Weighting: All tests listed below, together will count 2/3 of the final grade. Final exam counts 1/3 of the final grade.

Attendance: C.B.U.'s policy states that a student who cuts eight (8) classes may be given a failing grade for the course. Attendance is taken at the beginning of each class, if you are not present at the beginning of class you are considered tardy. Two tardies counts as one absences. No food or drink in class, please.

In Class Tests: Four written tests (Grades: 3, 4, 7 & 8) will be given as indicated on the schedule sheet plus a final exam. Each test will be worth approximately 100 points. You should keep a record of your grade as the semester progresses and at the end of each quarter you will be informed of your score to date. If on any test you feel an error has been made you have one week to check it out; bring your test with you! If there are discrepancies, the mark book takes precedence unless the test paper shows otherwise.

Homework: There are two types of homework: daily and practice (available on Web).

Daily: A specific homework assignment will be given regularly. This assignment will be collected at the beginning of the next class. Place it on the teacher’s desk when entering. The exercise will be graded on clarity of presentation, correctness, neatness and a written comment dealing with the work and/or class that day. (Also see Homework Procedures below for more details.) 20 points will be allowed for each homework. If a homework is not turned in the grade is zero (0). A homework may be only one day late; after that the grade is zero. An on time homework with a grade less than 75% may be corrected for partial credit if resubmitted the next class after being graded. All of these homeworks will count as two more tests (Grades: 1 & 5).

Practice: The other homeworks, those given on the Homework Sheet will be collected on test days and the cumulative score on it MAY raise your final grade if you are close (0.5%) to the next highest letter grade! As you enter class place your homework folder on the overhead projector stand; you may pick it up at the same place usually by the end of the test. This grade can make a significant difference on your final grade.
 
 

Labs: An integral part of this course will be the math labs. Lab reports will be done in groups, one report per group. The number of points for a given lab will vary around 50 points. The cumulative lab scores will count as two more tests (Grades 2 & 6). If a lab is done poorly (less than 75%) you will be given the chance to redo it properly. Redos will be accepted for a one week period after being returned the first time. No redos or late work of any type will be accepted after Friday, December 3, 1999.

Materials: Mathematics (homework and tests) are to be done in pencil. Eraser and ruler needed for graphs. Quadrille paper needed for graphs. Use a yellow cover with prongs for lab reports and a red cover with prongs for homework. Grades will be written on the cover in green. Homework grades are recorded only on the cover until the end of the semester. Therefore, if grade is unreadable or cover lost, homework will be considered not turned in. TI-86 Graphing Calculator is essential.

Formats: Tests: Name in upper right-hand corner; Calculus I A or B underneath name, date beneath Calculus I A or B.

Daily Homework: Same as tests. Date assigned, page and problem number underneath your name, etc.

Procedures:

1. Use standard 8.5" ´ 11" paper.

2. Show all necessary work providing clear, yet concise explanations. Box in or circle all of your answers. 3. Arrange problems in numerical order. 4. Use a straightedge to draw straight lines. Quadrille paper is required for graphs; label axes and the scale marks and points as is appropriate. 5. Staple all work together; paper clips and dog-earing are not acceptable. 6. Place your first and last name, course and section, and date assigned in the upper right-hand corner.

7. Assignments are to be turned in when due at the beginning of class. Don't wait for them to be collected. Makeups on homework assignments are rare and must be approved ahead of time.

Practice Homework: Name and Calculus I A or B on the front cover as above in "Tests". Each set of homeworks must begin with a new set of papers, with the assignments: page/problem numbers listed on the upper right-hand corner. (See Rules 1 to 4 above.)

Lab Report: Same as for homework but also each lab report must have the title of the lab at the very top of the first page of the report. Be sure to follow the directions of the lab exactly. [The answers requiring verbal responses must always be in complete sentences (paragraphs)].

Graphs: Axes and legend always labeled. All straight lines drawn with a ruler. All points and lines drawn are to be labeled.
 
