We worked on the fourth quarter project ([[file/view/Q4 Project.pdf|Q4 Project.pdf]]) for these final five class days. Here is an equation generator and here is another. To insert the angle symbol, go to Insert-Special characters... and choose Advanced. The code is 8736. To insert the symbol for theta, use code 952. Theta looks best italicized... For your diagrams, you can use the drawing tools in MS Word or you can use Geogebra. You can use Geogebra or Fooplot for your graphing.

HW:

You may use homework time to work on the quarter project if necessary.

Tuesday, June 2, 2009

We took the final exam.

HW:

None.

Friday, May 29, 2009

We took the Supercorrection follow-up test and then revised for the final exam.

We began class with this feedback survey for Mr. O'Brien. In W1, we reviewed for the final exam by doing trig problems (see below). In W2, we had a guest speaker.

HW:

p. 369/Chapter 4 test

Be ready for the Supercorrection follow-up test on Friday (several questions directly from the original test: [[file/view/U5T1 hpc.pdf|U5T1 hpc.pdf]]).

Friday, May 22, 2009

We began by discussing the final exam. We then spent the period working on Supercorrections. If you need to write a Supercorrection, here are some suggestions for each question:

Use your incorrect answers in the Law of Cosines to show how you could check your answer to a question with the Law of Sines.

Do this problem two ways: once by drawing 3-4-5 and 5-12-13 triangles and once by finding the angle measures of u and v using inverse trig ratios.

Do this problem two ways: once by graphing on your calculator and once by solving the related equation (getting everything in terms of sine). Show how the table can be used to confirm your answer.

Check with your calculator. Derive the identities.

Put all four expressions in your calculator and compare tables of values. Prove the three identities (LHS = RHS).

Graph on your calculator. Derive the double angle identity from the sum angle for sine.

Look on the sheet where we derived The Mother of All Identities. Use the method we used to derive the double angle for cosine. For part (b), after solving using the identity, solve graphically.

Construct an accurate diagram. If you didn't know the value of cos60˚, be sure to show how you derive it!

HW:

Finish Supercorrections (due Wed.)

Wednesday, May 20, 2009

Today was the test day.

HW:

Pick up your test after Period 2. Work on Supercorrections for one hour- wouldn't it be great to have your Supercorrections done before the long weekend?

Monday, May 18, 2009

We began with the revision quiz. We then worked on a neat triangle problem from an International Baccalaureate exam paper. We finished with general trigonometry revision.

HW:

Choose a minimum of 10 problems from p. 420-423 and from p. 482-483 and from 486 (all of Ch. 5 but only 6.1 & 6.2) to revise for the test. Don't just do the quickest questions- pick ones that look tricky! Answers are posted online.

You will have Sum and Difference and the Double-Angle Formulas on the test (in the same form as on the inside cover of your text). Be aware that bringing in any other identities or unit circle to the test (written on your calculator cover, in your calculator's memory, on the back of your hand, etc.) is considered cheating. Respect yourself and act with integrity.

These two applets are very helpful for understanding the Ambiguous Case with the Law of Sines: this one and this one.

Organize homework to be submitted on Wednesday (from May 6th until today). Remember that it doesn't make much sense to do unit homework *after* the test, so plan on submitting whatever you have on test day.

Thursday, May 14, 2009

While the juniors enjoyed their day off, the seniors and Mr. O'Brien used the day to catch up on math problems.

HW:

Thursday: p. 436/5, 19, 21, 23 & p. 444/35, 39, 43, 47

Tuesday, May 12, 2009

We began class with a look at the ambiguous case for the Law of Sines. We discussed the homework and proved the Law of Cosines. We then worked on homework problems.

HW:

Tuesday: p. 443/5, 9, 11, 29, 31, 33, 41, 45

Friday, May 8, 2009

We began class with some revision of Chapter 5- we went over the homework questions and the quiz. There will be a final quiz for Unit 5 on the revision day; it will consist of questions from the first three quizzes. We then discussed how to solve oblique triangles- i.e. a non-right angled triangle with one known side and two other known parts. We proved the Law of Sines (if you were absent, here is an online proof) and in the process derived an area formula. Next Tuesday, we will prove the Law of Cosines, and next Thursday, we will work on a selection of problems involving oblique triangles.

Thursday: p. 436/5, 19, 21, 23 & p. 444/35, 39, 43, 47

Wednesday, May 6, 2009

We began class by finishing up our derivations of identities- sum/difference and double angle. We then went over the homework and worked on revision problems. We finished with the quiz.

HW:

p. 420/17, 29, 33, 37, 39, 43, 44, 49, 53, 63, 75

Organize homework through 5/4 to be handed in Friday

Monday, May 4, 2009

We began class with the remaining homework questions from last class, and then we corrected the quiz together. We then went over homework and derived the Sum/Difference identities and the Double Angle identities. We ended class by looking at the remaining identities of the unit: Power Reducing, Half Angle, Product to Sum, and Sum to Product. Although we won't use them in this course, they are helpful in calculus.

HW:

p. 415/9, 11, 13, 19, 23, 25 (use the new identities)

Organize homework to be submitted Friday

Revise for Wednesday's homework quiz- you can use the identities listed on the inside of your textbook, so bring it to class Wednesday

Thursday, April 30, 2009

We began class with the quiz. We discussed homework and took notes on the Sum and Difference Formulas. We began to derive the formulas.

HW:

p. 404/3, 19, 33, 37, 39, 47, 55, 65, 71

Tuesday, April 28, 2009

We began class by correcting the quiz and then discussed the trig equation homework. We spent the remainder of the period working on problems.

HW:

p. 396/35, 39, 43, 69-77 odd

Homework quiz Thursday

Friday, April 16, 2009

Today was the quiz day.

HW:

None! Just be sure all your homework is finished and corrected.

Wednesday, April 15, 2009

We warmed up by proving two identities and then went over the identity homework. We spent the remainder of the class working on trig equation solving.

HW:

p. 396/7-33 odd, 45, 55, 61

Revise for Friday's homework quiz by looking over each of your homework assignments from April 3rd to April 13th.

Monday, April 13, 2009

We warmed up with an identity verification exercise and then went over homework. We spent the rest of the time working on verifying identities.

