Chapter 5. Geometry reviewed 9-4 and discussed 9-5: Tangents.

Today, Advanced Algebra studied for their quiz tomorrow on 9-1 thru 9-3. Geometry reviewed 9-5: Tangents. The homework that will be due next week is Definition sheets for Chapter 9.

The test for both classes will be on Thursday, May 7, 2009.

BE SAFE!

The Weekend has BEGUN!

2009-04-24T16:06:00.000-07:00

Hi, ya'll.
Today the students did work that helped review for the thrid quarter assessment that will be given on Monday. Advanced Algebra students should review for Chapters 7 and 8. Geometry students should review for Chapters 6,7 and 8.

Be Safe, I will see you on the after Tuesday!

It's Hump Day.

2009-04-22T14:08:00.000-07:00

So, in Advanced Algebra, we discussed 9-2: Direct, Indirect, and Joint Variations. A direct variation looks like the form of y = mx + b (i.e. y = kx). A indirect variation looks like the form of y = 1/x (i.e. y = k/x). A joint variation looks like the form of y = kxz. The difference between a joint variation and a direct variation is that a joint variation involves two or more independent variables. The direct variation involves only one independent variable.
The homework that is due next Wednesday is the following: pg. 559-560 12-28.

So, in Geometry, we discussed 9-4: Inscribed Angles and wrapped up our discussion of 9-3: Arcs and Chords. We mentioned the fact that inscribed angles have their endpoints on a circle. The angle formed is half of the measure of the opposite intercepted arc. The picture below shows this.
Iangles

Publish at Scribd or explore others: School Work

Remember to study for the assessment on Monday. If you have any questions contact me via the blog.

Be Safe!

It's The Day After Monday :)

2009-04-21T12:13:00.000-07:00

In Advanced Algebra, we began our discussion of Chapter 9: Rational Functions. 9-1 involves graphing rational functions. The important things to remember about graphing rational functions are: 1) knowing the vertical asymptotes, 2) knowing the horizontal asymptotes, 3) know the domain of the function, 4) knowing how to graph the function by hand and by graphing calculator, and 5) knowing how to label the graph.

Here is an example:
Graphing Rational Functions

Publish at Scribd or explore others: School Work engineering algebra

The homework is pg. 554 #13-24.

In Geometry, we continued our discussion of 9-3: Arcs and Chords. The important things to remember our theorems 9-2 and 9-3, which are respectively, [in a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.];[in a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.]
The homework is pg. 462 #16-24.

All homework is due tomorrow on Wednesday.Be Safe!

It's The Big Push! Week 32! A few weeks are left before school is out!

2009-04-20T11:50:00.000-07:00

Hi, everyone.
We are back in session. Today in Advanced Algebra, we reviewed for the Chapter 8 Test, which will be on Monday. I have recently found out the test will cover Chapters 7 and 8, a standardized test.

Today in Geometry, we began discussing 9-3: Arcs and Chords. We discussed Thm 9-2: a perpendicular diameter that intersects a chord splits the chord in half; Thm 9-3: chords are congruent iff they're equidistant from the center. The homework is pg. 462 #16-24, which will be collected on Wednesday.

Be Safe!

It's Spring Break!! Hooray!

2009-04-09T12:54:00.000-07:00

Hi, Y'all!

In Advanced Algebra, we took a test. It covered Chapter 8. No homework for the break. When you come back, we will breeze through Chapter 9. Our last Chapter for the year is Chapter 10. Tomorrow I will place the journal question from last week on the blog (I have a scanner at home!).

In Geometry, we reviewed the Chapter 8 Test. I will place a copy of the retake on the blog tomorrow (I have a scanner at home!). When we come back from break, we will start with 9-3. Our last Chapter for the year will be Chapter 11.

Notebook (binder checks) were due today. I was looking for the Chapter 8 Review notes and other such works.

Please be safe during spring break!

One More Day to Go...Before I Give You a Present!

2009-04-08T12:07:00.001-07:00

Hi, everyone.

Today in Advanced Algebra, we reviewed for the Chapter 8 Test. The test will cover
8-1 thru 8-8. Due tomorrow is the binder (notebook check) and homework.

