Module #6 Exam, Practice
Module #6 Practice Exam
Exam rules:
1. Read and follow the instructions.
2. No notes, no books, no calculators, no collaboration, and no cheating.
3. Failure to present your work in the appropriate manner may result in a penalty.
4. You have 75 minutes to complete the exam.
Practice exam notes:
1. The practice exam is longer than the actual exam.
2. Pay attention to the presentation expectations presented in the solutions.
3. If you have completed the practice diagnostics, then you have already done most of these problems.
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Last Update: December 29, 2011
Module #6 Exam, Practice
[2 Points Each] Solve by factoring.
#1) x2 − 8x − 48 = 0
#3) n2 + 14n + 24 = 0
#2) x2 − 4x = 0
#4) x2 − 49 = 0
[3 Points Each] Simplify.
#5)
#6)
x2 + 3x − 10
· (x + 5)
x2 − 25
2x2 − 3x − 20 4x2 − 15x − 4
÷
3x2 + 7x − 6
6x2 − x − 2
[3 Points Each] Solve the system of equations by substitution or elimination.
#7)
2x +
3x +
y
4y
=
=
6
4
#8)
5x +
x −
3y
6y
=
=
19
11
[1 Points Each] Simplify. Use absolute value notation when necessary. Use imaginary numbers where
appropriate.
√
√
#15)
100x2
#9)
169
√
√
#16)
x2 − 4x + 4
#10) − 169
p
√
y 2 + 16y + 64
#17)
#11)
−169
√
√
3
#12) 3 64
#18)
x6
√
p
#13) − 3 64
#19) 14 (x + 3)14
√
√
#14) 3 −64
#20)
x10
[1 Points Each] Simplify. Assume that no radicands were formed by raising negative quantities to
even powers.
p
√
#25) − 4 81y 4
#21)
16x2
p
p
#22) − (7c)2
#26) 8 (m + 3)8
√
√
#23) 3 27
#27)
t18
√
p
3
#24)
8x3
#28)
(x + 3)10
[1 Points Each] Write an equivalent expression using radical notation and simplify, if possible.
1
3
#33) a 2
#29) y 3
1
3
#30) 32 5
#34) 16 4
1
#31) (xyz) 2
3
2
#35) (125a3 ) 3
3
#32) (81) 4
#36) (25x4 ) 2
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Module #6 Exam, Practice
[1 Points Each] Write an equivalent expression using exponential notation.
p
#41) 7 x3 y 2 z 2
√
#37) 3 18
√
#42) ( 3 7xy)4
√
#38)
x7
2x
√
#43) √
5
3
2
#39)
m
z2
√
3a
#40) ( 3 cd)5
#44) √
5 2
c
[1 Points Each] Write an equivalent expression using positive exponents and simplify, if possible.
3
1
5
#46) (5xy)− 6
− 34
1
#47)
16
#48)
1
2
#49) 2a 4 b− 2 c 3
#45) a− 4
8c
2
#52)
a−3/5
4
#50) 5x− 3 y 5 z
− 56
2ab
#51)
c
6a
√
4
b
[2 Points Each] Simplify. Do not use negative exponents in your final answers.
1
1
#53) 11 2 · 11 3
3
5
#54) y · y
− 41
3
#58)
x−1/5
x−7/10
6
1
2
#55) (10 5 ) 5
#59) (7 3 ) 5
2
#56)
35/8
3−1/8
#57)
8−7/11
82/11
#60) (x3 y 4 ) 5
2
1
1
#61) (m 3 n− 4 ) 2
1
2
1
#62) (x− 3 y 5 ) 4
[2 Points Each] Simplify. Do not use fractional exponents in your final answer.
√
√
9
#67) ( 10 3a)5
#63)
x3
p
√
12
#68)
(ab)6
#64)
a3
p√
p
x
#69)
#65) 4 (7a)2
p
√
√
5 3
#66) ( 8 2x)6
#70)
2a
[1 Points Each] Simplify. Assume that no radicands were formed by raising negative numbers to even
powers.
p
√
#71)
300
#75) 3 8x3 y 2
√
√
#72)
27
#76) 3 −16x6
√
√
#73)
8x9
#77)
a10 b11
√
√
3
#74)
36a4 b
#78)
a6 b7 c13
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Module #6 Exam, Practice
[2 Points Each] Multiply and simplify. Assume that no radicands were formed by raising negative
numbers to even powers.
√ √
√ √
#84)
5a7 15a3
#79)
6 33
p p
√ √
#85)
6y 3 27y 5
#80)
10 35
√
√
√
√
3 2 4 3
#81) 3 9 3 3
#86)
s t s 4 t6
√
√
p
p
3
#82)
5a2 3 2a
#87) 3 x2 y 4 3 x2 y 5
√
√
√
√
4
4
#83)
2x5 10x2
20a3 b7 4a2 b5
#88)
[2 Points Each] Divide and simplify. Assume that variables represent positive numbers.
√
r
700x
81
√
#94)
#89)
25
7x
r
√
3
125
35
#90) 3
#95) √
3
8
5
r
√
4
56ab3
3 27a
#91)
√
#96)
3
8b
7a
s
p
3
189x5 y 7
81x4
p
#97)
#92) 4 8 4
3
y z
7x2 y 2
√
r
9 12
100ab
4 x y
√
#98)
#93)
5 2
z6
[2 Points Each] Rationalize the denominator. Assume that variables represent positive numbers.