HW:

p. 387/3-35 by 4's

Thursday, April 9, 2009

We investigated trigonometric identities, and learned how to verify identities. We spent most of the time working on problems.

We took the Supercorrections follow up test and worked on the project.

HW:

None!

Monday, March 30, 2009

We began with the homework quiz. We then signed up for a UT EID and used it to enroll in our online course (code 9999). The homework assignment posted there will be our work on Friday. We then created a graph for the Third Quarter Project together in Excel and worked on the project.

HW:

Do one hour's work on your quarter project (Third Quarter project.pdf) in Google Docs (you need to have two hours work done before you walk into class on Wednesday)

Revise your Supercorrections if necessary in preparation for Wednesday's Supercorrections follow-up test

Thursday, March 26, 2009

We Supercorrected. The quarter project has changed to a homework/classwork project. It will consist only of the work that you can do in your homework time over the weekend and for Wednesday's class (max of 1 hour per homework) and in class Monday and Wednesday.

HW:

Supercorrections due by Friday 2:15 pm

Revise your Unit 4 quizzes in preparation for Monday's quiz

Do one hour's work on your quarter project in Google Docs

Tuesday, March 24, 2009

We Supercorrected.

HW:

Supercorrections due by Friday 2:15 pm

Friday, March 20, 2009

Test day.

HW:

Pick up your corrected test 3rd period. Work on Supercorrections for one hour- they are due by next Friday.

Wednesday, March 18, 2009

We began class with a set of ten logic questions. We then discussed the homework. We went over what Friday's test will cover and we spent the remainder of the lesson revising.

HW:

Choose a minimum of 8 problems from p. 365-369 to revise for the test. Don't just do the quickest questions- pick ones that look tricky! Answers are posted online.

Organize homework to be submitted on Friday (from February 27th until today). Remember that it doesn't make much sense to do unit homework *after* the test, so plan on submitting whatever you have on test day.

Monday, March 16, 2009

We began class by working on trig application problems from the homework below, and then we corrected the last quiz and went over the inverse trig homework. We took notes on bearing and simple harmonic motion. We ended class with more work on the application problems.

HW:

p. 359/1, 5, 15, 17, 21, 23, 25, 29, 31, 33, 37, 43, 45, 53, 57, 59 (some of these are done in class)

Wednesday, March 11, 2009

After the quiz, we took another look at the two interesting trig graphs from last class. We then discussed inverse trig functions some more, taking a closer look at the homework.

HW:

p. 350/61, 65, 67, 71, 73, 91, 95, 96, 97

Spend some more time on the previous homework if necessary

Test is Friday- it's not too early to begin your revision...

Monday, March 9, 2009

We began class by thinking about two interesting trig graphs involving quotients. We then discussed the quiz and the homework, focusing on the four new trig graphs. We continued our trig work by extending into trig inverse functions.

HW:

p. 349/1-15 odd, 19-33 odd, 37-57 odd

Quiz Wednesday on Unit 4 homework- no calculator or unit circle

Thursday, March 5, 2009

After the quiz, we discussed the homework, focusing on how to determine the five key points from the transformations. We also revisited period with this applet. We then explored the graphs of the other four trig functions. Unfortunately, due to the number of snow days, the third quarter project is canceled. We will still do some work on it, but it will not be a formal project. Sorry!

HW:

Graph y = cot(x) and y = csc(x) like we did in class and write the domain and range for each. Check your graphs on your calculator and/or in the text.

We began class by working on the project. We then corrected the quiz and went over the homework. We explored transformations of trig functions using this applet.

Homework quiz Thursday- no calculator or unit circle...

Juniors: Go to the SAT website and do Geometry and Measurement Review Quiz #1 (an IOU for doing this)

Friday, February 27, 2009

We began class with the quiz, and then went over some of the homework problems. We plotted a graph of the sine and the cosine functions on graph paper from a table of values, and we looked at two computer animations that depicted the relationship between the unit circle and the function graphs. We ended class by connecting the graphs to some of the homework problems from the previous night.

Juniors: Go to the SAT website and do Data Analysis, Statistics, and Probability Review Quiz #1 (an IOU for doing this)

Unit 4 homework through Wednesday collected on Tuesday

Wednesday, February 25, 2009

We began class with the jigsaw again with the aim of improving speed. We then discussed the homework, focusing on the importance of good diagrams. We then looked at all 210 trig values and discussed how to use reference angles and quadrant signs to reason them out. We finished by making the table for the Third Quarter Project in Google Docs. We got our list of days of the year here and our sunrise and sunset times here.

HW:

p. 318/1, 3, 7, 11-17 all, 19, 21

Homework quiz Friday

Unit 4 homework through today collected on Tuesday

p. 309/63-69 all (these are a review of geometry trig problems- draw pictures and feel free to email/drop by if you need a revision of basic right triangle trig procedures)

Read pages 5 & 6 of the trig introduction packet for a brief historical background (U4 intro to trig.pdf)

In preparation for your Third Quarter Project, take a look at a classmate's Second Quarter Project.

Keep memorizing! This site has some very good advice about what you need to memorize (it's not much!) and what you can derive from your memorized information. If you use the quizlet flashcards from class, the Familiarize, Learn, and Test options are all useful, particularly if you sign in and make a custom symbol set (like mine from class). If you do use this site, you can earn an IOU for making the Top Users list.

Tuesday, February 10, 2009

We began class with some unit circle revision. We followed up with the homework quiz. We finished by discussing Francois and the past homework, focusing on the unit circle.

HW:

p. 309/17-28 all, 53-62 all

Keep memorizing!

Friday, February 6, 2009

We began class by correcting the quiz (Juniors who hadn't taken it took it). We then talked some more about the Unit Circle and the definitions of the six trig functions. This led to some identities- Reciprocal, Quotient, Pythagorean. We explored a trig equation which led us to the Co-function identities. We ended with homework questions.

