Sat math Essentials

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L E A R N I N G E X P R E S S A N S W E R S H E E T
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1.
If
w
1
8
, then 
w
2
3
?
a.
1
2
b.
1
4
c.
1
8
d.
1
1
2
e.
6
1
4
2.
Ben is three times as old as Samantha, who is two years older than half of Michele’s age. If Michele is 12,
how old is Ben?
a.
8
b.
18
c.
20
d.
24
e.
36
3.
The expression 
x
2
– 8
x
12 is equal to 0 when 
x
2 and when 
x
?
a.
–12
b.
–6
c.
–2
d.
4
e.
6
4.
Mia ran 0.60 km on Saturday, 0.75 km on Sunday, and 1.4 km on Monday. How many km did she run in
total?
a.
1
1
5
km
b.
1
3
4
km
c.
2
1
4
km
d.
2
3
4
km
e.
3
1
2
km
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M AT H P R E T E S T
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1 7

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5.
In the diagram above, line 
AB
is parallel to line 
CD
, and line 
EF
is perpendicular to line 
CD
. What is the
measure of angle 
x
?
a.
40 degrees
b.
45 degrees
c.
50 degrees
d.
60 degrees
e.
80 degrees
6.
The area of circle 
A
is 6.25
π
in
2
. If the radius of the circle is doubled, what is the new area of circle 
A
?
a.
5
π
in
2
b.
12.5
π
in
2
c.
25
π
in
2
d.
39.0625
π
in
2
e.
156.25
π
in
2
7.
David draws a line that is 13 units long. If (–4,1) is one endpoint of the line, which of the following could
be the other endpoint?
a.
(1,13)
b.
(9,14)
c.
(3,7)
d.
(5,12)
e.
(13,13)
A
G
E
B
K
D
M
C
F
L
I
H
J
x
140˚
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M AT H P R E T E S T
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1 8

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8.
The expression (
a
b
3
2
)(
a
b
–
–
3
2
) 
?
a.
0
b.
1
c.
(
a
b
–
–
9
4
)
d.
(
a
b
9
4
)
e.
b
–9
9.
If triangle 
ABC
in the figure above is an equilateral triangle and 
D
is a right angle, find the value of
x
.
a.
6
3
b.
8
3
c.
12
2
d.
13
e.
24
10.
If 10% of
x
is equal to 25% of
y
, and 
y
16, what is the value of
x
?
a.
4
b.
6.4
c.
24
d.
40
e.
64
A
E
B
D
C
x
12
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M AT H P R E T E S T
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1 9

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11.
Triangle 
BDC
, shown above, has an area of 48 square units. If
ABCD
is a rectangle, what is the area of the
circle in square units?
a.
6
π
square units
b.
12
π
square units
c.
24
π
square units
d.
30
π
square units
e.
36
π
square units
12.
If the diagonal of a square measures 16
2
cm, what is the area of the square?
a.
32
2
cm
2
b.
64
2
cm
2
c.
128 cm
2
d.
256 cm
2
e.
512 cm
2
13.
If
m
> 
n
, which of the following must be true?
a.
m
2
> 
n
2
b.
m
2
> 
n
2
c.
mn
> 0
d.
|
m
| > |
n
|
e.
mn
> –
mn
8
A
B
C
D
O
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M AT H P R E T E S T
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2 0

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14.
Every 3 minutes, 4 liters of water are poured into a 2,000-liter tank. After 2 hours, what percent of the tank
is full?
a.
0.4%
b.
4%
c.
8%
d.
12%
e.
16%
15.
What is the perimeter of the shaded area, if the shape is a quarter circle with a radius of 8?
a.
2
π
b.
4
π
c.
2
π
16
d.
4
π
16
e.
16
π
16.
Melanie compares two restaurant menus. The Scarlet Inn has two appetizers, five entrées, and four
desserts. The Montgomery Garden offers three appetizers, four entrées, and three desserts. If a meal
consists of an appetizer, an entrée, and a dessert, how many more meal combinations does the Scarlet
Inn offer?
17.
In the diagram above, angle 
OBC
is congruent to angle 
OCB
. How many degrees does angle 
A
measure?
18.
Find the positive value that makes the function 
f
(
a
) 
4
a
2
a
2
–
12
1
a
6
9
undefined.
55˚
C
B
A
O
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M AT H P R E T E S T
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2 1

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19.
Kiki is climbing a mountain. His elevation at the start of today is 900 feet. After 12 hours, Kiki is at an ele-
vation of 1,452 feet. On average, how many feet did Kiki climb per hour today?
20.
Freddie walks three dogs, which weigh an average of 75 pounds each. After Freddie begins to walk a fourth
dog, the average weight of the dogs drops to 70 pounds. What is the weight in pounds of the fourth dog?
21.
Kerry began lifting weights in January. After 6 months, he can lift 312 pounds, a 20% increase in the weight
he could lift when he began. How much weight could Kerry lift in January?
22.
If you take recyclables to whichever recycler will pay the most, what is the greatest amount of money you
could get for 2,200 pounds of aluminum, 1,400 pounds of cardboard, 3,100 pounds of glass, and 900
pounds of plastic? 
23.
The sum of three consecutive integers is 60. Find the least of these integers.
24.
What is the sixth term of the sequence:
1
3
,
1
2
,
3
4
,
9
8
, . . . ?
25.
The graph of the equation 
2
x
3
–
y
3
4 crosses the 
y
-axis at the point (0,
a
). Find the value of
a
.