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Algebra review

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Algebra review

  1. 1. Intermediate Algebraby Gustafson and FriskChapter 1A Review of Basic Algebra
  2. 2. Section 1.1: The Real Number SystemSETS: collections of objects. Natural Numbers  Integers Whole Numbers  Positive Numbers Rational Numbers  Negative Irrational Numbers Numbers Real Numbers  Even Numbers  Odd NumbersUse { } {x | x > 5} is read “the set of all x such that x is greater than 5”
  3. 3. Section 1.1: The Real Number SystemGRAPHS: plot on the number line. Individual numbers are dots -3 -2 -1 0 1 2 3 4
  4. 4. Section 1.1: The Real Number SystemGRAPHS: 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
  5. 5. Section 1.1: The Real Number SystemGRAPHS: 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
  6. 6. Section 1.2: Arithmetic & Properties of Real NumbersOPERATIONS: Addition Subtraction (the same as adding a number with the opposite sign) Multiplication Division (the same as multiplying by the reciprocal)
  7. 7. Section 1.2: Arithmetic & Properties of Real NumbersADDITION:Addends that have the same signs Add absolute values Keep the sign of the addendsAddends that have opposite signs Subtract absolute values Keep the sign of the addend with the largest absolute value
  8. 8. Section 1.2: Arithmetic & Properties of Real NumbersMULTIPLICATION: Multiply absolute values If the factors have the same signs, the product is positive If the factors have opposite signs, the product is negative
  9. 9. Section 1.2: Arithmetic & Properties of Real NumbersSTATISTICS: measures of central tendency Mean Median Mode
  10. 10. Section 1.2: Arithmetic & Properties of Real NumbersProperties: Associative – addition, multiplication Commutative – addition, multiplication Distributive – multiplication is distributed over addition a (b + c) = ab + ac
  11. 11. Section 1.2: Arithmetic & Properties of Real NumbersIdentities: Addition – zero Multiplication – oneInverses: Addition – opposites Multiplication – reciprocals
  12. 12. Section 1.3: Definition of ExponentsEXPONENTS: repeated multiplicationIn the expression: an a is the base and n is the exponent Exponents are NOT factors Means to multiply “a” n times
  13. 13. Section 1.3: Definition of ExponentsORDER 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.
  14. 14. Section 1.5: Solving EquationsAlgebraic Expression vs. Equation Expressions: a combination of numbers and operations Equation: a statement that two expressions are equal
  15. 15. Section 1.5: Solving EquationsEXPRESSIONS: Terms Like terms When multiplying, the terms do not need to be alike Can only add like terms!
  16. 16. Section 1.5: Solving EquationsTO 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.
  17. 17. Section 1.5: Solving EquationsTYPES 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.
  18. 18. Section 1.6 & 1.7: Solving Problems, Applications TYPES OF PROBLEMS:  Geometry  Percent  Physics (forces)  Uniform motion  Mixtures  Good ‘ole common sense analysis
  19. 19. Chapter 1: Basic Algebra ReviewSUMMARY: 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.

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