Problem of the Week
Hilton Memorial Lecture
WELCOME TO MATH 106
Refer to this page for daily announcements, assignments, and other resources and materials (including videos, pdfs, and even links for emergency remote meetings).
Revised schedule will be posted here soon.
NOTE: Each assignment is written on the day you are to do it, not the day it is due. So an assignment on Tuesday is to be done by Thursday. Tues assignments are usually a bit longer than other days.
I do not collect assignments unless I announce ahead of time that I will do so. It is up to you to work them through and to have questions for me when the class next meets.
WEEk 1 AUG 23-26
ALL CLASSES NOW MEET ALL DAYS IN SCIENCE II ROOM 255
Note, you can access a free e-book for about 12 more days at BVT press. Enter A2826662 in the Instant Access Code field and click on the “Go” button. Follow instructions to create an account.
WEEKEND AUG 26-28
Do this quiz as practice, using your notes. Hand it in with your actual quiz tomorrow.
WEEK 2 AUG 29-SEPT 2
* Mini-videos to watch tonight: Rules of negative numbers
Evaluating algebraic expressions
Thursday I was out this day, but you should have read this anyway.
Friday through Labor Day Though we will not have covered much into rational (“fractional”) exponents by the end of Friday's lecture, please read those sections and view the essential videos on them at the bottom of this homework section.
Here are Lecture Notes Week 2
WEEK 3 SEPT 6-9
Tuesday Repeating the exercises from the weekend: do these, and be ready with questions for me!
Do Sec 8.1 (p 279) #15-67 every other odd Do Sec 8.2 (p 284) #1-71 every other odd
At the top of this page, under the syllabus, is the Schedule and Readings and Exercise List for the semester
Start preparing for Exam 1, Monday Sept 19!
WEEK 4 SEPT 12-16
Mon and Tues Finish the Sec 8.4 homework – here's another video on Simplifying radicals
View Combining radicals with addition and subtraction and Rationalizing the denominator
Read Sec 8.5 and do the assigned p 301 #1-43 odd (as many as you can with the reading and the videos as a guide)
IMPORTANT: You will not need to rationalize a two term denominator on this exam!
Watch the Office hour Thursday video!
Watch for the review sheet soon! Work on it and bring your work to class to ask questions tomorrow ~
Friday Exam 1 has been moved to Monday, Sept 19.
There’s an excellent set of review exercises in your book!! See pp 45-49 for Ch 1 and pp 312-316 for Ch 8. Exclude imaginary numbers (anything with i) and rationalizing denominators if they entail sums or differences of radicals, which requires radicals.
WEEK 5 Sept 19-23
FRIDAY WE WILL MEET REMOTELY AT THE ZOOM LINK
Friday 9/23 through Wednesday 9/28
Sunday posting Here's the weekend homework!
WEEK 6 Sept 28-30
I accidentally posted a shorter version of the quiz than what I handed out in class on Friday. As long as you handed in one of these papers, you will have your homework credit. Obviously, I prefer you be in class and get the handout in order to avoid this kind of situation.
For tonight, go back and read sections 2.4 and 2.5. No written homework tonight, as I worked on something different with you today. However, please watch these videos on absolute value equations and inequalities:
Solving absolute value equations
Solving absolute value inequalities example 1
Solving absolute value inequalities example 2
Solving absolute value inequalities example 3
WEEKEND HW A familiar topic that you’ll enjoy!
Read Sec 7.1 and 7.2 Slope of line, equations of lines
Graphing lines from a point and slope
Find equation of line using point-slope form
Do exercises in Sec 7.1 (p 242) #2-20 even & Sec 7.2 (p 251) #2-30 even. (The videos will be very helpful.)
I’ll desk check these on Monday; show your work and be sure you show all your work!
WEEK 7 OCT 3-7
Monday There's a mini-quiz on absolute value equation and inequalities tomorrow (Tuesday)–no make-ups, don't miss it!
Practice question |5 - x| = 9 |5 - x| < 9 |5 - x| > 9
Solve each, expressing the answer algebraically, graphically, in interval notation.
Tuesday-Thursday By now you should be able to finish Sec 7.2 (p 251) #2-58 even
I will update the schedule to reflect our pace and topics in class. No quiz tomorrow.
We will finish Ch 7 tomorrow and Monday, so please bring your Ch 7 pp (all of them) to class Friday.
WEEKEND OCT 7-9
Look over Lecture notes from the last 2 weeks. The first page of Friday's outlines the topics for Exam 2, which is Thursday. I'm adding percent word problems. See practice problems under Monday homework.
IMPORTANT: The first part of Exam 2 will be on Thursday and the second part on Monday. We will go over word problems Friday and they start the new material Tuesday.
Thanks to Amanda for asking for better detail on the percent problems!
Wednesday Since Exam 2 is moved to Friday/Monday, I will have extra office hours tomorrow (Thursday) from 2 to 4.
You can also, at any time on the following fliers, see an EOP tutor:
FALL BREAK WEEKEND HOMEWORK OCT 21-23
Friday-Sunday REQUIRED VIEWING ON POLYNOMIALS
The next section is a topic that you have done recently, either during summer workshop or in several high school mathematics classes.
We are several sections behind! You are responsible for watching these videos and doing the worksheets that form the basis of Unit 4.
