Honors Advanced Algebra Mr. Kellner Chapter 1 Equations and Inequalities Assignment Guide

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1 Honors Advnced Alger Mr. Kellner Chpter 1 Equtions nd Inequlities Assignment Guide 1.1 Expressions nd Formuls Trget Gols: Use the order of opertions to evlute expressions Use formuls HW #1 pg 7 #4-6, odd, odd, 41, Properties of the Rel Numers Trget Gols: Clssify rel numers Simplify expressions Use the properties of rel numers to evlute expressions HW #2 worksheet Solving Equtions Quiz#1 Trget Gols: Trnslte verl expressions into lgeric expressions nd equtions, nd vice vers Solve equtions using the properties of equlity Solve literl equtions for the given vrile HW #3 pg 22 #7, odd, 34, odd, 54, 57, 58, 63 Quiz on 1.1 nd (continued) Applictions for Solving Equtions Trget Gol: Solve ppliction prolems y defining the vrile, setting up n eqution, solving the eqution, nd nswering the prolem HW #4 Worksheet 1.3B 1.4 Solving Asolute Vlue Equtions Quiz#2 Trget Gols: Evlute expressions involving solute vlues Solve equtions using solute vlue HW #5 pg 30 #17, 21, 24-34, 36-41, 45, 58, 60, 61 Quiz on 1.3A nd 1.3B 1.5 Solving Inequlities Trget Gols: Solve nd grph one-step inequlities. Express the solution set in intervl nottion Solve nd grph multi-step inequlities. Express the solution set in intervl nottion HW #6 pg 37 #7, odd, Solving Compound nd Asolute Vlue Inequlities Quiz#3 Trget Gols: Solve nd grph compound inequlities. Express the solution set in intervl nottion Solve nd grph solute vlue inequlities. Express the solution set in intervl nottion HW #7 pg 45 #9, 10, 13, 15-21, 35, 37-39, 45, 47, 73 Quiz on 1.4 nd 1.5 Chpter 1 Review HW #8 PreTest Tenttive Chpter one Test Dte: The retke test must e tken y: Don't let wht you cnnot do interfere with wht you cn do. John Wooden

2 Honors Advnced Alger Mr. Kellner Chpter 1: Equtions nd Inequlities Trget Gols By the end of this chpter, you should e le to pretest prolem # Use the order of opertions to evlute expressions. (1.1) got it needs work no clue prolems 1 nd 2 Use formuls. (1.1) got it needs work no clue prolem 4 Clssify rel numers. (1.2) got it needs work no clue prolem 5 Simplify expressions. (1.2) got it needs work no clue prolem 3 Identify properties of rel numers. (1.2) got it needs work no clue prolem 6 Trnslte verl expressions into lgeric exps. nd equtions, nd vice vers. (1.3) got it needs work no clue *prolems Solve equtions using the properties of equlity. (1.3) got it needs work no clue prolems 7, 8, 9 Solve literl equtions for the given vrile. (1.3) got it needs work no clue prolem 10 Solve ppliction prolems y defining the vrile, setting up n eqution, solving the eqution, nd nswering the prolem. (1.3) got it needs work no clue *prolems Evlute expressions nd solve equtions involving solute vlues. (1.4) got it needs work no clue prolems 11, 12 Solve nd grph inequlities. Express the solution set in intervl nottion. (1.5) got it needs work no clue prolems 13, 14 Solve & grph compound & solute vlue ineqs. Express solution in int. nottion. (1.6) got it needs work no clue prolems 15-18

3 H. Adv. Alger with Trigonometry Nme: Dy 1: 1-1 Expressions nd Formuls. Trget Gols: Use the order of opertions to evlute expressions Use formuls Period: Simplify 1. 4(6 + 2)

4 If you choose to use clcultor, plese do so crefully! Consider the following exmples: 3. ( ) 5(3) (7) 4. ( ) vs. -5 We cn evlute expressions y hnd or on the clcultor. Consider using the STO utton on the clcultor. If you do not know how to use the STO utton plese see me ASAP. 2 Evlute ech of the following if = 2, = 9, w= 5 nd x= x 3 w Assignment #1 pg 7 #4-6, odd, odd, 41, 43

5 H. Adv. Alger with Trigonometry Nme: Dy 2: 1-2 Properties of Rel Numers. Trget Gols: Clssify rel numers Simplify expressions Use the properties of rel numers to evlute expressions Period: Clssify: Rel Irrtionl Rtionl Integer Whole Nturl π

6 Write the letter of the correct property for ech sttement. A. commuttive property of ddition B. commuttive property of multipliction C. ssocitive property of ddition D. ssocitive property of multipliction E. identity property of ddition F. identity property of multipliction G. inverse property of ddition H. inverse property of multipliction I. distriutive property = x + mn = 2x + nm = (3 + 7) k + -6k = 0 5. (xy)z = x(yz) = = = Simplifying Expressions To simplify, we must get rid of ll prenthesis nd comine ny like terms (terms tht contin the sme vriles rised to the sme power) Comine like terms in the tle. If not possile write done 2x+ 3x= 2x+ 3y = 2 2 2x + 3x = 2xy + 3xy = 7. (6x + 3) + 4 = 6x + ( 3 + 4) 2x x = 2 2 2xy+ 3xy= Simplify ech expression x + 3y + 6x + 2y ( ) ( ) ( c + c) 4( cc+ ) 3 5 HW: worksheet 1.2

