precalculus final exam review questions 3 days. day 1
TRANSCRIPT
PrecalculusPrecalculus
Final Exam Review Questions3 Days
DAY 1
a. 180°k
c. 0° + 360°k
b. 90° + 180°k
d. 90° + 270°k
1.) Find the values of θ for which this equation is true: sin θ = 0
a. 180°k
c. 0° + 360°k
b. 90° + 180°k
d. 90° + 270°k
2.) Find the values of θ for which this equation is true: cot θ = 0
€
cotθ =cosθ
sinθ
a. y = 4cos 2θ
c. y = 4cos 4θ
b. y = 2cos 4θ
d. y = 2cos 2θ
3.) Which cosine equation has an amplitude of 2, period of 180°, and the phase shift of 0°.
€
360°
k=180°
k = 2
a. y = cos (3θ – 180°)
c. y = 3cos (θ – 90°)
b. y = 3cos (θ – 30°)
d. y = 3cos (θ – 360°)
4.) Which sine equation has an amplitude of 3, period of 360°, and the phase shift of 90°.
€
360°
k= 360°
k =1
€
−c
1= 90°
c = −90°
a.
c.
b.
d.
5.) Which graph represents this equation
€
y = 2sin(x − 45°)
a.
c.
b.
d.
6.) Which graph represents this equation
€
y =1
2cos
θ
2−180°
⎛
⎝ ⎜
⎞
⎠ ⎟
a. 30°, 150°
c. 30°, 210°
b. 0°, 90°
d. 0°, 30°, 90°
7.) Find the values of x if 0° ≤ x ≤ 360°, and satisfy this equation: x = arcsin ½
€
sin x =1
2
x = ????
a. 30°, 150°
c. 30°, 210°
b. 0°, 90°
d. 0°, 30°, 90°
8.) Find the values of x if 0° ≤ x ≤ 360°, and satisfy this equation:
€
x = arctan3
3
€
tan x =3
3
x = ????
a. 3/2
c. 1/2
b. 2
d. 4/5
9.) Evaluate sec (cos-1 ½). Assume all angles are in Quadrant I (for cos, sin, tan)
€
cos x =1
2x = 60°
sec(60°) = 2
a. 3/2
c. 1/2
b. 2
d. 4/5
10.) Evaluate cos (cot-1 4/3). Assume all angles are in Quadrant I (for cos, sin, tan)
4
35
a. 3/2
c.
b. 2
d. 0
11.) Evaluate . Assume all angles are in Quadrant I (for cos, sin, tan) €
tan arcsin2
2
⎛
⎝ ⎜
⎞
⎠ ⎟− cot arccos
2
2
⎛
⎝ ⎜
⎞
⎠ ⎟
€
3
3€
arcsin2
2= 45°
arccos2
2= 45°
€
tan(45°) − cot(45°)
1−1
= 0
a. 3/2
c.
b. 2
d. 0
12.) Evaluate . Assume all angles are in Quadrant I (for cos, sin, tan) €
tan arcsin3
2− cos−1 3
2
⎛
⎝ ⎜
⎞
⎠ ⎟
€
3
3€
arcsin3
2= 60°
cos−1 3
2= 30°
€
tan(60° − 30°)
= tan60°
=3
3
a. All real numbers
c. 0° < x < 180°
b. -1 ≤ x ≤ 1
d. -90° < x < 90°
13.) State the domain of y = Cos-1 x
a. All real numbers
c. 0° < x < 180°
b. -1 ≤ x ≤ 1
d. -90° < x < 90°
14.) State the domain of y = sin-1 x
a. All real numbers
c. 0° < x < 180°
b. -1 ≤ x ≤ 1
d. -90° < x < 90°
15.) State the domain of y = Cos-1 x + 1
a. x = 2
c. x = 0
b. x = -1
d. x = 1
16.) Determine a counterexample for the following statement:Arccos (x) = Arccos (-x) for -1 ≤ x ≤ 1
a. x = 2
c. x = 0
b. x = -1
d. x = 1
17.) Determine a counterexample for the following statement:Sin-1 (x) = -Sin-1 (-x) for -1 ≤ x ≤ 1
IT’s a TRUE STATEMENT
There is no counter example
a.
c.
b.
d.
