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Understanding Algebraic Expressions: Order of Operations, Exponents, and Set Theory

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Learn how to evaluate algebraic expressions, use order of operations, simplify sets using intersection and union, and understand inequality symbols and absolute value.

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Understanding Algebraic Expressions: Order of Operations, Exponents, and Set Theory

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  1. CHAPTER P SECTION 1 NOTES

  2. EXPONENTIAL NOTATION bn= b•b•b•b….•b EXAMPLES: 1. 53 2. 25 3. -34

  3. EVALUATING ALGEBRAIC EXPRESSIONS USING THE ORDER OF OPERATIONS THE ORDER OF OPERATIONS PARENTHESE (),[],{} EXPONENTS MULTIPLCATION DIVISION ADDITION SUBTRACTION EVALUATING AN ALGEBRAIC EXPRESSION: FIND THE VALUE OF AN EXPRESSION FOR A GIVEN VALUE OF A VARIABLE. 1. 9 + 7(X-6)3 FOR X = 8

  4. 2. X3 + 4X2 – 15 FOR X = -4 3. FOR X = 4 AND Y = 5

  5. INTERSECTION AND UNION OF SETS!!!!!!!!!!! SYMBOLS: ∩ INTERSECTION ᴜ UNION Ø NULL SET OR EMPTY SET DEFINITION: The intersection of sets A and B written A∩B is the set of elements common to sets A and B. The union of sets A and B, written AᴜB, is the set of elements that are members of set A or set B. The empty set or null set is the set that has no elements in it.

  6. EXAMPLES: A = {2,5,7,9,13,24} B = {3,5,7,13,26} C = {-2,-6,-14,-20,-56} FIND: 1. A∩B 2. AᴜC 3. B∩C 4. AᴜBᴜC

  7. INEQUALITY SYMBOLS: > < ≤ ≥

  8. EXAMPLES: TRUE OR FALSE 1. 56 > 45 -41 ≥ - 50 29 ≤ 12 -73 < -83 14 > 14 -67 ≥ -67

  9. ABSOLUTE VALUE DEFINITION: The Absolute Value of a given number is the distance that number is from zero on a number line { X if X ≥ 0 EXAMPLES: X = -X if X < 0 │5│ │-34│ │15-56│ -6│3│ │-12│-│10│ │-12 - 10│ SYMBOLS: ││

  10. DISTANCE BETWEEN TWO POINT ON THE REAL NUMBER LINE If a and b are any two points on a real number line, then the distance between a and b is given by: │a - b│ or │b - a│ EXAMPLES: 12 and 45 -6 and 7 -45 and -8

  11. HOMEWORK: PAGE 14-15 {1-74} THE EVENS

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