Sat math Essentials

a.
4
b.
15
c.
20
d.
24
e.
32
2.
The volume of a glass of water placed in the sun decreases by 20%. If there are 240 mL of water in the glass
now, what was the original volume of water in the glass?
a.
192 mL
b.
260 mL
c.
288 mL
d.
300 mL
e.
360 mL
3.
What is the tenth term of the pattern below?
2
3
,
4
9
,
2
8
7
,
1
8
6
1
. . .
a.
2
3
0
0
b.
2
3
10
c.
3
2
10
d.
(
2
3
)
2
3
e.
(
2
3
)
10
4.
How does the area of a rectangle change if both the base and the height of the original rectangle are
tripled?
a.
The area is tripled.
b.
The area is six times larger.
c.
The area is nine times larger.
d.
The area remains the same.
e.
The area cannot be determined.
5.
The equation 
y
= 
x
2
+
x
7
+
x
6
– 18
is undefined when 
x
=
a.
–9.
b.
–2.
c.
–6.
d.
0.
e.
9.
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P R A C T I C E T E S T 1
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6.
In the diagram above, angle 
A
is congruent to angle 
BED
, and angle 
C
is congruent to angle 
D
. If the ratio
of the length of
AB
to the length of
EB
is 5:1, and the area of triangle 
BED
= 5
a
2
+ 10, what is area of trian-
gle 
ABC
?
a.
5
a
2
+ 10
b.
25
a
2
+ 50
c.
25
a
2
+ 100
d.
125
a
2
+ 250
e.
cannot be determined
7.
The number 
p
is greater than 0, a multiple of 6, and a factor of 180. How many possibilities are there for
the value of
p
?
a.
7
b.
8
c.
9
d.
10
e.
11
8.
If
g
> 0 and 
h
< 0, which of the following is always positive?
a.
gh
b.
g
+ 
h
c.
g
– 
h
d.
|
h
| – |
g
|
e.
h
g
9.
The length of a room is three more than twice the width of the room. The perimeter of the room is 66 feet.
What is the length of the room?
A
E
B
D
C
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P R A C T I C E T E S T 1
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1 8 4

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10.
In the diagram above, lines 
K
and 
L
are parallel, and lines 
M
and 
N
are parallel. If
b
= 8, then 
a
= ?
11.
If 6
x
+ 9
y
– 15 = –6, what is the value of –2
x
– 3
y
+ 5?
12.
Find the measure of angle 
Z.
13.
If the distance from point (–2,
m
) to point (4,–1) is 10 units, what is the positive value of
m
?
14.
If
z
2
a
= 9, then 
a
= 3 when 
z
= ?
15.
The length of a rectangular prism is four times the height of the prism and one-third the width of the
prism. If the volume of the prism is 384 in
3
, what is the width of the prism?
16.
If 2
a
2
+ 
b
= 10 and –
4
b
+ 3
a
= 11, what is the positive value of
a
?
17.
Stephanie buys almonds at the grocery store for $1.00 per pound. If she buys 4 pounds of almonds and
pays a 5% tax on her purchase, what is Stephanie’s total bill?
18.
The ratio of the number of linear units in the circumference of a circle to the number of square units in the
area of that circle is 2:5. What is the radius of the circle?
B
 E
H
A
C
D
F
G
I
Z
3
2
2
3
2
2
M
N
K
L
10
a
+ 5
8
b
+ 1
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P R A C T I C E T E S T 1
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1 8 5

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S e c t i o n 3
1.
Which of the following number pairs is in the ratio 4:5?
a.
1
4
,
1
5
b.
1
5
,
1
4
c.
1
5
,
4
5
d.
4
5
,
5
4
e.
1,
4
5
2.
When 
x
= –3, the expression –2
x
2
+ 3
x
– 7 =
a.
–34.
b.
–27.
c.
–16.
d.
–10.
e.
2.
3.
What is the slope of the line –3
y
= 12
x
– 3?
a.
–4
b.
–3
c.
1
d.
4
e.
12
4.
Which of the following could be the equation of the parabola shown above?
a.
y
= (
x
+ 3)
2
+ 2
b.
y
= (
x
+ 3)
2
– 2
c.
y
= (
x
– 3)
2
+ 2
d.
y
= (
x
– 3)
2
– 2
e.
y
= (3
x
+ 3)
2
– 2
4
4
3
3
2
2
1
1
–1
–1
–2
–2
–3
–3
–4
–4
y
x
–
P R A C T I C E T E S T 1
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1 8 6

