Name: 
 

Advanced Math Practice Semester Test


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 
 
How long is the arc that corresponds to each central angle?
 

 1. 
60mc001-1.jpg
a.
mc001-2.jpgmc001-3.jpg
c.
mc001-6.jpgmc001-7.jpg
b.
mc001-4.jpgmc001-5.jpg
d.
mc001-8.jpgmc001-9.jpg
 
 
Find the measure of the central angle that corresponds to each arc length.
 

 2. 
mc002-1.jpgmc002-2.jpg
a.
300mc002-3.jpg
c.
150mc002-5.jpg
b.
60mc002-4.jpg
d.
210mc002-6.jpg
 
 
Find each trigonometric value. Round to the nearest hundredth.
 

 3. 
sin mc003-1.jpgmc003-2.jpg
a.
0.5
c.
0.97
b.
–0.5
d.
–0.97
 

 4. 
cos mc004-1.jpgmc004-2.jpg
a.
0.87
c.
–0.97
b.
–0.87
d.
0.97
 

 5. 
tan mc005-1.jpgmc005-2.jpg
a.
–0.58
c.
3.73
b.
–1.73
d.
0.27
 

 6. 
cot mc006-1.jpgmc006-2.jpg
a.
1.73
c.
3.73
b.
0.58
d.
0.27
 

 7. 
sec mc007-1.jpgmc007-2.jpg
a.
–1.15
c.
3.86
b.
1.15
d.
–3.86
 

 8. 
csc mc008-1.jpgmc008-2.jpg
a.
2
c.
3.86
b.
–2
d.
–3.86
 
 
Find the coordinates of the point at the end of each arc on the unit circle.
 

 9. 
mc009-1.jpgmc009-2.jpg
a.
(–0.5, 0.87)
c.
(0.5, 0.87)
b.
(0.87, –0.5)
d.
(–0.5, –0.87)
 
 
Starting in standard position, what quadrant does each angle end in?
 

 10. 
mc010-1.jpgmc010-2.jpg
a.
Quadrant II
c.
Quadrant IV
b.
Quadrant III
d.
Quadrant I
 
 
Convert each degree measure to radians.
 

 11. 
300mc011-1.jpg
a.
mc011-2.jpgmc011-3.jpg
c.
mc011-6.jpgmc011-7.jpg
b.
mc011-4.jpgmc011-5.jpg
d.
mc011-8.jpgmc011-9.jpg
 
 
Convert each radian measure to degrees.
 

 12. 
mc012-1.jpgmc012-2.jpg
a.
30mc012-3.jpg
c.
15mc012-5.jpg
b.
330mc012-4.jpg
d.
165mc012-6.jpg
 
 
Graph each system of equations and use that graph to estimate the two solutions to the system on 0 nar008-1.jpg x nar008-2.jpg 2nar008-3.jpg.
 

 13. 
mc013-1.jpg
a.
1.12, 2.02
c.
5.16, 2.02
b.
1.12, 4.26
d.
5.16, 4.26
 

 14. 
mc014-1.jpg
a.
1.77, 4.51
c.
1.37, 4.51
b.
1.77, 4.91
d.
1.37, 4.91
 
 
Find all solutions to each equation for nar009-1.jpg.
 

 15. 
mc015-1.jpg
a.
6.12, 3.31
c.
6.12, 4.54
b.
1.74, 4.54
d.
1.74, 1.4
 

 16. 
mc016-1.jpg
a.
5.67, 3.75
c.
5.67, 4.1
b.
2.18, 4.1
d.
2.18, 0.96
 

 17. 
mc017-1.jpg
a.
1.11, 2.03, 4.25, 5.18
c.
1.11, 4.25
b.
0.46, 2.68, 3.61, 5.82
d.
0.46, 5.82
 

 18. 
mc018-1.jpg
a.
0.46, 2.68, 3.61, 5.82
c.
0.46, 3.61
b.
1.11, 2.03, 4.25, 5.18
d.
1.11, 5.18
 

