Break is Here! (And a take home test...)

First and foremost, have an amazing break! Spend some quality time with family and friends, rest up, relax, play, and have fun! Use this time to recharge your batteries as we get closer to our midterm exam!

Speaking of the midterm exam, over break you must complete your midterm review take home test! This was provided in class, or you can find it under the "PDF Textbook and Classroom Assignments" link on the right! A few points...

• Get this done! No excuses!
• You will lose 10 points for each day this is late. The test will not be accepted after Thursday, January 5th. 
• Use your notes, PDF textbook, Khan Academy, and other online resources to ace this thing! Don't just try to do this all from memory!
• The more effort you put into this the more prepared you'll be for the midterm exam!
• And, of course, the better your test grade will be!
• This will be our last "big" test of the quarter! We will have one more "smaller" test after break on the new stuff we learn when we're back!
• Feel free to email/Remind me with questions! However, I will not answer any questions on Monday, January 2nd! (Don't procrastinate!)
• Get an A!

Again, thank you all so much for handling this week responsibly and just generally being awesome! I'll miss you guys over break! See you soon!

Finish test tomorrow?

Hey everyone! I'm hoping I'll be back tomorrow.

Tomorrow in class you will have the opportunity to finish anything on the test that you did not finish today (including if you need to do the calculator questions)!

We will start class by discussing one of the questions (the application about the software company) and one of the bonuses (the triangle one) together!

After we finish up with our test we'll start to think about some review, and look at our take home test for break (we'll start it in class Thursday!)

In case you're curious, after break we will have two "mini units"--we will cover a little bit about logarithms and we'll cover some multiple choice test taking strategies!

See you all tomorrow!

Math Test Tomorrow!

First and foremost, I apologize for being out today; I (obviously) did not anticipate being sick and never intended to be out. However, I have the utmost confidence that you can all prepare yourselves to succeed on tomorrow's test. The key to success on tomorrow's test is preparation! Study, study, study!

Here's an outline of what's on the math test tomorrow:

• Multiple Choice Section:
• Solve a linear system using elimination or substitution
• Determine the order of a matrix
• Solve a system using back-substitution
• Solve a system using your graphing calculator and matrices
• Use your calculator to find the inverse of a matrix
• Add/subtract matrices
• Use your calculator to find the determinant of a matrix
• Solve a system using the method of your choice (SAT Question)
• Write a system of equations to model a scenario (SAT Question)
• Open Ended
• Solve a system with back substitution
• Evaluate 5[A] - 9[B] by hand (show all work)
• Solve a system using your graphing calculator
• Multiply matrices (show all work)
• Solve a system by hand (method of your choice)
• Find the inverse of a 2x2 matrix by hand (given the formula)
• Find the determinant of a 2x2 matrix by hand
• Perform a sequence of row operations on a matrix
• Application: Given a system...
• Write the augmented matrix
• Write the coefficient and solution matrix
• Solve the system using your calculator
• Application: write and solve a system from a context (we'll discuss this together Wednesday, this will be counted as a bonus on tomorrow's test)

Weekend HW (and potential extra credit!)

Th;is weekend please complete the following (from our "Matrices and Systems of Equations Problem Set"): 

Section 8.1 (page 582): 59, 65, 71 (use rref and the augmented matrix to solve)
Section 8.3 (page 608): 47, 61, 63 (use "A inverse B" with the coefficient and solution matrix to solve)

• USE YOUR GRAPHING CALCULATOR AND MATRICES TO SOLVE (ignore the Gaussian directions). 
• This is practice for our test Tuesday!

You will  have a question like 82 or 85 in section 8.1 on  next week's test so it's a good idea to look at these! There will also be a question or two like 67/69/71 in section 8.3! If you do/try any of these with your homework and show me the work on Monday you can get an extra credit homework grade!

• (Extra Credit HW: section 8.1 #85, section 8.3 #67, 69, 71).

• If you do this extra credit you're not only getting some extra homework points, you're also doing some serious prep for our test! So do it!

Finally, if you did not turn in your graphing calculator lab, remember that it's DUE MONDAY! This should be an easy 100%!

• If you don't have a calculator but you do have an Android phone use the downloadable app on the right!
• If you don't have  calculator and you don't have an Android phone you'll have to come to finish Monday before school or during a free period/lunch on Monday! 

Check out this link for some videos to help with your graphing calculator (and matrices)!

Thursday HW!

Tonight please complete questions 1,2, 4, and 5 on the "Solving Multivariable Systems" worksheet provided in class (or below). For questions 2, 4, and 5 use your graphing calculator and matrices to solve the systems!

And if you're feeling ambitious here's your weekend homework (from the problem set I gave you yesterday)--more practice solving systems with matrices! USE YOUR GRAPHING CALCULATOR AND MATRICES TO SOLVE (ignore the Gaussian directions). 

Section 8.1 (page 582): 59, 65, 71 (use rref and the augmented matrix to solve)
Section 8.3 (page 608): 47, 61, 63 (use "A inverse B" with the coefficient and solution matrix to solve)

You will also have a question like 82 or 85 in section 8.1 on  next week's test so it's a good idea to look at these! There will also be a question or two like 67/69/71 in section 8.3! If you do/try any of these with your homework and show me the work on Monday you can get an extra credit homework grade!

(Extra Credit HW: section 8.1 #85, section 8.3 #67, 69, 71).

Wednesday HW!

