BARTON COLLEGE PRACTICE PLACEMENT TEST. a) 4 b) 4 c) 12 d) a) 7a 11 b) a 17 c) a 11 d) 7a 17. a) 14 b) 1 c) 66 d) 81

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1 . Simplify: (! 8) Simplify: (a 4) + (a ) (a+) 7a a 7 a 7a 7. Evaluate the expessin: 4a! 4ab + b, when a = and b = Fiefightes use the fmula S = 0.P + t cmpute the hizntal ange S in feet f wate fm a paticula hse, whee P is the nzzle pessue in punds. Find the hizntal ange if pessue is 90 lb. 44 feet 40 feet 9 feet 7 feet x! x. Simplify: ( ) 4x 8 8x! 8x 8! 4x. Simplify: w v 7 4u 4!! " # u v $ % & 8w ' v w u 4 0 w u 4 v 0 u v 4w Expess in scientific ntatin: " 0!.! 0." 0!." 0!7 8. Expand:.0! PAGE OF

2 9. Slve: x! = x = 4 x = x= x = 4 0. Slve: 8(x ) (x + 4) = 0 + x x = 9 x = 8 x = 8 x = 8 mv. Slve f m: F = F m = v m = Fv Fv F m = m = v. Slve P: A = P + Pt P = A! t A! t P = A P = + t A P = t. Slve: 4 = x! x x = x = x = 0 x = 4. Slve: x! = x = 4, 0 x =, x = 0, x =!,! x 4. Slve:! = x! 4 4! x x = 4 x = 4 x = N slutin x + x y! xy. Simplify: x! xy x y x(x + y) x(x y) x + y PAGE OF

3 7. Simplify: 4x! x + x! Cannt be simplified x! x + BARTON COLLEGE x + x! x + x + 8. Slve: (x ) 7 x x x x 9. Slve: x + < 4 x > x > x < x < 0. Jhn aveaged 8 ut f 00 n his fist thee tests. What was Jhn s sce n the futh test if his aveage afte the futh test dpped t 79 ut f 00? Cannt be fund The sales tax ate in Wilsn Cunty is.7%. Suppse ttal pice f an item that yu bught in Wilsn Cunty including taxes is $4.9, what is the pice (unded t tw decimal places) befe tax? $.9 $.99 $.94 $8.9. The lng tem paking ate at Raleigh Duham Aipt is $ pe hu ( pat f an hu) with $0 daily maximum (:00 a.m. t :00 a.m.). Suppse yu pak yu ca n Fiday aftenn at 8:0 p.m. and pick it up n the fllwing Tuesday at 9:0 a.m., what will be yu paking fee? $8 $ 0 $ 48 $ 8. Slve: x(0x + 8) = (x+) x =, 4 x =!, 4 x =!,! 4 x =,! 4 4. Slve: ( x! )! 8 = 0 x = ± x =, x =! ± x =! ± PAGE OF

4 . The pfit, P, ealized by a cmpany vaies diectly as the numbe f pducts s it sells. If a cmpany makes a pfit f $7800 n the sale f pducts, what is the pfit when the cmpany sells 000 pducts? $0,000 $00,000 $80,000 $0,000. If the vltage, V, in an electic cicuit is held cnstant, the cuent I, is invesely pptinal t the esistance, R. If cuent is 0mA (milliampee) when esistance is hms, find the cuent when the esistance is hms. 40mA 7mA 0mA 00mA 7. A ft lng tube is cut int tw pieces with ati 4:. Find the length f the shte piece. 9 feet feet feet 0 feet 8. A lage squae pizza has 49 pieces (squae slices). Jhn, Jack and Jane ate all the pieces in the ati 4:: espectively. Hw many pieces did Jack eat? 0 pieces pieces 4 pieces 8 pieces 9. Slve:! x + = x = 0 x =! x = x = V 0. Slve f V given =! h! h V = V = V! h =! h V =! h. Find the equatin f the staight line passing thugh the pints (, 4) and (,0). y = 4x + 4 y = 4x 4 y = 4x + 4 y = 4x 4. Detemine the x and y intecepts f the gaph f 7x y = (, 0) and (0, 7) (, 0) and (0, 7) (, 0) and (0, 7) (, 0) and (0, 7) PAGE 4 OF