 

Learning Aids: On the reserve shelf in the library there is a copy of The Student's Solutions Manual (containing worked-out solutions to every other odd problem) that accompanies the text. The Calculus Problem Solver is also on the reserve shelf.

The Math Center is located in Science 104 in the morning and Science 151 in the afternoon and evenings. Phone (S 151): 321-3399.

There are students available to help you if you get stuck with your homework. They are also there to help you use the computer programs, especially Maple, which is available in the Center.
 
 

 Return to Top

---

Daily Homework Assignments, First Quarter

Date Assigned	Homework Assigned
8/25-W	11/11,14
8/27-F	21/1,2,3,4,8
8/30-M	23/12,24
9/1-W	23/30;   30/20
9/3-F	34/13,15
9/8-W	39/8,14,20;   44/4,10
9/10-F	44/32,35;  49/9,10
9/13-M	50/23,24,27,31,33
9/15-W	Study Sections 1.9, 1.10
9/17-F	58/11,16,29,35   65/4
9/20-M	65/11,15   Test on chapter 1
9/24-F	Find the formula for the slope of the tangent line to any point on the curve: y = f(x) = x^2 + 2x - 4 and then at the point:  x = 3.  Do the same for the curve: y = g(x) = x^3 + 1 but at the point x = 2.
9/27-M	94/6,9.10;  103/8.20
Notice:	Friday, 10/1, by 12 noon all test corrections are to be in.
9/29-W	RS/ 14,23;  111/8,14;  120/6,12
10/1-F	RS/ 26,33;  133/3,6;  Read over Section 3.1
10/6-W	133/10,11d;   142/5,,11
10/8-F	133/12b,e,f;  151/1
10/11-M	Study for test on chapter 2.  Test will only cover chapter 2 and what you will need from chapter 1.
Note:	Assignments for the Second quarter may be found under that heading.  These assignemtns will start with chapter 3, p.152.

Return to Top

---

Daily Homework Assignments, Second Quarter

Date Assigned	Assignment
Remember:	You don't have to repeat a problem on the practice homework if it is assigned as daily homework.
10/15-F	152/6,9;    159/Finish #1,14,24
10/25-M	Study
10/27-W	165/1,9,10,14
10/29-F	173/1,6,14,18
11/1-M	195/1, 4-24 even, 26,30,34  (I will correct 5 of these problems)  Be sure to write down all of the steps for at least 3 problems in 4 - 24!
11/3-W For in  class Friday	Problems to work in class Friday 11/5/99  Work together in your new lab groups. Turn in one set of problems for the group as in labs.  Each member of the group is to sign the set of problems.   Give the papers  to Dr. Rubin as he comes into class for his 10:00 class on Friday.  196/46  201/1 - 30 even, 34  206/1 - 24 even, 27, 28  Read (carefully)  section 4.2  p199 especially.  Read ahead section 4.4, The Chain Rule (a critical concept).
11/3-W Turn in  Monday 11/8	Three problems passed out on the Fundametal Theorem of Calculus.
11/8-M	211/1 - 30 even
11/10-W	217/1 - 30 even,  222/1 - 22 even, 23,24  PRACTICE, PRACTICE and then PRACTICE!  "When in doubt, write it out!"
11/12-F	226/3,7,9,11,13,16,21
11/15-M	Read carefully sections 5.1 and 5.3.   Test Friday
11/17-W	Study for test Friday:  Sections: 3.1 - 3.4 and 4.1 - 4.7. Get a good night's sleep.
Note:	Lab 10:  Drop Example # 6 completely.
11/19or22	247/4a, 5,7,13,17,22
11/24-W	253/4,7,9 and 232/10,11,13,15,18  and practice sheet (on your own)   Note change 10:55 11/24/99
11/29-M	259/5,10,14
12/1-W	232/2,3
12/3-F	275/3,  297/1,2,5,13  Note: No late homwork after today.
12/6-M	302/1-15 odd  (Think of two times that you could come to a review session.)
12/8-W	307/5,7,10  (For you to practice, it won't be collected)
Topics for  Friday's Test	1.)  Given a function, accurately graph it by plotting its x- and y-intercepts, max and mins and inflection points.  2.)   A word problem involving max and min  3.)   Find the linear approximation of a function at a given point.  4.)   Problems to integrate including differential equations and the FTC part 2  (There might be another question or two.  Consider these points a guide.)
Note: Exam 12/14-T 8-10AM K119	Calculus Review will take place in Science 112 Monday, 12/13 at 8:00 AM (You may see me in my office or R345 any time I am there except Monday evening!) Math Center Hours Exam Week:     Sunday: 6 - 10 PM S151;   Monday: 8:30 AM - 12:30 S104, 1 - 5 PM S151, 7:15 -10:15 PM S151
Final Exam Topics:	1.)  Definitions: derivative, definite integral, function, graph of function, limit, continuity (and maybe more)  2.)  Differentiation and integration problems  3.)  Using the calculator to find functions, estimate definite integrals (i.e. sum seq( ), graph functions with         proper   windows, etc.  4.)  The Fundamental Theorem and its geometric interpretation  5.)  Word problems: max/min, rate of change, various function applications e.g. natural growth  6.)  Interpreting graphs  7.)  (Check back later for a few more additions.  The list is not exhaustive!  Review old tests, homeorks and chapter reviews.   Consider these points a guide.) (If you would like a copy of your computer genereated final grade, bring a self-addressed stamped envelopoe to the exam.)

