Sat math Essentials

c.
the price of a pair of Jump sneakers must decrease by 25%.
d.
the price of a pair of Speed sneakers must increase by 25%.
e.
the price of a pair of Jump sneakers must decrease by 33%.
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P R A C T I C E T E S T 3
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2 3 0

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5.
In the diagram above, line 
AB
is parallel to line 
CD
, angle 
EIJ
measures 140 degrees and angle 
CKG
meas-
ures 55 degrees. What is the measure of angle 
IKJ
?
a.
40 degrees
b.
55 degrees
c.
85 degrees
d.
95 degrees
e.
135 degrees
6.
A number cube is labeled with the numbers one through six, with one number on each side of the cube.
What is the probability of rolling either a number that is even or a number that is a factor of 9?
a.
1
3
b.
1
2
c.
2
3
d.
5
6
e.
1
7.
The area of one square face of a rectangular prism is 121 square units. If the volume of the prism is 968
cubic units, what is the surface area of the prism?
a.
352 square units
b.
512 square units
c.
528 square units
d.
594 square units
e.
1,452 square units
A
B
C
D
E
H
J
K
F
G
I
140˚
55˚
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P R A C T I C E T E S T 3
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2 3 1

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8.
In the diagram above,
ABDE
is a square and 
BCD
is an equilateral triangle. If
FC
= 6
3
cm, what is the
perimeter of
ABCDE
?
a.
30
3
cm 
b.
36
3
cm
c.
60 cm
d.
60
3
cm
e.
84 cm
9.
What is the value of (3
xy
+ 
x
)
x
y
when 
x
= 2 and 
y
= 5?
10.
The diagram above shows the breakdown by age of the 1,560 people who attended the Spring Island Con-
cert last weekend. How many people between the ages of 18 and 34 attended the concert?
11.
Matt weighs 
3
5
of Paul’s weight. If Matt were to gain 4.8 pounds, he would weigh 
2
3
of Paul’s weight. What is
Matt’s weight in pounds?
12.
If –6
b
+ 2
a
– 25 = 5 and 
a
b
+ 6 = 4, what is the value of (
a
b
)
2
?
13.
The function 
j
@
k
= (
k
j
)
j
. If
j
@
k
= –8 when 
j
= –3, what is the value of
k
?
Age
s
 of 
S
pring I
s
land Concert Attendee
s
>55
4%
<18
10%
33
–55
21%
18–24
41%
25–
3
4
24%
A
6
√⎯
3
B
E
D
F
C
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P R A C T I C E T E S T 3
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2 3 2

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14.
In the circle above, the measure of angle 
AOB
is 80 degrees and the length of arc 
AB
is 28
π
units. What is
the radius of the circle?
15.
What is the distance from the point where the line given by the equation 3
y
= 4
x
+ 24 crosses the 
x
-axis to
the point where the line crosses the 
y
-axis?
16.
For any whole number 
x
> 0, how many elements are in the set that contains only the numbers that are
multiples AND factors of
x
?
17.
A bus holds 68 people. If there must be one adult for every four children on the bus, how many children
can fit on the bus?
18.
In Marie’s fish tank, the ratio of guppies to platies is 4:5. She adds nine guppies to her fish tank and the
ratio of guppies to platies becomes 5:4. How many guppies are in the fish tank now?
S e c t i o n 3
1.
The line 
y
= –2
x
+ 8 is
a.
parallel to the line 
y
= 
1
2
x
+ 8.
b.
parallel to the line 
1
2
y
= –
x
+ 3.
c.
perpendicular to the line 2
y
= –
1
2
x
+ 8.
d.
perpendicular to the line 
1
2
y
= –2
x
– 8.
e.
perpendicular to the line 
y
= 2
x
– 8.
2.
It takes six people eight hours to stuff 10,000 envelopes. How many people would be required to do the job
in three hours?
a.
4
b.
12
c.
16
d.
18
e.
24
B
A
O
28
80˚
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P R A C T I C E T E S T 3
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2 3 3

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3.
In the diagram above of
f
(
x
), for how many values does 
f
(
x
) = –1?
a.
0
b.
1
c.
2
d.
3
e.
4
4.
The equation 
x
4
2
– 3
x
= –8 when 
x
=
a.
–8 or 8.
b.
–4 or 4.
c.
–4 or –8.
d.
4 or –8.
e.
4 or 8.
5.
The expression 
x
3
+
x
2
x
–
2
–
16
20
x
can be reduced to
a.
x
+
4
5
.
b.
x
+
x
4
.
c.
x
x
+
+
4
5
.
d.
x
x
2
+
+
5
4
x
.
e.
–
x
3 –
16
20
x
.
4
3
2
1
–1
–2
–3
–4
–4 –3 –2 –1 
1 2 3 4
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P R A C T I C E T E S T 3
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2 3 4

