End of Course Algebra I ~ Practice Test #2

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1 End f Curse Algebra I ~ Practice Test #2 Name: Perid: Date: 1: Order the fllwing frm greatest t least., 3, 8.9, 8,, 9.3 A. 8, 8.9,, 9.3, 3 B., 3, 8, 8.9,, 9.3 C. 9.3, 3,,, 8.9, 8 D. 3, 9.3,,, 8.9, 8 2: A star s clr gives an indicatin f temperature and age. The chart shws fur types f stars and the lwest temperature f each type. List the temperatures in rder frm lwest t highest. Type Lwest Temperature Clr A 1.35 Blue-White B 2.08 Blue G 9.0 Yellw P 4.5 Blue A. 1.35, 2.08, 4.5, 9.0 B. 1.35, , 9.0 C. 9.0, 1.35, 2.08, 4.5 D. 9.0, , 2.08, 3. Which numbers are bth less than O A and ? O B. 2 3 and 3 4 O C and -1.2 O D. 2 3 and : Fr what values f a is an integer? A. a = 1, 0 B. a 1 C. a = 1, a 0 D. a > 1

2 5: Evaluate 2w + 6y 2 fr w = 4 and y = 3. A. 330 B. 62 C. 60 D. 44 6: Simplify : A B C D : Simplify: A. B. 4 C. D. 8: Simplify the expressin using psitive expnents. A. x 3 B x 5 C. x 20 D. x 4 9: Yu wn a dr prize and are given a chice between tw ptins. A: $150 invested fr 10 years at 4% cmpunded annually, r B: $200 invested fr 10 years at 3% cmpunded annually. Which plan is best and what is the final amunt f the investment? Investment = P(1+r) t A. A; $242 B. B; $222 C. A; $4,338 D. B; $268 2

3 10: Select the set f rdered pairs that represents an expnential functin. A. (0,0) (-2,2) (1,1) (2,2) B. (4,6) (2,3) (6,8) (10,12) C. (1,1) (3,9) (2,4) (0,0) D. (0,0) (-1, 2) (-2, 3) (2,3) 11: Slve A = p + prt fr p A. B. C. D. 12: Slve fr r A. B. C. D. 13: Which f the fllwing pairs f equatins can bth be written s that y is a functin f x? A. x = 3; y = 2x + 1 B. y = x 2 + 1; x = 0 C. x 2 + y 2 = 1; x = y D. 3x 2y = 7; y = 2 x 14. The equatin f a functin is shwn. What is the dmain f f(x)? f ( x) x 1 O A. All real numbers O B. All real numbers except -1 O C. All real numbers greater than -1 O D. All real numbers between -1 and 1 3

4 15: Which f the fllwing pairs f equatins can bth be written s that y is a functin f x? A. y = 3/x; x = 3 B. 2x y = 0; x = y 2 C. y 4x 3 ; y = 3 x D. y x 3 ; x 2 + y 2 = 9 16: Which f the fllwing tables, situatins, r graphs represent a functin? A. The age in years f each student in yur math class and each student s she size. B. The number f degrees a persn rtates a spigt and the vlume f water that cmes ut f the spigt. C. Hurs studied Scre n test 85% 92% 90% 70% D. 17: A functin f(n) = 60n is used t mdel the distance in miles traveled by a car traveling 60 miles per hur in n hurs. Identify the dmain and range f this functin. What restrictins n the dmain f this functin shuld be cnsidered fr the mdel t crrectly reflect the situatin? A. Dmain: hurs car traveled Range: distance car traveled Restrictin: hurs must be greater than r equal t zer B. Dmain: distance car traveled Range: hurs car traveled Restrictin: distance must be greater than r equal t zer C. Dmain: hurs car traveled Range: miles per hur car traveled Restrictin: hurs must be greater than r equal t zer D. Dmain: distance car traveled Range: miles per hur car traveled Restrictin: distance must be greater than r equal t zer 18: What is the dmain and range f f ( x) x 5? A. Dmain: x can be all real numbers Range: f(x) can be all real numbers B. Dmain: x = 5 Range: f(x) = 0 C. Dmain: x 5 Range: f(x) is less than r equal t zer D. Dmain: x 5 Range: f(x) is greater than r equal t zer 4

