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Panlilio 2008-2009 Section 1.1 & 1.2 Objectives Use the order of operations to evaluate experations Use formulas Determine the sets of numbers to which a given number belongs Use the properties of real numbers to simplify expressions Panlilio 2008-2009 Order of Operations Please Excuse My Dear Aunt Sally The Order: 1. ___________ (and other groupings like brackets or fraction bars) 2. ___________ 3. All Multiplication and Division from _____ to ______ 4. All Additions and Subtractions from _____ to _____ Panlilio 2008-2009 Order of Operations Try these problems 2 10 4 3 2 Panlilio 2008-2009 7 3 5 2 4 7 14 6 23 7 4 Using Formulas When given a formula, just Plug AND Chug! The formula for the volume of a rectangular prism is V lwh . Find the volume of each cylinder given the following values: l=7, w=22, h=3 Panlilio 2008-2009 l=2.25, w=4.1, h=3 Cube with sides of length 8 Properties of Real Numbers Reals, R R= I= Z I W Q N Q= Z= W= Rational numbers can be expressed as a ratio m n Panlilio 2008-2009 N= Properties for Addition and Multiplication Addition Commutatitve Associative Identity Inverse Distributive Panlilio 2008-2009 Multiplication Name the Property x yz yz x 4(h 2k) 4h 8k 70 7 12 3 3 12 1 (8) 1 8 Panlilio 2008-2009 Section 1.4 & 1.5 Objectives Translate verbal expressions and sentences into algebraic expressions and equations Solve equations by using the properties of equality Solve equations for a specific variable Solve equations containing absolute value Panlilio 2008-2009 Translating Words into Math Twice the cube of a number Three less than a number is -7 Four times the sum of a number and 2 A number divided by 4 is 2/3 The product of a number and its square Panlilio 2008-2009 Properties of Equality For any real number a, a=a For all real numbers a and b, if a=b, then b=a For all real numbers a, b, and c, if a=b and b=c, then a=c If a=b, then a may be replaced by b For any numbers a, b, and c, if a=b then a+c=b+c and a-c=b-c For any real numbers a, b, and c, if a b a=b, then ab=b c and, if c0, c c Panlilio 2008-2009 Solving Equations Solve each equation: 4n 5 11 10 4 5 3x Panlilio 2008-2009 2 1 y 3 3 2 1.4c 9 2.3c 5 t 2t 3t 4t 10 5 3 1 y 6 8 24 Absolute Value Equations Absolute Value of a Number --> The number of units it is from 0 on the number line Absolute Value Equations --> Two Possible Scenarios: 1. The number inside is positive, or 2. The number inside is negative. Either way, when you take the absolute value, you get a __________. 2x 3 5 Panlilio 2008-2009 x 14 7 9x 4 8 Section 1.6 & 1.7 Objectives Solve inequalities and graph the solution sets Solve compound inequalities using and and or Solve inequalities involving absolute value and graph the solutions Panlilio 2008-2009 Solving Inequalities Solve each inequality. Graph the solution. 5y 3 2y 9 .5m 14 x3 x 4 Reminder! When solving inequalities: if you multiply or divide by a negative number, you have to ________ the inequality sign. Panlilio 2008-2009 Compound Inequalities “And” --> Must make both inequalities true. Shade the ___________. 5 2x 3 12 Panlilio 2008-2009 “Or” --> Can make either inequality true. Shade ______________. 2 x 4 and 8 x 4 5 x3 2 or 1.2x 3.3 2.3x 1.1 3 Absolute Value Inequalities Absolute Value Inequalities are Compound Inequalities. x2 4 Panlilio 2008-2009 4x 3 9 x 1 x 1 Homework 1.1 & 1.2: P.10 #19-51 EOO,54,56,58; P.17 #21-57 EOO,58 1.4 & 1.5: P.31 #19-53 Odd,56,60; P.41 #17-41 EOO,45,46 1.6 & 1.7: P.47#15-43 EOO,49,50,57-59; P.53 #15-43 EOO,45,46,49-55 Odd Chapter Review P.56 #1-27 Odd, #33-69 Odd Panlilio 2008-2009