Download ExamView - PreCalc H Final Exam Practice.tst

Name: ________________________ Class: ___________________ Date: __________
Final Exam Practice for PreCalc H
____
1. Graph the quadratic function.
f (x) = x2 + 3x
A)
C)
B)
D)
1
ID: A
Name: ________________________
____
ID: A
2. Graph the quadratic function.
f (x) = - x2 - 3x + 2
A)
C)
B)
D)
2
Name: ________________________
____
ID: A
3. Find the vertex of the parabola.
y = - x2 + 16x - 59
A) (–8, -5)
B) (8, 5)
C) (–8, 5)
D) (8, –29.5)
E) (5, 8)
____
4. Determine the x-intercept(s) of the quadratic function f &x '
A) &11, 0', &16, 0'
2
x 12x 37.
B) &6, 0', &22, 0'
C) &4, 0', &9, 0'
D) &11, 0', &9, 0'
E) no x-intercept(s)
____
5. Find two positive real numbers whose product is a maximum and whose sum is 130.
A) 63, 67
B) 65, 65
C) 70, 60
D) 74, 56
E) 77, 53
3
Name: ________________________
____
ID: A
6. Graph the polynomial function.
f ( x ) = x 4x + 4
4
____
2
A)
C)
B)
D)
7. The graph of the function g(x) is a translation of the graph of f (x) = x 3. Graph the function g(x) =
(x - 1) 3.
A)
C)
B)
D)
4
Name: ________________________
____
ID: A
8. Graph the polynomial function.
y = x + 2
3
____
A)
C)
B)
D)
4
3
2
9. Find all real zeros of the polynomial f &x ' x 8x 7x and determine the multiplicity of
each.
A) x 0, multiplicity 2; x
7, multiplicity 1; x 1, multiplicity 1
B) x
7, multiplicity 2; x
1, multiplicity 2
C) x
0, multiplicity 2; x
7, multiplicity 1; x
D) x
7, multiplicity 2; x
E) x
0,multiplicity 1;x
1, multiplicity 1
1, multiplicity 2
7,multiplicity 1;x
5
7,multiplicity 1; x
1,multiplicity1
Name: ________________________
____
ID: A
10. Find a polynomial with the given zeros.
6 ,
0,0,0,
A) x
B) x
C) x
D) x
6
5
6x
3
5
3x
3
5
3
x + 6x
2
+ 6x + 3
E) none of these
____
11. Use synthetic division to divide.
ô
äå 3
ååå 4x x 2 11x 6 õõõõ y &x 2 '
ö
æ
2
A) 4x 2x 2
2
B) 4x 7x 3
2
C) 4x 5x 6
2
D) 4x 5x 12
2
E) 4x 7x 4
6
Name: ________________________
____
ID: A
12. Use synthetic division to divide.
åäå 10 4x 3 8x 22x 2 õôõ y &x 5 '
åå
õõ
ö
æ
2
A) 4x 9x 5
2
B) 4x 18x 8
2
C) 4x 7x 10
2
D) 4x 2x 2
2
E) 4x 2x 4
____
3
2
13. Use synthetic division to express P(x) = 7x 14x 18x 20 in the form
(divisor)(quotient) + remainder for the divisor x 3.
2
A) ( x 7 )( 11x + 7x + 3 ) 11
2
B) ( x 3 )( 7x + 7x + 3 ) 11
2
C) ( x 3 )( 7x + 3 ) 11
2
D) ( x 3 )( 7x + x + 3 )
E) none of these
7
Name: ________________________
____
ID: A
3
2
14. Use synthetic division to express P(x) = 2x + 5x 7x + 29 in the form
(divisor)(quotient) + remainder for the divisor x + 4.
2
A) ( x + 4 )( 2x 3x + 9 ) + 5
2
B) ( x + 4 )( 2x 3x + 5 ) + 9
2
C) ( x 4 )( 2x 3x + 5 ) 9
2
D) ( x + 4 )( 9x x + 5 ) + 9
E) none of these
____
15. Use synthetic division to perform the division.
3
2
2x 17x 16x + 11
x+1
A) 2x
B) 2x
C) 2x
D) x
2
2
19x + 3 +
8
x+1
2
19x + 8 +
11
x+1
2
19x + 3
19x + 2 8
x+1
E) none of these
8
Name: ________________________
____
16. Let P(x) = 5x
ID: A
3 + 9x 2 10x + 6.
Use synthetic division to find the value P (8).
A) 6,124
B) 3,063
C) 3,061
D) 3,062
E) none of these
____
17. Do the operation and express the answer in a + bi form.
19
28
i
A) 19 i
B) - 19 i
C) - 190 i
D) - 19
E) 19
____
18. Find all zeros of the function f &x '
A) x
4, 3, 4 3i, 4 3i
B) x
4, 3, 4 3i, 4 3i
C) x
4, 3, 4 3i, 4 3i
D) x
4, 3, 4 3i, 4 3i
E) x
4, 3, 4 3i, 4 3i
ç
֍
÷
&x 4 ' &x 3 ' èèèé x &4 3i' øøøù èèèé x &4 3i' øøøù .
9
Name: ________________________
____
ID: A
19. Find a polynomial with the given zeros.
i,
5 ,i
A) x
3
5x
3
B) x 5x 2 + x 3
C) x 5 x 2 + 5x D) x
3
5
5
2
5x + x 5
E) none of these
____
20. Given that x 5 2i is a zero of f(x)
A) x 5 2i, 5 2i, 8
B) x
5 2i, 5 2i, 2
C) x
5 2i, 5 2i, 8
D) x
5 2i, 5 2i, 2
E) x
5 2i, 5 2i, 2
x 18x 109x 232, find all the zeros of f.
3
2
2
____
21. Determine the zeros (if any) of the rational function f &x '
A) x
4
B) x
7
,x
4
C) x
49, x
D) x
7, x
7
4
49
7
E) no zeros
10
x 49
.
x4
Name: ________________________
____
ID: A
22. Determine the zeros (if any) of the rational function g &x '
A) x
B) x
4
C) x
D) x
3, x
3, x
3
4
,x
3
4
3
3
E) no zeros
____
23. Graph the function.
y=
x
2
x +1
A)
C)
B)
D)
11
3
4
2
x 3
.