Return to Top

Practice Homework

Retrieve Practice Homework as Word 97 document

Section	Problems	Section	Problems
1.1	7,9,11,12, 13, 14, 19,20,22,23	4.4	1 – 30 odd, 35, 41, 43
1.2	7, 10, 12, 15, 17, 20, 22	4.5	1, 2 – 28 odd, 30, 32, 37
1.3	7,9,11, 5, 17,19,21, 22,27	4.6	1 - 23 odd, 27 33
1.4	1-8,9, 11, 15, 19, 21, 23	4.7	2, 4, 7, 10, 15, 16, 18, 21
1.5	odd number problems	4.8	1, 11, 12, 13, 18, 21
1.6	2-17,21,23,25,27	P237-8	odd numbers
1.7	2-23, 33,35,37	5.1	1, 5, 7, 8, 11, 13, 14, 15, 17, 18, 22, 27, 29
1.8	7,9,11,13,15,19, 27, 29,31,37	5.2	1, 5, 7, 9, 12, 18
1.9	3,5,13,18, 21,23,33,35	5.3	1, 3, 5,7, 10, 14
1.10	5,7,11,13,23,25,27	5.5	1, 2, 3, 9, 12, 19
1.11	odd numbers	P290	1-19 odd
2.1	3, 5,7,9,11,13,17	6.1	1, 2, 3, 5, 7, 9, 13, 14, 16
2.2	1,3,5,7,9,15,17,21,23	6.2	1 – 55 odd, 56, 59
2.3	3, 4, 8, 15, 17, 21, 25, 31	6.3	1,3,5, 7, 9, 13, 15
2.4	1, 7, 8, 9, 11, 14, 15	6.4	1, 5, 7,9,11, 13, 17, 19
2.5	3, 5, 9, 10, 11	P318	odd numbers
P133	1, 3, 5, 11a, 11d
P141	1, 2, 5, 11
3.1	1, 3, 5, 9, 11
3.2	1, 3, 5, 11, 15, 23,25
3.3	1, 5, 12, 16, 21
3.4	2, 7, 9, 11, 13, 15, 23
P186	3, 5, 8
4.1	odd numbers 1-24, 27, 29, 33, 42, 46
4.2	1 - 30 odd numbers, 33,35
4.3	1, 3 - 24 odd, 32, 34, 38

Return to Top

---

 
 
 
 
 
 

