Math 124College Algebra and Applications

1
Math 124-College Algebra and Applications

• Section 1 - Instructor Michael Mays
• MF lectures
• T lab
• W supplemental instruction (Dr. Miller)

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Course tools

• VISTA course management
• PRS (Personal Response System)
• CAS (Computer algebra systemDERIVE)

3
Number Properties

• Section P.1
• real numbers

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Automobile Expenses

• In coming to WVU this semester you may have
  driven your car. If the cost of gasoline per
  gallon is 3.05, determine your total gas costs
  c for your drive of m miles to WVU.
• Variable letter representing varying values such
  as c for total cost and m for total miles driven
• Mathematical Model An equation representing the
  problem. If your average gas mileage is 24 miles
  per gallon, then your total cost is
• c 3.05 (m/24)

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Models

• We substitute into models with numbers to make
  predictions, such as letting the total miles
  driven to WVU be m 62.
• c 3.05 (62/24) 7.87916667 So cost was 7.88.
• We will use the Real numbers as the replacement
  set of numbers for variables in this course,
  simply because we will create real-world models
  from real-world data

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Real Number System
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Real Number Line

• One-to-one correspondence between the Real
  numbers and points on a line (i.e. There is only
  one number for every point on the number line)
• Real numbers can be ordered a lt b implies a is
  to the left of b on the number line
• Question How many points are between any two
  numbers on the number line?
• Answer

There are infinitely many points
0
-2.3
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Field Properties of the Real Numbers
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Definition of and /

• Subtraction a b a (-b)
• Subtraction is the addition of a negative
• Division
• Division is the multiplication of a reciprocal

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Properties of Negation

• Determine the rules for the following.
• -(-a)
• (-a)b
• (-a)(-b)
• -(ab)

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Properties of Zero

• Determine the rules for the following.
• a 0
• a 0
• 0/a
• a/0
• If a b 0, then what do we know about either a
  or b?

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Skills Practice

• Provide the property that supports each step in
  the following simplification.
• a c b c
• (ac)(-c) (bc)(-c)
• a (c - c) b (c - c)
• a 0 b 0
• a b
• This is the Cancellation Property of Addition

Addition of (-c) to both sides
Associative Property for Addition
Additive Inverse
Additive Identity (zero)
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Cartesian Coordinate System