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6.
In the diagram above, if angle 
OBE
measures 110 degrees, what is the measure of arc 
AC
?
a.
20 degrees
b.
40 degrees
c.
55 degrees
d.
80 degrees
e.
cannot be determined
7.
The volume of a cylinder is 486
π
cubic units. If the height of the cylinder is six units, what is the total area
of the bases of the cylinder?
a.
9
π
square units 
b.
18
π
square units
c.
27
π
square units
d.
81
π
square units
e.
162
π
square units
8.
If
a
20
= , then 
a
=
a.
2
3
.
b.
5
.
c.
5.
d.
6
.
e.
6.
2
180
a
110˚
B
D
C
A
E
O
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P R A C T I C E T E S T 3
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2 3 5

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9.
In the diagram above,
ABC
and 
DEC
are right triangles, the length of side 
BC
is 15 units, and the measure
of angle 
A
is 60 degrees. If angle 
A
is congruent to angle 
EDC
, what is the length of side 
DC
?
a.
15
units
b.
1
2
5
units
c.
1
2
5
3
units
d.
9 units
e.
15
3
units
10.
If
q
is decreased by 
p
percent, then the value of
q
is now
a.
q
– 
p
.
b.
q
– 
1
p
00
.
c.
–
1
p
0
q
0
.
d.
q
– 
1
p
0
q
0
.
e.
pq
– 
1
p
0
q
0
.
11.
The product of (
a
b
)
2
(
a
b
)
–2
(
1
a
)
–1
=
a.
a
.
b.
1
a
.
c.
a
b
4
3
.
d.
a
b
4
4
.
e.
a
b
4
5
.
A
B
C
D
E
15
60˚
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P R A C T I C E T E S T 3
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2 3 6

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12.
Gil drives five times farther in 40 minutes than Warrick drives in 30 minutes. If Gil drives 45 miles per
hour, how fast does Warrick drive?
a.
6 mph
b.
9 mph
c.
12 mph
d.
15 mph
e.
30 mph
13.
A bank contains one penny, two quarters, four nickels, and three dimes. What is the probability of selecting
a coin that is worth more than five cents but less than 30 cents?
a.
1
5
b.
1
4
c.
1
2
d.
1
7
0
e.
1
9
0
14.
In the diagram above, what is the area of the rectangle?
a.
6
ab
square units
b.
8
ab
square units
c.
9
b
2
square units
d.
12
ab
square units
e.
16
b
square units
(–
a
,–
b
)
y
x
(
a
,–
b
)
(–
a
,3
b
)
(
a
,3
b
)
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P R A C T I C E T E S T 3
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2 3 7

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15.
If set 
M
contains only the positive factors of 8 and set 
N
contains only the positive factors of 16, then the
union of sets 
M
and 
N
a.
contains exactly the same elements that are in set 
N
.
b.
contains only the elements that are in both sets 
M
and 
N
.
c.
contains nine elements.
d.
contains four elements.
e.
contains only even elements.
16.
In the diagram above,
ABCD
is a square with an area of 100 cm
2
and lines 
BD
and 
AC
are the diagonals of
ABCD
. If line 
EF
is parallel to line 
BC
and the length of line 
CF
= 3
2
cm, which of the following is equal
to the shaded area?
a.
25 cm
2
b.
39 cm
2
c.
64 cm
2
d.
78 cm
2
e.
89 cm
2
A
B
D
C
F
E
O
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P R A C T I C E T E S T 3
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2 3 8

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A n s w e r K e y
Section 1 Answers
1.
e.
Divide the numerator and denominator of
4
x
x
by 
x
,
leaving 
1
4
. Divide the numerator and denominator
of
2
5
0
by 5. This fraction is also equal to 
1
4
.
2.
c.
Multiply the numbers of vocalists, guitarists,
drummers, and bassists in each town to find
the number of bands that can be formed in each
town. There are (7)(4)(4)(2) = 224 bands that
can be formed in Glen Oak. There are
(5)(8)(2)(3) = 240 bands that can be formed in
Belmont; 240 – 224 = 16 more bands that can be
formed in Belmont.
3.
a.
The equation of a parabola with its turning point
five units to the right of the 
y
-axis is written as 
y
=
(
x
– 5)
2
. The equation of a parabola with its turn-
ing point four units below the 
x
-axis is written as 
y
= 
x
2
– 4. Therefore, the equation of a parabola
with its vertex at (5,–4) is 
y
= (
x
– 5)
2
– 4.