3. If x and y are real numbers, what is the simplified radical form

Transcription

1 lgebra II Practice Test Objective:.a. Which is equivalet to ?. Which epressio is aother way to write 5 4? If ad y are real umbers, what is the simplified radical form of 5 y 5? 5 y y y 5 5 y 5 Objective.b 4. What is the simplified epressio of What is the simplified form of 5 5? ?

2 6. What is the sum of ad 5 7? 7. The area of a square is. What is the legth of a side of the square? Objective.a 8. Which epressio represets the quotiet? 4 z z 4 z z 4 4 z z 4 z z 4 9. Which epressio represets the quotiet? z 4 z 4z y y 8y 8 y 6 0. Which epressio represets the quotiet? y 8 y 8 y 4 y 4 y 4y ( y 4)

3 . rectagular prism has a volume of 8 4 ad a height of. Which epressio represets the area of the base of the prism? objective.b. What is the completely simplified equivalet of ?. Which epressio represets the result of this subtractio? What is the simplified equivalet of? 55 57

4 objective.b 5. Which epressio is equivalet to 4i? i i 64i 64i 6. circuit has a curret of (8 + 7i) amps, ad aother circuit has a curret of (5 i) amps. What is the differece betwee the currets of the two circuits? ( 4i) amps ( + 4i) amps ( 0i) amps ( + 0i) amps 7. Which epressio is equivalet to 6 4? 6 4 6i 6 i 6 i 8. What is the product of i ad 5 4i i 7i i 7i? 9. What is the completely simplified equivalet of 5 i 5 i 5 i 5 i 5 i? objective.a 0. What is the paret graph of the followig fuctio ad what trasformatios have take place o it: y? The paret graph is y, which is shifted uits up. The paret graph is y, which is shifted uits dow. The paret graph is y, which is shifted uits to the left. The paret graph is y, which is shifted uits to the right.

5 . What is the paret fuctio of this graph? f 4 f f 4 f objective.b, what is the value of f g. If f ( ) ad g( ) 4 7 7?. If f ( ) ad g( ) f g, what is the value of?

6 4. If f ( ) ad g( ), which graph correspods to the fuctio of fg? lie R lie S lie T lie U Objective.c 5. If f ( ) 7 ad g( ), what epressio represets ( f ( g( ))? If f g, how might f ad f ad g f ad g f ad g f ad g g be defied?

7 Objective.d 7. Which statemet is true for the fuctio f( ) 4? 4 is ot i the rage of the fuctio. 4 is ot i the domai of the fuctio. -4 is ot i the rage of the fuctio. -4 is ot i the domai of the fuctio. 8. What is the domai of the fuctio f : 0 : 5 :,4 :, 4 5 8? 9. Which itervals correctly defie the domai of f,4 ad 4,, 4 ad 4,, 4 ad 4,, 4 ad,? 4

8 0. omai: 0, Rage: y y the give costraits? Which graph correspods to. Which fuctio has the fewest domai restrictios for real umbers? f f f f Objective.e. What is the iverse of f f f f f?

9 . What is the iverse of the fuctio f f 4 4 f 4 f 4 f 4? 4. Which graph represets the iverse of f? 5. Which statemet about graphs ad their iverse is true? They are symmetric about y. They are symmetric about the origi. They are symmetric about the -ais. They are symmetric about the y-ais.

10 Objective.a 6. Profits, P, are equal to sales, S, mius epeses, E. If epeses are equal to travel, T, plus materials, M, which system of equatios models this situatio? P S E P S E E T M E T M P S E E T M P S E E T M 7. Tyroe wats to sped at most $0,000 o two televisios, R ad S. Each televisio must cost at least $,000, ad televisio R must cost at least twice as much as televisio S. Which system of iequalities models the amout of moey spet o each televisio? RS 0, 000 R S R,000 S,000 RS 0,000 S R R,000 S,000 RS 0,000 R S R,000 S,000 RS 0, 000 S R R,000 S, Meredith ivests $50,000 i her ew busiess. It costs the compay $0 to produce each uit, which is sold for $5. Let represet the cost ad R represet the reveue for uits. Which statemet is true about the graphs of the equatios 50,000 0 ad R 5? oth slopes are positive. oth slopes are egative. Oe slope is positive, ad the other is zero. oe slope is egative, ad the other is positive. Objective.b 9. Which quadrats cotai the solutios to this system of iequalities? y y 4 quadrats I ad IV quadrats II ad III quadrats III ad IV quadrats II, III, ad IV