√
r
3
3a
7
#102) √
#99)
3
2
5c
√
√
3
3 5
7x
√
#100)
#103) √
3
3y
2 7
r
r
2
3x
#101) 3
#104)
9
20
[1 Points Each] Simplify, if possible. Assume that all variables and radicands represent positive real
numbers.
√
√
√
√
#105) 6 5 + 2 5
#110)
3(6 − 3)
√
√
√
√ √
#106) 5 12 − 16 27
#111) 4 2( 3 + 5)
√
√
√
√
√ √
√
#107) 5 7 − 8 4 11 + 7 + 9 4 11
#112)
3(2 15 − 3 4)
√
√
√ √
√
#108) 9 50 − 4 2
#113) 3 2( 3 4 − 2 3 32)
√
√
√
√ √
3
3
#109) 2 9x3 − x
#114) 3 a( a2 + 24a2 )
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Module #6 Exam, Practice
[2 Points Each] Simplify, if possible. Assume that all variables and radicands represent positive real
numbers.
√
√
#115) (4 − 5)(2 + 5)
√
√ √
√
#116) ( 7 − 2)( 5 + 2)
√
√
#117) (2 − 3)(2 + 3)
√
√
√
√
#118) (3 7 + 2 5)(2 7 − 4 5)
√
#119) (3 + 10)2
√
√
#120) ( 5 − 3)2
[3 Points Each] Rationalize the denominator.
#121)
#122)
5
√
4− 5
√
1+ 2
√
3+ 5
[2 Points Each] Solve.
√
#125)
7x − 3 = 5
√
#126)
2x − 1 = 2
√
#127) 7 y = y
#123)
#124)
#128)
√
√
7+ 5
√
√
5+ 2
√
√
5 3 − 11
√
√
2 3−5 2
√
x − 2 − 7 = −4
#129) 3x1/2 + 12 = 9
#130) (5y + 31)1/4 = 2
[3 Points Each] Solve.
√
√
#131)
2t − 7 = 3t − 12
√
√
#132)
4x − 3 = 2 + 2x − 5
√
√
#133)
x + 2 + 3x + 4 = 2
[2 Points Each] Solve using the principle of square roots. Use imaginary numbers where appropriate.
#134) x2 = 100
#135) p2 − 50 = 0
#136) 9x2 − 49 = 0
Nevada State College
#137) t2 + 4 = 0
#138) (y − 4)2 = 18
2
3
17
#139)
x+
=
4
16
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Last Update: December 29, 2011
Module #6 Exam, Practice
[1 Points Each] Replace the blanks in each equation with constants to complete the square and form
a true equation. Write the entire equation.
#140) x2 + 16x +
= (x +
)2
#141) t2 − 10t +
= (t −
)2
#142) x2 + 2x +
= (x +
)2
#143) x2 + 3x +
2
#144) x2 + x +
3
5
#145) t2 − t +
3
= (x +
)2
= (x +
)2
= (t −
)2
[3 Points Each] Solve the equation by completing the square. Use imaginary numbers where appropriate.
#146) x2 + 6x = 7
#147) t2 − 10t = −23
#148) x2 + 12x + 32 = 0
#149) t2 + 8t − 3 = 0
#150) 9x2 + 18x = −8
#151) 3x2 − 5x − 2 = 0
[3 Points Each] Solve the equation by using the quadratic formula. Use imaginary numbers where
appropriate.
#152) 2x2 + 3x − 5 = 0
#153) u2 + 2u − 4 = 0
#154) x2 + 4x + 6 = 0
#155) t2 + 10 = 6t
#156) 2t(t + 2) = 1
#157) 7x(x + 2) + 5 = 3x(x + 1)
[2 Points Each] Sketch the parabola. You will be graded on the location of the vertex and the general
shape of the parabola.
#158) y = (x + 3)2 − 2
#161) y = −(x + 2)2 − 1
#159) y = −(x − 1)2 + 2
#162) y =
#160) y = 2(x + 3)2 + 1
#163) y = −2(x − 1)2 + 3
1
(x − 3)2 − 3
2
[2 Points Each] State the location of the vertex and the equation of the axis of symmetry of the given
parabola.
#164) y = (x − 5)2 + 2
#167) y = −(x − 2)2 − 4
#165) y = (x + 1)2 − 3
#168) y = −2(x − 1)2 − 3
#166) y =
#169) y = −2(x + 1)2 + 4
1
(x + 4)2 + 1
2
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Module #6 Exam, Practice
[3 Points Each] Solve the equation for the given variable.
#170)
#171)
#172)
W1
d1
=
for W2
W2
d2
t
t
+ = 1 for b
a b
1 1
1
+ = for q
p q
f
H
for t1
m(t1 − t2 )
a
#174) S =
for r
1−r
#173) S =
#175) I =
nE
for r
R + nr
[2 Points Each] Find the variation constant and an equation of variation.
#176) The variable y varies directly
with x, and y = 10 when x = 2.
#177) The variable y varies inversely
with x, and y = 6 when x = 3.
#179) The variable y varies inversely
with x, and y = 5 when x = 20.
#180)
The variable y varies directly
1
with x, and y = 2 when x = .
5
#178) The variable y varies directly
with x, and y = 80 when x = 16.
#181) The variable y varies inversely
1
with x, and y = 81 when x = .
3
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Last Update: December 29, 2011