Archive+Pre-AP+Calculus+White

=Unit 6: More Trigonometry=
 * Homework answers:** chapter1.pdf, chapter2.pdf, chapter3.pdf, chapter9.pdf, chapter4.pdf, chapter5.pdf, chapter6.pdf
 * Class Blog**
 * Calendar**

All homework is on the [|class blog].

Final exam answer key [|here].

= = =**Archive **= =Quarter 1 Projects= =Quarter 2 Projects= =Quarter 3 Projects= toc

=Thursday, November 19th, 2009= We began class by taking a look at our class blog, an 8th grade class blog, and another precalculus blog. We discussed how we will use the class blog and this Wikispaces site for the remainder of the year. We also revisited the blogging grading rubric ([|blogging rubric.pdf]). We then looked at the Mystery Function and its properties. We looked at the A20 homework and had a discussion of the *why* of zero powers, negative powers, and fractional powers. This led to a more detailed look at exponential functions and the number e. We ended class with some time to practice with the homework.

__HW__:
 * p. 226/7-11, 15, 19, 27, 33, 45-51 odd, [55, 59 formula on page 224]

=Tuesday, November 17th, 2009= Since we had no Juniors for most of class, we held off on our planned work- we only worked on Supercorrections for the time that Juniors were in class.

__HW__:
 * Finish Supercorrections to submit by Wednesday afternoon (if you need an extension, email Mr. O'Brien)
 * Finish Mystery Function and other homework if necessary

=Friday, November 13th, 2009= We began class by spending time Supercorrecting. We then worked on an exploration of a Mystery Function (if you are absent, be sure to do [|U3_Mystery_Function.pdf], as it will be included on the next quiz).

__HW__:
 * Finish Mystery Function if necessary
 * A20/11, 25, 31, 35, 55 (page A20 is at the back of the text)
 * Supercorrect- a good way to make a correction super is to use Grapher or Numbers to explore the problem from a different angle.

=Tuesday, November 10th, 2009= Today was the test day!

__HW__:
 * Spend one hour on Supercorrections. A good way to make a correction super is to use Grapher or Numbers to explore the problem from a different angle. Pick up your tests after class. If you parent/guardians are coming by this afternoon, I will give it to them. Otherwise, I will email you a copy so that you can work on it before class on Friday.

=Friday, November 6th, 2009= We warmed up with two inequalities. We formalized our steps for dealing with discontinuities in rational functions and for graphing end behavior asymptotes- here are Molly's notes. We spent the rest of the class discussing homework and reviewing.

__HW__:
 * p. 208/5, 19, 37, 51, 55, 71, 77, 105, 129, 141
 * Review for Unit 2 test- Purplemath has great alternative explanations to your text
 * Organize your homework- make sure each assignment is completely checked and corrected and that each has your name, date, and the assignment at the top. The grading rubric is available here: [|homework.pdf]. Stack your homework ordered from **oldest to newest** with the homework cover page on top. Staple your stack in the **lower right hand corner**. You will hand in your homework on the day of the test **before** you take your test.

=Wednesday, November 4th, 2009= We began class with a warm up rational function. We factored it, divided, sketched a graph, and solved an inequality. This allowed us to take a closer look at slant asymptotes and holes and how to examine them graphically, numerically, and algebraically. We also discussed the power of solving inequalities graphically. We corrected the quiz from last class and then went over the homework. We finished with another rational function inequality.

__HW__:
 * p. 204/11, 13, 15, 21, 37, 39, 43, 47, 49
 * Make sure homework is up to date for the coming Unit 2 test

=Monday, November 2nd, 2009= We began class with the quiz. We took a quick look after the quiz to see how the graphing calculators can work with complex numbers. We then warmed up with two strange functions- a rational function consisting of #15 divided by #11 from the previous night's homework and another consisting of #43 divided by #13. We looked at them in Grapher, and found their domains, the zeros, and their general shape (including vertical and horizontal/slant asymptotes). We looked at their tables of values to help determine the features of the graphs. We talked about how we could cleverly plot points – using the zeros, the y-intercept, and the signs of y-coordinates – to find these features without technology. We compared our analysis to the actual graph plotted with technology to learn some general features of rational functions. We held off on homework questions until next class.

__HW__:
 * p. 193/7, 11, 13, 15, 23, 37, 47, 57, 71 [Use your calculator and/or Grapher to explore- your goal should be to do each without technology on the quiz.]