Topic Schedule

Retrieve Topic Schedule as Word 97 document

Monday	Wednesday	Friday
	§ 1.1, .2 8/25	§ 1. 3 8/27 8/25
§ 1.4, .5 8/30	§ 1.6, .7 9/1 Wed: Lab 1	§ 1.7, 8 9/3 Thur: Lab 1
Labor Day 9/6	§ 1.8 9/8 Wed: Lab 2	§ 1.9, 10 9/10 Thur: Lab 2
§ 1.10 9/13	§ 1.11 & Underpinnings 9/15 of Calculus, pp. 77, 82 Wed: Lab 3	Review, § 2.1, 2 9/17 Thur: Lab 3
§ 2.3 9/20	Test 1 9/22 Wed: Lab 4	§ 2.4, 5 9/24  Thur: Lab 4
Limits 9/27 and Continuity, p. 127	Differentiation & 9/29 Linear Approximation, p.136 Wed: Lab 5	§ 3.1, 2 10/1 Thur: Lab 5
§ 3.2, 3 10/4	§ 3.3 10/6 Wed: Lab 6	§ 3.4 10/8 Thur: Lab 6
Definite Integral, p 181 10/11	Test 2 10/13 Wed: Lab 7	§ 4.1, 2 10/15 Thur: Lab 7
10/18 Break	10/20 Break	10/22 Break
§ 4.2, 3 10/25	§ 4.3 10/27 Wed: Lab 8	§ 4.4 10/29 Thur: Lab 8
§ 4.5 11/1	§ 4.6 11/3 Wed: Lab 9	§ 4.7, 8 11/5 Thur: Lab 9
Practice p. 237 11/8	Catch Up 11/10 Wed: Lab 10	§ 5.1 11/12 Thur: Lab 10
§ 5.2 11/15	§ 5.3 11/17 Wed: Lab 11	Test 3 11/19 Thur: Lab 11
§ 5.5 11/22	MVT p. 286 11/24	11/26 Thanksgiving Holiday
§ 6.1, 2 11/29	§ 6.3 12/1 Wed: Lab 12	§ 6.3 12/3 Thur: Lab 12
§ 6.4 12/6	Test 4 12/8 Wed: Lab 13	Review 12/10 Thur: Lab 13
	Return to Top

---

 
 
 
 
 
 
 

Calculus I Notes in Power Point

Display Power Point:  Chapter 1 Notes    Retieve as Power Point Document:  Chapter 1 Notes

Display Power Point:   Cahpter 2 Notes    Retieve as Power Point Document:  Chapter 2 Notes

Display Power Point:  Chapter 3 Notes   Retrieve as Power Point Document:  Chapter 3 Notes

Retrieve Basic Derivative Formula as Word 97 Document

Display Power Point:   Chapter 5 Notes   Retrieve as Power Point Document:   Chapter 5 Notes

Display Power Point:  Chapter 6 Notes    Retrieve as Power Point Document:   Chapter 6 Notes

Return to Top

---

 
 

Previous Test #1

Retrieve Previsous Test #1  as Word 97 Document

Name_________________________________ /100

Math 131 A,B Calculus I Spring ’98 Test #1 1/30 = F BJB Directions:

Do all work neatly in the answer booklet provided. Show all of your work. Partial credit is given. Leave no problem unanswered. Number problems as they are numbered on this paper. Simplify your answers as much as possible and circle your final answer where appropriate. In graphing problems label all axes and legends. Label all points and lines drawn. All problems are worth 10 points except where noted.

In your own words give a correct definition of:
 

1. function -

Don’t write here, read the directions!

