Sinusoids

Sinusoids are some of our 12 basic functions, period functions with repeating patterns. We will be spending time before and after vacation on this topic. There will be a skills quiz at some point.

12/20 HW p.357-358/13-41 odd, 42, 49, 50, 53, 73, 75
12/21 CW p.360/91-96   HW p.357-359/51, 52, 54-57, 59-69 odd, 70-80 even
12/22 or 12/23 Trig Game or Write a Sinusoid Problem

12/24 - 1/3 Christmas Break!

Circular Functions

Circular functions (4.3) are a big part of understanding trigonometry conceptually. We will spend a few days making sure you understand. Any problems posted in black are the problems you have to really push yourself to understand - don't just give up and wait for me to go over them.

12/13 Demana p.347-349/1,3,7,27-35 odd, 41-53 odd, 60-64, 67-76;
12/14 Brown p.272-27/17-27 odd, 29-32, 3-41 odd
12/15 Finding all solutions with circular trig HW finish handout
12/17 Quiz of 4.1-4.3, HW Graphing Trig Functions handout

Trigonometry begins!

Trigonometry is our longest unit spanning more than two months and three tests. We start in the Demana book but will move into the Brown book as we progress.

12/08 4.1 Angles and their measures
           HW p.325-328/3-39 by 3's, 44, 46, 52-56, 72-74

12/10 4.2 Right Triangle Trig (Note: I will be out this day)
           HW p.335-337/1, 7, 16, 19-23 odd, 59, 60, 61, 63, 66, 73, 75-78

Finishing up the Exp and Log Chapter

11/23  Proving and Using Log Properties
              HW finish handout
11/24  Half Day - A C F H
11/25  Thanksgiving Break

11/29  Extra Problems on Exponential and Log Functions
              HW handout 1-15 (answer key) and redo test proof
11/30  Log Transformations, More Log Properties & Log Applications
              HW problems listed on handout (answer key)
12/01  More Log Applications (Newton's Law of Cooling especially)
              HW problems listed on handout
12/03  Re-expression of data and Semi-log graphing
              HW finish handout

12/06  Review problems (answer key)
12/07  Test of Ch 3

Practicing with Log functions

This is all practicing log functions. Standard transformation rules apply.

HW p.281/3-36 by 3's, 37-40, 42-60 by 3's

Modeling with Exponential and Logistic Functions

Some of the homework problems involve regression. Here is a document that will remind you how to do them on the calculator. The example uses a quadratic but I have faith in your ability to extend the information to the exponential and logistic regressions.

HW 11/19 p.262-263/51-58 and p.271-273/12-15, 21-33 by 3's, 39, 42, 45, 58-61

Starting with Exponential Functions

We start with an explanation which is both review and a new way of looking at exponential functions.

HW p.261-264/8, 10, 13, 15, 19, 23, 25-30, 35, 39, 40, 45-49 odd, 61, 65, 66, 69-73

Answer key to today's giant problem

The work/answers are in blue, the corrected typo is highlighted in red. Download here.

Finishing up Ch 2

11/08  Rational and Power Functions worksheet
11/09  Solutions to rational equations
              HW p.232-235/3-45 by 3's, 51, 53, 55
11/10  Extra problems with rational functions
11/11  Veterans' Day - no school
11/12  Partial Fraction Decomposition and Solving Inequalities
              HW p.563/15,18,21,22,25,27-43 and p.242-243/5-50 by 5's, 57-59
11/15  Review
11/16  Test of Ch. 2 (Polynomial and Rational Functions)

Going towards Rational Functions - polynomial fractions

The last bit of the chapter concerns rational functions - fractions with polynomials in the numerator and denominator. Finding the factors and zeros of the polynomials becomes important for describing the behavior of the function as a whole.

11/02  Extra Complex Problems  HW finish worksheet
11/03  More Polynomials Problems  HW finish worksheet
11/05  Reviewing transformations of 1/x and rational functions
              HW p.225-227/15-18, 21-30 by 3's, 31-36, 39-60 by 3's, 73, 77, 78

Complex Numbers and Polynomials

We will be studying how complex numbers relate to polynomial functions. The new edition of the book covers all of this material in one section. It used to take two, with more homework problems. Given that I liked the old coverage of the material better, you will be given copies of all the homework problems (and the answers to the odds) from the old edition. We will be spending several days on the topic and will then have a quiz. The quiz will be skill based and could happen at any time after the first three days of basic instruction so stay on top of your homework.

10/26  Pop Quiz on 2.3-2.4
                  HW Euclid's Algorithm Worksheet
10/27  Complex Numbers
                  HW 2.5/Quick Review 8,10 and Exercises 6-8,14-16,23,24,26,27,31,32,33-39 odd
10/29  More with Complex Numbers
                  HW 2.5/Exercises 41-44, 45-53 odd, 59, 60, 62
11/01  Complex Zeros of Polynomials
                  HW 2.6/Exercises 3-39 by 3's, 46, 51, 53, 57

Starting Polynomials (Ch 2)

The beginning of the polynomial chapter is mostly review - and then it gets complex.