 19. 
csc x = 2
a.
0.52, 2.62
c.
2.09, 2.62
b.
0.52, 3.67
d.
2.09, 3.67
 

 20. 
sec x = –2.25
a.
2.03, 4.25
c.
5.17, 4.25
b.
2.03, 1.11
d.
5.17, 1.11
 

 21. 
cot x = –2.25
a.
2.72, 5.86
c.
0.42, 5.86
b.
2.72, 3.56
d.
0.42, 3.56
 

 22. 
If cos x = 0.9, find both values of sin x.
a.
0.44, –0.44
c.
0.56, –0.56
b.
0.9, –0.9
d.
0.1, –0.1
 
 
Find the maximum and the minimum of each function for 0 nar010-1.jpg x nar010-2.jpg 2nar010-3.jpg.
 

 23. 
y = –5cos x
a.
5, –5
c.
1, –5
b.
1, 1
d.
5, 1
 

 24. 
y = 9sin x – 2
a.
7, –11
c.
2, –2
b.
9, –9
d.
7, –2
 
 
Find the slope of each function between the two points.
 

 25. 
y = sin x; x1 = 4.3, x2 = 4.4
a.
–0.35
c.
–0.95
b.
0.93
d.
–0.92
 

 26. 
y = cos x; x1 = 4.1, x2 = 4.2
a.
–0.53
c.
–0.49
b.
0.85
d.
–0.57
 
 
With a unit circle, draw one line that indicates the two possible solutions to each equation on 0 nar012-1.jpg x < 2nar012-2.jpg.
 

 27. 
sin x = –0.25
a.
mc027-1.jpg
c.
mc027-3.jpg
b.
mc027-2.jpg
d.
mc027-4.jpg
 
 
Find sine, cosine, and tangent for each trigonometric value. Round to the nearest hundredth.
 

 28. 
mc028-1.jpgmc028-2.jpg
a.
0.5, –0.87, –0.58
c.
0.97, 0.87, 3.73
b.
–0.5, 0.87, –1.73
d.
–0.97, –0.26, 0.27
 

 29. 
Suppose f(x) is a periodic functions with period 7, and f(–9) = 3. Which of the following must be true?
a.
f(–2) = 3
c.
f(3) = 3
b.
f(7) = 3
d.
f(2) = 3
 
 
Find the period of each function.
 

 30. 
f(x) = –10 sin 8x – 9
a.
mc030-1.jpgmc030-2.jpg
c.
mc030-5.jpgmc030-6.jpg
b.
mc030-3.jpgmc030-4.jpg
d.
mc030-7.jpgmc030-8.jpg
 

 31. 
f(x) = –9 tan mc031-1.jpgx – 2
a.
mc031-2.jpgmc031-3.jpg
c.
mc031-6.jpgmc031-7.jpg
b.
mc031-4.jpgmc031-5.jpg
d.
mc031-8.jpgmc031-9.jpg
 
 
Which of the following is a solution to the equation?
 

 32. 
–10 sin 2(x – 5) + 6 = 14
a.
4.536
c.
4.6
b.
–0.927
d.
6.249
 

 33. 
8 cos 3(x + 3) + 2 = –5
a.
–2.121
c.
–3.292
b.
2.636
d.
–3.355
 

 34. 
–5 tan 3(x – 4) – 2 = 2
a.
3.775
c.
3.733
b.
–0.675
d.
3.691
 
 
Find the amplitude of the function.
 

 35. 
f(x) = – cos 4mc035-1.jpg(x – 5) – 2
a.
1
c.
5
b.
–2
d.
4
 
 
Find the vertical displacement of the function.
 

 36. 
f(x) = 4 sin 6mc036-1.jpg(x – 8) + 7
a.
4
c.
8
b.
7
d.
–7
 
 
Find the phase shift of the function.
 

 37. 
f(x) = 2 sin 2mc037-1.jpg(x – 10) – 6
a.
2
c.
10
b.
–6
d.
–10
 
 
Find the maximum and minimum of the function.
 

