Download FAMAT February 2013 Regional Algebra II Individual Test “NOTA

FAMAT February 2013 Regional
“NOTA” means “None Of These Answers”
1. Simplify the expression 2 3  32 
17
24
A)
B)
12
7
Algebra II Individual Test
1
C)
72
17
D) 17
E) NOTA

2. Which of the following is a factor of the polynomial 64 x 3  27y 6 ?


A) 4 x  3y 2

B) 4 x 12xy  3y 2
C) 4 x 12xy 2  9y 4
D) 4 x 12xy 2  3y 4 E) NOTA

3. Find the coordinates of the endpoints of the major axis of: 16x 2  9y 2  96x  36y  36  0


A) (-1, -2), (7, -2)

B) (3, 2), (3,  6)

C) (3,6), (3, -2)
D(-7,2), (1, 2)
E) NOTA
D) -i
E) NOTA

4.
Simplify: i
2011
A) -1

B) 1
C) i

5. The sum of three numbers is 108. The three numbers are changed in the following way: the first
number is decreased by 13, the second number is increased by 13, and the third number is multiplied
by 13. After these changes, the three results are all equal. Find the positive difference between the
largest and smallest of the three numbers.
A) 13
B) 26
C) 35
D) 61
E) NOTA
D) infinite sum
E) NOTA
6. Find the sum of the integral solutions of 5x  7  3x  6 .
A) 21
B) 18
C) 1

7. The linear functions 5x  2y  10 and x  3y  6 have graphs that intersect at the point (U, F) in the
coordinate plane. Find the value of U + F.
A) 
22
17

22
B)  
17
C) 36x 2  5x  50
D) 4
E) NOTA
8. The ratio of the number of boys to girls in a club is 5 to 7. If 24 more boys join the club, the ratio is
reversed. How many boys are inthe club originally?


A) 25
B) 35
C) 49
D) 70
E) NOTA
9. Factor the trinomial 36x 2  5x  50 into the form (Ax  B)(Cx  D), with A, B, C, and D integers,
and A and B non-negative. Find the value of A + B + C + D.
A) 8

B) 10

1
C) 28
D) Prime
E) NOTA
FAMAT February 2013 Regional
“NOTA” means “None Of These Answers”
Algebra II Individual Test
10. For what values of c does the equation 3x 2  6x  c have two distinct real roots?
A) c   3
B) c  3
C) c  3
D) c  3
E) NOTA





a 0 
11. If  2 1 0 
,
find
the
value
of ab – 2b + a.

3
10



 5  3 1   c b    8  31

  2  1 



A) 13
B) -107
D) 
C) -20
E) NOTA
12. What is the sum of the irrational roots of x 4  x 3  5x 2  3x  6  0 ?
A) 1  2 3
B) 2 3
C)
3
D) 0
E) NOTA

13. Given: log 2  M , log 3  A , and log 7  , which of the following is equivalent to log 504 ?



A) M 3 A 2
B) 3M  2A  
C) M 3  A 2   D) 6MA
E) NOTA


 64 4 3
 14. Simplify    over the set of real
 numbers.
 125 


A)

256
625
B)
625
256
C) 

625
256
D) 
256
625
E) NOTA
x
15. Given f (x)  2x 2  5x  7 and g(x) 
, find the value of f (g(2)) .


 1  x

A) -25
B) -9
C) -5
D) 5
E) NOTA
D) 24
E) NOTA
D) 12 + 26i
E) NOTA



16. Given x  y  11 and x 2  y 2  73 , find the value of x 2  y 2 .
A) 49
B) 48
C) 25


17. Simplify: 23i 2013 12i 2012 11i 2011  8i 2010
A) 20 + 12i
B) 20 + 4i

C) 20 + 23i

2
FAMAT February 2013 Regional
“NOTA” means “None Of These Answers”
Algebra II Individual Test
18. Evaluate: log 4 (log 9 (log 2 (log 2 256)))
A) -2
B) - ½
C) ½
D) 1
E) NOTA

19. Two of the roots of a cubic polynomial equation with integral, relatively prime coefficients are -1 and
3 – i. Which of the following is this equation?
A) x 3  7x 2 16x 10  0
C) x 3  7x 2  4 x 10  0
B) x 3  7x 2  4 x 10  0
D) x 3  5x 2  4 x 10  0
E) NOTA


20. The sum of 2 complex numbers is 2 + 3i. The difference of them is 4 – 5i. Find the product of these


2 complex numbers.
A) -7 + 13i
B) 7 -13i
C) 1-13i
D) 1 + 13i
E) NOTA
21. The Lincoln Math team bus leaves school at 5:45 am on its way to the February Regional. Fifty
minutes later, a student who overslept and missed the bus arrives at school and realizes he has
to drive himself to the competition. He drives at a constant speed of 72 mph and overtakes the
bus in one hour and 50 minutes. Assuming the bus drives at a constant speed, what is the speed
of the bus?
A) 65 mph
B) 623/5 mph
C) 572/3 mph
D) 49½ mph
E) NOTA
C) 30
D) 15
E) NOTA
6

2 
22. Find the constant term of x 
 .

x 
A) 240
B) 120

23. A quadratic function has minimum of -8 and an x-intercept of -5. Its axis of symmetry is x = -3. Find
the y-intercept of this quadratic function.
A) -5
B) 8
C) 10
D) -26
E) NOTA
24. Given log 2  J, log 3  S, and log 7  D. Express log(10!) in terms of J, S, and D.
A) 7J + 4S +D
B) 6J +4S + D
C) 7J +4S +D +2

D) can’t be determined
E) NOTA

25. If the equation 3x 2  6x 1  0 were solved by completing the square, the resulting equation would
be in the form (x  k) 2  p. Find the value of k – p.
A) 1
B) 1/3
C) - 5/12
D) 5/3
E) NOTA


3
FAMAT February 2013 Regional
“NOTA” means “None Of These Answers”
Algebra II Individual Test
26. What is the slope of the line that is perpendicular to the line defined by the equation:
log 20 2y  x log 300  2y log 5  log 3x
A) – 1/3
B) 2/3
C) 2
D) 3
E) NOTA
27. A pilot notices that her plane takes 2/3 as much time to travel 450 miles with a tailwind as it does to
 distance against the same wind. The speed of the plane in still air is 200 miles per
travel the same
hour. Find the speed of the wind in miles per hour.
A) 4
B) 15
C) 25
D) 30
E) NOTA
28. Leonardo’s Pizza Pi restaurant offers ten different toppings for their pizzas. The math team
wants to order a pizza with four different toppings for their team practice session. How many
different 4 topping pizzas are possible from Leonardo’s Pizza Pi?
A) 5,040
B) 2,520
C) 210
D) 105
E) NOTA
D) 2x 2  x  7
E) NOTA
29. Given f (x)  2x 2 13x 15 , find the value of f (x  2) .
A) 2x 2  5x  3
B) 2x 2 13x 13


C) 2x 2  5x  7

30. Sam and Thom can grade a set of papers together in 2 hours. Thom and Brandi can do the same



task in 4 hours. Sam and Brandi can do the same task in 2 hours and 24 minutes. How long
would it take the three of them working together to grade the set of papers?
A) 8 2/5 hr.
B) 23/5 hr.
C) 1 5/7 hr.
4
D) 1 1/5 hr.
E) NOTA