18.) Find the inverse of the function: y = 2x + 7
€
y =x − 7
2
€
y =x + 2
7
€
y = 2x − 7
€
y =x − 2
7
a.
c.
b.
d.
19.) Write a cosine equation with a phase shift 0 to represent a simple harmonic motion with initial position = -7, amplitude = 7, and period = 4
€
y = −7cosπ
2t
€
y = 7cosπ
2t
€
y = −7cos4t
€
y = 7cos4 t
a.
c.
b.
d.
20.) Write a sine equation with a phase shift 0 to represent a simple harmonic motion with initial position = 0, amplitude = 22, and period = 12
€
y = 22sinπ
6t
€
y = sinπ
6t
€
y = 22sin12t
€
y = −22sin12t
a. 1/2
c. 1
b. 2/3
d. 0
21.) Solve for 0° ≤ θ ≤ 90°: If cot θ = 2, find tan θ
a. 1/2
c. 1
b. 2/3
d. 0
22.) Solve for 0° ≤ θ ≤ 90°: If tan θ = 1, find cot θ
a. 1/2
c. 9/40
b. 0
d. 40/9
23.) Solve for 0° ≤ θ ≤ 90°: If sin θ = 40/41, find tan θ
a.
c.
b.
d.
24.) SIMPLIFY
€
cot x
€
tan2 x
€
1
€
csc2 x
€
tan x csc x
sec x
a.
c.
b.
d.
25.) SIMPLIFY
€
cos A
€
1− sin A
€
1+ sin A
€
cos2 A
€
cos2 A
1+ sin A
a.
c.
b.
d.
26.) Find a numerical value of one trig function.
€
tan x = ±2
2
€
2tan x = cot x
€
cot x = ±2
2
€
cos x = ±2
2
€
cos x = ±3
2
a.
c.
b.
d.
27.) Find a numerical value of one trig function.
€
tan x = ±2
2
€
sin x = 2cos x
€
csc x = 2
€
tan x = 2
€
cos x = 2
a.
c.
b.
d.
28.) Use the sum or difference identity to find the exact value of cos 255°
€
2 − 6
4€
6 − 2
4
€
2 + 6
4
€
6 + 2
4
€
cos255° = cos(225° + 30°)
= cos225°cos30° − sin225°sin30°
=− 2
2
⎛
⎝ ⎜
⎞
⎠ ⎟
3
2
⎛
⎝ ⎜
⎞
⎠ ⎟−
− 2
2
⎛
⎝ ⎜
⎞
⎠ ⎟1
2
⎛
⎝ ⎜
⎞
⎠ ⎟
=− 6
4−
− 2
4
a.
c.
b.
d.
29.) Use the sum or difference identity to find the exact value of sin 195°
€
2 − 6
4€
6 − 2
4
€
2 + 6
4
€
6 + 2
4
€
sin195° = sin(150° + 45°)
= sin150°cos45° + cos150°sin45°
=1
2
⎛
⎝ ⎜
⎞
⎠ ⎟
2
2
⎛
⎝ ⎜
⎞
⎠ ⎟+
− 3
2
⎛
⎝ ⎜
⎞
⎠ ⎟
2
2
⎛
⎝ ⎜
⎞
⎠ ⎟
=2
4+
− 6
4
a.
c.
b.
d.
30.) Use the sum or difference identity to find the exact value of tan (-105°)
€
2 − 3
€
6 − 2
4
€
2 + 3
€
6 + 2
4
€
tan(−105°) = tan(45° −150°)
=tan45° − tan150°
1+ tan45°tan150°
=1 − − 3
3
1+ 1( ) − 33
⎛ ⎝ ⎜
⎞ ⎠ ⎟
=
3 + 3
3
⎛
⎝ ⎜
⎞
⎠ ⎟
3 − 3
3
⎛
⎝ ⎜
⎞
⎠ ⎟
=3+ 3
3
⎛
⎝ ⎜
⎞
⎠ ⎟•
3
3 − 3
⎛
⎝ ⎜
⎞
⎠ ⎟
=3 + 3
3 − 3•
3+ 3
3+ 3
⎛
⎝ ⎜
⎞
⎠ ⎟=
9 + 3 3 + 3 3 + 3
9 + 3 3 − 3 3 − 3
=12 + 6 3
6
= 2 + 3
a.
c.
b.
d.
