Sat math Essentials

18.
a.
If
a
and 
c
are doubled, the fraction on the left
side of the equation becomes 
2
2
a
c
b
. The fraction
has been multiplied by 
2
2
, which is equal to 1.
Multiplying a fraction by 1 does not change its
value;
2
2
a
c
b
= 
a
c
b
= 
d
. The value of
d
remains
the same.
19.
c.
Triangle 
AOB
is isosceles because line 
OA
is con-
gruent to line 
OB
. Angles 
A
and 
B
are both 55
degrees, which means that angle 
O
= 180 – (55
+ 55) = 70 degrees. Angle 
O
is a central angle
and arc 
CD
is its intercepted arc. A central angle
and its intercepted arc are equal in measure, so
the measure of arc 
CD
is 70 degrees.
20.
e.
Simplify the numerator:
x
32
= 
x
16
2
=
4
x
2
. Simplify the denominator:
4
x
= 
4
x
= 2
x
. Divide the numerator and
denominator by 2:
= 
.
Section 2 Answers
1.
d.
This series actually has two alternating sets of
numbers. The first number is doubled, giving
the third number. The second number has 4
subtracted from it, giving it the fourth number.
Therefore, the blank space will be 12 doubled,
or 24.
2.
d.
The original volume of water,
x
, minus 20% of
x
, 0.20
x
, is equal to the current volume of water,
240 mL:
x
– 0.20
x
= 240 mL
0.8
x
= 240 mL
x
= 300 mL
3.
e.
Each term in the pattern is equal to the fraction
2
3
raised to an exponent that is equal to the posi-
tion of the term in the sequence. The first term
in the sequence is equal to (
2
3
)
1
, the second term
is equal to (
2
3
)
2
, and so on. Therefore, the tenth
term in the sequence will be equal to (
2
3
)
10
.
4.
c.
Since both dimensions are tripled, there are two
additional factors of 3. Therefore, the new area
is 3 
3 = 9 times as large as the original. For
example, use a rectangle with a base of 5 and
height of 6. The area is 5 
6 = 30 square units.
If you multiply the each side length by 3, the new
dimensions are 15 and 18. The new area is 15 
18, which is 270 square units. By comparing the
new area with the original area, 270 square units
is nine times larger than 30 square units; 30 
9 = 270.
2
x
2
x
4
x
2
2
x
)
)
–
P R A C T I C E T E S T 1
–
1 9 2

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5.
a.
An equation is undefined when the value of
a denominator in the equation is equal to
zero. Set 
x
2
+ 7
x
– 18 equal to zero and factor
the quadratic to find its roots:
x
2
+ 7
x
– 18 = 0
(
x
+ 9)(
x
– 2) = 0
x
= –9,
x
= 2