5 . The linea elatinship between the Fahenheit scale and Centigade scale f tempeatues is given 9 by F = C +. Which f the fllwing statements, if any, ae TRUE? A. 8 F cespnds t 0 C B. 40 C cespnds t 78 F Only A Only B Bth A and B Neithe A n B 4. Jhn (J) is yeas lde than his siste May (M) wh is yeas yunge than he bthe Paul (P). If J, M and P dente thei ages, which ne f the fllwing epesents the given infmatin?! J = M + " $ P = M #! J = M + " # M = P +! M = J + " $ P = M #! J = M + " $ M = P # " x! y =! 4. Slve the system: # $ x! y = 4 (, 0) (, )! $, # " % & '! 4 " #,0 $ % &. The sum f tw numbes is. Twice the smalle numbe is me than the lage numbe. The psitive diffeence between the numbes is 4 7. Find the cdinates f a pint A whse distance fm the igin (0, 0) is units. A (, ) A(-, ) A(4, -) A(, 4) 8. Cnside the cicle given by the equatin (x ) + (y + ) =. Find the cente and adius. (, ); (, ); (, ); (, ); 9. The inequality 8! x < 8 is equivalent t x < 0 x > 0 x<0 x > 0 < x < PAGE OF

6 40. The inequality x + 4! is equivalent t BARTON COLLEGE x x x x x - 4. The inteval slutin t the inequality x! > 0 x + is (,+! ) (!",) (!",! ) #(, +" ) (!,) 4. Let f ( x) =! x. Find f ( a! )! a!! a! a! a 4. Let f ( x) =! x and g( x) x ( f g)(0) =!. Which f the fllwing, if any, is false?! f " # $ % g & + =! ( f! g)( ) = 0 ( fg )( ) =! ( ) 44. Let f ( x) =! x and g( x) x ( f g )( 0) =! ( )( ) =!. Which f the fllwing, if any, is tue? g f 0 = 4 ( f f )( x) = 4! 4x + x ( ) g g ( x) = 4x! 4x + = 4. Let f ( x) =! x. Find the diffeence qutient ( + )! ( ) f x h f x h h h! 4x h 4. Cnside the quadatic functin ( ) f x = x! 4x +. Find the vetex f the gaph f f ( x ). (, ) (, ) (, ) (, 7) 47. The tempeatue, in degees Fahenheit, ve a twelve hu peid is given by the functin T(t) = 0.t + t + 0, whee t = 0 dentes :00 a.m. When is the mning tempeatue 47. F? nn :00 a.m. 0 a.m. 9:00 a.m. PAGE OF

7 48. Simplify and expess in the fm a + bi: ( + i)( + i) 8 + 0i 8 + i 8 i + i 49. Simplify and expess in the fm a + bi:! 4i + i i i 4 4i 4 + 4i x + 0. Find the dmain f the functin f ( x) = x +. all eal numbes x, x x,, x +. Find the equatin f hizntal asymptte f the functin f ( x) = x! y = y = y= y = 0 x. Find the invese functin f f(x) =!. f (x) = x + f (x) = x + f (x) = x + f (x) = x +. Which f the fllwing pais f expnential and lgaithmic fms is false? = /9 ; lg (/9) = (/) = 4; lg 4 (/) = 0 = 000; lg(000) = e = x ; ln(x) = 4. Wite in tems f lg(x), lg(y), lg(z):! lg y z " # x $ % & lg(y) 0. lg(z) lg(x) lg(y) + 0. lg(z) lg(x) lg(y) + 0. lg(z) + lg(x) lg(y) + 0.lg(z) + lg(x). Find the hydnium in cncentatin, H +, f a slutin given ph = 7. Nte: ph = lg(h + ) mles pe lite mles pe lite mles pe lite. 0 7 mles pe lite PAGE 7 OF