Tonight, please complete the following in your "Matrices and Systems of Equations Problem Set" (provided today in class).

Section 8.1 (page 582): 7, 9, 11, 13, 15, 37, 39, 45

Tomorrow we'll do some more with matrices and systems! See you there!

If you did not finish the graphing calculator lab you must do so by Monday--turn it in whenever you're done!

• If you don't have your own graphing calculator you will have to download the app (if you have an Android phone) OR you'll have to come before school/after school/during study hall to use one of mine!
• This should be an easy 100%!

Tuesday HW!

Tonight's Homework (find each inverse by hand--show work!)

Section 8.3 (page 608): 11, 15, 17, 39


Tomorrow in class we'll continue to work with matrices and our graphing calculator! We'll also start to connect matrices and systems of equations, and learn a new way to solve our multi-variable systems! See you there!

Monday/Tuesday HW!

Tonight, please complete the "multiplying matrices" worksheet provided in class (or below)!

And if you're feeling ambitious, tomorrow night you'll have some homework dealing with the inverse stuff we learned today!

Tomorrow's Homework (find each inverse by hand):

Section 8.3 (page 608): 11, 15, 17, 39

Weekend HW!

This weekend please complete the following problems in your chapter 8 problem set:

Section 8.1 (page 582): 93 (Order of Matrices)

Section 8.2 (page 597): 17, 27, 29, 31, 45 (Multiply Matrices and some add/subtract/scalar stuff)
Section 8.4 (page 616): 3, 5, 9 (Determinants)

On Monday we'll continue to work with matrices--we'll do some more multiplying, then we'll start to find inverses of 2x2 matrices! Then, on Tuesday we'll start to learn how we can use some of the matrix features of our graphing calculator! After that, we'll start to connect matrices and systems of equations to wrap up the unit!

Have an awesome weekend! One more full week of school before winter break!

Thursday HW!

Tonight, practice multiplying matrices! Please complete the problems below in your matrices problem set (or your PDF textbook)! THIS ASSIGNMENT WILL BE CHECKED ON MONDAY! So, it's your call--do this tonight if you don't want any weekend homework, or do it this weekend!

Section 8.1 (page 582): 93 (Order of Matrices)

Section 8.2 (page 597): 17, 27, 29, 31, 45 (Multiply Matrices (mostly))
Section 8.4 (page 616): 3, 5, 9 (Determinants)

Tomorrow we'll continue to work with matrices--we'll do some practice in groups with multiplication, determinants, adding and subtracting, and determinants--we'll also bring back some row operations! See you there!

Wednesday HW/Quiz Tomorrow!

Tomorrow we will start class with a (15 minute) quiz about matrices:

• Adding matrices 
• Subtracting matrices 
• Multiplying a matrix by a scalar (constant)
• Determining the order of a matrix
• Identifying a square matrix or column matrix or row matrix
• You will also have to explain how to add, how to subtract, and how to multiply by a scalar in your own words!

Tonight's homework = studying for tomorrow's quiz! 

Tonight please complete the following in your matrices problem set (provided in class today) or in our PDF textbook:

Section 8.1 (page 582): 1, 3, and 5

Section 8.2 (page 597): 5, 7, 13, 15 (*For 15 you will have to distribute, then subtract)

If you're feeling ambitious, here's tomorrow night's homework as well--some practice with multiplying matrices! (There will not be any multiplication of matrices on tomorrow's quiz):

Section 8.1 (page 582): 93

Section 8.2 (page 597): 17, 27, 29, 31, 45

Always be sure to check your answers--that's why the answers to the odd problems are provided (and that's why I give you odds for homework)! There's no point in practicing if we're practicing incorrectly!

Tuesday HW (same as Monday)!

Tonight, please complete questions 1a, 2a, 2b, and 3, and 5 on the "Solving Multivariable Systems!" worksheet we started in class (or below). This will be checked on Wednesday!

• For 1a solve with back substitution!
• For 3 you need to create a system that has this solution! There is not one answer to this--there are many, many answers! I would recommend making up a system that is in row echelon form--so start with z = 0 (bottom equation). Then, write an equation that incorporates y and z so that y = 1 (middle equation). Finally, write a (top) equation that incorporates x, y, and z so that x = 2 (given that y = 1 and z = 0).
• It is also possible to answer this with a system that is not in row echelon form.
• If you write two answers to question c--one system with the solution (2,1,0) in row echelon form, and another system with this solution that has an x,y, and z term for each equation--you will receive homework extra credit! You will have to turn this in to me tomorrow!
• For 5, even though it looks complex (because it's an application problem), your challenge is to solve that given system using your row operations! Good luck!
• If you were out today we worked on questions 2a and 2b in class--do those and you're all caught up!

Here are the answers so you can check yours:

1.) (-2, -3.3333, -4)

2a.) (-2, -3, 3)

2b.) (-5, -5, 3)

3.) Answer will vary (we'll discuss tomorrow)

5.) (1, 2, 1)

See you all tomorrow for some new stuff!

Weekend HW!

