Your course letter grade was submitted to the registrar May 2. Your course grade will be on-line at your "MyInfo" when they process them.
    We are happy for you to pick up your final exam. If your instructor is not here to hand it back, we will mail it to you if you leave us a self-addressed stamped business-sized envelope.

---

April 16
The Final Exam room and time is given here. Rooms are mostly new, so be sure sure you know the right room!
We recommend you study old final exams which are on-line here.
If you claim an academic time conflict, see here.
For the final exam you may bring a 5x8 double-sided sheet or card of notes written in your own hand. Make your card yourself.

There will be review sessions in Wilson 1-141 at 6:00-8:00 pm Sunday, April 28 and Monday, April 29, 2:00-4:00 pm in Wilson 1-141.

Warning:  We spend two full weeks on the three sections of Chapter 7. A lot of the final exam will be on Chapter 7, which it is full of new ideas that you must learn. Please continue to work on Precalculus all the way to the end of the semester. If you don't study Chapter 7 a poor final exam score will result and that will hurt your grade a lot. On the other hand, a good final exam score can help a lot. Take Chapter 7 seriously! (Here is what you need to know from Chapter 7.)

What is going to be on the exam? The final exam has about half its points on trig. Most of the trig is from Chapter 7 (Section 7.3 is on the exam, but not 7.4). You can expect
a multisided figure to solve as in Section 6.4
a derivation from Section 7.1
a derivation from a unit-circle figure as in Section 7.2  (resembling B17-B22)
a derivation from a right-triangle figure as in Section 7.2 (resembling B31-B44)
parts to find in a figure much like Figure 7.3.3
a derivation of one of the results from 7-3-2 through 7-3-5, given the previous results (like on a handout)
a problem of the sort found in 7.3 B4-48 that requires use of a trig identity. (The only trig identities you have to memorize are the Pythagorean Identity and the one for tangent. Any others you might need will be given.)
and more
    [We will have gone over these derivations in class several times. There will have been handouts covering these derivations. Memorize how the derivations go and then you can simply reproduce them on the exam.]

The final exam about half its points on the algebra from Chapters 1 through 5. You can expect:
problems resembling some of this semester's unit-exam problems that many students missed (Be sure you can do the previous exams from this semester!)
an expression to evaluate (like Section 1.2, B2-16)
a graph to read
lines in point-slope form
distance in a word problem
graphical factoring
percents in a word problem
word problems
an exponential equation to solve
and more

The formulas at the top of last semester's exam will again be there, as will the laws and identities at the top of its trig section.

---

April 10
This update has three parts:  About the results of Exam 3 and how you are doing in the course, about Chapter 7 and about the final exam.

    Section 6.4 has a lot on trig of the type used by surveyors. Here is a note on how surveyors formerly measured long distances. (It also tells you what an acre is.)

About Chapter 7:  Chapter 7 is different. Yes, we are nearing the end of the course, but there is still time for you to learn something new and different. In Chapter 7 you will learn how to derive trig results from simple pictures. You must learn the connections between simple results you know and other, less-familiar, results that can be derived from the things you know. Chapter 7 emphasizes reasoning. You must learn why the results follow from one another and how they connect. There will be a great deal of reasoning required on the final, so learn how it is done.
    Long ago we posted links to on-line trig activities. If you did not do them before, you will find them interesting and valuable for the current material and we strongly recommend you do them now.

Thoughts about Precalculus and Mathematics.  In mathematics, there are some things you simply must memorize. For example, you must memorize the definition of sine. Other things it is better if you understand them. For example, how are sine and cosine related? Both a unit-circle picture and a trig identity should leap to mind. 
    Chapter 7 requires memorization of the definition of the new term radian and some other things, but mostly emphasizes relations between trig functions. Most of these formulas (e.g. area of a sector) and identities (e.g. cos(θ + π/2) = - sin(θ)) are best learned by understanding them. Pictures help.  
    Previous homework has often emphasized doing calculations. Now, Chapter 7 asks you to understand trig identities in the same way that all higher math is understood--with well-known things connected together in a way that allows you to create (derive) and understand new things. We build from what is known to what is not yet known. This procedure is to pervasive in mathematics that much of the goal of Chapter 7 is to get you to be able to string together simple known things in order to derive other things (for example, trig identities).
    Sections 7.1, 7.2, and 7.3 give many important examples. Study how they fit and how those same methods can be used to create trig identities on demand, even if you do not memorize them.