8 . Slve: x e! = ( ) + ln x = x! ln( ) = x = + ln( ) x = + ln ( ) 7. Slve the equatin: lg ( x + )! lg ( x! ) = x = x = x = / x = 0 t! " 8. Suppse the ppulatin f a twn is given by the mdel P( t) = 70# $ % & numbe yeas since 000. Which f the fllwing statements is tue? The ppulatin in 000 was 8. The ppulatin dubles evey 0 yeas. The ppulatin is halved evey ten yeas The ppulatin is gwing by 0% evey ten yeas. /0, whee t dentes the! 9. If the angle " = adians, then 0 <! < <! < <! < <! < 0 0. If the light beam makes ne cmplete evlutin evey 0 secnds, hw lng will it take t sweep and angle f 0? less than secnds between and secnds between and 7 secnds between 7 and 0 secnds. Given an issceles tiangle with base length cm and altitude cm, find the length f the cnguent sides. 4 cm cm 0 cm 8 cm. If tan! = and sin! > 0, then cs! equals PAGE 8 OF

9 ! 0 0 0! 0. If csc! = and cs! < 0, then ct! equals!! 4. Find the exact value f csc( )!!. Find the exact value f ct( 40 )! ". If the angle! in standad psitin meets the unit cicle at,#, find the value f the functins $ % & ' sin (! ) and cs (! ). sin! = and cs! = " sin! = " and cs! = sin! = " and cs! = sin! = and cs! = " 7. Find the expessin that is equal t + sin! " sin! PAGE 9 OF

10 sin! + cs! csc! + csc! " 0 sec! + tan! tan! + ct! 8. Find the expessin that is equal t ( ) tan! + ct! tan! ct! ct! " sec! + csc! 9. The minute hand f a clck is cm lng. Hw fa des the tip f the minute hand tavel in minutes?! cm 9! cm! cm! cm 70. Find the aea f a sect f a cicle with cental angle θ= adians, if the adius f the cicle is in. 4 in in 7 in 8 in 7. The aea f the sect f a cicle with cental angle f = adians is m. Find the adius f the cicle. m 8m 4m m 4cs! + = cs! +, 0 "! < 0 7. Slve ( ) sin! # cs! + = 0, 0 $! $ " 7. Slve ( )( )!!!! N slutin " =,0 " = 0, " =,!! 74. Slve sin " = sin" +, # $ " $!!!!!!!! " = #, " =,# " =,# " = #, 7. In a ight tiangle ABC with m! C = 90, if AC = and sin( ) B =, find AB PAGE 0 OF

11 7. In tiangle ABC with m! A = 0, m! B = 4 and BC =, find AC. insufficient infmatin 77. In tiangle ABC with m! A = 0, m! B = 0 and AB =, find BC. insufficient infmatin 78. Eliminate the paamete t in the given paametic equatin!" x = cs # "$ y = + sin ( t) ( t) y = + x x = + y x + y = 9 x + ( y! ) = 79. Eliminate the paamete t in the given paametic equatin ( ) cs( ) ( t)!" x = sin t t # "$ y = sin x = y y = x xy = xy = 80. Given vects u =! 4,! and v =,, which if the fllwing statements, if any, is false. u = u + v = 0 v! u =,4 Nne f these PAGE OF

12 ANSWER KEY. c. b 4. c. c. b. c 4. c. c. b. c 4. a. b 4. d 4. a 44. b 4. a. d. a 4. d. b. c. a 4. c. b 7. a 7. b 47. b 7. b 8. c 8. c 48. c 8. d 9. a 9. b 49. b 9. d 0. b 0. c 0. a 70. a. d. a. d 7. c. c. a. d 7. a. c. a. b 7. a 4. b 4. d 4. b 74. a. d. b. a 7. a. d. b. a 7. b 7. d 7. c 7. c 77. b 8. c 8. c 8. c 78. d 9. c 9. d 9. b 79. b 0. d 40. b 0. d 80. b. PAGE OF