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people:mckenzie:math_108_hw

Chapter 3 textbook scan part 1 and part 2

In bold is the date on which the assignment is given. Prepare the work shown and be ready to ask/answer questions the following class day.

WEEK 1

**Tues-Wed Jan 16-17** Read Sec 1.1-1.2; do Comprehension Checks throughout the reading.

Do on pp. 31-32, Sec 1.1 and 1.2 problems.

Go to Practice worksheets and choose the one on radicals and rational exponents.

To help you, view Simplifying radicals with constants only and With variables

**Thurs-weekend Jan 18-20** *Read Sec 1.3 * Finish up Sec 1.1 and 1.2 problems. Do all problems for Sec. 1.3, pp 32-33.

**Add this to weekend** Read Sec 1.4 and view FACTORING VIDEOS:

Magic factoring (aka factoring by trial and error)

Factoring by grouping (with example using magic factoring)

Factoring sums and differences of cubes

WEEK 2

**Mon Jan 22** NEW CLASSROOM FOR ALL DAYS: LH 13 starting tomorrow, Tuesday,.

Study for quiz on Sections 1.1 to 1.3

Do all Sec 1.4 problems.

For Sec 1.5, view these videos along with reading the book – Operations on Rational Expressions:

Writing rat'l expressions in lowest terms

Multiplying, dividing rat'l expressions Ex 1

Multiplying, dividing rat'l expressions Ex 2

Multiplying, dividing rat'l expressions Ex 3

Adding, subtracting rat'l expressions, several examples

Adding, subtracting rat'l expressions, one more good example

**Tues-Wed Jan 23-24** Read Sec 1.5; do exercises pp 33-34 #1, 2, 3 a-i

Read Sec 1.6.

View Solving an equation involving two radicals Ex 1

and Ex 2

**Thurs Jan 25** Do Sec 1.6 p 34 #1 a-m

**Fri-Weekend Jan 26-28** View Completing the square to solve an equation: Ex 1 and Completing the square to solve an equation: Ex 2

After viewing, read Sec 2.2.

Do p 58 completing the square #1 all, #2 all, #3 a-g

Read 2.1; do p 58 polynomial division #1 a-f

WEEK 3

**Mon Jan 29** Study for Quiz 2: Factoring (special products, reverse FOIL, and grouping), simplifying a rational equation (state the restrictions on x at the end), solving a radical equation (don't forget to check your answer), solving a quadratic equation by completing the square.

Read Sec. 3.1 and 3.2. Look esp at the domain examples and comprehension checks.

Algebraically Finding the Domain of a Function

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

**Tues-Wed Jan 30-31** Read Sec 3.3 and 3.4

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

Watch the videos:

Evaluating piecewise functions

Domain of a composition of functions

￼**Thurs Feb 1** Read Sec 3.4 and 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 worksheet on finding inverse functions (especially the second set on the page):

Study for Quiz 3 on composition of fcns and their domain, finding the inverse of a fcn, showing a fcn is 1-1, using the definition (I'll leave an example on the board for that one, as I did on the first quiz).

**Fri-Sun Feb 2-4** Read Sec 3.3 and view: Even and odd functions

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

Extra practice worksheets on Odd/Even/Neither:

Odd, even or neither worksheet

More even, odd, neither practice

Study for Exam 1, on Tuesday Feb 6! It covers Ch 1, Ch 2.1 and 2.2 and Ch 3.

Topics: simplifying, performing operations on exponents and radicals; same for rational expressions; factoring; completing a square with leading coeff NOT equal to 1; solving equations (quadratic, radical, rational); function domain (interval notation); operations on fcns, esp composition and resulting domain; identifying even, odd fcns by evaluating f(-x) and comparing to f(x); showing a fcn is one to one, long division of polynomials, finding inverse of a fcn.

Key to practice worksheet for Exam 1

WEEK 4

**Mon Feb 5** Study for Exam 1

**Tues-Wed Feb 6-7** Next Unit: Ch 4, Ch 5 and Ch 6

Read Sec 4.1 and 4.2.

View Graphing piecwise functions 1

Domain and range of piecewise functions

*Snow day interruption*

**Fri-Sun Feb 9-11** Do Sec 4.1, which is about basic functions, shifted left, right, up or down, stretched or compressed.

Do Sec 4.1 pp 110-111 #1, 4, 6, 7, 8

View: Graphing transformed functions 1

Graphing transformed functions 2

WEEK 5

**Mon Feb 12** Read Sec 4.2; do pp 111-112 #1a-o, 4, 6, 7, 8.

Study for Tuesday quiz on parent functions and rigid transformations.

