Two evaluation surveys – Please take time to do both!

You should have received two separate survey email requests:

• One was from

Professor Foley (via Pearson)

– This one is an evaluation of the

Math 010/110 Teaching and Learning Center structure

. This will help us evaluate our course setup, software, tutor lab, TAs, and online grading/assignments/learning aids.

• The other was from

Dr. Chris Bendel

, MSCS dept. chair -- This one is an evaluation of the

teacher of your Math 010 or 110 class section.

This will give feedback to the department and to your own teacher about how you rate the effectiveness of instruction in your particular class section.

Your feedback on both of these surveys will be very helpful to us in evaluating and improving our teaching methods and the Math TLC program – THANK YOU!!!

Math Teaching and Learning Center and Open Lab Survey – If you haven’t had time to do this one yet, please take time to do it during class today!

LINK:

(Can also access through MyMathLab “ News Bulletins ” button if you didn’t save the email.)

https://uwstout.qualtrics.com/SE/

-

Your feedback on both of this survey will be very helpful to us in evaluating and improving the Math TLC program. THANK YOU!!!

Final Exam Review Assignments:

1. Four review homework assignments:

These are each worth 15 points, vs. the usual homework assignment of 4 points.

•

Unit 1 review homework (Chapters 1, 2, 3).

Due last Thursday.

•

Unit 2 review homework (Chapters 4, 5, 8):

Due today.

(If you need an extension on either the Unit 1 or 2 Review, see or email me TODAY so you can finish it and get access to the Unit 3 review HW.)

•

Unit 3 review homework (Chapter 6):

NOTE: You must get at least

80%

on the Unit 2 Review before you can start the Unit 3 review.

Due at the start of class tomorrow (Tuesday, May 7)

•

Unit 4 review homework (Chapter 7):

NOTE: You must get at least

80%

on the Unit 3 Review before you can start the Unit 4 review.

Due at the 8:00 p.m on Study Day (Wed., May 8)

Math 110 Final Exam:

• • •

Comprehensive

, worth

200 points

(20% of course grade) The practice final has

47 questions

, as does the regular final exam.

The questions will NOT be exactly the same as those on the regular final, but they will be similar in content and are distributed across sections the same way as on the regular final.

Each time you take the practice final you will get a different set of questions, AND your highest score will earn you that percentage of

20 extra credit points on the final

, so it will pay off if you can find the time to take it more than once.

•

IMPORTANT NOTE!!!

To get access to the practice final, you must have submitted all four final exam review homework assignments and have

scored at least 80% on each one

.

Math TLC Open Lab Hours:

Room 203 Jarvis Hall Science Wing

Regular hours through Tuesday, May 7 (8 AM – 6:30 PM)

Finals Week Open Lab Hours: Starting at

10 a.m

. on

Study Day

(Wed.) and

8 a.m

. on

Final Exam days

See schedule posted in the

classroom

and in the

open lab

and

online

at http://www.uwstout.edu/mathtlc

Make sure you know the day and time of the final exam for this section of Math 110.

Any questions on the Unit 2 Review Homework?

Please CLOSE YOUR LAPTOPS,

and turn off and put away your cell phones,

and get out your note taking materials.

Final Exam Review, Unit 3

Unit 3 Covers:

Chapter 6 (Rational expressions)

Unit 3: Chapter 6

(Rational Expressions) Don’t forget to review the

application problems

from section 6.6 homework and your work on the offline worksheet.

(Remember those fun problems about planes and cars, and three people doing a job at different rates?)

These were a common source of trouble for many students in previous semesters, so make sure you study the application problems on the Practice Test, and then

review the section 6.6 homework

if you need more work on those problems.

IMPORTANT:

Almost all problems in Chapter 6 on rational expressions require you to use one or more techniques for factoring polynomials.

DON’T FORGET TO REVIEW THESE FACTORING METHODS AND KNOW HOW AND WHEN TO USE EACH ONE!

Two methods that students often have trouble with are

factoring by grouping

and

sums/differences of cubes

, so make sure you review problems using these methods.

Domain

example: Find the domain of the expression

x

2

x

2  3

x

 4 

x

 20

Solution:

Set the denominator equal to zero and solve for x.

