Download jack74`s Math Tournament Round 1 (Non

jack74’s Math Tournament
Round 1 (Non Calculator Problems)
I vow to have the most honest integrity of a mathlete and will not do any cheating of any kind on this
test. This includes discussing with others, freestyle peeking, coughing and sneezing to represent multiple
choice and/or using rap songs that reveal the answers. This and test will be disclosed within the test
takers and the viewers of the thread and will not be shared or any solutions revealed until after the test.
1. What is the mode of the Fibonacci Sequence?
2. What is the units digit of 2727?
3. If 𝑐(𝑏) = 𝑏(𝑏 + 1)(2𝑏 − 1), evaluate 𝑐(2).
4. Jack and Allison are taking turns saying numbers. Jack starts with the number 3, and then Allison
multiplies it by 2 and says 6. Jack then multiplies that number by two and says the result, and so
on. What is the third number that Allison says?
5. Billy drinks 3 bottles of water every day. If he can drink 17,100 mL of water in 12 days, how
many mL are in a bottle?
6. Witches have 1024 warts and toads have 512 warts. There are 4 organisms in a hut. What is the
max number of warts that the organisms can have assuming that there is at least one of each
kind?
7. Jabba the Hutt takes 20 seconds to eat a pancake. Shrek the Ogre takes 30 seconds to eat a
pancake. Garfield the Cat takes 3 seconds to eat a pancake. How many minutes will it take for
them all to finish eating 550 pancakes?
8. One of the greatest hoaxes of all time was the giant humans hoax. People claimed to have
discovered the remains of gargantuan human skeletons the size of buildings, but in reality, they
were just plastered fakes or photo shopped imposters. The Cardiff Giant was a plaster sculpture
made to be a hoax at eleven feet tall. How many times taller is a photo shopped fake skeleton if
it towers at exactly 110 feet tall?
9. Mort the Alien eats 1,500 solar systems every day. If there is 1 star per solar system, 8 planets
for every star, and 17 moons for each planet, how many moons, planets, and stars does Mort
eat in 2 days?
10. A tour bus charges a group rate of $10 plus an additional $10 for every 3 people. Your family
pays $60 to take the tour. How many members of your family were on the tour bus?
11. The expression √10 + √10 + √10 + √… can be expressed in the form
positive integer. What is the value of a?
12. If 𝑥 − 𝑦 = 5 and xy=6, what is the value of 𝑥 2 + 𝑦 2 ?
13. Three of the following statements are false.
1.
2.
3.
4.
Mr. Red: “Mr. Blue did it”.
Mr. Blue: “Mr. Red did it.
Mr. Green: “Mr. Blue’s telling the truth”
Mr. Yellow: “Mr. Green’s not lying”
Who did it?
1±√𝑎
2
where a is a
14. Find the positive value of x: 𝑥 𝑥
𝑥 𝑥…
=4
Tiebreaker (Must show how you got the answer):
15a. What is the area of an conic section with eccentricity of 0 and a perimeter of 4𝜋. What is the area
of the conic section?
15b. What is the focal distance then?
Tiebreaker #2 (Only for tough scoring0
Directions: Visit the life hacks section and post the best life hack you know. Include the steps and logic
behind it. Most interesting life hack receives a house prize and an extra point.