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1. |
Solve the system of equations by substitution.
x = z
x - 2y + z = 6
2x + y - 2z = 1
What is the value of x + y + z? |
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A. |
9 |
B. |
8 |
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C. |
11 |
D. |
10 |
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Hint |
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2. |
The profit for each unit of lumber is $40 and the profit for each unit of plywood is $60. Write a profit function P(x, y) if x = the number of units of lumber and y = the number of units of plywood. |
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A. |
P(x, y) = 40x - 60y |
B. |
P(x, y) = 60x + 40y |
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C. |
P(x, y) = 40x + 60y |
D. |
P(x, y) = 60x - 40y |
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Hint |
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3. |
If y varies directly as the cube of x and y = 30 when x = 2, find x when
y = 468.75. |
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A. |
9 |
B. |
7 |
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C. |
3 |
D. |
5 |
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Hint |
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4. |
Solve the equation 2x2 -x + 4 = 0 by any method. |
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A. |
 i |
B. |
 i |
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C. |
1  i |
D. |
i |
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Hint |
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5. |
Find the value of k so that the remainder of (x3 - 3x2 + kx - 6) ÷ (x + 2) is 0. |
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A. |
k = 6 |
B. |
k = 11 |
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C. |
k = -11 |
D. |
k = -13 |
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Hint |
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6. |
Find sin 5 by referring to the graph of the sine function. |
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 |
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A. |
-1 |
B. |
0 |
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C. |
1 |
D. |
 |
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Hint |
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7. |
Write the equation of the ellipse whose center is at the origin, a = 6, and  . |
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A. |
 |
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B. |
 or |
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C. |
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D. |
 or  |
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Hint |
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8. |
Find the angle  of rotation for the graph of the equation
x2 - xy - y2 - 2x - 2y + 6 = 0. Round to the nearest degree. |
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A. |
52° |
B. |
-13° |
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C. |
30° |
D. |
-27° |
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Hint |
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9. |
Write the equation  in logarithmic form. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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10. |
Evaluate  . |
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A. |
3.5121 |
B. |
3.6444 |
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C. |
4.2934 |
D. |
3.0893 |
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Hint |
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11. |
Find n for a series for which a1 = 9, d = 4.5, and Sn = 40.5. |
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A. |
6 |
B. |
3 |
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C. |
5 |
D. |
4 |
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Hint |
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12. |
Using a standard deck of cards, how many 5-card hands are possible that have 4 aces and 1 king? |
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A. |
24 |
B. |
4 |
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C. |
96 |
D. |
1 |
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Hint |
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13. |
Find the domain of f(g(x)) given f(x) =  , and g(x) = x-1 |
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A. |
x 0, 1, -1 |
B. |
x1,-1 |
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C. |
x1 |
D. |
all real numbers |
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Hint |
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14. |
Find the first three iterates of the function g(x) = x2 + x for an initial value of x0 = 1. |
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A. |
 = 2
 = 6
 = 42 |
B. |
= 2
= 6
= 12 |
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C. |
= 2
= 6
= 36 |
D. |
= 0
= 2
= 4 |
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Hint |
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15. |
Solve this problem using matrix equations.How many liters of 0.25 solution and 0.40 solution should be combined to make 10 liters of 0.35 solution? |
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A. |
6.66 L of the 0.25 solution and 3.33 L of the 0.40 solution. |
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B. |
2.5 L of the 0.25 solution and 7.5 L of the 0.40 solution. |
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C. |
4.5 L of the 0.25 solution and 5.5 L of the 0.40 solution. |
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D. |
3.33 L of the 0.25 solution and 6.66 L of the 0.40 solution. |
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Hint |
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16. |
Solve |3x + 5| - 4 < 2. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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17. |
If y varies jointly as x and the cube root of z,
and y = 30 when x = -5
and z = 27, find y when z = -8 and x = 0.5. |
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A. |
y = 20 |
B. |
y = -2 |
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C. |
y = 2 |
D. |
y = 4 |
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Hint |
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18. |
Complete the identity sin4 x - cos4 x = __________. |
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A. |
sin2 x - cos2 x |
B. |
0 |
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C. |
1 |
D. |
tan4 x |
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Hint |
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19. |
If a rectangular prism represented by the vertex matrix below is translated using the vector  , find the vertex matrix for the translated image.
 |
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A. |
 |
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B. |
 |
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C. |
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D. |
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Hint |
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20. |
How many five-letter patterns can be formed from the letters of the word seven if v must always be the last letter? |
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A. |
10 |
B. |
8 |
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C. |
16 |
D. |
12 |
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Hint |
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