Precalculus Reform at the
University of Michigan:
Reformed UM Precalculus


Topics Covered in our Reformed Course

Characteristics of the Course

Homework Assignments

Typical Group Homework Problem

The following table represents the measured amount g, in grams, of a certain chemical compound that can be dissolved in one liter of water at various temperatures T, measured in degrees Celsius.

T     10   20   30   40   50   60   70   80   90
g   1.70 1.23 0.86 0.65 0.47 0.34 0.25 0.18 0.13


An Optimization Problem

Find the volume of the largest open box that can be formed from an 18.4" by 24.2" rectangle of cardboard by cutting congruent squares from each corner and folding up the flaps.

The students will find that


where x is the side of each square and V(x) is the corresponding box volume. (Of course, finding this formula is the hard part of the exercise.) To finish solving using the calculator, they will also find it useful to know that the natural domain for this function is the closed interval [0,9.2]. Some experimenting (or some estimating of the size of the function) shows that the natural range will fit in the closed interval [0,1000]. Those familiar with the TI-82 will now recognize the following as the resulting graph window settings screen and the output from the calculator's graphical optimization routine.

The maximum volume is therefore about 686 cubic inches.

"Prerequisite" Precalculus Knowledge

Gateway Testing

Homework Groups

In-Class Cooperative Learning

Instructor Training and Support

Advantages of our Reformed Precalculus

Disadvantages of our Reformed Precalculus

Questions? Want More Information?

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Last modified Fri 12 May 1995 12:19 EDT

Bob Megginson
Department of Mathematics
University of Michigan