Mathman 33 -
Algebra 1 Review (Semester 2) New


Terrain: Mostly flat.  May be muddy/standing water after rain

Difficulty: Depends on math ability

Placed by: The Dragon (Mathman) on May 17, 2009

Location: Washington County

Materials needed: Rubber stamp, stamp pad/inking pens, calculator, compass, clues

Dragon's Home Page
Mathman Home Page

This box is part of a series of letterboxes with mathematical clues.  The boxes are intended for both regular letterboxers and my students.  This box was developed for my Algebra class to satisfy their request for an extra credit opportunity.  It also serves as a review of their second semester material and for an activity to do together as a family.

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




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 .I’ll let you know if you’re "good to go”.

1) Solve the system:
3J - 2L = 383
  J + 4L = 865
2) Let B equal the number of roots the following equation has: x2 + 6x - 135 = 0 B=_____
3) Let E and M be the bounds of the following compound inequality: 

 (1/3)E - 49 ≥ 63 or 2M - 158 > 214
4) What happens with the following system of equations?  Let I be either "intersect", "parallel" or "same line".
4x - 7y = 12
-12x + 21y = -30
5) Let D, K, and N be their exponents when the following is simplified:
(Remember - no negative exponents in the final answer!)

6) Let A equal the value of the discriminant of 4x2 + 52x + 40 = 0 A=_____
7) Let F, G, and H be the coefficients of the polynomial (respectively) that results when you subtract (361x2 - 140x - 221) from (428x2 - 27x - 87) G=_____

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.


10) Let Q be the smallest two digit number formed by placing the roots (solutions) of the following equation next to each other:  x2 - 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=_____


12) Let P be the y-intercept, when the equation y = 5(x +37) + 8 is written in slope-intercept 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 = X2 +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 = _________


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.  Un-twist 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, re-tie 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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