Download MATH 115,09F Final Exam -White Page 1 of 10 The following 20

Final Exam -White
MATH 115,09F
The following 20 multiple choice questions are worth 5 points each.
1.
Solve for n:
nr + R
/ =•
nE
a. n =
b.
IR
n=Ir-E
c.
R
n=lE-r
d. n = R(!E-r]
R
n~ lE + r
2.
Find the slope of the line perpendicular to the line Ax + By = C.
a.
B
m- —
A
B_
A
b.
c. mA
a.
m = A—
B
e. m =
3.
-A + C
B
B
Given the graph to the right,
determine which of the following
is NOT true.
a.
b. g(jc)>0on[0,2]
c.
g(x} is decreasing on (-4,2)
d. The domain of g is (-00,00)
e. The range of g is [-2, 2]
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MATH 115. 09F_
4.
Final Exam -White_
Page 2 of 10
4x-3 . Wx + 2
Solve: - + 2 > 6
12
a. (8,00)
c.
(-3,oo)
d. (-oo,-3)
e. (-00,8)
5.
Given / (x) = -x2 - 3x +1, find and simplify the difference quotient: —
—
a. 2x + H2-3x
b. 2x2+2
c. -2x-h-3
d. -2x + h-6
e. -2x2-h2-3
6.
Let (-6,2) be a point on the graph of y = f(x). Under the transformation y = —/(x-3)
the point
rint (-6,2) will be translated to what point?
a. (-4^,8)
b. (-3,4)
d. (-3,7)
e. (-9,4)
MATH 115, 09F_
7.
Final Exam -White_
Let / (x) = (x - 1) and g (x) = Jx + 3 . Determine the domain of
a-
(l,oo)
b.
-«,
c-
-,
d. (- oo, -3) U (-3,1)11 (l,oo)
e.
8.
-3,
Let f(x) = (x-5) . Determine the equation for f~\x).
ab. /
c.
f
d. f-\) = -(x-5)3
e. /-1 * = *£ + 3/5
9.
jc — 7
Let f(x) = - andg(x)-3jc-8. Determine
8
/
rw \- (g o /)(*) =
8
3x-71
8
c-
- (go /)(») =
8~~
4JC-15
8
3jc-15
8
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— (x) .
MATH 115. 09F_
10.
Final Exam -White_
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A rectangular field bordered on one side by a river is divided into two equal corrals by three
wooden fences (of equal length perpendicular to the river). A stone wall is parallel to the river
and connects to the wooden fences to form the corrals. The area of the field is 350 square feet.
It costs $12 per linear foot for the wooden fances and $25 per linear foot for the stone wall.
Express the cost to enclose the the field, C, as a function of its dimension x, the length of the
wooden fence.
a.
b. C(jc) = — + 12*
x
c.
d.
e. C(x} = — +36x
x
11.
Determine the equation of the quadratic function with vertex at (-5, 7) and another
point at (-8, -2).
b.
c.
169
d.
e.
/(*) = - -^-(x-5)
2 +7
J\
\
12. Let logb2 = A and log63 = C. Write the following expression in terms of A and C.
4AC-C
a. A
b. 3C + A
c. 5C + A
d. 3C-A
e. None of the preceding.
MATH 115.09F
13.
Final Exam -White
Page 5 of 10
A building 290 feet tall casts a 60 ft shadow. If a person stands at the end of the shadow and
looks up to the top of the building, what is the angle of elevation from the person to the top of the
building? Round to the nearest tenth of a degree.
a.
78.3°
b. 11.9°
c. 58.4°
d. 11.7°
e.
14.
78.1°
A laboratory is performing an experiment with bacteria growth. Three samples have the
following growth models, where A is the number of bacteria present after t hours.
Sample X: A = l40eQ31t
Sample Y: A = l60e°'25t
Sample Z: A = l2leQ'l9t
Determine which of the following are true.
I. Sample X has the fastest growth rate.
II. When the experiment began, Sample 7 had 160 bacteria.
III. It will take about 5 hours for the bacteria in Sample Z to double.
a. Only I and III are true.
b. Only II and III are true.
c. Only I and II are true.
d. None are true.
e. All are true.