Name: ________________________
____
ID: A
24. Graph the function
x 9
x2
2
f (x ) =
A)
C)
B)
D)
12
Name: ________________________
____
ID: A
25. Graph the function.
x 5x 3
x3
2
h( x ) =
A)
C)
B)
D)
13
Name: ________________________
____
ID: A
26. Find the domain of the rational function.
2
y=
x
x6
A) ( f, 10 ) ‰ ( 10 , f)
B) ( f, 6 )
C) ( f, 6 ) ‰ ( 6 , f)
D) ( f, 2 ) ‰ ( 2 , f)
E) ( f, 4 ) ‰ ( 4 , f)
____
27. Find the inverse of the one-to-one function.
y = 6x + 7
A) y =
x6
7
B)
y=
x7
6
C)
y=
6
x7
D) y =
x+7
6
E) none of the above
____
2
1( x )
28. The function f ( x ) = x 5 is one-to-one on the domain ( x d 0 ) . Find f
.
A)
f 1( x ) = x 2 + 5
B)
f 1( x ) =
C)
f 1( x ) = D)
f
E)
f 1( x ) =
1
(x ) =
x+5
x+5
1
2
x 5
x5
14
Name: ________________________
____
29. Evaluate the function f(x)
A) 5.287
ID: A
x
1.3 at x
3.6. Round to 3 decimal places.
B) 4.680
C) 20.055
D) 2.572
E) 1.690
____
30. Graph the function using translations.
f (x ) = 2 x + 1 + 1
____
A)
C)
B)
D)
31. Write the logarithmic equation ln5
1.609...
5
A) e
B) 10
5
1.609. . .
C) 2.303e
1.609...
D) 2.303 u 10
E) e
5
1.609. . . in exponential form.
5
5
1.609. . .
1.609. . .
15
Name: ________________________
____
ID: A
32. Use a calculator to find the value for log0.70821 to four decimal places.
A) –0.1497
B) –0.3449
C) 0.8502
D) –0.8502
E) 0.1497
____
33. Find the value of x.
log 4 65,536 = x
A) x = 65,536
B) x = 32,768
C) x = 4
D) x = 8
16
Name: ________________________
____
ID: A
34. Find the graph of the function.
y = log 4 ( x 2 )
____
A)
C)
B)
D)
35. Find the graph of the function.
y = log 4 x
A)
C)
B)
D)
17
Name: ________________________
____
36. Evaluate the function f(x)
your calculator.)
A) –2.928
ID: A
1.256ln x at x
14.883. Round to 3 decimal places. (You may use
B) 3.391
C) –3.391
D) 2.150
E) undefined
____
37. Evaluate the logarithm log7 42 using the change of base formula. Round to 3 decimal places.
A) 3.738
B) 0.521
C) 1.921
D) 7.273
E) 1.623
____
38. Assume that x, y, and a are positive numbers. Use the properties of logarithms to write the
expression log a 9 xy in terms of the logarithms of x and y.
A)
1
log b x log b y
9
B) 9 log b x 9 log b y
C)
1
log b (x y)
9
D) log b x log b y
E)
1
1
log b x log b y
9
9
18
Name: ________________________
____
ID: A
39. Assume that x, y and a are positive numbers. Use the properties of logarithms to write the
6 7
expression log a x y in terms of the logarithms of x and y.
A) 6 log a x 7 log a y
B) 42 log a x y
C) 6 log a x 6 log a y
D) 42 log a x 7 log a y
E) 6 log a x 42 log a y
____
40. Assume that x is a positive number. Use the properties of logarithms to write the expression
log b (x + 6) log b x as the logarithm of one quantity.
A) log b
x
2
6
x
B) log b
x6
x
C) log b
x6
x
D) log b
x
E) log b (x
2
6
6
2 6x )
19
Name: ________________________
____
41. Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the
1
expression 2 log b x 6 log b y + log b z as the logarithm of one quantity.
7
A) log b
B) log b
C) log b
D) log b
E) log b
____
ID: A
1 /7
z
6 2
x y
1 /6
z
2 7
x y
1 /2
z
7 6
x y
1 /7
x
2 6
y z
1 /7
z
2 6
x y
42. Find the exact value of lne
A) 1.25
2.50
ln e without using a calculator.
B) 5
C) 2
D) 3
E) 2.5
____
x
åä 1 õô
43. Solve åååå õõõõ
æ5ö
A) 1
125 for x.
B) -1
C) -3
D) -5
E) no solution
20
Name: ________________________
____
ID: A
44. Simplify the expression.
log 3 3 6
A) 18
B) 3
C) 6
D) 36
E) none of these
____
45. Use the One-to-One Property to solve the following equation for x.
2
3x
A)
128
128
3
B) C)
7
3
D)
3
7
64
3
E) 2
____
46. Solve for x: 4
A) 7.587
x / 2
0.0052. Round to 3 decimal places.
B) 10.518
C) 13.291
D) –13.291
E) –3.794
21
Name: ________________________
____
ID: A
47. An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously.
How long will it take to double the investment?
A) 13.86 years
B) 14.86 years
C) 14.40 years
D) 13.40 years
E) 1 year
____
48. Determine the quadrant in which an angle, T, lies if T
A) 1st quadrant
B) 2nd quadrant
C) 3rd quadrant
D) 4th quadrant
____
49. Find (if possible) the supplement of
A)
2S
13
B)
5S
13
C)
12S
13
D)
11S
26
11S
.
13
E) not possible
22
5.40 radians.
Name: ________________________
____
ID: A
50. Determine two coterminal angles (one positive and one negative) for T
A) 127q, 233q
503q.
B) 307q, 413q
C) 127q, 323q
D) 217q, 143q
E) 217q, 323q
____
51. Convert 260q 59' 51" to degree-decimal form. Round answer to three decimal places.
A) 260.990q
B) 260.495q
C) 260.499q
D) 262.023q
E) 260.998q
____
52. Find the length of the arc, S, on a circle of radius 7 feet intercepted by a central angle of 330q.
Round to two decimal places.