This weekend please complete the following questions in your 7.3 problem set (or on pages 527-532 of your PDF textbook):

Use row operations (Gaussian elimination) to solve the following: 13, 15, 17, 19

• I KNOW THIS IS HARD! The only way to get better at this is to PRACTICE, so it's incredibly important you put a strong effort into your homework! (And check your answers!)
• YES, this will be on a quiz next week, and it will be on our unit test before winter break! So don't just try to avoid these!
• Don't give up! Remember, you're trying to get to row echelon form...so....
• First, try to use the row operations to get an equation with an leading x-coefficient of 1! Then write this as your first equation!
• After you can get an equation with an x-coefficient of 1, now try to get an equation with no x term and a y-coefficient of 1! We want this as our middle term!
• Finally, try to use your row operations to get an equation with no x and no y term, and only a z! This is our third (bottom) equation!
• Now, solve with back substitution!
• Remember to show the math, but also describe your row operations in words!
• If you want more help...
• Open the PDF textbook and look in section 7.3--you will find the examples we did in class with explanations!
• Or, google (or search in Khan) "Gaussian elimination" or "row operations" and find a video to watch to help!
• If you find a good one send it to me so I can share it with the class!
• If you want more practice...
• Try any of the odd problems from 13-37 and check your answers!

The most important thing is that you DON'T GIVE UP! Remember, there isn't a step-by-step process that will work every time! We have to come up with ideas and try them--if they fail, try something else!

Quiz Tomorrow (STUDY!)

Tomorrow we will start class with a quiz (15-20 minutes)! Tonight's homework is to study!

Here's what's on the quiz:

• Solve a linear system (2 equations with x and y) using substitution and/or elimination (showing all work)
• Solve a system graphically (using a graphing calculator)
• Determine if a point is a solution to a system
• Solve a system with 3 equations using back substitution
• Don't forget--you have to know how to identify if there are no solutions or infinite solutions as well!

I have assigned you some Khan Academy topics you can use to study for your quiz tonight! So, if you want to prepare, log into Khan, check your notifications, and use the assigned topics to review!

You can also use any of the odd problems (so you can check your answers) from our 7.1/7.2 problem set or our 7.3 problem set!

After our quiz we'll get back to work with this crazy row operation stuff! See you there!

When's Day HW!

Tonight please complete the following in your section 7.3 problem set (provided in class today), or on pages 527-532 in our PDF textbook:

1ab, 5, 7, 9

Tomorrow in class we'll continue to work with these multi-variable systems of equations and start to introduce more row operations and Gaussian elimination! Intense stuff! See you there!

Two's Day HW!

Tonight please complete the systems of equations review that we started in class! If you need a graphing calculator use the Desmos calculator on the right!

Monday HW!

Tonight, please complete the following in your Systems of Equations Review Problem set (or sections 7.1, 7.2 of your online textbook):

Section 7.1: 1ab
Section 7.2: 11, 15, 23, 37

Tomorrow we'll get back to work with systems of equations and we'll start to solve systems graphically! We'll also look at systems with some non-linear equations before we start to solve multi-variable systems! See you there!

IF YOU DID NOT TURN IN THE THANKSGIVING BREAK TAKE HOME TEST PLEASE BE SURE TO HAVE IT TOMORROW--THAT'S YOUR LAST CHANCE!

Thanksgiving Break = Take Home Test!

Have an awesome Thanksgiving break! Enjoy some time with friends and family, rest up, relax, and come back ready to learn lots of math! You do have some homework, and it's a test grade....

This weekend (Thanksgiving break) please complete the take home test questions provided in class or below!

• Part 1: Complete the SAT multiple choice question and the "solving equations" question (numbered 10,11)!
• For the SAT question you can either use the "SAT strategies" we learned with Mr. Mason OR you can add the rational expressions using a common denominator! 
• For the second question use your notes from yesterday!
• This is an 8 point test grade. 

• Part 2: Error Analysis
• On the second page you are given four "answers" that are incorrect--there is a mistake (somewhere) in each solution
• Your task:
• Identify the error/mistake that is made in the given (crossed out) solution. You must describe the error that was made in a complete sentence! (1 point)
• Then, show the correct solution!
• Pretty much do the problem yourself, correctly! Show this solution and circle your final answer! (2 points)
• You can do this in the space on the right or on separate paper--whatever works best for you!
• This is a 12 point test grade.

Feel free to email or send me a remind message if you have questions--just don't expect a response Sunday night! Get these done early!

Have an amazing break and I'll see you Monday for some new stuff!

Test Tomorrow!

Tonight, STUDY, STUDY, STUDY! Tomorrow we will have our first test of the quarter--put in the work and preparation tonight to start this quarter strong!

Here's what's on the test tomorrow (you also got a copy of this in class):

• Graphing rational functions with two vertical asymptotes (study your quiz!)
• Study your graphic organizers!
• Graphing rational functions with points of discontinuity (study your take home quiz!)
• Study your graphic organizers!
• Identifying limits and domain and range given the graph of a function
• Study our limits homework, limits classwork, and Friday's limits quiz
• Creating limit questions...
• Study last Monday's classwork we did in groups (it says "stamp" at the top)
• Adding,subtracting, multiplying and dividing rational expressions
• Study our adding/subtracting homework from last Wednesday night or the weekend homework!
• Solving equations with adding/subtracting rationals
• Using "SAT strategies" to plug in numbers with multiple choice!
• Study the notes/classwork and homework from Tuesday! (Mr. Mason's lesson)
• Also remember you can use Khan Academy to study!

Weekend HW!

This weekend, please complete the "Multiplying and Dividing Rationals" practice provided in class (or below)!