Your Job.  In Chapter 7, your job is to learn how to derive results that are closely related to things you already know. Use a step by step process.

7.1   Learn that radian measure is defined by s = rθ. Learn how to convert from radians to degrees and vice versa. Learn how to derive the area of a sector. How to derive the arc length when the central angle is given in degrees.

7.2   Learn that angles are regarded as rotations on a unit circle which begin with initial side along the positive x-axis. Two angles are "coterminal" if they terminate at the same point. Therefore, they have the same trig-function values. An angle and its reference angle have the same trig function values, except possibly for the sign (they might have a negative sign). Learn how derive trig identities by representing an angle θ in the first quadrant (not near 45 degrees) and locating the angle in question, say θ+π, and reading the picture for the trig function values of the new angle and how they relate to the trig function values of θ.
        Learn how right triangles can be used to illustrate angles with various trig-function values (given with letters), and can be read, with the help of the Pythagorean Theorem, to yield other trig functions values. So, for example, if sin θ is x/2, we can derive tan θ just by looking at a well-labeled picture.

7.3  Learn about derivation and how complicated formulas can be derived by a sequence of simple steps. In particular, learn how the sum-of-angles trig formulas can be derived from a well-labeled picture (learn Figure 7.3.3), and how the other important trig identities follow step-by-step from them (that is, learn the entire sequence from 7.3.1 through 7.3.5).

(7.4 is interesting, but will not be on the final exam.)


Final Exam room alert!  6:00 pm, Tuesday, April 30
Most rooms are different!
class hour, section number, instructor,  exam room
8:00 (001) Brandon Smart      Reid 401       [New!]          
9:00 and 10:00 (002 and 003)  Jade Schmidt    Reid 402   [New!]
11:00 (004) Michael Schwager   Reid 101     [New]
12:00 (005) Alisia DeHart   Wilson Reid 102   [New!]
1:10 and 2:10 (006 and 007) Jocelyn Short   Reid 103  [Same room as Exam 2, but not Exam 3]

   Details about the final are posted above.

---

Here is the curve for Exam 3, Spring 2013:
85-87  A-;  88-100  A;  
75-77  B-;  78-81  B;  82-84  B+ ;  
60-62  C-;  63-71 C; 72-74  C+ ;     
50-52  D-;  53-56 D; 57-59  D+;
below 50  F

How are you doing?  Add your three exam scores (Don't average them). If your quizzes are comparable and your homework has been handed in regularly, if the total is
at least 250 of 300, you are on track for at least an A-
at least 220, you are on track for at least a B-
at least 180, you are on track for at least a C-
at least 150, you are on track for at least a D-
  149 or below, you are on track for an F.

If you have handed in almost all the homework on time, you may get a notch higher. Often a good homework number raises, say, a C to C+.

    Most students in line for an unacceptably low grade decide to drop. There are 200 points on the final, and they can make a big difference, but it is not common for students to do much better on the final than on the first three exams. However, it does happen and some students "get it together" and do much better on the final, in which case they are rewarded with a better grade. On the other hand, some students fail to retain what they learned for earlier exams and do worse on the final, which is comprehensive. A poor final can lower your grade a lot. You are expected to remember everything! So, the final can help a lot or hurt a lot.

