SAT Math Hard Practice Quiz
Algebra and Functions
1.
Let
m
be an even integer. How many possible values of
m
satisfy
√
m
+ 7
≤
3 ?
(A)
One
(B)
Two
(C)
Three
(D)
Four
(E)
Five
2.
Let
x
be defined by
x
=
x
+ 3
x
−
1
for any
x
such that
x
6
= 1. Which of the following is equivalent to
x
−
1 ?
(A)
x
+ 2
x
−
1
(B)
4
x
−
1
(C)
2
x
+ 4
x
−
1
(D)
2
x
−
1
(E)
x
+ 2
x
−
2
3.
Let
a
and
b
be numbers such that
a
3
=
b
2
. Which of the
following is equivalent to
b
√
a
?
(A)
b
2
/
3
(B)
b
4
/
3
(C)
b
2
(D)
b
3
(E)
b
4
4.
Let
m
and
n
be positive integers such that one-third of
m
is
n
less than one-half of
m
. Which of the following is
a possible value of
m
?
(A)
15
(B)
21
(C)
24
(D)
26
(E)
28
5.
If
a
and
b
are numbers such that (
a
−
4)(
b
+ 6) = 0, then
what is the smallest possible value of
a
2
+
b
2
?
6.
Let
f
(
x
) =
ax
2
and
g
(
x
) =
bx
4
for any value of
x
. If
a
and
b
are positive constants, for how many values of
x
is
f
(
x
) =
g
(
x
) ?
(A)
None
(B)
One
(C)
Two
(D)
Three
(E)
Four
7.
Let
a
and
b
be numbers such that 30
< a <
40 and 50
<
b <
70. Which of the following represents all possible
values of
a
−
b
?
(A)
−
40
< a
−
b <
−
20
(B)
−
40
< a
−
b <
−
10
(C)
−
30
< a
−
b <
−
20
(D)
−
20
< a
−
b <
−
10
(E)
−
20
< a
−
b <
30
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