10/19  2.1  Review Linear and Quadratic facts
          HW p.77/48,50,52 and p.169,173/11-17 odd, 33-41 odd, 81-84
10/20  2.3  Higher Degree Polynomials
          HW p.193-195/3,5,13,18,21,24, 33-41 odd, 47-55 odd, 75
10/21  2.4  Real Zeros of Polynomial Functions
          HW p.205-209/13-31 odd, 49, 53, 76-79

10/25    More problems from 2.3 and 2.4
          HW Finish handout plus p.195-196/77 - 83 odd, 84

Big Giant Review Problem Answer Key

You can download the answer key to the BIG problem given out on Friday.

Please note that there were two typos in that problem and I have fixed them in the answer key (so your answers may vary from mine - want to try parts of the problem again without the typos for extra practice?). The first typo was a problem for most of the questions since it is in the function definition. The part of the function used for negative values of x should have simplified to -x^2. The other typo was in question one and should say even instead of odd.

I apologize for the graphs being so small. The only way to make piecewise functions is on my calculator - a very small screen.

Transformations

This is section 1.6 in the test but we will spend a week on it because the topic is so important for everything else we do.

09/29  Review Basic 6 Transformations, plus more!
        HW finish double transformations plus p.137-138/17-23 odd,25-28,33,34,4,45,57,67
10/01  Transformed Basic Functions, Unpacking composition
        HW Worksheet of more problems on transformation

10/04  Describing Transformation with Coordinates
        HW finish handout of problems
10/05  Reciprocal and Involution
        HW finish handout of problems
10/06  Transformation Quiz
10/08  Professional Developement Day - no school

10/11  Columbus Day - no school
10/12  Review Day 1
10/13  Review Day 2
10/15  Giant Review Problem

10/18  Chapter 1 Test

Newer Practice Test

There are links to old tests are at the right but I am including the test Mr. Verner gave last year as a practice test. The test is here and the answer key is here. Make sure you really try before looking at the answer key!

The rest of the material leading to a test revised

It is getting a tad confusing on the two dates (I will have to get E- and G-Block classes on the same schedule after the first test). I will make columns for now. Below is the proposal for the rest of the material leading up to the first test. If no book homework is listed, finish the day's handout.

E-Block   G-Block   Plan
  9/17          9/20      More Problems on Composition
  9/20         9/21      Function Descriptions and Combinations
  9/22         9/23      Inverses   HW p.126-128/13-21 odd,23-26,29,31,33-36,45-47,50,51
  9/24         9/24      Big Review Packet (Day 1)
  9/27         9/27      Big Review Packet (Day 2)
  9/28         9/28      Test of Function description and manipulation

Functions Operations, etc.

Section 1.4 is about functions operations: addition, subtraction, multiplication, division and (perhaps most importantly) composition. The big issue is the change of the domain for the new function. Try the Exploration on page 112 (if we don't finish it in class - it is good for you to think about what composed functions can turn into). There is also the issue of non-function relations and the functions implied by there equations. Ask again if the explanation in class and homework doesn't clarify the issue for you.

9/15 for E-Block, 9/17 for G-Block:   HW pp.116-118/5, 7, 12-42 by 3's, 51-55

Note: A test is coming relatively soon (next week probably) so make sure you are keeping up with homework and concepts!

The Big Twelve

The twelve basic functions are the ones we will come back to over and over during the course of the year. Several of them are related to each other in a variety of ways. You need to be completely familiar with their graphs and properties. We start with an exploration.

9/14 for E-Block, 9/16 for G-Block:
Exploration and CW; HW p.106-109/13-28, 45-55 odd, 64, 65, 68, 69
(Hint: use a and b instead of x and y for problem 69 - it is easier to understand that way.)

Starting assignments

The year started without homework so the breezy explanation of section 1.1 may be well supplemented by looking through and trying some of the problems in that section. We started in earnest after Labor Day in discussing Function Vocabulary. After a brief foray into chapter 10 for an explanation of limits, we continue looking at function details.

(The dates below are for the E-Block class. After Rosh Hashanah, the G-Block class is one day behind.)

9/07 Extrema, Increasing/Decreasing, Odd/Even Symmetry CW p.97/79
      HW p.94-95/1-4, 9-19 odd, 25-33 odd, 47-53 odd

9/08 Limits: definition, notation, evaluation
      HW p.763-764/1-23 odd, 26, 31, 37, 49, 61, 71

9/09 Rosh Hashanah - no school

9/10 Asymptotes and Holes
      HW p.95-98/35, 37, 39, 55-61 odd, 67, 68, 81, 86

9/13 Continuity, More Practice with descriptive vocab
      HW Worksheet

9/14 Twelve Basic Functions (section 1.3)

Welcome

This blog will be a source for the syllabus, homework, and hints. Sometimes I post a syllabus ahead of time and then things change so check back often. If you have any questions, please don't hesitate to email me or visit during my free blocks.