The last day to drop is the Friday after Exam 3, April 12. Are you going to continue, or not? Make up your mind quickly. If you do not want a letter grade, fill out a "Drop form," get two signatures, including your adviser's signature, and submit it to Montana Hall by the end of Friday, in which case you will get a "W" (withdrawn) instead of a letter grade. A "W" on your transcript does not affect your GPA, but gives you no credit for the course. The "instructor's signature" can be satisfied in three ways--your actual instructor can sign it (go to class to get it), or Dr. Esty can sign it, or it may be signed by an administrative assistant in the Main Math Office (Wilson Hall 2-214). However, you also need your adviser's signature, so allow some time to find that person. If you stay and get a low grade, it will count in your GPA, but it can be replaced if you take the course again and do better (perhaps in the summer). Low grades are replaced and erased by taking the course again and doing better.

---

March 8
Prior to each exam there are review sessions in the evening, 6-8 pm, two days before the exam and the day before the exam. For Exam 3, the review sessions, open to all M-151 students, will be in Wilson 1-141.

Exam 3 is Tuesday, April 9, at 6:00 pm.  Most exams are in new rooms.
This time you may create and bring one 5x8 card (or 5x8 size piece of paper), both sides, with notes in your own writing.
Rooms:
class hour    instructor       exam room
8:00 (001) Brandon Smart      Wilson 1-122       [Different from Exam 2, but same as Exam 1]          
9:00 and 10:00 (002 and 003)  Jade Schmidt    EPS 103      [New. Do you know where the building is?]
11:00 (004) Michael Schwager   Wilson 1-142     [New]
12:00 (005) Alisia DeHart   Wilson 1-121   [Same as last time]
1:10 and 2:10 (006 and 007) Jocelyn Short   EPS 103  [New. Do you know where the building is?]
    Exam day there is no class at the regular time.

If you have an academic time conflict or a disability, see here.

Exam 3 covers 4.4 through 6.4. 58 out of the 100 points are on trig.
    The trig problems will go rapidly if you have your calculator programmed with the Law of Cosines, two ways.
    There will be two long problems from 6.4, one of which uses bearing the way we describe it on pages 380ff. If you don't understand bearing, you will lose a significant number of points. Please practice with your calculator a lot so you can do the calculations quickly. We expect you to do calculations with your calculator without writing long Law-of-Cosines equations on the exam page. However, at each stage you must tell us what law you are using.
    There will be a word problem with exponential growth or decay.
    You may create and bring to the exam one 5x8 card (or 5x8 size piece of paper), both sides, with notes in your own writing. (We will do that for the final exam, too.)
    For more about the exam and Chapter 6 material, read the part immediately below (posted March 19).
   

---

March 19
Do the on-line activities for Chapter 6. (Very helpful.)
In Chapter 6, your job is to ... . (What you need to know.)
Calculator programs for trig. (Very useful and time-saving.)
Read about Exam 3.  (What's on the exam?)
You may create and bring to the exam one 5x8 card (or 5x8 size piece of paper), both sides, with notes in your own writing.
     (Read everything down to the first horizontal line, labeled "Feb. 21".)

 


Most students really like trig and do very well in Chapter 6, triangle-trig. Take this chance to improve your grade and feel good about your math skills by devoting some time to this material.

Information about Trig (for Chapters 6 and 7):  Do the on-line trig activities and program your calculator with two versions of the Law of Cosines.

Cool interactive, web-based, activities,
    for learning trigonometry (Chapters 6 and 7)
    Learn and have fun at the same time! 
I searched youtube for trig lessons. Most seemed slow and dull. I did not find an interesting lecture, and most of the lectures are advertising teasers to get you to buy their whole course. The activities I recommend (linked above) are the best I have found on the web. I recommend you read your text and try to follow it closely. A site called "Dave's short trig course"
http://www.clarku.edu/~djoyce/trig/
is fine, but I don't see that it offers anything your text does not. (If you find something on the web that good for learning trig, please let me know.)