**Tues-Wed Feb 13-14** Catch up on any Ch 4 problem sets and videos.

Read Sec 5.1: Understanding important features of polynomials in order to graph them.

View IMPORTANT video:

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

Do pp 150-151 #1-7

**Thurs Feb 15** Do p 151 #8, 9.

Read Sec 5.2. View:

Find equation using point-slope form

Parallel and perpendicular lines

**Fri-Sun Feb 16-18** Here is Quiz 5,
Take-home quiz on polynomial graphing

Other business:

I. On Friday we looked again at Sec 5.1, drawing on the fundamental theorem of algebra, that relating to factoring polynomials. We found out how to write the set of *possible* *rational* roots of a polynomial (as opposed to irrational roots like those we often see when we resort to the quadratic formula).

Go back and view Rational root (zeroes) theorem

and examples:

Rational root theorem, example

II. The topic of lines (Sec 5.2) is largely a prerequisite of Math 108, so we don't spend more than a half hour on it all told. The solutions are posted, but again, here again are the videos and problems:

Find equation using point-slope form

Parallel and perpendicular lines

Do Sec 5.2 pp 151-152 #3-6, 8 a b e, 9, 10, 11 a b, 12 a c, 16-18

WEEK 6

**Mon Feb 19**

I. MAKE SURE YOU HAVE DONE enough of SEC 5.2 problems to be able to do a multi-part problem on lines as we did today

II. Read Sec 5.3 (again, about roots of second degree polynomials, i.e., quadratic functions. Solving these is just like what we did in Sec 1.6. Check out My notes on quadratic equations, formula, and meaning of roots

View Using the discriminant to find the number of roots and More using the discriminant

Do p 153 #1, 2, 3

III. Read Sec 6.1. View Graphing a simple rational function

**Tues-Wed Feb 20-21**

I. Catch up on anything you have not finished from Ch 5.

II. Graphing a harder rational function

Do p 188 Sec 6.1 #2, 3

View Slant asymptotes

Read Sec 6.2-6.3; do Sec 6.2 pp 188-189, #3 a-d, 5 a b, 6 all

**Thurs Feb 22** Sec 6.3 p 190, #1 a-e and Sec 6.4 pp 190-191 #1-4.

WEEK 7

**Fri-Mon Feb 23-26** Study for Exam 2, Tues, Feb 27, Chapters 4, 5, 6.

Graphing rational function practice 'quiz' to be desk-checked (not collected) on Monday !

Study for Exam 2, Feb 27.

WEEK 8

**Feb 28-March 8 ** This is the period of both the break and two snow days, so please take note of reading and videos, as well as any problem sets you must stay on top of over the coming weekend.

**Thurs March 8 ** Read Sec 7.1

Go to Videos and view 'Solving quadratic and rational inequalities'

**Fri-Sun March 9-11** Do problems in Sec 7.1 p 215 #1 a-e, f, 2 a-c, e, 3 a-e, 6

Read Sec 7.2. View:

Absolute value equations--Example 1

Absolute value equations--Example 2

Eqns with two abs values, Example 1

Eqns with two abs values, Example 2

Eqns with two abs values, Example 3

WEEK 9

**Mon March 12** Using my notes Solving absolute value equations along with last set of videos:

Do Sec 7.2 p 215 #1, 2, 3, 5 a-h, 7, 8

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

View Overview: Absolute value equations and inequalities

Abs value inequalities Example 1a

**Tues-Wed March 13-14** Heads up: there will be a quiz on Ch 7 and 11 on either Thurs or Fri.

Read Sec 11.1.

View Solving linear systems by elimination method

Do Sec 11.1 #1 a b d, 2 a, 4-6 all parts

**Thurs March 15** Take home quiz handed out today, due tomorrow! The one linked here includes a question 3 b, which I deleted in the handout to fit whole quiz on one page. Tonight's reading and videos are topics on the quiz, so you do need to do this 'open book'.

Read Sec 11.2 (to help you with the quiz!)

View Solving systems of inequalities

Solving (graphing) systems of inequalities

Do Sec 11.2 #2 a d g h

**Fri-Sun March 16-18** Read 10.1

Week 10

**Mon March 19** Do p 348 Sec 10.1 #1, 2, 3 and first three sections of questions on Solving exp and log equations

Even more practice on first set of questions on p 5 of Alternate text pdf

Read Sec 10.2

View Properties of logarithmic functions

**Tues-Wed March 20-21** Study for short answer quiz based on first three sections of questions on the pdf Solving exp and log equations up through Exercise 6.

