"What do I need to get on Test 3 and the Final to get an ___ grade in this course?"

 

 

 

To:   Students of Marion W. Alexander

Date:   November 20,  2016.

How to calculate what score you should aim for on Test 3 and/or  the Final Exam to achieve your overall course grade objective.

 

Here's a question I hear a lot around the end of every semester: 

"What grade do I need to get on the final exam to be able to pass this course?"   

or

"What grade do I need to be able to get an "A" in this course?"   

 

       This document is here on my Learning Web page now  to help all my students learn how to make this sort of calculation for themselves,  at any point in the course.

         All you need to do this are the papers you have been handed back (the scores on them, that is) and your class' syllabus (always up on the Learning Web).    Let's just suppose your current class' syllabus has this,  under  "Assessments:"

 

                                    Assessments

 

                                                            Weekly quizzes               10%

                                                            Test 1                               20%

                                                            Test 2                               20%

                                                            Test 3                               25%

                                                            Final Exam                     25%

 

And... let's assume that you, Sam SAMPLE,  have gathered your scores and they are

                  Average on the Weekly quizzes

                               (after dropping lowest)                           76%

                                                            Test 1                               11%

                                                            Test 2                               59%

                                                            Test 3                                ??%

                                                            Final Exam                       ??%

 

 

Suppose you are doing this calculation before Test 3.   You don't know how you'll do on it and the final, but you HOPE to get grade "X,"  and that grade will help you achieve your overall course grade objective.   So,  you now make this assumption:

 

 

Average on the Weekly quizzes

                               (after dropping lowest)                           76%

                                                            Test 1                               11%

                                                            Test 2                               59%

                                                            Test 3                                X%

                                                            Final Exam                       X%

 

 

     A student with these type of grades may be wondering if they can pass the course.   Passing with a "C" requires that your

overall course grade is  a 70% or above.     Currently,  they are not doing  too well:

 

 

 

Current Score calculation for Sam Sample:

 

                                                ~10% of quiz grade is  76%   (taking their current quiz average as the final one,  even though there                                                                                                                      might be more quizzes to be taken.)

 

                                                20% of grade is Test 1 score of  11

                                                20% of grade is Test 2 score of  59.

 

                        So,  with only 50% of the grades available,  we would say Sam Sample's current grade is

 

                        Current grade =  (.10 * 76  +  .20* 11  + .20 * 59) / 50  =  21.6 / 50 =  .432    Current grade is 43%.

 

                         If Sam Sample's  current average is a 43%,  then they need to change how they study

                                                               and how they prepare for tests!      43%  would earn an "F."

 

 

So,  what grade,  "X," does Sam need on the Final  AND on Test 3 to recover from the first part of the semester.  Assuming that the grading policy  "the final exam can replace the worst midterm score,  assuming it exceeds it," is still in place,  Sam  can hope that "X" is GREATER THAN their worst midterm score,  that  "11" on Test 1.    Also,  we are going to assume that Sam does the same "much better score,"   that "X,"  on Test 3, as well.       

 

         Under those 2 crucial assumptions,   Sam could use this inequality to decide what is possible or what is not:

 

 

     What "X" would make

 

                                    .10 * 76  +  .20* X  + .20 * 59 +  .25*X + .25*X    ≥   70   ???

 

     Note 1:   If   "X" turns out to be greater than 100,  then it is impossible for Sam to pass this course.

    

     Note 2:   You can use the same  inequality to figure out what they would need to get a "B" by replacing the 70 with an 80,   what they would need to get an  "A" by replacing the 70 with a 90.

 

 

 

 

 

    

      So,  we solve for "X" in the inequality above:

 

                                                7.6  +  .20* X  + 11.8  +  .25*X + .25*X   ≥  70  

 

                                                7.6  +  .20* X  + 11.8  +  .25*X + .25*X   ≥   70  

 

                                                7.6   + 11.8  +  .20*X  +  .25*X + .25*X   ≥ 70  

 

                                                     19.4         +  .20*X  +  .25*X + .25*X   ≥ 70  

 

                                                                          .20*X  +  .25*X + .25*X ≥  70 -  19.4

 

                                                                          .20*X  +  .25*X + .25*X   ≥   50.6

 

                                                                                                        .70*X ≥    50.6

 

                                                                                                                X   ≥   50.6/.70

 

                                                                                                                   X   ≥   72.285 

 

 

                             So,  the news is good for Sam,   having done this calculation before Test 3,  that all they need to do,  to get a

                                                                                  "C" overall,  since 70% of the grade is still accessible to change,  that all they

                                                                                            need to do is achieve a 72% or higher on BOTH Test 3 and the Final.

 

 

 

 

 

Cautionary note!

 

 

                    However,  Sam would be counseled that  a LOT needs to change in their study habits.   If they continue as they

                                             have been,  the best prediction of how they are actually going to do on  Test 3 and the final is the

                                              average of how they have done on TESTS in that class  so far,  i.e. the average of the 11 and the 59,

                                              which is just a   (11 + 59)/2  = 35%  !

 

 

                    IF Sam just keeps studying as they have been their grade on the semester grade sheet will look like

 

                                                10 * 76  +  .20* X 35  + .20 * 59 +  .25*35 + .25* 35  = 43.9%,    which is an "F."