MACC Math Questions
March 13, 2017 (Makeup for January 30)
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.
In a cube, for what edge length does the volume, in cubic units, result in the same number
as its surface area, in square units? (Emcees read question again.) Begin (6)
This is the second directed question.
2.
Change 54 degrees to radians. (Emcees read question again.) Begin ( ) (read as 3 pie
over 10)
This is the third directed question.
3.
Simplify the following:
(read as the quantity 4 x plus 8, the quantity divided by the
quantity x squared plus 6 x plus 8). (Emcees read question again.) Begin (
divided by the quantity x plus 4 )
) (read as 4
This is the fourth directed question.
4.
A, B, and C are three collinear points, such that B is between A and C. Segment AB = 3/4
segment BC and segment AC = 28 units. Find the length, in units, of segment AB. (Emcees
read question again.) Begin (12)
This is the fifth directed question.
5.
For the graph of the following equation, find the equation of the axis of symmetry:
y = 3x2 + 6x – 17 (read as y equals 3 x squared plus 6 x minus 17). (Emcees read question
again.) Begin (x = -1)
This is the sixth directed question.
6.
Find the sum of the following series: 6 + 12 + 18 + . . . + 96 (read as 6 plus 12 plus 18
“dot, dot, dot” plus 96). (Emcees read question again.) Begin (816)
MACC Math Questions Page 2
This is the seventh directed question.
7.
Factor completely: a2 – 9a + 18 (read as a squared minus 9 a plus 18). (Emcees read
)(
)](read as the quantity a minus 3 times the quantity
question again.) Begin [(
a minus 6)
This is the eighth directed question.
8.
Find the value of the following: csc
question again.) Begin (
three)
√
(read as the cosecant of 4 pie over 3). (Emcees read
)(read as negative 2 times the square root of three over
This is the ninth directed question.
9.
Simplify the following: √
(read as 4 times the square root of 20 plus 9 times
√
the square root of 45). (Emcees read question again.) Begin ( √ ) (read as 35 times the
square root of 5)
This is the tenth directed question.
10.
Find the total surface area, in square meters, for a cylinder with a radius of 3 meters and a
height of 10 meters. Express your answer in terms of (pie). (Emcees read question
again.) Begin (78 or 78 m2)
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.
Find the value of the discriminant for the following quadratic equation:
y2 – 7y – 8 = 0 (read as y squared minus 7 y minus 8 equals zero). Begin (81)
This is the second tossup question.
2.
In which quadrant or quadrants do the sine and cosine have opposite positive and negative
signs? Begin (Both must be given: II and IV, or second and fourth, or two and four)
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This is the third tossup question.
3.
Solve for x in the following equation: 9log92 = x (read as 9 raised to the log to the base 9 of 2
power equals x). Begin (x = 2 )(read as x equals 2)
This is the fourth tossup question.
4.
State the slope of a line which would be parallel to the graph of the following equation:
3x + 4y = 2(read as 3 x plus 4 y equals 2). Begin (-3/4)
This is the fifth tossup question.
5.
Express the function: sin 47° (read as sine of 47 degrees) in terms of its cofunction. Begin
(cos 43°) (read as cosign of 43 degrees)
This is the sixth tossup question.
6.
In a bag are 7 pennies, 4 nickels, and 5 dimes. Three coins are selected at random. Find
the probability of selecting two pennies and one dime. Begin (3/16, or three- sixteenths)
This is the seventh tossup question.
7.
Find the base, in units, of a trapezoid with an area of 78 square units, a height of 6 units,
and another base of 10 units. Begin (16)
This is the eighth tossup question.
8.
The graph of the following equation is an example of which type of conic section:
4x2 + y2 +24x – 10y + 45 = 0(read as 4 x squared plus y squared plus 24 x minus 10 y plus 45
equals zero). Begin (An ellipse)
This is the ninth tossup question.
9.
What is the ratio, in simplest form of the measure, of a 70 degree angle to the measure of its
complement? Begin (7 to 2, or 7:2, or 7/2)
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.
What two operations conform to the associative property? Begin (Addition and
multiplication)
(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.
Mary can wash the windows of a building in 4 hours. Joseph can do the same job in 6
hours. If they work together, how many hours will it take them to wash the windows?
Begin (2 and 2/5, or 2 and 2/5 hours)
You have 20 seconds to answer this question:
2.
What is the amplitude of the graph of the following function: y = cos 5 x (read as y equals
the cosine of 5 x). Begin (1)
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.
When one positive integer is added to the square of the next consecutive positive integer,
the sum is 55. Find the two integers. Begin (6 and 7)
This is the second tiebreaker question. You have 10 seconds to answer the question.
2.
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 opposite leg? Begin (Cosecant,
or csc, or csc A, or csc of angle A)
This is the third tiebreaker question. You have 10 seconds to answer the question.
3.
The graph of the following equation is an example of which type of conic section:
y = x2 + 8x + y2 (read as y equals x squared plus 8 x plus y squared) Begin (A circle)