Download Name________________________________________ Rocket

Name________________________________________
Rocket City Math League
Apollo Test
2012 -2013
Round 1
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.
Time Limit: 45 minutes
1. Simonx the Plutodian cannot remember the ignition sequence for his hover car, but he knows that the sequence
10
is equal to the value of
x
2
. What is his hover car’s ignition sequence?
(1 point)
1
2. Now Simonx cannot remember the way to his friend Ampadivac house. He knows that there are
[ln(1000)][log(𝑒 2 )] right turns in the shortest path. How many right turns are in this path?
(1 point)
3. Find the reflection of the point a+bi in the complex plane over the imaginary axis in terms of a, b, and i.
(1 point)
4. Hyun Su and Raisa wanted to have a race to see whose rocket ship was faster. Raisa, being fully confident that
her rocket was far superior, even gave Hyun Su a three hour head start during the race. If Hyun Su’s rocket went at
a constant speed of 40 miles per hour, and Raisa’s rocket, after the three hour wait period, traveled at a constant
speed of 60 miles per hour in the same direction as Hyun Su’s rocket was traveling, how long after Raisa leaves, in
hours, would it take for Raisa’s rocket to catch up to Hyun Su’s?
(1 point)
5. Find the radius of the circle with the equation x2 + 6x + y2 - 10y + 22 = 0.
6. Find the area, in square units, of triangle ABC if AC is
BAC=60°.
6 6 units, AB is 12 units, and the measure of angle
7. Find the sum of the coefficients of the expansion of (3x-y)4.
8. If
1
1
1
1
(2 points)
+ 𝑥 3 + 𝑥 5 + ⋯ = 55 and 𝑓(𝑛) = 𝑛, find 𝑓(𝑥 + 1) + 𝑓(𝑥 − 1).
𝑥
(2 points)
(2 points)
(3 points)
9. Ally and Raisa need a rocket ship with enough transversal fuel to get them to Mars. They go to the local rocket
dealership to pick out the best rocket for the job and are shown four rockets. The Galaxy rocket has 40 gallons of
transversal fuel, gets 55 miles per gallon, and happens to go backwards using one gallon of fuel after every seven
gallons of fuel it uses going forward. The Starchild rocket only holds 27 gallons, and gets 40 miles per gallon, but it
only goes forwards. The Moondust rocket has 52 gallons of transversal fuel, gets 70 miles per gallon, and uses one
gallon to go backwards after every four gallons it uses to go forward. The Rumble rocket holds 34 gallons, gets 50
miles per gallon, and uses half a gallon to go backwards after ever three gallons it uses to go forwards. If Mars is
2000 miles away, which is the rocket ship Ally and Raisa should get for their trip?
(3 points)
10. If the solutions to the equation 5𝑥 3 − 11𝑥 2 + 9𝑥 = −6 are represented by 𝑚, 𝑛, and 𝑝, find the value of 𝑚2 +
𝑛2 + 𝑝2 .
(4 points)
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