A) S 40.32 feet
B) S
26.88 feet
C) S
80.63 feet
D) S
53.76 feet
E) S
32.25 feet
23
Name: ________________________
____
1
and cos 30q
2
53. Given sin30q
ID: A
3
, determine the following:
2
csc 30q
A) csc 30q
3
3
B) csc 30q
2
2
C) csc 30q
3
D) csc 30q
2
E) undefined
____
A) T
3
, find the value of T in degrees &0 T 90q ' without the aid of a calculator.
2
60q
B) T
45q
C) T
15q
D) T
90q
E) T
75q
54. If sinT
24
Name: ________________________
____
55. Using the figure below, if T
A) x
13
tan4q
B) x
8
cot26q
C) x
8
tan26q
D) x
4
sin13q
E) x
26
csc 8q
ID: A
26q and y
8, determine the exact value of x.
25
Name: ________________________
____
56. Given the figure below, determine the value of sin T .
A) sin T = B) sin T =
3
5
4
3
C) sin T = 4
5
D) sin T = 3
4
E) sin T =
____
ID: A
3
4
57. The point &5, 12' is on the terminal side of an angle in standard position. Determine the exact
value of tanT .
12
A) tanT 13
1
12
B) tanT
C) tanT
12
5
D) tanT
17
12
E) tanT
13
12
26
Name: ________________________
____
58. Given the equation below, determine two solutions such that 0q d T 360q.
csc T
____
ID: A
2
A) T
60q, 240q
B) T
30q, 150q
C) T
30q, 210q
D) T
45q, 225q
E) T
225q, 315q
59. Use an inverse function to write T as a function of x.
äå
ôõ
A)
õõ
T tan1 åååå
õõ
2x
1
æ
ö
B)
T tan1 åååå
C)
õõ
T tan1 åååå
õõ
2
æ
ö
D)
õõ
T tan1 åååå
õõ
x
1
æ
ö
E)
T sin1 &2x 1'
4
åä 2x 1 õôõ
õõ
õ
æ 4 ö
åä x 1 õô
äå 1 ôõ
27
Name: ________________________
____
çè ä
èè å 2S
60. Use the properties of inverse trigonometric functions to evaluate arctanèèèè tanåååå
èé æ 9
7S
A) 9
B)
2S
7
C)
9S
2
D)
2S
9
E)
____
ID: A
S
9
äå
11 ôõ
61. Find the exact value of cos åååå arctan õõõõ .
60 ö
æ
11
A)
60
B)
72
11
C)
61
11
D)
61
72
E)
60
11
28
ôõ ÷øøø
õõ øø .
õõ øø
ö øù
Name: ________________________
____
ID: A
62. Use fundamental identities to simplify the expression below and then determine which of the
following is not equivalent.
äå S
ôõ
sinåååå x õõõõ csc x
æ2
ö
A) 1
cos x
sinx
B)
C) cotx
1
tanx
D)
E) cos x csc x
____
63. Factor; then use fundamental identities to simplify the expression below and determine which of
the following is not equivalent.
cot D cot D cos D
2
2
2
A) cos D
2
B) 1 sin D
2
C) tan D
2
ä
ôõ
2å S
D) sin åååå D õõõõ
æ2
ö
1
E)
2
sec D
29
Name: ________________________
____
ID: A
9 tanT , use trigonometric substitution to write
64. If x
where S
2
A) 9 cscT
T
S
2
81 x as a trigonometric function of T,
2
.
B) 9 secT
C) 9 tanT
D) 9 sinT
E) 9 cosT
____
65. Use a graphing utility to approximate the solutions (to three decimal places) of the given equation
äå S S ôõ
in the interval åååå , õõõõ .
æ 2 2ö
6 sin2x 8 cos x 9 sin x
____
A) x
0.730
B) x
0.094
C) x
1.336
D) x
0.139
E) x
0.398
6
66. Find the exact value of the given expression using a sum or difference formula.
sin345q
A)
B)
C)
D)
3 1
2 2
3 1
2 2
3 1
2 2
3 1
2 2
30
Name: ________________________
____
ID: A
67. Write the given expression as the cosine of an angle.
cos 60q cos 65q sin60q sin65q
A) cos &65q '
B) cos &125q '
C) cos &5q '
D) cos &60q '
E) cos &130q '
____
68. Write the given expression as the sine of an angle.
sin100q cos 35q sin35q cos 100q
A) sin&70q '
B) sin&135q '
C) sin&65q '
D) sin&100q '
E) sin&35q '
____
69. Find the exact solutions of the given equation in the interval Y0, 2S '.
sin2x
sinx
A) x
2S
4S
, S,
3
3
B) x
0,
C) x
S
3
, S,
5S
3
S 7S 11S
2
D) x
0,
E) x
0
,
6
,
S 2S
3
,
3
6
, S,
4S 5S
,
3
3
31
Name: ________________________
____
ID: A
70. Use the figure below to determine the exact value of the given function.
cos 2T
____
A) cos 2T
12
13
B) cos 2T
9
13
C) cos 2T
12
5
D) cos 2T
7
13
E) cos 2T
5
13
71. Use the half-angle formulas to determine the exact value of the given trigonometric expression.
tan
3S
8
A) tan
3S
8
B) tan
3S
8
C) tan
3S
8
2 1
D) tan
3S
8
2
2
E) tan
3S
8
2
4
2
2 1
2
4
2
32
Name: ________________________
____
ID: A
72. Use the sum-to-product formulas to find the exact value of the given expression.
sin150q sin30q
A) 0
B) –1
C) 1
3
2
D)
E) ____
3
2
73. Determine the area of a triangle having the following measurements. Round your answer to two
decimal places.
A
126q, b
9, and c
10
A) 43.69 sq. units
B) 36.41 sq. units
C) 29.12 sq. units
D) 32.77 sq. units
E) 40.05 sq. units
33
Name: ________________________
____
ID: A
74. Given A 54q, b 11, and c 15, use the Law of Cosines to solve the triangle for the value of a.
Round answer to two decimal places.
