**Problem of the Week**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

people:mckenzie:math_108_hw

Chapter 3 textbook scan part 1 and part 2

Homework for the night of (due the following class day):

**Thurs Jan 19** Read Sec 1.1-1.3; do Comprehension Checks throughout the reading.

Do all problems for Secs. 1.1-1.3, pp 32-33 End behavior, roots and multiplicity of roots to graph a polynomial

Rational root (zeroes) theorem

Rational root theorem example
**Fri Jan 20** Read Sec 1.4; do all problems p 33 Sec 1.4

**Mon Jan 23** See Helpful videos and Helpful worksheets if you need extra practice.

Study for quiz tomorrow (Tuesday) on Section 1.1-1.4.

Read Sec 1.5; do exercises pp 33-34 #1, 2, 3 a-i

**Tues Jan 24** Read Sec 1.6. Have ready HW questions you didn't understand ready on Sec 1.5

**Thurs Jan 26** View Solving an equation involving two radicals Ex 1 and and Ex 2

Do Sec 1.6 problems,do all exercises p 34

Read Sec. 3.1. Look esp at the domain examples and comprehension checks.

**Fri-Sun Jan 27-29** *The first test is Tuesday February 7*

Ch 3 is essential to your understanding of all of mathematics. It addresses functions. Besides reading Ch 3 throughout the coming week, view these videos. Don't wait til before the first test to watch these.

View Algebraically Finding the Domain of a Function

Example of domain of a composition of functions

Do pp 84-85 Sec 3.1 #1 a, c, d, f, #4 all #6 a b #7, #9

Read Sec 3.2

**Mon Jan 30** Do p 85 #2, 3 b d, 4, 6 a b, 7

View Evaluating piecewise functions

**Tues Jan 31** Read Sec 3.2

View Evaluating piecewise functions

Do problems p 85 #2, 3 b d, 4, 6 a b, 7

Read Sec 3.3 and view One-to-one functions and Even and odd functions

Short quiz tomorrow (Thurs) on solving equations and on functions (including definition of a function).

**Thurs Feb 2** Do p 86 Sec 3.3 #1 a, b, c, d, 2 all, 4, 5 a b, 7

Read Sec 3.4.

Also view Understanding one-to-one functions and inverses

Finding the inverse of a function

Do Sec 3.4 pp 86-87 #1-5

EXTRA PRACTICE ON FUNCTION FEATURES

**Fri-Sun Feb 3-5** Be prepared to ask questions on Monday on any topic you don't understand, any HW problem or video item. The test on Tuesday is on Ch 1 and Ch 3.

SKILLS FOR TEST 1

Simplifying exponential and radical expressions with numbers and variables

Rationalizing a denominator.

Factoring: common factors, reverse FOIL (including magic factoring), special products, grouping

Simplifying rational expressions (entails factoring skills) and state the restrictions on x

Adding, subtracting rational expressions (entails finding LCD)

Multiplying, dividing rational expressions (entails cancelling)

Solving equations: quadratic (with an x squared term, but not using the quadratic formula—either factoring and taking a square root) radical equations (squaring both sides, sometimes twice, then checking solutions in the original); rational equations (getting a common denominator and setting = zero, then factoring, etc. and check that answer is in the domain).

Functions: definition, domain, notation, operations on functions and the effect on domain of combining functions, esp composition

Showing a function is odd, even or neither by the definitions of these concepts

Showing a function is one-to-one by the definition of the concept

Finding the inverse of a function

Knowing when a function has an inverse

Facts about domain and range of a function and its inverse (they trade places), which leads to the fact that the composition of a function with its inverse gives x.

Reading and interpreting piecewise functions.

**Tues-Wed Feb 7-8** Read Sec 4.1

**Thurs Feb 9** Do Sec 4.1 pp 110-111 #1, 4, 6, 7, 8 *This assignment will be collected on Friday.*

Read Sec 4.2 and view the videos:

Rigid transformations of functions 1

Rigid transformations of functions 2

**Fri Feb 10** Do pp 111-112 #1 a through o (these are the basic functions shifted left or right, up or down, flipped of x-axis or y-axis, stretched or compressed).

Read Sec 4.2 and view the videos from Thursday again.

Extra notes: Notes on transformations of graphs from another text, with illustrations

**Mon Feb 13** NEW: See your email and have questions for me based on what it addresses.

Do corrections on pp 3 and 4 of the test (to hand in).

Refer to Sec 4.1 and 4.2 essential diagrams of basic functions and transformations, noticing the domains and ranges of each.

Re-read: Notes on transformations of graphs from another text, with illustrations

View more transformations videos (see complete set on video page).

