Archive+Pre-AP+Calculus+Red

toc =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= =

Friday, November 20th, 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. We then worked on some practice problems- p. 243/47-59 odd, 69-79 odd, 80. We went over homework and learned how to solve exponential and logarithmic equations using p. 253/12, 14, 30, 56, 86, 94 as practice problems.

__HW__:
 * p. 253/9-23 odd, 27, 29, 35, 49, 57, 65, 81, 93, 99
 * If you miss class, be sure to do p. 243/47-59 odd, 69-79 odd, 80 and p. 253/12, 14, 30, 56, 86, 94 as these will be included on homework quizzes for this unit.
 * Look over your homework in preparation for the quiz next class

=Wednesday, November 18th, 2009= We began class with the Supercorrection Follow-up Test. We also learned the definition of the wonderful number e- if you are feeling particularly nerdy, check out the mnemonics for memorizing the digits of e at the bottom of this page. We then went over homework and took notes on the Big Three Log Properties (connecting them back to the Mystery Function). This led us to the very powerful Change of Base formula. We finished by looking briefly at the properties listed on p. 230 and concluded that it is not necessary to memorize them, as they are direct consequences of the definition of logarithm.

__HW__:
 * p. 243/11-45 odd, 61-67 odd

=Monday, November 16th, 2009= We began class with a warm up which connected transformations to exponent properties and another which explored the properties of exponents leading to The Lift-off Function. We discussed the Mystery Function, went over homework, and took a more detailed look at the graphs of exponential functions. We finished by looking at the inverse of the exponential function- the logarithmic function (aka the Mystery Function or the Lift-off Function)! This helpful graphic comes from [|Purple Math]:

__HW__:
 * p. 236/1-29 odd, 33, 39-44 all, 49-69 odd
 * Be sure you are ready for the Supercorrection Follow-up Test (blank copy of the test available here: [[file:math-ob/U2T1 pap.pdf|U2T1 pap.pdf]])

=Thursday, November 12th, 2009= We began class with some more Supercorrection time. We held off on discussing 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.

__HW__:
 * Finish Supercorrections to submit by Friday afternoon (if you need an extension, email Mr. O'Brien)
 * p. 226/7-11, 15, 19, 27, 33, 45-51 odd, [55, 59 formula on page 224]

=Monday, November 9th, 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, 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.

=Thursday, November 5th, 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 school or on Friday.

=Tuesday, November 3rd, 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's Nick's file. 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: [[file:math-ob/homework.pdf|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, October 30th, 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 revisit 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

=Wednesday, October 28th, 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.]
 * Quarter will be finished off with Math Team extra credit and quiz grade for blog participation. Extra credit IOU's can be used at the start of next week if your grade needs a boost.

=Monday, October 26th, 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

=Thursday, October 22nd, 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__:
 * Be sure your project is ready to be graded by Friday midnight.
 * p. 167/17, 19, 21, 29, 33, 37-51 odd, 65, 71

=Tuesday, October 20th, 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!)
 * Finish up the project

=Friday, October 16th, 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...

=Wednesday, October 14th, 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 ([[file:math-ob/U1T1pap.pdf|U1T1pap.pdf]]) before Friday's follow-up test- you will need to show the working, not just the correct answer.

=Thursday, October 8th, 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 hand 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.

=Tuesday, October 6th, 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 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.
 * Begin work on the quarter project- each partner needs to make one addition to the shared Google Doc.

=Friday, October 2nd, 2009= We began class by discussing the philosophy of Supercorrections. We looked at this and this example of a  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.

__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 ([[file:math-ob/Q1 Project.pdf|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.

=Wednesday, September 30th, 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%

=Monday, September 28th, 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: ). 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: [[file:math-ob/homework.pdf|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.

=Thursday, September 24th, 2009= We began class by correcting the previous homework and going over the two homework questions from the blog: p. 79/53 and 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

=Tuesday, September 22nd, 2009= Again, wish I could be with you! Remember to ask your scribe to communicate questions/concerns to me.

1. 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. Aim to take 20 minutes.

2. Use 30 minutes to discuss the Geogebra transformation homework and discuss previous homework questions in preparation for the quiz next class.

3. Answer the NCTM survey that your substitute will give to you.

4. Begin the homework below.

__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!)

=Friday, September 18th, 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 and write the answer to the questions on the packet your substitute will give you (digital copy here: ). Feel free to work together.

__HW__:
 * Open this Geogebra file ([[file:math-ob/FunctionTransformations2.ggb|FunctionTransformations2.ggb]]) and write the answer to the questions on the packet your substitute will give you (digital copy here: [[file:math-ob/FunctionTransformations2.pdf|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).

=Wednesday, September 16th, 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. 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

=Monday, September 14th, 2009= We began class with this brief non-calculator arithmetic assessment (the right one this time!). We then discussed the quiz 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: [[file:math-ob/symmetry.pdf|symmetry.pdf]]
 * Sign up for an [|SAT practice account] using your password from class

=Thursday, September 10th, 2009= 1. Begin class with the quiz which your substitute will hand out to you. When you finish, hand it in to the substitute.

2. After the quiz, take this one question survey and this brief non-calculator arithmetic assessment (doesn't count on the class grade).

3. Help Julia make her post to the blog, and remind her to choose the scribe for today's class. Today's scribe should aim to post to the blog by this evening.

4. 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). The problems are:
 * p. 49/35
 * p. 61/3, 5, 15, 17, 22, 23, 33, 37, 57, 59
 * p. 119/57, 71, 103

Thank you for filling out the student information survey, but what's the deal, **Maci and Nick?!?** Snap to it! Please have this done by 7 pm this evening. Grrr... : )

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 work through this Powerpoint tutorial and read p. 56-58 in your textbook. For another explanation of the CALC menu on your calculator, visit this page (ignore CALC-6:dy/dx and CALC-7:integral for now).

7. Work on the new homework problems below.

__HW__:
 * Quiz Friday on homework through Wednesday
 * 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.

=Tuesday, September 8th, 2009= We began class by learning about the [|class blog] (rubric available here: ). We learned how to add the class calendar to iCal. We discussed homework problems (as well as the Mr. O'Brien's spiral learning philosophy for mathematics homework) which led to an examination of functions numerically as well as graphically using the graphing calculator. We learned some calculator basics- if you missed class, be sure to get some help on those. Our discussion of domain and range included two rules for domain as well as a nice graphical interpretation (the visuals are [|here]). We finished by exploring the function f(x) = (x + 3)(x - 1)(x - 5) on the graphics calculator which led to a discussion of viewing windows, tables, zeros, inequalities, relative extrema, and intervals of increasing/decreasing/constant.

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

=Thursday, September 3rd, 2009= 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 Thursday
 * Explore this class website- it would be a good idea to bookmark it (by next Tues)
 * 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 Tues)
 * 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 Tues)
 * 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 Tues)

=Tuesday, September 1st= 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, 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.