7 H. Adv. Alger with Trigonometry Nme: Dy 3: 1-3A Solving Equtions. Trget Gols: Solve equtions using the properties of equlity Solve literl equtions for the given vrile Period: EXAMPLES Solve ech eqution, then check ech nswer. To SOLVE mens to To CHECK n nswer,. *Use STO if necessry! If vriles CANCEL nd the remining sttement is true, write. If flse, write. Solve ech eqution. 5 3x 5 4x 8 1. ( + ) = 2. ( ) 2 x - 3 = 5x - 6-3x

8 Hint: Multiply ech term y the to cncel frction(s) or y multiple of to cncel deciml(s). Solve ech eqution n = 3.4n w + = LITERAL EQUATIONS - Use the properties of equlity to solve for specified vrile Solve V = r h for r 3 π Assignment #3 pg 22 #7, odd, 34, odd, 54, 57, 58, 63 Quiz #1

9 H. Adv. Alger with Trigonometry Nme: Dy 4: 1-3B Applictions Period: Trget Gols: Solve ppliction prolems y defining the vrile, setting up n eqution, solving the eqution, nd nswering the prolem Prolem-Solving Pln: 1. Red the prolem crefully. 2. Choose one vrile sed upon the question eing sked. 3. Use this vrile to write expressions for other quntities. 4. Set up nd solve n eqution. 5. Check tht the nswer(s) mke sense. Ex 1. Aln ought 5 pounds of penuts for $2.50 per pound. He lso ought cshews for $6.00 per pound. If Aln spent $30.50, how mny pounds of cshews did he uy? Ex 2. The lengths of the sides of tringle re consecutive odd integers. The perimeter is 27 meters. Wht re the lengths of the sides? Ex 3. Soni is 3 yers older thn Meliss. The sum of their ges in 4 yers will e 59 yers. How old is Soni now? Assignment #4: Worksheet 1.3B

10 H. Adv. Alger with trigonometry Nme: Dy 5: 1-4 Solving Asolute vlue equtions. Period: Trget Gols: Evlute expressions involving solute vlues Solve equtions using solute vlue Evlute ech expression if x = -8 nd y = x y 2. 2y 7 + 3x+ 11

11 Asolute vlue is. The expression inside the solute vlue rs cn either e positive or negtive. Therefore open sentences involving solute vlues must e interpreted crefully. Alwys solve to isolte the solute vlue then rewrite, without ny solute vlue symols, into two sttements. x = n must e rewritten s follows: All solutions must e checked when solving n solute vlue eqution due to potentil extrneous solutions! Rememer to lwys isolte the solute vlue efore writing the compound sentence! Solve ech eqution. Check your solutions x = x+ 4 = 8x 16 Assignment #5 pg 30 #17, 21, 24-34, 36-41, 45, 58, 60, 61 Quiz #2

12 H. Adv. Alger with Trigonometry Nme: Dy Solving inequlities. Period: Trget Gols: Solve nd grph one-step inequlities. Express the solution set in intervl nottion Solve nd grph multi-step inequlities. Express the solution set in intervl nottion Inequlities Intervls Intervl Nottion Set Nottion Grph 1. Bounded Open Intervl (, ) < x< } 2. Bounded Closed Intervl [, ] x } 3. Bounded Hlf-Open Intervl [, ) x< } (, ] < x } 4. Unounded Open Intervl (,) x< } (, ) x> } 5. Unounded Closed Intervl (,] x } [, ) x } 6. Entire Rel Line (, ) x } < x< } We will use oth set-uilder nd intervl nottion on these notes (split the homework to use oth lso). ***Rule: When we multiply or divide oth sides y, we must the inequlity!

13 Solve ech inequlity. Then grph the solution. 1. 2x 9> 4x x x A numer decresed y 6 is no more thn 11. Agin rememer: If vriles cncel out nd the sttement is true your solution set is All Rel Numers If vriles cncel out nd the sttement is flse your solution set is No Solution Assignment #6 pg 37 #7, odd, 45

14 H. Adv. Alger with Trigonometry Nme: Dy Solving Asolute Inequlities. Period: Trget Gols: Solve nd grph compound inequlities. Express the solution set in intervl nottion Solve nd grph solute vlue inequlities. Express the solution set in intervl nottion Compound Inequlities - Two or more inequlities, when considered together, form compound inequlity. Contining nd Contining or Both inequlities re true t the sme time. Either of the inequlities re true, or oth of the inequlities re true. The grph is the intersection of the grphs of the two inequlities. (Where the grphs overlp). The grph is the union of the grphs of the two inequlities. (Where either of the grphs exist). Grph the solution sets. Write the solution in set-uilder nd intervl nottion. Ex 1) 2 x + 3< 4 Ex 2) 3t < 6 or 12 < 11t 1 The grphs of most nd prolems look like exmple 1 nd the grphs of most or prolems look like exmple 2. Occsionlly we encounter specil cses Ex 3) 2y > y 3 or y < 6 Ex4) x 4< 1 or x 1 Ex5) y 1< 2y+ 2< y+ 7

15 Asolute Vlue Inequlities Tret ll inequlities s equtions (with = signs) in your compound sentence s in section 1.4. Then test 3 criticl points nd shde where the sttement is true. EXAMPLES: Solve ech open sentence solute vlue nd grph ech solution set. Ex 6) x Ex 7) 24x 5> 6 Ex 8) Consider the following specil cses:. 4x = 16 (review). 4x < 16 c. 4x > 16 d. x > 0 Assignment #7 pg 45 #9, 10, 13, 15-21, 35, 37-39, 45, 47, 73 Quiz#3