Sat math Essentials

9
1 7 3

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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 7 5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
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
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 1
1.
2.
3.
4.
5.
6.
7.
8.
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
1
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8
9
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9.
10.
11.
12.
13.
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14.
15.
16.
17.
18.
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1 7 6
–
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 the expression 
2 +
3
x
= 
x
2
–
x
5
, then one possible value of
x
could be
a.
–1.
b.
–2.
c.
–5.
d.
1.
e.
2.
2.
In the graph above,
ABCD
is a square. What are the coordinates of point 
B
?
a.
(–1,–4)
b.
(–1,4)
c.
(–1,6)
d.
(–3,1)
e.
(–3,4)
3.
Line 
y
= 
2
3
x
– 5 is perpendicular to line
a.
y
= 
2
3
x
+ 5.
b.
y
= 5 – 
2
3
x
.
c.
y
= –
2
3
x
– 5.
d.
y
= 
3
2
x
– 5.
e.
y
= –
3
2
x
+ 5.
(–1,–3)
(6,4)
y
D
B
C
A
x
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P R A C T I C E T E S T 1
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1 7 7

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4.
If 30% of
r
is equal to 75% of
s
, what is 50% of
s
if
r
= 30?
a.
4.5
b.
6
c.
9
d.
12
e.
15
5.
A dormitory now houses 30 men and allows 42 square feet of space per man. If five more men are put into
this dormitory, how much less space will each man have?
a.
5 square feet
b.
6 square feet
c.
7 square feet
d.
8 square feet
e.
9 square feet
6.
Rob has six songs on his portable music player. How many different four-song orderings can Rob create?
a.
30
b.
60
c.
120
d.
360
e.
720
7.
The statement “Raphael runs every Sunday” is always true. Which of the following statements is also true?
a.
If Raphael does not run, then it is not Sunday.
b.
If Raphael runs, then it is Sunday.
c.
If it is not Sunday, then Raphael does not run.
d.
If it is Sunday, then Raphael does not run.
e.
If it is Sunday, it is impossible to determine if Raphael runs.
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P R A C T I C E T E S T 1
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1 7 8

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8.
In the diagram above, lines 
EF
and 
GH
are parallel, and line 
AB
is perpendicular to lines 
EF
and 
GH
. What
is the length of line 
AB
?
a.
5
b.
5
2
c.
5
3
d.
10
2
e.
10
3
9.
The expression 
(
(
x
x
2
2
+
+
2
4
x
x
–
–
1
2
5
1
)
)
is equivalent to
a.
5
7
.
b.
x
+ 5.
c.
x
x
+
+
5
7
.
d.
2
x
–
–
5
7
.
e.
2
4
x
x
–
–
1
2
5
1
.
10.
The point (2,1) is the midpoint of a line with endpoints at (–5,3) and
a.
(–3,4).
b.
(–7,2).
c.
(7,1).
d.
(9,–1).
e.
(–10,3).
11.
Lindsay grows only roses and tulips in her garden. The ratio of roses to tulips in her garden is 5:6. If there
are 242 total flowers in her garden, how many of them are tulips?
a.
22
b.
40
c.
110
d.
121
e.
132
120˚
10
D
A
E
F
G
B
C
H
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P R A C T I C E T E S T 1
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1 7 9

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12.
It takes eight people 12 hours to clean an office. How long would it take six people to clean the office?
a.
9 hours
b.
15 hours
c.
16 hours
d.
18 hours
e.
24 hours
13.
Greg has nine paintings. The Hickory Museum has enough space to display three of them. From how many
different sets of three paintings does Greg have to choose?
a.
27
b.
56
c.
84
d.
168
e.
504
14.
If the surface area of a cube is 384 cm
2
, what is the volume of the cube?
a.
64 cm
3
b.
256 cm
3
c.
512 cm
3
d.
1,152 cm
3
e.
4,096 cm
3
15.
In the diagram above, what is the sum of the measures of the angles 
x
,
y
, and 
z
?
a.
180 degrees
b.
360 degrees
c.
540 degrees
d.
720 degrees
e.
cannot be determined
x
y
z
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P R A C T I C E T E S T 1
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1 8 0

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16.
Given the following figure with one tangent and one secant drawn to the circle, what is the measure of
angle 
ADB
? 
a.
50 degrees
b.
85 degrees
c.
60 degrees
d.
110 degrees
e.
25 degrees
17.
D
C
A
B
110˚
60˚
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P R A C T I C E T E S T 1
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1 8 1
COST OF BALLONS
QUANTITY
PRICE PER BALLOON
1
$1.00
10
$0.90
100
$0.75
1,000
$0.60
Balloons are sold according to the chart above. If a customer buys one balloon at a time, the cost is $1.00
per balloon. If a customer buys ten balloons at a time, the cost is $0.90 per balloon. If Carlos wants to buy
2,000 balloons, how much money does he save by buying 1,000 balloons at a time rather than ten balloons
at a time?
a.
$200
b.
$300
c.
$500
d.
$600
e.
$800

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18.
If
a
c
b
= 
d
, and 
a
and 
c
are doubled, what happens to the value of
d
?
a.
The value of
d
remains the same.
b.
The value of
d
is doubled.
c.
The value of
d
is four times greater.
d.
The value of
d
is halved.
e.
The value of
d
is four times smaller.
19.
In the diagram above, line 
OA
is congruent to line 
OB
. What is the measure of arc 
CD
?
a.
27.5 degrees
b.
55 degrees
c.
70 degrees
d.
110 degrees
e.
125 degrees
20.
The expression 
is equivalent to
a.
2
2
.
b.
.
c.
.
d.
.
e.
.
2
x
2
x
x
2
x
2
2
x
2
2
x
32
4
x
A
C
B
D
O
55˚
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P R A C T I C E T E S T 1
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1 8 2

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S e c t i o n 2
1.
What is the next number in the series below?
3
16
6
12
12
8