Algebra II Honors - Midterm Exam Review **All questions are NO CALCULATOR, unless specified.**

Chapter1

1.Forthefunctiony=–x2–6x–7,findthevertexandaxisofsymmetry.

Ⓐvertex(3,–2);axisofsymmetryx=3Ⓑvertex(–3,2);axisofsymmetryx=4Ⓒvertex(–3,2);axisofsymmetryx=–3Ⓓvertex(3,–2);axisofsymmetryx=–4

2.Ifthegraphofy=ax2+bx+copensdown,whichofthefollowingmustbetrue?

Ⓐa<0 Ⓑa>0Ⓒc<0 Ⓓc>0

3.Whichfunctiondoesnothaveamaximumvalue?

Ⓐy=–x2–5x–6Ⓑy=–x2–x–6Ⓒy=3x2–15x+2Ⓓy=49–x2

4.Whatisthevertexofy=–3(x–2)2–4?Ⓐ(–2,–4) Ⓑ(–2,4)Ⓒ(2,–4) Ⓓ(2,4)

5.Whatarethex–interceptsofy=–2(x–7)(x+2)?

Ⓐ–7and2 Ⓑ7and–2Ⓒ14and–4 Ⓓ14and–2

6.Factortheexpressionm2–4m–21.

Ⓐ(m–7)(m–3) Ⓑ(m–7)(m+3)Ⓒ(m+7)(m–3) Ⓓ(m+7)(m+3)

7.Whichvalueofcmakestheexpressionx2–5x+caperfectsquaretrinomial?

Ⓐ 52

− Ⓑ 52

Ⓒ 254 Ⓓ25

8.Whataretherootsoftheequationz2+11z–42=0?

Ⓐ–3,–14 Ⓑ3,–14Ⓒ–3,14 Ⓓ3,14

9.Factortheexpression8x2+28x+12.Ⓐ2(x+2)(4x+3)Ⓑ2(x+3)(2x+1)Ⓒ4(x+1)(2x+3)Ⓓ4(x+3)(2x+1)

10.Simplifytheexpression 22 3+

Ⓐ 413 Ⓑ2

Ⓒ 4 2 3− Ⓓ 4 2 35

−

−

11.Whatarethesolutionsoftheequationw2=–9w?

Ⓐ–9,3 Ⓑ0,–9Ⓒ0,9 Ⓓ1,9

12.Whatarethesolutionsof23=2(x–3)2+7?Ⓐ 3± Ⓑ3 2 2±

Ⓒ 2 2± Ⓓ6 4 2±

13.Whatarethesolutionsof–3–y2=24?Ⓐ 3 3± Ⓑ 3 3i±

Ⓒ 9 3± Ⓓ 9 3i±

14.Whatisthestandardformofthe

expression2ii+?

Ⓐ 1 12i + Ⓑ 2 1

3i −

Ⓒ 12i+ Ⓓ 2 1

5 5i+

15.Whatisthevertexofy=3x2–30x+77?

Ⓐ(–5,–2) Ⓑ(–5,2)Ⓒ(5,–2) Ⓓ(5,2)

16.Whatisthevalueofcifthediscrimantof–2x2–3x+cis41?

Ⓐ–4 Ⓑ4

Ⓒ112 Ⓓ 25

4

17.Howmanyrealnumbersolutionsdoestheequation7x2–5x+1=0have?

18.Arectangulargardenis25feetlongby10feetwide.Youhaveenoughmulchtocover1000squarefeet.

a.Youwouldliketoextendboththelengthandthewidthofthegardenbyxfeettouseupallofthemulch.Writeanequationtorepresenttheareaofthenewgarden.

b.Solvetheequationfrompart(a).c.Whichsolutiondoyouhavetoreject?Explain.

19.Graphthefunctiony=x2–2x+1.Labelthevertexandtheaxisofsymmetry.

20.Tellwhetherthefunctiony=x2–5x+6hasaminimumvalueoramaximumvalue.Thenfindthatvalue.

21.Graphthefunctiony=2(x–1)2.Labelthevertexandtheaxisofsymmetry.

22.Graphthefunctiony=–(x+2)(x–2).Labelthevertex,theaxisofsymmetryandthex–intercepts.

23.Writethequadraticfunctiony=2(x+3)(x–1)instandardform.

24.Writethequadraticfunctiony=5(x–2)2–5instandardform.

25.Determinewhichnumbersetseachquantitybelongsto.

a.4.35 b. 49 c.− 34 d.π

26.Statethedomainandtherangeofeachfunctioninintervalnotation.

