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1. |
Which of the following describes the system of equations 2x - y + 4 = 0 and 4x - 2y + 7 = 0? |
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A. |
consistent and independent |
B. |
none of these |
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C. |
inconsistent |
D. |
consistent and dependent |
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Hint |
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2. |
Solve the system of equations x = 4 and 3x - 4y = 12 by graphing. |
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A. |
 |
B. |
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C. |
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D. |
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Hint |
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3. |
If you solve the following system of equations by substitution, which statement is true?
x = z
x - 2y + z = 6
2x + y - 2z = 1
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A. |
You can substitute x for z into the second and third equations. |
B. |
Neither method will work. |
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C. |
Both methods will work. |
D. |
You can substitute z for x into the second and third equations. |
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Hint |
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4. |
Find the values of x and y for which the matrix equation
 is true. |
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A. |
x = -1, y = -3 |
B. |
x = 1, y = -3 |
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C. |
x = -3, y = 1 |
D. |
x = -3, y = -1 |
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Hint |
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5. |
Triangle ABC has vertices A(7, 2), B(3, -1), and C(1, 4). Find the image of the triangle after a reflection over the x-axis. |
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A. |
A'(7, -2), B'(-1, 3),
C'(-1, -4) |
B. |
A'(2, 7), B'(-1, 3), C'(4, 1) |
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C. |
A'(7, -2), B'(3, 1), C'(1, -4) |
D. |
A'(-7, -2), B'(-3, 1),
C'(-1, -4) |
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Hint |
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6. |
Find the value of  . |
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A. |
3 |
B. |
-3 |
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C. |
-17 |
D. |
17 |
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Hint |
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7. |
The graph of the system of inequalities is shown below. Name the coordinates of the vertices of the polygonal set. |
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A. |
(1, -4), (3, 0), and (0, 1) |
B. |
(-1, 1), (-1, 4), and (2, 1) |
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C. |
(1, -1), (-1, 3), and (2, 1) |
D. |
(0, 0), (2, 0), and (2, 6) |
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Hint |
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8. |
Find the maximum value of f(x, y) = 2x + y - 2 for the polygonal convex set determined by the system of inequalities. |
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A. |
18 |
B. |
6 |
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C. |
14 |
D. |
12 |
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Hint |
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9. |
Solve the system of 3 equations by substitution. x = 3y + 2z
2x + 3y + 2z = 3
-x + y - z = 6 |
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A. |
(1, 3, -4) |
B. |
no solution |
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C. |
(8, 4, -2) |
D. |
infinite solutions |
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Hint |
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10. |
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A. |
 |
B. |
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C. |
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D. |
impossible |
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Hint |
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11. |
The image of  after Rot180 · Ry-axis is the same as which other reflection, if the vertices are A(1,1), B(2,6), C(6,4)? |
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A. |
reflection over the y-axis |
B. |
reflection over the line y = x |
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C. |
none of these |
D. |
reflection over the x-axis |
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Hint |
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12. |
Set up a matrix equation for this chemistry problem. 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. |
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B. |
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C. |
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D. |
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Hint |
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13. |
Sam has $10,000 to deposit in two different savings accounts. He wants at least $3,000 in the account that earns 3% interest. He wants no less than $5,000 in the account with 7% interest. Write a system of inequalities to represent this situation. |
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A. |
x  3000
y  5000
x + y 10,000 |
B. |
x 5000
y 3000
x + y 10,000 |
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C. |
x 3000
y 5000
x + y 10,000 |
D. |
x 3000
y 5000
x + y 10,000 |
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Hint |
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14. |
Sam has $10,000 to deposit in two different savings accounts. He wants at least $3,000 in the account with 3% interest. He wants no less than $5,000 in the account with 7% interest.Graph this system of inequalities. |
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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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