Math 120 Final Review: Multiple Choice Version 1
Find the domain of the following functions:
1. √19 a. ∞, 19
b. √19, ∞
√
2. a. ∞, 8 8, 5 5,9 9, ∞
b. 5,9 9, ∞
c. ∞, 19 19, ∞
d. All real numbers
c. 0, ∞
d. All real numbers
3. a. All real numbers
b. | 0
4. ln6 a. 6, ∞
b. 6, ∞
c. |
d. |
7
7
c. ∞, 6
d. ∞, 6
5. Find the domain and the range for the following function
y
x
10
-10
(5,-10)
a. D: 10, ∞, R: ∞, ∞
b. D: 2, 8, R: 10, 0
c. D: ∞, 2 8, ∞, R: 2, 8
d. D: ∞, ∞, R: 10, ∞
6. Find an equation of variation for the given situation: ) varies jointly as and the square of * and
,
inversely as +, and ) , when 2, * 3, and + 8.
a. ) b. ) 34 5
6
74 5
6
c. ) d. ) 74
6
34
6
Solve the following exponential and logarithmic applications:
7. Let 8 represent a mass of plutonium 241 (241Pu) (in grams), whose half-life is 14.4 years. The quantity
3 <⁄3=.=
of plutonium 241 present after 9 years is given by 8 100 :,;
after 10 years.
a. 0.0068 g
b. 61.79 g
. Determine the quantity present
c. 47.84 g
d. -23.18 g
8. You deposit $7550 in an account that pays 7.25% interest, compounded continuously. How long to the
nearest year will it take for the money to triple?
a. 3 years
c. 15 years
b. 28 years
d. 41 years
9. The antler spread @ (in inches) and shoulder height A (in inches) of an adult male American elk are
related by the model A 116 log@ D 40 176. Approximate the shoulder height of a male
American elk with an antler spread of 55 inches.
a. 53.4 inches
c. 1.54 inches
b. 58 inches
d. 405.4 inches
10. The speed of the wind F (in miles per hour) near the center of a tornado and the distance G (in miles)
the tornado travels are related by the model F 93 log G D 65. On March 18, 1925, a large tornado
struck portions of Missouri, Illinois, and Indiana with a wind speed at the center of about 283 miles per
hour. Approximate the distance traveled by this tornado.
c. 61.8 miles
a. 293 miles
b. 220.8 miles
d. 236.4 miles
Evaluate the following functions as indicated:
11. Find H 1 when 5 , D 4 5.
a. 6H , D 5H 4
b. 5H , 6H D 4
J
12. Find I6 when I 3
a.
b.
J
J
c. 5H , 6H 4
d. 5H , 21H D 4
J
c. d.
Find an equation of the line satisfying the following conditions:
13. Point:3,2; L 7
a. ) 7 D ,
b. ) 7 ,
14. y-intercept: 0, 18; L 4.7
a. ) 18 D 4.7
b. ) 4.7 18
7
c. ) D ,
,
d. ) 7 D c. ) 18 4.7
d. ) 4.7 18
15. Through Point: 1, 5, & perpendicular to 7 D 8) 47
=
,
c. ) a. ) b. ) JJ
d. ) =J
Match the functions or equations to their graphs:
16. 3 5
a.
c.
y
y
4
4
3
3
2
2
1
−6
−5
−4
−3 −2
1
x
−1
−1
1
2
3
4
5
−6 −5 −4 −3 −2
6
x
−1
−1
−2
−2
−3
−3
−4
−4
−5
−5
1
2
3
4
5
6
−6
−6
d.
b.
6
6
y
5
5
4
4
3
3
2
2
1
−6
−5
−4
−3 −2
y
1
x
−1
−1
1
2
3
4
5
−6
6
−5
−4
−3 −2
−1
−1
−2
−2
−3
−3
−4
−4
17. I 4, 6
a.
x
1
2
3
4
5
c.
y
y
10
10
5
5
x
x
−10
−5
6
5
−10
10
−5
5
10
5
10
−5
−5
−10
−10
d.
b.
y
y
10
10
5
5
x
x
−10
−5
5
10
−10
−5
−5
−5
−10
−10
18. A 2 D 1 D 2
a.
5
c.
y
5
y
x
x
−5
−5
5
5
−5
−5
d.
b.
5
y
5
y
x
x
−5
−5
5
5
−5
−5
19. M 3
a.
c.
6
y
y
4
4
2
x
2
−6
−4
−2
2
4
6
x
−6
−4
−2
2
4
−2
6
−2
−4
−4
−6
b.
d.
6
y
y
4
4
2
x
2
−6
−4
−2
2
x
−6
−4
−2
2
4
6
−2
−2
−4
−4
−6
4
6
20. D 4, D ) D 3, 16
a.
10
c.
10
y
5
y
5
x
−10
−5
5
x
10
−10
−5
5
−5
−5
−10
−10
b.
10
d.
10
10
y
5
y
5
x
−10
−5
5
x
10
−10
−5
5
−5
−5
−10
−10
21. N D 1 2,
a.
10
c.
y
y
5
5
x
−5
5
x
−5
5
−5
b.
d.
y
y
x
x
−5
−5
5
−5
−5
Solve the following equations:
22. |7L D 4| D 9 15
,
3O
a. , , 3O
b. ,
5
,
c. d. No solution
23. √4 3 2 3
a. 1, 3
b. 3
24. 2 , D 6 3
a.
b.
25.
JP√J
,
JP√J
,,
=
,
a. ,
b. 3
D
,J
3
26. 23,, 16
a. 2
b. 10
3 c.
d.