HW:

p. 308/1-15 odd, 31, 32, 33-51 odd

Make sure your homework is up to date for Tuesday's quiz

Here are some Powerpoint quizzes that Mr. Fitzgerald put together to help with the memorization:

After the homework quiz, we revised radian and degree conversions and went over homework questions. We then looked at how the sine function of any angle is defined and how the cosine function of any angle is defined (the links are to great applets). This led us to the six trig function definitions (here in quizlet.com) and to the wonderful unit circle (again, our unit circle applet). We looked at pages 3 and 4 of the trigonometry intro notes (U4 intro to trig.pdf) for a discussion of how the unit circle helps us evaluate trig functions at common angle values. We ended with a look at the signs of the trig functions in each of the quadrants and how this tells us which functions are even and which are odd.

HW:

p. 299/1-51 odd

Keep working on your memorization. Here are some of the resources you can use:

We began class by revising the common angles in radians and degrees, and then we played a bit of a game. That led to a further discussion of radians and degrees including two clever formulas for calculating arc length and sector area for angles measured in radians. We also briefly discussed the difference between angular speed and linear speed. We then discussed the old homework- p. 290/1-69 odd and Francois.

HW:

Do p. 291/71-93 odd, 100-106 all

Review last week's homework in preparation for Wednesday's quiz

Keep working on your memorization of the common radian-degree conversion

Thursday, January 29, 2009

Due to the shortened lesson, we held off discussing Francois. Instead, we focused on the first two pages of the trigonometry introduction (U4 intro to trig.pdf) covering the basics of angles and our new mathematical method of measuring angles: the radian.

HW:

Finish Francois if necessary- be prepared to discuss on Monday

Do p. 290/1-69 odd

Memorize the common radian-degree conversion: this flashcard site may help you to quiz yourself and this circle will help you visualize the angles (turn off the coordinates if they get in the way)

Tuesday, January 27, 2009

We began class with the following:

Look over your final exam- are there any mistakes in marking?

Look at your Quarter 2, Midterm Exam, and Semester grades in Powerschool- are there any mistakes in my calculations? Keep in mind that this is not necessarily your final grade, but if reflects my raw calculations up to this point.

After discussing the previous semester and advice for the coming semester, we paused for a moment to appreciate the chance to begin again, to have a fresh start. We then began Unit 4 with a brief look at special triangles and the circumference of a circle. For the remainder of the class, we worked on Francois and his Pedometer.

HW:

Take a look back over your Course Outline (course_methodology.pdf) in preparation for your fresh start to the semester.

Re-correct any Supercorrection questions if necessary

The four Unit 3 homework assignments are due on the day of the midterm

Wednesday, January 14, 2009

After the homework quiz, we discussed the geometric sequence homework further, focusing on the infinite geometric series.

HW:

Revision problems for Unit 3 ([[file/view/U3HW.pdf|U3HW.pdf]])- answers are A*BCACE (#2 has a typo- correct answer is an=–6n+5)

Monday, January 12, 2009

We began class with the Supercorrections Follow-up Test and then discussed the arithmetic sequence homework. We finished with notes on geometric sequences.

We warmed up with several sequence questions similar to the ones from homework last class. We then discussed the Supercorrections and the project briefly. We went over the homework and discussed how the calculator could help with some problems. We finished with notes on a special type of sequence: the arithmetic sequence.

Supercorrection follow-up test on Monday- four questions just like the test. You can use your calculator on all four questions- a nice reward for all your hard work on Supercorrections. Any Supercorrection corrections are also due Monday.

Tuesday, January 6, 2009

We warmed up by looking for the 20th term of a number of sequences. That led us to a discussion of the apparent nth term and how to use the calculator in both function and sequence mode. We then discussed closed form vs. recursive form of sequences and finished with a look at sigma notation and summing on the calculator.

HW:

Check out this link for a revision of function and sequence mode on your calculator and this link for a revision of finding summations on your calculator.

The last four classes of 2008 are devoted to your Supercorrections and project. For a reminder of what I'm looking for in quality Supercorrections, look over the sheet from last time (available here) and my comments on your last Supercorrections. Be sure to have your text book open as you Supercorrect- use Purple Math, too. The goal is to learn something you didn't know before the test and then to put that down on paper. I don't want just the right answers and a trite comment like "I made a careless error" or "I should have studied more." When you finish, be sure to check your final answers with someone and/or the answer key. I depart for the UK at 2:15 on Wednesday afternoon. I will leave a copy of the test answer key with each of the math teachers and my sub- you can also email me with questions. I will be back for class on Tuesday.

HW:

Finish your Supercorrections and work on your project rough draft.

December 11, 2008

Today was test day.

HW:

Pick up your test period 3 today and begin your Supercorrections (due next Friday)

Begin your quarter project by sharing a Google Doc with obrienbluester@gmail.com (due Tuesday, 12/23)

December 9, 2008

Today was our revision day. We began class by working on some test rejects ([[file/view/U2 test reject.pdf|U2 test reject.pdf]]). We then corrected the quiz and spent the class discussing old homework questions and revising specific material. The test will include one page with the calculator and one page without. Six questions come from Chapter 2 material and seven come from Chapter 3 material. You may have the entire 80 minutes; there will be Supercorrections.

HW:

Choose 8 problems from the Chapter 2 Review/Test, Chapter 3 Review/Test, and/or the test rejects (answers: [[file/view/U2 test reject solutions.pdf|U2 test reject solutions.pdf]]). Include them with your homework packet.

Organize and staple your homework packet from November 12th through today.

Revise for the test (see information under December 5th). Rest. Psych yourself up. Don't be late and don't be sick- Thursday is game day...

December 5, 2008

We began class with the quiz. We then took notes and went over the p. 265 homework. We talked about using logarithmic scales to make sense of very small or very large numbers (like Richter, pH, and decibel). We talked about how to make sense of compound interest formulas and how as the number of compoundings per time period increases, the amount earned plateaus. We looked briefly at half-life. We finished with general models and linked them with our function work using the graphing calculator, noting the difference between rounding and truncating.

HW:

p. 265/19, 21, 27, 43, 45, 55, 59, 61, 63

Finish any old homework this weekend so that you can focus your review next week

It's not too early to review for Thursday's test. The material you will be tested on is listed on p. 207 (exceptions: review problems 43-46, 107-110) and p. 270. Your book is an excellent resource (certainly the review exercises give you plenty of problems!), but you may find some different perspectives helpful:

We warmed up with the homework problems for p. 253 listed below. We then went over homework questions. We spent the remainder of the period working on the real life examples from p. 265.