5 19: Belw is the graph f f ( x) 2 x 1 5. Determine the dmain and range f this functin. A. Dmain: x 0 Range: f ( x) 0 B. Dmain: x 5 Range: f ( x) 5 C. Dmain: x can be all real numbers Range: f ( x) 5 D. Dmain: x can be all real numbers Range: f(x) can be all real numbers 20: Accrding t the USPS gvernment website, dated January 2011, the ging rate f a letter depended n its weight in unces and culd be priced as fllws: Up t 1 z $.44 Up t 2 z $.61 Up t 3 z $.78 Up t 3.5 z $.95 Weights larger than 3.5 z, large envelpe prices apply. Hw much wuld a letter weighing 2.5 unces cst? A. $.61 B. $.78 C. $1.05 D. $ : AT&T s website lists prices fr cell phne plans. As f January 2011, the cell phne prices fr an individual plan depending n minutes used can be priced as fllws: 450 minutes fr $ minutes fr $ minutes fr $ minutes fr $ Hw much wuld an individual cell phne plan cst if a persn wants t make sure they are cvered fr 1000 minutes? A. $79.99 B. $99.99 C. $ D. $

6 22: Ms. Namtvedt wants t register her math club fr the Washingtn State Mathematics Cmpetitin held n March 9, The fees fr cmpeting are as fllws: $15 per participant fr the first 6 participants $100 fr 7 10 participants $130 fr participants $115 fr participants $175 fr mre than 20 participants Hw much wuld math club be charged if registering 14 participants? A. $78 B. $130 C. $140 D. $210 23: Marilyn kept track f hw tall her sn was every year since he was brn. If Marilyn were t write a functin relating height, h, and years, y, what wuld be the independent variable? A. height, h B. years, y C. height per year, h/y D. year per height, y/h 24: Tammy wanted t be a prfessinal basketball player. Ever since she was a child she wuld keep track f what was the average salary fr a female basketball player since the year If Tammy were t write a functin relating salary, s, and years, y, what wuld be the dependent variable? A. salary, s B. years, y C. salary per year, s/y D. year per salary, y/s $1000 $900 $800 $700 $600 $500 $400 $300 $ : The chart shws the amunt f ttal salary (cmmissin plus base salary) paid t emplyees f a car dealership in ne week. Number f cars sld Ttal Salary $200 $300 $400 $600 $800 $900 Which equatin best represents ttal salary (T) that an emplyee makes fr selling any number f cars, c, in a week? A. T(c) = 100c B. T(c) = 100c C. T(c) = 100(c + 200) D. T(c) = c

7 26: A ppulatin f bacteria dubled every hur, starting with 4 bacteria. The chart belw represents the ttal ppulatin, p, at a given hur, t Number f bacteria per hur hur Number f bacteria Which equatin best represents the ttal ppulatin (P) f bacteria at a given hur, t. A. P(t) = 2 t B. P(t) = 2 t + 4 C. P(t) = 4 t D. P(t) = 4(2 t ) 27: The graph belw shws a mdel fr the relatinship between the banking angle and the turning radius fr a bicycle traveling at a particular speed. Fr the values shwn, the banking angel B and the turning radius r can be apprximated by an inverse variatin. Radius Banking Angle Which equatin best represents the banking angle B fr the turning radius r? A. B(r) = 28r B. B(r) = 2r 28 C. B ( r) r D. B( r) r 7

8 28: Which equatin listed belw best represents the set f data in the table? x y A. y = 3x + 2 B. y = 3x + 2 C. y = x 2 D. y = x 6 29: Which functin includes all f the rdered pairs in the table? x f(x) A. f(x) = x 3 B. f(x) = x + 7 C. f(x) = 2x 2 3 D. f ( x) x 27 30: Which equatin listed belw best represents the set f data in the table? x y A. x y = 2 B. 2x y = 2 C. x + y = 2 D. x + 2y = 2 31: Fr the functin f ( x) 3 x 1, find f ( 5). A. 12 B. 2.4 C. 12 D : Fr the functin f ( x) 4x 6, find f ( 2). A. 14 B. 7 C. 2 D. 2 33: Fr the functin f ( x) x 3, find f (6) 1 A. 2 B. 6 C. 3 D. 9 8

