Download A-addition (in order from left to right)

Section 1.1 Expressions and Formulas
Algebra II Notes
Order of Operations
Please excuse my dear Aunt Sally
P-parentheses
E-exponents
M-multiplication (in order from left to right)
D-division (in order from left to right)
A-addition (in order from left to right)
S-subtraction (in order from left to right)
Variables – symbols, usually letters, used to represent unknown quantities.
Algebraic Expression- An expression that contains at least one variable.
Formula- A mathematical sentence that expresses the relationship between certain
quantities.
Section 1.2 Properties of Real Numbers
Real Numbers – All of the numbers that you use in everyday life.
m
Rational Number – a number that can be expressed as a ratio
, where m and n
n
are integers and n is not zero. The decimal form of a rational number is either a
terminating or repeating decimal.
Irrational Number – a real number that is not rational. The decimal form of an
irrational number neither terminates nor repeats.
Real Number Properties
For any real numbers a, b, and c;
Property
Addition
Multiplication
Commutative
a b  ba
a b  b  a
Associative
ba  bg c  a  bb  cg ba  bg c  abb  cg
Identity
a 0  a  0a
Inverse
a  a  0  a  a
Distributive
a b  c  ab  ac and
bg bg
b g
Section 1.3 Solving Equations
a  1  a  1 a
If a  0, then a 
bb  cga  ba  ca
1
1
1 a
a
a
Open Sentence – a mathematical sentence containing one or more variables.
Equation- states that two mathematical expressions are equal.
Solution – a value that makes the expression true
To Solve an Equation
1. Undo the given operations within the problem.
2. Isolate the variable by doing the following:
A. Add or subtract the same non-zero number to both sides.
B. Multiply or divide the same non-zero number to both sides.
3. Check your solution.
Properties of equality
Property
Symbols
Reflexive
aa
Symmetric
If a = b then b = a
Transitive
If a = b and b = c then a = c
Substitution
If a = b, then either a may be replaced by b
or b may be replaced by a.
Section 1.4
Solving Absolute Value Equations
Absolute Value- like distance, it can only be a positive number or zero
For any real number a:
If a
 0, then
a  a.
If a < 0, then a  a
Empty Set – When an absolute value equation has not solution.
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To solve an absolute value equation:
1. Isolate the absolute value on one side of the equal sign.
2. Split the absolute value equation into two equations, one with a positive nonabsolute value expression and one with a negative non-absolute value
expression.
3. Solve each of the equations independently.
4. Check both solutions.
Section 1.5 Solving Inequalities
Trichotomy Property or the Property of Order
a<b
a=b
a>b
To solve a linear inequality:
1.
Isolate the variable to one side of the inequality by doing the following
transformations:
2.
3.
4.
a. Adding or subtracting the same number from both sides. (this does not
change the inequality)
b. Multiplying or dividing by the same non-zero positive number. (this does
not change the inequality)
c. Multiplying or dividing by the same non-zero negative number. (this
changes the direction of the inequality symbol)
Solve the inequality like an equation.
Check your solutions.
Optional: graph your solution.
a. ,  has a shaded endpoint. 
b. <,> has an open endpoint.
Section 1.6 Solving Compound Sentences and Absolute Value Inequalities
Compound Inequality - Two inequalities separated by and or by or . The graph of a
compound inequality containing and is the intersection of the two solution sets.
If separated by and, then both inequalities must be true.
If separated by or, then one of the inequalities must be true.
Graphing:
1. If there is an and, the graph is between the endpoints.
2. If there is an or, the graph is to the right of the right endpoint and to the left of
the left endpoint.
To solve absolute value inequality:
1. If x  c then x < -c or c < x
2. If x  c then c < x < c , c < x and x < c