Download Match 8

MACC Math Questions
For Use on February 22, 2016
Both teams (A and B) are given the first ten questions. These are all 20-second questions.
Directed math questions will be read twice by the emcee before time starts at “Begin”. There will
be no repeats on directed math questions. Directed questions are answered by writing the answer
on the answer sheet. When time has been called, the team captain will hand in one, and only one,
answer sheet. Make sure the answer is circled if the sheet contains more than the answer—for
example if you have worked the problem on the answer sheet. Once sheets are received by the
emcee, none can be changed or exchanged. There are only ten directed questions. Each team may
score points on each directed question.
Emcee must read both answers aloud for questions in the directed round.
This is the first directed question.
1.
3y y
= + 6 (read as 3 y over 4 equals the quantity y over 4 the quantity plus 6)
4
4
(Emcees read question again.) Begin (12)
Solve for y:
This is the second directed question.
2.
Find the following trigonometric ratio, simplifying all radicals: sin (-315) (read as sine of
√
negative 315). (Emcees read question again.) Begin
2)
(read as the square root of 2 over
This is the third directed question.
3.
−
(Read as 32 y squared, minus 8 y to the sixth.
Completely factor the following:
(Emcees read question again.) Begin [
( + )( − )] (read as 8 y squared times
the quantity 2 plus y squared, the quantity times the quantity 2 minus y squared)
This is the fourth directed question.
4.
Twelve apples are purchased for $4.80. At this rate, if 36 apples are purchased, how much
change is left from a $50 bill? (Emcees read question again.) Begin ($35.60)
This is the fifth directed question.
5.
Solve for x: the equation x2 – 12x + 16 = 0 (read as x squared minus 12 x plus 16 equal
zero) (Emcees read question again.) Begin 6 ± 4 5 (read as 6 plus or minus 4 times the
square root of 5, or 6 plus 4 times the square root of 5 and 6 minus 4 times the square root
of 5)
(
)
This is the sixth directed question.
6.
A triangle has sides with the measures 3x -1, x -3, and 4x + 5. If the perimeter of the
triangle is 41, what is the length of the shortest side? (Emcees read question again.) Begin
(2)
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This is the seventh directed question.
7.
What are the coordinates of the point (3, 4) after a rotation of ninety degrees in a
counterclockwise direction about the origin? (Emcees read question again.) Begin (- 4, 3)
This is the eighth directed question.
8.
Find two positive integers such that the difference of their squares is 72, and the sum of
their squares is 170. (Emcees read question again.) Begin (7 and 11)
This is the ninth directed question.
9.
For the parabola = −
(read as x equals negative one half y squared), give the
formula for the axis of symmetry and describe the direction of opening, or orientation.
(Emcees read question again.) Begin (Both must be given: the axis of symmetry is y = 0,
and the direction of opening is to the left.)
This is the tenth directed question.
10.
Ann, Beverly, and Caroline start a business and share its profits in the ratio of their
investments. If Ann invested $900, Beverly $600, and Caroline $500, how much does Ann
receive on a profit of $40,000? (Emcees read question again.) Begin ($18,000)
That ends the portion of the match with directed questions. Coaches, if you have any team
member substitutions, please send those team members to the stage at this time. (Note:
Allow time for substitutes to be seated, introduce substitute team members.)
Please remove all written notes from your team tables. Any new material written after the first
question begins may NOT be shared in any way. No form of conferring is allowed during
the tossup portion of the match. Conferring includes sharing of written or verbal
information or signals.
We will now have ten tossup questions. They are all 10-second questions. Remember, the person
who buzzes in must give the answer immediately. Please wait until I recognize the team
before you give an answer. The penalty for buzzing in early and giving a wrong answer is
minus 2 points, and the question will then be reread in its entirety to the other team.
This is the first tossup question.
1.
If the terminal side of an angle in standard position lies along an axis, then the angle is
referred to by what specific term? Begin (Quadrantal; or quadrantal angle)
This is the second tossup question.
2.
Do the following three numbers represent the lengths of the sides of an acute, right, obtuse
triangle, or not a triangle at all: √ , √ (read as 9 times the square root of 2), and 17?
Begin (Acute)
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This is the third tossup question.
3.
How many faces does an octagonal prism have? Begin (10)
This is the fourth tossup question.
4.
Express the angle measure 330 degrees in radians. Begin
(read as 11 pie over 6)
This is the fifth tossup question.
5.
What rule uses determinants to solve systems of equations? Begin (Crammer’s Rule)
This is the sixth tossup question.
6.
A right triangle has hypotenuse 25 inches and one leg 7 inches. What is the length of the
other leg in inches? Begin (24)
This is the seventh tossup question.
7.
) (read as the quantity negative five raised to
Simplify the following: (−
the negative one power, the quantity raised to the negative three power). Begin (-125)
This is the eighth tossup question.
8.
Assuming all surfaces are smooth, give the mathematical name for the following solid: a
nickel. Begin (Right cylinder; Note: if “cylinder” is given, ask for more elaboration)
This is the ninth tossup question.
9.
For any rational number “a”, “a” always equals “a”. This statement refers to which
specific mathematical property of equality? Begin (The reflexive property)
This is the tenth and final tossup question.
(Emcee note – if match is tied after this question go to the three tie breakers at the end of these
questions – use all three, even if tie is broken on first or second question!)
10.
A regular polygon has 5 diagonals. What is the measure of each of its exterior angles in
degrees? Begin (72)
(Emcees – Ask if there are any appeals that need to be noted.)
EMERGENCY QUESTIONS (To be used in an emergency only –DO NOT USE AS EXTRA TIE
BREAKERS – but they can be used in place of tie breakers as they would be used if a
question has a mistake, if the emcee “flubs” a question, etc.):
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You have 20 seconds to answer this question:
1.
3
(read as the sine of A equals the square root of 3 over 2), what is A in
2
If the sin A =
degrees and radians? Begin (60 degrees and
π
3
radians (“pie” thirds or pie over 3 radians)
You have 20 seconds to answer this question:
2.
A rectangular solid has dimensions 12 inches by 7 inches by 5 inches. What is the surface
area of the solid in square inches? Begin (358)
TIE BREAKERS (To be used in cases of tie games – use all three questions, even if the tie is
broken with the first or second question; in case teams are still tied at the end of these
three questions – the game remains a tie.):
This is the first tiebreaker question. You have 10 seconds to answer the question.
1.
What is the name of the set with no members, also known as the empty set? Begin (Null)
This is the second tiebreaker question. You have 10 seconds to answer the question.
2.
What type of polygon has one or more interior angles greater than 180 degrees?
Begin (Concave)
This is the third tiebreaker question. You have 10 seconds to answer the question.
x
3.
Solve for x: 8 3 = 64 (read as 8 to the x over 3 power equals 64) Begin (6)