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Alpha Individual FAMAT State Convention 2012
Answer “E” will be “NOTA” meaning none of the above answers is correct.
1. Find the fifteenth term of the arithmetic series given by:  m  3n    2m  3n   ...
a) 15m-3n
b) -41m-3n
c) -13m-3n
d) -41m+3n
e) NOTA
2. What is the lim 4 x2  4 x  2 x ?
x 
a) -1
b) 0
3. How many solutions does
a) 0
b) 2
c) - 
d) DNE
sin 2 x  tan x
 1 have over the domain 0, 2  ?
cos 2 x  cot x
c) 4
d) 8
e) NOTA
e) NOTA

2
3
and
   2 . What is A  B =?
4. If A  cos157.5 and B  sin , if cos  
2
2
2
2 2
2
1
a)  2
b)
c)
d) e) NOTA
2
4
4
5. Suppose that exactly three answers to a standard Mu Alpha Theta test are E. The remaining
27 answer choices are randomly chosen to be A, B, C, or D. What is the expected score if a
student were to bubble B to all 30 problems? (Expected score need not be an integer.)
11
27
13
15
a)
b)
c)
d)
e) NOTA
4
4
4
4
6. What is the sum of the solutions to the equation: x 2 log 2  5 x  log 64  5 x log 5 ?
a) -5
b) -1
c) 0
d) 5
e) NOTA
 1 3 2 


7. Matrix A   2 2 1  Find the sum of the entries in the third row of A1 .
 1 1 4 


1
a) 0
b) 1
c) -2
d)
7
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e) NOTA
Alpha Individual FAMAT State Convention 2012
8. Two flies go back and forth across a room with constant but different speeds, turning at the
opposite wall without loss of time. They leave opposite walls at the same instant, meeting for
the first time 700cm from one wall and meet for the second time 300 cm from the opposite wall.
What is the width (in cm) of the room?
a) 800
b) 1000
c) 1200
d) 1800
e) NOTA
9. The centers of two circles of radii of lengths 4 and 7 are 20 units apart. Find the length of the
common internal tangent segment.
a) 521
b) 20
c) 3 31
d) 9
e) NOTA
5  3x
1  3x
d) y = -1 and y = 5
e) NOTA
d) 2cis  36
e) NOTA
10. What are the horizontal asymptote(s) of the graph of: y 
a) y = -1
b) y = 5
c) y = -1 and y = 0
11. Which of the following is not a fifth root of -32?
a) 2cis324
b) 2cis180
c) 2cis 72
1
2
3
98


 ... 
. Express your answer as a fraction in
1 2  3 2  3  4 3  4  5
98  99 100
y
simplest form . Find y + x.
x
a) 149
b) 194
c) 14851
d) 24749
e) NOTA
12. Evaluate:
13. Find the distance between one of the foci and the point with the largest y value in the conic:
11x 2  28 y 2  168 y  208  0
a) 2
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b)
273
7
c)
5 14
7
d)
410
7
e) NOTA
Alpha Individual FAMAT State Convention 2012
14. A sphere is inscribed in a cone of height 8 and radius 6. Find the volume of the sphere.
9
a)
b) 32 3
c) 32
d) 36
e) NOTA
2
15. How many solutions does the equation cos 14x   cos  28x   0 have over the
domain 0, 2  ?
a) 2
b) 3
c) 28
d) 42
e) NOTA
16. If 4 boys and 5 girls are seated at random at 9 desks in a row, what is the probability that the
boys and girls are in alternate seats?
1
1
1
1
a)
b)
c)
d)
e) NOTA
126
512
2880
63
17. Hyun Jee is flying in an airplane and spots the entrance to Universal Studios at an angle of
depression of 15 degrees. She looks at the entrance again seconds later and sees it at an angle of
depression of 30 degrees. If the plane traveled horizontally 300 yards toward the entrance in that
time, how many yards above the ground is Hyun Jee’s plane?
a) 100
b) 150
c) 150 3
d) 350 3
e) NOTA
18. Given: xy  x  y  1  0
3x 2  y 2  2 y  0
Find the solution(s) and then find the sum of the abscissa(s).
a) -2
b) -1
c) 0
d) 1
e) NOTA


19. Find the minimum value of f(x) if f  x     15sin  3x   8cos  3x    2 .
2

a) -21
b) -13
c) -7
d) -5
e) NOTA
20. If x  y  7 , then what does x2  x 1  xy  3x  3 y  2  y 2  y  1 equal?
a) 294
b) 322
c) 343
d) 392
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e) NOTA
Alpha Individual FAMAT State Convention 2012
1
1 

21. Given: 223
is a mixed number  . Simplify the expression as a mixed number,
 223
225
225 

b
a and then find a + b + c.
c
a) 34
b) 43
c) 48
d) 60
e) NOTA
22. Identify the following conic: 2 x 2  5xy  2 y 2  6 x  8 y  12  0
a) Parabola b) Circle
c) Ellipse
d) Hyperbola
e) NOTA
 3
 1
23. If adjacent maximum and minimum points of a sinusoid are  ,  and   ,  and the
 2 2
 2
equation in sine can be represented by: y  A sin B  x  C   D , where the absolute value of C is
as small as possible. What is A  B  C  D =?


a) 0
b)
c)
8
4
24. Find a x b given a  4i  3 j  4k and b  5i  2 j  8k
a) 46
b) 41
c) 20i  6 j  32k
d)

2
d) 32i  12 j  23k
e) NOTA
e) NOTA
25. A parabola with vertex (-2,3) passing through (-10,-5) has a vertical directrix. What is the
distance from the vertex to the focus?
1
1
a)
b)
c) 8
d) 2
e) NOTA
4
2
26. If P(A) = .35, P(B) = .4, and the probability of A given B is .28, what is the probability of B
given A?
a) .14
b) .32
c) .50
d) .70
e) NOTA
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Alpha Individual FAMAT State Convention 2012
2

3
3
,  y 
27. Given cot x  , 0  x  and cos y 
, find tan  x  y 
5
2
5
2
7
23
1
23
a)
b)
c)
d)
26
26
2
14
28. r  5 is a?
a) Line
b) Circle
c) Inward spiral
d) Limacon
m
1
1 1
  , then a possible value of x is?
and
n
mn m n
3 i
 3 i
1 i 3
1 i 3



a)
b)
c)
d) 
2 2
2
2
2
2
2
2
e) NOTA
e) NOTA
29. If x 
30. If antilog 0.9047 = 8.03, the antilog 3.9047 =?
a) 0.803
b) 8030
c) 0.0803
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d) 803
e) NOTA
e) NOTA