Rocket City Math League
Senior Division
2014-2015
Inter-School Test
Answers must be written inside the corresponding box on the answer sheet. All answers must be written in exact, reduced, simplified, and
rationalized form. Also, figures are not necessarily drawn to scale. No calculators, books, or other aides may be used.
1. How many distinct ways are there to arrange the letters in the word TELESCOPE?
2. Let
f ( x  1)  x3  2 x2  4. What is
3. Solve for
f (3) ?
x : 5,2x  1,4  3,2,9  61.
(1 point)
(1 point)
(1 point)
4. Aliens Fillup and Nuceter are playing a game based on the complex plane where they jump away from the origin and need to
estimate the distance between themselves. Fillup’s coordinate is 5  2i and Nuceter’s coordinate is  6  3i. What is the exact
distance between Fillup and Nuceter?
(1 point)
5. Sven is trying to create a galactic art project where there are different layers to the picture. Each layer contains a different square
taken from a 6 6 grid. What is the maximum amount of layers that Sven can have?
(1 point)
6. Solve for
x: 4
5x4
 810 x  8
(2 points)
7. On the planet Barnacles, numbers are dealt with in base 6 instead of base 10 on Earth. If Zumkini, the yoga instructor, says she
needs 231 yoga mats on Earth, how many mats would she need to tell the manufacturing company on Barnacles to make in order
to receive the correct quantity?
(2 points)
8. The computers aboard space stations are much faster than the typical computers on Earth. Space Station RCML contains 2
computers. One processes data at 982 alienbytes per minute while another processes data at 578 alienbytes per minute. At that pace,
how many seconds will it take to process 8245 alienbytes working together?
(2 points)
9. Astronaut Luna leaves planet Trigonautical in her spaceship. Astronaut Reed wants to see her so he reads Luna’s travel plan that
is set on a map of the Cartesian Plane. Reed sees that Luna is following the line y  6 x  8 along a plane in space, first leaving
from the point where the line crosses the y-axis and continuing where the x-values increase . Astronaut Reed leaves planet
Trigonautical at the same point as astronaut Luna, but a malfunction causes Reed to travel through space following the path
y  x 3  7 x 2  16 x  8. If Astronaut Reed continues to fly where the x-values increase, at which points do Astronaut Luna’s and
Astronaut Reed’s paths cross, including the starting point?
10.
(2 points)
A circle inscribed in a trapezoid is shown to the right. Given that AB  3 x  5,
CD  4 x  5, BF  6, DH  13, and the trapezoid’s perimeter is 84 , find
 AH  DC

 FC .

 GC

(3 points)
11. Elsa is skating on the frozen Lunar Lake. Her path is mapped by the parametric equations below, where x and y are measured
in meters and the surface of the ice is modeled by the Cartesian plane. As Elsa skates, she notices that her path outlines a certain
area of ice. What is the area inside of the outline Elsa makes in square meters? (The parameter is in radians where 0  t  2 )
x(t )  21cos t
12. Determine
k
so that the function
y (t )  18 sin t
f
6 x  17 x  23x  kx  8
f ( x)  
2 xk 2  7 x 2  81
4
3
2
is continuous at
if
x  2
if
x  2
(3 points)
x  2.
13. A new type of microorganism is being cultivated in space. Regina initially places approximately 6e
(3 points)
13
microorganisms into a
26
cultivating dish. 7 hours later, approximately 7e microorganisms are in the dish. Using Regina’s approximations, what is the
growth constant per hour of the microorganism if it continues to grow exponentially? (Leave answer in natural logarithmic form)
(4 points)
14. Sevgi is trying to find her best friend Abily sunglasses that can protect her eyes while on a trip to the Sun Museum. Out of the
17 stores in the mall, 6 have strong enough sunglasses being sold. Sevgi is running out of time and can only go to the 8 stores
closest to her. What is the probability that at least one of the 8 stores has the sunglasses Sevgi needs to give to Abily?
(4 points)
11
15. Find the value of
 f ( ) where:
i 0
i
f ( i ) 
3 cos  i  10 sin  i  6
 
and  i   i
sin( 2 i )  4 sin  i
6 2
(5 points)
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