On Monday in class we'll learn a little bit of new stuff with some "solving equations" and we'll review for our test on Tuesday! Start studying now! Here's what's on the test Tuesday:

• Graphing rational functions with two vertical asymptotes (study your quiz!)
• Study your graphic organizers with answer keys too!
• Graphing rational functions with points of discontinuity (study your take home quiz!)
• Study your graphic organizers with answer keys too!
• Identifying limits and domain and range given the graph of a function
• Study our limits homework, limits classwork, and today's limits quiz (you'll get it back Monday)!
• Creating limit questions...
• Study Monday's classwork we did in groups (it says "stamp" at the top)
• Adding,subtracting, multiplying and dividing rational expressions
• Study our adding/subtracting homework from Wednesday night or the weekend homework!
• Solving equations with adding/subtracting rationals (we'll look at this Monday)
• Using "SAT strategies" to plug in numbers with multiple choice!
• Study the notes/classwork and homework from Tuesday! (Mr. Mason's lesson)
• Also remember you can use Khan Academy to study!

Finally, here are the answers to your homework so you can check!

Quiz Tomorrow and Extra Credit Homework!

Tomorrow we will start class with a quick quiz on limits! There is also a domain and range question and a couple f(#) questions! Use your notes (powerpoint slides) and last weekend's homework to study!

There is no assigned homework tonight...however, if you want to replace a homework zero (or just get some homework extra credit), you can log 20 minutes in Khan Academy as an extra credit homework assignment! If you didn't already, I would recommend working on the limits topic I assigned to you (check your notifications)!

I would strongly recommend doing this and using this time on Khan to review for Tuesday's test or tomorrow's quiz! The topics you might review in Khan to review are...

• Graphing Rational Function
• Points of Discontinuity (Rational Functions)
• Vertical and Horizontal Asymptotes (Rational Functions)
• Finding zeros (x intercepts) (Rational Functions)
• Finding limits graphically
• Adding, subtracting, multiplying, and dividing rational expressions!

Tomorrow we'll do some more work with multiplication and division of rationals after our limits quiz! See you there!

Wednesday HW

Tonight, please complete the front side (questions 1-5) of the "Arithmetic Operations with Rational Functions" worksheet provided in class (or below)!

Your challenge is to add or subtract the rational expressions (using a common denominator), and then simplify your answer!

And here's an answer key for your homework so you can check!

2'S Day HW!

Tonight, please complete the 4 SAT problems provided in class (or below)! Use the SAT strategies we discussed today!

• You can use the SAT strategies or find common denominators to solve these...I'd recommend the SAT strategies, they will be much more efficient, and it's less likely you make a mistake
• For the two questions on the left you can simply substitute each given (MC) value into the equation to see which value makes the equation true!
• For the two questions on the right, choose a number to substitute for x, then see which multiple choice expression gives the same value as the given expression when we substitute!

Tomorrow we'll get back to work with some more adding/subtracting rational functions! 4 more days of learning until our test next Tuesday--see you there!

Monday HW!

Tonight you need to spend at least 15 minutes working on Khan Academy! However, if you already spent 15 minutes on Khan over the weekend we'll count that as tonight's homework! So in other words, you have to log 15 minutes into Khan between Friday and tonight. I have "assigned" two topics to you to practice limits; you can check your notifications when you log into Khan to see these topics.

I would recommend working on the assigned (limits) content, but you can review any content you like--just get those 15 minutes in!

Tomorrow in class we'll start some new stuff with Mr. Mason! We'll look at some SAT problems where we have to add and/or subtract rational functions! See you there!

3 Day Wknd = Limits HW!

First and foremost, enjoy your 3 day weekend! Rest up, relax, and have some fun! Enjoy some time with your family and friends, and come back ready for a week of hard work! We'll have 6 more days of learning after this weekend, and then a test (then it's Thanksgiving)!

For this weekend, please complete the limits homework provided in class (or below)--I'm definitely checking!

Get this done sooner than later so you don't have to worry about it--it won't take long! Have a great weekend everyone!

Take Home Quiz Tonight!

Tonight's homework = take home quiz! Be sure to get it done and in tomorrow--start out the second quarter on the right foot (not with a 0 on a quiz!). You are expected to do this even if you were out today! If you were out or lost yours you can show all work and graph the function on separate paper! If this is not turned in tomorrow you will lose 4 points for each day this is late (until Monday). 

• Use your notes about points of discontinuity and graphing to help!
• Use your homework from Monday night and the answer keys provided in class as examples/samples
• Look in section 2.6 of our online textbook for more examples!
• Use Khan Academy--look up rational functions!

Want some bonus points/extra credit on your take home quiz? Either on the back or next to the graph provide the domain and range of the function you graphed!

Tomorrow in class we'll get back to work with limits! See you there!

Monday HW!

Tonight (or tomorrow) please complete the two graphic organizers provided in class using the functions below:

If you lost your graphic organizer (or you were out), you can do these on separate paper: complete each of the following and label your work, then use this information to graph the function:

• Find the x-intercept(s)
• Find the y-intercept
• Find the vertical asymptote(s)
• Find the horizontal asymptote
• Find the coordinates of the point of discontinuity
• Record the coordinates of some "additional points" (no work needed here, you can use your calculator)
• Graph the function
• Identify the domain and range

Have a great day off! And if you didn't get your KHAN work done from the weekend, get that done too! I re-opened that topic!

See you all on Wednesday for some new stuff!

Weekend HW = KHAN!

This weekend you should work on the topic that I have assigned to you in Khan Academy!