11 40. What is the solutio to this system of equatios? y 5 0 y 4 0, y, y, y, y 4. The corers of a triagle are (,), (4,4), ad (6,). Which system of iequalities describes the iterior of the triagle? 4y y y8 y y4 y8 4y y4 y8 y y y8 Objective.c 4. What is the solutio set of this system of equatios? y 0 y 0,,,0,0,,,0, 0,,0,, 4. What is the solutio set of this system of equatios? y 7y 0,5, 5,,5, 5,8 5,8, 8,5 8,5, 8,8

12 44. What is the solutio set of this system of equatios? y y, 4,,4, 4,,4,4,, 4,4,,4 Objective.a 45. How may real roots does the fuctio give by the graph have? 0 real roots real root real roots 4 real roots 46. What umber is added to both sides of the equatio it by completig the square? to solve

13 47. What is the solutio of 5 0? Objective.b f? 48. What is the y-itercept of (0, -) (0, ) (-, 0) (, 0) 49. What are the coordiates at the miimum poit of (-, -) (-, ) (, -) (, ) 50. Which fuctio represets this graph? f 4? f 4 f 4 f 4 f 4

14 5. Which statemet best describes these two fuctios? f 6 g 5 They have o commo poits. They have the same -itercepts. The maimum of f() is the same as the miimum of g(). The maimum of g() is the same as the miimum of f(). 5. Which statemet best describes these two fuctios? f 4 g 7 The maimum of f() is less tha the miimum of g(). The miimum of f() is less tha the maimum of g(). The maimum of f() is greater tha the miimum of g(). The miimum of f() is greater tha the maimum of g(). Objective.c 5. The legth of a rectagular swimmig pool is 0 feet greater tha the width. The surface area of the pool is,500 square feet. What are the legth ad width of the pool? legth = 0 ft, width =0 ft legth = 50 ft, width =0 ft legth = 60 ft, width =40 ft legth = 50 ft, width =0 ft 54. The profit, P, (i dollars) for ce ar Retal is give by P 00 0., where is the umber of cars reted. How may cars have to be reted for the compay to maimize profits? 500 cars,000 cars,500 cars 5,000 cars 55. The reveue, R, at a bowig alley is give by the equatio R,400, where is the umber of frames bowled. 800 What is the maimum amout of reveue the bowlig alley ca geerate? $800 $,00 $,800 $,400

15 Objective Which best describes the graph of circle ellipse parabola hyperbola y? What is the equatio of a circle with ceter (-4, ) ad diameter 6? 4 ( y ) 6 4 ( y ) 6 4 ( y ) 9 y 4 ( ) Which statemet describes the equatio y 6 8? It is a vertical parabola. It is a vertical hyperbola. It is a horizotal parabola. It is a horizotal hyperbola. 59. What is the equatio of the give parabola? y y y y 6

16 60. What is the equatio of the graphed Hyperbola? y 4 4 y 4 4 y y What is the verte of the parabola y (-, -9) (, -9) (-9, -) (-9, ) 9? 6. What is the equatio of the ellipse whose ceter is at the origi, major ais has legth of 0 uits alog the -ais, ad mior ais has legth of 6 uits? y a b y 5 9 y 9 5 y 0 y 00 6

17 Objective.5a 6. Which fuctio is best represeted by the data i this table? f ( ) f( ) f ( ) f ( ) X 0 4 Y What are the horizotal asymptote ad y-itercept for the graph of this fuctio f( ) 7? symptote: y=7, Itercept: (0, 7) symptote: y=-7, Itercept: (0, 7) symptote: y=7, Itercept: (0, 8) symptote: y=-7, Itercept: (0, 8) 65. Which fuctio is best represeted by this graph? f f f f ( ) log ( ) log ( ) log ( ) ( ) log ( )

18 66. Which fuctio is best represeted by this graph? f ( ) f f( ) f( ) ( )

19 67. Which graph represets the fuctio f ( ) log( )? objective.5b 68. Which fuctio is the iverse of f ( ) log? f ( ) e f( ) f( ) 0 f( ) log log If, what is the value of?