A) 12.33
B) 17.78
C) 13.69
D) 23.24
E) 15.06
____
75. Find the component form of vector v with initial point &6, 2' and terminal point &7, 3'.
A) v
13, 5
B) v
3, 5
C) v
13, 5
D) v
5, 13
E) v
8, 10
34
Name: ________________________
____
ID: A
76. Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are
drawn to the same scale as the graph below.]
u v
35
Name: ________________________
ID: A
A)
D)
B)
E) none of these
C)
36
Name: ________________________
____
____
A) 9u v
11, 11
B) 9u v
37, 11
C) 9u v
19, 34
D) 9u v
41, 11
E) 9u v
13, 43
4, 2 , determine 9u v.
78. Find the vector v that has a magnitude of 4 and is in the same direction as u, where u
A) v
4
8
,
5
5
B) v
2
1
,
5
5
C) v
2
4
,
5
5
D) v
3
3
,
5
5
E) v
____
1, 5 and v
77. Given u
ID: A
79. Given u
6
3
,
5
5
2, 6 and v
3, 1 , find u ˜ v.
A) 12
B) 6
C) 0
D) 16
E) –20
37
3, 6 .
Name: ________________________
____
ID: A
80. Find the angle between the vectors u and v if u
1, 4 , and v
decimal places.
A) 155.24°
B) 155.93°
C) 157.17°
D) 158.13°
E) 158.58°
____
81. Find the angle between the vectors u and v.
A)
B)
C)
D)
E)
____
82. Determine whether u are v and orthogonal, parallel, or neither.
1 3
u
,
, v 2, 9
3 2
A) orthogonal
B) parallel
C) neither
38
3, 4 . Round answer to two
Name: ________________________
____
ID: A
83. Determine whether u are v and orthogonal, parallel, or neither.
u 4, 7 , v 28, 8
A) orthogonal
B) parallel
C) neither
39
Name: ________________________
____
ID: A
84. Plot the following complex number.
A)
D)
B)
E)
C)
40
Name: ________________________
____
ID: A
85. Find the absolute value of the complex number 1 2i.
3
A)
B) 3 3
C) 5
D) 4 5
E)
____
5
86. Write the complex number shown below in trigonometric form.
A)
B)
C)
D)
E)
41
Name: ________________________
____
ID: A
87. Find the trigonometric form of 11 11i.
äå
3S
3S ôõõõ
isin
A) 11 åååå cos
õ
4
4 õö
æ
11 äååå
3S
3S ôõõõ
isin
B)
åå cos
õ
2 æ
2
2 õö
äå
3S
3S ôõõõ
isin
C) 11 åååå cos
õ
2
2 õö
æ
åä
3S
3S
isin
D) 11 2 åååå cos
4
4
æ
E)
121
4
åäå
åå cos 3S isin 3S
å
8
8
æ
õôõ
õõ
õ
ö
õôõ
õõ
õ
ö
____
88. Find the trigonometric form of the complex number shown below.
4 i
äå åä
äå 1 ôõ õôõ
äå 1 ôõ õôõ ôõõ
åäå
å åå
å
õ
å
å
õ
å
õ
å
17 åå cos åå arctanåå õõ õõ isinåå arctanåååå õõõõ õõõ õõõõ
A)
å
å åæ
æ 6 ö õö
æ 6 ö õö õö
æ
æ
äå äå
ô
äå
åä 3 õô ôõõ
åä 3 õô ôõõ õõ
å å
å
17 åååå cos ååå arctanåååå õõõõ õõõ isinååå arctanåååå õõõõ õõõ õõõõ
B)
å åæ
åæ
æ 20 ö õö
æ 20 ö õö õö
æ
äå äå
äå
äå 1 ôõ ôõõ
äå 1 ôõ ôõõ ôõõ
åå åå
åå
å
õ
õ
å
õ
å
17 åå cos åå arctanåå õõ õõ isinåå arctanåååå õõõõ õõõ õõõõ
C)
å
å åæ
æ 4 ö õö
æ 4 ö õö õö
æ
æ
äå äå
äå
äå 1 ôõ ôõõ
äå 1 ôõ ôõõ ôõõ
å å
å
17 åååå cos ååå arctanåååå õõõõ õõõ isinååå arctanåååå õõõõ õõõ õõõõ
D)
å åæ
åæ
æ 8 ö õö
æ 8 ö õö õö
æ
äå
åäå äåå
äå 3 ôõ ôõõ
äå 3 ôõ ôõõ õôõ
å
17 åååå cos ååå arctanåååå õõõõ õõõ isinååå arctanåååå õõõõ õõõ õõõõ
E)
å
å åæ
æ 4 ö õö
æ 4 ö õö õö
æ
æ
____
89. Find the trigonometric form of 8 3 8i.
äå
7S
7S ôõõõ
isin
A) 8 åååå cos
õ
6
6 õö
æ
åä
7S õôõõ
7S
isin
B) 16 åååå cos
õ
6
6 õö
æ
åä
4S õôõõ
4S
isin
C) 64 åååå cos
õ
3
3 õö
æ
äå
4S ôõõõ
4S
isin
D) 16 åååå cos
õ
3
3 õö
æ
äå
4S ôõõõ
4S
isin
E) 8 åååå cos
õ
3
3 õö
æ
42
Name: ________________________
____
ID: A
90. Represent the complex number below graphically.
A)
D)
B)
E)
C)
43
Name: ________________________
____
ID: A
åä
7S
7S
isin
91. Find the standard form of the complex number 6 åååå cos
12
12
æ
hundredth.
A) 1.55 5.8i
õôõ
õõ . Round values to the nearest
õ
ö
B) 3 5.2i
C) 1.55 5.8i
D) 1.55 5.8i
E) 3 5.2i
____
92. Find the standard form of the complex number 9 åäæ cos &34q14'' isin&34q14'' õôö . Round values to the
nearest hundredth.
