2025年美國(guó)托福數(shù)學(xué)真題及答案

一、單項(xiàng)選擇題，(總共10題，每題2分)。1.If\(x+3=7\),then\(x\)isequalto:A.4B.3C.7D.10答案：A2.Theareaofarectanglewithlength12cmandwidth5cmis:A.17cm2B.60cm2C.30cm2D.15cm2答案：B3.Whatisthevalueof\(\frac{3}{4}\div\frac{1}{2}\)?A.\(\frac{1}{2}\)B.\(\frac{3}{2}\)C.\(\frac{4}{3}\)D.\(\frac{2}{3}\)答案：B4.If\(2x-5=11\),then\(x\)isequalto:A.8B.7C.6D.5答案：A5.Thesumoftheinterioranglesofatriangleis:A.90degreesB.180degreesC.270degreesD.360degrees答案：B6.Anumberisdivisibleby6ifitisdivisibleby:A.2onlyB.3onlyC.2and3D.4答案：C7.Thevalueof\(\sqrt{49}\)is:A.7B.-7C.49D.-49答案：A8.Ifatraintravelsataspeedof60milesperhour,howfarwillittravelin3hours?A.20milesB.180milesC.90milesD.360miles答案：B9.Theslopeofalinepassingthroughthepoints(1,2)and(3,6)is:A.1B.2C.3D.4答案：B10.Theequationofalinewithslope2andy-intercept3is:A.\(y=2x+3\)B.\(y=3x+2\)C.\(y=\frac{1}{2}x+3\)D.\(y=3x-2\)答案：A二、多項(xiàng)選擇題，(總共10題，每題2分)。1.Whichofthefollowingareprimenumbers?A.2B.3C.4D.5答案：A,B,D2.Thefactorsof12are:A.1B.2C.3D.4E.6F.12答案：A,B,C,D,E,F3.Thesolutionstotheequation\(x^2-4=0\)are:A.2B.-2C.4D.-4答案：A,B4.Theanglesinaquadrilateralare:A.90degreesB.120degreesC.180degreesD.360degrees答案：C,D5.Thecoordinatesofthemidpointofalinesegmentwithendpoints(2,3)and(4,7)are:A.(3,5)B.(2,5)C.(3,7)D.(4,3)答案：A6.Thepropertiesofrealnumbersinclude:A.CommutativepropertyB.AssociativepropertyC.DistributivepropertyD.Identityproperty答案：A,B,C,D7.Thefunctions\(f(x)=x^2\)and\(g(x)=2x\)are:A.LinearB.QuadraticC.Neither答案：B,C8.Thesolutionstotheinequality\(2x+3>7\)are:A.\(x>2\)B.\(x<2\)C.\(x>4\)D.\(x<4\)答案：C9.Thegeometricmeanof4and9is:A.2B.3C.4D.6答案：B10.Theprobabilityofrollinga6onafairsix-sideddieis:A.\(\frac{1}{6}\)B.\(\frac{1}{3}\)C.\(\frac{1}{2}\)D.1答案：A三、判斷題，(總共10題，每題2分)。1.Thenumber0isaprimenumber.答案：False2.Thesumoftheanglesinapentagonis360degrees.答案：False3.Theequation\(x+5=5\)hasasolution.答案：True4.Thenumber\(\sqrt{16}\)isequalto-4.答案：False5.Theslopeofahorizontallineisundefined.答案：False6.Theproductoftwonegativenumbersispositive.答案：True7.Themedianofatriangleisalinesegmentjoiningavertextothemidpointoftheoppositeside.答案：True8.Theequation\(2x=4\)isequivalentto\(x=2\).答案：True9.Theareaofacircleisgivenbytheformula\(A=\pir^2\).答案：True10.Themodeofasetofnumbersisthenumberthatappearsmostfrequently.答案：True四、簡(jiǎn)答題，(總共4題，每題5分)。1.Explainthedifferencebetweenanequationandanexpression.答案：Anequationisamathematicalstatementthatassertstheequalityoftwoexpressions,typicallyinvolvingvariablesandconstants.Itiswrittenwithanequalsign(=)andrepresentsabalancebetweenthetwosides.Anexpression,ontheotherhand,isacombinationofnumbers,variables,andoperators(suchasaddition,subtraction,multiplication,anddivision)thatrepresentsavaluebutdoesnotcontainanequalsign.Forexample,\(3x+4\)isanexpression,while\(3x+4=10\)isanequation.2.WhatisthePythagoreantheoremandhowisitused?