31.) If tan x = 4/3 and cot y = 5/12, find sin (x – y)
€
56
33€
416
425
€
87
425
€
−16
65
xx
3
45
x
5
1213
y
€
sin(x − y)
=4
5
⎛
⎝ ⎜
⎞
⎠ ⎟
5
13
⎛
⎝ ⎜
⎞
⎠ ⎟−
3
5
⎛
⎝ ⎜
⎞
⎠ ⎟12
13
⎛
⎝ ⎜
⎞
⎠ ⎟
=20
65−
36
65
a.
c.
b.
d.
32.) If sin x = 8/17 and tan y = 7/24, find cos (x – y)
€
56
33€
416
425
€
87
425
€
−16
65
xx
15
817
x
24
725
y
€
cos(x − y)
=15
17
⎛
⎝ ⎜
⎞
⎠ ⎟24
25
⎛
⎝ ⎜
⎞
⎠ ⎟+
8
17
⎛
⎝ ⎜
⎞
⎠ ⎟
7
25
⎛
⎝ ⎜
⎞
⎠ ⎟
=360
425+
56
425
a.
c.
b.
d.
33.) If tan θ = 5/12 and θ is in Quadrant III, find the exact value of cos 2θ
€
56
33€
120
169
€
119
169
€
−16
65
xx θ5
12
13
€
cos2θ = cos2 θ − sin2 θ
=12
13
⎛
⎝ ⎜
⎞
⎠ ⎟2
−5
13
⎛
⎝ ⎜
⎞
⎠ ⎟2
=144
169−
25
169
a.
c.
b.
d.
34.) If tan θ = 5/12 and θ is in Quadrant III, find the exact value of sin 2θ
€
150
140€
120
169
€
119
169
€
−16
65
a.
c.
b.
d.
35.) Use a half-angle identity to find the value of sin
€
−2 + 3
2€
13π
12
€
2 + 3
2€
−2 − 3
2
€
2 − 3
2
a.
c.
b.
d.
36.) Use a half-angle identity to find the value of cos
€
−2 + 3
2 €
19π
12
€
2 + 3
2€
−2 − 3
2
€
2 − 3
2
a. 0°, 90°
c. 0°, 180°
b. 30°, 150°
d. 120°
37.) Solve for 0° ≤ x ≤ 180°:
€
2sin2 x + sin x = 0
a. 0°, 90°
c. 0°, 180°
b. 30°, 150°
d. 120°
38.) Solve for 0° ≤ x ≤ 180°:
€
2cos2 x = sin x +1
DAY 2
a. 0°, 90°
c. 0°, 180°
b. 30°, 150°
d. 120°
39.) Solve for 0° ≤ x ≤ 180°:
€
2sin2 x − cos2 x = 0
a.
c.
b.
d.
40.) Write the equation 5x – y + 3 = 0 in normal form.
€
−5
26x +
1
26y −
3
26= 0
€
5
26x −
1
26y −
3
26= 0
€
1
26x +
−5
26y −
3
26= 0
€
−5
26x +
1
26y +
3
26= 0
a.
c.
b.
d.
41.) Write the equation 5x + y = 7 in normal form.
€
−5
26x +
1
26y −
3
26= 0
€
5
26x −
1
26y −
3
26= 0
€
5
26x +
1
26y −
7
26= 0
€
−5
26x +
1
26y +
3
26= 0
a.
c.
b.
d.
42.) Write the standard form of the equation of a line for which the length of the normal is 3 and the normal makes a 60° angle with the positive x-axis.
€
x − 3y + 64 = 0
€
x + y − 5 2 = 0
€
x + 3y − 6 = 0
€
3x − y + 4 = 0
a.
c.
b.
d.
43.) Write the standard form of the equation of a line for which the length of the normal is 2 and the normal makes a 150° angle with the positive x-axis.
€
x − 3y + 64 = 0
€
x + y − 5 2 = 0€
x + 3y − 6 = 0€
3x − y + 4 = 0
a.
c.
b.
d.
44.) Write the standard form of the equation of a line for which the length of the normal is 32 and the normal makes a 120° angle with the positive x-axis.
