The first problem graphs a modified trigonometric function.  Did Hugh S. Carryman's henchman arrive at the dock when the tide was low or high?

The first writing assignment is here.

The second problem optimizes the volume of a box folded from a giant sheet of cardboard.

The second writing assignment is here.  An excellent solution is here.

The third question compares distance, velocity, and acceleration.  Will the runway be long enough that Rhoda and Roger can fly away and escape the clutches of their captors?

The third writing assignment is here.

The first problem compares linear with exponential functions.  Should Tara wash a jar twice with a lot of water each time, or many times with small amounts of water?

The first writing assignment is here.  
An excellent solution is here.

The second problem optimizes the volume of a small paper bag.  It also introduces us to the oh-so-dreamy Justin Lumberpond (sigh).

The second writing assignment is here.
An excellent solution is here.

The third problem examines acceleration of a falling object.  The ex-girlfreind is back and murder is afoot!

The third writing assignment is here .
An excellent solution is here.

The first problem uses exponential functions; it requires technological help in the solution.

How much money was put into the bank, and what was the interest rate, if we know how much money we made in the short and long run?

The first writing assignment is here.
An excellent, to-the-point solution is here.
Another excellent, more flowery solution is here.

The second problem optimizes the cost of a box that requires soldering.

How should we build a storage box the most cheaply?

The second writing assignment is here.
An excellent solution is here.

The third problem looks at acceleration due to gravity (and maybe air resistance?).

Did Victor Dendron conspire to murder Gus Gusterson?

The third writing assignment is here.
An excellent solution is here.

The first problem uses one of my favorite problem contrasting average velocity with the average of several velocities.

Does Overby-Fitzpatrick deserve a speeding ticket?

The first writing assignment is here.
An excellent solution is here.

The second problem optimizes the center of mass; surface area and volume of rectangular objects play an important role.

How high should Overby-Fitzpatrick pack papier-mache in his rail cars?

The second writing assignment is here.
An excellent solution is here.

The third problem compares constant velocity with constant deceleration.

Did Overby-Fitzpatrick murder Peter Moss by stopping a train?

The third writing assignment is here.
An excellent solution is here.

In the first paper, Clay wants to figure out when in the future he should sell his Vase. 

This paper uses the Fundamental Theorem of Calculus, the product rule, and graph-reading skills.

The first paper is here.  An excellent solution is here.

In this paper, Clay needs to determine both the height and the capacity of the Enure Vase.

This paper uses volume of solids of revolution and Riemann Sums.

The second paper is here.  An excellent solution is here.

In this paper, Clay suffers from a bout of lead poisoning.  Is Eve L. Vellen at it again?

This paper uses coupled linear differential equations.

The third paper is here.

In the first paper, W. Avering wants to figure out when he should have sold his rubber making equipment to have maximized profit.  

This paper uses the Fundamental Theorem of Calculus, the product rule, and graph-reading skills.

The first paper is here.  An excellent solution is here.

In this paper, Avering tries to determine the shape of the storage tank that Eve L. Vellen sold him.  If he's wise, he'll calclulate volumes using integration and solids of revolution.

The second paper is here.  An excellent solution is here.

In this paper, W. Avering is trapped in an underground chamber using methods that are half Batman, half Rube Goldberg.  Solving the problem requires both infinite series and understanding of the motion of falling objects.

The third paper is here.  An excellent solution is here.

The first problem uses geometry and optimization to design a greenhouse.

The first writing assignment is here.
An excellent solution is here.

The second problem uses first-order differential equations in the clean-up of a pollen spill.

The second writing assignment is here.
An excellent solution is here.

The third problem calculates the average height of a weird trapezoidal object; it uses 3-d geometry and could involve integration.

The third writing assignment is here.
The letter from Tasha is here.
An excellent solution is here.
The photos of the finished loft are here.

The first problem uses Riemann sums to find the volume of a (somewhat) cylindrical object.

The first writing assignment is here.
An excellent solution is here.

The second problem has students determine the areas of slices of a circle, in order to find the volume of water in his cylindrical tank.

The second writing assignment is here.
An excellent solution is here.

The third problem (which is almost calculus III material) uses 3-d geometry and arclength to solve a problem with the intersection of two cylinders of different diameters.

The third writing assignment is here.
An excellent solution is here.

After all the work they did to help Brent, students get a follow-up letter from the law.

 Here is advice to stay away from Brent!

The first problem deals with catenaries (is her high-wire made of titanium or aluminum?).

The first writing assignment is here.
An excellent solution is here.

The second problem cools a large amount of jello (using Newton's Law of Cooling).

The second writing assignment is here.
An excellent solution is here.

The third problem deals with attempted murder by rhinoceros (using damped oscillators and 2nd order differential equations).

The third writing assignment is here.
An excellent solution is here.