27.Statethedomainandtherangeofeachfunctioninintervalnotation.

28.Writetheequationoftheparabolawiththegivenvertexandpoint.vertex(-3,1)passingthrough(2,-4)

Chapter2

1.Whatisthesimplifiedformof2 1

3

8 ?12a bcab c

−

Ⓐ2 223ab c Ⓑ 2 2

23ab c

Ⓒ 2

23ab Ⓓ 2

3abc

2.Whatis(3.2×105)(1.4×10–2)writteninscientificnotation?

Ⓐ4.48×103 Ⓑ4.48×107Ⓒ44.8×103 Ⓓ44.8×107

3.Whichequationisthegraphofthepolynomialfunctionshown?

Ⓐf(x)=–2x3+x2–2Ⓑf(x)=3x4–x2+1Ⓒf(x)=x3–x+7Ⓓf(x)=–2x4+x2–1

4.Whatisthedegreeofthepolynomialh(t)=–8t2+5–3t3?

Ⓐ1 Ⓑ2 Ⓒ3 Ⓓ4

5.Whatisthegreatestcommonmonomialfactorof9x3y2+15x2y–6xy2?

Ⓐ3x2 Ⓑ3y2Ⓒ3xy Ⓓ3x2y2

6.Givenf(x)=3x–5evaluatef-1(0).

7.Whatisthecompletefactorizationof3x4–3x2?

Ⓐ3x2(x2–1)Ⓑ3x2(x–1)(x+1)Ⓒ3x(x–1)(x+1)Ⓓ3(x4–x2)

8.Ifx+3isafactorofx3–x2–17x–15,whatisanotherfactor?

Ⓐx+1 Ⓑx–1Ⓒx+5 Ⓓx–3

9.Ifx–2isafactorofapolynomialf(x),whichofthefollowingstatementsdoesnothavetobetrue?

Ⓐf(2)=0Ⓑf(–2)=0Ⓒ2isarootoff(x).Ⓓ2isazerooff(x)

10.Whichisnotapossiblerationalsolutionoff(x)=3x3–11x2+5x–6?

Ⓐ 12

± Ⓑ 23

±

Ⓒ± 2 Ⓓ± 6

11.Howmanyzerosdoes0=–7m3–m4+1have?

12.Usedirectsubstitutiontoevaluate2x3–4x2+8x–3forx=–2

13.Usesyntheticsubstitutiontoevaluate4x4–2x3–3x2+3xforx=2.

14.Graphf(x)=–x4+1.

15.Performtheindicatedoperation.(x+4)2(x–2)

16.Performtheindicatedoperation.(x3+2x–1)–(2x2+4x–2)

17.Factorthepolynomialcompletelyusinganymethod.x3+3x2+x+3

18.Divide.(x3–4x2–2x+3)÷(x+1)

19.Findallrealzerosoff(x)=x3–7x–6. 20.Graphthefunctionf(x)=(x+1)2(x+4).

21.Identifytheendbehaviorforeachofthefollowing.a.f(x)=-3x4+3x2+1 b.f(x)=5x(3x–1)2

22.Whichpolynomialrepresentsthevolumeoftheconeshown?

Ⓐ 323xπ – πx2–4πx+ 20

3π

Ⓑ 220 103 3 3

xxπ π π+ −

Ⓒ2

3xπ− 4πx+ 20

3π

Ⓓ34

3xπ+ 4πx2–5πx– 50

3π

Chapter31.Whatisthevalueof(–243)3/5?Ⓐ–27 Ⓑ–3Ⓒ3 Ⓓ27

2.Whatisthesolutionto3x5+350=–379?

Ⓐ5

7293

− Ⓑ–3

Ⓒ3 Ⓓ5

7293

3.Whichexpressionisthesimplestformof3 34 32 32−

Ⓐ 33 4 Ⓑ 36 4

Ⓒ6 Ⓓ 316 2 4−

4.Whatisthesimplifiedexpressionofthelengthofthetriangle’shypotenuse?

Ⓐ 3 2 1 22 3x x+ Ⓑ2x3/2+3x1/2Ⓒ 34 9x x+ Ⓓ4x3+9x2

5.Whatisthesimplifiedformof2 3 716 3 36 ?z z z− +

Ⓐ 3z z− Ⓑ 314z z

Ⓒ 414z z Ⓓ 392z z

6.Ifh(t)=t2/3–9andj(t)=3t+5t2/3,whatish(t)–j(t)?