Transformations of square root functions 1 and 2

Continue with Sec 4.2 pp 111-112 #2, 5, 6

**Tues-Wed Feb 14-15** Understanding important features of polynomials in order to graph them

**Fri Feb 17**

**Sec 5.2** Equation of a line (point slope, slope-intercept); slopes of parallel and perpendicular lines; distance and midpoint). Work on this section over the weekend. We will review it after 5.1 and 5.3 are done.

Do pp 151-152 #3, 4, 5, 6, 8 a b e, 9, 10, 11 a b, 12 a c, 16, 17, 18

If you haven't watched them yet, view these short videos:

Find equation using point-slope form

Parallel and perpendicular lines

Do the problems pp 150-151 #1-9. Solutions are already posted; check your understanding against them.

**Sec 5.3** Read the section and view “Solving quadratic equations” by Factoring, Completing the squareUsing the quadratic formula.

Also, understanding how to Use the discriminant to find the number of roots and More using the discriminant

Remember, the number of solutions goes to the way the parabola crosses the x-axis:

Discriminant = 0 means parabola touches x-axis once = 1 root

Discriminant < 0 means parabola doesn't intersect x-axis = no roots

Discriminant > 0 means parabola intersects x-axis twic = 2 roots

Do p 153 #1, 2, 3, 4, 8, 9, 10

**Mon Feb 20** Keep working on the Sec 5.2 problems on lines. If you have questions, jot them down to ask in class:

pp 151-152 #3, 4, 5, 6, 8 a b e, 9, 10, 11 a b, 12 a c, 16, 17, 18

Watch Long division of polynomials

Rational root (zeroes) theorem

End behavior, roots and multiplicity of roots to graph a polynomial

Continue working on problems Sec 5.1 pp 150-151 #1-9. Solutions are already posted; check your understanding against them.

**Tues-Wed Feb 21-22** Read Sec 6.1 and 6.2

View:

Graphing a simple rational function

Graphing a harder rational function

View Slant asymptotes

Do p 188 Sec 6.1, #2 all, #3

Sec 6.2 p 189 #3 a-d, 5 a b, 6 all

**Thurs Feb 23** Read Sec 6.3 and 6.4

Do Sec 6.3 p 190 #1 a b c d e

Sec 6.4 pp 190-191 #1 a c d g, #3

Do the Take-home quiz on transformations and polynomial sketch

Complete the Ch 6 rational function handout.

Be able to identify all features of a rational function: y-intercept, roots, VA, HA, and SA, and holes, if any, naming each item correctly. Asymptotes to be given in equation form.

**Fri-Mon Feb 23-27** To help you study, here are the keys to all the handouts and take-home quiz:

Key to Ch 5 Polynomial Function Graphing handout

Key to Ch 6 Rational Function Graphing handout

Key to transformation and polynomial graph take home quiz

And here is a list of problems to focus on for Exam 2. Please have questions to ask on Monday:

**Ch 4**

Study each parent function as graphed throughout your text.

Comprehension Check 4.1.

Examples 4.2.2 to 4.2.6.

p 11 problems #1 c, e, h, i, k, l, n, o

**Ch 5**

5.1: Study Examples 5.1.7, 5.1.8 and 5.1.9 (like the quiz).

pp 150-151 problems #2 a, b, d, e #3 a, b #4, 5, 6, 7, #8 c, #9 a, c, e, f

5.2: Study all Comprehension Checks and Examples, as well as Important Ideas 5.2.1, 5.2.2 and 5.2.4

pp 151-152 #3, 4, 8 b, e, and in the following, do several parts of each of #9, #10, #11; also #16-18

5.3: Know how to solve a quadratic equation (i.e., find the roots)

p 153 #1 b, 2a, b, d, e, 3 b, c, d, e, 4 a-f, 6 a-d

**Ch 6** Look at all the graphed examples in this chapter. See the Videos link for a section on rational function graphing.

6.1: p. 188 #2 b, c, e, f, 3 a, b

6.2: p 189 #3 a, c, f, 5 a, 6 a, c, d, e

6.3: p 191 #1 a, b, c, d

6.4: p 191 #1 b, d, g, h

**Fri-Tues Mar 3-7** Read Sec 7.1 and 7.2. Here is a pdf of those sections if you haven't been able to get the book yet. Textbook pdf of Sec 7.1 and 7.2

View the following videos. View two a day, watch each one twice. Work through the problem with the teacher:

Solving quadratic inequalities

**Thurs Mar 9** View:

Absolute value equations--Example 1

Eqns with two abs values, Example 1

Do problems in Sec 7.1 p 215 #1 a-e,f, 2 a-c,e 3 a-e, 6

Quiz tomorrow on the recipe we had today for solving an inequality.