I strongly recommend you enter two versions of the Law of Cosines as programs into your calculator. The programs are very short and given here:

Calculator Programs:

Here is a TI-83 calculator program to do the Law of Cosines (SAS version to solve for the opposite side). Program 1:
Hit PRGM
            Follow each line here with ENTER. Comments you do not type are in black.
Go to NEW
Enter the name, letter by letter, say, LAWCOS   (the blinking "A" means Alphabetic mode which refers to the letters in green on your keyboard. Otherwise, to enter "D" hit "ALPHA (a green key) D")

Name:  LAWCOS
Prompt A,B,C
sqrt(A² + B² - 2*A*B*cos(C)) -> D
Disp D

[In the above, "sqrt" means the square root key, and "->" is the arrow or "STOre" key.]
In the above program A and B are adjacent sides and C is the included angle. D is the opposite side (which we would call lower-case "c" if we could).

Keystroke details:
1)  Hit "PRGM"
2)  go to "NEW" and hit "ENTER"
3)  Type in a name, say, "LAWCOS" and ENTER
4)  Find the "Prompt" command by hitting "PRGM" [again], arrow over to "I/O" (input/output), arrow down to "Prompt" and hit ENTER.
5)  Type in "A,B,C"  [Use the alpha key to use the alphabet. There is a comma key]
6)  Type in the formula (above)
7)  "Display" the result (D) by typing PRGM, I/O and selecting "Disp" and alpha D
8)  Quit and run it on a problem where you know the answer, to check it. (Reproduce one of the calculations in the text.)
 

Program 2: To use the Law of Cosines to solve for an angle, use this program (short!):

COSANG
Prompt A,B,C
cos^-1((C²-A²-B²)/(-2*A*B)) -> E
Disp E

In this program, A and B are adjacent sides and C is the opposite side, and E is the angle between the adjacent sides (which would normally be denoted upper-case "C"). "cos^-1" is "2nd cos" on your calculator.

This site will be updated when we get closer to Chapter 7.
Be sure to do the trig activities.

******

In Chapter 6, your job is to

6.1  Recognize the geometric cases and learn that the Angle-Side-Side case may yield two different triangles. Know the Pythagorean Theorem and that the sum of the angles of a triangle is 180 degrees. Learn the terms "alternate interior angles" and "vertical angles" discussed at the end of page 343 and beginning of 344. 

6.2.  Memorize the definitions of sine, cosine, and tangent two ways, both in a right triangle and in a unit circle (You must understand the unit-circle versions. The web activities are very good for that.) Learn how inverse sine and inverse cosine work, especially on the unit circle. Learn that solving "sin x = c" yields two possible answers, not just the one a calculator gives which is sometimes not the one you want. Memorize the values of the trig functions at the three most famous acute angles, 30, 45, and 60 degrees.

6.3.  Learn to solve triangles by learning the Law of Sines and Law of Cosines (two ways) and when to use them, described as geometric cases. Program them into your calculator and learn how to use them. In the A-S-S case the Law of Cosines and the Quadratic Formula can be combined to find the third side (and there will often be two answers). 

All you need to know to solve trig figures in Chapter 6 is:  the angles in a triangle sum to 180 degrees, the Pythagorean Theorem, the definitions of sine, cosine, and tangent, the Law of Sines, and the Law of Cosines.

6.4.  Learn to solve multi-sided figures by subdividing them into triangles and then using triangle-trig methods. Learn how "bearing" is expressed. Also, learn to sketch a reasonably good picture of trigonometric figures.

    It is not that much, but it does require some memorization.

Prior to each exam there are review sessions in the evening, 6-8 pm, two days before the exam and the day before the exam. For Exam 3, the review sessions, open to all M-151 students, will be in Wilson 1-141.

Exam 3 is Tuesday, April 9, at 6:00 pm.  Most exams are in new rooms.
This time you may create and bring one 5x8 card (or 5x8 size piece of paper), both sides, with notes in your own writing.
Rooms:
class hour    instructor       exam room
8:00 (001) Brandon Smart      Wilson 1-122       [Different from Exam 2, but same as Exam 1]          
9:00 and 10:00 (002 and 003)  Jade Schmidt    EPS 103      [New. Do you know where the building is?]
11:00 (004) Michael Schwager   Wilson 1-142     [New]
12:00 (005) Alisia DeHart   Wilson 1-121   [Same as last time]
1:10 and 2:10 (006 and 007) Jocelyn Short   EPS 103  [New. Do you know where the building is?]
    Exam day there is no class at the regular time.

