Graphing - SSAT Upper Level Quantitative
Card 1 of 428
Define an operation 
as follows:
For all complex numbers 
,
Evaluate 
Define an operation
For all complex numbers
Evaluate
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Multiply both numerator and denominator by the conjugate of the denominator, 
, to rationalize the denominator:
Multiply both numerator and denominator by the conjugate of the denominator,
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Raise 
to the power of 4.
Raise
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Refer to the above diagram. If the red line passes through the point 
, what is the value of 
?
Refer to the above diagram. If the red line passes through the point
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One way to answer this is to first find the equation of the line.
The slope of a line. given two points 
can be calculated using the slope formula
Set 
:
The line has slope 3 and 
-intercept 
, so we can substitute 
in the slope-intercept form:
Now substitute 4 for 
and 
for 
and solve for 
:
One way to answer this is to first find the equation of the line.
The slope of a line. given two points
Set
The line has slope 3 and
Now substitute 4 for
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Refer to the above red line. A line is drawn perpendicular to that line, and with the same 
-intercept. Give the equation of that line in slope-intercept form.
Refer to the above red line. A line is drawn perpendicular to that line, and with the same
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First, we need to find the slope of the above line.
The slope of a line. given two points 
can be calculated using the slope formula
Set 
:
The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be 
. Since we want this line to have the same 
-intercept as the first line, which is the point 
, we can substitute 
and 
in the slope-intercept form:
First, we need to find the slope of the above line.
The slope of a line. given two points
Set
The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be
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What are the coordinates of point B?
What are the coordinates of point B?
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Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is 
.
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
is then the coordinate of the point.
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point A?
What are the coordinates for point A?
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Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is 
.
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point A.
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point C?
What are the coordinates for point C?
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Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is 
.
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point C.
Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point D?
What are the coordinates for point D?
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Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is 
.
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point D.
Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point E?
What are the coordinates for point E?
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Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is 
.
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point E.
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point F?
What are the coordinates for point F?
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Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is 
.
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point F.
Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point G?
What are the coordinates for point G?
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Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is 
.
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point G.
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point H?
What are the coordinates for point H?
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Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is 
.
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point H.
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point J?
What are the coordinates for point J?
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Since there is no movement on the x-axis, the x-coordinate is 
.
Go up the vertical y-axis until you reach the point. The y-coordinate is 
.
are the coordinates of point J.
Since there is no movement on the x-axis, the x-coordinate is
Go up the vertical y-axis until you reach the point. The y-coordinate is
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What are the coordinates for point K?
What are the coordinates for point K?
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Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is above the point. The x-coordinate is 
.
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point K.
Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is above the point. The x-coordinate is
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point L?
What are the coordinates for point L?
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Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is 
.
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point L.
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is
Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What are the coordinates for point M?
What are the coordinates for point M?
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Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is 
.
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is 
.
are the coordinates for point M.
Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is
Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is
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What is the vertex of the function 
?
What is the vertex of the function
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The 
-coordinate of the vertex is 
, where 
.
To get the 
-coordinate, evaluate 
.
The vertex is 
.
The
To get the
The vertex is
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Which point best represents the coordinates 
?
Which point best represents the coordinates
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The sign in front of each number represents which direction to go on the x or y-axis starting at the origin 
. If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.
To get to 
, move left on the x-axis by 
, then move up on the y-axis by 
.
The sign in front of each number represents which direction to go on the x or y-axis starting at the origin
To get to
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Which point best represents the coordinate 
?
Which point best represents the coordinate
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The sign in front of each number represents which direction to go on the x or y-axis starting at the origin 
. If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.
To get to 
, only move up by 
on the y-axis. Do not move along the x-axis because the x-coordinate is 
.
The sign in front of each number represents which direction to go on the x or y-axis starting at the origin
To get to
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Which point best represents the coordinate 
?
Which point best represents the coordinate
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To get to 
, move right on the x-axis by 
then move up on the y-axis by 
.
The sign in front of each number represents which direction to go on the x or y-axis starting at the origin 
. If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.
To get to
The sign in front of each number represents which direction to go on the x or y-axis starting at the origin
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