2016 DIVISION FESTIVAL OF TALENTS
Category C:
[2 points each]
1, ≤1 . (1) in the piecewise function, () = {3 >1 be defined? 15.2. For which values of will the function ℎ( ) = 8− √ 8− 15.3. ( ) =21 and ( ) = 2. Find (∘)(). 15.4. Given ℎ( ) = √ 3, find the value of ℎ( 47) . ++? 15.5. What is the horizontal horizontal asymptote of the graph of ( ) = +− 15.6. Two functions, and are inverses of each other. Another function, ℎ is related to in such a way that (ℎ ∘ )( ) = . What is the value of (ℎ)()? 15.7. The function for the height of an object dropped from a 100-meter tall platform at a time of seconds is approximated by () =5 100 .
15.1. Evaluate
t
What is the height of the object after 4 seconds? 15.8. A triangle, a circle, a square, a circle, a pentagon, a circle... circle... If this pattern continues, which nth term would correspond to a dodecagon? 15.9. Write the biconditional of the statement, “ If , then is irrational.” 15.10. The graphs of any two inverse functions, and , are reflections of each other across which line?
= () −()
0
> = 0
20 meters 23rd
= iff n is irrational
= or () =
identity function
[3 points each]
() = 1, what is ( 1) (1)? 30.2. What is the remainder when 2 is divided by 3? 30.3. If 2 = 4 , what is ?
30.1. If
2 5
30.4. A fence is to enclose a rectangular rectangular vegetable farm with an area of 400 square meters. If is the length of one side si de of the fence, find the function fu nction representing the perimeter of the fencing material required.
()
() =
30.5. In the Division Division level DAMATH DAMATH competition, competition, Matthew has won 6 out of 8 games. How many games must he win consecutively to raise his winning percentage to 90 percent? [5 points each]
,,
60.1. Let and and be three consecutive even numbers such that What is the value of ?
> > .
60.2. There are 100 people in a room. Sixty of them claim to to be good at math but only 50 are actually good at math. If 30 of them truthfully deny that they are good at math, how many people are good at math but refuse to admit it?
( ) = () ⋅ () for all positive integers , , and (1) = 2,
60.3. If
2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL)
12
12
10
find
(2016). Hint: The Hint: The answer is in exponential form.
60.4. A box with a square base is to have a volume of 8 cubic cubic meters. Let be the length of the side of the square base and be the height of the box. What are the possible measurement of the side of the th e square base if the height should not be longer than the side of the square base?
ℎ
60.5. If
() = 42, for what values of will is −() be defined? () =123.
C1. Give the inverse inverse of the function function
C2. Suppose that the half-life of a certain radioactive substance is 10 days and there are 100 grams initially. Determine the amount of substance after 30 days. C3. What is the domain of
? () = −+
DOD1. Give the range range of the function, function,
≥ ≥ −() = 12.5 grams
(∞,) ∪(,∞)
() = 47 in interval notation.
2016 DIVISION FESTIVAL OF TALENTS
≥
Category C:
2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL)
[2 points each]
1, ≤1 . 15.1. Evaluate (1) in the piecewise function, fu nction, ( ) = { 3 >1 Read as: of equals 1 if ≤1 and 3x if >1. be defined? 15.2. For which values of will the function ℎ() = 8− √ 8− 15.3. ( ) =21 and () = 2 . Find (∘)() . 15.4. Given ℎ( ) = √ 3, find the value of ℎ( 47). ++? 15.5. What is the horizontal horizontal asymptote of the graph of ( ) = +− 15.6. Two functions, and are inverses of each other. Another function, ℎ is related to in such a way that (ℎ ∘ )() = . What is the value of (ℎ)() ? 15.7. The function for the height of an object dropped from a 100-meter tall platform at a time of t seconds is approximated by . What is the height of the object after 4 seconds?
() =5 100
15.8. A triangle, a circle, a square, a circle, a pentagon, a circle... If this pattern continues, which nth term would correspond to a dodecagon?
15.9. Write the biconditional biconditional of the statement, “ If
15.10. The graphs of any two inverse functions, each other across which line?
= , then is irrational.
() () and −(), are reflections of
[3 points each]
() = 1, what is ( 1) (1)? 30.2. What is the remainder when 2 is divided by 3?
30.1. If
30.3. If
”
2 = 4, what is ? 2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL)
30.4. A fence is to enclose a rectangular vegetable farm with an area of 400 square meters. If is the length of one side of the fence, find the function representing the perimeter of the fencing material required.
()
30.5. In the Division Division level DAMATH competition, Matthew has won 6 out of 8 games. How many games must he win consecutively to raise his winning percentage to 90 percent?
[5 points each]
,,
60.1. Let and and be three consecutive even numbers such that is the value of ?
> > . What
60.2. There are 100 people in a room. Sixty of of them claim to be good at math but only 50 are actually good at math. If 30 3 0 of them truthfully deny that they th ey are good at math, how many people are good at math but refuse to admit it?
( ) = () () ⋅ () for all positive integers , , and (1) = 2, find (2016). Hint: The Hint: The answer is in exponential form.
60.3. If
60.4. A box with a square base is is to have a volume of 8 cubic meters. meters. Let be the length of the side of the square base ba se and be the height of the box. What are the possible measurement of the side of the t he square base if the height should not be longer than the side of the square base?
ℎ
60.5. If
() = 42, for what values of will is −() be defined?
C1. Give the inverse of the function
() =123.
C2. Suppose that the half-life of a certain radioactive substance is 10 days and there are 100 grams initially. Determine the amount of substance after 30 days. C3. What is the domain of
? () = −+
DOD1. Give the range of the function,
() = 47 in interval notation.
2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (TEAM-ORAL)