9 34: Fr the functin f ( x) 3x 6, find x when f ( x) 0. A. 2 B. 0 C. 6 D. 9 35: Fr the functin f ( x) 9x 17, find x when f ( x) 1. A. 17 B. 8 C. 1 D. 2 36: Fr the functin f ( x) 2x 9, find x when f ( x) 3. A. 9 B. 3 C. 3 D. 6 37: Slve the equatin and chse the crrect answer: y 12 4 A. y = -16 B. y = -8 C. y = 8 D. y = 16 38: Slve the inequality and chse the crrect answer: x 5 8 A. x > -3 B. x > 3 C. x > 11 D. x < 3 39: Gerge has eight mre than twice the number f marbles yu have. Write an expressin fr the number f marbles Gerge has. Chse the crrect answer: A. 8 2n B. 2n - 8 C. 8 + (-2n) D. 2n + 8 9

10 40: Write an abslute value equatin fr all the numbers 2 units frm 7. Chse the crrect answer: A. x 7 2 B. x 2 7 C. x 7 2 D. x : The equatin 2 x has tw real slutins. Determine the negative slutin f the equatin and chse the crrect answer. A. -1 B. -2 C. -3 D : Slve fr x: 2(x 3) + 4x = x Chse the crrect answer: A. 2 B. 5 C. 4 D. 6 43: Slve x 6 4 Chse the crrect answer: (and be able t graph the slutin n a number line) A. 2 < x < 10 B. 2 > x > 10 C. x < 2 and x < 10 D. x > 2 and x > 10 10

11 44. Which equatin represents the line that passes thrugh the pints (2, 2) and (4, 1)? O A. O B. O C. O D. 45: Find an equatin fr a line with y-intercept equal t -2 and slpe equal t 3. A. y = -2x + 3 B. y = -2x - 3 C. y = 3x - 2 D. y = 2x 2 46: Find an equatin fr a line with a slpe f -1 that ges thrugh the pint (-3, 2). A. y = -x + 1 B. y = -x 1 C. y = 2x - 1 D. y = 3x 2 47: Find an equatin fr a line that ges thrugh the pints (1, 8) and (-2, -1) A. B. C. D. y 3x 5 y 3x 5 y 1 3 x y 1 3 x : Use the equatin y 7 2(x 2) (withut sketching the graph) t describe the graph. A. the graph has a negative slpe and y-intercept f -2 B. the graph has a negative slpe and y-intercept f 3 C. the graph has a psitive slpe and y-intercept f -2 D. the graph has a psitive slpe and y-intercept f 3 49: Write the equatin 50: Write the equatin 3x 2y 5 in slpe-intercept frm. Slpe Intercept frm is: y 1 2(x 2) in standard frm. A. 2x +y =-3 B. -2x + y = 3 C. 2x y 3 D. y = 2x

12 51: Write the equatin y 1 x 5 in standard frm 2 A. C. x 2y 10 B. y 1 2 x 5 D. x 2y 10 y 1 2 x Mary is ging t depsit an equal amunt f mney int a checking accunt each mnth until she has saved $500. The amunt f mney, y, in the accunt after x mnths can be mdeled by the equatin. What des the slpe f the graph f the equatin represent? O A. The amunt f mney depsited mnthly O B. The amunt f mney riginally in the accunt O C. The number f mnths it wuld take t earn $100 O D. The number f mnths it wuld take t reach $ Refer t the graph belw t answer the fllwing questins abut three different cell phne plans: Blue, Green, and Red. The graphs relate ttal minutes per mnth used fr each cell phne plan and mnthly cst in dllars. 12

13 54: What can be said abut the initial cst f each cell phne plan? A. All the plans begin with the same cst. B. The Red Plan csts the mst. (slid line) C. The Blue Plan csts the mst. (dash, dt, dt, dash) D. The Green Plan csts the mst. (dash) 55: Which plan csts the least if yu have 300 minutes f cell phne use in the mnth? A. Blue Plan (dash, dt, dt, dash) B. Green Plan (dash) C. Red Plan (slid line) D. Cannt be determined 56: What is the least number f minutes yu can use and have the Green and Red Plans cst the same amunt? A. 100 minutes B. 200 minutes C. 250 minutes D. 300 minutes E. 400 minutes 57: If smene needed t use their cell fr mre than 600 minutes every mnth, which plan wuld yu recmmend s they paid the smallest mnthly fee? A. Blue Plan (dash, dt, dt) B. Green Plan (dash) C. Red Plan (slid line) D. Cannt be determined 13

