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1. |
Find (x) if f(x) = 3x2 + 1 and g(x) = 2x + 3. |
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A. |
6x2 + 5 |
B. |
12x2 - 36x + 28 |
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C. |
6x2 - 5 |
D. |
12x2 + 36x + 28 |
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Hint |
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2. |
Find the x- and y-intercepts for 3x + 4y - 12 = 0. |
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A. |
(-3, 0) and (0, -4) |
B. |
(0, 4) and (3, 0) |
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C. |
(0, 3) and (4, 0) |
D. |
(-4, 0) and (0, -3) |
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Hint |
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3. |
The compound inequality 300 < x + y < 1200 and x = 2y is shown in the graph below. List the possibilities of Bobcats and Lions produced to meet the imposed conditions. |
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A. |
All points on the segment of the line 2x = y whose endpoints are (100, 200) and (400, 800) and whose coordinates are integers. |
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B. |
All points on the segment of the line x = 2y whose endpoints are (100, 200) and (400, 800) and whose coordinates are integers. |
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C. |
All points on the segment of the line x = 2y whose endpoints are (200, 100) and (800, 400) and whose coordinates are integers. |
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D. |
All points on the segment of the line 2x = 2y whose endpoints are (200, 100) and (800, 400) and whose coordinates are integers. |
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Hint |
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4. |
Solve the system of equations 2x + 3y = -7 and x - y = 4 by graphing. |
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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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5. |
If you use the elimination method to solve the system of equations 3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method?
Method I: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3. Then add the two equations.
Method II: Multiply both sides of the first equation by 3, and multiply both sides of the second equation by 4. Then add the two equations.
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A. |
Neither Method I nor Method II is correct. |
B. |
Both Method I and Method II are correct. |
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C. |
Method II |
D. |
Method I |
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Hint |
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6. |
If you solve the following system of equations by elimination, which of the following is the best choice for the first step?
2x + y - z = 3 x + y + z = 5 x - 2y + z = 2
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A. |
Neither method will work. |
B. |
Add the first and second equations to eliminate the z variable. |
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C. |
Subtract the second and third equation to eliminate the z variable. |
D. |
Both methods will work. |
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Hint |
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7. |
Find the values of x and y for which the matrix equation is true. |
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A. |
x = -3, y = -1 |
B. |
x = -1, y = -3 |
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C. |
x = 1, y = -3 |
D. |
x = -3, y = 1 |
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Hint |
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8. |
Which of the following is a graph of the inequalities l + g > 100 and l > 70? |
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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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9. |
Use the function P(x, y) = 40x + 60y to determine how many of each item should be produced in order to maximize profit. |
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A. |
(300, 500) |
B. |
(100, 400) |
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C. |
(100, 800) |
D. |
(500, 400) |
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Hint |
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10. |
Solve |x - 1| - 8 < 3. |
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A. |
{x | -10 < x < 12} |
B. |
{x | 5 < x < 10} |
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C. |
{x | -8 < x < 10} |
D. |
{x | -4 < x < 3} |
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Hint |
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11. |
Locate the extrema for the graph of y = f(x). |
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A. |
The extrema are (-2, 1) and (4, 3). |
B. |
The extrema are (-2, 1) and (1, -1). |
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C. |
The extrema are (-1, 1) and (4, 3). |
D. |
The extrema are (-2, 1), (1, -1) and (4, 3). |
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Hint |
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12. |
Find the roots of x3 + 2x + 3 = 0. |
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A. |
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B. |
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C. |
-1, 2 |
D. |
1, -2 |
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Hint |
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13. |
Find the number of positive real zeros for f(x) = 3x5 + 2x3 + x2 + 7x - 1 = 0. |
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A. |
no positive real zeros |
B. |
4 or 2 or 0 positive real zeros |
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C. |
4 or 2 positive real zeros |
D. |
exactly 1 positive real zero |
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Hint |
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14. |
The angle of elevation of a ladder leaning against a wall is 55°. The ladder is 30 feet long. How high up the wall does it reach? |
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A. |
about 42.84 ft |
B. |
about 17.21 ft |
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C. |
about 24.57 ft |
D. |
about 52.30 ft |
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Hint |
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15. |
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A. |
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B. |
impossible |
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C. |
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D. |
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Hint |
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16. |
The quadrilateral with vertices A(-1,5), B(2,7), C(4,5) and D(3,3) is reflected over the line y = x . Find the image of the quadrilateral after the reflection. |
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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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17. |
Solve the system of inequalities by graphing. 2x + y 3 2x + y -2 y 4 x < 1 |
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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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18. |
Find the maximum value of f(x, y) = x - 4y for the system of inequalities. 2x + y 3 2x + y -2 y 4 x < 1 |
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A. |
-3 |
B. |
-17 |
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C. |
16 |
D. |
-16 |
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Hint |
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19. |
Solve |4 - x| < 0. |
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A. |
{x|x > 4} |
B. |
no solution |
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C. |
{x|x < 4} |
D. |
all real numbers |
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Hint |
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20. |
Given the function f(x) = , find the inverse. |
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A. |
f -1(x) = x - 4 |
B. |
f -1(x) = 1  |
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C. |
f -1(x) = 4  |
D. |
f -1(x) =  |
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Hint |
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