Sat Math Medium Practice Quiz With Answer Key Page 11
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16SAT Math Medium Practice Quiz Answers
Algebra and Functions
3. A
(Estimated Difficulty Level: 3)
It is really helpful to recognize that (x + 3)(x
3) =
1. A
(Estimated Difficulty Level: 3)
2
2
2
x
9. The equation x
y
= (x + y)(x
y) is called
the difference of two squares and is useful to memorize
2
for the SAT. Since f (x) = x
9 and the least possible
First, convert the words into an equation:
2
value of x
is zero, then the least possible value of f (x)
n
n
is 0
9 =
9, so answer A is correct.
=
+ 12.
3
2
From here, you could work with the answers by substi-
tuting them into the equation until it works. Or, use
algebra to solve the equation:
4. D
(Estimated Difficulty Level: 3)
n
n
2n
3n
n
Since c is 24 greater than b, and b is 24 greater than
=
=
= 12
3
2
6
6
6
a, c must be 48 greater than a (c = a + 48). Also,
c/a = 3, which means that c = 3a. We substitute to
so that n =
72. (You could also solve the equation
get 3a = a + 48 so that a = 24, which means that
by multiplying through by 6 first to get rid of the frac-
b = a + 24 = 48.
tions.)
If the algebra was too tricky, you also could have used
the answers by plugging them in for b, solving for a and
c, and then checking to see if c/a = 3.
2. C
(Estimated Difficulty Level: 3)
5. C
(Estimated Difficulty Level: 3)
Work with the answers, plugging them in for k until
the equation works. You will see that when k =
2,
Use the graph to find f (4) as follows. First, go to x = 4
the left-hand side of the equation becomes:
on the x-axis. Next, go vertically up until you reach the
line for the function f . Finally, go over horizontally to
2
( 4)
2
16
2
+
=
= 2
1 = 1
find the y-value for that point (see the graph below).
8
2
8
2
y
g
so that answer C is correct.
5
Or, use algebra to solve the equation:
4
2
2
(2k)
k
k
k
3
f
+
=
+
= 1.
8
2
2
2
2
Multiply both sides by 2 and put everything on one side:
1
2
x
k
+ k
2 = 0.
O
1
2
3
4
5
Factor this to get:
(k + 2)(k
1) = 0,
You should see that when x = 4, the y-value of function
f is 2. Since a = f (4), we know that a = 2 and we need
so that k =
2 since we need the negative solution.
to find g(2). Repeat the process, now using the line for
Whew! Working with the answers may have been easier.
the function g. You will see that g(2) = 3.
pg. 11
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