Ⓐ–4t2/3–3t–9 Ⓑ4t2/3+3t+9Ⓒ3t+6t4/3 Ⓓ–7t7/3–9

7.Whatisg(f(x))iff(x)=3x2andg(x)=2x1/2?

Ⓐ 6x Ⓑ 2 x 3

Ⓒ6 x Ⓓ6x

8.Givenu(x)= 4 1x− andv(x)=x–5whatisthedomainofu(v(x))?

ⒶAllrealnumbers Ⓑx≥0

Ⓒx≥ 14 Ⓓx≥ 21

4

9.Whichfunctionrepresentstheinverseofthegraphshown?

Ⓐy=–5x+3 Ⓑy= 15x–3

Ⓒy= 15x+3 Ⓓy=5x+3

10.Whatistheinverseofthepowerfunction

g(t)=– 827t3?

Ⓐh(t)=– 323t Ⓑh(t)=– 38

27t

Ⓒh(t)=– 332t Ⓓh(t)=– 3

2t

11.Whichofthefollowingpairsoffunctionsarenotinversesofoneanother?

Ⓐu(x)=x–2;v(x)=x+2

Ⓑu(x)=5x–1;v(x)= 15x + 1

5

Ⓒu(x)=x3+1;v(x)= x −13

Ⓓu(x)= 2x − ;v(x)=x2+2

12.Thegraphofy= x isshifted2unitsupand3unitstotheleft.Whichistheequationofthetranslatedfunction?

Ⓐy= 2x − –3

Ⓑy= 2x + –3

Ⓒy= 2x + +3

Ⓓy= 3x + +2

13.Whatarethedomainandrangeofthefunctiony=5 2x − ?

ⒶDomain:allrealnumbers;range:allrealnumbers

ⒷDomain:x≥2;range:allrealnumbersⒸDomain:allrealnumbers;range:y≥0

ⒹDomain:x≥2;range:y≥0

14.Whatis(are)thesolution(s)tox–2= 2 1x− ?

Ⓐx=1 Ⓑx=5Ⓒx=1and5 ⒹNosolution

15.Solve(x–5)2/3–2=2?16.Evaluate–274/3withoutusingacalculator.

17.Verifythatfandgareinversefunctions.

f(x)=2x+5,g(x)= 52x −

18.Findtheinverseofthefunction.

f(x)= 2 53x+

19.Graphthefunction.Thenstatethedomainandrange.

y=2 2x + –2

20.Graphthefunction.Thenstatethedomainandrange.

y= 31 32x + –1

21.Solvetheequation.

4= 3 2 8x −

22.Solvetheequation.

x+2= 28 x−

23.Solvetheequation.

3 5x + = 4 2x−

24.Letf(x)=2x3–5andg(x)=3x2.Performtheindicatedoperationandstatethedomain.

f(g(x))

25.Identifytheremainder.

a. 4x4 −3x2 +3x −1x2 − x +1

b.3x5 − 4x3 + 2x − 5( ) x +1( )−1

Chapter41.Whichfunctionisshowninthegraph?

Ⓐf(x)=2(2.3)x–2Ⓑf(x)=4(2.3)xⒸf(x)=4(2.3)x+2Ⓓf(x)=5(2.3)x–3

2.Gasolinecosts$1.99pergallon.Ifthepricepergallonincreasesanaverageof6%permonth,whichfunctionmodelstheexponentialgrowthofthepricing?

Ⓐf(x)=1.06(1.99)xⒷf(x)=1.99(1.06)xⒸf(x)=[1.06(1.99)]x

Ⓓf(x)= 1.991.06x

3.Whichfunctionrepresentsexponentialgrowth?

Ⓐu(t)=–7.0 23

t⎛ ⎞⎜ ⎟⎝ ⎠

Ⓑu(t)=–7.0 32

t⎛ ⎞⎜ ⎟⎝ ⎠

Ⓒu(t)=7.0(0.8)t

Ⓓu(t)=7.0 109

!

"#

$

%&

−t

4.Whatisthehorizontalasymptoteofthefunctiony=2(0.3)x–1–4?

Ⓐy=–4 Ⓑy=0.3Ⓒy=2 Ⓓy=4

5.Whatisthesimplifiedexpressionof

( )237?

14

x

x

ee

Ⓐ 512

xe Ⓑ 812

xe

Ⓒ 29 –12

x xe Ⓓ 872

xe

6.Whichfunctiondoesnotmodelexponentialdecay?

