Name _____________________________________
Rocket City Math League
2014-2015
Round 2
Apollo Test
Answers must be written inside the adjacent answer boxes. All answers must be written in exact, reduced, simplified, and rationalized form. Figures
are not necessarily drawn to scale. No calculators, books, or other aides may be used.
Time limit: 45 minutes
x
to make the equation x  15 x  36  0 true?
2
1.
What is the smaller value of
(1 point)
2.
What is the sum of the solutions of x  6  4  5 ?
(1 point)
3.
What is the sum of the prime factors of 5,610 ?
(1 point)
4.
Gracie is launching her favorite rocket. The path of the rocket can be represented on the Cartesian
plane by a line going through the origin with a slope of 3 .The ground is represented by the xaxis where the rocket can only travel through the first quadrant. What is the measure of the
smallest angle in degrees formed by the path of the rocket and the ground?
(1 point)
5.
When the square of the 648th positive even integer is divided by the cube of the 18 th positive even
integer the value is equivalent to the sum of the first n integers greater than 0. What is the value of
(2 point)
n?
6.
The first term in a geometric series is 15,625 and the fifth term is 400. What is the geometric mean
of the second and tenth terms in the series given that the common ration is positive?
(2 point)
7.
What is the sum of the squares of the roots of the polynomial x 3  5 x 2  4 x  20  0 if one of the
roots is 2i ?
(2 point)
8.
Martha the Martian is placing a plasma shield generator in an asteroid field for a friend’s space
banana farm. At each corner of the generator is a Beacon. The Beacons are placed on a grid at
points (-2,1), (-1,6), (3,0), and (4,3). What is the area of the quadrilateral formed by the beacons?
(3 point)
9.
RJ Jared is studying the movements of asteroids in space. In space there is movement in the form
of a hyperbola. The hyperbola has asteroids constantly flowing through both parts but the two
paths in the hyperbola never touch because of the curvature. He finds that the hyperbola is
represented by the following equation: 25 x 2  9 y 2  100 x  54 y  559  0. In order to help RJ
Jared find the curvature, what is the eccentricity of the hyperbola? (Eccentricity = c/a where c =
distance from the center of the hyperbola to one of the foci and a = the distance from the center of
the hyperbola to the vertex of one of the curves)
(3 point)
2
2
1

ln x 10 ln x , P( x)  e cos((x 6 x7)) x , A( x)   2 x 2  14 x  49 ,
5

10. If S ( x)  
C ( x) 
x
 74 , and E ( x)  3 x  17 , find S ( P( A(C ( E (6))))). Write your answer in
8
scientific notation.
(4 points)
The material on this page is the property of the Rocket City Math League. Reproduction other than for non-profit educational purposes is strictly prohibited without the
expressed written consent of the RCML.
Rocket City Math League
www.rocketcitymath.org
Sponsored by Mu Alpha Theta - National Math Honor Society
www.mualphatheta.org