The terrific internet teacher Professor Dave gives lectures that are very clear and enjoyable. Most of these videos have a 'Checking comprehension' section at the end. Do these sections. They will help you with the homework.
DO ODD NUMBERED PROBLEMS: I WILL DESKCHECK THE WORKSHEETS ON MONDAY
All the worksheets will come from the **Open access text**
Over the weekend you did work from Sections 5.1, 5.2 and 6.1. Worksheet answers are on the following pp of this pdf:
Polynomial wksht 4--Factor by grouping
Polynomial wksht 5--Trinomial factoring, leading coeff = 1
"First Year math tutoring hours"
Dan McKinney "Math Master tutoring and review sessions"
In Open Access Text do:
Poly wksht 6 -- factoring, leading coeff NOT = 1, do odd only
Poly wksht 7 -- Factoring special products, do all odd except #30-40
And if you like, Poly wksht 8 -- Factoring all kinds, your choice for practice
Do Poly wksht 9 -- Solving quadratic equations by factoring, odd only (first several are already factored)
View: Professor Dave shows how to complete the square to solve for the roots of a quadratic trinomial we can’t factor (this is a replacement of the previous one; Professor Dave uses the familiar formula)
Do 1-8 in Poly wksht 10 -- Complete the square, fill in the value that completes the square
Professor Dave derives the quadratic formula for finding the roots of a quadratic equation
Do Poly wksht 11 --Solving quadratic equations by quadratic formula , odd only
Mon-Wed Finishing quadratic polynomials and study for Exam 3
Exam 3 topics
General form of a polynomial expression in x: be able to identify degree and coefficients; sometimes the coefficients are zero because a term is not seen.
Given a list of expressions in x, be able to eliminate those which are NOT polynomials.
Evaluate polynomial expressions for a given x.
Remember, the square root of 1 is 1 and the square root of 0 is 0.
Factoring by GCF (both numerical and variable – know the exponent rule that dividing like bases requires subtracting the exponents); factoring by trinomial factoring, factoring by grouping; factoring special products (difference of squares.
There is no factoring for a sum of squares).
Reduce a rational expression (which is a polynomial divided by another polynomial) by factoring them.
(a - b)/(b - a) = -1
Completing a square: find the constant to add to the x terms so you create a square of a sum or a difference.
We use the zero product property on the factored polynomial to find the roots of the polynomial equation. It is this: if AB = 0 then either A = 0 or B = 0.
Be able find the roots (x-intercepts, zeros) of quadratic equations by factoring and/or by using the quadratic formula (which comes from completing the square).
YOU MUST MEMORIZE THE QUADRATIC FORMULA.
General form of the quadratic polynomial equation y = ax^2 + bx + c, whose graph is a parabola.
Know that the y-intercept of any polynomial is simply the constant coefficient ao. In the case of the quadratic (parabola), it is simply the c.
Reducing roots after using the quadratic formula. This entails radical simplification and regular fraction reducing.
Two-term quadratics don't need to be factored. Just use the fact that if x^2 - c = 0, then x = +/- square root of c; but if x^2 + c = 0, then no real number solution exists.
Be able to graph these simple two-term quadratics:
y = x^2, y = x^2 + c, and y = x^2 - c; know that the first has one root, (0, 0), which is also its y intercept. The second has no roots, only a y-intercept. The third has two roots, x = +/- c.
All parabolas have a y-intercept, but they may be lacking roots.
Go over the Lecture notes for Weeks 9 and 10 up through Tues review day. Look over the worksheets and any problems you had to do in the Kohlman text.
WEEKEND NOV 6-7
Solving systems of linear equations! You can do this without me. It's all algebra we have done. Have at it!
Solving linear systems by substitution
Mon-Tues I didn't put any hw up on Monday, my oversight!!
Friday to Sunday
So please view Prof Anil Kumar's explanation, which is given in clear, deliberative detail. He is one of my favorite internet teachers: Domain with a quadratic under a radical
ANNOUNCEMENT REGARDING TUES/THURS CLASS TIMES:
Except for Tuesday, Nov 29, Unit 4 exam day, the 8:30 class will begin at 8:45 and end the usual time, and the 10:05 class will begin at the usual time and end at 11:15. It is imperative you arrive on time for these classes!
Monday and Friday classes are at the usual times.
On Thursday, we will go over Worksheets 13 and 14, so please be sure all these are done, or if you had trouble, you know which problems you want to see especially.
WEEK 13 THANKSGIVING WEEK
WEEK 14 Exam 4 and final topic
CHANGE OF EXAM DATE
Because I never posted the worksheet and video for function composition, I must move the exam to Thursday.
View Function composition
Read the examples and do all the problems on this Worksheet 16 -- Function composition
TOMORROW IS THE FULL 85 MINUTES, so be on time, 8:30, and second class you will stay till 11:30.
WEEKEND DEC 3-4
This will be desk checked – intro material was covered Friday; if you were absent, seek notes from classmates
View Inverse functions
Read the material and do all #1-10 on Worksheet 17 -- Inverse functions
Monday Do 11-39 odd, finding the inverse function in Worksheet 17 -- Inverse functions (review the video therein)
Tuesday classes will meet remotely at the link I send a few minutes before your class (8:30 and 10:05)
Thursday-Friday This is the last homework. If you ignore it before tomorrow you will be lost. Watch the videos, read the worksheets and do the problems.