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Grissom Math Tournament
Algebra II Test
April 16, 2005
1. Simplify the following if if i =
A.
1 34
 i
39 39
B.
31 34
 i
39 39
1 :
C.
2  3i
.
8  5i
1 34
 i
89 89
31 34
 i
89 89
D.
E. None of these
2. If C(-3, 1) is the midpoint of the line segment joining A(-2, -4) and B(x, y), then find the equation
of the line passing through B and perpendicular to AB .
A. x – 5y = -34 B. x + 5y = -22 C. 5x – y = -26 D. x + 5y = 20
E. 5x + y = -14
3. The product of three consecutive integers is 4080. What is their sum?
A. 45
4. Simplify
A. 4(3 2 )
B. 48
2
0
C. 52
 21  2 2  ...  2 7  2 8
B. 8
D. 54

1
3
C. 8(3 2 )
D.
3
6. If
B. 24
C. 22
E.
255
5. Rectangle ABCD is made up of 15 congruent squares.
How many rectangles with length equal twice the width
are contained in the given figure?
A. 26
E. 120
3
511
A
B
D
C
D. 18
E. 12
D. 5
E. 6
D. 2411
E. 2412
a  b2 .
a 2
 , then find the value of 2
b 3
a  b2
A. -6
B. -5
C. 2
7. Find the sum of the positive integral divisors of 2005.
A. 406
B. 2006
C. 2011
8. Which of the following points lie on the graph of y = 3|x| + 2?
A. (-3, 5)
B. (-2, 4)
C. (-1, 5)
D. (3, 7)
E. (2,6)
9. In a class of 32 students, on a given test, the number of A’s was equal to the number of F’s. The
number of B’s was equal to four times the number of A’s. The number of C’s was 6 times the
number of F’s. The number of D’s equals the number of B’s. Find the number of C’s.
A. 2
B. 4
C. 8
D. 12
E. none of these
10. The roots of the equation x2 + Ax + B = 0 are 5 and 4. The roots of x2 + Cx + D = 0 are 2 and 9.
Which of the following is a root of x2 + Ax + D = 0?
A. -3
B. 4
C.
3  41
2
11. Find the largest solution to the equation:
A. 3
B. 19
D. 6
E.
11  41
2
3x  25  3  2x  7 .
C. 28
D. 57
E. 60
12. Find the product of the real numbers a and b such that 2(a + bi) – 3(1-2i) = -5 + 10i.
A. -8
B. -2
C. 2
1
13. Solve the following for a:
A. 2 2
B. 3
1
86  a 3 
D. 4
E. 8
D. 9
E. 27
7
3 2
C. 4
x
14. Find the difference between the largest and smallest values of x for which 2
1
A.
1
2
B.
3
2
C.
5
2
D.
7
2
E.
9
2
1 3
x
1  10
0
2
15. If g(x) = x2 - x then find
A. 4x - 2
g( x  h )  g( x  h )
.
h
B. 6x - 2
C. 4x
D. 6x
16. If the roots of 2x2 + 8x – 1 = 0 are a and b, find
A. -34
B. 16
17. Expand ( 2 +
A.16 2 - 16 2i
E. 6x + 2
1
1
 2
2
a
b
C. 17
D. 34
E. 68
D.128 - 128 2i
E. 256 2 + 256 2i
2 i )7.
B. 32 2 + 32 2i C. 64 - 64 2i
18. If f(x+1) = 2f(x) and f(2) = 12, what is f(-2)?
A.
1
3
B. -12
C. 1/12
D. 3
E.
3
4
19. Solve for x:
log 3 9 x  log 4 64 2 x  log 2
2
A. -1, -2
B. 1, 2
1
16
C. -1, 2
 n! 
 4! 
D. 1, -2
2
20. Find the sum of the values of n for which:   
A. 9
B. 11
C. 13
E. NOTA
7!5!
 n! 
 240  .
4  4!
 4! 
D. 15
E. 17
21. Let f(x) = 3x2 – 12x + 8. Function g(x) is created by performing the following transformations
on f(x):
1) rotate the graph 90° counter-clockwise about its vertex.
2) shift the graph up two units
3) reflect the graph across the line y = x.
Which of the following is the equation of g(x)?
A. g(x) = -3x2 – 12x – 10
B. g(x) = -3x2 - 12x - 6
D. g(x) = 3x2 + 12x - 8
E. g(x) = 3x2 – 12x + 8
C. g(x)= -3x2 + 12x – 10
22. If (a, 0) and (0, b) are equidistant from the point (1, 4) and (9, 0) then find the value of a + b.
A. -5
B. -4.5
C. -4
D. -3.5
E. 3
23. In the expansion of (2a + 3b – 5c)4, find the coefficient of the ab2c term.
A. -2160
24. If x 
B. -1440
C. -1080
D. -900
E. -720
10  2
10  2
and y 
, then find the value of log 2 ( x 2  xy  y 2 ) .
2
2
A. 0
B. 1
C. 2
D. 3
E. 4
25. In a certain factory, machines A, B, and C produce widgets. Of their production, machines A, B,
and C produce 2%, 1%, and 3% defective widgets respectively. Machine A produces 35% of the
total output of widgets, machine B produces 25%, and machine C produces 40%. A widget is
chosen at random from the factory’s production and is found to be defective. Find the probability
it was produced on machine C.
A.
1
2
B.
6
11
C.
23
45
D.
24
43
E.
28
45
Tie Breaker 1. How many integers between 5 and 2005 are not multiples of an odd prime number?
Tie Breaker 2. Mr. Grissom is older than his wife. In fact, by adding his son’s age to his wife’s age,
you obtain Mr. Grissom’s age. Six years from now, Mr. Grissom will be three times as old as his
son and twice the difference between his wife’s and son’s ages. What is the sum of Mr. and Mrs.
Grissom’s ages?
Tie Breaker 3.
If log b 3  4 and log b2 27 
3a
, then find a 4  b 4 .
2