VIEWS: 22 PAGES: 18 CATEGORY: Technology POSTED ON: 4/23/2009
VENN DIAGRAMS AND SET OPERATIONS p. 60-65 OBJECTIVES: • Use Venn diagrams to visualize set relationships • Perform operations with sets • Apply set operations to the Real number system Algebraic Expressions and Formulas, p. 270-276 OBJECTIVES: •Evaluate algebraic expressions and formulas •Understand the vocabulary of algebraic expressions •Simplify algebraic expressions Venn Diagrams p. 61 “Disjoint” sets have no U A B elements in common. U A The set B is a “proper” subset of A. B U The sets A and B have A B some common elements. Definition of Intersection of Sets p. 62 The intersection of sets A and B, written AB, is the set of elements common to both set A and set B. This definition can be expressed in set builder notation as follows: A B = { x | x A AND x B} Definition of the Union of Sets p. 63 The union of sets A and B, written A B, is the set of elements that are members of set A or of set B or of both sets. This definition can be expressed in set-builder notation as follows: A B = {x | x A OR x B} The empty set in intersection and union, p.64 For any set A, 1. A 2. A A DeMorgan’s Laws, p.65 A B A B A B A B REAL NUMBERS – the set of numbers used to measure or count things in everyday life. Examples: Natural numbers: {1, 2, 3, 4, …} Whole numbers: {0, 1, 2, 3, 4, …} Integers: {…-3, -2, -1, 0, 1, 2, 3, …} Rational numbers: {p/q | p and q are integers, q 0} Irrational numbers: nonrepeating or nonterminating decimals Algebraic Expressions, p. 270 Variables- letters used to represent numbers. Algebraic expression- a combination of variables and numbers using the operations of addition, subtraction, multiplication, or division, as well as powers or roots. Using the Order of Operations, p. 270 1. Perform operations within grouping symbols 2. Evaluate exponential expressions 3. Multiply and divide in order that they occur, from left to right 4. Add and subtract in order that they occur, from left to right Vocabulary of Algebraic Expressions, p. 272 Terms- parts of an algebraic expression that are separated by addition Coefficient- the numerical part of a term Constant term- a term that consists of just a number Like terms- terms that have the same variables with the same exponents Properties of real numbers, p. 273 Let a, b, c be real numbers. Commutativity: a + b = b + a ab = ba Associativity: (a + b) + c = a + (b + c) (ab) c = a (bc) Distributive: a(b + c) = ab + ac (a + b) c = ac + bc Rectangular coordinate system, or Cartesian plane, p. 58 y-axis Quadrant II 3 Quadrant I 2 1 Origin x-axis -4 -3 -2 -1 1 2 3 4 -1 Quadrant III -2 Quadrant IV y-axis 3 ( 1.2 , 2.9 ) ( -3 , 2 ) 2 1 -3 x-axis -4 -3 -2 -1 1 2 3 4 -1 ( 4, -1 ) -2 The Graph of an Equation p. 337 Example : Use solution points to sketch the graph of the equation y = –2x with -3 < x < 3. Input Output Ordered Pair x y = – 2x ( x, y ) x = –1, y = – 2(–1 ) = 2 ( –1, 2) x = 0, y = – 2( 0 ) = 0 ( 0, 0) x = 1, y = – 2( 1 ) = – 2 ( 1, – 2 ) x = 2, y = – 2( 2 ) = – 4 ( 2, – 4 ) x -1 0 1 2 y 2 0 –2 –4 y x -1 0 1 2 y 2 0 –2 –4 x ( – 1, 2), ( 0, 0), ( 1, –2),( 2,–4) Refer to p. 336 for ‘Graphing in the Cartesian Plane’ Are these the only ordered pairs or solution points for the equation y = –2x ? Definitions y Equation in two variables- an expression that expresses a relationship between two quantities. x Example : y = –2x Solution- an ordered pair (a, b) such that if a is substituted for x and b is substituted for y in an equation, then the equation is true. Example : ( – 1, 2), ( 0, 0), ( 1, –2), ( 2,–4) HOMEWORK EXERCISES p. 65-66 # 1 – 65 alternate odd CRITICAL THINKING p. 66 # 79, 80, 81 READ p.60 – 65 Set Operations and Venn Diagrams with three sets OFFICE: Beach Building, Room 113 OFFICE PHONE: 614-8281 OFFICE HOURS: M-F 9:00-10:15 PM or by appointment HOMEWORK Work p. 277 #1-4, 31-56 alt. odd,61-76 alt. odd, 92 p. 343 # 1-20, 23-28 odd Office hours: M-F 9:00-10:15 or by appointment Tutoring: Walker Memorial 206, M-Th 4:30-6:30