HW:

p. 253/101, 97, 95, 91, 87, 59, 55, 53, 39, 33 (whichever are not finished in class)

p. 265/15, 17, 25, 35, 37, 39, 49, 51, 53, 57 (skim p. 257-263 and use the examples as starting points for the problems)

Review old homework in preparation for Friday's homework quiz on Chapter 3 (not including tonight's problems)

December 1, 2008

We warmed up with a few log/exponential problems, corrected the quiz, and then worked a few equations involving logs/exponentials: p. 253/12, 14, 30, 56, 86, 94. We spent the remainder of the period working the homework problems.

We began class with a warm up- p. 243/47-59 odd, 69-79 odd, 80. We went over homework and ended with the quiz. The second quarter project was distributed (available here: Second Quarter Project.pdf), but it does not need to be started.

HW:

None! (The warm up problems p. 243/47-59 odd, 69-79 odd, 80 will be on the next quiz, though.)

November 18, 2008

We began class with a warm up- the Liftoff Function. We then went over homework. We 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

November 14, 2008

We began class with a warm up which connected transformations to exponent properties. We went over homework, and this led to a more detailed explanation of exponential functions, including a graphical look. We finished by looking at the inverse of the exponential function- the logarithmic function! This helpful graphic comes from Purple Math:

HW:

p. 236/1-29 odd, 33, 39-44 all, 49-69 odd

November 12, 2008

We began class with an exploration of a Mystery Function (if you are absent, be sure to do [[file/view/Mystery_Function.pdf|Mystery_Function.pdf]], as it will be included on the next quiz). We then corrected the quiz and briefly discussed exponential functions and the number e.

HW:

A20/11, 25, 31, 35, 55

p. 226/7-11, 15, 19, 27, 33, 47

November 7, 2008

We began class with 20 minutes of homework questions and then took the quiz for one hour.

We warmed up with two more rational function problems which led to two new interesting graphical features- holes and oblique asymptotes. We spent the rest of the class discussing homework and reviewing.

HW:

p. 208/5, 19, 37, 51, 55, 71, 77, 105, 129, 141

Organize Oct. 28-Nov. 5 homework to be handed in Friday

Review all Unit 2 homework for Friday's quiz

November 3, 2008

We began class with a warm up problem- a rational function consisting of #13 from p. 179 divided by #19. We looked for the domain, zeros, and aysmptotes as well as the features of the graph. We corrected the quiz from last class, and then we connected the warm up problem to our new work on solving nonlinear inequalities. We looked at the problem numerically, graphically, and algebraically. We discussed a way of finding horizontal asymptotes using algebra. We then went over the homework. We finished with another rational function inequality.

HW:

p. 204/11, 13, 15, 21, 37, 39, 43, 47, 49

October 30, 2008

We began class with the quiz- the Unit 2 homework was collected at this point. We then warmed up with a strange function- a rational function consisting of #15 divided by #11 from the previous night's homework. We looked for the domain, the zeros, and its general shape. Before discussing it, we went over #65 from the previous homework. We then looked at the table of values for the warm up and determined the domain and some interesting features- including zeros, vertical and horizontal/slant asymptotes. This led to a revision of long division and factoring from previous homework assignments. We talked about how we could cleverly plot points- using the y-intercept and the signs of y-coordinates. We then compared our analysis to the actual graph plotted with technology. We then repeated the process with #19 divided by #13 from the previous homework.

HW:

p. 193/7, 11, 13, 15, 17, 19

Finish any outstanding first quarter work by midnight Saturday

Bring IOU's to class on Monday if you'd like to use them this quarter

October 28, 2008

We began class by going over the quiz. We then discussed the previous two homework assignments- p. 159 & p. 167. This led us to a discussion of zeros of polynomials and the Fundamental Theorem of Algebra.

HW:

p. 179/11, 13, 15, 19, 55, 63, 65

Organize Unit 2 homework and staple to cover page for final homework grade of 1st quarter

Quiz Thursday covering homework from 2.1-2.4

October 24, 2008

Mr. O'Brien will not be in class today, so here's the schedule:

Take quiz (up to 30 minutes).

Check homework and go over questions. Help each other out if the sub's not a math teacher- I will go over any remaining questions next class.

Work on the homework- you may also find the textbook explanations helpful.

HW:

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

October 22, 2008

We began class with p. 149/42, 91. 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.

HW:

p. 159/8, 13, 21, 23, 25, 35, 59, 63

Redo homework problems from 2.1 and 2.2 in preparation for Friday's quiz (not required, but suggested!)

October 20, 2008

We began class by going over the quadratic function homework. We then took notes on polynomial functions- properties, the Leading Coefficient Test, zeros (including multiplicity), and sketching graphs.

HW:

p. 149/1-8 all, 11, 19, 21, 29, 33, 39, 41, 51, 89

October 16, 2008

Those who finished the Supercorrections follow-up test early worked on the project. 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 a quadratic, completing the square, the vertex, the axis of symmetry, the max/min, the y-intercept, and the x-intercepts (including the quadratic formula- prove it for extra credit). We finished with some work time for the project or homework.

HW:

p. 134/1-8, 17, 19, 23, 41, 45, 63, 75, 79

Finish project if necessary

October 14, 2008

We began class by going over the Supercorrections. We then spent the rest of the period working on the project.

HW:

Be sure that you can do all 12 problems from the Unit 1 test correctly- there will be a 4 question test follow-up on Thursday. The four questions will come directly from the test (with very small variations).

Work on finishing off your project (final draft due midnight Saturday)

October 9, 2008

We worked on Supercorrections and the project.

HW:

Submit Supercorrections by Friday at noon and be sure that your project is shared with obrienbluester@gmail.com- I will give your comments on your rough draft on Monday.

October 7, 2008

We began class by running a couple laps. We then discussed the quarter project expectations (intro-body-conclusion, responses not numbered, etc) and spent the rest of the class working on Supercorrections and the quarter project.

HW:

Work on Supercorrections and the quarter project (details listed after October 3rd)

October 3, 2008

We began class by discussing the philosophy of Supercorrections. We looked at this model Supercorrection and this example of a completed set of Supercorrections. 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 next Friday, October 10th at noon, but Supercorrections are best done slowly- aim to only do one or two a day. There will be a little more class time next Tuesday.