A) 8.5 3.69i
B) 7.44 5.06i
C) 7.44 5.06i
D) 3.91 6.28i
E) 3.91 6.28i
____
93. Perform the operation shown below and leave the result in trigonometric form.
çè ä
ô ÷øø çèè ä
ô ÷øø
èè åå
èè 6 åå cos 5S isin 5S õõõõ øøø èèè 3 åååå cos 4S isin 4S õõõõ øøø
èè å
6
6 õö øøøù èèèé åæ
5
5 õö øøøù
èé æ
çè ä
÷
èè åå
2S
2S ôõõõ øøøø
è
å
isin
A) èèè 18 åå cos
õø
3
3 õö øøøù
èé æ
çè ä
÷
2S
2S ôõõõ øøøø
èèè ååå
isin
B) èèè 9 åå cos
õø
3
3 õö øøøù
èé æ
çè ä
÷
èè åå
õôõ øøøø
49
49
S
S
è
õõ ø
isin
C) èèè 18 ååå cos
30
30 õö øøøù
èé æ
÷
èçè äå
49S
49S ôõõõ øøøø
èè åå
9
cos
isin
è
D) èè åå
õø
30
30 õö øøøù
èé æ
çè ä
÷
èè åå
5S ôõõõ øøøø
5S
è
å
isin
E) èèè 18 åå cos
õø
6
6 õö øøøù
èé æ
44
Name: ________________________
____
ID: A
94. Multiply the complex numbers below and leave the result in trigonometric form.
çè ä
ô ÷øø çèè ä
ô ÷øø
èè åå
èè 7 åå cos 6S isin 6S õõõõ øøø èèè 10 åååå cos 4S isin 4S õõõõ øøø
èè å
7
7 õö øøøù èèèé åæ
9
9 õö øøøù
èé æ
äå
82
82 ôõ
A) 17 åååå cos S isin S õõõõ
63
63 ö
æ
äå
10
10
B) 17 åååå cos S isin S
63
63
æ
åä
10
10
C) 70 åååå cos S isin S
63
63
æ
åä
82
82
D) 70 åååå cos S isin S
63
63
æ
äå
58
58
E) 70 åååå cos S isin S
63
63
æ
____
ôõ
õõ
õõ
ö
õôõ
õõ
õ
ö
õôõ
õõ
õ
ö
ôõ
õõ
õõ
ö
95. Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.
&4 4i' &8 8i'
åä
5S
5S õôõõ
isin
A) 32 åååå cos
õ
4
4 õö
æ
äå
3S
3S ôõõõ
isin
B) 64 åååå cos
õ
2
2 õö
æ
äå
S
S ôõ
C) 32 åååå cos isin õõõõ
2
2ö
æ
äå
S
S ôõ
D) 64 åååå cos isin õõõõ
2
2ö
æ
äå
3S
3S
isin
E) 32 åååå cos
4
4
æ
ôõ
õõ
õõ
ö
45
Name: ________________________
____
____
ID: A
96. Given A 53q, B 73q , and c 8, use the Law of Sines to solve the triangle for the value of a.
Round answer to two decimal places.
A) a
6.77
B) a
8.10
C) a
7.90
D) a
9.58
E) a
6.68
97. Determine which ordered pair is a solution of the system.
êí
í x 8y 10
ëí
íí 2x y 5
ì
A) (1, –2)
B) (2, 1)
C) (–5, 4)
D) (–2, 1)
E) (–4, –5)
46
Name: ________________________
____
ID: A
98. Solve the system of equations by graphing.
êí
íí
í 4x 3y = 2
ëí
íí
íì 8x + 9y = 94
A) (11, 0)
B) (–5, –6)
C) (5, 6)
D) (–1, 12)
E) (6, 5)
____
99. Solve the system.
êí
íí
í 8x
ëí
íí
íì -4x
36y
=
16
+
18y
=
-8
A) x = 2, y = 9
B) x = 3, y = 4
C) (x,
2x 4
)
9 9
D) x = 1, y = 4
E) no solution
47
Name: ________________________
ID: A
____ 100. Solve the system by substitution, if possible.
êí
íí
í y = 9x 21
ëí
íí
íì 3x y = 3
A) (9, –2)
B) (6, 3)
C) (–3, 10)
D) (3, 6)
E) no solutions
____ 101. Solve the system by substitution, if possible.
êí
íí
í 4x + 3y = -6
ëí
íí
íì 8x + 6y = 36
A) (5, 2)
B) (3, 2)
C) (2, 5)
D) (1, 6)
E) no solutions
48
Name: ________________________
ID: A
____ 102. Solve the system by the method of substitution.
êí
íí y 5x
ëí
íí y x 3 4x 2 12x
ì
A) (0, 7)
B) (0, 0)
C) (7, –5), (–7, 5)
D) (7, –5)
E) no real solution
____ 103. Solve the system, if possible.
êí
íí x + y + z = 15
íí
í
ëí 7x + y + z = 75
íí
íí 3x + y z = 29
íì
A) x = 10, y = 2, z = 3
B) x = –10, y = –2, z = –3
C) x = 3, y = 10, z = –3
D) x = 12, y = 9, z = –3
E) no solution; inconsistent system
49
Name: ________________________
ID: A
____ 104. Find the equation of the circle
x y Dx Ey F
2
2
0
that passes through the points &3, 8', &2, 3', &8, 3'.
2
2
A) x y 6x 6y 7 0
B) x y 3x 3y 7
2
2
0
C) x y 6x 6y 43
0
D) x y 6x 6y 25
0
E) x y 3x 3y 25
0
2
2
2
2
2
2
____ 105. Write the partial fraction decomposition of the rational expression.
7
x 13x 40
1
7 äååå 1
A)
åå
3 æx5 x8
1
7 äååå 1
B)
åå
3 æx5 x8
ôõ
õõ
õõ
ö
äå 1
1
åå
åå
æx8 x5
ôõ
õõ
õõ
ö
2
C)
D)
E)
