MACC Math Questions
East/West Tournament Round 3
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.
The sum of the measures of the interior angles of a regular polygon is 3420°. How many
sides does this polygon have? (Emcees read question again.) Begin (21)
This is the second directed question.
2.
Find four consecutive even integers such that the fourth is the sum of the first and second.
(Emcees read question again.) Begin (4, 6, 8, and 10)
This is the third directed question.
3.
Solve for x in the following:
(read as 5 divided by the quantity 2 x minus
3, equals 4 divided by the quantity 2 x minus three, minus the quantity 1 divided by 3 x).
(Emcees read question again.) Begin ( )
This is the fourth directed question.
4.
The edges of one cube are 3 units longer than the edges of another cube. The total surface
area of the first cube exceeds the total surface area of the second cube by 234 square units.
How long is each edge of the larger cube? (Emcees read question again.) Begin (8)
This is the fifth directed question.
5.
Find the greatest common factor for 330 and 945. (Emcees read question again.) Begin
(15)
This is the sixth directed question.
6.
If the surface area of a sphere is 36 (read as 36 pie) square units, what is the radius of the
sphere in units? (Emcees read question again.) Begin (3)
MACC Math Questions Page 2
This is the seventh directed question.
7.
Find the value of the following expression and give your answer in ordinary notation -- not
scientific -- notation:
(read as the quantity 3 point 3 times ten to the negative 3, the
quantity divided by the quantity 2 point 2 times ten to the negative 5). (Emcees read
question again.) Begin (150)
This is the eighth directed question.
8.
A circle graph shows the percent of different materials found in a typical city trash
collection. Paper and paperboard account for 38% of this total. Find the measure, to the
nearest whole degree, of the central angle for this part of the circle graph. (Emcees read
question again.) Begin (137)
This is the ninth directed question.
9.
If (pronounced theta) is in standard position, terminates in the fourth quadrant, and
cosine is three-fifths, what is sine ? (Emcees read question again.) Begin ( )
This is the tenth directed question.
10.
The lengths, in units, of the diagonals of a kite are 12 and 24. Find the area, in square
units, of the kite. (Emcees read question again.) Begin (144)
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.
The areas of two circles have a ratio of 9 to 4. What is the ratio of their radii? Begin (3 to
2)
This is the second tossup question.
2.
Give the degree of the following trinomial: 5x4 – 3x2y3 + 6xy2 (read as 5 x to the fourth,
minus 3 x squared y cubed, plus 6 x y squared) Begin (5th degree)
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This is the third tossup question.
3.
What type of conic section is represented by the following formula:
(read as the
quantity x squared divided by 25, the quantity minus the quantity y squared divided by 9
equals 1)? Begin (Hyperbola)
This is the fourth tossup question.
4.
Simplify the following: √
(read as the square root of the quantity 7 over 81). Begin
( √ ) (read as one-ninth times the square root of 7) or
√
(
(read as the square root of 7 divided by nine).
This is the fifth tossup question.
5.
Any number that can be expressed as the ratio of two integers, such “a” divided by “b”
where “b” is not equal to zero, is referred to by what specific term? Begin (Rational
number)
This is the sixth tossup question.
6.
Give all of the possible number of intersections that the graphs of one line and one
hyperbola could have. Begin (All must be given: 0, 1, and 2)
This is the seventh tossup question.
7.
The area of what figure is found by using the formula A = s2 (read as A equals s squared)?
Begin (Square)
This is the eighth tossup question.
8.
In geometry, what is the specific term for a statement formed from the original statement
by negating both the hypothesis and the conclusion? Begin (Inverse)
This is the ninth tossup question.
9.
Find the value of the following:
(read as tangent of 225 degrees). Begin (1)
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 are the possible slopes of lines that make an angle of measure 45 degrees with the xaxis? Begin (Both must be given: plus or minus one)
(Emcees – Ask if there are any appeals that need to be noted.)
MACC Math Questions Page 4
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.):
You have 20 seconds to answer this question:
1.
Richard has 37 coins, all nickels, dimes, and quarters. They are worth $5.50. He has four
more quarters than nickels. How many dimes does he have? Begin (9)
You have 20 seconds to answer this question:
2.
The third term in an arithmetic series is 9, and the seventh term is 12. Find the first term.
Begin ( ) or 7.5
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, use the additional tiebreaker questions.):
This is the first tiebreaker question. You have 10 seconds to answer the question.
1.
If an angle of negative two hundred and fifty degrees is in standard position, in which
quadrant is the terminal side? Begin (II, or the second quadrant)
This is the second tiebreaker question. You have 10 seconds to answer the question.
2.
Express the following in radians: 130 ° (130 degrees) Begin (
) (read as 13 pie over 18)
This is the third tiebreaker question. You have 10 seconds to answer the question.
3.
If two triangles are similar and their perimeters are in a ratio of 2 to 1, what is the ratio of
their areas? Begin (4 to 1)
Additional tiebreaker questions
4. What is 5 degrees in radians? Begin ( ) (read as pie over 36)
5. If a polyhedron has 7 faces and fifteen edges, how many vertices does it have? Begin (10)
6. What is the measure, in degrees, of an interior angle of a regular decagon? Begin (144)