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