MATH PLACEMENT REVIEW GUIDE

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1 MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your use uring the test, you re enourge to prtie oing si rithmeti prolems without lultor. This review is for levels of mth from rithmeti through intermeite lger. Choose the prolems pproprite to your level of skill. In orer tht we my reuse these mterils, plese o not write iretly on the review guie.

2 Prt : Arithmeti Review Guie Arithmeti overs the following topis: opertions with whole numers, frtions, eimls, rtios n proportions, n perents. Diretions: All frtions n rtios must e reue ompletely. Write your nswers on the nswer sheet. Opertions with Frtions. Reue the frtion to lowest terms: Fin the prout: Divie:..... Multiply: Sutrt: M:\Plement Review.o Pge Upte: /00

3 . Fin the sum: Opertions with Deimls. A: Write s eiml numer Roun 98.9 to the tenths ple If one squre yr of rpet osts $., how muh will. squre yrs ost?. $0.98. $.9. $09.. $0.0. If Angie s gross py for. hours ws $.0, wht ws her py per hour?. $./hr. $./hr. $./hr. $.9/hr Opertions with Rtios n Proportions. Two inhes on mp equls 0 miles. Write the rtio of mp inhes to miles Fin the missing prt of the proportion: x = If it tkes Tom 8 minutes to wlk miles, how mny minutes will it tke him to wlk miles?. min.. min.. min.. 80 min. M:\Plement Review.o Pge Upte: /00

4 Opertions with Perentges. Chnge the perent to frtion: % Chnge the eiml numer to perent:.9..9%..9%. 9%..9%. The 980 Census Report liste the popultion of Pullmn s,. The 990 Census Report liste the popultion s 8,. Fin the perent hnge in the popultion. Roun the perent to the nerest tenth...9%..%..%..% 8. Frost s Refrigertion eie to inrese their si servie ll hrge y 8%. Wht will e the new hrge for servie ll if they h een hrging $.0?. $.80. $.00. $.0. $.90 Prt II: Introution to Elementry Alger Review Guie Introution to Elementry Alger overs the following topis: introution to vriles, opertions with signe numers, solutions to liner equtions n inequlities, opertions with positive integer exponents, evlution n mnipultions of formuls, n solving si wor prolems. Opertions with Signe Numers 9. Simplify: ( ) ( ) Simplify: - (-) + (-) Simplify: 9 + ( ) M:\Plement Review.o Pge Upte: /00

5 Vriles. Trnslte to n lgeri expression: Twie the sum of x n y. (x) + y. x + y. x + y. + x + y. Evlute: (x y) (x + y) when x = - n y = Simplify: x 0x +. x +. x +. x. x. Simplify: (x + ) (x ). x. x. x +. x +. Multiply: 9... Simplify: [ 9 x ( x )]... x. x. x +. x + 8 Solutions to Liner Equtions n Inequlities 8. Solve: -x + = Solve: x = Solve: x + > x +. x > -. x > -8. x < -. x < M:\Plement Review.o Pge Upte: /00

6 . Solve: (x ) x = Opertions with Positive Integer Exponents. Simplify: (-) Simplify: ( + ) ( + ) Solving Bsi Wor Prolems. A or is 8 feet long n is ut into three piees. The seon piee is twie s long s the first piee n the thir is three feet longer thn the seon. Wht is the length of eh piee?., 0,., 8,.,, 0. 8,,. The perimeter of retngle is feet n the with is feet. Wht is the length in feet? The re of tringle is squre feet. If the se is feet, wht is the height of the tringle? Seven less thn four times numer is. Wht is the numer?.... Mnipultion of Formuls 8. Solve: v = k + gt for t. t = v + g k. t = v - g k. t = v + k g. t = v k g M:\Plement Review.o Pge Upte: /00

7 Prt III: Elementry Alger Elementry Alger overs the following topis: liner n qurti equtions, inequlities, exponents, polynomils, grphing, n systems of equtions in two vriles. Grphing of Liner Equtions 9. Grph x y =. Inite x- n y-interepts (if ny)..... (0, ) (0, ) (0, 0) (, 0) (, 0) (-, 0) (0, -) Polynomils 0. Sutrt the following polynomils: (x x + x ) (x x x + ). x + x + 9x x +. x x 9x x +. x x + x + x. x + x x x +. Sutrt (x + ) from the sum of (x ) n (x + ). x. x +. x + 0. x 0. Multiply: (x + ) (x ). x + x. x + x. x x. x + x. If x = - n y =, evlute: x + xy Ftor ompletely: 9x. (9x ) (9x + ). (x ) (x ). (x ) (x + ). (x ) M:\Plement Review.o Pge Upte: /00