2. graph of a function – 3. Given the function  for -1 £ x £ 4, the domain of p, find p^-1(x) and its domain and graph y = p^-1(x) in its domain on the first set of axes. Use appropriate legends (units that fit each axis). (15 points) Using your calculator and given the function: y = f(x) = x⁴ - 2x³ + x - 4
  4. Find a window (having integer values) that "best shows" the important parts of the function f(x). (5 points)

5. Graph the function f(x) as it appears in your TI window on the second set of axes and be sure to label it properly.

  6. Find all of the solutions to the equation f(x) = 0 . (5 points) 7. Find the point(s) where y = g(x) = x intersects f(x). (5 points) 8. Drawing your own set of axes, draw (and label) a graph that accurately represents the temperature of the contents of a cup left overnight in a room. Assume the room is at 70° and the cup is originally filled with water slightly above the freezing point.   9. Each year the world’s annual consumption, C, of electricity rises at the rate of about 0.3%. If the consumption of electricity in 1997 was approximately 3* 10⁸ kilowatt-hours, what would you predict the consumption of electricity to be in 2001?   We are given the following data of the population of a small country over a ten-year period:

Year	1985	1987	1989	1991	1993	1995
Population	100,004	108,104	116,860	126,326	136,559	147,620

10. Find a formula that expresses the growth of the population in this country. (5 points) 11. What would you have expected the population to be in 1998? In 2001? (5 points) 12. In a short essay, cite the most significant thing you have learned in this course so far and give a reason why.
 

Return to Top

---

Algebra Reveiw Sheet

Retrieve Algebra Review Sheet as Word 97 Document

Math Review

This is your first assignment! It is to be handed in to your instructor on Friday, August 27^th. Use standard 8.5" x 11" paper, but not paper with a ragged edge torn from a composition notebook. Write legibly in pencil or erasable ink. Arrange problems in numerical order. Do not use a calculator. Show your work. Simplify all expressions and circle your answers.

1. Multiply:.                                            2. Subtract:  .

3. Divide:  .                                 4. Divide twenty-four by one-half.

5. Simplify:  .                                                 6. Simplify: .

7. If , find the value of  .

8. Suppose a friend covers the total bill including a tip of 20% at Perkins restaurant, but you want to reimburse her for the tip. If the total was $18, how much should you reimburse her?

  9. If you drive to Nashville from CBU, a distance of 210 miles, and it takes you three-and-a-half hours, what was your average speed?   10. Simplify: 3x - {2x - 2[x - (x - 1)] + 2} . 11. Solve:  .

12. Solve:  . 13. Find all solutions of the inequality:  .

14. Solve for x: (x - 4)(x + 8) = 7 - (3 - x)(x + 5) .

15. Multiply a²x⁴ + a⁴x² - 2a⁴ by 2x - 3a .

16. Suppose your scores on the first three math exams are: 80, 90, 100. What score would you need to make on the fourth exam in order to end up with a 91 average?

In Problems 17 through 20, factor the following expressions:

17.                          18. 

19.                             20. 

In Problems 21 through 26, perform the indicated operations on the following fractions and simplify:

21.                              22.

23.                          24. 

25. 26. 

27. Find  if  and .

28. The conversion of Celsius temperatures C  to Fahrenheit temperatures F is given by the formula . Find the Celsius temperature corresponding to .

  29. Consider the algebraic expression 7x³y² - 3xy + 4x² - y +12.

1. What is the coefficient of the second term?
2. What are the factors of the first term?
3. What is the degree of this expression?

In Problems 30 through 35, simplify the expressions with radicals and/or negative exponents so that there are only expressions with positive fractional exponents remaining.

30.                               31. 

32.                                      33. 

34. (x^-2 + y^-2)^-2                       35. 

Problems 36 and 37 concern graphing equations.

36. The following parts are about the equation: .
 

1. 
2. Write the equation in slope-intercept form.
3. Determine its slope.
4. Graph the equation on the set of axes and label it.
5. Where does the graph cross the x-axis?
6. Where does the graph cross the y-axis?
7. Graph the equation  and label it to distinguish it from the graph in (c).
8. What is the slope of the equation in (f)?

37. The following parts are about the equation: .
 

1. 
2. ; 
3. What type of function is it?
4. If , what type of equation would you have?
5. Solve the equation in (c).
6. What are the zeros of the function?
7. Graph and label the function on the set of axes.
8. Label the x- and y-intercepts of the function.
9. Find the vertex and label it on the graph.