If you have an academic time conflict or a disability, see here.

What is on the exam?  Exam 3 emphasizes Sections 4.4 through 6.4. (Yes, 4.4 will appear again.)  It will be about 60% on trig and 40% on material before trig, mostly logs and exponentials. Be careful when studying old exams. Some previous third exams only covered through Section 6.3, but this one will cover through 6.4, including multi-sided figures and bearing. (In the past, 6.4 was often on the Final Exam.) You are still responsible for all the older material, including formulas for the growth of money from the section on percents.
    This time you may create and bring one 5x8 card (or 5x8 size piece of paper), both sides, with notes in your own writing.
    The exam will give the Laws of Sines and Cosines. (You should have the Law of Cosines programmed into your calculator and know how to use it.)
    There is always either a Richter-scale problem or a decibel problem.
   Most exam questions address material newly learned in this course, not material you already know from previous courses. Expect questions at the level of the "B" problems in the text. We recommend you look at previous exams, which are available for purchase at CopyCats in the SUB and for viewing on-line here. You can study by working "B" problems from the text which are solved in the solutions manual. 

    The last day to drop without a letter grade in the course is Friday, April 12, three days after the exam. Make up your mind rapidly. Expect your course letter grade to be very similar to your exam letter grades, slightly modified by your homework and quiz performance if they are good. The final will be comprehensive and will cover some of everything. Because it worth twice a unit exam, a good final can help a lot and a bad final can hurt a lot.
    If you do not want a letter grade, fill out a "Drop form," get two signatures, and submit it to Montana Hall by the end of Friday, April 12, in which case you will get a "W" (withdrawn) which does not affect your GPA but gives you no credit for the course. The "instructor's signature" can be satisfied in several ways-- it can be signed by your actual instructor or Dr. Esty or an administrative assistant in the main math office (Wilson Hall 2-214). However, you also need your adviser's signature, so allow some time to find that person. If you stay and get a low grade, it will count in your GPA, but it can be replaced if you take the course again and do better. Low grades are replaced and erased by taking the course again and doing better.
    Many students still enrolled have not attended much recently. Probably they should drop. It is very rare for non-attending students to do well enough on exams to avoid bad grades.

Cognitively passive learning behaviors (surface-learning approaches)
    I came to class.
    I reviewed my class notes.
    I made index cards.
    I highlighted the text.

Cognitively active learning behaviors (deep learning approaches)
    I wrote my own study questions.
    I tried to figure out the answer before looking it up.
    I closed my notes and tested how much I remembered.
    I broke down complex processes step-by-step.

Here is a Harvard article on learning and how it relates to time and sleep.

---

Feb. 21

---

Feb. 21
Look at previous exams to get a feeling for what might be asked. There is usually, but not always:

a word problem with distance
a word problem with average percent change (Examples 24, 25 page 241-242)
finding a polynomial through points (3.4 Example 9, 4.2 Example 11)
a line problem that needs point-slope form  (the whole section 3.1)
a quadratic formula problem with unusual letters (page 134)
a problem where a square root must be eliminated (pages 222-224)
a problem requiring the use of properties of power functions (table, page 191)
numerous, mostly shorter, problems on other topics from 3.1 through 4.5.

    This time Exam 2 has four word problems. To save time, two of the four have instructions that read, "SET UP one equation with one unknown which could be solved for ... (whatever is asked for). [You not bother to actually solve it if your equation is correct]."   

Prior to each exam there are review sessions in the evening, 6-8 pm, two days before the exam and the day before the exam.
For Exam 2, the review sessions, open to all M-151 students, will be in Wilson 1-141. Come prepared to show you have seriously tried the problems you ask about. Asking questions on Monday is not sufficient preparation for a Tuesday exam. Most of your preparation should have been done long before Monday!
There will be no class at the regular hour on the day of the exam.