 38. 
f(x) = –4 sin 10mc038-1.jpg(x + 5) + 10
a.
14; 6
c.
10; –10
b.
4; –4
d.
9; 1
 

 39. 
A ferris wheel has a maximum height of 46 m and a minimum height of 6 m. The wheel rotates once every 75 seconds. Find a function H(t) that gives the height of a person t seconds after they reach the top of the ferris wheel.
a.
mc039-1.jpg
c.
mc039-3.jpg
b.
mc039-2.jpg
d.
mc039-4.jpg
 

 40. 
You are walking counter-clockwise around a circle with a radius of 10 meters. You complete one trip around the circle every 45 seconds. Find a function G(t) that gives your x-coordinate in relation to the center of the circle t seconds after you reach the top of the circle.
a.
mc040-1.jpg
c.
mc040-3.jpg
b.
mc040-2.jpg
d.
mc040-4.jpg
 
 
Find the magnitude of each complex number.
 

 41. 
mc041-1.jpg
a.
15
c.
9
b.
12
d.
21
 

 42. 
(mc042-1.jpg)3
a.
125
c.
5
b.
15
d.
4
 
 
Find the direction of each complex number. Round to the nearest degree.
 

 43. 
mc043-1.jpg
a.
273mc043-2.jpg
c.
267mc043-4.jpg
b.
87mc043-3.jpg
d.
93mc043-5.jpg
 

 44. 
(mc044-1.jpg)3
a.
142mc044-2.jpg
c.
13mc044-4.jpg
b.
77mc044-3.jpg
d.
167mc044-5.jpg
 
 
Find the magnitude and direction of each complex number.
 

 45. 
4 cis 270mc045-1.jpg
a.
4; 270mc045-2.jpg
c.
2; 270mc045-4.jpg
b.
4; 90mc045-3.jpg
d.
2; 90mc045-5.jpg
 

 46. 
z4; z = 4 cis 150mc046-1.jpg
a.
256; 240mc046-2.jpg
c.
16; 240mc046-4.jpg
b.
256; 150mc046-3.jpg
d.
16; 150mc046-5.jpg
 

 47. 
6z; z = 4 cis 180mc047-1.jpg
a.
24; 180mc047-2.jpg
c.
10; 180mc047-4.jpg
b.
24; 0mc047-3.jpg
d.
10; 0mc047-5.jpg
 

 48. 
zw; z = 2 cis 270mc048-1.jpg, w = 5 cis 120mc048-2.jpg
a.
10; 30mc048-3.jpg
c.
7; 30mc048-5.jpg
b.
10; 0mc048-4.jpg
d.
7; 0mc048-6.jpg
 
 
For each absolute value and argument, write z in the form a + bi. Round to the nearest tenth.
 

 49. 
|z| = 6; arg(z) = 150mc049-1.jpg
a.
–5.2 + 3i
c.
3 + 3i
b.
–5.2 – 5.2i
d.
3 – 5.2i
 

 50. 
z = 9 cis 300mc050-1.jpg, w = 8 cis 330mc050-2.jpg; Find |zw|.
a.
72
c.
18
b.
17
d.
16
 

 51. 
z = 4 cis 60mc051-1.jpg, w = 6 cis 30mc051-2.jpg; Find arg(zw).
a.
90mc051-3.jpg
c.
120mc051-5.jpg
b.
0mc051-4.jpg
d.
60mc051-6.jpg
 
 
Use the angle sum identities to find the exact value of the expression.
 

 52. 
sin 165°
a.
mc052-1.jpg
b.
mc052-2.jpg
c.
mc052-3.jpg
d.
mc052-4.jpg
 
 
Rewrite each expression in the form nar025-1.jpg.
 

 53. 
mc053-1.jpg
a.
mc053-2.jpg
c.
mc053-4.jpg
b.
mc053-3.jpg
d.
mc053-5.jpg
 
 
Determine if each trigonometric identity is true or false.
 