=Thursday, October 29th, 2009= We began class with a warm up working on our speed at catching careless errors which led into going over the quiz. We then took a few minutes to look over the quarter projects. We then discussed the homework. This led us to a discussion of zeros of polynomials, conjugate pairs, the Rational Zero Test, and the Fundamental Theorem of Algebra.

__HW__:
 * p. 179/11, 13, 15, 37, 43, 47, 55, 63, 65
 * Revise homework for quiz next class covering homework from 2.1-2.4

=Tuesday, October 27th, 2009= We began class with the quiz and then discussed how the remainder theorem can be used with a function like f(x) = x⁴ – 3x³ + 3x² – 3x + 2 to find a value like f(3) painlessly with synthetic division. We also looked at how its corollary, the factor theorem, can be used to find the zeros of this function. This led us to a look at non-real zeros. We discussed i, the standard form of a complex number, operations with complex numbers, and the complex conjugate. You may find [|this three page explanation about complex numbers] to be a nice change from reading in the text. We ended with work time.

__HW__:
 * p. 167/17, 19, 21, 29, 33, 37-51 odd, 65, 71

=Friday, October 23rd, 2009= We began class with p. 149/42 and y = x^4 – x^3 –3x^2 + x + 2 using the GDC (and Wolfram Alpha) which led to a discussion of how to graph these polynomial functions without the aid of technology. We then went over questions from the homework. We took notes on polynomial and synthetic division and used them to find zeros algebraically. We also saw how The Remainder Theorem can be helpful in finding function values, zeros, and factors. If you'd like a nice explanation of long division or synthetic division, Purple Math does a good job:

@http://www.purplemath.com/modules/polydiv.htm @http://www.purplemath.com/modules/synthdiv.htm

__HW__:
 * p. 159/8, 13, 21, 23, 25, 35, 37, 49, 59
 * Go over homework problems from 2.1 and 2.2 in preparation for quiz next class (not required, but suggested!)

=Wednesday, October 21st, 2009= We took advantage of the Pop Tech opportunity- no class.

__HW__:
 * Finish the project

=Monday, October 19th, 2009= We began class by working on the Supercorrection follow-up test. We then looked more particularly at quadratic functions beginning by matching graphs and equations (p. 134/1-8). This led to a discussion of the standard form of polynomial functions in general (p. 149/1-8 all)- properties, the Leading Coefficient Test, zeros (including multiplicity), and sketching graphs.

__HW__:
 * p. 134/1-8, 17, 23, 41, 45, 79 [If you need a review of any of quadratic basics- standard form, completing the square, vertex, axis of symmetry, max/min, y-intercept, x-intercepts, quadratic formula-, just let me know via the class blog.]
 * p. 149/1-8 all, 11 (quick sketch without calculator), 19, 21, 29, 33, 39, 41, 51
 * Work on finishing up project
 * Extra credit: derive the quadratic formula from ax² + bx + c = 0 using completing the square...

=Thursday, October 15th, 2009= We spent the period working on the projects.

__HW__:
 * Spend a good hour each on your project- this is your last dedicated homework time for the project. If you have questions about your project, feel free to email Mr. O'B or stop by during a study hall.
 * Be sure to go over the twelve test questions ([|U1T1pap.pdf]) before Friday's follow-up test- you will need to show the working, not just the correct answer.

=Tuesday, October 13th, 2009= We spent the class working on the project. We began class by learning how to make graphs in Grapher on your laptops- this seems to be a better option than fooplot, although you are free to use either. We learned how to make equations using the Google Docs equation editor. This editor is based on Latex. This site has more palettes and this site has some ready made formulas- feel free to copy the Latex code from either site into the Google Docs equation editor; that is a great way to learn how Latex works. We also discussed how the final draft should flow- introduction, linking sentences, and conclusion. There should be no numbered question answers in the final draft- the project questions can form the basis of your linking sentences, though.

__HW__:
 * Be sure that you've handed in your Supercorrections before next class- your name should be on each sheet, they should not be stapled, and the Supercorrections and the original test should be dropped off in the wire basket.
 * Continue to work on the quarter project- each partner needs to make additions to the shared Google Doc. You will have all period next class, and the rough draft will be commented upon after that period (although it will not be graded). If you have questions about your project, feel free to email Mr. O'B or stop by during a study hall.