Ⓐr(x)= –334

xe

Ⓑr(x)= –343

xe

Ⓒr(x)=4e–3x

Ⓓr(x)= 334

xe

7.Whichexpressionisequivalenttox?Ⓐlogx Ⓑlog2xⒸlog10x Ⓓlog10x

8.Whatisanequivalentexpressionfor2log43+log42?

Ⓐ2log46 Ⓑlog46Ⓒlog412 Ⓓlog418

9.Whichofthefollowingisnotequivalenttolog58?

Ⓐ ln 8ln 5

Ⓑ2log54

Ⓒ3log52 Ⓓlog54+log52

10.Whatistheinverseofthefunctiony=82x?

Ⓐy= ln2ln8x Ⓑy= 2 ln

ln 8x

Ⓒy= ln 82 ln x

Ⓓy= 2ln8ln x

11.Whatisthesolutiontotheequationlog44x+2log4x=4?

Ⓐ1 Ⓑ2Ⓒ3 Ⓓ4

12.Apheasantfarmerstartedherfarmwith120pheasants.Ananalysisofherrecordsshowsthatherpheasantpopulationhasincreasedby15%eachyear.Thefarmerwantstodetermineamodelofpheasantpopulationgrowthusinganexponentialfunction.Accordingtohermodel,whatwillthepheasantpopulationbein10years?

Ⓐ311 Ⓑ485Ⓒ501 Ⓓ1380

13.Whatisthevalueofxintheequation

3x=( )2 –101 ?

9

x⎛ ⎞⎜ ⎟⎝ ⎠

14.Graphthefunctiony=2•3x+1–2.Statethedomainandrange.

15.(Calculator)Yourgrandparentsdeposited$2000intoacollegesavingsaccountforyou5yearsago.Iftheaccountpays2.5%annualinterest,compoundedquarterly,findthecurrentbalanceofthesavingsaccount.

16.(Calculator)Youbuyacomputerfor$1200.Thevalueofthecomputerdecreasesby30%eachyear.Findthevalueofthecomputerafter4years.

17.Statethedomainandrangey=e–3x. 18.Evaluatethelogarithmwithoutusingacalculator.a.log525b.log1/381

c.10log5xd.log416x

19.Expandtheexpression.

a.In16x2

b.log532

4xy

20.Condensetheexpression.

a.log32x+3log34x

b.In72x–2In2y

21.Solve.

a.27(2x+4)=( –46)1

9

x⎛ ⎞⎜ ⎟⎝ ⎠

b.log2(x+8)=4

c.log6x+log6(x+16)=2

22.Statethedomainandrangeof

y=log3(x+2)–2.

ANSWERSCh11.C 2.A 3.C 4.C 5.B 6.B 7.C 8.B9.D 10.C 11.B 12.B 13.B14.D15.D 16.B 17.018.a.1000=(10+x)(25+x)b.x=15orx=–50c.x=–50becauseyoucannothaveanegativelength.19.

20.minimum;−1/ 4 21.

22.

23.y=2x2+4x–624.y=5x2–20x+1525.a)R,Q b)R,Q,Z,W,

N,Dc)R,Q d)R,I,T

26.D: −∞,∞( ) R: −4, 4[ ] 27.D: −∞,3( ] R: −∞, 2( ]

28.y=−15(x+3)2+1

Ch21.B 2.A 3.A 4.C 5.C

6.53

7.B 8.A9.B 10.A 11.412.–5113.4214.

15.x3+6x2–3216.x3–2x2–2x+117.(x+3)(x2+1)18.x2–5x+319.–2,–1,320.

21.

a)x→∞, f x( )→−∞

x→−∞, f x( )→−∞ b)

x→∞, f x( )→∞

x→−∞, f x( )→−∞

22.A

Ch31.A 2.B 3.B 4.C 5.B 6.A 7.B8.D 9.C 10.C 11.D 12.D 13.D14.B15.13,-316.–8117.f(g(x))=x,g(f(x))=x

18.f–1(x)=3 52x −

19.

20.

21.3622.323.724.54x6–5;allrealnumbers

Ch41.C2.B3.B4.A5.A6.D7.C8.D9.B10.A11.D12.B13.414.

15.$2265.4216.$288.1217.

18.a.2b.-4c.5xd.2x19.a.In16+2lnxb.3log5x+log52–log5y–log54

20.a.log3128x4b.ln 2

18xy

21.a.10b.8c.222.

domain:allrealnumbers;range:allrealnumbers

domain:x≥–2;range:y≥–2

domain:allreals;range:y>–2

domain:allreals;range:y>0

domain:x>-2;range:allreals