The beginning of Trig...

Trigonometry is our longest unit spanning more than two months and three tests. We start in the Demana book but will move into our second book, the Brown book, as we progress.  We begin with Right Triangle Trig, mostly review from last year.  

12/12  4.1 Angles and their measures

           HW p.325-328/3-39 by 3's, 44, 46, 52-56, 72-74

12/14  4.2 Right Triangle Trig

           HW p.335-337/1, 7, 16, 19-23 odd, 59, 60, 61, 63, 66, 73, 75-78

Circular functions (4.3) are a big part of understanding trigonometry conceptually. We will spend a few days making sure you understand. Problems 67-76 on 12/17 are the problems you should really push yourself to understand - don't just give up and wait for me to go over them.

12/17  4.3 Circular Functions
           HW Demana p.347-349/2,3,7,27-35 odd, 41-53 odd, 60-64, 67-76;

12/18  More Practice CW Brown p.272/3-10,  13, 14 and worksheet
           HW Brown p.272-274/17-27 odd, 29-32, 33-41 odd

12/19  Finding all solutions with circular trig HW finish handout

12/21  Quiz of 4.1-4.3 and game

12/22 - 1/02 Christmas Break! (Parent Conferences on 1/02)

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 quick skills quiz.

1/03  4.4 Graphing Trig Functions handout (G-Block in class, E-Block for homework)

1/04  4.4 Sinusoids
         HW Demana p.357-358/13-41 odd, 42, 49, 50, 53, 73, 75

1/07  CW p.360/91-97   HW p.357-359/51, 52, 54-57, 59-69 odd, 70-80 even

1/08  Trig Evaluation Practice and Extra Problems

         HW finish problems 1-12 of Extra Problems worksheet

1/09  Discuss Extra Problems Worksheet (and Professional Developement - Half Day (B A G F))

         HW finish Extra Problems worksheet (13-21)

1/11  Solving with Sinusoids  CW problems 1-5 (answer key)

         HW problems 6 - 9

1/14  Continue Solving with Sinusoids

         HW finish rest of handout, problems 10 - 17

1/15  Quiz of 4.1-4.4

1/16  4.5 Graphs of the other Trig functions and 4.7 Inverse Trig functions

         HW p.366-368/13-16,18-39 by 3's,43,60,63,64 and p.385/37-40

1/18  Extra Sinusoid and Inverse Trig Problems (and End of Term 2)

         HW in Brown: p.290-291/11-14, 27-29, p.306-307/30,31,33,36, p.314-316/15,17,18,21,25,26

1/21  Martin Luther King Day - no school

1/22  Review (answer key)
1/23  Practice Test (answer key)

1/25  Test of Ch 4
         HW Trig Area and Identity intro

Ch 3: Exponential and Logarithmic Functions

We start with an explanation which is both review and a new way of looking at exponential functions.
Some of the 11/27 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.

11/26  Intro/Review of 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
11/27  Modeling with Exponential and Logistic Functions
           HW p.262-263/51-58 and p.271-273/12-15, 21-33 by 3's, 39, 42, 45, 58-61
11/28  Practicing with log functions.  Standard transformation rules apply.
           HW p.281/3-36 by 3's, 37-40, 42-60 by 3's

11/30  Proving and Using Log Properties

           HW finish handout

12/03  Extra Problems on Exponential and Log Functions

           HW handout 1-15 (answer key)

12/04  Log Transformations, More Log Properties & Log Applications

           HW problems listed on handout (answer key)

12/05  More Log Applications (Newton's Law of Cooling especially)

           HW problems listed on handout

12/07  Re-expression of data and Semi-log graphing

           HW finish handout

12/10  Review problems (answer key)

12/11  Test of Ch 3

Conjugate Proof Exemplars

Here is a link to the good/better/best proofs.  It is worth your while to understand what makes one proof better than another (for the good of your future proofs).

Rational Functions

We are going to do a quick unit on Rational Functions (a way of putting our polynomial studies to work).  The pacing is rather aggressive so we can finish before Thanksgiving.  Make sure you keep up with your homework.