Work on your quarter project with your partner. These are the things you need to do before class on Tuesday: read over your project, start your shared Google Docs file, test the equation editor (to make beautifully formatted equations like this: ), test the graph editor, and begin your rough draft. Your rough draft will be due by midnight next Sunday, October 12th. There will be class and homework time next week to work on your rough draft.

October 1, 2008

Today was test day. We all appreciated the Finely Crafted Unit 1 Test.

HW:

Pick up your marked test at the end of period 3. Begin Supercorrections of any careless mistakes.

Look over the quarter projects (cover page: Q1project.pdf and Q1project.2.pdf). Decide on a partner, and if you would like to claim a quarter project, do so on the discussion tab of this page (first come first served).

September 29, 2008

We began class with a piecewise function warm-up connecting equations to tables and graphs. We then discussed strategies for success in Honors Precalculus- focusing mainly on homework (we took a look at homework problems 9 and 31 on page 89 and then compared them to Example 3 and Example 4 in the text & we looked at problem 25 on page 81 and compared it to the answer in the back). 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: hw_policy.pdf). We looked at page 115-116 to review the topics to be covered on Wednesday's test, and spoke briefly about Supercorrections.

HW:

Organize your homework- make sure each assignment is labeled, checked, corrected (in a different color), and stapled to the homework cover page (oldest first)

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, 137, 149, 151, 154b, 161.

September 25, 2008

We started class with the quiz, and then we went over some homework questions. We discussed real world modelling and variation. We looked at this spreadsheet for problem 8 on page 110 and learned how to make a regression line on the calculator.

HW:

p. 109/5, 7, 19, 21-24 all, 35-38 all

Do Algebra and Functions Practice Quiz #1 (click on the Practice Quizzes tab) on the SAT practice site.

Test Wednesday on Unit 1

September 23, 2008

We began class with a warm-up exercise on checking answers. We then took some time to look at homework questions. We took notes on function inverses- how to find them informally and formally, and how to work with them graphically. We finished by either working on the SAT practice quiz or discussing past homework problems.

HW:

p. 99/3, 9-12, 15, 19, 21, 23, 55, 61, 65, 67

Do Number and Operations Practice Quiz #1 (click on the Practice Quizzes tab) on the SAT practice site. (Email if you need a new access code.)

Post a note on the discussion tab of this page.

Quiz Thursday through 9/19 homework

September 19, 2008

Because so many people are off to the Common Ground Fair today, we slowed things down. The last quiz of the unit and the test have each been bumped up one day (see calendar above). Those who were in class were able to review some of the old concepts using this Sketchpad file: transform practice.gsp. We corrected the quiz and discussed homework before revisiting function combinations and compositions.

HW:

If you weren't in class, skim p. 84-88.

Sign up for a Wikispaces account (you don't need to fill in Option 4) and join this space

p. 89/1, 5, 9, 31, 41, 47, 49, 51

Quiz bumped to Thursday next week

September 17, 2008

We took the quiz, and then continued to talk about transformations. We did some Graphisthenics, connected p. 71/19, 23, 27 to our transformation work, and looked more closely at the Greatest Integer Function. We looked at p. 79/7 from the homework more closely to discuss transformations further- especially dilations. We connected tables to the equations and graphs.

We began class by correcting the quiz and then spent some time discussing homework questions in preparation for the quiz next class. We explored transformations of functions and took some notes on translations, reflections, and dilations.

HW:

Quiz up through September 11th homework on Wednesday

p. 71/7, 53-60

p. 79/7, 9, 11, 12

September 11, 2008

We began class with the quiz, spent some time discussing homework problems we've been working on, took some notes on tests for symmetry in graphs, and finished by spending some more time discussing homework problems (with a focus on GDC solutions to complement algebra solutions.

HW:

Do the ten problems on the symmetry sheet from class: symmetry.pdf

September 9, 2008

We began class by revisiting 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) and finding a nice viewing window for h(x) = e^xsin(2x) + 1. This led to a quick look at ZDecimal, Trace, inequalities, and an interesting discovery about visual deceptions when dealing with function graphs. We finished by working further on the p. 61 homework.

HW:

Quiz Thursday on first two homework assignments (Sept. 3 & 5)- if you still have any questions that you feel should be discussed in class, let me know via email by midnight Wednesday, and I won't include them on the quiz.

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- feel free to borrow one at study hall!)

September 5, 2008

We began class with a competition to find the common algebra errors (if you missed class, here it is: common_algebra_errors.pdf). We then finished discussing the Course Methodology. We went over 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. I had hoped that we would explore the function f(x) = (x + 3)(x - 1)(x - 5) on the graphics calculator which would lead to a discussion of viewing windows, tables, zeros, inequalities, relative extrema, and intervals of increasing/decreasing/constant. Since the common algebra errors warm-up took more time than I had intended, we will have to revisit this next class.

HW:

p. 61/3, 5, 15, 17, 22, 23, 33, 37, 57, 59, 79, 83- make a start on all, but we will take more notes next class which should make the problems clearer

September 3, 2008

We began class with the homework quiz. Following the quiz, we went over the Course Methodology and discussed expectations for class. 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. Our investigation of functions reminded us of the point-slope form of a line. 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.

p. 35/69, 75

p. 49/41, 49, 51, 57, 61, 65, 75-78

p. 117/57, 71, 103

Friday, August 29th

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.

When was one million seconds ago? How about one billion seconds ago? For more on this problem, click here.

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.

Suppose a string were tied tight around the earth. If one additional meter were added to the string, and the string was lifted the same distance off the surface of the earth, how high would it rise? For more on this problem, click here.

If you're interested in how we name large numbers, click here.

HW:

Explore this class website- it would be a good idea to bookmark it.

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)

Cover your text book.

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).

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).

