1) If f(x) = 3x + 2 and g(x) = x - 4, (g/f)(1) is:

Select one:

a. Undefined

b. -3/5 c. -5/3 d. 3/5 e.5/3

2) What is the equation of the line passing through (-1, 4) and parallel to y = 2x + 1?

Select one:

a. y = 2x + 6

b. y = 2x + 1

c. y = 2x

d. No such line exists

e. None of these

3) What is 2cis(-/3) in rectangular coordinates?

Select one:

a. (-1, - sqrt 3) b. (1, - sqrt 3) c. (1, sqrt 3) d. (-1, sqrt 3) e. Impossible

4). What is the exact value of sin (120 degrees)?

Select one:

a.

b. .866

c. 3/2

d. -1/2

e. None of these

5). Solve the system: 2x + 3y = 7, 3x - 5y = 1

Select one:

a. (2, 1)

b. (1, 2)

c. (0, 0)

d. There is no solution

e. None of these

6) What are the possible rational roots of f(x) = x⁴ -7x + 8?

Select one:

a. {8}

b. {+-1, +-2, +-7, +-8}

c. {+-1, +-2,+-8}

d. {+-1, +-8}

e. {+-1, +-2, +-4, +-8}

7) The graph of y = -2 sin (x - 2) + 1 has amplitude of:

Select one:

a. 0

b. 1

c. 2

d. 3

e. 4

8) What are the possible rational roots of f(x) = 3x⁴ - x³ + x² - x + 5?

Select one:

a. {1, 5} b. {1/3, 5/3} c. {1, 1/3, 5, 5/3} d. {1, 1/5, 3, 3/5} e. {1, 1/3, 5, 5/3}

9) If an ant is 100 feet away from a tree growing straight up, and the ant has to look up at an angle of 68 degrees to see the top of the tree, how tall is the tree? Select the closest answer.

Select one:

a. 200 feet b. 140 feet c. 80 feet d. 20 feet e. 10 feet

10). What is (2, - /6) in rectangular coordinates?

Select one:

a. 0

b. (sqrt 3, 1)

c. (sqrt 3, -1)

d. - 1 / (sqrt (2) + sqrt (6))

e. Impossible

11). What is the vertex of f(x) = x² + 3x + 2?

Select one:

a. 7

b. (0, 2)

c. (-3/2, -1/4)

d. -3/2

e. None of these

12) What is the vertex of f(x) = x² + 4x + 2?

Select one:

a. (2, 2) b. (- 2, - 2) c. (- 2, 2) d. (2, - 2)

e. None of these

13). What is the exact value of sin (22.5 degrees)?

Select one:

a. .383

b. sqrt (2)

c. sqrt (2 - sqrt(2)) / 2

d. sqrt ((2 + sqrt (2)) / 4)

e. Impossible

14). The graph of y = 4sin (3x + 2) + 1 has amplitude of:

Select one:

a. 0

b. 1

c. 2

d. 3

e. 4

15). If f(x) = 3x +2 and g(x) = x -4, (f/g)(4) is:

Select one:

a. Undefined

b. 0

c. 14

d. (3, 2, 4)

e. None of these

16). What is the period of y = 3cos (8x + /2) + 5?

Select one:

a. 2 b. c. /2 d. /3 e. /4

17). The half-life of carbon 14 is 5,730 years. Approximately, how old is a bone that has 70% of its original carbon 14?

Select one:

a. 7,500 years

b. 7,000 years

c. 6,500 years

d. 6,000 years

e. Less than 6,000 years

18). What is the equation of the line passing through (1, -4) and parallel to y = -x + 1?

Select one:

a. -x + y + 3 = 0 b. x - y + 3 = 0 c. x + y - 3 = 0 d. x + y + 3 = 0 e. None of these

19). Solve the system: x + y + z = 6, 2x - y + z = 3, x + y - z = 0

Select one:

a. (0, 0, 6)

b. (3, 2, 1)

c. 1

d. (1, 2, 3)

e. None of these

20). If an ant is 50 feet away from a tree growing straight up, and the ant has to look up at an angle of 70 degrees to see the top of the tree, how tall is the tree? Select the closest answer.

Select one:

a. 20 feet

b. 50 feet

c. 1,400 feet

d. 140 feet

e. 1,000 feet