MATH 115,09F
15.
Final Exam -White
If you invest $500 into an account paying 5% interest, compounded annually, how long will it
\nt
1 + - . Round to the nearest year.
n)
a. 17 years
[
b.
127 years
c. 1 year
d. 18 years
e. 145 years
16.
Evaluate the expression: 2 tan —h cos—esc—
4
3 6
8 + V3
o
b.
c.
d.
e.
17.
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..
.
A
2 + V3
1 + V2
V2 + V3
3
Given that 6 =
6
, determine which of the following is/are true.
I. The terminal side of 9 is located in quadrant III.
II. cot# = ->/3
III.
v5
2
a. None are true.
b. Only I and III are true.
c. All are true.
d. Only I and II are true.
e. Only II and III are true.
MATH 115,09F
18.
Final Exam -White
Given y = 4 cos \3x
Page 7 of 10
, determine which of the following is/are true.
I. The period is —.
II. The amplitude is 3.
III. The phase shift is — (to the right).
6
IV. The phase shift is — (to the right).
a. None are true.
b. Only I, II and III are true.
c. Only I, II and IV are true.
d. Only I and III are true.
e. Only II and IV are true.
19.
Determine an equivalent expression to sin \x + — \.
a. -sin*
b. tanx
c.
CQSJC
d. sinx
e.
20.
-cos*
Determine all solutions in [0, 2;r) of the trigometric equation: 5 sin 9 + 1 = 3 sin 9
6 ' 6
b. < 9 = ,
3 3
c. *=£6 —
6
d. 0 =**,?*
4 4
n
4?r Sn
e. 9- — , —
3
3
Final Exam -White
MATH 115.09F
Page 8 of 10
The following 5 multiple choice questions are worth 2 points each.
Use the graphs below for questions 21-25.
b.
a.
c.
e.
d.
Determine the graph which best represents each fuction type. Each graph should be used once.
21.
Rational
22.
Trigonometric
23.
Logarithmic
24.
Polynomial
25.
Exponential
Questions 21 - 25 are multiple choice.
Please remember to bubble in on the answer sheet.
Final Exam -White
MATH 115.09F
Page 9 of 10
The folio whig 15 multiple choice questions are worth 2 points each.
Determine domain, range and asymptote for each of the following functions. Choose your answers
from the appropriate list. Any answer may be used more than once.
3jc+3
Domain Choices
Range Choices
Asymptote Choices
a. (—00,00)
a. (-00,00)
a. none
b. (-«,5)U(5,oo)
b. x = 3
c. (5,oo)
b. (-oo,0]
c. [5,0,)
d. (-05,3)
d. (5,oo)
e. (-oo,0]
e. (-oo,3)U(3,oo)
d. >> = 3
e. v = 5
Domain
Range
Asymptote
26. /(*)
31. /(*)
36. g(x) _
27. g(X)
32. g(x)
37. h(x)
(vertical)
28. h(x) .
33. h(x)
38. h(x)
(horizontal)
29. k(x) .
34. k(x) .
39. k(x)
30. r ( x ) .
35. r(x) .
40. r ( x )
C•
v* —
*C
A
•*"• */
Questions 26 — 40 are multiple choice.
Please remember to bubble in on the answer sheet.
MATH 115.09F
Name
Final Exam -White
.__
Instructor
Page 10 of 10
Section
Problems 41 and 42 are free response. Page 10 should be turned in with your Answer Sheet.
. 2
41.
(5 pis) Verify the identity: 1
42.
(5 pts) Verify the identity: cos2 x tan2 x + cos2x - cos2 x
1 + cosx
= cos x
M115 09F – Final Exam Question Answer 1 C 2 A 3 B 4 E 5 C 6 D 7 E 8 C 9 C 10 A 11 No Correct Answer 12 D 13 A 14 C 15 D 16 E 17 B 18 D 19 C 20 A Question 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Answer B E D A C A A B C A C B E A D A C D C E