## Table of Contents

Quarter 1 ProjectsQuarter 2 ProjectsQuarter 3 Projects## Thursday, June 4, 2009 - Tuesday, June 16, 2009

We worked on the fourth quarter project ([[file/view/Q4 Project.pdf|Q4 Project.pdf]]) for these final five class days. Here is an equation generator and here is another. To insert the angle symbol, go to Insert-Special characters... and choose Advanced. The code is 8736. To insert the symbol for theta, use code 952. Theta looks best italicized... For your diagrams, you can use the drawing tools in MS Word or you can use Geogebra. You can use Geogebra or Fooplot for your graphing.HW:## Tuesday, June 2, 2009

We took the final exam.HW:## Friday, May 29, 2009

We took the Supercorrection follow-up test and then revised for the final exam.HW:## Wednesday, May 27, 2009

We began class with this feedback survey for Mr. O'Brien. In W1, we reviewed for the final exam by doing trig problems (see below). In W2, we had a guest speaker.HW:## Friday, May 22, 2009

We began by discussing the final exam. We then spent the period working on Supercorrections. If you need to write a Supercorrection, here are some suggestions for each question:HW:## Wednesday, May 20, 2009

Today was the test day.HW:## Monday, May 18, 2009

We began with the revision quiz. We then worked on a neat triangle problem from an International Baccalaureate exam paper. We finished with general trigonometry revision.HW:## Thursday, May 14, 2009

While the juniors enjoyed their day off, the seniors and Mr. O'Brien used the day to catch up on math problems.HW:## Tuesday, May 12, 2009

We began class with a look at the ambiguous case for the Law of Sines. We discussed the homework and proved the Law of Cosines. We then worked on homework problems.HW:## Friday, May 8, 2009

We began class with some revision of Chapter 5- we went over the homework questions and the quiz. There will be a final quiz for Unit 5 on the revision day; it will consist of questions from the first three quizzes. We then discussed how to solve oblique triangles- i.e. a non-right angled triangle with one known side and two other known parts. We proved the Law of Sines (if you were absent, here is an online proof) and in the process derived an area formula. Next Tuesday, we will prove the Law of Cosines, and next Thursday, we will work on a selection of problems involving oblique triangles.HW:## Wednesday, May 6, 2009

We began class by finishing up our derivations of identities- sum/difference and double angle. We then went over the homework and worked on revision problems. We finished with the quiz.HW:## Monday, May 4, 2009

We began class with the remaining homework questions from last class, and then we corrected the quiz together. We then went over homework and derived the Sum/Difference identities and the Double Angle identities. We ended class by looking at the remaining identities of the unit: Power Reducing, Half Angle, Product to Sum, and Sum to Product. Although we won't use them in this course, they are helpful in calculus.HW:## Thursday, April 30, 2009

We began class with the quiz. We discussed homework and took notes on the Sum and Difference Formulas. We began to derive the formulas.HW:## Tuesday, April 28, 2009

We began class by correcting the quiz and then discussed the trig equation homework. We spent the remainder of the period working on problems.HW:## Friday, April 16, 2009

Today was the quiz day.HW:## Wednesday, April 15, 2009

We warmed up by proving two identities and then went over the identity homework. We spent the remainder of the class working on trig equation solving.HW:## Monday, April 13, 2009

We warmed up with an identity verification exercise and then went over homework. We spent the rest of the time working on verifying identities.HW:## Thursday, April 9, 2009

We investigated trigonometric identities, and learned how to verify identities. We spent most of the time working on problems.HW:## Friday, April 3, 2009

We worked on the problem set in our online course (code 9999).HW:## Wednesday, April 1, 2009

We took the Supercorrections follow up test and worked on the project.HW:## Monday, March 30, 2009

We began with the homework quiz. We then signed up for a UT EID and used it to enroll in our online course (code 9999). The homework assignment posted there will be our work on Friday. We then created a graph for the Third Quarter Project together in Excel and worked on the project.HW:## Thursday, March 26, 2009

We Supercorrected. The quarter project has changed to a homework/classwork project. It will consist only of the work that you can do in your homework time over the weekend and for Wednesday's class (max of 1 hour per homework) and in class Monday and Wednesday.HW:## Tuesday, March 24, 2009

We Supercorrected.HW:## Friday, March 20, 2009

Test day.HW:## Wednesday, March 18, 2009

We began class with a set of ten logic questions. We then discussed the homework. We went over what Friday's test will cover and we spent the remainder of the lesson revising.HW:## Monday, March 16, 2009

We began class by working on trig application problems from the homework below, and then we corrected the last quiz and went over the inverse trig homework. We took notes on bearing and simple harmonic motion. We ended class with more work on the application problems.HW:## Wednesday, March 11, 2009

After the quiz, we took another look at the two interesting trig graphs from last class. We then discussed inverse trig functions some more, taking a closer look at the homework.HW:## Monday, March 9, 2009

We began class by thinking about two interesting trig graphs involving quotients. We then discussed the quiz and the homework, focusing on the four new trig graphs. We continued our trig work by extending into trig inverse functions.HW:## Thursday, March 5, 2009

After the quiz, we discussed the homework, focusing on how to determine the five key points from the transformations. We also revisited period with this applet. We then explored the graphs of the other four trig functions. Unfortunately, due to the number of snow days, the third quarter project is canceled. We will still do some work on it, but it will not be a formal project. Sorry!HW:## Square Root Day, 2009

We began class by working on the project. We then corrected the quiz and went over the homework. We explored transformations of trig functions using this applet.HW:## Friday, February 27, 2009

We began class with the quiz, and then went over some of the homework problems. We plotted a graph of the sine and the cosine functions on graph paper from a table of values, and we looked at two computer animations that depicted the relationship between the unit circle and the function graphs. We ended class by connecting the graphs to some of the homework problems from the previous night.HW:## Wednesday, February 25, 2009

We began class with the jigsaw again with the aim of improving speed. We then discussed the homework, focusing on the importance of good diagrams. We then looked at all 210 trig values and discussed how to use reference angles and quadrant signs to reason them out. We finished by making the table for the Third Quarter Project in Google Docs. We got our list of days of the year here and our sunrise and sunset times here.HW:## Thursday, February 12, 2009

We began class with a warm-up puzzle and then continued with a little unit circle and trig values practice (before we began the trig values practice, we reminded ourselves how the sine function and cosine function work). We then corrected the quiz and discussed when a calculator is appropriate and when it is not. We went over homework questions and then we made the table for the Third Quarter Project (Third Quarter project.pdf) in Google Docs. We got our list of days of the year here and our sunrise and sunset times here.HW:## Tuesday, February 10, 2009