8 . Ftor ompletely: x x. (x + ) (x ). (x ) (x ). (x ) (x + ). (x ) (x + ). Ftor ompletely: x + 9x + 0. (x + ) (x + ). (x + ) (x + ). (x + ) (x + 0). nnot ftor. Multiply n simplify: x x 0 x x. x.. 0( x x ) ( x )( x ). x x + 8. A n simplify (if possile): x 0 x + + x x x +.. x x 0 + x x x x 0.. x + 9 x 0 ( x + )( x ) 0 + x ( x + x )( x x + ) 9. Use long ivision n ivie: (x x + ) ) (x ). x + + x. x + x + x. x + x. none of the ove Inequlities 0. Solve: x < x. {x x < }. {x x < -}. {x x > -}. {x x > } Exponents. Simplify: (x y) (xy). 8x y. y. 8x y. x y x M:\Plement Review.o Pge Upte: /00

9 . Simplify: Qurti Equtions. Solve: x x =. x = or x =. x = or x = -. x = x +. x = 0 Liner Equtions. Fin the slope n the y-interept of the line: x + y = 9. slope = ; y-interept = 9. slope = -; y-interept = 9. slope = -; y-interept =. slope = - ; y-interept =. Fin the slope-interept eqution of the line pssing through the points (, -) n (, ). y = x. y = x. y = x +. y = x. Solve for P: P = A Prt. P = A Prt. P = rt A. P = A + rt. P = A rt Systems of Equtions in Two Vriles. Solve the following liner system: x + y = 9 n x + y =. x = 0, y =. x = -, y =. x =, y = 0. x =, y = - 8. Mihel hs numer of imes n qurters totling $.0. The numer of qurters is five more thn twie the numer of imes. How mny oins of imes oes he hve?. 0 imes. 8 imes. 00 imes. imes M:\Plement Review.o Pge 8 Upte: /00

10 Prt IV: Intermeite Alger Review Guie Intermeite Alger overs the following topis: lgeri opertions n onepts, solving equtions n inequlities, lgeri frtions, exponents, roots n rils, grphing of liner n qurti funtions n equtions, n introution to logrithms. 9. Fin the slope of the line piture elow Below is the grph of funtion showing y = ƒ(x). Use it to nswer the following questions Wht is ƒ( )?. Wht is x if ƒ(x) =?. Fin the eqution in slope-interept form of the stright line ontining the point (, ) n hving the slope.. Let ƒ(x) = x +. Fin n simplify ƒ(t ). M:\Plement Review.o Pge 9 Upte: /00

11 . Ftor the following polynomil or etermine tht the polynomil is prime: +. Whih of the following re grphs of funtions?..... Solve the given inequlity n grph the solution set on numer line: x 9 + x. Solve the given inequlity n write the solution set in intervl nottion: x + > 0. Write using rtionl exponents (in lowest terms): x y 8. Simplify. Assume tht represents non-negtive numer Rtionlize the enomintor: + 0. Simplify. Do not ssume tht x represents non-negtive numer. x. Solve for : 0 = + 9. A ookse is foot tller thn it is wie. A igonl re, foot longer thn the height of the ookse, is neee for support. Wht is the length of the re?. Simplify. Express your nswer in the form + i. ( + i)( i) (i + ). Solve for x: x + x = + x. Let ƒ(x) = x + x 8. Fin the vertex n x n y interepts of the grph of ƒ.. Solve for t: t t + = 0. A ll is tosse in the ir. Its istne in feet ove groun t seons lter is given y the formul (t) = + 9t t. Wht is the ll's mximum height? 8. Let x g( x) =. Fin g( ). M:\Plement Review.o Pge 0 Upte: /00

12 Mth Plement Review Guie Answer Key Prt I Prt II Prt III Prt IV ) ) or. y = x. t +. ( ).. n... (, ) (, ). / / x y / x x. = or. feet. i. x = -. Vertex: (, ) x- interepts: (, 0) n (, 0) y-interept: (0, -8). t = or. 0 feet 8. g(-) = 8 M:\Plement Review.o Pge Upte: /00

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