Sat math Essentials

a:
3 
3 
5 
9 
5 
45
Answer choice 
b:
3 
5 
5 
15 
5 
75
Answer choice 
c:
2 
5 
9 
10 
9 
90
Answer choice 
d:
3 
5 
9 
15 
9 
135
Answer choice 
e:
5 
5 
9 
25 
9 
225
Answer choice 
d
equals 135, which is the same as the approximate volume of the cylinder.
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G E O M E T R Y R E V I E W
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1 3 6

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Practice Question
Mr. Suarez painted a circle with a radius of 6. Ms. Stone painted a circle with a radius of 12. How much
greater is the circumference of Ms. Stone’s circle than Mr. Suarez’s circle?
a.
3
π
b.
6
π
c.
12
π
d.
108
π
e.
216
π
Answer
c.
You must determine the circumferences of the two circles and then subtract. The formula for the circum-
ference of a circle is 
C
2
π
r.
Mr. Suarez’s circle has a radius of 6:
C
2
π
r
C
2
π
(6)
C
12
π
Ms. Stone’s circle has a radius of 12:
C
2
π
r
C
2
π
(12)
C
24
π
Now subtract:
24
π
12
π
12
π
The circumference of Ms. Stone’s circle is 12
π
greater than Mr. Suarez’s circle.
C o o r d i n a t e G e o m e t r y
A 
coordinate plane
is a grid divided into four quadrants by both a horizontal 
x
-axis and a vertical 
y
-axis.
Coor-
dinate points
can be located on the grid using 
ordered pairs
. Ordered pairs are given in the form of (
x
,
y
). The 
x
represents the location of the point on the horizontal 
x
-axis, and the 
y
represents the location of the point on the
vertical 
y
-axis. The 
x
-axis and 
y
-axis intersect at the 
origin
, which is coordinate point (0,0).
Graphing Ordered Pairs
The 
x
-coordinate
is listed first in the ordered pair, and it tells you how many units to move to either the left or
the right. If the 
x
-coordinate is positive, move from the origin to the right. If the 
x
-coordinate is negative, move
from the origin to the left.
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G E O M E T R Y R E V I E W
–
1 3 7

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The 
y
-coordinate
is listed second and tells you how many units to move up or down. If the 
y
-coordinate is
positive, move up from the origin. If the 
y
-coordinate is negative, move down from the origin.
Example
Graph the following points:
(0,0)
(3,5)
(3,
5)
(
3,5)
(
3,
5)
Notice that the graph is broken up into four quadrants with one point plotted in each one. The chart below
indicates which quadrants contain which ordered pairs based on their signs:
POINT
SIGNS OF COORDINATES
QUADRANT