Under an HP TfT grant, a Calculus II redesign was developed that enhanced the standard curriculum with field trips, science labs student in class presentations, online groups and web based activities.   Because students were required to learn more than the standard curriculum -about Calculus applications to various fields, how to write Power Point presentations, use Excel, Mathematica etc. - at the same amount of class time, it was necessary to address the question whether the traditional curriculum was covered in the same depth.  For that purpose a control class with similar student body composition was used each semester and the students from the two groups (the class that had adopted the redesign and the control class) were asked common test questions during their testing times.  Both classes were meting M-F mornings, and had similar student composition.  Confidence intervals were constructed for a total of 18 questions that showed the performance of the two groups in traditional curriculum questions not to be of significant difference.  Representative examples of the results are given below.

In addition, the Sp06 section of Calculus II that was taught with the redesign was administered the same final exam as the section taught in Fall of 2004 by the same instructor at the same institution;  the results are summarized at the end of this page.  At the 5% level of significance, the average scores in the Sp06 section were higher.

Problem A:  (10 points) In each part, match the differential equation with the correct direction field.  Justify your answer. (3 possible answers were given)

a)                                 b)

Problem B:  (10 points) The region bounded by  and  is rotated about the line .  Set up the appropriate integral to find the volume of the resulting solid.  (Do not evaluate the integral.)

Problem C:  (10 points) Solve the initial value problem  , .  Express your answer as an explicit function.

Problem D:  (10 points) Suppose you want to find the arc length of the curve  from  to .  Set up the appropriate integral. (Do not evaluate the integral).

Problem E:  (10 points) Solve the differential equation .  Express your answer as an explicit function of x.

Problem F:  (10 points) At time t=0 a tank contains 25 ounces of salt dissolved in 100 gal of water. Then brine containing 4 ounces of alt per gallon of brine is allowed to enter the tank at a rate of 3gal/min. and the mixed solution is drained from the tank at the same rate.  How much salt is in the tank after 25 min?

Problem G:  (10 points) At time t=0 a tank contains 25 ounces of salt dissolved in 100 gal of water. Then brine containing 4 ounces of alt per gallon of brine is allowed to enter the tank at a rate of 3gal/min. and the mixed solution is drained from the tank at the same rate.  How much salt is in the tank after 25 min?

COMPREHENSIVE FINAL EXAM.  The Spring 2006 section of Calculus II that was taught with the redesign took the same final exam as the section taught in Fall of 2004 by the same instructor at the same institution;  the results are summarized below.  At the 5% level of significance, the average scores in the Sp06 section were higher.