14 58: The sides AB and DC are A. unrelated B. parallel C. perpendicular D. ppsite 59: The sides AD and DC are A. unrelated B. parallel C. perpendicular D. ppsite 60: The actual slpe f side AB is: A. ¼ B. ¼ C. ½ D. ½ E. 2 F : Tw lines divide the crdinate plane int the fur lettered regins shwn. M N P Q One regin represents the slutin set t the system f inequalities given. Which regin represents the slutin set fr the system f inequalities given? O A. O B. O C. O D. Regin M Regin N Regin P Regin Q 14

15 62: y = 2x + 5 x + 3y = -6 What is the slutin t the simultaneus linear system pictured abve? A. (0, 4) B. (-2, 0) C. (-3, -1) D. (-2, 0) 63: Slve the fllwing simultaneus linear equatins algebraically: 2x y 2 x y 1 A. (-1,-2) B. (-1/3,-4/3) C. (0,-1) D (-1,0). 64: An academic team is ging t a state mathematics cmpetitin. There are 30 peple ging n the trip. There are 5 peple wh can drive and 2 types f Vehicles; vans and cars. A van seats 8 peple, and a car seats 4 peple, including drivers. Let v = number f vans and c = number f cars. v + c 5 8v + 4c > 30 Hw many vans and cars des the team need fr the trip? A. 3 cars and 3 vans B. 3 vans and 2 cars C. 3 cars and 2 vans D. 3 vans and 1 car 15

16 Use the fllwing situatin fr the next three questins: A gas statin s 10,000-galln undergrund strage tank cntains 1,000 gallns f gasline. Tanker trucks pump gasline int the tank at a rate f 400 gallns per minute. Hw lng will it take t fill the tank? 65. Find a functin that represents this situatin, where x is the time in minutes and y is the amunt f gas in the tank. A. y 400x 10,000 B. y 400x 1,000 C. y 400x 10,000 D. y 400x 9,000 66: If the flw rate increases frm 400 t 500 gallns per minute, hw will the graph f the functin change? A. The y-intercept will increase B. The y-intercept will decrease C. The slpe will decrease D. The slpe will increase 67: If the initial amunt f gasline in the tank changes frm 1,000 t 2,000 gallns, hw will the graph f the functin change? E. The y-intercept will increase F. The y-intercept will decrease G. The slpe will decrease H. The slpe will increase Refer t the fllwing tw functins t answer the next 3 questins. Functin A: y 3 x Functin B: y 1 3 x 68: Which statement best describes the transfrmatin f the graph f y x f y x 2? O A. O B. O C. O D. The graph shifts up 2 units. The graph shifts dwn 2 units. The graph shifts left 2 units. The graph shifts right 2 units. t the graph 69: What can be said abut the fllwing tw functins? A. Functins A and B reflect exactly acrss the x-axis B. Functins A and B reflect exactly acrss the y-axis C. The functins d nt reflect D. The functins cannt be graphed 16

17 70: Which functin s end behavir is negative? A. Functin A B. Functin B C. Neither D. Bth 71: Which functin has a greater rate f change? A. Functin A B. Functin B C. Neither D. Bth 72: A quadratic functin is represented by the given graph. Which values represent the zers f the functin? O A. O B. O C. O D. r r r r 73: What are the slutins t the equatin? O A. O B. O C. O D. r r r r 17

18 74: A lcal cmpany has a salary dispute. The wrkers claim that they are underpaid as cmpared t the natinal average. Management claims that they are actually verpaid as cmpared t the natinal average. Things t cnsider when answering the fllwing questins: In this cmpany there are nly a few f the wrkers earning salaries which are quite high; in fact these salaries are way abve the natinal average. Bth f the claims made can be accurately supprted by apprpriate summary statistics. Wuld it be in the managements best interest t use the mean r the median when quting the average salary f the wrkers at this lcal cmpany? Explain. What wuld be in the wrkers best interest when quting the average f lcal salaries? Explain. 18