€
x − 3y + 64 = 0
€
x + y − 5 2 = 0€
x + 3y − 6 = 0€
3x − y + 4 = 0
a.
c.
b.
d.
45.) Find the distance in units between P(-3, 5) and 12x + 5y – 3 = 0
€
1.9€
4.2
€
14
13€
0.9
a.
c.
b.
d.
46.) Find the distance in units between P(-5, 0) and x – 3y + 11 = 0
€
1.9€
4.2
€
14
13€
0.9
a.
c.
b.
d.
47.) has a magnitude of 1.5 cm and a amplitude of 135°. Find the magnitude of its vertical and horizontal components.
€
x ≈ 2.1 cm
y ≈ 3.6 cm
€
vv
€
x ≈1.8 cm
y ≈1.8 cm
€
x ≈ 2.3 cm
y ≈1.4 cm
€
x ≈1.1cm
y ≈1.1cm
a.
c.
b.
d.
48.) has a magnitude of 4.3 cm and a amplitude of 330°. Find the magnitude of its vertical and horizontal components.
€
x ≈ 2.1 cm
y ≈ 3.6 cm
€
vv
€
x ≈1.8 cm
y ≈1.8 cm
€
x ≈ 2.3 cm
y ≈1.4 cm
€
x ≈1.1cm
y ≈1.1cm
a.
c.
b.
d.
49.) has a magnitude of 4.2 m. If , what is the magnitude of ?
€
12.6 m
€
vv
€
vw = 3
v v
€
vw
€
8.4 m
€
4.3 m
€
2.6 m
a.
c.
b.
d.
50.) has a magnitude of 4.2 m. If , what is the magnitude of ?
€
12.6 m
€
vv
€
vw = −2
v v
€
vw
€
8.4 m
€
4.3 m
€
2.6 m
a. (3, -2)
c. (5, -5)
b. (7, 5)
d. (2, 6)
51.) Find the ordered pair that represents the vector from A(-2, 5) to B(1, 3). ?
a. (3, -2)
c. (5, -5)
b. (7, 5)
d. (2, 6)
52.) Find the ordered pair that represents the vector from A(-9, 2) to B(-4, -3). ?
a.
c.
b.
d.
53.) If is a vector from A(12, -4) to B(19, 1), find the magnitude of
€
AB
€
AB
€
74
€
2 10
€
5 2
€
13
a.
c.
b.
d.
54.) If is a vector from A(-9, 2) to B(-4, -3), find the magnitude of
€
AB
€
AB
€
74
€
2 10
€
5 2
€
13
a.
c.
b.
d.
55.) Write the as the sum of unit vectors for points C(-1, 2) and D(3, 5).
€
−2v i − 5
v j
€
2v i + 7
v j
€
2v i − 7
v j
€
2v i + 5
v j
€
CD
a.
c.
b.
d.
56.) Find an ordered pair to represent in each equation if = (1, -3, -8) and = (3, 9, -1)
€
(−5,−21,−6)
€
vu =
v v − 2
v w
€
vv
€
vw
€
(2,12,7)
€
(−5,−39,−29)
€
(1,33,38)
a.
c.
b.
d.
57.) Find an ordered pair to represent in each equation if = (1, -3, -8) and = (3, 9, -1)
€
(−5,−21,−6)
€
vu = 4
v v − 3
v w
€
vv
€
vw
€
(2,12,7)
€
(−5,−39,−29)
€
(1,33,38)
a. (3, -2, 10)
c. (5, -5, 2)
b. (7, 5, -3)
d. (-4, -1, 0)
58.) Find the ordered triple that represents the vector from A(8, 1, 1) to B(4, 0, 1). ?
a.
c.
b.
d.
59.) Find the inner product of: (3, 5) (4, -2)
€
2
€
0
€
9
€
7
a.
c.
b.
d.
60.) Find the inner product of: (4, 2) (-3, 6)
€
2
€
0
€
9
€
7
a.
c.
b.
d.
61.) Find the inner product of: (7, -2, 4) (3, 8, 1)
€
2
€
0
€
9
€
7
a.
c.
b.
d.
62.) Find the cross product: (7, 2, 1) x (2, 5, 3)
€
(−8,19,−2)
€
(9,−6,0)
€
(4,12,16)
€
(1,−19,31)
a.
c.
b.
d.
