Download Math February 6, 2017

MACC Math Questions
Match 4
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.
State the vertex for the following equation: f(x) = 4x2 – 8x + 4 (read as f of x equals 4 x
squared minus 8 x plus 4) (Emcees read question again.) Begin (1, 0) (read as one
comma zero)
This is the second directed question.
2.
Find the area, in square units, of a regular pentagon with a side length of 4 units, and an
apothem of 5 units. (Emcees read question again.) Begin (50)
This is the third directed question.
3.
Find the least common multiple of: 3x - 6 and x – 2 (read as the quantity 3 x minus 6 and
the quantity x minus 2) (Emcees read question again.) Begin [3(x – 2), or 3x - 6](read as 3
times the quantity x minus 2, or the quantity 3 x minus 6)
This is the fourth directed question.
4.
Solve for x in the following equation: x2 + 6x = 27 (read as x squared plus 6 x equals 27).
(Emcees read question again.) Begin (Both answers must be given: (x = 3 or x = - 9 )
(read as x equals 3 or x equals negative 9)
This is the fifth directed question.
5.
Find the length, in units, of the longer diagonal of a rhombus if the area is 6 square units
and the ratio of the lengths of the diagonals is 2 to 3. (Emcees read question again.) Begin
( √ ) (read as 3 times the square root of 2)
This is the sixth directed question.
6.
Find the sine for the angle whose terminal side contains the point (- 8, - 6)(read as negative
8 comma negative 6). (Emcees read question again.) Begin ( )(read as negative threefifths)
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This is the seventh directed question.
7.
Simplify the following:
(read as the quantity x squared minus x minus 20, the
quantity divided by the quantity x squared plus 9 x plus 20). (Emcees read question again.)
Begin (
) (read as the quantity x minus 5, the quantity divided by the quantity x plus 5)
This is the eighth directed question.
8.
Find the distance between the following two points: (- 2, 3) and (2, - 4)(read as negative
two comma 3 and 2 comma negative 4). (Emcees read question again.) Begin (√ ) (read
as the square root of 65)
This is the ninth directed question.
9.
Find the lateral area, in square units, of a regular square pyramid with a base edge of six
units and a height of four units. (Emcees read question again.) Begin (60)
This is the tenth directed question.
10.
A water tank can be filled by one pipe in 10 hours. The drain pipe for this tank can empty
it in 15 hours. If both pipes are open, how many hours will it take to fill the tank? (Emcees
read question again.) Begin (30)
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 a standard number cube is rolled, what is the probability of rolling a prime number?
Begin (1/2)
This is the second tossup question.
2.
Which of the six trigonometric functions are negative in quadrant III (three)? Begin (Only
these must be given: cosine, secant, sine, and cosecant, or sin, csc, cos, and sec)
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This is the third tossup question.
3.
Three times the square of a positive number equals 21 times the number. Find the number.
Begin (7)
This is the fourth tossup question.
4.
Use words in place of letters for your answer to this question. What is the formula for the
volume of a cone? Begin (Volume equals 1/3 times times radius squared times height)
(read as pie)
This is the fifth tossup question.
5.
For a right triangle with an acute angle A, which trigonometric function of angle A is
represented by the ratio of the hypotenuse divided by the adjacent leg? Begin (Secant, or
sec)
This is the sixth tossup question.
6.
Find the value of the discriminant for the following quadratic equation: x2 – 2x = 8 (read
as x squared minus 2 x equals eight). Begin (36)
This is the seventh tossup question.
7.
What is the type of logarithm that has e as a base? Begin (Natural, or natural log)
This is the eighth tossup question.
8.
Simplify the following: √
√
square root of negative 7). Begin (
(read as the square root of negative 14 times the
√ )(read as negative 7 times the square root of 2)
This is the ninth tossup question.
9.
The measures of two complementary angles are in the ratio of 7 to 3. What is the measure,
in degrees, of each angle? Begin (Both must be given: 63 and 27)
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.
Change the following radian measure to a degree measure:
6). Begin (- 30) (read as negative thirty degrees)
(read as negative pie over
(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.
Factor the following: x3 + 8 (read as x cubed plus 8). Begin [(x + 2)(x2 - 2x + 4)](read as
the quantity x plus 2, the quantity times the quantity x squared minus 2 x plus 4)
You have 20 seconds to answer this question:
2.
Find the value of the following: sine -240 ° (read as sine of negative 240 degrees) Begin
√
( ) (read as the square root of 3 over 2)
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.
Evaluate the following:
(read as 64 to the two-thirds power). Begin (16)
This is the second tiebreaker question. You have 10 seconds to answer the question.
2.
What is the ratio in simplest form of the measure of a right angle to the measure of one
angle of an equilateral triangle? Begin (3 to 2, or 3 : 2, or 3/2)
This is the third tiebreaker question. You have 10 seconds to answer the question.
3.
Twice the greater of two consecutive odd integers is 13 less than three times the lesser.
Find these two integers. Begin (17 and 19)