We began class with some unit circle revision. We followed up with the homework quiz. We finished by discussing Francois and the past homework, focusing on the unit circle.HW:## Friday, February 6, 2009

We began class by correcting the quiz (Juniors who hadn't taken it took it). We then talked some more about the Unit Circle and the definitions of the six trig functions. This led to some identities- Reciprocal, Quotient, Pythagorean. We explored a trig equation which led us to the Co-function identities. We ended with homework questions.HW:## Wednesday, February 4, 2009

After the homework quiz, we revised radian and degree conversions and went over homework questions. We then looked at how the sine function of any angle is defined and how the cosine function of any angle is defined (the links are to great applets). This led us to the six trig function definitions (here in quizlet.com) and to the wonderful unit circle (again, our unit circle applet). We looked at pages 3 and 4 of the trigonometry intro notes (U4 intro to trig.pdf) for a discussion of how the unit circle helps us evaluate trig functions at common angle values. We ended with a look at the signs of the trig functions in each of the quadrants and how this tells us which functions are even and which are odd.HW:## Monday, February 2, 2009

We began class by revising the common angles in radians and degrees, and then we played a bit of a game. That led to a further discussion of radians and degrees including two clever formulas for calculating arc length and sector area for angles measured in radians. We also briefly discussed the difference between angular speed and linear speed. We then discussed the old homework- p. 290/1-69 odd and Francois.HW:## Thursday, January 29, 2009

Due to the shortened lesson, we held off discussing Francois. Instead, we focused on the first two pages of the trigonometry introduction (U4 intro to trig.pdf) covering the basics of angles and our new mathematical method of measuring angles: the radian.HW:## Tuesday, January 27, 2009

We began class with the following:- Look over your final exam- are there any mistakes in marking?
- Look at your Quarter 2, Midterm Exam, and Semester grades in Powerschool- are there any mistakes in my calculations? Keep in mind that this is not necessarily your final grade, but if reflects my raw calculations up to this point.
- Take this very short survey reflecting on the first semester.
- Form a group of three or four, and give your advice to a new student.

After discussing the previous semester and advice for the coming semester, we paused for a moment to appreciate the chance to begin again, to have a fresh start. We then began Unit 4 with a brief look at special triangles and the circumference of a circle. For the remainder of the class, we worked on Francois and his Pedometer.HW:## Friday, January 16, 2009

We discussed Unit 3 and the midterm exam.HW:## Wednesday, January 14, 2009

After the homework quiz, we discussed the geometric sequence homework further, focusing on the infinite geometric series.HW:## Monday, January 12, 2009

We began class with the Supercorrections Follow-up Test and then discussed the arithmetic sequence homework. We finished with notes on geometric sequences.HW:## Thursday, January 8, 2009

We warmed up with several sequence questions similar to the ones from homework last class. We then discussed the Supercorrections and the project briefly. We went over the homework and discussed how the calculator could help with some problems. We finished with notes on a special type of sequence: the arithmetic sequence.HW:## Tuesday, January 6, 2009

We warmed up by looking for the 20th term of a number of sequences. That led us to a discussion of the apparent nth term and how to use the calculator in both function and sequence mode. We then discussed closed form vs. recursive form of sequences and finished with a look at sigma notation and summing on the calculator.HW:## December 15, 2008 until December Break

The last four classes of 2008 are devoted to your Supercorrections and project. For a reminder of what I'm looking for in quality Supercorrections, look over the sheet from last time (available here) and my comments on your last Supercorrections. Be sure to have your text book open as you Supercorrect- use Purple Math, too. The goal is to learn something you didn't know before the test and then to put that down on paper. I don't want just the right answers and a trite comment like "I made a careless error" or "I should have studied more." When you finish, be sure to check your final answers with someone and/or the answer key. I depart for the UK at 2:15 on Wednesday afternoon. I will leave a copy of the test answer key with each of the math teachers and my sub- you can also email me with questions. I will be back for class on Tuesday.HW:## December 11, 2008

Today was test day.HW:## December 9, 2008

Today was our revision day. We began class by working on some test rejects ([[file/view/U2 test reject.pdf|U2 test reject.pdf]]). We then corrected the quiz and spent the class discussing old homework questions and revising specific material. The test will include one page with the calculator and one page without. Six questions come from Chapter 2 material and seven come from Chapter 3 material. You may have the entire 80 minutes; there will be Supercorrections.HW:## December 5, 2008

We began class with the quiz. We then took notes and went over the p. 265 homework. We talked about using logarithmic scales to make sense of very small or very large numbers (like Richter, pH, and decibel). We talked about how to make sense of compound interest formulas and how as the number of compoundings per time period increases, the amount earned plateaus. We looked briefly at half-life. We finished with general models and linked them with our function work using the graphing calculator, noting the difference between rounding and truncating.HW:## December 3, 2008

We warmed up with the homework problems for p. 253 listed below. We then went over homework questions. We spent the remainder of the period working on the real life examples from p. 265.HW:## December 1, 2008

We warmed up with a few log/exponential problems, corrected the quiz, and then worked a few equations involving logs/exponentials: p. 253/12, 14, 30, 56, 86, 94. We spent the remainder of the period working the homework problems.HW:## November 20, 2008

We began class with a warm up- p. 243/47-59 odd, 69-79 odd, 80. We went over homework and ended with the quiz. The second quarter project was distributed (available here: Second Quarter Project.pdf), but it does not need to be started.HW:## November 18, 2008

We began class with a warm up- the Liftoff Function. We then went over homework. We 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:## November 14, 2008

We began class with a warm up which connected transformations to exponent properties. We went over homework, and this led to a more detailed explanation of exponential functions, including a graphical look. We finished by looking at the inverse of the exponential function- the logarithmic function! This helpful graphic comes from Purple Math:HW:## November 12, 2008

We began class with an exploration of a Mystery Function (if you are absent, be sure to do [[file/view/Mystery_Function.pdf|Mystery_Function.pdf]], as it will be included on the next quiz). We then corrected the quiz and briefly discussed exponential functions and the number e.HW:## November 7, 2008