7
3
ôõ
õõ
õõ
ö
7
7
7
2
40x
40
x
7
2
x 13x 40
50
Name: ________________________
ID: A
____ 106. Write the augmented matrix for the system of linear equations.
êí
íí x 7y 4z 5
íí
íëí 2y 3z 3
íí
íí x
4z 5
ì
èçè
ø÷
èè 1 7 4 5 øøø
èè
øø
èè
øø
èè
ø
3 øøøø
A) èèè 1 2 3
èèè
øøø
èè
ø
èè 1 1 4 5 øøø
èèé
øøù
èçè
ø÷
èè 1 7 4 5 øøø
èè
øø
èè
øø
èè
ø
3 øøøø
B) èèè 0 2 3
èèè
øøø
èè
ø
èè 1 0 4 5 øøø
èèé
øøù
èçè
ø÷
èè 1 7 4 5 øøø
èè
øø
èè
øø
èè
ø
2 3
3 øøøø
C) èèè
èèè
øøø
èè
ø
èè 1
4 5 øøø
èèé
øøù
èçè
ø÷
èè 1 7 4 5 øøø
èè
øø
èè
øø
èè
ø
3 øøøø
D) èèè 3 23 0
èèè
øøø
èè
ø
èè 1 4
0 5 øøø
èèé
øøù
çè
÷ø
èè
ø
èè 1 7 4 5 øøø
èè
øø
èè
øø
è
3 øøøø
E) èèè 0 2 3
èèè
øøø
èè
ø
èè 1 4 0 5 øøø
èèé
øøù
51
Name: ________________________
ID: A
____ 107. Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix
çè
÷ø
èè
ø
èè 6 9 0 øøø
èè
øø
èè
øø
èè
ø
èé 0 9 7 øøù
New Row-Equivalent Matrix
çè
÷ø
èè
ø
èè 6 27 14 øøø
èè
øø
èè
øø
èè
ø
9
7 øøù
èé 0
A) Add 2 times R1 to R2.
B) Add –2 times R2 to R1.
C) Add –2 times R1 to R2.
D) Add 2 times R1 to R1.
E) Add 2 times R2 to R1.
____ 108. Write the system of linear equations represented by the augmented matrix. Then use
back-substitution to solve. (Use variables x, y, and z.)
ø÷ø
èçè
èè 1 7 9
12 øøøø
èè
øø
èè
ø
èè
èè 0 1 7 23 øøøø
èèè
øøø
ø
èèè
èè 0 0 1
3 øøøø
èèé
øù
A) x = 83, y = –5, z = –4
B) x = –2, y = –1, z = 3
C) x = –1, y = 2, z = –3
D) x = –1, y = –2, z = 3
E) x = 2, y = 3, z = 1
52
Name: ________________________
ID: A
____ 109. Solve the system by Gauss - Jordan elimination.
êí
íí
íí
íí
íí
í
ëí
íí
íí
íí
íí
íì
1
3
2
x + y z = 8
3
4
3
x+
1
1
y + z = 18
2
3
1
1
x y z = 24
6
8
A) ( 6 , 8 , 24 )
B) ( 6 , 8 , 24 )
C) ( 6 , 8 , 24 )
D) ( 0 , 8 , 24 )
E) ( 6 , 8 , 24 )
____ 110. Find 9A.
çè
èè
èè 5
A = èèè
èè
èè 4
é
7
çè
èè
èè 7
A) èèèè
èè
èé 6
÷ø
ø
72 øøøø
øø
øø
63 øøù
èçè
èè 45
è
B) èèèè
èè
éè 36
63
çè
èè
èè 45
C) èèèè
èè
èé 4
7
÷ø
ø
8 øøøø
øø
øø
7 øøù
6
54
6
ø÷ø
72 øøøø
øø
øø
63 øøù
÷ø
ø
8 øøøø
øø
øø
7 øøù
53
çè
èè
èè 5
D) èèèè
èè
èé 36
63
èçè
èè 45
è
E) èèèè
èè
éè 4
ø÷ø
7 øøøø
øø
øø
54 øøù
6
÷ø
ø
8 øøøø
øø
øø
63 øøù
Name: ________________________
ID: A
____ 111. Find the product.
çè
èè
èè 3
èè
èè
èè
èé 6
÷ø
ø
8 øøøø
øø
ø
3 øøøù
çè
èè
èè 4
èè
èè
èè 4
èé
÷ø
ø
5 øøøø
øø
ø
4 øøøù
çè
èè
èè 12
A) èèèè
èè
èé 36
÷ø
ø
47 øøøø
øø
øø
42 øøù
çè
èè
èè 44
D) èèèè
èè
èé 36
çè
èè
èè 12
B) èèèè
èè
èé 24
÷ø
ø
40 øøøø
øø
øø
12 øøù
E) cannot multiply
çè
èè
èè 44
C) èèèè
èè
èé 24
÷ø
ø
47 øøøø
øø
øø
12 øøù
54
÷ø
ø
47 øøøø
øø
øø
42 øøù
Name: ________________________
ID: A
____ 112. Find the product.
çè
èè
èè
èè
èè
èè èè
èè
èèè èé
÷ø
1 øøøø
øø
ø
5 øøøø
øø
ø
9 øøøø
ù
çèè
èè 9
èé
çè
èè 1
èè
èè
è
A) èèèè 5
èè
èèè
èè 9
é
çè
èè 9
èè
èè
è
B) èèèè -45
èè
èèè
èè -7
é
èçè
èè 9
èè
èè
C) èèèè -45
èè
èèè
èè -81
é
6
÷ø
7 øøøø
ù
÷ø
-7 øøøø
øø
ø
35 øøøø
øø
ø
63 øøøø
ù
6
7
6
-6
30
-6
-6
30
54
D)
÷ø
øø
øø
øø
ø
-45 øøøø
øø
ø
9 øøøø
ù
çè
èè 9
èèé
-7
E) 102
ø÷
-7 øøøø
øø
ø
35 øøøø
øø
ø
63 øøøø
ù
55
30
÷ø
63 øøøø
ù
Name: ________________________
ID: A
____ 113. Find the inverse of the matrix.
çè
èè
èè 16
èè
èè
èè
èé 1
çè
èè
èè
èè
èè
A) èèèè
èèè
èè
èè
é
÷ø
ø
1 øøøø
øø
ø
16 øøøù
16
255
1
255
çè
èè
èè 16
èè èè 255
B) èèèè
èèè
èè 1
èè 255
é
çè
èè
èè 16
èè
èè 255
C) èèèè
èèè
1
èèè èé 255
÷ø
øø
øø
øø
øø
øø
øø
16 øøøø
ø
255 øøù
çè
èè
èè 16
èèè è 255
D) èèèè
èèè 1
èè
èè 255
é
1
255
1
255
16
255
÷ø
øø
øø
øø
øø
øø
øø
øøø
øø
øø
ù
çè
èè
èè 16
èè
èè 255
E) èèèè
èèè
èè 0
èè
é
÷ø
øø
øø
øø
øø
øø
øø
16 øøøø
ø
255 øøù
1
255
56
÷ø
øø
øø
øø
øø
øø
øø
16 øøøø
ø
255 øøù
1
255
÷ø
øø
ø
0 øøøø
øø
øø
ø
16 øøøø
ø
255 øøù
Name: ________________________
ID: A
____ 114. Solve the system of linear equations
êí
íí 8x 24y 8z 5
íí
10 using an inverse matrix.
