Algebra 2 Final Practice
#1
3
radians in degree measure.
4
4
Express
radians in degree measure.
3
3
Express
radians in degree measure.
5
5
Express
radians in degree measure.
6
3
Express
radians in degree measure.
8
#2
x
Solve the equation for x: 6  216
Solve the equation for x: 3x  81
Solve the equation for x: 4 x  256
1
Solve the equation for x: 3 x 
9
x
Solve the equation for x: 7  343
#3
2
Given the function f ( x)  (5  x) . Find the numerical value of f ( 3) .
1. Express
2.
3.
4.
5.
1.
2.
3.
4.
5.
1.
2. Given the function f ( x)  2( x  3) 2 . Find the numerical value of f (2) .
3. Given the function f ( x)  ( x  5) 2 . Find the numerical value of f ( 3) .
4. Given the function f ( x)  2 x 2  7 . Find the numerical value of f ( 2) .
5. Given the function f ( x)  3  x 2 . Find the numerical value of f (5) .
#4
1. Find the area of a triangle with two adjacent sides of lengths 16.3 and 11.2, and
the included angle measuring 56.90. Express your answer to the nearest tenth.
2. Find the area of a triangle with two adjacent sides of lengths 4 and 5.7, and the
included angle measuring 51.20. Express your answer to the nearest tenth.
3. Find the area of a triangle with two adjacent sides of lengths 51 and 35, and the
included angle measuring 1260. Express your answer to the nearest tenth.
4. Find the area of a triangle with two adjacent sides of lengths 8.4 and 13, and the
included angle measuring 310. Express your answer to the nearest tenth.
5. Find the area of a triangle with two adjacent sides of lengths 156 and 209, and the
included angle measuring 49.70. Express your answer to the nearest tenth.
#5
1. Find the product: (2  5i )(6  3i ) .
2. Find the product: (3  7i )(2  8i ) .
3. Find the product: (5  i )(9  3i ) .
4. Find the product: (2  7i )(3  6i ) .
5. Find the product: (2  4i )(5  3i ) .
#6
3
 0 for all x in the interval 0  x  2 ,
2
3
sin x 
 0 for all x in the interval 0  x  2 ,
2
3
tan x 
 0 for all x in the interval 0  x  2 ,
3
csc x  2  0 for all x in the interval 0  x  2 ,
3 cos x  4  2 for all x in the interval 0  x  2 ,
#7
1. Solve the equation cos x 
2. Solve the equation
3. Solve the equation
4. Solve the equation
5. Solve the equation
3
1I
F
G
H25J
K.
F1 I
find f GJ.
H16K
find f b
.
216g
F1 I
find f GJ.
H16K
F1 I
find f G J.
H32 K
1. If f ( x)  x 2 find f
3
2. If f ( x)  x 2
2
3. If f ( x)  x 3
4. If f ( x)  x
3
4
3
5. If f ( x)  x 5
1.
2.
3.
4.
5.
The roots of the equation
The roots of the equation
The roots of the equation
The roots of the equation
The roots of the equation
I
F
 is:
G
H4 J
K cosbg
F I F I
The value of 2 sinGJ cosGJis:
H2 K H3 K
F I F I
The value of 2 sinGJ cosGJis:
H3 K H4 K
F I
The value of sinGJ 2 cosbg
H6 K  is:
F I F3 I
The value of 2 cosGJ sinG Jis:
H6 K H2 K
1. The value of 2 sin
2.
3.
4.
5.
#8
2 x  5x  k  0 will be imaginary when k =?
5x 2  3x  k  0 will be imaginary when k = ?
3x 2  7 x  k  0 will be real when k = ?
2 x 2  3x  k  0 will be real when k = ?
7 x 2  4 x  k  0 will be equal when k = ?
#9
2
4.
5.
#10
The period of the function y  2 cos(3x) is:
The period of the function y  3 cos(2 x) is:
1
The period of the function y  2 cos x is:
2
The amplitude of the function y  2 cos(3x) is:
The amplitude of the function y  2 cos(4 x) is:
1.