11/08  After the Polynomial Test, review Rational Functions (What are they? What do they look like? What do the zeros of the numerator tell you?  What do the zeros of the denominator tell you?  What else do you remember about them?)
11/09  Big Giant Algebra 2 coverage review
           HW p.225-227/15-18, 21-30 by 3's, 31-36, 39-60 by 3's, 73, 77, 78

11/12 Veterans' Day - no school
11/13  Extra Problems Worksheet (work in pairs)
           HW finish worksheet (answer key)
11/14  Harder Graphing and Solving Equalities
           HW finish handout and p.232-235/3-45 by 3's, 51, 53, 55
11/16  Solving Inequalities and Review Problems
           HW finish handout and p.242-243/5-50 by 5's, 57-59

11/19  One Giant Problem (answer key)
11/20  Rational Function Half-Test
11/21  Half-Day A C F H
11/22  Thanksgiving

Finishing up the Polynomials

The schedule announced in class has changed a bit because of storm.

10/29  Hurricane - no school
10/30  Hurricane damage - no school
10/31  Recap of complex numbers
           HW work through packet, answer key for 1-10 are here
11/02  Go over Complex Conjugates Proof; More Polynomial Problems
           HW finish packet, answer key is here

11/05  Finding Equations of Polynomials
           HW finish handout
11/06  Professional Development Day - no school
11/07  Test of Polynomials (E-Block)
11/08  Test of Polynomials (G-Block)

Looking forward:
The rest of the chapter is on Rational Functions (fractions with polynomial numerators and denominators) which will end in a quiz or test.
11/12  Veterans' Day
11/22  Thanksgiving
11/26  we start a full week of school!

Polynomials

Chapter 2 begins with Polynomials. The beginning of the polynomial chapter is mostly review - and then it gets complex (literally!).  The chapter includes how complex numbers relate to polynomial functions.  We will be spending a couple of weeks on polynomials and complex numbers.  Quick, skill-based check-in quizzes could happen at any time after the first three days of basic instruction so stay on top of your homework.

The homework problems on complex zeros are from the old edition of the book which used to take two sections to cover the material.  I liked some of the problems that were deleted in the new edition so you will be given copies of the pages.

10/15  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

10/16  2.3  Higher Degree Polynomials

           HW p.193-195/3,5,13,18,21,24, 33-41 odd, 47-55 odd, 75

10/17  2.4  Real Zeros of Polynomial Functions

           HW p.205-209/13-31 odd, 49, 53, 76-79

10/19  More problems from 2.3 and 2.4

           HW Finish handout plus p.195-196/77 - 83 odd, 84

10/20  2.4  GCF for Polynomials

           HW Euclid's Algorithm Worksheet

10/21  2.5  Complex Numbers

           HW 2.5/Quick Review 8,10 and Exercises 6-8,14-16,23,24,26,27,31,32,33-39 odd

10/22  2.5  More with Complex Numbers

           HW 2.5/Exercises 41-44, 45-53 odd, 59, 60, 62

10/24  2.5  Complex Zeros of Polynomials

           HW 2.6/Exercises 3-39 by 3's, 46, 51, 53, 57

10/29  Extra Complex Problems

Practice Test for Transformations

Here is a link for a Practice Test.

Transformations

This is section 1.6 in the text but we will spend a week on it because the topic is so important for everything else we do.  Dates are for G-Block up to the Transformation Quiz.  

09/27  Review Basic 6 Transformations, plus more!
               HW finish Day 1 handout plus p.136-138/3-24 by 3's, 25-28, 29, 31   09/28  More Graphical Transformations (incl. domain & range, inverse, absolute value)
                HW finish Day 2 handout

10/01  Describing Transformation with Coordinates
               HW finish Day 3 handout
10/02  Reciprocal and Involution
               HW finish Day 4 handout
10/04  One Giant Review Problem (G-Block only)  
10/05  Transformation Quiz
               (I will give out the One Giant Review Problem to E-Block for the long weekend.)
10/08  Columbus Day - no school
10/09  Review Day 1
10/11   Review Day 2
10/12   Chapter 1 Test

The practice test

First of all, the One Giant Review packet does not seem to have the small circles that represent composition.  Everywhere you see "g   f" you should interpret as "g(f(x))".