• Log into your account and you will see that a topic/mission has been assigned!
• You must correctly answer 5 questions in a row to finish--this will take different amounts of time for all of us! 
• Your homework grade will be based on whether you successfully completed these 5 questions in a row! If you worked to try to do so but didn't get to 5 in a row, you will get half credit!

On Monday we will do some more work with "points of discontinuity," and then we'll start to learn about limits! See you there!

Quick Quiz Tomorrow!

Tonight...STUDY! Tomorrow we will start class with a quick (10-15 minute) quiz! You will be given a rational function and will be asked to find all asymptotes, intercepts, some additional points (with a graphing calculator), and then graph! (This is pretty much the same as your graphic organizers!)

• Look over the book problems from Monday/Tuesday night
• Then look over your graphic organizers that we completed in class yesterday--grade yourself on these using the answer keys provided!

After our quiz we will start to learn a little more about rational functions and introduce points of discontinuity.

And don't forget: STAMPS ARE DUE TOMORROW! Have them counted/ready BEFORE class! If you do not turn in your stamps tomorrow, or you count them in class, you will receive a 0 for your stamp grade!

Wednesday HW and Classswork!

Tonight, please complete the two graphic organizers for the functions below (provided in the center of each organizer):

If you were out today, here's what we did--get this work done so you're all caught up!

• Today we worked in groups to complete two more of these webs!
• Find vertical asymptotes
• Find horizontal asymptote
• Find the x intercepts
• Find the y intercept
• Find the coordinates of additional points
• Identify the domain and range
• Graph the function!
• (Same as the homework!)
• Here are the functions we graphed in class:

Tomorrow in class we'll do some more practice; then on Friday we'll start class with a quiz--graph one rational function! Then we'll start to learn about "points of discontinuity!"

TUESDAY HW!

Please complete the following in your section 2.6 problem set (or page 193 in our PDF textbook);


Page 193: 31, 37, 39, 41

For each number listed above, complete the following:

• Find the vertical asymptote(s)
• Find the horizontal asymptote
• Find the x-intercept(s)
• Find the y-intercept
• Then, use the information above to...
• Find the coordinates of some additional points
• GRAPH each function!
• YOU DO NOT HAVE TO GRAPH #39! (It has 3 vertical asymptotes, and we won't see these types of graphs on our test, so just find the intercepts and asymptotes)

Also, remember that STAMPS ARE DUE BY FRIDAY! See the blog post below (Friday's post, look for blue) for directions with your stamps!

Monday HW!

Please complete the following in your section 2.6 problem set (or page 193 in our PDF textbook); I will check both Monday and Tuesday's homework on Wednesday since tonight is Halloween!

Page 193: 31, 37, 39, 41

Monday's Homework: for each number listed above, complete the following:

• Find the vertical asymptote(s)
• Find the horizontal asymptote
• Find the x-intercept(s)
• Find the y-intercept

Tuesday's Homework: use the information found above (Monday's homework), along with some "additional points," to graph each of the rational functions above (31, 37, 39, 41). 

Tomorrow in class we'll continue to work with asymptotes and intercepts and use these to start graphing rational functions! See you there!

And don't forget--STAMPS are DUE WEDNESDAY! See the blog post below (Friday's post) for more details on what to do with your stamps!

Weekend HW: Khan and Stamps!

This weekend, get some KHAN time in! You need 20 minutes by Monday! You can also do up to 60 minutes in Khan Academy for extra credit (since this is our last Khan grade of the quarter)!

• I would recommend using Khan to study/review the following:
• FACTORING or
• Rational Functions or
• Vertical and Horizontal Asymptotes

Also, stamps are due next Wednesday! It might be a good idea to start gathering/organizing/counting your stamps now! Here's what you have to do with your stamps:

• Find all your stamps!
• Put all your stamps together...
• Some people rip/cut out the actual stamp and then put them all in an envelope or tape them all to a piece of paper
• Or, other people just turn in the entire paper with the stamp on it (you'll get them all back, so you'll get the examples back for your notes) and paperclip them all or put them all in an envelope or ziploc bag
• Any way you organize/collect your stamps is fine with me!
• Count the number of stamps and record the total (with your name) on the front
• Double check!
• I will use the random name generator to randomly check the counts for 5-10 people in each class; if your total does not match the number of stamps I count, you will receive a 0...
• So count twice! Even if you're off by one or you actually have more stamps than you told me, you get a 0! 
• You are literally counting the number of orange "terrific" stamps! 
• If a paper does not have a stamp on it, it does not count!
• If you include papers that aren't actually stamps you will earn a 0!
• I will collect these on Wednesday; all of the stamps next week will count for the second quarter, so you have all of your first quarter stamps!
• Turn in all of your stamps! Don't try to stash any for the future--the stamp changes each quarter, so the orange terrific stamps have no value after this quarter!

PreCalc

Tonight....KHAN ACADEMY!

There is no textbook problems or anything else tonight, so it's a good chance to get your 20 minutes on Khan Academy!

I would recommend doing some Khan work with rational functions, as this will be the focus for the next two weeks!  

Wednesday = Khan?!

Tonight there is no homework--hopefully you're feeling confident about your test today! I'll get those graded in the next couple days (you'll get them Monday at the latest).

Tomorrow in class we'll start our new unit--rational functions! Mr. Mason will be here to teach us our introductory lesson to this topic!