63.) Find the cross product: (-1, 0, 4) x (5, 2, -1)
€
(−8,19,−2)
€
(9,−6,0)
€
(4,12,16)
€
(1,−19,31)
a.
c.
b.
d.
64.) Name the polar curve of: r = 5 + 2cos θ
€
rose
€
cardiod
€
spiral
€
limacon
a.
c.
b.
d.
65.) Name the polar curve of: r = 3 + 3sin θ
€
rose
€
cardiod
€
spiral
€
limacon
a.
c.
b.
d.
66.) Name the polar curve of: r = 2θ
€
rose
€
cardiod
€
spiral
€
limacon
a.
c.
b.
d.
67.) Convert into polar coordinates.
€
1
4, π
⎛
⎝ ⎜
⎞
⎠ ⎟
€
1,π
6
⎛
⎝ ⎜
⎞
⎠ ⎟
€
3
2,π
2
⎛
⎝ ⎜
⎞
⎠ ⎟
€
2, 0( )
€
0,3
2
⎛
⎝ ⎜
⎞
⎠ ⎟
a.
c.
b.
d.
68.) Convert into polar coordinates.
€
1
4, π
⎛
⎝ ⎜
⎞
⎠ ⎟
€
1,π
6
⎛
⎝ ⎜
⎞
⎠ ⎟
€
3
2,π
2
⎛
⎝ ⎜
⎞
⎠ ⎟
€
2, 0( )
€
3
2,1
2
⎛
⎝ ⎜
⎞
⎠ ⎟
a.
c.
b.
d.
69.) Convert into rectangular coordinates.
€
1,1( )
€
2, − 5( )
€
3, − 2.01( )
€
−1.72, 3.01( )
€
13, − 0.59( )
a.
c.
b.
d.
70.) Convert into rectangular coordinates.
€
1,1( )
€
2, − 5( )
€
3, − 2.01( )
€
−1.72, 3.01( )
€
2, 45°( )
a.
c.
b.
d.
71.) Change this polar equation into a rectangular equation.
€
x 2 + y 2 =144
€
y = 4
€
x = −2
€
y = −x
€
θ =−45°
a.
c.
b.
d.
72.) Change this polar equation into a rectangular equation.
€
x 2 + y 2 =144
€
y = 4
€
x = −2
€
y = −x
€
rsinθ = 4
a.
c.
b.
d.
73.) Change this rectangular equation into a polar equation.
€
x 2 + y 2 = 7
€
r = −5cscθ
€
r =10secθ
€
r =5
2sinθ
€
r = ± 7
a.
c.
b.
d.
74.) Change this rectangular equation into a polar equation.
€
x =10
€
r = −5cscθ
€
r =10secθ
€
r =5
2sinθ
€
r = ± 7
a.
c.
b.
d.
75.) Identify the conic section:
€
x 2 + y 2 + 6y − 8x + 24 = 0
€
circle
€
hyperbola
€
ellipse
€
parabola
a.
c.
b.
d.
76.) Identify the conic section:
€
x 2 − 6x − 4 y + 9 = 0
€
circle
€
hyperbola
€
ellipse
€
parabola
a.
c.
b.
d.
77.) Identify the conic section:
€
27x 2 + 9y 2 − 6y −108x + 82 = 0
€
circle
€
hyperbola
€
ellipse
€
parabola
a.
c.
b.
d.
78.) Identify the conic section:
€
x 2 − 4y 2 +10x −16y + 5 = 0
€
circle
€
hyperbola
€
ellipse
€
parabola
a.
c.
b.
d.
79.) What is the correct vertex of this conic section :
€
x 2 − 2x +1 = 8y −16
€
(1, 2)
€
(0, 4)
€
(2, 7)
€
(1, − 3)
a.
c.
b.
d.
80.) What is the correct vertex of this conic section :
€
y 2 + 6y + 9 =16 −16x
€
(1, 2)
€
(0, 4)
€
(2, 7)
€
(1, − 3)
a.
c.
b.
d.
81.) Which conic section has a directrix of y = 0
€
y =1
8x −1( )
2+ 2
€
y = x −1( )2
+ 2
€
x =1
2y 2
€
y =−1
5x −1( )
2+ 5
a.
c.
b.
d.
