Clues:
First, complete the following algebra problems. The
values of the variables will be inserted into the final clues. Solve these
problems before searching for the box. If you’d like to check your answers
before going to look for the box, see me or email your answers to me at
tkuehl@kmlhs.org
.I’ll let you know if you’re "good to go”.
1) Solve the system:
3J  2L = 383
J + 4L = 865 
J=_____
L=_____ 


2) Let B equal the number of roots the following equation
has: x^{2} + 6x  135 = 0 
B=_____ 

E=_____ 
3) Let E and M be the bounds of the following
compound inequality:
(1/3)E  49 ≥ 63 or 2M  158 > 214 
M=_____ 


4) What happens with the following system of equations?
Let I be either "intersect", "parallel" or "same line".
4x  7y = 12
12x + 21y = 30 
I=_______ 

D=_____ 
5) Let D, K, and N be their exponents when the following is
simplified:
D^{8}K^{4}N^{2}
_______________________________
D^{6}K^{7}N^{17}
(Remember  no negative exponents in the final answer!) 
K=_____
N=_____ 


6) Let A equal the value of the discriminant of 4x^{2} + 52x + 40 = 0 
A=_____ 

F=_____

7) Let F, G, and H be the coefficients of the polynomial
(respectively) that results when you subtract (361x^{2}  140x  221) from
(428x^{2}  27x  87) 
G=_____
H=_____


S=_____ 
8) Let S be the lower bound and the T be the
upper bound of the solution to the following absolute value inequality:
2x  130 ≤ 10 
T=_____ 


9) For the equation y = 3(x  32)^{2} + 96
Let O be the maximum.
Let C be the the amount the graph has been shifted to the right.

O=_____
C=_____ 


10) Let Q be the smallest two digit number formed by
placing the roots (solutions) of the following equation next to each other:
x^{2}  11x + 18 = 0 
Q=_____ 


11) Let U, V, and R be the coefficients of the polynomial
(respectively) when the following is simplified: (8x  7)(2x  20) + 229x 
U=_____
V=_____
R=_____ 


12) Let P be the yintercept, when the equation y = 5(x +37)
+ 8 is written in slopeintercept form. 
P=_____ 


(There will also be some problems you’ll have to solve while
finding the box.)
Next, enter the values for A, B, C, etc you found into
their respective places in the following clues. Then go searching for the box.
You'll get the values for X, Y, Z, W, α, and θ while searching for the box.
Go to A =________ Wallace
Lake Rd. in Washington County. Enter the place and park in the lot
immediately to your left by the playground and office.
Count the number of swings (all together) in the
playground: X = _______
Count the number of vertical spokes there are in the bike rack: Y = ______
(This number should be odd since one spoke is missing...)
Head over to the brown dumpster and continue west to Picnic Shelter #B = _______
Close by, find the horseshoe pits and sit on the new bench
between them.
Take a bearing of C = _______ degrees and walk in
that direction until you get to two paths that form the shape of an absolute
value graph: _________
Stand at the vertex and take the path bearing D = _______ degrees (NOT the path bearing E = _______
degrees). Follow the path as it twists and turns. You will soon pass
a bench on your left, then cross over an earthen bridge, then arrive at another
absolute value graph. Take the path bearing F = _______
degrees (NOT the path bearing G = _______
degrees). You will pass another bench,
then the path will eventually end as it enters a picnic area. Stand by the
pole at the end of the path (before entering the picnic area) and take a bearing
of H = _______ degrees. Spot the stop sign
in the distance on that bearing and walk over to it.
Look both ways before crossing the road. While looking, you should see the
posted speed limit. Write this value down: Z = ________. Then stand in the middle of the path on
the other side of the road (the path should be I = ___________
to the road). Head down the path at a
bearing of J = _________ degrees and stop at the
intersection of paths with a pole with K = ________ stripes on it.
Standing in the middle of the intersection, take the path that heads on a
bearing of L = ________ degrees. Cross the
wooden bridge and follow the path as it bends left. Pass yet another
bench, and after a longer walk, you come to another intersection that forms a
"T". Take the path that heads on a bearing of M = ________degrees (NOT the path that heads at N =
_________degrees). At the next
intersection of trails, take the path bearing O = _________ degrees (NOT the path bearing P = ________
degrees).
Then at the next intersection of trails, take the path bearing Q = _________
degrees (NOT the path bearing R = ________
degrees). You should pass another bench
near an area with an old fence, then head back into a wooded area with many
birch trees. Soon you will need to walk on a long boardwalk. When
you arrive at the end of the boardwalk, take S = ________ more steps and veer to the right as the path splits. Take T =
________ more steps as you bend right, until you
come to another absolute value graph. Take the path bearing U = ________
degrees (NOT the path bearing V = _________
degrees). Walk down this path until you
come to a "U" turn with a sign that says "Trail Closed".
Now you need to do some math....
To find the value of W:
Use the value for X you found and evaluate W = X^{2} +5X  63
W = ________
To find the value of θ:
Use the value of Y you found and evaluate θ = 47  7Y
θ = _________
To find the value of α:
Use the value of Z you found. If α varies directly as Z, and α = 56 when Z
= 28, find the constant of variation. Then use it to find α when Z is the
value of the speed limit you found.
α = _________
BEFORE RETRIEVING THE BOX, BE SURE NO ONE IS AROUND TO
SEE YOU TAKE THE BOX OUT! DO NOT BRING ATTENTION TO YOURSELF OR THE HIDING
LOCATION OF THE BOX!
Standing at the tip of the "U" in the "U" turn, spot the group of W = ________
tall birch trees in the woods at a bearing of θ =
________ degrees. Walk the α = ________
steps into the woods on that bearing and you
should find the box tied to the bottom of one of the birch trees. Untwist
the wire to release the box.
Stamp the letterbox stamps on this sheet below, and stamp your
stamp into the letterbox log book. Write a nice note to me next to your
stamp and date it. Be sure to include the names of everyone with you.
Read what other people who have found the box have said. Be sure to take
your picture with the camera in the box as well!
Return all the letterbox parts into their bags and seal the
bags tightly! Replace the sealed bags into the box and seal the box
tightly! When no one is looking, retie the box to the bottom of the birch
tree. Then turn in this completed activity sheet to me for
grading.
Letterbox stamps:
Before you set out read the
waiver of
responsibility and disclaimer.
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