Theta Individual State Convention 017 1. 15 1 16 15 i i i i i =? a. 1 b. i c. 1- i d. i e. NOTA. Mr. Lu has $.7 in pennies, nickels, dimes, quarters and half dollars. If he has an equal number of coins of each kind, then the total number of coins Mr. Lu has is? a. b. 5 c. 10 d. 15 e. NOTA. One leg of an isosceles right triangle is lengthened by 8 feet and the other leg is shortened by 8 feet to make a new right triangle. If the hypotenuse of the new triangle is feet longer than the hypotenuse of the original triangle, what is the length of the legs (in feet) of the original triangle? a. 7 b. 15 c. d. 0 e. NOTA 4. Mr. Lu drives D miles to Buchholz at x mph (note: x > 10 mph). On his way home, he drives the same route at (x 10) mph. Find his average driving speed in mph for the round trip? D D x 10x x 10x a. b. c. d. e. NOTA x 5 x 10 x 5 x 10 10 5. Find the greatest integer k for which k 9? a. 4 b. 5 c. 6 d. 7 e. NOTA
Theta Individual State Convention 017 6. Find the area defined by the intersection of the solutions of the two inequalities: x 8x y 0 x y 4 a. 4 b. 4 c. 1 d. 1 e. NOTA 7. Find "m" given that the area bounded by the x-axis and the lines x=1, x=4, and y=mx+4 is 7. a. - b. -1.5 c. d. -0.5 e. NOTA 8. The measure of two angles are in the ratio :5. The measure of the larger angle is 6 more than one third the difference of the two angles. What is the sum of all possible measures of the angles? a. More information needed b. 6 c. 75 d. 105 e. NOTA x x x x x x 1 9. How many asymptotes does the graph of g(x) have, if g x? a. 1 b. c. d. 4 e. NOTA 10. Given that x x 7, what is the smallest possible value of x x? a. -0 b. -18 c. 18 d. 0 e. NOTA
Theta Individual State Convention 017 11. The set L is the set whose elements are...,, 1,0,1,,.... Of the following 5 operations applied to any pair of elements: (1) addition, () subtraction, () multiplication, (4) division, and (5) finding the arithmetic mean, under which operations is set L closed? a. 1,, b. 1,,5 c. 1,,,4 d. 1,,,5 e. NOTA 1. Write the equation of the set of points equidistant from the line y = 5 and the point (5, 0). x a. y x 5 b. y x 10x 50 c. y 10x 10x 10 x d. y x e. NOTA 10 1. The size of the Buchholz Math Team is decaying rapidly and can be described by the rt function: A Pe. It is known that in 4 years the team will be half what it is now. What is the rate constant, r? a. ln(0.5) b. 0.5ln c. 0.5ln(0.66) d. 0.5ln(0.5) e. NOTA y y 14. Simplify: x x 1 1 1 a. 1 b. x y c. y x d. 1 xy e. NOTA 15. The line segment joining the midpoints of the diagonals of a trapezoid has length. If the longer base is 97, what is the length of the shorter base? a. 89 b. 90 c. 91 d. 9 e. NOTA
Theta Individual State Convention 017 7 7 16. The equation x x x a. no solutions. b. one integral solution. c. infinitely many solutions. d. two equal solutions e. NOTA 17. The medians to the legs of an isosceles triangle intersect each other at right angles. If the base of the triangle is, what is the area of the triangle? a. 1.5 b. c..5 d..0 e. NOTA 18. For a given value of k the product of the roots of x kx k 1 0 is 7. The roots are? a. imaginary b. irrational c. rational but not integral d. integral e. NOTA 19. Find the equation of the line that passes through the intersection of x y 5 x y 0 and is perpendicular to x y = 5. 1 a. y x 5 b. y x c. y x 4 d. y x e. NOTA 0. Together Wiggie and Lu can complete a math marathon in 1 days. Wiggie works 4 times as fast as Lu. How many days would it take Wiggie if he worked alone? a..4 b. 9.6 c. 15 d. 60 e. NOTA
Theta Individual State Convention 017 1. Let L be the sum of the interior angles of a polygon U for which each interior angles measure is 7.5 times the exterior angle at the same vertex. Then L is? a. 660 and U is regular b. 660 and U is not regular c. 700 and U is regular d. 700 and U may or may not be regular e. NOTA. If g x 4 x then g(x+1)-g(x)=? a. g(x) b. g(x) c. g(x) d. 4g(x) e. NOTA. Triangle ZLU is isosceles with base ZU. Points W and F are respectively on LU and ZL and such that ZU=ZW=WF=FL. The number of degrees in angle L=? a. 5 5 7 b. 1 6 c. 0 d. 40 e. NOTA 4. The base of a rectangular solid is a square with an area of 5. If the diagonal of the solid is 11, then its height is? a. 11 b. 7 c. d. 74 e. NOTA 5. If i is a root of 4 5x x ax bx 7 0 and a and b are both real then a+b=? a. -5 b. -1 c. 1 d. 5 e. NOTA
Theta Individual State Convention 017 6. The product of the solutions to the equation log x x 10 is? a. -1 b. 0.1 c. 1 d. 10 e. NOTA 1 1 1 1 9 10 =? 7. 1 1... 1 1 a. 0.5 b. 0.55 c. d. 0.7 e. NOTA 8. The number of positive integers L for which the equation Lx 1 = L has an integer solution for x is a. b. 4 c. 5 d. 6 e. NOTA 0 1 4 0 5 1 1 Y : If x does not equal zero, then what is Y? 16 16x 16 9. x 64 a. 1 b. 14 c. 19 d. 9 e. NOTA 0. The number of digits in the number 1 5 8 is? a. 10 b. 11 c. 1 d. 0 e. NOTA