答案：ThePythagoreantheoremstatesthatinaright-angledtriangle,thesquareofthelengthofthehypotenuse(thesideoppositetherightangle)isequaltothesumofthesquaresofthelengthsoftheothertwosides.Itisexpressedas\(a^2+b^2=c^2\),where\(c\)isthelengthofthehypotenuseand\(a\)and\(b\)arethelengthsoftheothertwosides.Thistheoremisusedtofindthelengthofonesideofaright-angledtrianglewhenthelengthsoftheothertwosidesareknown.3.Describethedifferencebetweenmean,median,andmode.答案：Themeanistheaverageofasetofnumbers,calculatedbysummingallthenumbersanddividingbythecountofnumbers.Themedianisthemiddlenumberinasortedlistofnumbers,ortheaverageofthetwomiddlenumbersifthelisthasanevennumberofelements.Themodeisthenumberthatappearsmostfrequentlyinasetofnumbers.Thesethreemeasuresprovidedifferentinsightsintothecentraltendencyofadataset.4.Explaintheconceptofafunctioninmathematics.答案：Afunctioninmathematicsisarelationbetweenasetofinputsandasetofpermissibleoutputs,whereeachinputisrelatedtoexactlyoneoutput.Functionsaretypicallydenotedbyaletter(suchas\(f\))andcanberepresentedbyequations,graphs,orothermeans.Forexample,\(f(x)=x^2\)isafunctionthattakesaninput\(x\)andoutputsitssquare.Functionsarefundamentalinmathematicsandareusedtomodelvariousreal-worldphenomena.五、討論題，(總共4題，每題5分)。1.Discusstheimportanceofunderstandingfractionsineverydaylife.答案：Understandingfractionsiscrucialineverydaylifeastheyareusedinvariouscontextssuchascooking,measuring,andmanagingfinances.Incooking,fractionshelpinfollowingrecipesaccuratelybymeasuringingredientslike\(\frac{1}{2}\)cupofsugar.InconstructionandDIYprojects,fractionsareusedformeasuringlengthsandangles.Additionally,fractionsareessentialinmanagingfinances,suchascalculatingdiscounts,interestrates,anddividingbillsamongpeople.Asolidunderstandingoffractionsenhancesproblem-solvingskillsandpracticallifeskills.2.Explainhowgeometryisusedinarchitecture.答案：Geometryplaysavitalroleinarchitectureasitprovidesthefoundationfordesigningandconstructingbuildingsandstructures.Architectsusegeometricprinciplestocreateaestheticallypleasingandfunctionaldesigns.Forexample,theuseoftrianglesensuresstabilityinstructures,whilecirclesandarcsareusedincreatingdomesandarches.Geometryalsohelpsincalculatingthedimensionsandspatialrelationshipsofdifferentcomponentsofabuilding,ensuringthatitmeetsbothpracticalandaestheticrequirements.Understandinggeometryenablesarchitectstocreatestructuresthatarebothsafeandvisuallyappealing.3.Discussthesignificanceofalgebrainsolvingreal-worldproblems.答案：Algebraissignificantinsolvingreal-worldproblemsasitprovidesasystematicwaytorepresentandsolveequationsandinequalitiesthatariseinvariousfields.Inbusiness,algebraisusedtoanalyzefinancialdata,optimizeprofits,andmanageresources.Inscience,algebrahelpsinformulatingandsolvingequationsthatdescribephysicalphenomena,suchasmotionandchemicalreactions.Inengineering,algebraisessentialfordesigningandanalyzingsystemsandstructures.Byusi