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 12/04 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.

12/02  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
12/03  Math Department Professional Developement - no class

12/04  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

12/06  Practicing with log functions.  Standard transformation rules apply.

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

12/09  Proving and Using Log Properties (proof exemplars)

           HW finish handout

12/10  Extra Problems on Exponential and Log Functions

           HW handout 1-15 (answer key)

12/11  Log Transformations, More Log Properties & Log Applications

           HW problems listed on handout (answer key)

12/13  More Log Applications (Newton's Law of Cooling especially)

           HW problems listed on handout

12/16  Re-expression of data and Semi-log graphing

           HW finish handout

12/17  Review problems (answer key)

12/18  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.

11/12  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

11/13  Extra Problems Worksheet (work in pairs)

           HW finish worksheet (answer key)
11/15  Makeup rest of Polynomial Test

11/18  Harder Graphing and Solving Equalities

           HW finish handout and p.232-235/3-45 by 3's, 51, 53, 55

11/19  Solving Inequalities

           HW p.242-243/5-50 by 5's, 57-59

11/20  One Giant Problem (Problem and answer key)
11/21  Professional Developement Day - no school

11/22  Partial Fraction Decomposition
           HW p.562-564/5-25 odd (not 11), 33-45 odd, 49-52, 55, 56

11/25  Review (Practice Test and Answer Key)
           HW finish handout (includes p.247,249/67-81 odd, 91, 92, 94, 95

11/26  Rational Function Half-Test

11/27  Half-Day A C F H

11/28  Thanksgiving

Polynomials

We are back in the Demana book with Chapter 2: 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.

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

I will be out on November 7th and 8th so I may change the schedule a bit.  Check back.

10/23  2.1 and 2.3  Linear, Quadratic and Higher Degree Polynomial facts

           HW p.77/48,50,52 and p.169,173/11-17 odd, 81-84  and  HW p.193-195/3,5,18,21,24,45,47,75

10/25  2.4  Real Zeros of Polynomial Functions

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

10/28  More problems from 2.3 and 2.4 plus LCM and GCF (alternative method for GCF)

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

10/29  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

10/30  2.5  More with Complex Numbers

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

11/01  2.5  Complex Zeros of Polynomials  End of Term 1

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

11/04  Extra Complex Problems

           HW work through packet, answer key for 1-10 are here

11/05  Go over Complex Conjugates Proof; Finding Equations of Polynomials

           HW finish handout

11/06  More Polynomial Problems

           HW finish packet, answer key is here

11/08  Test of Polynomials (practice test and solutions)

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.

11/11  Veterans' Day

11/21  Professional Development Day - no school

11/28  Thanksgiving

Sequences, Series and Inductive Proof

A quick unit on Sequences and Series. All the homework is in the Brown book (Ch 13).

10/09   Explicit & Recursive; Geometric, Arithmatic, Harmonic Sequences

            HW pp.477-479/18-33 by 3's, 34, 37, 39, 44, 45, 48-50, 53, 56

            HW pp.481-485/1,2,11,12,13-17 odd,19,20,22,23,26,27,29,32-34

10/11  Ch 1 Functions and Transformations Test

10/14  Columbus Day - no school

10/15  Finite and Infinite Series; Sigma Notation

           CW pp.508-510/9, 11, 25, 27, 39

           HW pp.489-492/10-13, 17, 19, 27, 29, 35, 39, 41, 44

10/16  Limits and Sums of Infinite Sequences and Series

           HW pp.496-498/3-33 by 3's, 34-36 (skip 18 and 27)

           HW pp.502-505/9-21 odd, 29, 31, 33, 37, 38, 47, 48

10/18  Proof by Induction
           HW p.513-514/1, 3, 5, 6, 8, 11, 13-16, 19, 22, 24, 25

10/21  More Proof by Induction and General Review
10/22  Sequence and Series Quiz

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.  

09/30  Review Basic 6 Transformations, plus more!
               HW finish Day 1 handout plus p.136-138/3-24 by 3's, 25-29, 31   
10/01  More Graphical Transformations (incl. domain & range, inverse, absolute value)
                HW finish Day 2 handout
10/02  Describing Transformation with Coordinates
               HW finish Day 3 handout
10/04  Reciprocal and Involution
               HW finish Day 4 handout
   

10/07  Review Day 1 (putting all of chapter 1 together) (answer key for Big Giant Review Problem)
10/08   Review Day 2  (Here is a link for a heavy-on-the-transformation Practice Test and its solutions)
10/09   Chapter 1 Test

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.)

9/02 Labor Day
9/03 Brain Awakening Problems (E-Block only)
9/04 Rosh Hashanah - no school

9/05 Pretest (based on summer work - I will be out)

9/09 Domain and Range (with some new notation)

        HW finish handout and read section 1.2

9/10 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

9/11 Limits: definition, notation, evaluation

        HW p.763-764/1-23 odd, 26, 31, 37, 49, 61, 71
9/12 Half Day C B A G

9/13 Asymptotes, Holes, and Continuity

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

9/16 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.)

9/17 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

9/18 More Problems on Composition

         HW finish worksheet

9/20 Function Descriptions and Combinations HW finish worksheet

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

9/24 Big Review Packet (Day 1) (Answer Key)

9/25 Big Review Packet (Day 2)

9/27 Test of Function description and manipulation

Welcome...and a note

Hello!  Welcome to Honors Advanced Math.  The year is one with many new kinds of mathematics - some of the most science and engineering based math you will learn.  Please remember to look over the summer assignment.  The pre-test will be on Friday, September 6th in class.  (Remember that this test is a diagnostic tool and doesn't count for a grade.  Do the summer assignment and you will be fine!)