Return to Top

---

1.)  I want to and I can

2.) Define the situation

3.) State the objective

4.) Explore the options

5.) Plan your method of attack

6.) Take action

7.)  Look back

 * * * * *     * * * * *                       * * * * *                    * * * * *

The Seven Step Problem Solving Paradigm in Detail for Math:

      1.)  I want to and I can:

   State the above at the beginning of the problem in writing.  Questions you should ask yourself to confirm that attitude include:  Have I read the chapter?  Have I reviewed my notes from class?  Am I willing to seek help if I get stuck?

 2.)  Define the situation:

  a)  Word Problems:
    i.   Read the problem carefully and complete-ly.
    ii.  State (write) what you are given: the things known, the things unknown.
    iii. Represent an unknown by a symbol.  Write down in words exactly what this symbols represents, including the proper units of measure.  (Sometimes more than one unknown and symbol will have be used but first try to write other unknowns in terms of the first unknown.)
    iv.  Draw a diagram, a box, a figure, etc. and as much as possible fill in the picture with the knowns and un-knowns.  Make a physical model out of paper, string, etc. if possible, and label it.

  b)  Graphing:
    i. Identify (write down) the type of func-tion.
    ii.  Identify the domain and range.  Specify them in proper mathematical symbols.
    iii. Consider if the problem is easier by hand or by use of a computer?

  c)  Algorithms:  Ask and answer these questions (in writing):
    i. What name is given to the process?
    ii. Under what conditions will I want to use this process?
    iii. How does this process depend upon the processes I've learned before?  i.e. what previous math processes might I need to work this type of problem?
    iv. How does it fit into my overall knowledge of mathematics? For example: Is this process a variation of the use of the Pythagorean Theorem?

  d)  Writing:
    i. Specify what type (letter, expository, freewrit-ing, transactional) of writing will be expected.
    ii. Specify who the audience is.
    iii. Specify exactly what the topic is.

 3.)  State the objective:

  a)  Word Problems:
    State exactly what it is you are looking for.  Write it out in your own words; then use a symbol from (2aiii.) above, if applicable.  Note what units the answer must have.

  b)  Graphing:  Answer these questions on paper:
    i. Is this to be a rough informal sketch or a formal well executed graph?
    ii. Are specific points required?
    iii. Is this strictly a mathematical graph or is it a graph applied to physical reality?

  c)  Algorithms:  Consider these questions and respond:
    i. Why should I learn this process?
    ii. What is this process good for in the larger scheme of things?
    iii. Does this process bring any refinement to what I have learned so far?
    iv. What kind of results can I expect from the process?

  d)  Writing:  Ask and answer:
    i. Is the writing to clarify my own thoughts?
    ii. Am I writing to inform someone else?
    iii. Am I writing in order to help start a thinking process?
    iv.  Is this work to be published?  i.e. is anyone else besides me, the author, going to see it?

 4.)  Explore the options:
   In general, think of any possible ways you might attack the situation.  Review anything that comes to mind concern-ing how you might be able to get to the problem, e.g. consult text, notes, friend, diction-ary, etc.  Make a list of those that you can think of.  Write down the steps you might follow in doing the problem.

  a)  Word Problems:
    i. Refer to other problems of a similar nature to see if any previous problems would be helpful.
    ii.   Look for relationships in the problem between the things that are given, facts (the knowns), and the things that might be needed to solve the problem but are not directly given (the unknowns).  Write down (underline, highlight) these relation-ships as part of the working of the prob-lem.
    iii. Translate these relationships into mathe-matical statements using the unknown(s).  (You may have to expand your diagram, box, figure, etc.)

  b)  Graphing:
    i. Do a simple sketch.
    ii. Plot several points by hand (using calcu-lator) and label them.
    iii. Select proper computer program.

  c)  Algorithms:
    i. Distinguish the problem as an expression or an equation.  Write down at the beginning of the problem what type it is.
    ii. Think of the mathematical operations that can be applied to this situation.  Write them down for reference.
    iii. Consult a reference book for other opera-tions that might apply, e.g. text book, give page.  (Write down name and page of book, if consulted.)

  d)  Writing:
    Determine the type, style and form of writing to use considering the factors above (2d and 3d).  Name the ones you use.