**Fri-Sun Mar 10-12** Solutions posted for Sec 7.1 problems..

Sec 7.2: *Use videos listed on Thurs as your guide on the problems* on p 215 #1, 2, 3, 5 a-h, 7, 8

Read Sec Sec 7.3 and view the videos in conjunction with the reading.

View //Overview//: Absolute value equations and inequalities

Abs value inequalities Example 1a and Example 1b

Example 2a and Example 2b

**Mon March 13** All HW solutions for Sections 7.1, 7.2 and 7.3 are posted. Keep them at hand as you work through Sec 7.3 problems p 216 #2 a-d, 2 f-j

If you have not finished Sec 7.2 yet, that is ALRIGHT. I will cover it tomorrow in the first 15 minutes.

Read Sec 11.1 and view Solving linear systems by elimination method

**BLIZZARD HOMEWORK** Because of Storm Stella, you have two nights of assignments to complete. One is the pretty easy Ch 11.1 on solving linear systems of equations. (Be prepared for class on this, which means you must try the problems…they are quite straightforward, not new). Then you have the absolute value take-home, which I will collect on Thursday. Read below:

**Tues-Wed March 14-15** Do Sec 11.1 #1 a, b, d, 2 a, 4-6 all parts

You can solve these linear systems by elimination or substitution.

Question: What does an answer indicate about a system of linear equations?

Answer: It tells if the functions intersect at a unique point, or at two points, like a line going through a circle or parabola, or at every point, which is a co-linear systems)

Read Sec 11.2. View Solving (graphing) systems of inequalities

** To hand in on Thursday** |Absolute value take-home

You may use notes and book and especially the Absolute value summary revised, but no friends!

**Thurs March 16** For tomorrow (St Patrick's Day!):

Be sure you have done Sec 11.1 #1 a, b, d, 2 a, 4-6 all parts

Read Sec 11.2.

View Solving (graphing) systems of inequalities

Do Sec 11.2 #2 a, d, g, h

**Fri-Sun March 17-19** Read Sec 10.1 and view Solving exponential equations

**Mon Mar 20** Study for quiz on Sec 7.1 and 7.2 systems of inequalities. Maybe a question on exponential functions.

Do p 348 Sec 10.1 #1, 2, 3

Read Sec 10.2 View Properties of logarithmic functions

**Tues Mar 21** Do Sec 10.2 #1, 2, 3 a-g, 4, 7, 9, 10, 11

**Thurs Mar 23** See these videos for examples of solving logarithmic and exponential equations:

Solving exponential equations without and with logs

3 examples of solving exponential equations

Example solving logarithmic equations

Another example solving logarithmic equations

Continue with problems Sec 10.2 #18, 19 a, 20 b, 21 a,b, 22, 23

**Fri-Sun Mar 24-27** Note: Material is added for Monday, the Sigma Notation section:

Do the worksheets:

Solving log and exponential equations 1 and

Solving log and exponential equations 2

Read Sec 2.4. View the following, noting that the lecturer is using 'k' for the index rather than 'i' (both are common letters for this process):

Sigma (summation) formula properties and

Example of changing upper and lower bounds of a sum

Read my Sigma Notation notes

Do p 60 #4 a, b, e, k, j, l; #3 a, b, c Solutions are already posted on HW Solutions page for this section.

**Mon Mar 28** Study for Exam 3. See email with focus problems.

**Thurs Mar 31** Beginning Trigonometry Unit. Read 8.1 and 8.2 CAREFULLY.

View Converting degrees to radians

and Basic sine and cosine functions

To hand in: Test 3 last page corrections and graph as shown

**Fri-Sun Mar 31-Apr 2** You might not be able to do the reference angle worksheets yet that I handed out today, but see what you can do after reading Read Sec 8.2.

By the way, the notation in the book for radian measure is an “r” that looks like an exponent! I don't care for that, but it is an arcane notation that is not seen in most books.

Again, view Basic sine and cosine functions

Using the video and examples in the book, do p 282 #1-10

**Mon Apr 4**

For the trig unit, when you feel overwhelmed, don't forget to go to Helpful videos for the *Trig Videos*. Watch the relevant video for the item at hand.

NOTE: Sec 8.2 requires more of a foundation than you have. One more lecture, first. But plenty of work you can do.

Here are tonight's tasks:

1. Do the worksheet on coterminal and reference angles. See Finding a reference angle

2. Look at the circle we labeled today with degrees and pi radians.

Draw one again and try to fill in the values of the various angle divisions with both their degree and pi radian equivalents.

