Mathematics 120 (Precalculus) Fall, 2006

Review: Examination III

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. For each of the quadratic functions below:

Determine the "vertex" (e.g. nose) of the graph and draw a sketch:

(Note: This sketch should show any x-intercepts and the y-intercept.)

a. y = (x - 2)²

b. y = -(x + 4)²

c. y = x² - 6x +5

d. y = 3x² - 6x +5

e. y = -3x² - 6x +5

f. y = x² + 4x

g. y = x² - 7x + 2

h. y - 6 = x² + 8x - 11

2. Solve the following quadratic inequalities:

a. x² + 3x ≥ 0

b. x² - 5x + 4 < 0

c. -x² + 6x ≥ 0

d. -2x² + 8x ≤ 0

e. x² + 16 > 0

3. Compute the complex numbers shown and write your answer in the form a + bi:

a. 5 + 3i + 2(3-4i) =

b. 7i^{5 =}

c. (-2i)^{3 =}

d. (3 + 2i)(3 -2i) =

e. (3-2i)/(-1 + 3i) =


4. Solve the following quadratic equations:

a. x² + 3x + 4 = 0

b. -x² + 3x + 4 = 0

c. x² + 4x = 0

d. x² + 2x + 4 = 0

e. x² + 3x - 4 = 0

5. a. Find arccos (1/2

b. Find arcsin (-1/2)

c. Find arcsin (-(√2)/2)

d. Find arc tan (1)

e. Is it possible to find: arcsec (-1000)? (Explain)

f. Is it possible to find arcsin (-3)? (Explain)

g. Is it possible to find arctan (-344)? (Explain)

6. Find:

a. sin (330°)

b. cos (225°)

c. sin (-315°)

d. tan (210°)

e. cos (120°)

f. tan ß where ß is a positive angle in quadrant II if sin ß = 7/10

g. sin ß where ß is a negative angle in quadrant IV and cos ß = 4/5

h. sec ß where ß is a positive angle in quadrant III if tan ß = 6/7

i. csc ß where ß is a positive angle in quadrant III if cos ß = -7/11

j. tan ß if ß is in quadrant II and ß = arcsin 3/8.

k. sin ß if ß is in quadrant III and ß = arctan ß = 2/3


7.. Find the value of:

a. 2⁵ - 32(4^-2) =

b.

c.

d.

e.

f. 3^-2 + (-3)³ =

g

h.

8. Know the trig functions for the 30-60-90 and 45-45-90 triangles.

9. Graph y = 3 log₁₀ x

10. Graph y = - log₂ x³

11. Know the formulas for sin 2x and cos 2x. (Yes, memorize them.)

12. Draw a graph of:

a. y = 2 sin x

b. y = cos 2x

c. y = sin x + 3

d. y = cos (x + π/2)

13. Is it possible to compute: log (-3)? (Explain)

14. Simplify:

a. (x²)(x⁵)

b. (x²)(x-²¹)