Sat practice Test #8 Answer Explanations

Choice D is correct. Since x 
3
– 9x = x (x + 3)(x − 3) and
x 
2
– 2x – 3 = (x + 1)(x – 3), the fraction 
f(x)
_ 
g(x) can be written as

x(x + 3)(x − 3)
_____________
(x + 1)(x − 3) . It is given that x > 3, so the common factor x – 3 is not 
equal to 0. Therefore, the fraction can be further simplified to 
x(x + 3)
_
x + 1 .

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ANSwER ExPlANATIONS
| SAT Practice Test #8
Choice A is incorrect. The expression 1 
_ 
x + 1 is not equivalent to 
f(x)
_ 
g(x)
because at x = 0, 1 
_ 
x + 1 as a value of 1 and 
f(x)
_ 
g(x) has a value of 0.
Choice B is incorrect and results from omitting the factor x in the 
factorization of f (x). Choice C is incorrect and may result from 
incorrectly factoring g (x) as (x + 1)(x + 3) instead of (x +1)(x – 3).
QUESTION 9
Choice A is correct. The standard form for the equation of a circle is 
(x – h)
2
+ (y – k)
2
= r 
2
, where (h, k) are the coordinates of the center
and r is the length of the radius. According to the given equation, the
center of the circle is (6, –5). Let (x
1
, y
1
) represent the coordinates of 
point Q. Since point P (10, –5) and point Q (x
1
, y
1
) are the endpoints
of a diameter of the circle, the center (6, –5) lies on the diameter, 
halfway between P and Q. Therefore, the following relationships hold:

x
1
+ 10
_ 
2 = 6 and 
y
1
+ (−5)
_
2 
= −5. Solving the equations for x
1
and y
1
, 
respectively, yields x
1
= 2 and y
1
= −5. Therefore, the coordinates of 
point Q are (2, –5).
Alternate approach: Since point P (10, −5) on the circle and the center 
of the circle (6, −5) have the same y-coordinate, it follows that the 
radius of the circle is 10 – 6 = 4. In addition, the opposite end of the 
diameter  
_
 
PQ must have the same y-coordinate as P and be 4 units away 
from the center. Hence, the coordinates of point Q must be (2, –5).
Choices B and D are incorrect because the points given in these 
choices lie on a diameter that is perpendicular to the diameter  
_
 
PQ . If 
either of these points were point Q, then  
_
 
PQ  would not be the diameter 
of the circle. Choice C is incorrect because (6, −5) is the center of the 
circle and does not lie on the circle.
QUESTION 10