Remember, you need to complete 20 minutes on Khan Academy by Monday! Since there is no other homework tonight it's a good time to get some Khan time in! Don't forget!

• If you want to get a head start on the "new stuff" for tomorrow, do some research about rational functions, or vertical and horizontal asymptotes!

See you all manana!

Test Tomorrow!

Tonight.....study!!!!!

This is our last test of the third quarter--so end strong! Get an A! The test starts with 4 multiple choice questions and the rest are open ended.

Here's an outline of what's on the test (section # listed in parentheses):

• Factor a polynomial completely given one of its factors/solutions (2.3)
• Use a graphing calculator to find real zeros of a polynomial (2.3 and 2.5)
• Find all zeros of a function by factoring (2.3, 2.5)
• Is ___ a factor of a polynomial? OR, Is x = # a zero/solution of a polynomial? (2.3)
• Use synthetic substitution to evaluate a function (2.3)
• Add, subtract, multiply, and divide complex numbers (2.4)
• Simplify powers of i (2.4)
• Write the equation of a polynomial in standard form given its zeros (2.3, 2.5)
• Find all zeros, real and complex/imaginary of a function (2.5)
• Identify how many total zeros a function has (2.5)

Use your 2.3 quiz, 2.4 take home quiz, today's stamp, and your 2.5 classwork from today as your primary studying tools! You can also do the "quiz" questions below for extra practice! (answers are in red so you can check!)

See you tomorrow!

Monday HW!

Tonight, please complete the following in your 2.5 problem set (or online textbook):

Page 179-183: 37, 65, 67, 113

• For 65 and 67 first find the real zero on the graphing calculator (use the Desmos link on the right if you don't have one!), then use synthetic--you should end up with a quadratic that you will have to solve using the quadratic formula!

Tomorrow in class we'll answer any homework questions and do some more practice in class before our test on Wednesday! See you there!

Weekend HW!

This weekend, you have two homework responsibilities:

1.) Be sure to spend at least 20 minutes on Khan Academy by Monday!

2.) In the problem set (image) below, complete each of the following: 57, 59, 63, 69

• For 57 simply use the quadratic formula to find the zeros of the polynomial
• For 59, you can either "solve for x" without factoring, or can factor this as a difference of two perfect squares!
• For 63 and 69, look at today's example from class...
• First, find real zeros using a graphing calculator (there is a Desmos online calculator linked on the right if you don't have one!)
• Pay attention to whether the graph "crosses" or "bounces"--if it bounces at a zero, use that zero twice!
• Perform (repeated) synthetic division
• For 63, you should do synthetic one time and arrive at a quadratic--then, use the quadratic formula to find the zeros from this quadratic, as it cannot be factored
• For 69, you will do synthetic twice and then you can find the remaining zeros without any more factoring

Thursday!!!

Tonight there is no formal homework to be checked tomorrow....however, you do have a couple things to consider...

1.) Remember, you need to log at least 20 minutes on Khan Academy by Monday! Today is a good chance to get some of that done as you don't have any other homework! Use Khan to start preparing for next Wednesday's test--look up some stuff on...

• Complex Numbers
• Factoring
• Finding real and imaginary zeros of polynomials!

2.) Here is an extra credit quiz opportunity! If you like, complete the 18 multiple choice questions provided in class or below! This will ONLY be accepted tomorrow, so it's a one time option! Complete each of the questions and turn this in--I'll count whichever grade is better, the take home quiz you turned in today or this multiple choice grade! If you did not turn in your take home quiz today it is essential that you do these MC to avoid a 0!

• YOU MUST SHOW WORK FOR EVERY QUESTION EXCEPT #17 to receive credit! No work, no credit!

Tuesday!

Tuesday homework:  it's probably a good idea to get some time logged into Khan! Remember you need 20 minutes by Monday--you could do some SAT review tonight!

Wednesday HW: please be sure to complete your complex numbers take home quiz for Thursday! Be sure to show at least some work for every problem to receive full credit!

If you lost yours the quiz is below:

On Thursday (in class) we will start section 2.5! See you there! 

Monday HW!

We have a crazy schedule this week--we don't have class on Wednesday and we have a 1/2 day on Thursday! We will finish section 2.4 (complex numbers) in class tomorrow, and then we will have a quick quiz on Thursday! Be ready!

Tonight, please complete the following in your 2.4 problem set, or page 167 in our PDF textbook:

17, 19, 27, 29, 33, 47, 49, 51, 59

This is practice for our quiz on Thursday! If you can do these you should be pretty set on the quiz!

And here's an outline for the week, in case you're curious:

Monday/Tuesday: 2.4 notes/discussion/examples

Wednesday: no class

Thursday: 2.4 quiz (add, subtract, multiply, divide complex numbers and simplify powers of i), then start 2.5 notes

Friday: 2.5 notes/examples (we will have another test next week!)

Weekend HW: KHAN!

This weekend your only homework is to get your 20 minutes logged in Khan Academy! Annnnnd, this weekend you can spend EXTRA TIME for EXTRA CREDIT! Every additional 20 minutes you spend can fill in a past homework zero! You can do up to 100 total minutes (that would make up 4 past homework zeros)!

Use Khan Academy to support what we're doing in class! Here are some topics I would recommend reviewing to help with our unit moving forward:

• Imaginary Numbers/Complex Numbers (adding, subtracting, multiplying, dividing, and simplifying powers of i)
• Simplifying square roots
• FACTORING a trinomial (or factoring quadratics)
• Any SAT prep (SAT day is next Wednesday!)
• Long and synthetic division (this will be back in our next section, 2.5)
• Finding zeros of polynomials

Take advantage of this opportunity--put in lots of work! Have an awesome weekend and I'll see you Monday!

**Remember that if you use the Khan Academy app you will have to show me the log of your minutes---to avoid this, I'd recommend just using the site (khanacademy.org) rather than the app!

Thursday HW = Study!

Tonight, STUDY, STUDY, STUDY! You will have 20 minutes to complete your quiz, so STUDY! You have to know what you're doing!

And remember, you need to log 20 minutes on Khan Academy by Monday--so why not use it to study for your test tonight?! Then you can earn some time and study all at once!

Here's an outline of what's exactly on tomorrow's test--it is modeled after today's classwork, so use that (and the key I gave you) to study! If you can do the classwork without your notes you can get a 100% on your quiz!

• Find the (real) zeros of a function using the graphing calculator
• Use synthetic substitution to evaluate a function for a given x value
• Determine if a given x value is a solution to a polynomial
• Determine if a given term is a factor of a polynomial
• Use the given solution of a polynomial to completely factor a polynomial and find all zeros 
• Use the given factors of a polynomial to completely factor and find all zeros

Check out section 2.3 in your PDF textbook for more examples!

After the quiz it's on to imaginary numbers--see you there!

Enjoy your Thursday!

Wednesday HW!

Tonight, please complete the following on the front page of your 2.3 problem set (last homework from 2.3!):

Page 159-161: 57, 59, 65, 67, 89, 91

• For 57 and 59 use repeated synthetic division to "get down to" a quadratic
• Then, factor this quadratic...
• Now, write the original polynomial in its completely factored form
• Finally, use this completely factored form to find all the zeros of the polynomial
• For 65 and 67...
• First, use a graphing calculator to find one of the exact zeros (find one that's a whole number!)
• Next, use synthetic division to rewrite the polynomial as a product of a linear and quadratic term
• Now, use the quadratic formula (or factor, if possible) to find the remaining zeros from the quadratic factor!
• For 89, 91...
• This is some factoring review! Do some research about "factoring quadratics" for help!

Tomorrow in class we will do some classwork and maybe start section 2.4; then, on Friday, we will start class with a quick (20 minute) quiz on section 2.3! This homework is direct practice for that quiz, so put in a strong effort! 

Tuesday HW!

Tonight, please complete the following on the front page of your 2.3 problem set (or page 159-161):

Page 159-161: 45, 49, 51, 75, 87

• For 45, use synthetic substitution! (This is really 4 different problems, parts a,b,c, and d)
• For 49 and 51...
• First, use synthetic division to show the given x value is a factor/solution of the polynomial given (show the remainder is 0!)
• Then, after you divide, you can write the original polynomial in factored form (look at today's notes)
• Now, use this factored form to "factor completely" and find the zeros/roots/solutions/x-intercepts for the polynomial!

Tomorrow we'll do a little more practice with section 2.3--finding zeros and factoring polynomials--and then it's on to 2.4 for Thursday! See you there!

If you want a head start, here's tomorrow's homework:

Page 159-161: 57, 59, 65, 67, 89, 91

• For 57 and 59 use repeated synthetic division to "get down to" a quadratic
• Then, factor this quadratic...
• Now, write the original polynomial in its completely factored form
• Finally, use this completely factored form to find all the zeros of the polynomial
• For 65 and 67...
• First, use a graphing calculator to find one of the exact zeros (find one that's a whole number!)
• Next, use synthetic division to rewrite the polynomial as a product of a linear and quadratic term
• Now, use the quadratic formula (or factor, if possible) to find the remaining zeros from the quadratic factor!
• For 89, 91...
• This is some factoring review! Do some research about "factoring quadratics" for help!

TAKE HOME TEST!

This weekend be sure to COMPLETE YOUR TAKE HOME TEST! (due Tuesday!)

Be sure to SHOW ALL WORK for any questions marked with **!

As we discussed in class, tests make up a significant portion of your grade; today's test in class and this take home test will collectively have a major impact on your average!

Be sure to put your best effort into your take home test and have it done on time! You will lose 10 points for each day this is late, and no tests will be accepted after Thursday! Use your notes for help, use your resources on the right--look up some videos through Youtube or Yay Math or Khan! Also use the PDF of our textbook to look at examples of problems in sections 2.1, 2.2, and 2.3! Put in an A level effort so you get a strong test grade!

And finally, the take home test is due even if you were out! You can find the take home test under the "PDF Textbook and Classroom Assignments" link! If you have trouble with the link for some reason, send me an email and I'll respond with a copy (carofano.fm@easthartford.org). 

On Tuesday we'll get back to working with polynomials and finding zeros; we'll start to learn how to use division to then find all zeros of a polynomial! Until then, rest up, relax, and have an awesome 4 day weekend!

TEST TOMORROW!

Tomorrow we have our test on sections 2.1, 2.2, and the long/synthetic division from 2.3! STUDY, STUDY, STUDY!

Tomorrow's test will have a MAJOR impact on your grade (hopefully in a good way)--so be ready! Prepare yourself!

