( ) 1. Algebra 2: Final Exam Review. y e + e e ) 4 x 10 = 10,000 = 9) Name

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1 Algebr : Finl Exm Review Nme Chpter 6 Grph ech function. Determine if the function represents exponentil growth or decy. Determine the eqution of the symptote, the domin nd the rnge of the function. ) y x+ = ) y = + x x y e + ) = ( ) Growth OR Decy Growth OR Decy Growth OR Decy Asymptote Asymptote Asymptote Domin Domin Domin Rnge Rnge Rnge Simplify ech of the following. ) 8e 9 ) ( ) x 6e e 6) ( 6 x ) ( 0 x e e ) Write the following in logrithmic form. 7) = 6 8) 8 = 9) 0 = 0,000 Write the following in exponentil form. 0) log = ) log00 = ) ln = 0 Evlute. ) log 6 ) log ) log

2 Expnd the expression using the properties of logrithms. log 7x 7) 6) 6 ( ) x ln y Condense the expression using the properties of logrithms. log x log y + log z 9) ln x ln x 8) Solve the following. Check for extrneous solutions. 0) x+ 6 = ) x e + = ) log x 7 = ) log ( x ) = ) ln ( x + ) = ) ( x) ( x ) log + log = Grph the following. Determine the eqution of the symptote, the domin nd the rnge of the function. 6) y = log ( x + ) 7) y = log ( x) + 8) y = ln ( x ) Asymptote Asymptote Asymptote Domin Domin Domin Rnge Rnge Rnge

3 Chpter 7 Perform the indicted opertion. 9) 80x y xy 0) x x 6x 96 x 8 x 6x + 9 x x + 0 x x ) ( x x ) ) x + 0 ) x 9 x + 8 x + x ) + x + x + x ) 6 x + x x + x 6) + x y Solve. Check for extrneous solutions. 7) = 7 8) x x + ( x ) 8 = x x + 9) x + x + + = x + 6 x x + 6

4 Grph. Determine the eqution of the symptote, the domin nd the rnge of the function. 0) y = x ) y = x + + ) x y = x Asymptote Asymptote Asymptote Domin Domin Domin Rnge Rnge Rnge Chpter 8 Determine the next two terms in the sequence. Determine if the sequence is rithmetic, geometric or neither. Write n explicit rule for the n th term. ),,8,,... ),,,... ),9,8,6... 6),,, ),,,... 8),,9,7... Determine the sum. 9) 0 n 0) ( n + 8 ) n= n= ) ( ) 8 n= n Write recursive formul for the sequence. ),,6,7,8... ),,6,08... ) 0,,0,,0...

5 Determine the first terms of the sequence. Write n explicit formul for the n th term. ) = n n = 6) n = = n Write n explicit formul for the n th term of the rithmetic sequence. 7) = d = 8) 0 = = Chpter 9 9) For the following tringle, determine the vlue of ll six trigonometric functions for the given ngle,θ. θ 60) Let θ be n cute ngle of right tringle. If trigonometric functions. 0 secθ =, determine the vlue of the other five 9 6) Let (-, 7) be point on the terminl side of n ngle θ in stndrd position. Evlute the six trigonometric functions of θ.

6 6) A prsiler is ttched to bot with 00 foot rope. The ngle of elevtion from the bot to the prsiler is. Estimte the prsiler s height bove the bot. Convert ech of the following ngles from degree to rdins or rdins to degrees. 6) 0 6) -0 6) 66) π 0 Drw ech of the following ngles. 67) 68) 69) 9 70) 7π Evlute. 7) π cos = 6 7) tn = 7) cos( 0 ) = 7) sin 0 = 7) π sin = 76) tn(8 π ) = 77) 8π sin = 78) tn π = 6

7 Simplify. 79) ( θ ) + cot sinθ 80) sin θ sin θ 8) cscθ tnθ cosθ Determine the exct vlue using sum or difference formul (you my use your formul sheet). 8) sin(0 ) 8) cos( ) Grph. Determine the period, mplitude, domin nd rnge of the function. π 8) y = sin x 8) y = cos ( x) 86) y ( x π ) = sin + Period: Period: Period: Amplitude: Amplitude: Amplitude: Domin: Domin: Domin: Rnge: Rnge: Rnge: π π 7

8 Chpter The verge weight for n 8 yer old mle is pounds with stndrd devition of 8. pounds. Use this informtion to nswer the following questions. 87) Wht is the z-score corresponding to mle weighing 70 pound? 88) Wht is the probbility tht mle weighs more thn 9 pounds? 89) Wht is the probbility tht mle weighs between 60 nd 70 pounds? 90) Wht is the probbility tht mle weighs under 0 pounds? 9) The owner of dnce studio sks dncers wht their fvorite type of dnce is, nd of them sy bllet. Identify the popultion nd the smple. 9) You wnt to determine whether students in your school like the new lunch menu. Identify the type of smple described. ) You list ll the students lphbeticlly nd then select every fifth student. b) You mil questionnires nd use only the questionnires tht re returned. c) You sk ll of the students in three different second hour clsses. d) You rndomly select twenty students from ech grde level t your school. 8

9 9) Determine which of the following questions, if ny, re bised. ) Does eting nutritious, whole-grin foods improve your helth? b) Do you ever ttempt the dngerous ctivity of texting while driving? c) How mny hours do you sleep ech night? d) How cn the myor of your city improve his or her public imge? 9) Identify the method of dt collection. ) A resercher records whether people t locl prk hve dog. b) A florist fertilizes 0 plnts with regulr fertilizer nd 0 plnts with new orgnic fertilizer. The florist compres the plnts fter 0 weeks nd determines which fertilizer is better. c) A meteorologist uses computer progrm to help determine how long it will tke for hurricne to rech the shoreline. 9) In survey of 9 people in the U.S., % of mrried couples sy they met online. ) Wht is the mrgin of error for the survey? b) Give n intervl tht is likely to contin the exct percent of ll mrried couples who met online. 96) The tble shows the results of two different rndomized comprtive experiments. ) Find the men of the control group. b) Find the men of the tretment group. Control Group 8 7 Tretment Group c) Find the experimentl difference of the mens. 9