Download Practice Test over Fractional Exponents, Radicals, & Complex Numbers

1
Intermediate Algebra (Math 0303)
Practice Test over Rational Exponents, Radicals, Equations with Radicals, & Complex Numbers
Simplify:
68
#2
Evaluate:
 8 3


 125 
#3
Multiply:
(
#4
Simplify:
#5
Rationalize:
#6
Rationalize:
#7
Multiply:
(
x+2
#8
Multiply:
(
x + 2y
#1
2
3
)(
x +5 2 x +3
24 x 3 y 7
2
3
4
3+3
)(
x −2
)
3
)
)
2
112 x 5 y 9 − 2 xy 4 28 x 3 y
#9
Combine:
#10
Rationalize:
#11
Solve the equation:
x=
#12
Solve the equation:
x+4=7
#13
Solve the equation:
x−3 = 4
#14
Solve the equation:
2 x + 11 = −3x
#15
Solve the equation:
x −1 = x − 9
1
3
9x2
2
5
3
− 16
#16
Evaluate:
#17
Simplify:
i22
#18
Combine:
(7 − 3i ) − [2 − (5 + 2i )]
#19
Multiply:
(3 + 2i )(4 − i )
#20
Rationalize:
5
4 − 2i
4
SOLUTIONS
Practice Test over Rational Exponents, Radicals, Equations with Radicals, & Complex Numbers
#1
#2
#3
68
Simplify:
Evaluate:
Multiply:
68 = 4 ⋅ 17 = 4 ⋅ 17 = 2 17
2
 13
 8
8



 =
1
 125 
 125 3

2

2
  38 
4
2


=
=
=


 3

25
5
  125 

(
)
2
3
)(
x +5 2 x +3
2 x 2 + 3 x + 10 x + 15
2 x + 13 x + 15
#4
Simplify:
3
24 x 3 y 7
3
8 ⋅ 3x 3 y 6 y
2 xy 2 3 3 y
#5
Rationalize:
2
3 2 3 2 3
⋅
=
=
3
3 3
9
#6
Rationalize:
4
3 − 3 4( 3 − 3) 4( 3 − 3) − 2( 3 − 3)
⋅
=
=
=
3−9
−6
3
3 +3 3 −3
#7
Multiply:
(
x+2
x−4
)(
x −2
)
Use the difference of squares rule:
2
(a + b)(a – b) = a – b
2
5
Use the binomial square
rule:
2
2
2
(a ± b) = (a ± 2ab + b )
( x + 2 y ) = ( x + 2 y ) ( x + 2 y)
(x + 2 ⋅ 2 y x + 4 y )( x + 2 y )
(x + 4 y x + 4 y )( x + 2 y )
3
2
2
2
#8
Multiply:
x x + 2 xy + 4 y x 2 + 8 y 2 x + 4 y 2 x + 8 y 3
x x + 2 xy + 4 xy + 12 y 2 x + 8 y 3
x x + 6 xy + 12 y 2 x + 8 y 3
112 x 5 y 9 − 2 xy 4 28 x 3 y
16 ⋅ 7 x 4 xy 8 y − 2 xy 4 4 ⋅ 7 x 2 xy
#9
Combine:
4 x 2 y 4 7 xy − 2 xy 4 ⋅ 2 x 7 xy
4 x 2 y 4 7 xy − 4 x 2 y 4 7 xy
0 x 2 y 4 7 xy
0
#10
Rationalize:
3
1
3
9x
2
⋅3
3x
=
3x
3
3
3x
27 x
x=
#11
Solve the equation:
3
=
3
3x
3x
2
5
( x ) =  25 
2
 
x=
4
25
2
6
(
x+4=7
)
x + 4 = (7 )
2
2
x + 8 x + 16 = 49
x + 8 x = 33
(8 x )
2
#12
Solve the equation:
121 + 4 ≠ 7
11 + 4 ≠ 7
= (33 − x )
2
64 x = 1089 − 66 x + x 2
Check:
x 2 − 66 x − 64 x + 1089 = 0
x 2 − 130 x + 1089 = 0
( x − 121)( x − 9) = 0
x − 121 = 0, x − 9 = 0
x = 121, x = 9
9+4=7
3+ 4 = 7
x=9
#13
Solve the equation:
(
x−3 = 4
)
2
x − 3 = 42
x − 3 = 16
x = 19
Check:
19 − 3 = 4
16 = 4
x = 19
2 x + 11 = −3x
(2
)
Check:
x + 11 = (− 3 x )
2
2
4(x + 11) = 9 x 2
#14
Solve the equation:
4 x + 44 = 9 x 2
9 x 2 − 4 x − 44 = 0
(9 x − 22)( x + 2) = 0
9 x − 22 = 0, x + 2 = 0
22
x=
, x = −2
9
x = -2
2 − 2 + 11 = −3(−2)
2 9=6
2⋅3 = 6
2
22
22
+ 11 ≠ −3( )
9
9
2
22 99 − 66
+
≠
9
9
9
121
22
≠−
9
3
11
22
2⋅ ≠ −
3
3
22
22
≠−
3
3
2
7
(
) (
2
x −1 =
x−9
)
2
x − 2 x +1 = x − 9
#15
Solve the equation:
− 2 x = −10
25 − 1 = 25 − 9
Check:
5 − 1 = 16
4=4
x =5
( x)
2
= 52
x = 25
x = 25
#16
Evaluate:
#17
Simplify:
− 16 = 16 ⋅ −1 = 4i
( )
5
i 22 = i 4 i 2 = i 2 =
4
Remember that i = 1.
#18
Combine:
(7 − 3i ) − [2 − (5 + 2i )]
7 − 3i − [2 − 5 − 2i ]
7 − 3i − [− 3 − 2i ]
7 − 3i + 3 + 2i
7+ 3 − 3i + 2i
10 - i
#19
Multiply:
(3 + 2i )(4 − i ) = 12 − 3i + 8i − 2i 2 = 12 + 5i − 2(− 1) = 12 + 5i + 2 =
14 + 5i
#20
Rationalize:
5
4 + 2i 20 + 10i 10(2 + i ) 10(2 + i) 10(2 + i)
⋅
=
=
=
=
=
4 − 2i 4 + 2i 16 − 4i 2 16 − 4(− 1) 16 + 4
20
2+i
2