íëí 16x 40y
íí
íí 24x 8y 16z 5
ì
çè
÷ø
è
ø
çè ÷ø èèè 5 øøø
èèè x øøø èèè 8 øøø
èè øø èè
øø
èè øø èè
øø
ø
è
è
A) èèè y øøø èèè 0 øøøø
èè øø èè
øø
èè øø èè
ø
èè z øø èè 15 øøø
èé øù èè
ø
èè 8 øøø
èé
øù
çè
÷ø
è
è
øø
è
çè ÷øø èè 0 øøø
øø
èè x øø èè
øø
èè øø èè
ø
èè øø èè
èèè øø èèè 5 øøøø
B) èè y øø èè
øø
èèè øøøø èèè 4 øøø
èè z øø èè
èè ø èè 5 øøøø
é ù èèè øøø
èè 8 øø
é
ù
çè
÷
èè 5 øøø
è
çè ÷ø èèè 8 øøøø
øø
èèè x øøø èèè
ø
èè øø èè
èè øø èè 15 øøøø
øø
C) èèèè y øøøø èèèè èè øø èè 8 øøøø
èè øø èè
øø
èè z øø èè
èé øù èè 5 øøøø
èè
øø
èèèé 4 øøøù
èçè 5 ø÷ø
è ø
èçè ø÷ø èèè øøø
èè x øø èè 8 øø
èè øø èè øø
èè øø èè øø
D) èèèè y øøøø èèèè 0 øøøø
èè øø èè øø
èè øø èè øø
èè z øø èè 5 øø
èé øù èè øø
èè 4 øø
èé øù
èçè 5 ø÷ø
è
ø
çè ÷ø èèèè 8 øøøø
èèè x øøø èè
øøø
èè øø èèè
èè øø èè 15 øøøø
øø
E) èèèè y øøøø èèèè èè øø èè 8 øøøø
èè øø èè
øø
èè z øø èè
èé øù èè 5 øøøø
èè øø
èè 4 øø
èé
øù
57
Name: ________________________
ID: A
____ 115. Write the first six terms of the sequence defined by the function.
f(n) = 2n(n - 1)
A) 0, 4, 12, 24, 40, 60
B) -4, 0, 12, 24, 40, 60
C) 4, 12, 24, 40, 60, 168
D) -4, -12, 24, -40, -60, 0
E) 4, 12, 24, 40, 60, 84
____ 116. Evaluate the sum.
800
¦2
k =1
A) 8
B) 800
C) 1,605
D) 1,600
E) 2
58
Name: ________________________
ID: A
____ 117. Evaluate the sum.
8
¦ 5k
k =1
A) 180
B) 176
C) 40
D) 45
E) 360
____ 118. Use a calculator to find the sum. Round to four decimal places.
9
¦ k 2 1
k 4
A) 3.8579
B) 5.8579
C) 0.2000
D) 1.6913
E) 1.4913
59
Name: ________________________
ID: A
____ 119. Find the sum of the infinite series.
f
äå 1 ôõ i
¦ 4 åååå 4 õõõõ
i 1 æ
ö
A) undefined
B)
4
5
C) 4
D)
8
3
E)
4
3
____ 120. Find a formula for an for the arithmetic sequence.
a1
2, d
6
A) a n
2 7n
B) a n
4 6n
C) a n
2 6 n 1
D) a n
6 2(n 1)
E) a n
n1
åä 1 õôõ
õõ
2 åååå
õ
æ 6 ö
____ 121. Find a formula for an for the arithmetic sequence.
a4
23, a 7
44
A) a n
2 7n
B) a n
5 2n
C) a n
7 2n
D) a n
2 7 n
E) a n
5 7n
60
Name: ________________________
ID: A
____ 122. The first two terms of the arithmetic sequence are given. Find the indicated term.
a1
6, a 2
0, a 8
A) 42
B) –36
C) –42
D) 48
E) 36
61
Name: ________________________
ID: A
____ 123. Match the arithmetic sequence with its graph from the choices below.
A)
D)
B)
E)
C)
62
Name: ________________________
ID: A
____ 124. Find the indicated nth partial sum of the arithmetic sequence.
1.9, 4.8, 7.7, 10.6, ...., n=20
A) 419
B) 647
C) 589
D) 590
E) 588
____ 125. Determine whether the sequence is geometric. If so, find the common ratio.
2, –6, 18, –54,...
A) –3
B) 2
C) 1
3
D) 3
E) not geometric
____ 126. Find the indicated nth term of the geometric sequence.
4th term: a 3
A)
4
81
B)
3
64
C)
4
243
D)
4
27
E)
4
9
4
,a
9 6
4
243
63
Name: ________________________
ID: A
____ 127. Find the sum of the infinite geometric series.
f
äå 1 ôõ n
¦ 4 åååå 6 õõõõ
n 0 æ
ö
A) 24
5
B)
24
5
C)
4
5
D) 4
5
E) undefined
____ 128. Find the sum of the infinite geometric sequence.
f
¦ 6-( 14 )n 1
n=1
A) s = 22.8
B) s = 10.8
C) s = 76.8
D) s = 16.8
E) s = 4.8
64
Name: ________________________
ID: A
____ 129. Find the sum of the infinite geometric sequence.
5 + 2.5 + 1.25 ...
