Download Study Guide Module 3

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Study Guide- Module 3
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Integers
Absolute Value
Compare integers
Rational Numbers
Coordinate geometry
Reflections
Integers:
Positive and negative whole numbers including zero.
The Number Line
Negative Numbers (-)
Positive Numbers (+)
(The line continues left and right forever.)
The further to the right a number is the greater it is!
The opposite of a positive number is a negative Ex. the opposite of 4 is -4
The opposite of a negative number is a positive Ex. The opposite of -6 is 6
Zero is its own opposite!
Opposite Integers (2 numbers that are the same distance from zero on a number
line):
Opposite of 3 is –3
Opposite of 10 is –10
Absolute Value (the distance from zero):
*Absolute value is represented by 2 bars.
│ -3 │ = 3
│ 3 │= 3
Opposite of –1200 is 1200
Comparing Integers:
-2 < 4
-7 < -5
│-14 │ > 11
Rational Numbers:
A rational number is a number that can be in the form p/q
where p and q are integers and q is not equal to zero.
Number
5
1.75
.001
0.111...
√2
(square root of 2)
Coordinate Geometry
This is a coordinate plane. It
has two axes and four
quadrants. The two number
lines form the axes. The
horizontal number line is called
the x-axis and the vertical
number line is called the y-
As a Fraction
5/1
7/4
1/1000
1/9
Rational?
Yes
Yes
Yes
Yes
?
NO !
axis.
The center of the coordinate
plane is called the origin. It has
the coordinates of (0,0).
Locations of points on the
plane can be plotted when one
coordinate from each of the
axes are used. This set of x
and y values are called
ordered pairs.
Assuming one box equals one unit follow the examples below:
Ex: (x, y) Quadrant I
If you have to plot the point (1, 2)
Always start at the origin and move to the right one and up two
This is in the first quadrant!
Ex: (-x, y) Quadrant II
If you plot the point (-3, 2)
Always start at the origin and move to the left three and up two
This is in the second quadrant!
Ex: (-x,-y) Quadrant III
If you have to the plot the point (-4,-1)
Always start at the origin and move to the left four and down one
This is in the third quadrant!
Ex: (x,-y) Quadrant IV
If you have to plot the point (5, -6)
Always start at the origin and go to the right five and down six
This is in the fourth quadrant!
You can also plot points that are on the x and y axis…..
Ex: (0, 5) This means stay at zero but move up five
(5, 0) This means move to the right five and stay at zero.
These are examples of x and y intercepts!!!!!
Reflections:
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Reflection in the x-axis.
A reflection in the x-axis can be seen in the picture below in
which A is reflected to its image A'. The general rule for a
reflection in the x-axis: (A,B)
(A, −B)
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Reflection in the y-axis.
A reflection in the y-axis can be seen in the picture below in
which A is reflected to its image A'. The general rule for a
reflection in the y-axis: (A,B)
(−A, B)