Download Math February 16, 2017

MACC Math Questions
February 16, 2017
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.
Find four consecutive odd integers such that the sum of the first and twice the second is
175. (Emcees read question again.) Begin (57, 59, 61, and 63)
This is the second directed question.
2.
In triangle DEF, the measure of angle E is 50% of the measure of angle D. The measure
of angle F is 60% of the measure of angle E. Find the measures of each angle. (Emcees
read question again.) Begin (All must be given: angle D is 100° , angle E is 50°, and angle
F is 30°)
This is the third directed question.
3.
Find the value of the following: cot
(read as the cotangent of negative pie over six).
(Emcees read question again.) Begin ( √ ) (read as negative the square root of 3)
This is the fourth directed question.
4.
Solve the following inequality:
(read as the quantity negative three - fourths x is
greater than six - sevenths) (Emcees read question again.) Begin (
less than negative eight - sevenths)
) (read as x is
This is the fifth directed question.
5.
Find the area, in units, of a trapezoid with a height of 12 units and a base of 18 units, and
another base of 30 units. (Emcees read question again.) Begin (288)
This is the sixth directed question.
6.
Factor the following: x3 + 8 (read as x cubed plus 8). (Emcees read question again.) 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)
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This is the seventh directed question.
7.
Find the cotangent for the angle whose terminal side contains the point (0, - 6) (read as zero
comma negative 6). (Emcees read question again.) Begin (0)
This is the eighth directed question.
8.
Abby is 3 years younger than Mary. In 7 years, the sum of their ages will be 63. What are
their ages now? (Emcees read question again.) Begin (23 and 26, or Abby is 23 and Mary
is 26)
This is the ninth directed question.
9.
The measure of two supplementary angles is in the ratio of 5 to 7. What is the measure, in
degrees, of each angle? (Emcees read question again.) Begin (Both must be given: 75 and
105)
This is the tenth directed question.
10.
Evaluate the following:
(read as eight factorial divided by the quantity two factorial
times six factorial). (Emcees read question again.) Begin (28)
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.
For a right triangle with an acute angle A, which trigonometric function of angle A is
represented by the ratio of the opposite leg divided by the hypotenuse? Begin (Sine)
This is the second tossup question.
2.
Solve for x in the following equation:
3 power equals x). Begin (x = 3)
(read as 7 raised to the log to the base 7 of
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This is the third tossup question.
3.
Two dice are thrown, one green and one red. What is the probability that both will show a
different number? Begin (5/6)
This is the fourth tossup question.
4.
What is the sum of the whole numbers from 1 to 10? Begin (55)
This is the fifth tossup question.
5.
What term is given to an angle which intercepts an arc whose length is one unit? Begin
(Radian)
This is the sixth tossup question.
6.
What is the sum of the measures, in degrees, of the angles of an 11-gon, or 11-sided
polygon? Begin (1,620)
This is the seventh tossup question.
7.
What number is 0.3 % (read as zero point three percent ) of 6,270 ? Begin (18.81)
This is the eighth tossup question.
8.
What is the geometric mean between “a” and “b”? Begin (√
of the quantity a times b)
) (read as the square root
This is the ninth tossup question.
9.
What mathematical term refers to the number of units a certain number is from zero on
the number line? Begin (Absolute value)
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.
The graph of the following equation is an example of which type of conic section:
x2 + 3 + y2 + 9y – 10x = 2 (read as x squared plus 3 plus y squared plus 9 y minus 10x equals
2) Begin (A circle)
(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.
What is the amplitude of the graph of:
(read as y equals one-half times the
cosine of theta). Begin ( )
You have 20 seconds to answer this question:
2.
Find the degree of the following polynomial: 2xy2z + 5xyz5 + x4 (read as 2 x y squared z,
plus five x y z to the fifth, plus x to the fourth) Begin (7, or seventh degree)
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.
The volume of a cone is 72 (read as pie) cubic centimeters, and its height is equal to the
length of its radius. Find the height of the cone in centimeters. Begin (6)
This is the second tiebreaker question. You have 10 seconds to answer the question.
2.
Seventy-nine decreased by five times a number is 49. What is the number? Begin (6)
This is the third tiebreaker question. You have 10 seconds to answer the question.
3.
Change forty-five degrees to radians. Begin ( ) (read as pie over 4)