Exam 2 is Tuesday, March 5, at 6:00 pm. If you have a time conflict or a disability, see here.
Exam 2 Room Alert!  It is not in the usual room and most are not in last exam's room either. The room is:
M&F class hour, section number, instructor,       exam room
8:00 (001) Brandon Smart      Wilson 1-141                  
9:00 and 10:00 (002 and 003)  Jade Schmidt    Linfield 301      [Do you know where the building is?]
11:00 (004) Michael Schwager   Gaines 043    [Do you know where the building is?]
12:00 (005) Alisia DeHart   Wilson 1-121   [same as last time]
1:10 and 2:10 (006 and 007) Jocelyn Short   Reid 103  [across the hall from last time]
    Exam day there is no class at the regular time.

Exam 2 covers Sections 1.1-3.1-4.5. Old exams are on-line here.
For reasons discussed below (about the world changing rapidly), expect somewhat more emphasis on problems testing your reading and writing skills.

 
About Chapter 4. Your job is to:

4.1.  Learn the shapes of monomials and the approximate possible shapes of polynomials of degrees 1, 2, 3, 4, etc. Learn how many local extrema they can have and how many solutions a polynomial equation of degree n can have.

4.2.  Learn how to factor cubics that factor in integers by using the Factor Theorem and a graph.  Learn how the Factor Theorem and a graph makes factoring easy if the expression factors in integers.

4.3.  Eliminating a square root by squaring may introduce extraneous solutions. Learn to check for extraneous solutions in any problem where you square both sides. Learn that when the relevant theorem is stated with "if..., then..." there is a risk of extraneous solutions, but if the relevant theorem is stated with "iff" there is not. Learn how to solve the equation "x^p = c" for x, given the possible values of p and c.

4.4.  [This might be the most important section of all, for percents appear in every newspaper and percents are used when discussing  money, credit, investment, and changes of all kinds.]  Learn how percents are used to discuss change using multiplication. Successive application of percentage changes is given by successive multiplications. Learn to avoid addition and subtraction in percent problems. Learn how money grows (the Compound Interest Formula, 4-4-6) and how the APY (= effective rate) is computed. Averages are computed using roots, not division (4-4-8).

    This time Exam 2 emphasizes Sections 3.1-4.5, including 4.4 on percents, which the old Fall exams have but the old Spring exams do not (It was on Exam 3 in Spring 2011 and Spring 2012). The "Annuities" part of Section 4.4 (page 243) will not be on the exam. Of course, there will be word problems. We hope the reading and writing you have done have helped prepare you for doing word problems.
     Similar old exams are available at CopyCats in the SUB and on our site here. The top of the exam says which sections it covers.

4.5.  Rational functions are quotients of polynomials. The most important features occur where the top is zero (usually then the rational function value is 0) or the bottom is zero (usually then there is a vertical asymptote). The end-behavior-model determines horizontal asymptotes. If your graph doesn't look somewhat like its end-behavior-model for large values of x, your graph is not representative.

4.6.  Learn that inequalities can not necessarily be treated like equalities (equations) because multiplication (or division) by negative numbers would change the direction. Therefore, multiplication or division by expressions that might be negative is problematic. If an expression is compared to zero (say P(x)/Q(x) > 0), the Theorem on Zeros and Signs tells you to identify the zeros of P(x) and Q(x) and consider the intervals with those zeros as endpoints. The solution is some combination of those intervals. You can identify which combination from a good graph.
   Absolute value inequalities are very important in calculus, so you should learn how to convert "|x - c| < d" into an equivalent interval "a < x < b" and the interval "a < x < b" into an equivalent inequality of the form "|x - c| < d".

    (Section 4.6 will be on Exam 3, not Exam 2.)

---

Expect your course letter grade to resemble your exam letter grades, possibly modified upward if you almost always do the homework on time and take the required quizzes.
    If you did well, congratulations!
    If you want to do better next time,
1) study two hours outside class for each class hour, on average,
2) read the text (You learn to read by reading, and improving your math reading and writing skills is a major goal of this course)
3) use the Math Learning Center for free tutoring,
4) study efficiently with this advice and this advice from former students

As in any college course, your instructor does not have time to cover all the material during class. But the text covers it all. You are expected to read the text and learn from it outside class.