We began class with 20 minutes of homework questions and then took the quiz for one hour.HW:## November 5, 2008

We warmed up with two more rational function problems which led to two new interesting graphical features- holes and oblique asymptotes. We spent the rest of the class discussing homework and reviewing.HW:## November 3, 2008

We began class with a warm up problem- a rational function consisting of #13 from p. 179 divided by #19. We looked for the domain, zeros, and aysmptotes as well as the features of the graph. We corrected the quiz from last class, and then we connected the warm up problem to our new work on solving nonlinear inequalities. We looked at the problem numerically, graphically, and algebraically. We discussed a way of finding horizontal asymptotes using algebra. We then went over the homework. We finished with another rational function inequality.HW:## October 30, 2008

We began class with the quiz- the Unit 2 homework was collected at this point. We then warmed up with a strange function- a rational function consisting of #15 divided by #11 from the previous night's homework. We looked for the domain, the zeros, and its general shape. Before discussing it, we went over #65 from the previous homework. We then looked at the table of values for the warm up and determined the domain and some interesting features- including zeros, vertical and horizontal/slant asymptotes. This led to a revision of long division and factoring from previous homework assignments. We talked about how we could cleverly plot points- using the y-intercept and the signs of y-coordinates. We then compared our analysis to the actual graph plotted with technology. We then repeated the process with #19 divided by #13 from the previous homework.HW:## October 28, 2008

We began class by going over the quiz. We then discussed the previous two homework assignments- p. 159 & p. 167. This led us to a discussion of zeros of polynomials and the Fundamental Theorem of Algebra.HW:## October 24, 2008

Mr. O'Brien will not be in class today, so here's the schedule:HW:## October 22, 2008

We began class with p. 149/42, 91. 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.HW:## October 20, 2008

We began class by going over the quadratic function homework. We then took notes on polynomial functions- properties, the Leading Coefficient Test, zeros (including multiplicity), and sketching graphs.HW:## October 16, 2008

Those who finished the Supercorrections follow-up test early worked on the project. 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 a quadratic, completing the square, the vertex, the axis of symmetry, the max/min, the y-intercept, and the x-intercepts (including the quadratic formula- prove it for extra credit). We finished with some work time for the project or homework.HW:## October 14, 2008

We began class by going over the Supercorrections. We then spent the rest of the period working on the project.HW:## October 9, 2008

We worked on Supercorrections and the project.HW:## October 7, 2008

We began class by running a couple laps. We then discussed the quarter project expectations (intro-body-conclusion, responses not numbered, etc) and spent the rest of the class working on Supercorrections and the quarter project.HW:## October 3, 2008

We began class by discussing the philosophy of Supercorrections. We looked at this model Supercorrection and this example of a completed set of Supercorrections. 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:## October 1, 2008

Today was test day. We all appreciated the Finely Crafted Unit 1 Test.HW:## September 29, 2008

We began class with a piecewise function warm-up connecting equations to tables and graphs. We then discussed strategies for success in Honors Precalculus- focusing mainly on homework (we took a look at homework problems 9 and 31 on page 89 and then compared them to Example 3 and Example 4 in the text & we looked at problem 25 on page 81 and compared it to the answer in the back). 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: hw_policy.pdf). We looked at page 115-116 to review the topics to be covered on Wednesday's test, and spoke briefly about Supercorrections.HW:## September 25, 2008

We started class with the quiz, and then we went over some homework questions. We discussed real world modelling and variation. We looked at this spreadsheet for problem 8 on page 110 and learned how to make a regression line on the calculator.HW:## September 23, 2008

We began class with a warm-up exercise on checking answers. We then took some time to look at homework questions. We took notes on function inverses- how to find them informally and formally, and how to work with them graphically. We finished by either working on the SAT practice quiz or discussing past homework problems.HW:## September 19, 2008

Because so many people are off to the Common Ground Fair today, we slowed things down. The last quiz of the unit and the test have each been bumped up one day (see calendar above). Those who were in class were able to review some of the old concepts using this Sketchpad file: transform practice.gsp. We corrected the quiz and discussed homework before revisiting function combinations and compositions.HW:## September 17, 2008

We took the quiz, and then continued to talk about transformations. We did some Graphisthenics, connected p. 71/19, 23, 27 to our transformation work, and looked more closely at the Greatest Integer Function. We looked at p. 79/7 from the homework more closely to discuss transformations further- especially dilations. We connected tables to the equations and graphs.HW:## September 15, 2008

We began class by correcting the quiz and then spent some time discussing homework questions in preparation for the quiz next class. We explored transformations of functions and took some notes on translations, reflections, and dilations.HW:## September 11, 2008

We began class with the quiz, spent some time discussing homework problems we've been working on, took some notes on tests for symmetry in graphs, and finished by spending some more time discussing homework problems (with a focus on GDC solutions to complement algebra solutions.HW:## September 9, 2008

We began class by revisiting 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) and finding a nice viewing window for h(x) = e^xsin(2x) + 1. This led to a quick look at ZDecimal, Trace, inequalities, and an interesting discovery about visual deceptions when dealing with function graphs. We finished by working further on the p. 61 homework.HW:## September 5, 2008

We began class with a competition to find the common algebra errors (if you missed class, here it is: common_algebra_errors.pdf). We then finished discussing the Course Methodology. We went over 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. I had hoped that we would explore the function f(x) = (x + 3)(x - 1)(x - 5) on the graphics calculator which would lead to a discussion of viewing windows, tables, zeros, inequalities, relative extrema, and intervals of increasing/decreasing/constant. Since the common algebra errors warm-up took more time than I had intended, we will have to revisit this next class.HW:## September 3, 2008

We began class with the homework quiz. Following the quiz, we went over the Course Methodology and discussed expectations for class. 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. Our investigation of functions reminded us of the point-slope form of a line. 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:## Friday, August 29th

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.

- When was one million seconds ago? How about one billion seconds ago? For more on this problem, click here.
- 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.
- Suppose a string were tied tight around the earth. If one additional meter were added to the string, and the string was lifted the same distance off the surface of the earth, how high would it rise? For more on this problem, click here.

If you're interested in how we name large numbers, click here.HW: