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!