    The Math Department had an American instructor of high school math in China give a talk about high school in China. Here is a Chinese school week.

In Chapter 3, your job is to:

3.1  Change how you think about lines.  Learn to use the "point-slope" form and the "two-point" form of lines in preference to the famous "y = mx + b" (slope-intercept) form. Do not simplify to slope-intercept form (unless there is a good reason to). Learn how to use point-slope form and two-point form when the points are given functionally or with letters rather than numbers. Learn how linear interpolation works using the "two-point" form.

3.2  Learn how to "complete the square" of quadratics. Learn that when the square is complete the expression exhibits the location of the graph and its axis of symmetry, which is also visible in the Quadratic Formula. Learn how to apply the Quadratic Formula to solve equations in which the unknown is not "x" or the coefficients are not the usual letters (This is related to a good understanding of "placeholders").

3.3  Learn how the formula for distance in the plane is essentially the Pythagorean Theorem. Similarly, equations of circles are given by the distance formula and the Pythagorean Theorem.

3.4  Learn that quadratics which can be written "ax ² + bx + c" often may instead be written in factored form "k(x - b)(x - c)" (the "b" and the "c" are not the same in the two forms).  We can use graphs to factor and identify quadratics using the "Factor Theorem." If the graph of a quadratic intersects the x-axis at x = c, then "x - c" is a factor. The constant factor, k, is not determined by where the graph crosses the x-axis, however it can be found using one other point.

3.5  Learn that indirect word problems require you to "Build your own formula" which expresses the operations in the particular problem. Cue words indicate operations you express in your formula. Guess-and-check can help you see the operations you need to put into the formula. Usually we build specialized formulas from components that are well-known basic formulas, so write down relevant basic formulas. 

3.6.  Learn how to approach problems you don't know how to do! (This is what is called "problem solving.") The key is to begin writing the stated information symbolically (even if you don't, at first, see where it is going).

---

Jan. 31
Exam 1 information is below.

Can Smart Machines do your Job?
http://www.sci-tech-today.com/news/Can-Smart-Machines-Do-Your-Job-/story.xhtml?story_id=13200DRQLE20
January 25 this article came out reinforcing my point about what you are to learn in this course. The article begins by discussing a man who makes $67,000 a year whose job is being replaced by machines. It continues with a broader discussion of the economy and how many good jobs are disappearing. 

A very similar article, "New technology is erasing many middle class jobs," was printed in the Bozeman Daily Chronicle Sunday, Jan. 27, 2013: http://tinyurl.com/az5v6ra
(The full URL is here:)
http://www.heraldtribune.com/article/20130123/ARCHIVES/301231035/-1/todayspaper?Title=New-technology-is-erasing-many-middle-class-jobs-By-BERNARD-CONDON-and-PAUL-WISEMAN-AP-Business-Writers

---

Jan.24
There will be optional review sessions the Sunday and Monday before each exam and the final. They will be in Wilson 1-141 from 6:00 - 8:00 pm. Come prepared to show you have seriously tried the problems you ask about. Do not kid yourself that asking questions on Monday is good preparation for a Tuesday exam. Most of your preparation should have been done long before Monday!

Exam 1 Room Alert!  Exam 1 is Tuesday Feb. 5, at 6:00 pm. It is not in the usual room. The room is:
M&F class hour, section number, instructor,       exam room
8:00 (001) Brandon Smart      Wilson 1-122                          
9:00 and 10:00 (002 and 003) Jade Schmidt    Reid 105      [Do you know where the building is?]
11:00 (004) Michael Schwager   Wilson 1-132
12:00 (005) Alisia DeHart   Wilson 1-121
1:10 and 2:10 (006 and 007) Jocelyn Short   Reid 105
    Exam day there is no class at the regular time.

