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Math 115 Practice Test #5 (Chapters 8 & 9)
36
2
2.
Simplify. Assume all variables represent positive numbers.
48 x 3 y 2
a)
4.
5.
6.
b)
−
Simplify.
3.
a)
−49
1.
b)
Simplify.
−2 5
a)
20
b)
72a 4b7
5
12
)(
c)
)
Solve each equation.
a)
6 x − 2 = 3x − 5
3
128x 6 y 5
d)
d)
24
100
3
128c 5 d 2
4
3 18 − 2 32 + 5 50 + 72
b)
Rationalize the denominators.
5
a)
7a
5
25
81
1
2
c)
Perform the indicated operations.
a)
4 2 +1 3 − 5
(
c)
b)
2
3− 5
b)
8x − 2 =
x
7. Solve each equation by the method indicated.
a) by factoring
2 x2 − 5x − 7 =
0
b) by using the square root property
c) by completing the Square
x 2 = 45
x2 − 8x − 7 =
0
d) by using the Quadratic Formula
5x2 =
−8 x − 1
8. Solve each quadratic equation by your method of choice.
a) 6 x 2 + 18 x = 0
b) 9 x 2 + 12 x = −4
c) 4 x 2 = 16
d) ( x + 3) 2 =
49
9. In the right triangle ABC, a = 2 cm, b = 6 cm, find the side c by using the Pythagorean
Theorem.
B
c
a
C
A
b
____________________________________________________________________________
Solutions:
5
9
1. a) 3 2
b)
Not a real number
c) −
2. a) 4 xy 3 x
b)
6a 2b3 2b
c) 20 x 2 y
3. a) −1
b)
4. a)
15
6
c)
4 6 − 20 2 + 3 − 5
8. a)
7
; x = −1
2
x=
−3; x =
0
9. 2 10 cm
d) 6c 2 d 2c
2 y2
2
2
b) − 3 − 5
6. a)=
x 3;=
x 1 needs to be rejected since it is extraneous!
7. a) x =
3
6
5
b) 32 2
35a
7a
5. a)
d)
b) x = ± 3 5
b) x = −
2
3
b)
x=2
x=
−4 ± 11
5
c)
x= 4 ± 23
d)
c)
x = ±2
d) x = 4, x = −10