19 75: Each bx-and-whisker plt shws the prices f used cars (in thusands f dllars) advertised fr sale at three different car dealers. If yu want t g t the dealer whse prices seem least expensive, which dealer wuld yu g t? Use statistics frm the displays t justify yur answer. Cmpany A Cmpany B Cmpany C Explain yur answer belw: Nte: The scale ges frm 0 t : Calculate the mean and standard deviatin f the fllw data set: 15, 18, 21, 14, 23, 12, 15, 18, 20, 20, 19, 18 A. mean = standard deviatin = 3.19 B. mean = standard deviatin = 3.06 C. mean = 18 standard deviatin = D. mean = 18 standard deviatin =

20 77: Calculate the median f the fllw data set: 15, 18, 21, 14, 23, 12, 15, 18, 20, 20, 19, 18 78: A. median = B. median = 13.5 C. median = 15 D. median = 18 Mr. Shapir fund that the amunt f time his students spent ding mathematics hmewrk is psitively crrelated with test grades in his class. He is cncluding that ding hmewrk makes his students test scres higher. Explain any flaws in Mr. Shapir s reasning: 79: Dr. Wilsn nticed that as her patients ate mre brccli, their chlesterl levels drpped. She cncluded that eating brccli causes lwer chlesterl levels in the bld. Explain any flaws in Dr. Wilsn s cnclusin: 20

21 80: The fllwing scatter plt shws the ttal fuel cst fr a train run frm San Francisc t Seattle fr trains with different numbers f cars attached t the lead engine. Fuel Cst vs Train Length Fuel Cst (in thusands) The assciated leastsquares regressin equatin is: = 0.84(Number f Cars) Number f Train Cars Fuel Cst Use the abve equatin t predict the ttal fuel cst fr a train with 50 cars. Cmment n any cncerns yu may have with using this equatin t make such a predictin: 81: Due t budget cnstraints at a particular cmpany, every emplyee receives a 2% decrease t their salary. What impact des this salary decrease have n the mean and n the range f emplyee salaries at the cmpany? A. The mean and range bth decrease. B. The mean and range d nt change. C. The mean des nt change but the range decreases. D. The mean decreases but the range des nt change. 21

22 82: At a particular cmpany, every emplyee receives a 4% cst-f-living increase t their salary. What impact des this cst-f-living increase have n the mean and n the range f emplyee salaries at this cmpany? 83: A. The mean increases but the range des nt change. B. The mean des nt change but the range increases. C. The mean and range bth increase. D. The mean and range d nt change. Suppse that a distributin f a set f numbers has a mean 20 and a standard deviatin f 5. If 2 is added t each scre, what will the new mean and standard deviatin f this set f numbers? 84: mean standard deviatin A B C D Suppse that a distributin f a set f numbers has a mean 20 and a standard deviatin f 5. If 2 is multiplied t each scre, what will the new mean and standard deviatin f this set f numbers? mean standard deviatin A B C D

23 85. A scatterplt is shwn. y x Which statement describes the crrelatin f the data graphed in the scatterplt? O A. O B. O C. O D. Strng negative Strng psitive Weak negative Weak psitive 86: Write a recursive frmula fr the arithmetic sequence 5, 9, 13, 17 What is the slpe f the line that cntains these pints. Hw is the slpe related t the sequence? A. a n = a n-1 + 4; a 1 = 5, m=4, linear functin B. a n = a n-5 + 1; a 1 = 1, m=4, quadratic functin C. a n = a n-1 + 4; a 1 = 5, m=5, quadratic functin D. a n-1 = a n + 4; a 1 = 5, m=1, linear functin 87: Given the recursive functin a n = a n with a 1 = 1, what are the values at a 2, a 3 A. 5, 10 B. 2, 6 C. 6, 11 D. 1, 6 88: Write the recursive frmula fr the gemetric sequence 5, 10, 20, 40 and determine the 20 th term. A. a n = 5 2 n-1, 2,621,440 B. a n+1 = 2a n, 2,621,440 C. a n = 5 2 n-1, 5,242,880 D.. a n+1 = 2a n, 5,242,880 23