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2004 Mu Alpha Theta Convention
Hustle: Algebra II
2 5 
1. Find matrix AB if A = 
 and B =
1  3
0  2
8 1  .


2. Simplify log24+log39+log416+…+log100.
3. If one solution of 2x3 + 5x2 – 28x – 15 = 0
is x = -1/2, find the sum of the remaining
two solutions.
4. Which of the following equations does
NOT describe a conic section?
A) x2 – y2 = 4
B) x2 + y2 = 4
2
C) y = x + 4
D) y2 = 3
5. Find the third quadrant point of intersection
of the graphs of x2 – y2 = 16 and x2 + y2 =
34.
6. If [x] denotes the greatest integer function,
find all values of x for which [2x + 1] = -1.
Give your answer in interval notation.
7. Find the 150th term of the arithmetic
sequence 8, 5, 2, -1, . . . .
8. Find k so that the roots of the equation
5x2+x+1=k are equal.
9. Find k if the graph of y = 2x2 + 2kx – k
contains the point (2, 3).
10. Solve for x if x 2 2  3x  8  0 .
x2
11. Find all x so that x
1
4 9
2 3  0.
1 1
12. Solve for x if 9x - 103x + 9 = 0.
13. Simplify (6 – 3i)(4 + 3i).
14. Find x so that
3
2 x 2  15x  2 .
15. Find the remainder when 2x3 – 5x2 + 6x – 5
is divided by 2x – 1.
16. If (a, b) is the center of the graph of
4x2 – 3y2 – 8x + 18y = 35, find ab.
17. Find all x so that 9x – 2 = 27x.
18. If f ( x) 
x 1
, find f –1(4).
2
19. Solve for x if log5(2x + 1) – log5x = 2.
20. Find k if 1 + 3 ln 2 = ln k.
21. Evaluate, if possible, 96 + 24 + 6 + 3/2 + …
22. If two numbers differ by 7, what is their
least possible product?
23. Find g(3) if g is a linear function so that
g(1) = -2 and g(4) = 8.
24. Solve for x if 11  x   5 x  1 .
25. Find the simplest form of the fractional
equivalent of 0.0712 .
2004 Mu Alpha Theta Convention
Hustle: Algebra II
2 5 
1. Find matrix AB if A = 
 and B =
1  3
0  2
8 1  .


1
 40
Solution: 

 24  5
2. Simplify log24+log39+log416+…+log100.
Solution: 9(2) = 18
3. If one solution of 2x3 + 5x2 – 28x – 15 = 0
is x = -1/2, find the sum of the remaining
two solutions.
Solution: Use synthetic division to obtain
the equation 2x2 + 4x – 30 = 0 which has
sum of solutions –4/2 or -2
4. Which of the following equations does
NOT describe a conic section?
A) x2 – y2 = 4
B) x2 + y2 = 4
C) y2 = x + 4
D) y2 = 3
Solution: D
5. Find the third quadrant point of intersection
of the graphs of x2 – y2 = 16 and x2 + y2 =
34.
Solution: 2x2 = 50, so x = 5 or –5; y = 3 or
–3 so third quadrant point is (-5, -3)
6. If [x] denotes the greatest integer function,
find all values of x for which [2x + 1] = -1.
Give your answer in interval notation.
Solution: -1 < 2x + 1 < 0 so [-1, - 1/2)
7. Find the 150th term of the arithmetic
sequence 8, 5, 2, -1, . . . .
Solution: 8 + 149(-3) = -439
8. Find k so that the roots of the equation
5x2+x+1=k are equal.
Solution: 1 – 4(5)(1 – k) = 0 so k = 19/20
9. Find k if the graph of y = 2x + 2kx – k
contains the point (2, 3).
2
Solution: 3 = 8 + 4k – k so k = -5/3
10. Solve for x if x 2 2  3x  8  0 .
Solution: x  2 2 ,
2
by the quadratic
2
formula
x2
11. Find all x so that x
1
4 9
2 3  0.
1 1
Solution: 2x + 12 + 9x – 18 – 3x2 – 4x = 0
if x = 3, 2
2
12. Solve for x if 9x - 103x + 9 = 0.
Solution: (3x – 9)(3x – 1) = 0 so x = 2, 0
13. Simplify (6 – 3i)(4 + 3i).
Solution: 24 + 18i – 12i + 9 = 33 + 6i
14. Find x so that 3 2 x 2  15x  2 .
Solution: 2x2 + 15x – 8 = 0 so x = ½, -8
15. Find the remainder when 2x3 – 5x2 + 6x – 5
is divided by 2x – 1.
Solution: By synthetic substitution, -3
16. If (a, b) is the center of the graph of
4x2 – 3y2 – 8x + 18y = 35, find ab.
Solution: Center is (1, 3) so ab = 3
17. Find all x so that 9x – 2 = 27x.
Solution: 2x – 4 = 3x so x = -4
x 1
, find f –1(4).
2
Solution: 4 = (x + 1)/2 so x = 7
18. If f ( x) 
19. Solve for x if log5(2x + 1) – log5x = 2.
Solution: (2x + 1)/x = 25 so x = 1/23
20. Find k if 1 + 3 ln 2 = ln k.
Solution: ln e + ln 8 = ln 8e, so k = 8e
21. Evaluate, if possible, 96 + 24 + 6 + 3/2 + …
Solution: Infinite geometric series, ratio =
¼, so sum is 128
22. If two numbers differ by 7, what is their
least possible product?
Solution: Find minimum value of f(x) =
x(7 + x), which is –49/4
23. Find g(3) if g is a linear function so that
g(1) = -2 and g(4) = 8.
Solution: Slope is 10/3, so (g(3)–8)/(3–4) =
10/3, so g(3) = 14/3
24. Solve for x if 11  x   5 x  1 .
Solution: x = -5/4 (-5 is
extraneous)
11  x  5 x  2  5 x  1
4 x  10  2  5 x
4 x  20 x  25  5 x
2
25. Find the simplest form of the fractional
equivalent of 0.0712 .
Solution: Let n = 0.0712 then 100n =
7.1212 and so 99n = 7.05; n = 47/660
Mu Alpha Theta National Convention 2004
Hustle - Algebra 2
Answers
#
Answer
#
Answer
1
 40
1


24
5


14
1
,8
2
2
3
4
5
18
-2
D
(-5, -3)
15
16
17
18
-3
3
-4
7
6
 1
 1, 2 

19
1
23
7
-439
20
8e
21
128
8
9
10
19
20
5
3
 2
2 2,
2
22
23
11
3, 2
24
12
0, 2
25
13
33+6i
49
4
14
3
5
4
47
660