3. Read the other handout, which explains the six trigonometric functions.

*Be prepared to answer the questions on it in class tomorrow.*

**Tues-Wed Apr 4-5** Sec 8.2.

The videos that will help you understand it is Converting from rectangular to polar coordinates

Watch Deriving the values of the unit circle

Complete the table we started in class on the special trig ratios. Put it at the bottom of the page that you draw your OWN circle labeled with degrees and pi radians, just like the handout. *Do yours in several colors*, preferably on a heavier piece of paper like a notebook back, that can stand up to constant handling!

If you did this already, you don't need to do it again.

Do the problems on the second page of the handout entitled “The Six Trigonometric Ratios of an Angle”

**Spring Break Homework April 8-17**

View Unwinding the unit circle to graph sine and cosine functions

Read Sec 8.3 and 8.4.

**Tues-Wed April 18-19**

1. Go back over Sec 8.2, 8.3 and 8.4 problems. Especially be able to do those whose solutions are posted.

Pay attention to p 283 #4, 5, 6, 7

2. *Print and memorize* Trigonometric function graphs

3. See HW solutions for quiz 1.

4. Do the worksheets: Find the other five trig ratios

5. Finish reading Sec 8.5.

6. Watch this link, which has both text and video on how to graph trig functions and transformations.

Graphing sine and cosine functions

**7.** Watch the series of videos by Patrick on graphing trigonometric transformations:

Transformations of trig graphs 1

Transformations of trig graphs 2

Transformations of trig graphs 3

Transformations of trig graphs 4

**8.** Start the problems p 285 #2 a b d, 3 a b, #4 a b c

**Thurs April 20** Do #1-8 on Graphing trig functions with a period and amplitude change

The model is

y = A sin(Bx), y = A cos(Bx), y = A tan(Bx)

in which amplitude = A, period = 2pi/B for sine and cosine (as seen in class), period = pi/B for tangent.

Notice the period change has to do with the original function's period: 2pi for sine and cosine; pi for tangent.

Now do Graphing trig functions with phase shift (Notice the use of degrees in the argument of the angle. We will use ONLY pi radian measure)

The model is y = A sinB(x + C) + D and y = A cosB(x + C) + D y = A tanB(x + C) + D

in which the horizontal shift is C right or left, depending on sign of C.

Notice that you need the form to be B(x + C) where the coeff on x is factored out.

**Fri April 21** There are two sections to the HW. The inverse trig functions and the take home of material to date.

Work independently. You may use your notes, but you should strive to do most of this without consulting your notes. The extent to which you need to look things up is a good indication of your preparedness for this portion of the material.

Show work on separate paper (answers only on the attached itself.) If you can't get to a printer, number each answer clearly, but again, show work on separate page so I may mark it quickly.

*Inverse trig functions*:

This can be a tricky topic. Study the pdf Inverse trig functions explained. I have copies but if you can print it before Monday, that would be nice. In any case READ IT and refer to it for all inverse function HW.

Inverse trig functions explained

Draw small graphs of the following (you can use the graph paper). Do them down the left side of the page:

y = sin x on the closed interval [-pi/2, pi/2]

y = cos x on the closed interval [0, pi]

y = tan x on the closed interval [-pi/2, pi/2]

You've drawn each fcn restricted to the portion of the domain where its inverse is defined; that is, where the function is one-to-one.

Using the pdf, draw to the left of each graph its inverse. Notice the x-axis is not the ratio and the y-axis is the angle.

NOW VIEW UP TO THE END OF PART 1, MINUTE 14:00: Evaluating inverse trig functions

**Mon April 24** Watch the rest of Evaluating inverse trig functions

Do Sec 8.6 p 286 1-6 for which I have already posted solutions.

Do #1-18 on:

Worksheet on evaluating inverse trig fcns

Patrick's videos should be of help: Evaluating trig inverses

**Tues-Wed April 25-26** Finish Worksheet on evaluating inverse trig fcns #19-30

Read Sec 8.7; do *pages 1 and 2* of today's worksheet Basic trig identities

View Proving a trig identity Example 1 and Proving a trig identity Example 2

Then, do p 288 #3 a-j.

**Thurs April 27** Read Sec 8.8. Here are two video discussions.

Determining quadrant of an angle

Do the problems on the worksheet Double and half-angle identities

**Fri-Sun April 28-30** View Solving single angle trig equations

Solving multiple angle trig equations

Worksheets as done in class: Trig equations worksheet and solutions to trig equations worksheet

Do Sec 8.9 p 290 problems #1 a, b, #2a, c, #3 a, b, c

people/mckenzie/math_108_hw.txt · Last modified: 2017/04/25 14:31 by mckenzie

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