Sat practice Test #8 Answer Explanations

Choice B is correct. The maximum value of the function f occurs at the 
highest point on the graph of y = f (x); the highest point on the graph 
is (4, 3). For any point on the graph of f, the y-coordinate gives the 
value of the function at the x-coordinate; therefore, the maximum value 
of the function f is 3. It is stated that k is the maximum value of f, so 
k = 3. Thus, g (k) = g (3). From the table of values for g, it can be seen 
that when x = 3, g (3) = 6.

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ANSwER ExPlANATIONS
| SAT Practice Test #8
Choice A is incorrect and may result from using the x-coordinate of the 
maximum point as the value of k. Choice C is incorrect; it is the value 
of k, not of g (k). Choice D is incorrect and may be the result of giving 
the value of x that makes g (x) = 3 instead of finding the value of g (x) 
when x = 3.
QUESTION 31
The correct answer is 102. Since each molecule of water has 2 atoms 
of hydrogen, 51 molecules of water have a total of (51)(2) = 102 atoms 
of hydrogen.
QUESTION 32
The correct answer is 2. Substituting x = 1 in the equation x − 1 
_ 
2 a = 0 
gives 1 − 1 
_ 
2 a = 0. Adding
1 
_ 
2 a to both sides of this equation gives 1 =
1 
_ 
2 a. 
Multiplying both sides of this last equation by 2 gives 2 = a.
QUESTION 33
The correct answer is 30. Since the equations x + 2y = 10 and
3x + 6y = c represent the same line in the xy-plane, they must be 
equivalent equations. The expression 3x + 6y on the left-hand side of 
the second equation is equivalent to 3(x + 2y), which is 3 times the left-
hand side of the first equation. Thus, to be equivalent, the right-hand 
side of the second equation, c, must be 3 times the right-hand side of 
the first equation, 10. Therefore, c = 30.
QUESTION 34