Secondly, the sections and topics covered by the test are:

1.2    Descriptive Vocab for functions
10.3  Limits (useful in defining end behavior and continuity!)
1.3    The 12 Basic Functions (get used to them, they will all be back)
1.4    Adding, Subtracting, Multiplying, Dividing, and Composing Functions (what happens to the domain?)
1.5    Inverses (algebraically, graphically, numerically) - skip the parametric stuff, we'll do it later

The downloads: the Practice Test and, (thanks Mr. Verner!) the Solutions.
I am also posting an answer key to the One Giant Review (all done!)

 Remember that you can email me with your questions over the weekend.  Enjoy!

Getting Started

After the pretest, we start by 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. All the Wednesday dates are Thursdays for G-Block.  After Rosh Hashanah, the dates and assignments may change a bit.)

8/29 Domain and Range (with some new notation)

        HW finish handout for the next class after the pretest

9/03 Labor Day

9/04 Pretest (based on summer work - see the previous post for the assignment)

9/05 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

9/06 Half Day C B A G

9/07 Limits: definition, notation, evaluation

        HW p.763-764/1-23 odd, 26, 31, 37, 49, 61, 71

9/10 Asymptotes, Holes, and Continuity

        HW p.95-98/35, 37, 39, 55-61 odd, 67, 68, 81, 86

9/11 Twelve Basic Functions (section 1.3)

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.

        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.)

9/12 Functions operations (section 1.4): 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 their equations. Ask again if the explanation in class and homework doesn't clarify the issue for you.

         HW pp.116-118/5, 7, 12-42 by 3's, 51-55
9/14 More Problems on Composition
         HW finish worksheet

9/17 Rosh Hashanah - no school

9/18 Function Descriptions and Combinations HW finish worksheet

9/19 Inverses   HW p.126-128/13-21 odd,23-26,29,31,33-36,45-47,50,51

9/21 Big Review Packet (Day 1)

9/24 Big Review Packet (Day 2)
9/25 Test of Function description and manipulation

9/26 Yom Kippur - no school

Welcome!

This blog is intended to provide a syllabus, homework, and any hints or requests that I may have of you.  We cover a lot of very interesting math this year - and it goes fast.  Make sure that you keep up.  As one of my previous students in the class said, when asked for advice to new Honors Advanced Math students, "For G-d's sake, do you homework!"  I concur.

The first week of school we meet only once, a 70 minute block where we will get acquainted and then jump right in to an activity to remind you about different kinds of functions and their domain and ranges.  The intention of the teachers of the course is to have a pre-test on the summer material on Tuesday, September 4th during class.  If you have not done your summer work, lost the sheet listing the problems, or never got a book before vacation, I am listing the problems below.  See me to get a book.

I hope you are as ready for an exciting year as I am!


Summer Work:

P.2  p.17 – 19   problems 12 – 18 by 3’s, 41 – 55 odd

P.3  p.26 – 27   problems 25 – 28, 61

P.4  p.36           problems 7 – 23 odd (do them all with point-slope form – see p. 29 if necessary)

P.5  p.46 – 47   problems 3 – 24 by 3’s, 39, 43, 47, 51, 55, 57, 58

P.6  p.52 – 53   problems 3– 42 by 3’s

Sections 1.4 (function arithmetic and composition), 1.6 (graphical transformations), and 2.6 (rational functions) are aimed at students coming from Algebra 2, level 1. These topics are covered in a high level of detail in Honors Algebra 2, but students who had Algebra 2, level 1 may have significantly less familiarity with these topics. If you are in this situation, we encourage you to read these sections and do the problems listed below. Students who had Algebra 2 Honors are also encouraged to look at these sections and to do these problems as necessary.

1.4  p.116-118  problems 1, 5, 11, 15, 19, 45-50 all, 52-54

1.6  p. 136-137 problems 3-30 by 3’s

2.6  p. 225-226 problems 23-29 odd, 31-35 odd