Sat math Essentials

c.
y
= 
x
2
2
–
x
4
+
x
4
+ 4
d.
y
= 
x
2
–
+
x
2
3
+
x
+
2
2
e.
y
= 
x
x
2
2
+
+
2
6
x
x
+
+
2
8
2.
If graphed, which of the following pairs of equations would be parallel to each other?
a.
y
= 2
x
+ 4,
y
= 
x
+ 4
b.
y
= 3
x
+ 3,
y
= –
1
3
x
– 3 
c.
y
= 4
x
+ 1,
y
= –4
x
+ 1
d.
y
= 5
x
+ 5,
y
= 
1
5
x
+ 5
e.
y
= 6
x
+ 6,
y
= 6
x
– 6
3.
If
b
–
a
4
= 
4
a
b
+ 1, then when 
a
= 8,
b
could be equal to
a.
–2.
b.
4.
c.
6.
d.
7.
e.
8.
4.
The average of five consecutive odd integers is –21. What is the least of these integers?
a.
–17
b.
–19
c.
–21
d.
–23
e.
–25
5.
Line 
AC
is a diagonal of square 
ABCD
. What is the sine of angle 
ACB
?
a.
1
2
b.
2
c.
d.
e.
cannot be determined
3
2
2
2
–
P R A C T I C E T E S T 2
–
2 0 7

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6.
If the height of a cylinder is doubled and the radius of the cylinder is halved, the volume of the cylinder
a.
remains the same.
b.
becomes twice as large.
c.
becomes half as large.
d.
becomes four times larger.
e.
becomes four times smaller.
7.
=
a.
b
b.
b
– 
a
2
c.
a
b
– 1
d.
a
b
2
– 1
e.
a
b
2
– 
a
8.
The ratio of the number of cubic units in the volume of a cube to the number of square units in the surface
area of the cube is 2:3. What is the surface area of the cube?
a.
16 square units
b.
24 square units
c.
64 square units
d.
96 square units
e.
144 square units
9.
If a number is chosen at random from a set that contains only the whole number factors of 24, what is the
probability that the number is either a multiple of four or a multiple of six?
10.
There are 750 students in the auditorium for an assembly. When the assembly ends, the students begin to
leave. If 32% of the students have left so far, how many students are still in the auditorium?
11.
If point 
A
is at (–1,2) and point 
B
is at (11,–7), what is length of line 
AB
?
12.
Robert is practicing for the long jump competition. His first four jumps measure 12.4 ft, 18.9 ft, 17.3 ft,
and 15.3 ft, respectively. If he averages 16.3 feet for his first five jumps, what is the length in feet of his
fifth jump?
13.
There are seven students on the trivia team. Mr. Randall must choose four students to participate in the
trivia challenge. How many different groups of four students can Mr. Randall form?
a
b
– 
a
a
1
–1
–
P R A C T I C E T E S T 2
–
2 0 8

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14.
The graph above shows the sales by month for the Greenvale and Smithtown branches of SuperBooks.
From January through May, how much more money did the Smithtown branch gross in sales than the
Greenvale branch?
15.
In the diagram above, what is the length of side 
FG
?
16.
DeDe and Mike both run the length of a two-mile field. If DeDe runs 5 mph and Mike runs 6 mph, how
many more minutes does it take DeDe to run the field?
105
180
105˚
105˚
36
C
D
B
A
E
F
J
G
I
H
S
ale
s
 of the Greenvale and 
S
mithtown Branche
s
 of 
S
uperBook
s
S
ale
s
 in Thou
s
and
s
 of Dollar
s
Month
s
 of 2004
January February March April May
Greenvale
S
mithtown
40
32
24
16
8
0
–
P R A C T I C E T E S T 2
–
2 0 9

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17.
Point 
A
of rectangle 
ABCD
is located at (–3,12) and point 
C
is located at (9,5). What is the area of rectangle
ABCD
?
18.
In the diagram above, the radius of the circle is 20 units and the length of arc 
AB
is 15
π
units. What is the
measure in degrees of angle 
AOB
?
S e c t i o n 3
1.
All of the following are less than 
2
5
EXCEPT
a.
1
3
.
b.
0.04.
c.
3
8
.
d.
3
7
.
e.
0.0404.
2.
If 3
x
– 
y
= 2 and 2
y
– 3
x
= 8, which of the following is equal to 
x
y
?
a.
2
3
b.
2
5
c.
2
1
2
d.
4
e.
6
A
B
O
20
–
P R A C T I C E T E S T 2
–
2 1 0

