Sat practice Test #8 Answer Explanations

Choice C is correct. Since a has the exponent − 1 
_ 
2 , a can be isolated by 
raising both sides of the equation to the −2 power.
 
 a  
( 
− 1 
_ 
2
)
( 
−2 
)
= x 
−2
 a = x 
−2
 a = 1 
_ 
x 
2
Alternate method:
a 
− 1 
_ 
2
= 1 
_ 
a 
1 
_ 
2
= 1 
_ 
√ 
_
a
So,
1 
_ 
√ 
_
a = x
Square both sides of the equation:
1 
_ 
a =  x
2
Then take the reciprocal of both sides:
 a = 1 
_ 
x 
2
Choice A is incorrect and may result from incorrectly taking the square 
root of both sides to eliminate the exponent of a. Choice B is incorrect 
and may result from incorrectly taking the square root of both sides 
to eliminate the exponent of a, and incorrectly multiplying by −1 to 
make the exponent positive. Choice D is incorrect and may result from 
incorrectly multiplying by −1 to make the exponent positive.

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ANSwER ExPlANATIONS
| SAT Practice Test #8
QUESTION 14
Choice D is correct. A rational expression is undefined when the 
denominator is 0. To determine the values of x that result in a 
denominator of 0, set the denominator equal to 0 and solve for x:
 x 
2
+ 3x − 10 = 0
(x + 5)(x − 2) = 0
 x + 5 = 0 or x − 2 = 0
 x = −5 or x = 2
Among the answer choices, only the value x = 2 is listed, so choice D
is correct.
Choice A is incorrect. When x = −3, the denominator is
(−3)
2
+ 3(−3) − 10 = −10, so the given expression is not undefined. 
Choice B is incorrect and may result from incorrectly factoring the 
denominator or incorrectly assuming that if (x − 2) is a factor, then
x = −2 is a solution. Choice C is incorrect and may result from 
giving the value of the denominator that makes the given expression 
undefined rather than the value of x that makes the denominator
equal to 0.
QUESTION 15