(Notice that this boils down to a factoring problem.)

x 2 – x – 20 = 0 (x – 5)(x + 4) = 0 (x – 5) = 0 gives x = 5, and (x + 4) = 0 gives x = -4 Therefore the domain is

{x | x ≠ 5 and x ≠ -4}

Example

Multiply the following rational expressions.

a

3 

a

3 2   

a

 2

a

3 6

a

2  2

b

3

Solution:

Factor each polynomial completely, then cancel all factors that appear on both the top and the bottom.

ANSWER

:

a

2  3

a

2

NOTE: This problem uses factoring by grouping , factoring out a GCF (twice!), and the sum of cubes formula. Whew!

Example

Add the following rational expressions.

x

2  4

x

 6 ,

x

2

x

 5

x

 6

x

2  4

x

 6 

x

2

x

 5

x

 6  (

x

4  3 )(

x

 2 )  (

x x

 3 )(

x

 2 )  4 (

x

 3 ) (

x

 3 )(

x

 2 )(

x

 3 ) 

x

(

x

 3 ) (

x

 3 )(

x

 2 )(

x

 3 ) (

x

4

x

  12 2 )(

x



x

2   3 )(

x

3

x

 3 )  (

x



x

2 

x

 12 2 )(

x

 3 )(

x

 3 ) 

Dividing a polynomial by a monomial:

Divide each term of the polynomial separately by the monomial.

Example

 12

a

3  36

a

 15 3

a

  12

a

3 3

a

 36

a

3

a

 15 3

a

  4

a

2  12  5

a

Example

Dividing a trinomial by a

binomial

: 7

x

 3 28

x

2 28

x

2 4

x

 5   23

x

12

x

 15   35 35

x x

 15  15

Divide

7

x

into 28

x

2 .

Multiply

4

x

times 7

x

+3.

Subtract

28

x

2 + 12

x

from 28

x

2 – 23

x

.

Bring down

-15.

Divide

7

x

into –35

x

.

Multiply

-5 times 7

x

+3.

Subtract

–35

x

–15 from –35

x

–15.

Nothing to

bring down

.

So our answer is 4

x

– 5.

HOW WOULD YOU CHECK THIS ANSWER???

Example of a

complex fraction

: 10 3x 5 6x .

Solution: view as a division problem: 10 ÷ 5 = 10 · 6x = 4 3x 6x 3x 5

Example: Solving a rational equation: Solve 2x + 1 = 1 2x – 1 x 2x – 1 .

Solution:

1. Multiply both sides by the LCD x(2x – 1).

This gives 2x(x) + 1(2x – 1) = 1(x) 2. Now simplify this equation: 2x 2 + 2x – 1 = x 2x 2 + x – 1 = 0 3. Solve either by factoring or by using the quadratic formula. Answers: x = -1, x = 1/2

Example (continued):

NOW

CHECK BOTH ANSWERS

in original equation: Note that when you plug in

x = -1

, everything checks out OK ( you get -1/3 = -1/3)

BUT

when you plug in

x = 1/2

, you get zeroes in some denominators, so this number is NOT a solution. (it gives 1 + 1 = 1 0 ½ 0 So the final answer is just x = -1 (if you write x = -1, 1/2 , you’ll get

ZERO

credit.)

REMINDER: Comprehensive Practice Final:

Once you finish the Unit 3 and 4 Final Review homework assignments with at least an 80% score, you will have access to the practice final, with as many attempts as you want.

The practice final is worth

10 points, plus a possible bonus of up to 20 extra credit points on the final exam.

Your best percentage score on the practice final will earn that percent of 10 points toward your course grade, plus that best score percent times 20 extra credit points will be added on to your final exam point score before partial credit points are added.

This makes it extremely important for you to make sure you work to get at least 80% on each of the four final exam review homework assignments so that you can get access to the practice final.

Math TLC Open Lab Hours:

Room 203 Jarvis Hall Science Wing

Regular hours through Tuesday, May 7 (8 AM – 6:30 PM)

Finals Week Open Lab Hours: Starting at

10 a.m

. on

Study Day

(Wed.) and

8 a.m

. on

Final Exam days

See schedule posted in the

classroom

and in the

open lab

and

online

at http://www.uwstout.edu/mathtlc