20 70. Which equatio represets the solutio for i the formula 6? log 6 log log log 6 log log6 log log6 7. What is the value of log 0? 0 ½ 0 7. If log 80, what is the value of? If 4Log, what is the value of? Objective:.5c 74. If the loudess of fizz i a ca of soda pop is represeted by F 4log 0 5, where is represeted by the itesity of soud, how loud is the fizz if 0? 4 decibels 8 decibels 6 decibels decibels

21 75. The formula, r, gives the aual iterest rate, r, required for your moey to double i years. If it takes 8 years for your moey to double, what was the approimate aual iterest rate? % 4% 8% 8% 76. The populatio, P, of prairie dogs icreases accordig to the equatio P,50e rt, where t is the umber of years, ad r is the rate of growth. Which equatio solves for r? P l,50 r t t r P l,50,50 l P r t t r,50 l P 77. The mass of a radioactive sample is give by M ( t) M00 kt, where t is the time i years, M 0 is the iitial mass, ad k is a costat. If 400 grams of this material decays to 40 grams i 0 years, what is the value of k? Objective.6a 78. Which equatio has - ad as solutios?

22 79. Which of these is a root of f ( ) 4? Give that ad are factors of the polyomial, 7, what is the third factor? What is the solutio set of, 5, 5, 5, 5 0 0? 8. rectagular prism has a volume of 0 cubic iches. The legth of the prism is 5 iches, the width is (-) iches, ad the height is (+) iches. What are the width ad height of the prism? width: i., height: 8 i. width: 4 i., height: 6 i. width: 6 i., height: 4 i. width: 8 i., height: i. 8. What is divided by ?

23 Objective.6b 84. I which directio does the graph of the parabola up left right dow y ope? 85. What is the graph of the polyomial y?

24 86. Which fuctio is represeted by this graph? f ( ) f ( ) f ( ) f ( ) 87. Which statemet describes the characteristics of the graph 4 of f ( ) 5? The graph primarily icreases i the third quadrat ad icreases i the first quadrat.. The graph primarily decreases i the secod quadrat ad icreases i the first quadrat.. The graph primarily icreases i the third quadrat ad decreases i the fourth quadrat.. The graph primarily decreases i the secod quadrat ad decreases i the fourth quadrat. Objective.6c 88. What is the y-itercept of the graph of y 4?

25 89. What are the - ad y-itercepts of this graphed fuctio? -itercepts: (-, 0), (., 0), (7, 0); y-itercepts: (0, 8) -itercepts: (-0, 8); y-itercepts: (-, 0), (., 0), (7, 0) -itercepts: (, 0), (-., 0), (-7, 0); y-itercepts: (0, 8) -itercepts: (0, 8); y-itercepts: (, 0), (-., 0), (-7, 0) 90. What is the set of -itercepts of this graphed fuctio? {} {-, } {-, } {-,, }

26 9. What is the set of approimate y-values of the relative miimum ad maimum of this graphed fuctio? {} {-, } {-, } {-,, } 9. What are the properties of the poit (0, ) i this graphed fuctio? It is a relative miimum ad a -itercept. It is a relative maimum ad a -itercept. It is a relative miimum ad a y-itercept. It is a relative maimum ad a y-itercept.

27 Objective.6 9. The itesity, L, of light varies iversely with the square of the distace, r, from the source of the light. Give that k is the costat of proportioality, which equatio describes this relatioship? L kr k L r L k r L kr 94. compay is sellig a item ad determies that the profit from sellig the item for a price of dollars is give by the fuctio below. P( ) ( 6) 4 4 Which price will maimize the profit? $4 $ $6 $0 95. The path of a kicked soccer ball ca be modeled by the fuctio f ( ) 6, where is the horizotal distace (i meters) ad f( ) is the height (i meters). If the height is meters, what is the horizotal distace? 4 meters 6 meters meters 4 meters 96. ladscape desiger has to costruct a rectagular flower bed with a perimeter of 00 feet ad the maimum possible area. What is the area of the flower bed? 5 sq. ft 00 sq. ft 65 sq. ft,500 sq. ft Objective.7a 97. What is the value of i this ratioal equatio 4 5?

28 98. What is the solutio set of this ratioal equatio {6} {-} {, 6} {-, -6} 5 9? What is the value of i this ratioal equatio 4 4 5? What is the solutio set of this ratioal equatio? {-,-} {-, } {-, } {, } Objective.7b 0. What is the vertical asymptote of the graph of 4 4 f( ) 4?