 54. 
sec2 x – tan 2 x = sin2 x + cos2 x
a.
True
b.
False
 

 55. 
sec2 x – tan 2 x = sin2 x – cos2 x
a.
False
b.
True
 

 56. 
cos (x + mc056-1.jpg) = –sin x
a.
True
b.
False
 

 57. 
sin (x + mc057-1.jpg) = cos x
a.
True
b.
False
 
 
Graph all of the solutions of the equation on the complex plane.
 

 58. 
mc058-1.jpg = 0
a.
mc058-2.jpg
c.
mc058-4.jpg
b.
mc058-3.jpg
d.
mc058-5.jpg
 
 
Find the smallest n so that z is an nth root of unity.
 

 59. 
z = cis 216mc059-1.jpg
a.
20
c.
22
b.
40
d.
28
 
 
The powers of z lie on a regular polygon on the complex plane. How many sides does this polygon have?
 

 60. 
z = cis 5mc060-1.jpg
a.
72
c.
74
b.
144
d.
80
 
 
Do the powers of z lie on a regular polygon in the complex plane?
 

 61. 
z = cis 75mc061-1.jpg
a.
No
b.
Yes
 

 62. 
What is the maximum number of points of intersection between a line l and the equation f(x) = Ax8 + Bx6 + Cx4 + Dx?  A, B, C, and D are real number coefficients.
a.
8
c.
6
b.
7
d.
1
 
 
Does the polynomial f(x) change signs?
 

 63. 
f(x) = 2x5 + 5x4 – 5x2 – 5x + 5
a.
Yes
b.
No
 
 
Find the average rate of change of f(x) between a and b.
 

 64. 
f(x) = –5x2 + 7; a = 5, b = 8
a.
–65
c.
–0.02
b.
–74
d.
2.65
 
 
Find the equation of the secant of f(x) through the points a and b.
 

 65. 
f(x) = –3x2 – 9; a = –4, b = –2
a.
y = 18x + 15
c.
y = 18x – 21
b.
y = 18x + 70
d.
y = 18x + 32
 

 66. 
Find the remainder when mc066-1.jpg is divided by x – 2.
a.
–32
c.
160
b.
2
d.
–2
 

 67. 
Expand f(x) = x2 – 11x + 20 in terms of x – 3.
a.
(x – 3)2 – 5(x – 3) – 4
c.
(x – 3)2 – 4(x – 3) – 5
b.
–(x – 3)2 + 5(x – 3) + 4
d.
–(x – 3)2 + 4(x – 3) + 5
 
 
Find the slope of the tangent to f(x) at the given point.
 

 68. 
f(x) = x2 – 4 at (–3, 5)
a.
–6
c.
–8
b.
–4
d.
–2
 

 69. 
f(x) = –3x3 – 4x2 + 2x – 3 at (2, –39)
a.
–50
c.
–174
b.
–103
d.
–15
 

 70. 
mc070-1.jpg at (5, 148.41)
a.
5
c.
4
b.
6
d.
148.41
 
 
Find the equation of the tangent to f(x) at the given point.
 

 71. 
f(x) = 3x3 + x + 10 at (–3, –74)
a.
y = 82x + 172
c.
y = 10x – 44
b.
y = 37x + 37
d.
y = 145x + 361
 
 
Find the vertical asymptote of the graph of f(x).
 

 72. 
mc072-1.jpg
a.
5
c.
–2
b.
1
d.
2
 
 
Find the hole in the graph of f(x).
 

 73. 
mc073-1.jpg
a.
3
c.
–1
b.
2
d.
1
 
 
Find the horizontal asymptote of the graph of f(x).
 

 74. 
mc074-1.jpg
a.
–1
c.
3
b.
–2
d.
–3
 
 
Find the limit of f(x) as x nar039-1.jpg.
 

 75. 
mc075-1.jpg
a.
1
c.
2
b.
–5
d.
5
 
 
Find the limit of f(x) as x nar040-1.jpg.
 

 76. 
mc076-1.jpg
a.
1
c.
3
b.
–3
d.
–2
 

 77. 
Which value for D produces a hole in the graph of f(x)?
mc077-1.jpg
a.
–2
c.
6
b.
2
d.
–3
 



 
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