Absolute Value Equations and Inequalities notes
Absolute Value Equations
Absolute Value
o
A number is its distance from zero on the number line and
distance is nonnegative
an absolute value equation such as |2y-4|=12 has two solutions
o
12
o
-12
It is eas
Probability notes
Experimental Probability
Probability measures how likely to occur an event is
You can express probabilities as percents or as real numbers
The probability of an impossible event is 0 or 0%
The probability of a certain event, which must h
Linear Systems notes
Graphing Systems of Equations
System of Equations
o
Linear System
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A system that has a unique solution
Dependent System
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If the graph of each equation in a system of two
variables is a line
Independent System
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Set of two or more eq
Algebraic Expressions notes
Evaluating Algebraic Expressions
Variable
o
o
Symbol that represents one or more numbers
Usually a number
Algebraic Expression
o
Variable Expression
o
An expression that contains one or more variables
Another name for an Algebr
Linear Equations notes
Graphing Linear Equations
Linear function
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A function whose graph is a line
Linear Equation
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Used to represent a linear function
o
Example:
o
Y=3x+2
A solution of a linear equation is any ordered pair(x,y) that
makes the equation
Pi notes
The number pi
The ratio of the circumference of a circle to its diameter
History
Archimedes
o
o
Considered to perimeters of inscribed and circumscribed
regular polygons of 96 sides
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287-212 B.C.
Found that 223/71 < pi < 22/7
Tsu Chung-Chi
o
700
Solving Inequalities notes
Solving and Graphing Inequalities
As with an equation, the solutions of an inequality are the numbers
that make it true
An equation such as -2x=10 has only one solution, -5
o
o
On the other hand, the inequality -2x<10 is true fo
Subsets of Real Numbers notes
Subsets of Real Numbers
Algebra deals with operations and relations among numbers,
including real numbers and imaginary numbers
Subsets of Real Numbers
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Natural Numbers
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Natural numbers are the numbers used for counting
1,
Solving Equations
Solving Equations
An equation that contains a variable may be true for some
replacements of the variable and false for others
Solution of the Equation
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A number that makes the equation true
You can use the properties of equality to solv
Relations and Functions notes
Graphing Relations
Relation
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Set of pairs of input and output values
You can write a relation as a set of ordered pairs
Domain
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Set of all inputs, or x-coordinates, or the ordered pairs
Range
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Set of all outputs, or y-coor