==
J
27. :J; 18
c. -3
d. No solution
JP√3
,
7P√J
,
3,
c. d. 3
c. 6 D
d. 4
3
a. ln 7
b. ln 6
c. 28. ln 2 D ln 9 ln 19
a. 1
b. 0
QRS 37
QRS ,
QT 3
QT J
QT 3
d. QT J
3 3⁄,
c. :3;
d. U VW
3
29. Write the quadratic function in standard form, @ A, D H. Indentify the vertex:
, D 5 D 2
,
3
3
a. D 5, 23; 5, 23
c.
:
D
; ; : , ;
,
,
=
,
=
b. D 5 23; 5, 23
,
3
3
d. : D ; ; : , ;
,
=
,
=
30. How can the graph of 2, 5 be obtained from the graph of ) , ?
a. Shift the graph 2 units left and 5 units down.
c. Shift the graph 2 units left and 5 units up.
b. Shift the graph 5 units right and 2 units down.
d. Shift the graph 2 units right and 5 units down.
31. Write a quadratic function the has -intercepts, (-4, 0) & ( 2, 0) and opens downward.
a. 4 D 2
c. D 4 2
b. D 4 2
d. 4 D 2
32. Graph the quadratic function, 2 , 7 D 5 and determine the interval(s) for which X 0.
a. ∞, 1 Y , ∞
c. ∞, 1 : , ∞
b. 1, ,;
,
d. 1, , Z
,
33. Identify the equation which matches the following graph.
6
y
4
2
x
−6
−4
−2
2
4
6
−2
−4
a. ) 2 1
b. , D ) , 1
c. ) 2 1
d. ) , 1
−6
34. Solve the following inequality and write solution in interval notation: , D 9 D 14 X 0
a. ∞, 7 2, ∞
c. 2, ∞
b. ∞, 7
d. 7, 2
Determine whether the function is odd, even, or neither.
35.
4
y
2
x
−6
−4
−2
2
4
6
−2
−4
−6
−8
a. Even
b. Odd
c. Neither
36. If a function is even, then for every point , ) on the graph of there exists another point on the
graph in the form:
a. , )
b. , )
c. , )
37. Which of the following equations is not a function of ) with respect to ?
a. 2 D 3) 6
c. , D ) , 16
,
b. ) 6 5
d. ) 4 J 5 , D 3 7
38. Find the inverse function for the following function: 3
c. 3 1
a. 3 3
d. 3 3
b. 3 ) D 39. What principal should be deposited at 8.375% compounded monthly to ensure the account will be
worth $20,000 in 10 years?
a. $10,884.35
c. $5,141.21
b. $8,681.04
d. $6,097.12
) 2 5 , D ) , 85
a. 6, 7 & 2, 9
c. No Solution
b. 6, 7 & 2, 9
d. 3.1, 11.2 & 7.1, 9.2
41. If the function, ) ] · 2< , is used to model the growth in revenue of a business, then ) represents:
a. The initial amount of revenue.
c. The amount of revenue after 9 years.
b. The time in years
d. None of the above
Predict the end behavior of the graph of _:
3
42. 4 J
J
a. Up on both sides
c. Down left & up right
b. Down on both sides
d. Up left & down right
Divide the first polynomial by the second and state the quotient and the remainder.
43. 2 = D 3 , D 5,
1
a. Quotient: 2 = D J D 4 , D 3; Remainder: 8
c. Quotient: 2 = 3 J ; Remainder: 6
b. Quotient: 2 = D J , D 2 D 1;
d. Quotient: 2 = D J D , D 4 D 3;
Remainder: 6
Remainder: 8
Use the rational zero test to find all the rational zeros of _`.
44. 2 J D 7 , 17 10
3
a. Zeros: 5, 2, 1
c. Zeros: 5, 2,
,
3
b. Zeros: 5, 2, ,
d. Zeros: 5. 2, 1
45. Perform the indicated operations with the following complex numbers and write answers in standard form:
2 D 9a5 D 8a
a. 62 61a
c. 72a , D 61a D 10
b. 82 D 29a
d. 62 D 61a
40. Find the point(s) of intersection for the following system of equations: [
46. Write the following equation in exponential form: log 49 2
b. 2 49
a. 49, 7
c. 7, 49
47. Evaluate the logarithm: ln b .
a. 5 ln b
b. 1
48. Expand the logarithmic expression: log c
a. 5 log c L D 3 log c M 2 log c j 7
b. 5 log c L D 3 log c M 2 log c j D 7
de f g
h5 c i
d. √49 7
c. b d. 5
c. log c L D log c MJ D log c j, log c k d. L MJ j, k The augmented matrix is in row-echelon form and represents a system of linear equations. Solve the
system using backward substitution:
1 0 6 8
49. l0 1 2m 9n
0 0 0 0
a. 8 *, 9 D *, * |* is a real number|
c. 8, 9, * |* is a real number|
b. 8 6*, 9 D 2*, * |* is a real number|
d. 8 D 6*, 9 2*, * |* is a real number|
50. What is the solution to @ , D k D u 0?
a. cP√c 5 =vw
,v
√c 5 =vw
b. k P
,v
c. d. cP√c 5 =vw
,v
cP√c 5 =vw
,v
Math 120 Final Review: Multiple Choice Version 1 Key
1. A
26. D
2. B
27. D
3. D
28. C
4. C
29. C
5. D
6. B
7. B
8. C
9. A
10. B
11. C
12. B
13. A
14. B
15. D
16. C
17. A
18. D
19. B
20. D
21. C
22. A
23. B
24. A
25. B
30. D
31. C
32. A
33. C
34. A
35. A
36. C
37. C
38. D
39. B
40. A
41. C
42. D
43. D
44. B
45. D
46. C
47. D
48. A
49. B
50. C