Download Test - Mu Alpha Theta

Mu Alpha Theta National Convention: Hawaii, 2005
Gemini Test - Mu Division
1.
At what point does the graph of
x
7
 1  2 y  2z  9 ?
2
 3 18 
A)  ,  , 7 
2 7 
2.
1
64
3
B) f ( x)  x
1
3
C) f ( x ) 
1
x
D) f ( x)  sin x
E)NOTA
B) -49
C) 149
D) -29
E) NOTA
B)
1
32
C)
1
16
D)
3
64
E) NOTA
B) 5,912,613
C) 844,620
D) 5,912,592
E) NOTA
Which of the answer choices is closest to the variance of the weight of all rainbow trout in
the Hiwassee River based the following sample of 9 rainbow trout with weights rounded to
the nearest pound? 3 4 11 6 5 7 6 2 4
A) 2.7
7.
E)NOTA
If A is the least common multiple of 3549 and 4998 and B is their greatest common factor,
evaluate A-B.
A) 844,641
6.
 13

D)   , 2, 7 
 2

When three points are randomly chosen on a circle, what is the probability that all three of
them are within 45 degrees of each other?
A)
5.
3

C)  , 2, 2 
2

What is the next term of the sequence 1, 7, 4, -17, -29, 22, 109, ____?
A) 43
4.
 1

B)   , 2, 7 
 2

Which of the following has a vertical line tangent to it at x = 0?
A) f ( x)  x
3.
2 x  10
1 7  3z
 y 
intersect the graph of
3
3
6
B) 5
C) 7
D) 5.3
E) NOTA
x3  1
If f  x  
and g  x   f  f  x   , evaluate g   0 .
x 1
A)
1
2
B)
3
4
C)
1
8
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D)
3
2
E) NOTA
Mu Alpha Theta National Convention: Hawaii, 2005
Gemini Test - Mu Division
4
8.
Evaluate:  e x sin( x)dx
1
A) sin(e x )  e4
C)
B)

( e 4  e)
 2 1
Evaluate:
 9x
2


D) sin(e x )(e4  e)
2
9.

e4  e
2
 1

E) NOTA

 5 x  3 6 x3  5 x 2  4 x  3 dx
1
A)
3421
12
B)
17101
60
C)
856
3
D)
1145
4
E) NOTA
10. Four numbers are in arithmetic sequence such that the sum of the first two is 35 more than
the last and two times the sum of the first and last is 18 more than three times the third.
What is the product of the first two terms of the sequence?
A) 36
C) 108
B) 144
D) not enough information
E)NOTA
11. What is the surface area, in square meters, of a regular octahedron with a volume of 9 2
cubic meters?
A) 9 2
B) 18 3
C) 3 3 6
D) 81
E) NOTA
12. The delivery time for a package sent within the United States is normally distributed with a
mean of 4 days and a standard deviation of 1 day. If 300 packages are being sent, which of
the following is closest to the number of packages that will arrive in fewer than 3 days?
A) 96
B) 102
C) 198
D) 48
E) NOTA
13. Determine the slope of the line normal to the graph of y  ln x at ( e2 ,1 ).
A)
e2
2
B)
2
e2
C) 2e 2
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D)
1
2e 2
E) NOTA
Mu Alpha Theta National Convention: Hawaii, 2005
Gemini Test - Mu Division
14. What is the area of the largest square that can be contained in a regular hexagon with sides
measuring 6 cm?
A) 432  216 3
B) 27 3
C) 216  108 3
D) 48 3
E) NOTA
15. How many integer solutions to the equation x1  x2  x3  x4  10 exist if xi  1 ?
A) 84
B) 126
C) 105
D) 70
E) NOTA
16. How many three-digit numbers are divisible by 4 and do not contain the digit 2?
A) 148
B) 124
C) 136
D) 132
E) NOTA
17. A gambler repeatedly bets $1 that a coin will land on heads when tossed. Each time the coin
comes up heads the gambler wins $1; each time the coin comes up tails he loses $1. The
gambler decides he will quit playing when either he is ruined (loses all his money) or when
he has $100. If he starts with $20, what is his probability of going broke?
A) 0.80
B) 0.20
C) 0.50
D) 0.75
E) NOTA
18. Which of the following is equivalent to 1444 in mod 713?
A) 926
B) 629
C) 713
D) 144
E) NOTA
19. If the square of a positive two-digit number is decreased by the square of the number formed
by reversing the digits, which of the following will not always evenly divide the result?
A) 9
B) 11
C) the product of the digits of the original number
D) the sum of the digits of the original number
E) NOTA
cot x

for all x  . If f were to
cos x
2

 
be defined so that it is continuous at x  , determine f   .
2
2
20. Consider the function, f, defined on 0  x   by f  x  
A) 2
B) 1
C) 0
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D) -1
E) NOTA
Mu Alpha Theta National Convention: Hawaii, 2005
Gemini Test - Mu Division
21. Find the coordinates of the absolute maximum point for the curve y  xe kx where k is a
fixed positive number.
1 1
A) ( , )
k ke
1 e
B) ( ,  )
k k
1 1
C) ( , k )
k e
D) (0,0)
E) NOTA
22. What is the domain of the function log6 (log6 (log6 ( x))) ?
A) x : x  0
B) x : x  1
C) x : x  6
D) x : x  36
23. A quadrilateral inscribed in a circle has side lengths of 2 5, 5,3 2, and
area of the circle.
A)
25

4
B) 5
C) 25
D)
25

2
E) NOTA
7 . Find the
E) NOTA
24. In the expansion of  x  1 , if n = 97, how many of the coefficients are integral multiples of
n
97?
A) 97
B) 96
C) 95
D) 94
E) NOTA
C) 1188
D) 1192
E) NOTA
13
25. Evaluate:
 5u
u  3du
6
A) 1200
B) 1196
26. Assume x and y are both positive. For what y is ln( x + y) = ln(x) + ln(y)?
A) y 
1  x2
1 x
B) y 
x
x 1
C) y 
x2
1  x2
1  x2
1 x
E) NOTA
8341674
25
E) NOTA
D) y 
3333  6673
27. Evaluate:
1000
A) 667333
B) 334666
C) 343657
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D)
Mu Alpha Theta National Convention: Hawaii, 2005
Gemini Test - Mu Division
28. Farmer Joe wants to build a rectangular enclosure with
a dividing fence in the middle of the rectangle. He
plans to put some horses on one side and some cows on
the other. Also, the Ocoee River will serve as one
border of the rectangle so that no fencing is needed
there. The fence along the outside costs $6 per foot but
the dividing fence costs $12 per foot. If Farmer Joe
wants to spend $1200 for this project, what is the
maximum area, in square feet, that he can enclose?
A) 100 sq. ft.
B) 1250 sq. ft.
C) 2500 sq. ft.
4
29. Find the inverse matrix of A, if A = 8

7
 2 2 1
 4 2 7 


A) 8 3 5
B)  3 5 4  C)


 5 6 4 
 3 4 3 
D) 25 sq. ft.
2 3 
3 5  .
2 4 
 4 2 7 
1 0 0 
 5 8 3 D) 



0 1 0 
 3 4 3 
0 0 1 
E) NOTA
E) NOTA
30. The formula x(t) gives the position of a particle along the x-axis. The relationship between x
and t is given by t  x  x3  5 . What is the particle's velocity when it is at position x = 2?
A)
4
21
B)
8
49
C)
21
4
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D)
49
8
E) NOTA