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3.
Which of the following sets of numbers contains all and only the roots of the equation 
f
(
x
) = 
x
3
+ 7
x
2
– 8
x
?
a.
{–8, 1}
b.
{8, –1}
c.
{0, –8, 1}
d.
{0, 8, –1}
e.
{0, –1, –8, 1, 8}
4.
What is the equation of the line that passes through the points (2,3) and (–2,5)?
a.
y
= 
x
+ 1
b.
y
= –
1
2
x
+ 4
c.
y
= –
1
2
x
d.
y
= –
3
2
x
e.
y
= –
3
2
x
+ 2
5.
An empty crate weighs 8.16 kg and an orange weighs 220 g. If Jon can lift 11,000 g, how many oranges can
he pack in the crate before lifting it onto his truck?
a.
12
b.
13
c.
37
d.
46
e.
50
6.
The measures of the length, width, and height of a rectangular prism are in the ratio 2:6:5. If the volume of
the prism is 1,620 mm
3
, what is the width of the prism?
a.
3 mm
b.
6 mm
c.
9 mm
d.
18 mm
e.
27 mm
7.
A box contains five blue pens, three black pens, and two red pens. If every time a pen is selected, it is
removed from the box, what is the probability of selecting a black pen followed by a blue pen?
a.
1
6
b.
1
1
0
c.
5
1
0
d.
2
3
0
e.
7
9
7
0
–
P R A C T I C E T E S T 2
–
2 1 1

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8.
In the diagram above, lines 
NO
and 
PQ
are parallel to each other and perpendicular to lines 
JK
and 
LM
.
Line 
JK
is parallel to line 
LM
. If angle 
CBD
is 70 degrees, what is the measure of angle 
ZBK
?
a.
10 degrees
b.
20 degrees
c.
70 degrees
d.
90 degrees
e.
110 degrees
9.
Monica sells pretzels in the cafeteria every school day for a week. She sells 14 pretzels on Monday, 12 pret-
zels on Tuesday, 16 pretzels on Wednesday, and 12 pretzels on Thursday. Then, she calculates the mean,
median, and mode of her sales. If she sells 13 pretzels on Friday, then
a.
the mode will increase.
b.
the mean will stay the same.
c.
the median will stay the same.
d.
the median will decrease.
e.
the mean will increase.
10.
What is the tenth term of the pattern below?
1,
1
0
0
24
,
5
9
12
,
2
8
56
,
1
7
28
, . . .
a.
1
2
b.
2
9
c.
9
2
d.
9
4
e.
1
A
J
M
L
Q
N
D
C
B
O
P
K
Z
70˚
–
P R A C T I C E T E S T 2
–
2 1 2

---

11.
Which of the following statements is always true if
p
is a rational number?
a.
|
p
| < |3
p
|
b.
|
p
2
| > |
p
+ 1|
c.
|–
p
| > 
p
d.
|
p
3
| > |
p
2
|
e.
|
p
–
p
| > 
p
–
p
12.
In the diagram above, side 
OB
side 
OC
. Which of the following is the measure of minor arc 
BC
?
a.
27.5 degrees
b.
45 degrees
c.
55 degrees
d.
70 degrees
e.
110 degrees
13.
If
g
^
h
= 
2
g
h
, then (
h
^
g
)^
h
=
a.
2
h
.
b.
4
h
.
c.
h
g
2
.
d.
2
g
h
2
.
e.
4
g
h
2
.
14.
Four copy machines make 240 total copies in three minutes. How long will it take five copy machines to
make the same number of copies?
a.
2 minutes
b.
2 minutes, 15 seconds
c.
2 minutes, 24 seconds
d.
2 minutes, 45 seconds
e.
3 minutes, 36 seconds
A
B
C
55˚
O
–
P R A C T I C E T E S T 2
–
2 1 3

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15.
If 40% of
j
is equal to 50% of
k
, then 
j
is
a.
10% larger than 
k
.
b.
15% larger than 
k
.
c.
20% larger than 
k
.
d.
25% larger than 
k
.
e.
80% larger than 
k
.
16.
In the diagram above,
FDCB
is a rectangle. Line 
ED
is six units long, line 
AB
is ten units long, and the
measure of angle 
ECD
is 60 degrees. What is the length of line 
AE
?
a.
8
b.
c.
20
d.
20 – 
e.
20 – 4
3
3
2
3
2
10
6
A
D
E
C
B
F
60°
–
P R A C T I C E T E S T 2
–
2 1 4

---

A n s w e r K e y
Section 1 Answers
1.
b.
Substitute 6 for 
m
:
6
3
2
– 4(6) + 10 = 
3
3
6
– 24 + 10
= 12 – 14 = –2.
2.
b.
The midpoint of a line is equal to the average of
the 
x
- and 
y
-coordinates of its endpoints. The
average of the 
x
-coordinates = 
–2
2
+ 8
= 
6
2
= 3.
The average of the 
y
-coordinates = 
–8
2
+ 0
= –
8
2
=
–4. The midpoint of this line is at (3,–4).
3.
e.
If 4
x
+ 5 = 15, then 4
x
= 10 and 
x
= 2.5. Substi-
tute 2.5 for 
x
in the second equation: 10(2.5) +
5 = 25 + 5 = 30.