In Geometry, we reviewed 9-1 and 9-2. For assistance go to Glencoe.com, go to the mathematics section for Geometry 2001 edition under chapter 11 Circles, and look at our textbook. There are practice lessons, videos and such that were used during class today related to Circles and Arcs and angels.

BE SAFE, PLEASE!

It is a Tuesday. Two days left....

2009-04-07T12:40:00.000-07:00

Hi Y'all.

In Advanced Algebra, we discussed Inverse Relations today. We also began studying for the test on Thursday, which is Chapter 8. The homework is review for the test which is pg. 540-541 #10 - 44 even.

In Geometry, we discussed Chapter 9: Arcs and Angels. We derived a formula for arc length. measure of the arc length of AB = (M) (Circumference of the circle containing AB), where M = (the central angle measure/ 360 degrees) and Circumference os C = 2 (pi) r = D (pi). The homework is pg.456 #37-49.

Be Safe!

It's Week 30! A Seasonal Break Is Coming!

2009-04-06T11:55:00.001-07:00

Hi, everyone.

It's the last week before Spring (Easter) Break. A test has passed and a test is coming.

In Advanced Algebra, we discussed 8-8: Inverses Functions and Relations. If the composition of two functions equals x, then the functions are inverses of one another. There are two methods to see if functions are inverses of one another:
1)graph them such that the graphs are reflections over f(x)= x and 2) algebraically compose the functions within one another to obtain x,
that is f(g(x))= x and g(f(x))= x . The homework is pg. 532 #19-24, 31-34.

In Geometry, we discussed a new chapter, 9 - Circles. Today we covered 9-1: Exploring Circles and 9-2: Angles and Arcs. The class drew circles covering the various terms involving circles, seeing the relationship between circumference, diameter, and radius, and saw the relationship between circles, their interior angles and the arcs. The classwork/homework was pg. 456 #19-36.

Later this week, Advanced Algebra will take a test in Chapter 8 (Thursday); Geometry will continue in Chapter 9.

BE SAFE!

Apologies...My computer went down again! It's the end of the week.

2009-04-03T12:48:00.000-07:00

Hi, Y'all.

It's Friday. Advanced Algebra will take a test next Thursday. Today we covered 8-7: Composition of Functions. The homework is pg. 524 #23-39. On Thursday, we wrapped up 8-6: Solve Polynomials Using Quadratic Techniques. On Wednesday, the homework was pg. 518 #27-35. On Tuesday we finalized 8-5: The Rational Zero Theorem.

In Geometry, we took a test today on Chapter 8. Yesterday, we reviewed for the test. On Wednesday, we wrapped up our discussion on the Laws of Cosines. Next week we start Chapter 9: Circles.

The next notebook check will be
Be Safe!

It's Week 29! The Start of the Final Card Marking!

2009-03-30T12:41:00.000-07:00

In Advanced Algebra, we discussed the Rational Zero Root Theorem. This theorem only finds rational roots, not irrational roots. The homework asks you to find the possible rational roots to a polynomial function. The homework is pg. 513 #16-21. We will spend another day on it. The Chapter 8 Test is next week. All with the homework of this week, Journal #2 is due on Friday as well.

In Geometry, we wrapped up our discussion on the Law of Sines. We might do another word problem on the Law of Sines. We will begin Law of Cosines. The Chapter 8 Test is next week. The homework for today is pg. 429 #25-32.

Be safe!

The End of the Card Marking!

2009-03-27T12:41:00.000-07:00

Well everyone, it is the last day for the 3rd quarter. Another quarter to go before the close of the school year.

In Advanced Algebra, we worked on 8-4: Roots and Zeroes. We did some application problems. Question 7 of the worksheet is a journal problem due next Friday. I will put it up on Saturday. Next week we will begin 8-5: Rational Root Theorem.

In Geometry, we review 8-4: Angles of Depression and Elevation. We began 8-5: Laws of Sines. The homework is on pg. 429 #16-24. Next week we will talk about Laws of Cosines and take the test on Thrusday. It will be a busy week.

Be Safe and Enjoy the Weekend!

It's Friday Eve, the day before books close!

2009-03-26T13:14:00.001-07:00

Hi, Everyone.

In Advanced Algebra, we continued our discussion of 'Roots and Zeroes'. We mentioned the purpose of Decartes' Rule of Signs. Based on the number of sign changes with p(x) as x is positive and p(x) as x is negative, can determine the number of real and imaginary roots.

