Download Math MACC-SWAC Set 12 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.
1 2
5 1
Find the slope of the line that passes through the points  , and  ,  . Begin
2 3
6 4
5
 1
  1 or  
4
 4
This is the second directed question.
2.
1 6 7
w z (read as the fifth root of the quantity one thirty second w to the sixth
32
1

power z to the seventh power). Begin  wz 5 wz 2 
2

Simplify:
5
This is the third directed question.
3.
Solve for x; 2  4 x  4  6 (read as two plus the square root of the quantity 4x minus 4 is
less than or equal to 6). Begin (1 < x < 5) (read as one is less than or equal to x which is less
than or equal to five)
This is the fourth directed question.
4.
At what point do the two lines with equations 7x – 3y = 13 and y = 2x – 3 intersect? Begin
(4, 5)
This is the fifth directed question.
5.
In a right triangle XYZ, angle Y is a right angle, angle X equals 2a degrees and angle Z
a
equals deg rees . What is the measure of angle Z in degrees? Begin (18)
2
This is the sixth directed question.
6.
What is the sum of the measures of the interior angles of a convex 19-gon? Begin (3060)
This is the seventh directed question.
7.
What is the equation in standard form for the line that passes through the points (-1, 4) and
(-4, 5)? Begin (x + 3y = 11)
MACC/SWAC Math Questions - Page 2
This is the eighth directed question.
8.
The system of equations, x – 2y + z =a,
x –y + z =b and 3x +2y – 3z =c, has (2, 1, 3) as
its solution for which values of a ,b, and c? Begin (a = 3, b=4 and c= -1)
This is the ninth directed question.
9.
What is the converse of the following statement and is it true or false: “ If triangle ABC is a
right triangle, one of its angles has a measure greater than 90o”? Begin (If triangle ABC
has an angle with measure greater than 90, then triangle ABC is a right triangle – false)
This is the tenth directed question.
10.
A circle has a radius with endpoints at (2, 5) and (-1, -4). What is the area of the circle in
terms of “pie”? Begin 90 
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.
Solve the equation x2 + 2x – 120 = 0. Begin ( {-12, 10} )
This is the second tossup question.
2.
3

Solve for n, 32n+1 = 81 (read as three to the 2n +1 power equals 81). Begin  n  
2

This is the third tossup question.
3.
What is the sum of the interior angles of a regular decagon? Begin (1440o)
This is the fourth tossup question.
4.
What is a segment that divides an angle in half called? Begin (bisector or angle bisector)
MACC/SWAC Math Questions - Page 3
This is the fifth tossup question.
5.
  5  17
 5  17 

and
Solve for x in the quadratic equation x2 + 5x + 2 = 0 Begin 

2
2


This is the sixth tossup question.
6.
Factor 6x3 + 12x2 + 30x Begin 6x(x2 + 2x + 5) (read as six x times the quantity x squared
plus two x plus five)
This is the seventh tossup question.
7.
What is the equation in standard form of the parabola with its vertex at the origin and
directrix x = -3? Begin (y2 = 12x)
This is the eighth tossup question.
8.
For acute angle, θ (read as “thay-ta”, in a right triangle what trigonometric function is
defined as the side adjacent to θ divided by side opposite θ ? Begin (cotangent)
This is the ninth tossup question.
9.
Four theorems represented by three letters each are used to prove triangles congruent.
Name two of them. Begin (any two of the following – SSS(side, side, side), SAS(side, angle,
side), ASA (angle, side, angle) or AAS(angle, angle, side))
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.
If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is
congruent, how do the two lines relate to each other? Begin (they are parallel)
(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.
What is the equation of an ellipse with a co-vertex at (2, 0) and focus at (0, 5)? Begin
 x2 y2

 
 1
 4 29

MACC/SWAC Math Questions – Page 4
You have 20 seconds to answer this question:
2.
Triangle KLM has vertices K(3, 2), L(-1, 5) and M(-3, -7). List the angles in order from the
least to the greatest measure. Begin (angle M, angle L, angle K or MLK)
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.
If triangle MNP is congruent to triangle RST, then segment PM is congruent to what
segment? Begin (TR)
This is the second tiebreaker question. You have 10 seconds to answer the question.
2.
What is the geometric mean between 4 and 9? Begin (6)
This is the third tiebreaker question. You have 10 seconds to answer the question.
3.
What is focus of the parabola with equation y2 = 24x? Begin ((6, 0))