Student Name ________________________ School ____________________________
Grade ________ Math Department Head _______________________________
Directions: Solve as many as you can of the problems and list your solutions on this sheet of paper. On separate sheets, in an organized way, show how you solved the problems. You will be awarded full credit for a complete correct answer which is adequately supported by mathematical reasoning. You can receive half credit for correct answers which are the result of guesses, conjectures or incomplete solutions. Included as incomplete solutions are solutions that list some, but not all, solutions when the problem asks for solutions of equations. The decisions of the graders are final. You may earn bonus points for "commendable solutions" solutions that display creativity, ingenuity and clarity. Your answers and solutions must be postmarked by November 4, 2002 and submitted to Tony Trono, Vermont State Mathematics Coalition, 419 Colchester Avenue, Burlington, VT 05401. (For Coalition information and a copy of the test: http://www.vermontinstitutes.org/vsmc)
Answer: ___________,___________,___________
Complete the pictured five by five array using only the
digits 1, 2, 3, or 4 so that:


Answer: ___________,___________,___________
b) Another sequence is defined by the formula and for n = 2, 3, 4, ... .
Find a formula for in terms of n and use the formula to evaluate
.
Answer: a) = ________,
= ________,
b) = ________,
=________
a) Find m.
b) Find the coordinates of the point of intersection of the two lines.
Answer: a)______________, b)______________
a) Find the area bounded by the graph of g(x) and the xaxis.
b) Find the length of the graph of graph of g(x).
Answer: a)______________, b)______________
Answer: _________________
In the early 1500s, the mathematician Tartaglia solved
the general cubic equation. That success began a search among
mathematicians for a solution to the general quartic (fourth degree)
equation. The following system of equations in the box leads to a
quartic equation in b.
a) Write the quartic equation in b. b) Find solutions of this system of equations for real numbers (a, b, c) correct to the nearest hundredth.