 5.)  Plan your method of attack:

  a)  Word Problems:
     Look at the mathematical statements (equa-tions, inequalities, etc.) from (4aii.) and list the possible methods you have learned for solving the types of relation-ships represented.  Write something down on paper immedi-ately!

  b)  Graphing:
    i. Choose proper graphing materials.
    ii. Set up legends (scaling).  Make them legible.

  c)  Algorithm:  Questions to consider (write out your respons-es):
    i. What rules do I know for sure apply?
    ii. If I'm not sure what which rules apply, how can I become more certain as to which rules do apply?
    iii. How can I check to see if I'm making mistakes?
    iv. How will I know when I'm finished?
    v. Write down the steps that make up the algorithm.

  d)  Writing:  (Cite sources used if applicable):
    i. Gather materials needed.
    ii. Collect information.
    iii. If appropriate, make an outline.

 6.)  Take action:
   In general, DO SOMETHING!  Write something down; doodle some picture; do something to the equation; sketch some sort of graph.  But in particular:

   a)  Word Problems:
    i.   Solve the equation(s) (inequalities) by a method that seems most applicable.  (See (6cii.) below.)
    ii.  Check the work on the solution by seeing if the value of the unknowns found make the origi-nal equation (statement) true.  (Substitute values found into the original equation.)

  b)  Graphing:
    i. Plot significant points, e.g. y-intercept
    ii. Solve for zeros of the function to get x-inter-cept(s).
    iii. Draw curve (accurately).

  c)  Algorithm:
    i. Write neatly.
    ii. If dealing with an equation, write only one equation per line, i.e. only one "=" per line.
    iii. If dealing with an expression, have only one "=" per line in an orderly column down the paper.
    iv. Every time an "=" is used, ask the ques-tion:  "Does this operation really maintain equali-ty?"  (Place a "t:" in front of each line when you are certain it is true.)

  d)  Writing:
    i. Get something down on paper, immediately!   Start writing ideas down and don't worry about form, spelling, syntax etc. until you run out of ideas.
    ii.   Review what you have written.
    iii. Perhaps make outline.
    iv. Write the composition.

 7.)  Look back:
   In general,  always look over the work you have done for gross errors.  Visually check out what you have just done.  Does it "look good?"  Does it "feel right?"  "Trust your feelings ('The FORCE is with you!')."

  a)  Word Problems:
    i.   Use the solution for the unknown(s) to answer the original question posed.  (See 3a.)  Write out:  "The answer to ..., is ..."
    ii.  Does the solution have the correct units? (Did you write them as part of (7ai.)?)
    iii. Does the solution seem plausible? i.e. Is it of the order of magnitude one could reasonably expect?  Is the answer in the "ballpark" of what you would expect the answer to be?  How does com-pare to any "benchmarks" you know?
    iv.  Could you go back and refine the problem?  Is there an easier way to do it that you can think of now?  Are there any notes you might want to keep on how to attack this type of problem in the fu-ture?

  b)  Graphing:  Answer the questions:
    i. Does the shape of the curve conform to the general form expected?
    ii. Do the plotted points fit the curve well?
    iii. Can anyone intelligently interpret this graph from what has been put down on the paper whether by hand or by computer?  If not, make appropriate corrections.

  c)  Algorithms:  Respond to the following:
    i. Have only allowable operations been used?
    ii. Is there an uneasy feeling about some step of the problem even if you placed "t:" in front of the line?
    iii. If there is a mistake in a long algebraic process, then, if after a quick run-through the error cannot be found, it is usually better and easier to start all over than to keep going back over the material again and again.  Save the old page(s) and turn it (them) in with the final copy.

  d)  Writing:
    Depending upon the purpose and audience of the paper, review the work and make revisions.  Turn in all rejects with the final copy.  Label the rejects as such.
 
 

Return to Top