Point Rebate Information
Math 126
Fall 2005
R. Koehler

Be sure to follow all these directions:

• Write on one side of each page, only.
• Do not use both sides of any sheet!!!!!   I will not give any credit for anything written on the back of any rebate page..
• Include your test paper.
• Staple your test paper and rebate pages together, with the test paper on the top, and your rebate pages in order underneath.

Basic Requirements
You may earn back up to 50% of the points that you miss on any test or quiz, except for the final examination. For example, if you score 18 out of 30 on a quiz, you missed 12 points. Therefore, if you turn in point rebates that is wholly acceptable, you may earn back 50% of 12 points = 6 points, making your quiz grade 18 + 6 = 24 out of 30. Your rebate may be worth less than the 50%. This score is largely subjective.

Point rebates are due at the beginning of the next class after the quiz/test is returned to the class. If you are absent when papers are returned, it is your responsibility to get your paper from me, either in class or during office hours. No late point rebates will be accepted. Rebates may be done on quizzes and tests, only. There are no point rebates on problem sets, nor on the final exam.

Neatness counts! Your rebate must be neat and legible. Remember, the points you earn back on your rebate is largely a subjective rating of how well you have convinced me that you now know the concept.

What I am looking for when I read your point rebate
As you do your point rebate, keep in mind that the underlying goal of your point rebate must be to convince me that you now know how to do the problem, and it is highly unlikely that you will make the same or a similar mistake again.

What you must do
You must include the following in your point rebate : You do not need to copy the question - just be sure to include you test paper.

1. If it is numerical/algebraic, or involves work to find the answer, you must show a complete and correct solution to the problem with all steps shown, regardless of the error you made. Do not just give just the answer.  If the answer is non-numeric in nature, just the correct answer must be stated. Part 2 will be your justification.
2. A brief statement of the correct procedure, each concept, and/or each definition involved in finding the answer.
3. Your wrong answer, and a brief statement of what you did incorrectly.

• If #1 above is not done or is incorrect, no points may be gained back.
• If you believe your original answer may actually be a correct one, and does not agree with mine, give a full justification for your answer, instead of the statement of what you did incorrectly.

Example 1:    Find the mean of the data 50, 70, 90.
Your work – what you show on your rebate page(Do NOT copy the entire statement of the problem):

1. 50 + 70 + 90 = 210
   210 / 3 = 70 ANS
2. The mean or average of a set of data is the sum of the data values, divided by the number of data items.
3. I got the answer of 150. Instead of adding the three numbers and then dividing by 3, I entered into the calculator: 50 + 70 + 90/3. When I entered this, I got 150, because only the 90 was divided by 3
   I should have put parentheses around the three data numbers: (50 + 70 + 90)/3 This forces the three numbers to be added first, and then divided by 3, and gives the correct answer of 70.

Example 2:  Write an equation of the linear function f (x) for which f (2) = 5 and f (6) = -3 .
Your work – what you show on your rebate page (Do NOT copy the entire statement of the problem):

     1.  The line passes through the points  (2, 5)  and (6, -3) ,
          Thus the slope is (5 - -3)/(2 - 6) = -2
          Using   y - y1 = m (x - x1) , and substuting either one of the pointspoint and tthe slope:
                     y - 5 = -2 (x-2)
                     y - 5 = -2x + 4
                           y = -2x + 9   or  f (x) = -2x + 9
      2.  Since f (2) = 5 , the line passes through (2, 5), and since f (6) = -3, it also passes 
           through  the point (6, -3).  We then can use the slope formula to find the slope of the line.
           Finally, substitute either poijnt together with the slope into the point-slope form for the
           equation of a line and solsving for y, the result is obtained.
       3. My answer was f (x) = -2x - 3.  My error was forgetting the parentheses around
           the x - 2, and as a result, not distributing the -2 over the entire -2 as well as the x.  .. 
         

Example 3:     Find the derivative of the function f (x) = 3x⁴ - 2x³ + x - 5
Your work – what you show on your rebate page (Do NOT copy the entire statement of the problem):

1. f (x) = 3x⁴ - 2x³ + x - 5
   so f ' (x) = 4(3)x^4-1 - 3(2)x^3-1 + 1x^1-1 - 0 = 12x³ - 6x² + 1
2. Differentiate term-by-term. When finding the derivative of a single algebraic term, use the Power Law:  multiply the coefficient of the term by the exponent on x; then lower the exponent by one. To find the derivative of a polynomial, differentiate each term separately. The derivative of a term of degree 1 is the coefficient, and the derivative of a constant is 0.
3. My answer was 12x³ - 6x² + 1 - 5. I forgot that the derivative of the constant, 5, should be zero.
   I just copied the 5 into the derivative. I should have ignored it.