Mathematics 120 (Precalculus) Fall, 2006

Review: Examination II

prepared by:

Joseph Malkevitch
Mathematics Department
York College (CUNY)
Jamaica, NY 11451

email: malkevitch@york.cuny.edu
web page: http://www.york.cuny.edu/~malk

1. Given the functions below:

a. f(x) = x2 - 2x
b. f(x) = -x3 + x2

Compute:

i. f(-2)

ii. f(-3)

iii. f(1/2)

iv. f(x + 2)

v. f(a +3)

2. If f(x) = 2x -3 and g(x) = -x2 + 3

a. f(4) =

b. f(-2) =

c. g(-3) =

d. (g o f)(3) =

e. (f o g)(-5) =

f. (g o f)(x) =

g. (f o g)(x) =

h. Find functions f and g such that (f o g)(x) is given by (3x -3)5

3. Find the inverse of the following functions:

a. y = g(x) = -3x + 7

b. y = h(x) = x3 + 8

c. y = s(x) = -x2 + 4 (domain: x less than or equal to 0).

4. Compute the value of:

a.

b.

c.

d.

e.

5. Draw a graph of y = h(x) = -x3

a. Draw y = h(x+3)

b. Draw y = h(x-3)

c. Draw y = -h(x)

d. Draw y = h(x) + 6

e. Draw y = h(x) - 4

f. Draw y = |h(x)|

g. y = 1(x+2/3)3 - 5

i. Graph y = 2|x-5|

j. Graph y = -3x3

6. a. Use long division to divide x3 - 5x2 - 11 by x + 2. What quotient and remainder do you get?

b. Use long division to divide x3 - 5x2 - 11x + 7 by x2 - x + 4. What quotient and remainder do you get?

7. Use synthetic division to check:

a. Is 2 a root of x4 - x3 - 6x2 - x + 6 = 0?

b. The quotient when x4 - x3 - 6x2 - x + 6 is divided by x - 4.

c. The remainder when x4 - x3 - 6x2 - x + 6 is divided by x +3.

d. Is x-3 a factor of x4 - x3 - 6x2 + 6.

8. i. Convert the following angles in degrees to radians

ii. Determine for each of the following angles in what quadrant the angle lies

a. 360

b. 780

c. -210

d. 135

e. -225

f. -18

g. +10

9. i. Convert the following angles in radians to degrees.

ii. Determine for each of the following angles in what quadrant the angle lies.

a. -6¹

b. 3¹/4

c. -5¹/2

d. 19¹/6

f. -39¹/4

g. -18

h. 10

10. Find the quadrant in which each of the angles above is located.

11. Find the reference angle R which is associated with each of the angles above.

12. Compute:

a. sin 90°

b. cos 720º

c. sin 3¹/4

d. cos -210°

e. sin 23¹/3

f. cos -25¹/6

g. cos 225°

h. sin -330°