Review: Examination III
Prepared by:
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://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 = x2 + 4x
e. y = x2 - 8x + 2
f. y - 6 = x2 + 8x - 11
2. Sketch graphs of the following functions indicating the coordinates of the y-intercept:
a. y = 2x
b. y = 3x - 4
c. y = 2x+3
d. y = (-3)2x
e. y = log10 x
f. y = log10 (x + 2)
g. y = -2 log10 (x - 3)
3. Compute the complex numbers shown and write your answer in the form a + bi:
a. 5 + 3i + 2(3-4i) =
b. 7i5 =
c. (-2i)3 =
d. (3 + 2i)(3 -2i) =
e. (3-2i)/(-1 + 3i) =
4. Simplify using the laws of logs:
a.
b.
c.
d.
5. a. Find arccos (1/2)
b. Find arcsin (-1/2)
c. Find arcsin (-(Ã2)/2) and arccos (-(Ã2)/2)
d. Find arc tan (1) and arc sin ((Ã3)/2)
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 a positive angle 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 (show y-intercept):
a. y = 2 sin x
b. y = cos 2x
c. y = sin x + 3
d. y = cos (x + ¹/2)
13. Is it possible to compute: log (-3)? (Explain)
14. Simplify:
a. (x2)(x5) =
b. (x2)(x-21) =
c. (2xy)3 =
d. (x3)5 =
e. (2y3)5 =
f. (-x)3 =
g. 24 - 3(4-2) =
h. (-3)3 - 64(2-2) =