    If you have an academic time conflict with our 6:00 pm exam (say, you have a class that meets at 6:00 Tuesday evenings), or a documented disability (with a "blue card" from Student Services), please contact the course supervisor Prof. Esty right away:  994-5354 or westy at math.montana.edu.  See here for details. 

---

Jan. 15
About Exam 1: Exam problems are mostly like the "B" homework problems. Look at old versions of Exam 1, on-line here. However, not all old first exams cover the same sections. This semester the first exam covers Sections 1.1 through 2.3, and the old first exams only went through 2.1 or 2.2. Last Fall's exam covered through 2.2 (It says on the top of the exam which sections it covers.) So, be sure you can also do problems from Section 2.3 for this semester's exam.
    If there is something you don't know, or don't know how to do, be sure to study that. There are several levels of algebra, and most of the algebra you previously learned is at a lower level--a level that will not be emphasized on the exam. The exam tests you on higher-level skills--on material newly learned in this course. Make sure you can do the "B" problems.
    You are responsible for reading and writing mathematics. On the exam we will state theorems or definitions that you have not seen before and ask you to read them and use them. This is a skill that cannot be picked up in an hour or two. We strongly recommend you learn to read math by reading your text.
    On the exam we may ask you to state methods symbolically (as in Section 1.4). This is a reading and writing course and problems on the old exams show you we mean it. If you don't read the text and learn how symbolic mathematics is written, you will have a hard time with the exams. Read in order to learn to read and write.
    There are problems you will find hard if you have not put a lot of time in playing with your calculator. You do not develop calculator skills without practicing a lot.
    Be sure to bring your graphing calculator with the Quadratic Formula programmed into it.

We have free tutoring all day long in the "Math Learning Center". (The linked page lists hours with a Precalculus instructor. However, the MLC is closed the hour before the exam.)  

Exam 1, like previous exams, comes with instructions. It says, "Show clear supporting work on problems with several steps. Algebraic problems that display little or no supporting work will get little or no credit. You do not need to show work on one-step calculator problems. To solve numerical problems guess-and-check is legal unless you are requested to solve them 'algebraically.'”

Section summaries:  Your job is to
1.1.  Learn what it means for a problem to be indirect and to become comfortable with working indirectly, that is, writing about operations you don't actually do.

1.2. Learn how order is expressed in written mathematics and on your personal calculator so well that you can rapidly evaluate complicated expressions correctly. This requires learning how to insert parentheses that are not in the usual written mathematics. Practice until you can get five problems from B2-B16 correct in a row.

1.3.  Learn how functional notation is used to express sequences of operations. Learn to distinguish the function from the notation used to express it, and how to apply that function to expressions other than "x". (This is also discussed in Section 2.2.)

1.4.  Learn how to read definitions and theorems (They express mathematical methods). Learn how to write mathematical methods in symbolic notation. (This is a course-long project, begun in Section 1.1 and treated as the focus of Section 1.4. Reading and writing are essential to word problems, so learning to read and write symbolically is critical.)

1.5.  Learn to read graphs (that is, extract information they contain). Learn how to graph with your graphing calculator and obtain a "representative" graph. Learn to select and modify windows, and use the calculator's capabilities to determine key points on graphs. (This is continued in Section 2.1.)

1.6.  Recall the usual algebraic ways to solve equations. Learn to rapidly classify equations according to which way to solve them, chosen from the "four ways to solve an equation." (This is a section on making good algebraic decisions.)

2.1  Learn how to choose windows that make graphs "representative" or have a particular look. Learn how changes in the window will change the appearance of graphs. (This section continues Section 1.5)

2.2.  Learn how notation expresses functional composition. Learn how given graphs are affected by composition with addition, subtraction, multiplication, division, and attaching a negative sign.

2.3  Learn that solutions to "f(x) = c" may not be unique if the function is not "one-to-one." Learn how to recognize when a function is not one-to-one and how to deal with the complications that occur when your calculator has an inverse function but the original function is not one-to-one. 

---

Jan. 9, 2013

Thoughts about Learning.

Reading takes a lot of effort!  But, you will be learning an extremely valuable skill.