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 9 9
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a b c d e
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a b c d e
a b c d e
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a b c d e
a b c d e
S e c t i o n 1
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a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
S e c t i o n 2
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2 0 0
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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
–
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
a b c d e
S e c t i o n 3

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S e c t i o n 1
1.
If
m
= 6, then the expression 
m
3
2
– 4
m
+ 10 is equal to
a.
–12.
b.
–2.
c.
6.
d.
12.
e.
22.
2.
Which of the following is the midpoint of a line with endpoints at (–2,–8) and (8,0)?
a.
(3,4)
b.
(3,–4)
c.
(–5,4)
d.
(5,–4)
e.
(6,–8)
3.
If 4
x
+ 5 = 15, then 10
x
+ 5 =
a.
2.5.
b.
15.
c.
22.5.
d.
25.
e.
30.
4.
A music store offers customized guitars. A buyer has four choices for the neck of the guitar, two choices for
the body of the guitar, and six choices for the color of the guitar. The music store offers
a.
12 different guitars.
b.
16 different guitars.
c.
24 different guitars.
d.
36 different guitars.
e.
48 different guitars.
5.
Which of the following is the set of positive factors of 12 that are NOT multiples of 2?
a.
{ }
b.
{1}
c.
{1, 3}
d.
{1, 2, 3}
e.
{2, 4, 6, 12}
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P R A C T I C E T E S T 2
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2 0 1

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6.
The graph of
f
(
x
) is shown above. How many values can be found for 
f
(3)?
a.
0
b.
1
c.
2
d.
4
e.
cannot be determined
7.
The expression 
x
x
3
2
–
+
2
5
5
x
x
can be reduced to
a.
1.
b.
x
2
–
5
25
.
c.
x
+ 5.
d.
x
–
1
5
.
e.
x
+
x
5
.
8.
Which of the following is the vertex of the parabola which is the graph of the equation
y
= (
x
+ 1)
2
+ 2?
a.
(–1,–2)
b.
(1,–2)
c.
(–1,2)
d.
(1,2)
e.
(2,–1)
4
3
2
1
–1
–2
–3
–4
–4 –3 –2 –1 
1 2 3 4
y
x
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P R A C T I C E T E S T 2
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2 0 2

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9.
a
b
c
is equivalent to
a.
c
a
b
.
b.
b
a
c
.
c.
.
d.
e.
a
c
b
.
10.
If the statement “No penguins live at the North Pole” is true, which of the following statements must also
be true?
a.
All penguins live at the South Pole.
b.
If Flipper is not a penguin, then he lives at the North Pole.
c.
If Flipper is not a penguin, then he does not live at the North Pole.
d.
If Flipper does not live at the North Pole, then he is a penguin.
e.
If Flipper lives at the North Pole, then he is not a penguin.
11.
If
p
< 0,
q
> 0, and 
r
> 
p
, then which of the following must be true?
a.
p
+ 
r
> 0
b.
r
p
< 
r
q
c.
pr
< 
rq
d.
r
+ 
q
> 
q
e.
p
+ 
r
< 
r
+ 
q
a
b
c
1
a
b
c
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P R A C T I C E T E S T 2
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2 0 3

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12.
The pie chart above shows the distribution of video rentals from Al’s Video Vault for a single night. If 250
videos were rented that night, how many more action movies were rented than horror movies?
a.
10
b.
20
c.
22
d.
25
e.
30
13.
If the circumference of the circle in the diagram above is 20
π
units, what is the area of triangle 
ABC
?
a.
40 square units
b.
80 square units
c.
80
π
square units
d.
160 square units
e.
160
π
square units
8
O
C
A
B
Al’
s
 Video Vault Rental
s
Drama
42
%
Comedy
24
%
Action
22
%
Horror
12
%
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P R A C T I C E T E S T 2
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2 0 4

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14.
The area of an isosceles right triangle is 18 cm
2
. What is the length of the hypotenuse of the triangle?
a.
6 cm
b.
6
2
cm
c.
18
2
cm
d.
18
3
cm
e.
36
2
cm
15.
If
a
< 
4
3
3
x
< 
b
, and 
a
= 4 and 
b
= 8, which of the following could be true?
a.
x
< 
a
b.
x
> 
b
c.
a
< 
x
< 
b
d.
4 < 
x
< 8
e.
none of the above
16.
The length of a rectangle is one greater than three times its width. If the perimeter of the rectangle is 26
feet, what is the area of the rectangle?
a.
13 ft
2
b.
24 ft
2
c.
30 ft
2
d.
78 ft
2
e.
100 ft
2
17.
Based on the diagram above, which of the following is true?
a.
i
= 
e
+ 
f
b.
g
+ 
i
= 
h
+ 
e
c.
e
+ 
i
= 
e
+ 
h
d.
e
+ 
g
+ 
i
= 180
e.
e
+ 
f
+ 
g
+ 
h
+ 
i
= 360
e
h
f
g
i
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P R A C T I C E T E S T 2
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2 0 5

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18.
Which of the following is an irrational number?
a.
4
9
b.
4
–3
c.
–(
3
3
)
d.
e.
(
32
)
3
19.
In the diagram above, the length of a side of square 
ABCD
is four units. What is the area of the shaded
region?
a.
4
b.
4 – 
π
c.
4 – 4
π
d.
16
π
e.
16 – 4
π
20.
The value of
d
is increased 50%, then decreased 50%. Compared to its original value, the value of
d
is now
a.
25% smaller.
b.
25% larger.
c.
50% smaller.
d.
50% larger.
e.
the same.
C
A
B
D
O
4
72
200
–
P R A C T I C E T E S T 2
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2 0 6

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S e c t i o n 2
1.
Which of the following expressions is undefined when 
x
= –2?
a.
y
= 
x
x
+
– 2
2
b.
y
= 
x
2
+ 4
x
x
+ 4