2.
3.
4.
When simplified the function
When simplified the function
When simplified the function
When simplified the function
1.
2.
3.
F
IJ
G
HK
#11
f ( x )  sec x  cot x is equivalent to:
f ( x )  sin x  csc x is equivalent to:
f ( x )  tan x  cot x is equivalent to:
f ( x )  sec x  cot x  sin x is equivalent to:
5. When simplified the function f ( x)  sin x
F
1
cos x I

G
Hcsc x sin x J
Kis equivalent to:
2
1.
2.
3.
4.
5.
#12
Find the value of x, to the nearest ten minutes, given cos x  0.4872 .
Find the value of x, to the nearest ten minutes, given cos x  08335
.
.
Find the value of x, to the nearest ten minutes, given sin x  0.4376 .
Find the value of x, to the nearest ten minutes, given tan x  13887
.
.
Find the value of x, to the nearest ten minutes, given csc x  16742
.
.
1.
2.
3.
4.
5.
If
If
If
If
If
1.
2.
3.
4.
5.
#14
In which quadrant does the sum of 2  3i , and ,4  7i lie?
In which quadrant does the sum of 4  6i , and ,3  2i lie?
In which quadrant does the sum of 2  3i , and ,1  5i lie?
In which quadrant does the difference of 2  3i , and ,4  7i lie?
In which quadrant does the difference of 8  2i , and ,4  5i lie?
#13
x  log 6 53 , find the value of x to the nearest hundredth.
x  log 3 62 , find the value of x to the nearest hundredth.
x  log 7 235 , find the value of x to the nearest hundredth.
x  log 8 29 , find the value of x to the nearest hundredth.
x  log 4 133 , find the value of x to the nearest hundredth.
#15
1. The expression 3x  5 in expanded form equals:
b g
The expression b
2 x  7gin expanded form equals:
The expression b
3x  2gin expanded form equals:
The expression b
8 x  1gin expanded form equals:
The expression b
5x  2 y gin expanded form equals:
2
2.
3.
4.
5.
2
2
2
2
#16
1. Reduce the algebraic fraction to lowest terms:
2. Reduce the algebraic fraction to lowest terms:
3. Reduce the algebraic fraction to lowest terms:
4. Reduce the algebraic fraction to lowest terms:
5. Reduce the algebraic fraction to lowest terms:
1.
2.
3.
4.
5.
t 2  25
.
2t 2  9t  5
4  4r
.
2r 2  r  3
8a 2  16a
.
a 2  4a  4
2 y 2  18
.
2y  8
x 2  12 x  36
.
x2  7x  6
#17
The graph of the equation 3x  5 y  35 is the conic section:
The graph of the equation 3x 2  5 y 2  35 is the conic section:
The graph of the equation 2 x 2  2 y 2  98 is the conic section:
The graph of the equation 8 x 2  3 y 2  24 is the conic section:
The graph of the equation 4 x 2  8 y 2  64 is the conic section:
1. Express
2. Express
3. Express
4. Express
5. Express
2
2
#18
2 log x  3 log y as a single logarithm.
1
log x  2 log y as a single logarithm.
2
1
3 log x  log y as a single logarithm.
4
log x  5 log y as a single logarithm.
1
4 log x  log y as a single logarithm.
3
1.
2.
3.
4.
5.
#19
If y varies inversely with x, and y = 7 when x = 2, find the value of y when x = 4.
If y varies inversely with x, and y = 2 when x = 8, find the value of y when x =
12.
If y varies inversely with x, and y = 15 when x = 6, find the value of y when x =
9.
If y varies inversely with x, and y = 18 when x = 12, find the value of y when x =
7.
If y varies inversely with x, and y = 25 when x = 3, find the value of y when x =
10.
