Download GeminiRound3Test - Rocket City Math League

Name________________________________________
Rocket City Math League
2009-2010
Round 3
Gemini Test
Answers must be written inside the adjacent answer boxes. All answers must be written in exact, reduced, simplified, and rationalized form. All
decimals and mixed numbers must be written as improper fractions. No calculators, books, or other aides may be used.
1. Lumpji’s new mattress is a triangle with side lengths 96 inches and 101 inches. What is the product of the
smallest and largest possible integer value of the third side of his mattress?
(1 point)
2. Find the volume of a rectangular prism with face surface areas of 28, 28, 52, 52, 91, and 91 square units.(1 point)
3. The figure below represents an inter-planetary rocket way. DE=5 light years;
DA=3 light years; EA=4 light years; and AC=10 light years. If DE and BC are
parallel to each other, how long would it take, in hours, to travel from D to B to
C moving at a rate of 0.2 light years/hour? ( Figure not to scale)
(1 point)
D
E
A
C
B
4. Aila is building a pen for her mega space dog Malkan. She has only has 42 feet of fencing to use, and she wants
to maximize the amount of space. What is the largest possible area she can enclose with her fencing?
(1 point)
5. Sareemara is painting the outside of her hover car that is shaped like a cube, and the distance from one corner to
the corner farthest from it is
13 . What is the area that will be painted?
(2 points)
6. Retsa is planning to visit some stars in the Cubixyon constellation, which is composed of 8 stars in the form of a
cube with side length of 1 lightano. After he visits one of the stars, he will visit a second star and then return home.
If the distance between the two stars Retsa visits can be no more than 1.5 lightanos, then how many pairs of stars
can he choose from for his visit?
(2 points)
7. The spotlight from the bottom of a spaceship to the ground illuminates a cone-shaped region. Flo-Yo is on a
circular disk with a radius of 3 meters. The edge of his disk is tangent to the edge of the illuminated region and the
disk is 10 meters below the bottom of the spaceship (the vertex of the illuminated region). If the distance between
the bottom of the spaceship and the ground is 20 meters, how many square meters are in the area of the shadow
that Flo-Yo's disk casts on the ground?
(2 points)
1
8.
What is the volume of the shape formed by rotating the area bound by the lines y  6 , y  x  1 , and the
2
y-axis about the y-axis?
(2 points)
9.
R= the number of distinct diagonals in a regular 18-gon
C = the length of the common internal tangent of two circles with radii 2 and 5 whose centers are 25 units apart
M= the measure of the radius of a circle inscribed in a right triangle with the lengths 20, 21, and 29
L= the measure of the apothem of a regular hexagon inscribed in a circle with area of 256.
Find
R
M2

L
.
C
(3 points)
10. Edna picks two real numbers m and n where 0  m  5 and 0  n  8 . What is the probability that
(3 points)
m  n  1 ?
11. Find the coordinates of the vertex of a parabola that contains the points (-6, -7), (3, 20), and (-7, 0).
12.
Triangle ABC has side lengths a, b, c.
(3 points)
B
a= 4 4 4 4...
b= The number of distinct permutations of GEO
c= the positive difference between the 8th term and 9th term
of the Fibonacci sequence
What is the length of the angle bisector from vertex B?
(4 points)
c
A
a
D
C
b
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