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5.
If 0.34 < 
x
< 0.40 and 
1
5
6
< 
x
< 
2
9
0
, which of the following could be 
x
?
a.
1
3
b.
2
5
c.
3
8
d.
3
7
e.
4
9
6.
A store prices a coat at $85. During a sale, the coat is sold at 20% off. After the sale, the store raises the price
of the coat 10% over its sale price. What is the price of the coat now?
a.
$18.70
b.
$61.20
c.
$68.00
d.
$74.80
e.
$93.50
7.
The expression 4
x
2
– 2
x
+ 3 is equal to 3 when 
x
= 0 and when 
x
= 
a.
–
1
2
.
b.
–
1
4
.
c.
1
8
.
d.
1
4
.
e.
1
2
.
8.
A spinner is divided into eight equal regions, labeled one through eight. If Jenna spins the wheel, what is
the probability that she will spin a number that is less than four and greater than two?
a.
1
8
b.
3
9
2
c.
3
8
d.
1
2
e.
3
4
9.
The length of an edge of a cube is equal to half the height of a cylinder that has a volume of 160
π
cubic
units. If the radius of the cylinder is 4 units, what is the surface area of the cube?
a.
64 square units
b.
96 square units
c.
100 square units
d.
125 square units
e.
150 square units
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P R A C T I C E T E S T 1
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1 8 7

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10.
The function 
m
#
n
is equal to 
m
2
– 
n
. Which of the following is equivalent to 
m
#(
n
#
m
)?
a.
–
n
b.
n
2
– 
m
c.
m
2
+ 
m
– 
n
2
d.
(
m
2
– 
n
)
2
– 
n
e.
(
n
2
– 
m
)
2
– 
m
11.
Which of the following has the greatest value when 
x
= –
1
4
?
a.
x
–1
b.
–
8
3
x
c.
4
x
+ 3
d.
16
x
e.
8
1
1
x
12.
In the diagram above, lines 
M
and 
N
are parallel. All of the following are true EXCEPT
a.
a
+ 
b
= 
j
+ 
l
.
b.
g
= 
h
.
c.
c
+ 
f
= 
f
+ 
b
.
d.
g
+ 
e
+ 
f
+ 
h
= 360.
e.
d
+ 
e
= 
f
+ 
j
.
M
N
a
b
c
d
e
f
g
h
i
j
k
l
–
P R A C T I C E T E S T 1
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1 8 8

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13.
Melissa runs the 50-yard dash five times, with times of 5.4 seconds, 5.6 seconds, 5.4 seconds, 6.3 seconds,
and 5.3 seconds. If she runs a sixth dash, which of the following would change the mean and mode of her
scores, but not the median?
a.
5.3 seconds
b.
5.4 seconds
c.
5.5 seconds
d.
5.6 seconds
e.
6.3 seconds
14.
If
x
≠
0 and 
y
≠
0,
=
a.
x
y
+ 1.
b.
x
y
+ 
x
.
c.
x
y
+ 
y
.
d.
2
xy
.
e.
y
2
+ 
x
.
15.
The scatterplot above shows the speeds of different runners over time. Which of the following could be the
equation of the line of best fit?
a.
s
= –2(
t
–15)
b.
s
= –
t
+ 25
c.
s
= –
1
2
(
t
– 10)
d.
s
= 
1
2
(
t
+ 20)
e.
s
= 2(
t
+ 15)
S
peed
(km/h)
Time
(
s
ec)
20
15
10
5
0
5 10 15 20
x
y
y
+ 
xy
x
x
y
–
P R A C T I C E T E S T 1
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1 8 9

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16.
The radius of the outer circle shown above is 1.2 times greater than the radius of the inner circle. What is
the area of the shaded region?
a.
6
π
m
2
b.
9
π
m
2
c.
25
π
m
2
d.
30
π
m
2
e.
36
π
m
2
O
5 m
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P R A C T I C E T E S T 1
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1 9 0

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A n s w e r K e y
Section 1 Answers
1.
a.
Cross multiply and solve for 
x
:
3(2
x
) = (2 + 
x
)(
x
– 5)
6
x
= 
x
2
– 3
x
– 10
x
2
– 9
x
– 10 = 0
(
x
– 10)(
x
+ 1) = 0
x
= 10,
x
= –1
2.
b.
Point 
B
is the same distance from the 
y
-axis as
point 
A
, so the 
x
-coordinate of point 
B
is the
same as the 
x
-coordinate of point 
A
: –1. Point 
B
is the same distance from the 
x
-axis as point 
C
,
so the 
y
-coordinate of point 
B
is the same as the
y
-coordinate of point 
C
: 4. The coordinates of
point 
B
are (–1,4).