Cowculus 1
The “Booty” of Friess Lake


Terrain: Moderate, some up and down steps/slopes

Difficulty: Need to know Calculus...
Created by: The Guys of KML's 06-07 AP Calculus class

Placed by: The Dragon (Mathman)

Location: Washington County

Materials needed: Rubber stamp, stamp pad/inking pens, calculator, compass, clues
Note: Bring bug spray during summer!

Dragon's Home Page
Mathman Home Page

This box is the first in a series of letterboxes with Calculus clues.  Thanks to Z-fan for the idea...

Students and parents of students should read my introduction to letterboxing before seeking the boxes.


Story: A long time ago, seven pirate mathematicians were sailing on a lake when all of a sudden a great storm took them by surprise, and their ship began to sink. The mathematicians had sworn by oath that they would guard and protect the vast treasure that they carried on board. Only two of the mathematicians survived the storm with the treasure. They clung to a piece of timber, and eventually drifted to shore. Battered and beaten, they needed to return to their homeland for new supplies. They were too weak to carry the treasure and it was not safe to transport over the land. They mutually chose a secret location along the shore and decided to hide the treasure and return for it later. However, the two men never returned for the treasure, so it remains hidden to this day along the shores of the waters now called Friess Lake.


Instructions: This task sheet contains the information required to find the treasure. There are spaces on this set of sheets that are available to record information found and calculated on your journey.  Problems that can be solved before the journey are stared with an asterisk. 


From US 41/45 head west on State Road 167 for 5.5 miles

Turn left to head south on Friess Lake Rd for 0.3 miles

Turn left into park entrance, Glacier Hills County Park.

Take the main road east all the way until you reach the stop sign at the top of the hill.

Turn left and park just to the north of the building with a large stone chimney.



Start at the north side of the building by the doors next to the maps and park information board. Locate and record the following information on the WCPS rules sign on the side of the building:

Range of number of adults for group alcohol use, $3.00 fee. AA [____ , ____]


Range of number of adults for group alcohol use, $7.00 fee. BB [____ , ____]

You may want to take a map to guide you as you search for the hidden treasure. Remember to protect the “booty” from thieves and be careful on your adventure.

Step 1
*Integrate the following:  = ______ (A)
Face in the direction of bearing A______.

What is the number that you see on a sign off in the distance?  B = ______

Step 2 *Integrate the following analytically: = _______ (C)
To the nearest whole number, find the displacement = _______ (D) of an object over the interval t=[AA] if the object's velocity is

Find the displacement = _______ (E) of an object over the interval t=[BB] if 


Starting even with the pet waste sign, face bearing direction C______ and walk D______ steps.  Pause and count the number of stairs next to you: F = ______  Then walk E______ steps further on bearing C.

Step 3 *At how many different values of x does the graph of f(x) = sin(x) have a horizontal tangent over the closed interval [0,162π]? Answer = ______ (G)


*Find the slope of the line tangent to the graph of f(x) = x2 +4x +3 when x = 57

Answer = ______ (H)


Now face the bearing direction of G______ and walk H______ steps.  From the wooden sign before you, record the four digits of the cabin numbers in the order they appear:
I = __
____ J = ______ K = ______ L = ______  (Don’t they remind you of a childhood joke?)


Step 4 Find the slope of the line tangent to the graph of at x = B (See Step 1 for B.) Answer = ______ (M)
Continue by walking on the trail at a bearing of M______ degrees.  Walk until the trail reaches a large opening.  Stand by the light pole on the right side of the trail.


Step 5 Evaluate: _____ (N)
*Find the volume of the object formed by rotating the area enclosed between the graphs of
y = 2 + x - 2x2  and y = -1 around the line y = -5.5. Round answer up to nearest multiple of ten.

Answer = ______ (O)

From the light pole, walk N______ steps on a bearing of O______ degrees. You should intersect with a paved trail.

Step 6 *Determine the object defined as the surface of revolution of the function about the
-axis for x≥1: ____________________ (Hint: It can be filled up with π cubic units of paint, but an infinite number of square units of paint are needed to cover its surface!) Walk to the foot of the stairs of the nearby building which would most likely be associated with this object.

Step 7
Next, walk on a bearing of C______. This takes you along a trail. Count the number of stairs you come to as you descend them: Stairs = ______  Stop when you reach the bottom of the stairs.

Step 8
Count the number of silver gas tanks in the area: P = ______.  Now, walk on a bearing of the number of stairs.

Step 9
OH, NO! There is an obstacle in your way! Do not go around it but rather go through it.

Enter through the door that says "Restrooms/Winter Sports Warming Room". Upon entering, go through the door on your right. Walk to the other end of the room and exit through the door. Then, turn right and go out another door. You should be in a spot which would indicate that your displacement since you began is =______

Step 10
*Find the length of one "period" of the curve Round to the nearest whole number.  Answer = ______ (Q)

Now walk on a bearing of Q______.  Take the stairs that you meet, and count the number of steps:  R = ______

Step 11
Use the values of I, J, K, and L to solve this math riddle: Take the greatest of the numbers and subtract the value of the second digit of three times the greatest number. Then add to that number the half of the sum of all the digits minus one. Answer = ______ (S)


*It takes a force of 11 Newtons to stretch a spring 2 meters beyond its natural length. How much work is done to stretch the spring 4 meters from its natural length?  Answer = ______ (T)

At the top of the stairs where the concrete ends, change your course.  Take S______ steps on a bearing of T______.


Step 12 Look at the ground in front of you. Can you see the giant "washer"? Hey, speaking of washers…did you like the washer problem in step 5?


Step 13 Cross to the other side of the "washer". Count the number of swings U = ______ then walk over to the cream and green colored sign on the west side of the playground. What is the range for the children’s ages that can play? V = ______ to  W = ______.


Step 14 Follow the road toward the volleyball and basketball court. Count the LITTLE brown, wooden poles on the right side of the road up to the stop sign. (Yes, there are a few extra poles that shouldn’t be counted.)  Y = ______


Step 15 Take a load off and sit on one of the little poles near the stop sign.  Find= ______ (X)


Step 16 Now using what you learned about limits, head on a bearing of X______. Surprisingly, even road signs acknowledge that some things cannot be done.

Step 17 You should be walking along the trail used by vehicles during winter. Continue on the trail past the first opening on the right. Go until you reach the second trail opening on the right. There is a white pole with red and black lines. Turn right. This is a shortcut to another path. Turn right again on the next path.

Step 18
After a short while you should be walking next to the lake. Continue on the path until you reach another white pole with black and red lines. Stay left when the trail divides.

Step 19
Evaluate: WV  = ______ (Z)  Starting even with the pole walk Z______ steps then go U______ steps on a bearing of Q______.

Be careful that no one is nearby and watch out for the pirates on the “sea”!

You will find the treasure in the base of the tree. Reach in the large hole to the right.  Remove the rock holding the treasure safely in place.  Make sure to return the treasure and the rock in the same spot in the tree for future treasure hunters.

We hope you enjoyed this letterbox, and maybe it will bring up your sinking Calculus grade!

Before you set out read the waiver of responsibility and disclaimer.

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