A) s = 10
B) s = 20
C) s = 2.5
D) s = 15
E) s = 5
____ 130. Change the decimal to a common fraction.
0.4
A)
4
90
B)
4
99
C)
4
9999
D)
4
9
E)
4
999
____ 131. Find the probability for the experiment of drawing two marbles (without replacement) from a bag
containing four green, six yellow, and five red marbles such that the marbles are different colors.
37
A)
105
B)
37
30
C)
74
105
D)
2
15
E)
2
3
65
Name: ________________________
ID: A
____ 132. Give the coordinates of the circle's center and its radius.
x 2 + y 2 16 = 0
A) (1, 1); r = 16
B) (0, 0); r = 4
C) (1, 1); r = 4
D) (0, 0); r = 16
E) none of these
____ 133. Give the coordinates of the circle's center and its radius.
( x 1 ) 2 + ( y + 8 ) 2 = 16
A) (-1, 8); r = 16
B) (1, -8); r = 4
C) (1, -8); r = 16
D) (-1, 8); r = 4
E) none of these
____ 134. Find the equation of the parabola with vertex at (0, 0) and focus at (0, 3).
2
A) x = y + 3
2
B) x = 12y
2
C) x = 3y
2
D) y = 12x
E) none of these
66
Name: ________________________
ID: A
____ 135. Find the center and vertices of the ellipse.
2
2
y
x
49
4
1
A) center: (7, 2)
vertices: (–7, –2), (7, 2)
B) center: (0, 0)
vertices: (0, –7), (0, 7)
C) center: (7, 0)
vertices: (0, –2), (0, 2)
D) center: (0, 0)
vertices: (–2, 0), (2, 0)
E) center: (0, 0)
vertices: (–7, 0), (7, 0)
____ 136. Find the center and foci of the ellipse.
(y 9)
&x 5 ' 2
5
9
A) center: &5, 9'
2
foci: &5, 7', &5, 11'
B) center: &5, 9'
foci: &5, 11', &5, 7'
C) center: &5, 9'
foci: &7, 9', &3, 9'
D) center: &5, 9'
E) center: &5, 9'
foci: &3, 9', &7, 9'
foci: &3, 9', &7, 9'
____ 137. Find the vertices and asymptotes of the hyperbola.
2
9y 16x
2
144
A) vertices: &0, r4'
asymptote: y
r
4
x
3
B) vertices: &0, r4'
asymptote: y
r
3
x
4
C) vertices: &r4, 0'
asymptote: y
r
4
x
3
D) vertices: &r4, 0'
asymptote: y
r
3
x
4
E) vertices: &r4, 3'
asymptote: y
r
4
x
3
67
Name: ________________________
ID: A
____ 138. Find the standard form of the equation of the hyperbola with the given characteristics.
foci: &0, r7'
vertices: &0, r6'
2
A)
2
y
x
36
49
B)
2
y
x
36
13
C)
2
y
x
36
13
D)
2
y
x
36
13
E)
2
y
x
36
13
1
2
1
2
1
2
49
2
49
____ 139. Find the graph of the following ellipse.
9x 2 + 16y 2 36x 64y + -44 = 0
A)
C)
B)
D)
68
Name: ________________________
ID: A
____ 140. Write the equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at
(0, 7).
2
2
y
x
+
=1
A)
33
49
B)
2
2
y
x
=1
33
49
C)
2
2
y
x
+
= 1
49
33
2
2
y
x
+
=1
D)
33
49
E) none of these
____ 141. Find the standard form of the equation of the ellipse with the following characteristics.
foci: &r4, 0'
2
major axis of length: 12
2
A)
y
x
36
20
B)
2
y
x
36
16
C)
2
y
x
16
36
1
2
1
2
1
2
2
y
x
D)
144
16
1
2
E)
2
y
x
144
128
1
69
Name: ________________________
ID: A
____ 142. Write the equation of the ellipse with foci at (2, 4), (6, 4), and b = 2.
(x 4)
A)
8
2
2
B)
(x 4)
8
2
C)
(x 4)
8
D)
(x + 4)
8
E)
(x 4)
4
(y 4)
4
2
(y 4)
+
4
2
(y 4)
+
4
2
2
+
2
(y + 4)
4
(y 4)
+
8
=1
=1
= 1
2
=1
2
=1
____ 143. Find the standard form of the equation of the hyperbola with the given characteristics.
asymptotes: y
vertices: (0, –1), (10, –1)
A)
äå y 1 ôõ 2
2
&x 5 '
æ
ö
25
9
1
B)
äå y 1 ôõ 2
2
&x 5 '
æ
ö
25
9
1
C)
äå y 5 ôõ 2
2
&x 1 '
æ
ö
9
25
1
D)
äå y 1 ôõ 2
2
&x 5 '
æ
ö
25
9
1
E)
äå y 1 õô 2
2
&x 5 '
æ
ö
25
9
1
70
3
x 4, y
5
3
x4
5
Name: ________________________
ID: A
____ 144. Graph the hyperbola.
9x 2 9y 2 = 81
A)
C)
B)
D)
____ 145. Graph the hyperbola.
y 2 9x 2 + 2y + 54x = 89
A)
C)
B)
D)
71
Name: ________________________
ID: A
____ 146. Find the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (7, 0).
2
2
y
x
+
=1
A)
16
33
B)
2
2
y
x
=1
16
33
C)
2
2
y
x
=1
33
16
D)
2
2
y
x
=1
16
33
E) none of these
____ 147. Identify the conic by writing the equation in standard form.
10y 20x 60y 160x 255 0
2
2
åä y 3 ôõ
&x 4 '
æ
ö
1; hyperbola
A)
5
5
2
4
2
äå y 3 ôõ
2
&x 4 '
æ
ö
1; hyperbola
B)
5
5
2
4
2
äå y 3 ôõ
2
&x 4 '
æ
ö
1; hyperbola
C)
97
97
2
4
2
2
åä y 3 õô
&x 4 '
æ
ö
1; ellipse
D)
149
149
5
10
2
äå y 3 ôõ
2
&x 4 '
æ
ö
1; ellipse
E)
149
149
5
10
2
2
72