29 0. What is the graph of the fuctio f( )?

30 0. Which fuctio is represeted by this graph? f( ) f( ) f( ) f( ) 04. How may vertical asymptotes does the graph of y 4 0 vertical asymptotes vertical asymptote vertical asymptotes 4 vertical asymptotes have?

31 0bjective.7c 05. What is the horizotal asymptote of this graph? 0 y 0.5 y Which statemet correctly describes the asymptotes of the graph of this ratioal fuctio? The vertical asymptote is asymptote. The vertical asymptote is asymptote. The horizotal asymptote is asymptote. The horizotal asymptote is asymptote., ad there is a egative slat y, ad there is a egative slat, ad there is a positive slat y, ad there is a positive slat

32 07. How may -itercepts does the graph of y What are the vertical ad horizotal asymptotes of 4, ad y y 4, ad 4, ad y y 4, ad have? 9 f( ) 6? Objective.7d 09. If the surface area of a closed cylider is 5 square iches, which equatio represets the height of the cylider i terms of r? S rh r 5 r h r 5 r h r h5 r h5 r 0. homeower stocked his pod with fish. The umber of fish, F, 9 t icreases accordig to the equatio, F, where t is the time i 0.05t years. What is the approimate umber of fish after 0 years? 49 fish 69 fish 8 fish 9 fish. The cost,, i thousads of dollars, to remove percet of the trash 450 left by a torado is modeled by the equatio 5. pproimately what percet of trash will be removed if 00 thousad dollars are spet? 4% 50% 59% 64%

33 Objective.a. Nacy made a scatter plot of how much moey she had left at the ed of each day of her vacatio. Which table best represets the data i her scatter plot? ay 4 5 Moey $00 $00 $00 $00 $00 ay 4 5 Moey $00 $00 $00 $400 $500 ay 4 5 Moey $500 $00 $00 $400 $00 ay 4 5 Moey $500 $400 $00 $00 $00

34 . Which set of data best represets the data o the scatter plot? Time Memory Time Memory Time Memory Time Memory

35 4. Which scatter plot best represets the lack of correlatio betwee shoe size ad hair legth?

36 objective.b 5. The test scores ad hours studied of 6 studets were put ito a scatter plot. If aother studet studies hours, what is the most likely test score based o this data? Which of these observatios would be cosistet with a epoetial model of populatio growth? The populatio started out large, decreased i size, the became large agai. The populatio is observed to icrease at a faster rate as time passes. The populatio is observed to icrease steadily over time. The populatio grew very quickly but the declied.

37 Objective.c 7. Which equatio most closely models the data i the scatter plot? y y y y 8. Which type of fuctio best models the data i this scatter plot? epoetial logarithmic quadratic liear

38 9. Studets i a sciece classroom perform a eperimet to fid the rate at which a hot liquid cools i a freezer. They plot the temperature over time ad obtai the followig graph. Which type of fuctio best models the data i this scatter plot? epoetial logarithmic quadratic liear 0. Which equatio most closely models the data i the scatter plot? y 4 6 y 6 y 6 y 5 6

39 . Which equatio best models the data i this scatter plot? y 5 y 0.5 y y Objective.. What is the th term i the sequece {,, 5, 7, }? 4 5 rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r)

40 . What is the sum of the first 6 terms of the series ?,906 7,8 5,64,48 rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r) 4. child puts $.00 ito a piggy bak. Oe week later, he puts $.5 i the bak. Two weeks later, he puts $.50 i the bak, ad so o. How much moey does he put i the bak o the 5 th week? $ 6.5 $7.00 $9.00 $00.00 rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r)

41 5. What is the value of i the geometric sequece,,,,... 8? rithmetic Sequeces & Series th term : a a ( ) d -4-9 Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r) 6. Which formula could be used to fid the sum of a arithmetic series if the last term is ukow? rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s s a ( ) d s a ( ) d s a ( ) d s a ( ) d a ( r ) ( r)

42 7. I a arithmetic sequece begiig with 6 ad edig with 405, how may itegers are divisible by 9? 4 itegers 4 itegers 44 itegers 45 itegers rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r) 8. How may terms are there i a geometric series if the first term is, the commo ratio is 4, ad the sum of the series is,0? 4 terms 5 terms 6 terms terms rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r)

43 swers