Read this:
Descartes' Rule of Signs is a useful help for finding the zeroes of a polynomial, assuming that you don't have the graph to look at. This topic isn't so useful if you have access to a graphing calculator because, rather than having to do guess-n-check to find the zeroes (using the Rational Root Test, Descartes' Rule of Signs, synthetic division, and other tools), you can just look at the picture on the screen. But if you need to use it, the Rule is actually quite simple.
Use Descartes' Rule of Signs to determine the number of real zeroes of:f (x) = x5 – x4 + 3x3 + 9x2 – x + 5.
Descartes' Rule of Signs will not tell you where the polynomial's zeroes are (you'll need to use the Rational Roots Test and synthetic division, or draw a graph, to actually find the roots), but the Rule will tell you how many roots you can expect.
First, I look at the polynomial as it stands, not changing the sign on x, so this is the "positive" case:
f (x) = x5 – x4 + 3x3 + 9x2 – x + 5
Ignoring the actual values of the coefficients, I then look at the signs on those coefficients:
f (x) = +x5 – x4 + 3x3 + 9x2 – x + 5
I draw little lines underneath to highlight where the signs change from positive to negative or from negative to positive from one term to the next:
Then I count the number of changes:
There are four sign changes in the "positive" case. This number "four" is the maximum possible number of positive zeroes (x-intercepts) for the polynomial f (x) = x5 – x4 + 3x3 + 9x2 – x + 5. However, some of the roots may be generated by the Quadratic Formula, and these pairs of roots may be complex and thus not graphable as x-intercepts. Because of this possibility, I have to count down by two's to find the complete list of the possible number of zeroes. That is, while there may be as many as four real zeroes, there might also be only two, and there might also be zero (none at all).
Now I look at f (–x) (that is, having changed the sign on x, so this is the "negative" case):
f (–x) = (–x)5 – (–x)4 + 3(–x)3 + 9(–x)2 – (–x) + 5
= –x5 – x4 – 3x3 + 9x2 + x + 5
I look at the signs:
f (–x) = –x5 – x4 – 3x3 + 9x2 + x + 5
...and I count the number of sign changes:
There is only one sign change in this "negative" case, so there is exactly one negative root. (In this case, I don't try to count down by two's, because the first subtraction would give me a negative number.)
There are 4, 2, or 0 positive roots, and exactly 1 negative root.
Some texts have you evaluate f (x) at x = 1 (for the positive roots) and at x = –1 (for the negative roots), so you would get the expressions "1 – 1 + 3 + 9 – 1 + 5" and "–1 – 1 – 3 + 9 + 1 + 5", respectively. But you would not simplify, and the numerical values would not be the point; you would analyze only the signs, as shown above.
Using Descartes' Rule of Signs, determine the number of real solutions to4x7 + 3x6 + x5 + 2x4 – x3 + 9x2 + x + 1 = 0.
I look first at the polynomial f (x) (this is the "positive" case):
f (x) = +4x7 + 3x6 + x5 + 2x4 – x3 + 9x2 + x + 1
There are two sign changes, so there are two or, counting down in pairs, zero positive solutions. Now I look at the polynomial f (–x) (this is the "negative" case):
f (–x) = 4(–x)7 + 3(–x)6 + (–x)5 + 2(–x)4 – (–x)3 + 9(–x)2 + (–x) + 1
= –4x7 + 3x6 – x5 + 2x4 + x3 + 9x2 – x + 1
There are five sign changes, so there are five or, counting down in pairs, three or one negative solutions. Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved
There are two or zero positive solutions, and five, three, or one negative solutions.
In the above example, the maximum number of positive solutions (two) and the maximum number of negative solutions (five) added up to the leading degree (seven). It will always be true that the sum of the possible numbers of positive and negative solutions will be equal to the degree of the polynomial, or two less, or four less, or.... For instance, if I had come up with a maximum answer of "two" for the possible positive solutions in the above example but had come up with only, say, "four" for the possible negative solutions, then I would known that I had made a mistake somewhere, because 2 + 4 does not equal 7, or 5, or 3, or 1.
Use Descartes' Rule of Signs to find the number of real roots of f (x) = x5 + x4 + 4x3 + 3x2 + x + 1.
I look first at f (x):
f (x) = +x5 + x4 + 4x3 + 3x2 + x + 1
There are no sign changes, so there are no positive roots. Now I look at f (–x):
f (–x) = (–x)5 + (–x)4 + 4(–x)3 + 3(–x)2 + (–x) + 1
= –x5 + x4 – 4x3 + 3x2 – x + 1
There are five sign changes, so there are as many as five negative roots.
There are no positive roots, and there are five, three, or one negative roots.
Use Descartes' Rule of Signs to determine the possible number of solutions to the equation 2x4 – x3 + 4x2 – 5x + 3 = 0.
I look first at f (x):
f (x) = +2x4 – x3 + 4x2 – 5x + 3
There are four sign changes, so there are 4, 2, or 0 positive roots. Now I look at f (–x):
f (–x) = 2(–x)4 – (–x)3 + 4(–x)2 – 5(–x) + 3
= +2x4 + x3 + 4x2 + 5x + 3
There are no sign changes, so there are no negative roots.
There are four, two, or zero positive roots, and zero negative roots.
Descartes' Rule of Signs can be useful for helping you figure out (if you don't have a graphing calculator that can show you) where to look for the zeroes of a polynomial. For instance, if the Rational Roots Test gives you a long list of potential zeroes, and you've found one negative zero, and the Rule of Signs says that there is at most one negative root, then you know that you should start looking at positive roots, because there are no more negative roots, rational or otherwise.
Similarly, if you've found, say, two positive solutions, and the Rule of Signs says that you should have, say, five or three or one positive solutions, then you know that, since you've found two, there is at least one more (to take you up to three), and maybe three more (to take you up to five), so you should keep looking for a positive solution.