1. If f ( x)  x  3x and
2. If f ( x)  x 2  3x and
3. If f ( x)  2 x 2  x and
4. If f ( x)  x 2  3x and
5. If f ( x)  3x 2  x and
2
1.
2.
3.
4.
5.
#20
g( x)  3x find f ( g (3)) .
g( x)  3x find f ( g ( 5)) .
g ( x )  5x find f ( g (2)) .
g ( x )  5x find f ( g ( 2)) .
g( x)  8x  5 find g ( f (2)) .
#21
Find the solution set for the inequality x 2  2 x  15  0 .
Find the solution set for the inequality x 2  9 x  14  0 .
Find the solution set for the inequality x 2  4 x  32  0 .
Find the solution set for the inequality x 2  8x  12  0 .
Find the solution set for the inequality 3x 2  14 x  5  0 .
#22
1. Find the value of angle X to the nearest degree if
arc A = 2100 and arc B = 1500.
2. Find the value of angle X to the nearest degree if
arc A = 2000 and arc B = 1600.
3. Find the value of angle X to the nearest degree if
arc A = 1900 and arc B = 800.
4. Find the value of angle X to the nearest degree if
arc A = 1500 and arc B = 700.
5. Find the value of angle X to the nearest degree if
arc A = 1650 and arc B = 750.
A
B
X
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
1.
2.
3.
#23
What is the solution set for the equation
What is the solution set for the equation
What is the solution set for the equation
What is the solution set for the equation
What is the solution set for the equation
If
If
If
If
If
x 8  4  7.
x 3 4  2.
2x  5  4  6 .
x 5 4  9 .
3x  7  5  8 .
#24
tan A  0 and sec A  0 , in what quadrant does the terminal side of angle A lie?
tan A  0 and csc A  0 , in what quadrant does the terminal side of angle A lie?
cos A  0 and tan A  0 , in what quadrant does the terminal side of angle A lie?
sin A  0 and sec A  0 , in what quadrant does the terminal side of angle A lie?
cot A  0 and cos A  0 , in what quadrant does the terminal side of angle A lie?
#25
2  3i
Simplify and express in a + bi form:
.
4  5i
3  2i
Simplify and express in a + bi form:
.
2  3i
4  5i
Simplify and express in a + bi form:
.
2  3i
7  2i
Simplify and express in a + bi form:
.
4i
1  3i
Simplify and express in a + bi form:
.
6  2i
#26
Simplify the complex fraction:
4. Simplify the complex fraction:
6 1
1 x


5 y
2x 2
5
25
36 y 
x
y
Simplify the complex fraction:
5. Simplify the complex fraction:
1
2
9 2
a  1
x
a
1
2
3
1
x
a
Simplify the complex fraction:
x y
x
1 1

x y
1.
2.
3.
4.
5.
If
If
If
If
If
log x 49  2 , find the value of x.
log x 64  3 , find the value of x.
log 3 81  x , find the value of x.
log 7 x  3 , find the value of x.
log 6 12  x , find the value of x.
#27
#28
1. Find the domain of f ( x )  x  9 .
2. Find the domain of f ( x )  2 x  14 .
x2
3. Find the domain of f ( x ) 
.
2x  3
5x
4. Find the domain of f ( x) 
.
x4
x 5
5. Find the domain of f ( x ) 
.
x3
#29
1. Solve for all values of x given the equation: 2 x  7  15 .
2. Solve for all values of x given the equation: 2 x  3  21 .
3. Solve for all values of x given the equation: 3x  5  30 .
4. Solve for all values of x given the equation: 7 x  1  22 .
5. Solve for all values of x given the equation: 2 x  6  20 .
#30
1. Rationalize the denominator and express the answer in simplest terms:
2. Rationalize the denominator and express the answer in simplest terms:
3. Rationalize the denominator and express the answer in simplest terms:
4. Rationalize the denominator and express the answer in simplest terms:
5. Rationalize the denominator and express the answer in simplest terms:
3
.
7
4
.
6
3
.
12
3 5
.
5
7
.
3