=**Wednesday, October 7th, 2009**= We began class by working more on Supercorrections. After 30 minutes, we transitioned to the quarter project. We began the shared Google Docs file and worked on the mathematics for the project.

__HW__:
 * Work on Supercorrections- they are best done slowly- aim to only do one or two a day.
 * Begin work on the quarter project- each partner needs to make one addition to the shared Google Doc.

=Monday, October 5th, 2009= We began class by discussing the philosophy of Supercorrections. We looked at this [|model Supercorrection] and this example of a [|completed set of Supercorrections] and Supercorrected one test question together. We then took a look at the online grade spreadsheet to see how the different components of the course fit together to give a grade- there shouldn't be any mysteries, nor should there be unnecessary worrying about grades. We spent the rest of the class working on Supercorrections and finished with a few words about the quarter project ([|Q1 Project.pdf]).

__HW__:
 * Work on Supercorrections- they are not due until the end of next week, but Supercorrections are best done slowly- aim to only do one or two a day. There will be a little more time next class.
 * Copy the [|online grade spreadsheet] to your Google Docs and update your grades.
 * Get ready for the quarter project ([|Q1 Project.pdf]) by doing the following:
 * 1) Choose a partner.
 * 2) Decide which project you and your partner would like to work on and email your top 3 choices to Mr. O'Brien. First come first served!
 * 3) Create a test document in [|Google Docs].
 * 4) Use this [|equation editor] to make a beautifully formatted equation like this [[image:http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=%5Cfrac%7B%5Csqrt%7Bx%2B7%7D%7D%7B3x%7D%3Dx%5E3%2B3x]]. Put your equation in your test document on Google Docs.
 * 5) Use this [|graph editor] to make a cool graph and put your graph in your test document on Google Docs.

=Thursday, October 1st, 2009= Today was test day. We all appreciated the Finely Crafted Unit 1 Test.

__HW__:
 * Read about Supercorrections
 * Log onto your SAT practice account and do Algebra and Functions Practice Quiz #3- Extra Credit for a score of 100%

=Tuesday, September 29th, 2009= We began class with a little competition finding the equations for the graphs of functions that are transformations of our parent functions. We then corrected the quiz and talked about the importance of balancing clever calculator usage with non-calculator work. We went over the homework and spoke about how to organize homework assignments for test day (homework grading rubric is available here: [|homework.pdf]). We looked at page 115-116 to review the topics to be covered on the unit test (Opportunity Day) next class and spoke briefly about Supercorrections.

__HW__:
 * Do a minimum of six problems from p. 117-122 (be sure to check and correct) to revise from the test- choose ones that you need practice with! These are some good questions (at least one will appear on the test): p. 117/61, 72, 89, 93, 101, 113, 129, 133, 137, 149, 151, 161.
 * Organize your homework- make sure each assignment is completely checked and corrected and that each has your name, date, and the assignment at the top. The grading rubric is available here: [|homework.pdf]. Stack your homework ordered from **oldest to newest** with the homework cover page on top. Staple your stack in the **lower right hand corner**. You will hand in your homework on the day of the test **before** you take your test.

=Friday, September 25th, 2009= We began class by discussing one question we didn't get to last class: p. 79/65. We then took the homework quiz and went over homework. We took notes on function inverses- how to find them informally and formally, how to work with them graphically, and when they exist.

__HW__:
 * p. 99/3, 9-12, 15, 19, 21, 23, 27, 55, 61, 63, 67, 89

=Wednesday, September 23rd, 2009= We began class with a little SAT practice. Please log into your SAT practice account, click on the Practice Quizzes tab, scroll down the page, and click on the **Number and Operations** Practice Quiz #1. Using a piece of scrap paper (and a calculator if you'd like), answer the questions as best you can. When you finish, review the solutions for the questions that you miss. We then discussed previous homework questions and the Geogebra transformation homework in preparation for the quiz next class. We finished with an NCTM survey.

__HW__:
 * Skim p. 84-87 with the goal of revising combinations of functions and composition of functions
 * p. 79/5
 * p. 89/1, 5, 21, 31, 41, 47, 49, 51
 * Quiz next class on all Unit 1 homework up through today (but not the new homework!)

