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Unformatted text preview: Intermediate Algebra
Intermediate Algebra
by Gustafson and Frisk Chapter 1
A Review of Basic Algebra Section 1.1: The Real Number System
Section 1.1: The Real Number System SETS: collections of objects. Natural Numbers
Whole Numbers
Rational Numbers
Irrational Numbers
Real Numbers Use { } Integers
Positive Numbers
Negative Numbers
Even Numbers
Odd Numbers {x  x > 5}
{x  x > 5}
is read “the set of all x such that x is greater than 5” Section 1.1: The Real Number System
Section 1.1: The Real Number System GRAPHS: plot on the number line. Individual numbers are dots 3 2 1 0 1 2 3 4 Section 1.1: The Real Number System GRAPHS: plot on the number line. Intervals including end points [
3 2 1 0 1 2 3 4 [ 3 2 1 0 1 2 3 4 Section 1.1: The Real Number System GRAPHS: plot on the number line. Intervals not including end points (
3 2 1 0 1 2 3 4 ( ) 3 2 1 0 1 2 3 4 Section 1.2: Arithmetic & Properties of Real Numbers
Section 1.2: Arithmetic & Properties of Real Numbers OPERATIONS: Addition
Subtraction (the same as adding a number with the opposite sign)
Multiplication
Division (the same as multiplying by the reciprocal) Section 1.2: Arithmetic & Properties of Real Numbers
Section 1.2: Arithmetic & Properties of Real Numbers ADDITION: Addends that have the same signs Add absolute values Keep the sign of the addends
Addends that have opposite signs Subtract absolute values Keep the sign of the addend with the largest absolute value Section 1.2: Arithmetic & Properties of Real Numbers
Section 1.2: Arithmetic & Properties of Real Numbers MULTIPLICATION: Multiply absolute values
If the factors have the same signs, the product is positive
If the factors have opposite signs,
If
the product is negative
the Section 1.2: Arithmetic & Properties of Real Numbers
Section 1.2: Arithmetic & Properties of Real Numbers STATISTICS: measures of central tendency Mean Median Mode Section 1.2: Arithmetic & Properties of Real Numbers
Section 1.2: Arithmetic & Properties of Real Numbers Properties: Associative – addition, multiplication
Commutative – addition, multiplication Distributive – multiplication is distributed over addition
a (b + c) = ab + ac Section 1.2: Arithmetic & Properties of Real Numbers
Section 1.2: Arithmetic & Properties of Real Numbers Identities: Addition – zero
Multiplication – one Inverses: Addition – opposites
Multiplication – reciprocals Section 1.3: Definition of Exponents
Section 1.3: Definition of Exponents EXPONENTS: repeated multiplication
In the expression: an a is the base and n is the exponent Exponents are NOT factors Means to multiply “a” n times Section 1.3: Definition of Exponents
Section 1.3: Definition of Exponents ORDER OF OPERATIONS: If an algebraic expression has more than one operation, the following order applies:
1. Clear up any grouping.
2. Evaluate exponents.
3. Do multiplication and division from left to right.
4. Do addition and subtraction from left to right. Section 1.5: Solving Equations
Section 1.5: Solving Equations Algebraic Expression vs. Equation Expressions: a combination of numbers and operations
Equation: a statement that two
Equation:
expressions are equal
expressions Section 1.5: Solving Equations
Section 1.5: Solving Equations EXPRESSIONS: Terms
Like terms
When multiplying, the terms do not need to be alike
Can only add like terms! Section 1.5: Solving Equations
Section 1.5: Solving Equations TO SOLVE AN EQUATION IN ONE VARIABLE:
If you see fractions, multiply both sides by the LCD. This will eliminate the fractions.
Simplify the algebraic expressions on each side of the equal sign (eliminate parentheses and combine like terms).
Use the addition property of equality to isolate the variable terms from the constant terms on opposite sides of the equal sign.
Use the multiplication property to make the coefficient of the variable equal to one.
Check your results by evaluating. Section 1.5: Solving Equations
Section 1.5: Solving Equations TYPES OF EQUATIONS: CONDITIONAL: if x equals this, then y equals that.
IDENTITY: always true no matter what numbers you use.
CONTRADICTION: never true no matter what numbers you use.
FORMULAS: conditional equations that model a relationship between the variables. Section 1.6 & 1.7: Solving Problems, Applications
Section 1.6 & 1.7: Solving Problems, Applications TYPES OF PROBLEMS: Geometry
Percent
Physics (forces)
Uniform motion
Mixtures
Good ‘ole common sense analysis Chapter 1: Basic Algebra Review
Chapter 1: Basic Algebra Review SUMMARY: KNOW YOUR VOCABULARY! You can’t follow directions if you don’t know what the words in the instructions mean.
Memorize the processes and the properties.
I will provide formulas for your reference.
Ask questions if you are unsure.
Always check your work to make sure that you answered the question, and that your answer is reasonable. This powerpoint was kindly donated to
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 Fall '10
 BrettCrow
 Algebra, Sets

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