Download Math MACC-SWAC Set 9 2009

MACC/SWAC Math Questions
Both teams(A and B) are given the first ten questions. These are all 20-second questions. These
are then 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.
This is the first directed question.
1.
What is an equation, in standard form for the ellipse that satisfies the set of conditions
endpoints of major axis (2, 12) and ( 2, -4) and the endpoints of the minor axis at (4, 4) and
 ( y  4) 2 ( x  2) 2

(0, 4)? Begin 

 1
4
 64

This is the second directed question.
2.
3 p  21 p 2  7 p
Simplify the expression 2
(read as the fraction with numerator the

3p
p  49
quantity 3 p minus 21 and denominator p squared minus 49 times the fraction with
numerator the quantity p squared plus 7 p and denominator 3 p). Begin (1)
This is the third directed question.
3.
Given that f(x) = x2 - 3 (read as f of x equals x squared minus three) and g(x) = 2x + 1
 1
(read as g of x equals two x plus one) what is the value of (fg)    (read as the quantity f
 2
times g of negative one half)? Begin (0)
This is the fourth directed question.
4.
What is the solution of the system of equations x – y = 5 and 2x + y =1? Begin (2, -3)
This is the fifth directed question.
5.
What is the perimeter of rectangle GHIJ with vertices G(-7, -3), H (-7, 3), I(1, 3), and J (1, 3) ? Begin (28)
This is the sixth directed question.
6.
The point (-3, -4) lies on the terminal side of an angle θ(theta) in standard position, what is
 5
csc θ (cosecant theta)? Begin   
 4
This is the seventh directed question.
7.
A square has apothem 3. What is its area? Begin (36)
MACC/SWAC Math Questions - Page 2
This is the eighth directed question.
8.
Simplify the expression y 3
3
y
3
(read as y to the three times the square root of three
 
power divided by y to the square root of three power). Begin y 2
3
This is the ninth directed question.
9.
What is the standard equation of the ellipse with vertices (-5, 0) and (5, 0) and foci (-3, 0)
 x2 y2

and (3, 0)? Begin  
 1
 25 16

This is the tenth directed question.
10.
What is the equation of the perpendicular bisector of the line segment between the points
1


(6, -3) and (2, 5)? Begin  y  x  1
2


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.
What is the log264 (read as log base two of 64)? Begin (6)
This is the second tossup question.
2.
What do you call a system of equations that has no solution? Begin (inconsistent)
This is the third tossup question.
3.
What are the next four terms of the arithmetic sequence 55, 49, 43, . . . .? Begin (37, 31, 25,
19)
This is the fourth tossup question.
4.
How many 3 digit codes can be entered for an answering machine? Begin (1000)
MACC/SWAC Math Questions - Page 3
This is the fifth tossup question.
5.
If the lines containing each side of a polygon are drawn and at least one of the lines contains
a point on the inside of the polygon, how would you classify that polygon? Begin (concave)
This is the sixth tossup question.
6.
What type of number is written as a + bi where a and b are real numbers? Begin (complex)
This is the seventh tossup question.
7.
What is the equation of the line which passes through the points (5, 7) and (5, -8)? Begin (x
=5)
This is the eighth tossup question.
8.
For any real number a and integers m and n, am times an = what?(read as a to the m power
times a to the n power). Begin (am + n)
This is the ninth tossup question.
9.
For acute angle, θ (read as “thay-ta”, in a right triangle what trigonometric function is
defined as the side opposite θ divided by the side adjacent to θ? Begin (tangent)
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.
1
1
=
times a = 1 where a is not equal to zero represents
a
a
what property? Begin (multiplicative inverse)
For any real number a, 1 times
(SWAC 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.):
You have 20 seconds to answer this question:
1.
Evaluate
13!
(read as 13 factorial divided by 9 factorial). Begin (17,160)
9!
You have 20 seconds to answer this question:
2.
What is the sum, in degrees, of four angles if two are complementary and two are
supplementary? Begin (270)
MACC/SWAC Math Questions – Page 4
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.
 3

What is the tangent of a 30 degree angle? Begin 

 3 
This is the second tiebreaker question. You have 10 seconds to answer the question.
2.
What type of reasoning uses a number of specific examples to arrive at a plausible
generalization or prediction? Begin (inductive)
This is the third tiebreaker question. You have 10 seconds to answer the question.
3.
How many sides does a regular polygon have if the sum of its interior angles is 1080o? Begin
(8)