82.) Which conic section has a directrix of x = 1/2
€
y =1
8x −1( )
2+ 2
€
y = x −1( )2
+ 2
€
x =1
2y 2
€
y =−1
5x −1( )
2+ 5
a.
c.
b.
d.
83.) Which conic section has focal point
€
4x 2 + y 2 − 32x + 4y + 64 = 0
€
4, − 2 ± 3( )
€
x 2 + 2y 2 − x + 4 y +10 = 0
€
4x 2 + 9y 2 − 8x − 36y + 4 = 0
€
x 2 + 5y 2 − x + 8y + 50 = 0
DAY 3
a.
c.
b.
d.
84.) Which conic section has focal point
€
4x 2 + y 2 − 32x + 4y + 64 = 0
€
1± 5, 2( )
€
x 2 + 2y 2 − x + 4y +10 = 0
€
4x 2 + 9y 2 − 8x − 36y + 4 = 0
€
x 2 + 5y 2 − x + 8y + 50 = 0
Center is (1, 2)
Center is (4, -2)
Center is (½, -1)
Center is (1, 2)
Center is (½, -4/5)
Just matchup the centers
a.
c.
b.
d.
85.) What is the eccentricity of this conic section:
€
1
€
4x 2 + 9y 2 + 54y + 45 = 0
€
5
3
€
4.5
€
−3
€
4(x 2) + 9(y 2 + 6y + __) = −45 + __9 81
€
4(x 2) + 9(y + 3)2 = 3636 36 36
€
x 2
9+
(y + 3)2
4=1
€
a = 3
b = 2
c = 5
Eccentricity = c/a
a.
c.
b.
d.
86.) What is the eccentricity of this conic section:
€
1
€
(y +1)2 = 3(x + 4)
€
5
3
€
4.5
€
−3
a.
c.
b.
d.
87.) Which standard form equation of an hyperpola has slant asymptotes:
€
x 2
36−
y 2
81=1
€
y = ±3
2x
€
x 2
1−
y 2
9=1
€
(x + 6)2
36−
(y + 3)2
9=1
€
(x + 2)2
64−
y 2
81=1
a.
c.
b.
d.
88.) Which standard form equation of an hyperpola has slant asymptotes:
€
x 2
36−
y 2
81=1
€
y = ±1
2x
€
x 2
1−
y 2
9=1
€
(x + 6)2
36−
(y + 3)2
9=1
€
(x + 2)2
64−
y 2
81=1
a.
c.
b.
d.
89.) Express using radicals:
€
21
2 a3
2b5
2
€
2a3b5
€
x 6y 3z3
€
x 2y 4z3
€
22 a2b23
a.
c.
b.
d.
90.) Express using radicals:
€
x 6y 3( )
12 z
32
€
2a3b5
€
x 6y 3z3
€
x 2y 4z3
€
22 a2b23
a.
c.
b.
d.
91.) Express using rational exponents:
€
1024a3
€
32a3
2
€
271
5 x 2y
€
12x 3y 5
€
c7
3
a.
c.
b.
d.
92.) Write this in logarithmic form:
€
25 = 32
€
log2 32 = 5
€
log5
1
125= −3
€
log6
1
216= −3
€
log3 27 = 3
a.
c.
b.
d.
93.) Write this in logarithmic form:
€
6−3 =1
216
€
log2 32 = 5
€
log5
1
125= −3
€
log6
1
216= −3
€
log3 27 = 3
a.
c.
b.
d.
94.) Evaluate each expression:
€
6log6 5
€
256
€
3
€
−3
€
5
a.
c.
b.
d.
95.) Evaluate each expression:
€
log8 8256
€
256
€
3
€
−3
€
5
a.
c.
b.
d.
96.) Solve:
€
log4 (3x) = log4 27
€
256
€
3
€
9
€
5
a.
c.
b.
d.
97.) Solve:
€
35x = 85
€
10.0795
€
0.8088
€
0.4815
€
2.2843
a.
c.
b.
d.
98.) Solve:
€
10.0795
€
0.8088
€
0.4815
€
1.8x −5 =19.8
€
2.2843
a.
c.
b.
d.
99.) Solve:
€
10.0795
€
0.8088
€
0.4815
€
x = log312.3
€
2.2843
a.
c.
b.
d.