See this page for Solutions to "Solving exp and log equations"

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

3 examples of solving exponential equations

Example solving logarithmic equations

Another example solving logarithmic equations

Exponential problems not requiring logarithms

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

**Thurs March 22** Finish the Sec 10.2 problems (we're caught up now).

Read Sec 2.4 and view videos on sigma notation, which I will post soon. Also read my summary of stigma notation and finding finite sums of a number sequence

**Fri-Sun Mar 23-25** 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

Example of changing upper and lower bounds of a sum

Here's a nice: Summary of sigma notation

Again, here are my notes on Sigma Notation

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.

Study for Exam 3. Ch 7, 10, 11, and Sec 2.4

Week 11

**Mon-Thurs Mar 26-29 ** Exam 3: Study for it, take it, go over it.

*HOMEWORK FOR SPRING BREAK*

**Mon-Sun April 2-April 8** :!: Begin Trigonometry Unit. Read 8.1 and 8.2 CAREFULLY.

View Converting degrees to radians

Basic sine and cosine functions

Weeks 12-16 Trigonometry Unit (HW over the Spring Break)

**Mon April 9**

Using the video and examples in the book, do Sec 8.1 p 282 #1-6

View AGAIN as needed Basic sine and cosine functions

**Tues-Wed April 10-11** Do worksheets Trig worksheets:

Coterminal and reference angles

Here are videos to help:

Finding quadrant an angle lies in

**For Friday, to hand in: Circle art assignment**

- On
*unlined*paper (copy paper is good), draw a*nice*circle (use a jar lid or compass, a straight edge for the rays). It should be no less than 6 inches.

*Neatly*mark off with a*straight edge*and label*accurately*the angles of 0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, 360.

- Next to each degree mark, write the pi radian equivalent, as discussed in class today.

- Use different colors to mark off the different fractions of pi. Some colors might overlap. Don't stress on that! Just make the thirds different than the fourths and the sixths.

The rest of the project will be explained on Thursday in class:

- In a corner, draw thumbnails of the five triangles. (Two of them look like line segments, the 0 and 90 degree base angle ones.) Label the sides with the appropriate 1,sq rt 3, sq rt 2.

- Next to that, fill in a small table of trig angles and sine, cosine and tangent ratios in quadrant I.

**Thurs April 12** Especially important tonight, please view:

Trick to remember basic trig table

Sign of trig functions in quadrants I, II, III, and IV

Do Sec 8.2 p 283 #1-10 and Sec 8.3 p 284 #1-5

**Fri-Sun April 13-15** Do worksheet Trig ratios of special angles, handed out on Friday.

View Deriving values of the unit circle

Then do make your own Unit Circle, either on the back of your circle art or on another sheet. The radius is 1 unit, so the (x, y) coordinates become (cos theta, sin theta). Fill in the points on the circle (as begun in class).

Especially important this weekend, view Finding coordinates of the point on the unit circle where the terminal side of angle theta intersects the circle.

Read Sec 8.4 Do pp 284-285 #1-9.

Week 13

**Mon-Tues April 16-17** View UNWINDING THE UNIT CIRCLE TO GRAPH TRIG FUNCTIONS

Read *thoroughly* Sec 8.5.

Memorize Basic graphs of trigonometric functions

Know domains and ranges of sine, cosine and tangent functions. Be able to sketch these accurately.

**Thurs April 19** I hope you took the initiative to start Sec 8.5 problems. If not, please do Sec 8.5 p 285 #2 a b d #3 a b #4 a b c

Have you viewed Graphing sine and cosine functions yet? Do so again before reading Graphing sine and cosine graphs and their transformations

Then view 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

**Fri-Sun April 20-22** Take-home, trig quiz 2.

You may use your unit circles and notes, but not another person.

Read Sec 8.6.

As done in class today, practice drawing small graphs of the following.

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, where the function is one-to-one. To the left of each graph, draw its inverse. Notice the x-axis is now the ratio and the y-axis is the angle.

Do Sec 8.6 p 286 #1-6.

Week 14

**Mon-Tues April 23-24** More practice on Worksheet on evaluating inverse trig fcns Only do #1-30

**Tues-Wed April 24-25** Finish up inverse functions.

Read 8.7 and view Proving a trig identity Example 1 and Proving a trig identity Example 2

**Thurs April 26** Do p 288 #3 and *pages 1 and 2* of worksheet Basic trig identities

Read Sec 8.8. See two video discussions.

**Friday April 27** Do worksheet Double and half-angle identities

Week 15

Be sure to do the take-home quizzes for desk checks.

Print these for tomorrow:

Have questions prepared for any and all of the worksheets for me to go over tomorrow (Tuesday).

Exam 4 is on Thursday.

people/mckenzie/math_108_hw.txt · Last modified: 2018/04/30 15:30 by mckenzie

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