=Monday, September 21st, 2009= I wish I could be there with you- have your scribe use the class blog to communicate questions/concerns with me while I am away. Please read my comments that I will post while I am away, so we can hit the ground running when I return to school on Wednesday of next week!

1. Take the quiz for 30 minutes.

2. Discuss homework for 20 minutes. I expect you will have some good discussions!

3. Open this Geogebra file ([|FunctionTransformations1.ggb]) and write the answer to the questions on the packet your substitute will give you (digital copy here: [|FunctionTransformations1.pdf]). Feel free to work together.

__HW__:
 * Open this Geogebra file ([|FunctionTransformations2.ggb]) and write the answer to the questions on the packet your substitute will give you (digital copy here: [|FunctionTransformations2.pdf]).
 * Continue to work on the transformation homework from last class.
 * Log into your SAT practice account, click on the Lessons tab, click on View Lesson, and watch the introduction to the SAT (turn on your sound).

=Thursday, September 17th, 2009= Since Mr. O'Brien will be away from school Friday, Monday and Tuesday helping to educate the math students of the world (or is writing an International Baccalaureate exam helping to torture the math students of the world?), we began class by testing to ensure that our SAT practice accounts were working. We also ensured that Geogebra was working by downloading and playing with this test file ([|FunctionTransformations2.pdf]). We then went over old homework problems and the symmetry problems (by reviewing the five elements of a well structured argument and looking at them graphically) in preparation for the quiz next class. We then revised the library of eight parent functions (on p. 70 and the inside cover of the text) that we all need to know from Algebra 2- constant (linear), identity (linear), absolute value, square root, quadratic, cubic, reciprocal, and greatest integer. We ended class by revisiting the three types of transformations of functions- translations (shifts), reflections (flips), and dilations (stretches/shrinks). Taken together, we can now sketch something like y = 2|x - 3| + 1 without ever turning on our GDC's!

__HW__:
 * Quiz next class on all Unit 1 homework up through today (but not the new homework!)
 * p. 71/31, 43, 53-60
 * p. 79/11, 17, 25, 31, 47, 53, 65

=Tuesday, September 15th, 2009= We began class by discussing the quiz, the arithmetic warm up from last class, and some of our previous homework, with a focus on GDC solutions to complement algebra solutions. We finished class with some some notes on tests for symmetry in graphs.

__HW__:
 * Do the ten problems on the symmetry sheet from class: [|symmetry.pdf]
 * Sign up for an [|SAT practice account] using your password from class

=Friday, September 11th, 2009= We began class with the quiz. After the quiz, we took this one question survey and completed this brief non-calculator arithmetic assessment (doesn't count on the class grade). We revisited our table making skills on the GDC (graphics display calculator) by exploring p. 50/75-78 a bit more. We then explored the function y = x^3 - 3x^2 - 13x + 15 on the GDC and learned more about viewing windows, tables, zeros, inequalities, relative extrema, and intervals of increasing/decreasing/constant. We then practiced our calculator skills by finding the domain of f(x) = (2 - x - x^2)^(1/4). This led to a quick look at ZDecimal, Trace, and inequalities. We finished by working further on the previous homework.

__HW__:
 * Quiz Monday on homework through Thursday
 * p. 49/29, 33, 63, 89
 * p. 63/47, 53, 61
 * p. 71/19, 23, 27 (you will need a GDC to do these problems)
 * Read the class blog and comments.

=Wednesday, September 9th, 2009 (3²/3²/3²)= Apologies for being out ill today, but I don't want to spread whatever I've got. I'm not sure how class will go without me, but here's the step by step plan for what I would like to have happen.

1. Go to the class blog. Read the first entry and post a comment (who can figure out how to post a comment?!). As a class, choose the first person to be the scribe who will blog about class today (I've invited you all as authors to the blog- check your email). If the scribe needs help posting his/her contribution, just email me for assistance. Your contributions to the blog will be graded quarterly as a quiz (rubric available here: [|blogging rubric.pdf]).

2. Please open up iCal on your Macbook and subscribe to the class calendar. To do this, go to Calendar-Subscribe in iCal. The URL for our class calendar is available here. When you subscribe, be sure to un-check the three boxes and choose auto-refresh. Help each other out! If you double click on an assignment in the class calendar, you will find a description of the homework. This information is available even if you are not connected to the internet- great for use at home if your Macbook can't get online.