The class has a worksheet to try out for tomorrow's class discussion.

In Geometry, we continued our discussion of Angle of Depression and Angle of Elevation. The class was given a worksheet to practice at home. Remember to draw pictures to figure things out.

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X-Men Last Stand...It involves some mathematics?

2009-03-25T12:33:00.000-07:00

Hi, everyone.

In Advanced Algebra, we discussed 8-4: Roots and Zeroes. We mentioned the fact that every polynomial function has at least one root: real or imaginary. The roots can take the form: a + bi. For instance, the roots to x^2 + 1 = f(x) are +i and -i. They appear in the form 0 + i and 0 - i. This means that (x - (0 - i))(x -(0 + i)) = x^2 + 1 = f(x). We also generated polynomial functions from roots. That is, if x = -2, 3 and 4i. Then the polynomial function (in factored from) looks like (x + 2)(x - 3)(x - (0-4i))(x - (0+4i)), a quartic function. The homework is on pg. 507 #32-40.

In Geometry, we discussed 8-4: Angles of Elevation and Depression. Using trigonometric ratios, we determined the values of angles or side measures in word problems.

The example used in class is the following....watch the clip
http://www.youtube.com/watch?v=eiL31ZBxoy8

Looking at the clip on youtube...Look at time 1:00. As Magneto is meters and seconds away from lowering the bridge on the guards, he thinks-"I wonder what the angle of depression is to the guard as I am about to finish them!" The image of the bridge and Alcatraz forms a special image. The distance from Magneto's eye line to the guard's eye line is 1,000 ft (the hypotenuse). Magneto is 100 ft above the guard (the altitude). Based on this information, you can use 'sine of x' to figure the problem out. So, sin (x) = (100/1,000). Once you take the inverse of each side, sin^-1(100/1,000) = x -which is the angle of depression. Make sure your calculator is in degrees and not radians. The homework is pg. 422 #22-25.

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On This Day, Tommy Hilfiger and Peyton Manning were born.

2009-03-24T13:21:00.000-07:00

Hi, Everyone.

Today was a busy and hectic day.

In Advanced Algebra, we took a group quiz on 8-1 thru 8-3. It involved the Remainder Theorem, and various functions with their tables of values. Tomorrow we will tackle 8-4: Roots of a Function.

In Geometry, we took a group quiz on 8-1 thru 8-3. It involved the geometric mean and the Pythagorean Theorem with some trigonometric functions mixed in. Tomorrow we will use trigonometric functions in word problems, 8-4.

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