Download Math February 27, 2017

MACC Math Questions
February 27, 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.
)
Simplify: (
(
) (read as one third times the quantity six x plus three,
plus 2 times the quantity one half x minus one). (Emcees read question again.) Begin
(3x - 1) (read as 3 x minus 1)
This is the second directed question.
2.
Simplify: √
√ (read as the square root of two-thirds plus the square root of five-
sixths. (Emcees read question again.) Begin (
√
√
) (read as the quantity two times the
√
√
square root of six plus the square root of thirty, the quantity divided by 6) or
(read as the quantity the square root of 6 the quantity divided by 3 plus the quantity the
square root the quantity divided by 6).
This is the third directed question.
3.
The sum of the measures of the interior angles of a polygon is four times the sum of the
measures of its exterior angles, one angle at each vertex. How many sides does the polygon
have? (Emcees read question again.) Begin (10)
This is the fourth directed question.
4.
The absolute value of the sum of negative 7 and twice a number is equal to 23. Find the
possible values for the number. (Emcees read question again.) Begin (Both answers must
be given: 15 and -8)
This is the fifth directed question.
5.
Find the least positive angle, in terms of
that is coterminal with
(read as nine pie
divided by 2). (Emcees read question again.) Begin ( )(read as pie divided by 2)
MACC Math Questions Page 2
This is the sixth directed question.
6.
Find the difference and state the answer in its simplest form in the following:
(read as 7 divided by the quantity y minus 8, minus 6 divided by the quantity 8 minus y).
(Emcees read question again.) Begin ( ) (read as 13 divided by the quantity y minus 8)
This is the seventh directed question.
7.
What is the degree of the following polynomial: 2x2y + 3xy2 – x2y2 (read as two x squared
y, plus 3 x y squared, minus x squared y squared). (Emcees read question again.) Begin
(4)
This is the eighth directed question.
8.
The sum of twice a number and negative six is nine more than the opposite of the number.
Find the number. (Emcees read question again.) Begin (5)
This is the ninth directed question.
9.
Solve for “x” in the following equation: 2 log7 3 + 3 log7 2 = log7 x (read as 2 times the log
base 7 of 3, plus 3 times the log base 7 of 2 equals log to the base 7 of x). (Emcees read
question again.) Begin (x = 72)
This is the tenth directed question.
10.
Multiply the following, and give the answer in simplest terms: (x2 + x + 1)(x – 1)(read as
the quantity x squared plus x plus 1, times the quantity x minus 1). (Emcees read question
again.) Begin (x3 – 1) (read as the quantity x cubed minus 1)
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.
An angle with measure of 945° is in standard position. Name the quadrant which contains
this angle’s terminal side. Begin (III, or the third quadrant)
MACC Math Questions Page 3
This is the second tossup question.
2.
Find the cosine of 1560°. Begin (
)
This is the third tossup question.
3.
Which type of conic section is represented by the graph of the following equation:
9x2 – 4y2 = 4 (read as 9 x squared, minus 4 y squared equals 4). Begin (Hyperbola)
This is the fourth tossup question.
4.
If the radius and height of a cylinder are both multiplied by 3, how is the volume of the
cylinder affected by these changes? Begin (Multiplied by 27)
This is the fifth tossup question.
5.
A penny, a nickel, and a dime are tossed. Find the probability that one or two heads will
result. Begin (3/4, or three out of four)
This is the sixth tossup question.
6.
What term describes the locus of points that is equidistant from a given point called the
focus and a given line called the directrix? Begin (Parabola)
This is the seventh tossup question.
7.
What percent of 75 is 36? Begin (48, or 48%)
This is the eighth tossup question.
8.
For any numbers, “a”, “b”, and “c”, a(b c) = (a b)c (read as “a” times the quantity “b times
c” equals the quantity “a times b”, the quantity times “c”). Which mathematical property
is illustrated here? Begin (Associative property of multiplication)
This is the ninth tossup question.
9.
Is the following statement always true, sometimes true, or never true: The three angle
bisectors of a triangle intersect at a single point? Begin (Always true)
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.
In triangle ABC, side AB = side AC = 12 units, and side BC = 22. Is angle A acute, obtuse,
or right? Begin (Obtuse)
(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.
|
Solve: |
(read as the absolute value of the quantity 10 minus 2 x is greater
) (read as x is
than or equal to 6). Begin (Both answers must be given: (
greater than or equal to 8 or x is less than or equal to 2)
You have 20 seconds to answer this question:
2.
A square with side of 8 units is inscribed inside a circle. Find the circumference of the
circle in terms of . Begin ( √ ) (read as 8 pie times the square root of 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.
Find the following: tan
(read as the tangent of the quantity negative pie divided by 3)
Begin ( √ ) (read as negative the square root of 3)
This is the second tiebreaker question. You have 10 seconds to answer the question.
2.
A regular polygon has exterior angles each with a measure of 10 degrees. How many sides
does this polygon have? Begin (36)
This is the third tiebreaker question. You have 10 seconds to answer the question.
3.
What type of sequence of numbers occurs where each new term is generated by adding the
two previous terms? Begin (Fibonacci, or Fibonacci sequence)