100.) Solve:
€
48.52
€
17.63
€
42.92
€
ln4.5 = lne0.031t
€
19.52
a. 5, 10, 20, …
c. 1.5, 3, 4.5, …
b. 9, 3, 1, ..
d. 2, 4, 8, …
101.) Which sequence below is arithmetic. :
a. 4, 8, 12, …
c. 1.5, 3, 4.5, …
b. 9, 3, 1, ..
d. -5, -3, -1, …
102.) Which sequence below is geometric. :
a. 9
c. -25
b. -5
d. 10
103.) Find 16th term in the sequence:
1.5, 2, 2.5, …
a. 9
c. -25
b. -5
d. 10
104.) Find 19th term in the sequence:
11, 9, 7, …
a.
c.
b.
d. 10
105.) Find 9th term in the sequence:
€
2, 2, 2 2,...
€
16 2
€
12 2
€
15 2
a.
c.
b.
d. 59
106.) What is the sum of the first 11 terms of the arithmetic sequence: :
-3 – 1 + 1 + …
€
74
€
56
€
77
a.
c.
b.
d. 270
107.) What is the sum of the first 9 terms of the geometric sequence: :
0.5 + 1 + 2 + …
€
265.5
€
255.5
€
235
a.
c.
b.
d.
108.) Evaluate the limit of
€
1
€
0
€
3€
limn → ∞
1− 2n
5n
€
−2
5
a.
c.
b.
d.
109.) Evaluate the limit of
€
1
€
2
€
3€
limn → ∞
(n + 2)(2n −1)
n2
€
−2
5
a.
c.
b.
d.
110.) Find the sum of this infinite geometric series:
€
4
3
€
0
€
3€
2
3+
1
3+
1
6+
1
12+ ...
€
−2
5
a.
c.
b.
d.
111.) Find the sum of this infinite geometric series:
€
4
3
€
0
€
3€
2
7+
4
7+
8
7+ ...
€
Does not exist
a.
c.
b.
d.
112.) Evaluate the limit of
€
1
€
2
€
3€
limn → 3
x 2 − x − 6
x − 3
€
5
a.
c.
b.
d.
113.) Evaluate the limit of
€
1
€
2
€
0€
limx → 2
x 2
x 4 − 4
€
5
a.
c.
b.
d.
114.) Evaluate the limit of as x approaches 1 for
f(x) = 2x + 1 and g(x) = x – 3
€
1
€
−3
€
0
€
f g(x)[ ]
€
5
a.
c.
b.
d.
115.) Evaluate the limit of as x approaches 1 for
f(x) = 3x – 4 and g(x) = 2x + 5
€
17
€
−3
€
0
€
f g(x)[ ]
€
5
a.
c.
b.
d.
116.) Find the derivative of:
€
4x + 7
€
18x 2 − 26x − 5
€
−2x(2x 2 −1)
(x 2 +1)4
€
f (x) = (2x − 3)(x + 5)
€
4x
4x 2 −1
a.
c.
b.
d.
117.) Find the derivative of:
€
4x + 7
€
18x 2 − 26x − 5
€
−2x(2x 2 −1)
(x 2 +1)4
€
f (x) = x 2(x 2 +1)−3
€
4x
4x 2 −1
a.
c.
b.
d.
118.) Find the derivative of:
€
4x + 7
€
18x 2 − 26x − 5
€
−2x(2x 2 −1)
(x 2 +1)4
€
f (x) = 4 x 2 −1
€
4x
4x 2 −1
a.
c.
b.
d.
119.) Find the integral of:
€
x 2 −12x + C
€
18x 2 − 26x + C
€
1
5x 5 − 5x + C
€
2x −12 dx∫
€
2 1− x 2 + C
a.
c.
b.
d.
120.) Find the integral of:
€
x 2 −12x + C
€
18x 2 − 26x + C
€
1
5x 5 − 5x + C
€
x 4 − 5 dx∫
€
2 1− x 2 + C
a.
c.
b.
d.
121.) Find the integral of:
€
x 2 −12x + C
€
18x 2 − 26x + C
€
1
5x 5 − 5x + C
€
−2x
1− x 2dx∫
€
2 1− x 2 + C