Here's an outline of what's on your test: (the section of the book is listed in parentheses)

• Use your notes to study!
• Look over the stamp problems from yesterday and today!
• Use your PDF textbook and other links (like Khan) to study!
• Also, look over your 2.1 and 2.2 quiz to study!
• Convert a quadratic to standard form (2.1)
• Given a quadratic equation, find the vertex, x-intercepts, y-intercept, and then sketch the graph (2.1)
• Divide polynomials using synthetic division (2.3)
• Given a function, identify the degree, leading coefficient, constant term, describe end behavior with appropriate notation (2.2)
• Divide polynomials using long division (2.3)
• Find the zeros for a given polynomial by factoring (2.2)
• Determine if two quadratics have the same axis of symmetry (2.1)
• Write the standard form of a polynomial given its zeros (2.2)
• Factor (2.1, 2.2, and 2.3)
• Factor by grouping, factor with a difference of two squares, factor a "trinomial:--three terms
• Find the "a" value for a given quadratic (2.1; look over our 2.1 SAT questions)
• Given a polynomial, determine the end behavior, find the x and y intercepts, find some additional points, and then graph the polynomial (2.2)

Tuesday HW!

Tonight, please complete questions 1, 2, and 5 from the worksheet we started today in class (or below)!

And here are the answers to your homework so you can make sure you're getting these all right!

If you were out, today we took some quick notes to review for the test about quadratics and zeros of polynomials, then we started to work on the problems below (the ones we're finishing for homework) in class! Do these so you're mostly caught up!

Tomorrow we'll continue to do a little review and learn some more about synthetic division!

And don't forget, we have a TEST THURSDAY!  

Monday HW!

Tonight, please complete the following in your 2.3 problem set--some synthetic division practice (there are currently some technical issues with our PDF file, I'm working on it...)

Page 159 (front page): 19, 21, 25, 27

• Remember to list your terms in order of degree--highest exponent to lowest!
• Also be sure to fill in any "missing terms" with 0's!

Good luck! Tomorrow we'll do some more work in 2.3 with division and talk a bit about our upcoming test! See you there!

Weekend HW

You have two things to get done this weekend:

1.) Be sure to have spent 20 minutes on Khan Academy by Monday!

• If you use the Khan Academy APP I do not get a report of your minutes; you will have to log into your Khan account in the app and show me your total minutes for the past week--you can do so before school, after school, or at the start of class!

2.) Please complete the following in your 2.3 problem set (or, page 159 in the textbook PDF):

• Page 159: 5, 7, 13, 15 (These are all practice with long division of polynomials)

On Monday we will continue to work with division of polynomials, as we start to learn synthetic division. We'll work more with this on Tuesday, and then....we will have a mid-unit 2 test next Wednesday! The test will cover 2.1 (quadratics), 2.2 (polynomials), and how to do long and synthetic division (from 2.3). 

 Have an awesome weekend! Rest up, relax, and come back ready for four days of hard work! See you Monday!

Thursday HW = Study and Extra Credit!

Study for your QUIZ TOMORROW ON SECTION 2.2!

• The quiz will have the following questions...
• Given a function describe the end behavior (in appropriate math notation)
• Write the equation of a polynomial given its zeros
• Find the zeros of a polynomial and then state whether the graph crosses or bounces at those points
• Graph a polynomial
• Look at the examples in section 2.2 of our online (PDF) textbook (linked on the right) for more help!
• OR, use Khan Academy to get some minutes in! 

Also, here's a chance for some extra credit! Do this problem tonight for some extra credit homework!

And don't forget--you need 20 minutes logged in Khan Academy! Might as well just use Khan to do some studying tonight to get some studying and your homework done!

Finally, here is a major opportunity to boost your grade:

• You can retake the Unit 1 Test if you did not perform well on it (or even if you did)!
• You must make up the test after school or during study hall, but you must do so before the end of next week (Thursday, 10/6)
• Use your first unit 1 test to study! If you do not use this to study there is no benefit to re-taking the test!
• In addition, your second score will replace the first score, even if it is lower--it shouldn't be if you actually take the time to study and prepare for the re-take! No "winging it!"
• Take advantage of this opportunity! This will not be provided for tests on a regular basis!
• (We will also have a test on sections 2.1 to 2.3 in the next week or two)

Wednesday HW!

Tonight, please complete the following in your 2.2 problem set ("textbook"):

Page 149: 51, 67, 71, 101 

• For 67 and 71 I expect to see all of the work--x intercepts, y intercept, and then use the end behavior and additional points to graph!
• This homework is practice for our 2.2 quiz on Friday! 
• The quiz will have the following questions...
• Given a function describe the end behavior (in appropriate math notation)
• Write the equation of a polynomial given its zeros (like 51, 67)
• Find the zeros of a polynomial and then state whether the graph crosses or bounces at those points (like our weekend homework problems)
• Graph a polynomial (like 67, 71)

Also, here is a major opportunity to boost your grade:

• You can retake the Unit 1 Test if you did not perform well on it (or even if you did)!
• You must make up the test after school or during study hall, but you must do so before the end of next week (Thursday, 10/6)
• Use your first unit 1 test to study! If you do not use this to study there is no benefit to re-taking the test!
• In addition, your second score will replace the first score, even if it is lower--it shouldn't be if you actually take the time to study and prepare for the re-take! No "winging it!"
• Take advantage of this opportunity! This will not be provided for tests on a regular basis!
• (We will also have a test on sections 2.1 to 2.3 in the next week or two)

Tomorrow in class we will answer any homework questions and then get more into section 2.3, division of polynomials and finding zeros!