3. Responsibility check. The substitute will check to see that you have something written for each of the homework problems due for today (even if it is just the problem). These problems are: S/he will also check that you have your textbook covered (if not, there are covers by the window). Thank you for filling out the student information survey, but these students still need to do so (by this evening): **Marcel, Petra, Sophia**.
 * p. 10/37
 * p. 35/69, 75
 * p. 49/41, 49, 51, 57, 61, 65, 75-78

4. No one has emailed me any topics that they would like to review from Sections 1.1-1.4. If you would like me to review any of these topics in class, please have the Sscribe indicate so in tonight's blog post.

5. Please use this time to discuss and correct the homework questions. Work in groups, use the file with all the written solutions at the top of this webpage, and help each other out. If there is any problem that you are not able to work through together as a class, please have the scribe indicate so in tonight's blog post, and that question will not be on any quiz until we have had a chance to discuss it as a class.

6. Please look at this website for a graphical explanation of domain and range.

7. Skim over p. 56-58 in your text in preparation for tonight's homework.

8. Work on tonight's homework (it will not be on Friday's quiz).

If you have any concerns about how math class is going (particularly Juniors who missed much of last class), please be sure to let me know. The scribe can blog about it, but you can also send me a personal email (address on the main page of this website). Thanks for being so responsible!

__HW__:
 * p. 49/35
 * p. 61/3, 5, 15, 17, 22, 23, 33, 37, 57, 59
 * p. 119/57, 71, 103
 * Quiz Friday on homework from last class

=Friday, September 4th, 2009=
 * Note**: Juniors missed the first half of class due to an assembly. Here is the "quiz" we discussed in class: [|course_outline_quiz.pdf] (it was actually a game for extra credit, so all you need to do is read through the questions and answers to make sure you understand the Course Methodology).

We began class by checking homework and having our course methodology "quiz". During the "quiz", we discussed what Pre-AP Calculus is all about, expectations for class, the importance of homework, how to get help, and more. We then discussed functions by examining [|this applet]. The importance of viewing functions numerically and graphically is the reason each of us must have a graphics calculator for this class- and the future. We examined some other interesting functions using [|this applet] which led to a discussion of domain and range. We finished with a brief look at the textbook and talked about how to format homework assignments. For what it's worth, the student website for your text is available [|here] (navigate by chapter in the upper left of the page).

__HW__:
 * Take a look through sections 1.1-1.4 in your textbook to remind yourself of some of what you're expected to remember from previous math courses. Pay particular attention to the blue boxes. If there's any topic or formula that you'd like to review in class, just send me an email or let me know at the start of next class.
 * p. 10/37
 * p. 35/69, 75
 * p. 49/41, 49, 51, 57, 61, 65, 75-78
 * Quiz Friday
 * Explore this class website- it would be a good idea to bookmark it (by next Wed)
 * Create a Google Account by going [|here] (you do not need to use Gmail, but you will need a Google Account for some class activities this year). Be sure to check your email and confirm your account. Check your login and record your user name and password in case you forget either. (by next Wed)
 * Please complete this student information sheet (plan on spending about half an hour on this- I would like some thought on some of the questions). (by next Wed)
 * Optional extra credit: Read pages 1-7 of [|this essay] and email me a one paragraph reaction of what you've read. (For more on this essay, click here.) (by next Wed)

=Wednesday, September 2nd= We thought about the following...

For each of the following problems, first estimate an answer and then try to calculate an answer using your mathematical skills. If you're interested in how we name large numbers, [|click here]. For a visualization of a trillion dollars, [|click here].
 * 1) When was one million seconds ago? How about one billion seconds ago? For more on this problem, [|click here].
 * 2) If a piece of paper could be folded in half fifty times, how high would the stack of paper be? For more on this problem, [|click here]. Have you heard that it is impossible to fold a piece of paper more than eight times? If so, [|click here].

We explored both problems using technology and learned how the second can earn you a very nice month's allowance. Mr. O'Brien shared his background ([|Mr. O'Brien's Travels.kmz]), and we finished with some quiet reading of the course methodology.

__HW__:
 * Read the course methodology and come to class prepared to discuss it (a copy is available on the home page).
 * You will have a quiz next class on the above- be prepared!
 * Give the parent/guardian letter to your parent/guardian (a copy is available on the home page).
 * Cover your text book.