number sense poway unified school district数感宝威学区.doc

number sense poway unified school district数感宝威学区 POWAY UNIFIEDSCHOOL DISTRICTAelerated PRE-ALGEBRA STANDARDSAND EXEMPLARSSPRING,xx1.1NUMBER SENSERead,write,and parerational numbersin scientific notation(positive andnegative powersof10)with approximatenumbers usingscientifiotation.?Write548,200in scientifiotation3111?Write0.00147in scientifiotation?The radiusof theearths orbitis150,000,000,000meters.What isthis number in scientifiotation?a)1.510?b)1.510?c)1510?d)15010?a)3.6000b)36c)360d)3,6001.2*Add,subtract,multiply,and dividerational numbers(integers,fractions,and terminatingdecimal)and takepositive rational numbers towhole-number powers.?34(63)7(4+(2)133511?48?,.6(3.21)Write7.28x10?4in standardnotation Write0.00591x108in standardnotation11111093.6x102=?422?7?2?1315105058110.6(3.21)?The fivemembers of a bandare gettingnew outfits.Shirts cost$12each,pants cost$29each,and bootscost$49a pair.What is the totalcost of the newoutfits for all of the members?a)$90b)$95c)$45023?.?141?d)$500Simplify:11?131412?a)13345695b)c)d)?23.065?(?10.5)3(?4+12)+7(?3)43213?079?325?1.785?0.0984(1.23)(4.78)Write theprime factorizationof72.Which of the followingnumerical expressionsresults in a negativenumber?a)(?7)+(?3)b)(?3)+ (7)c) (3)+ (7)d) (3)+(?7)? (11)3244?a)45b)46c)165d)166One hundredis multiplied by a number between0and1.The answerhas tobe a)Less than0.b)Between0and50but not25.c)Between0and100but not50.d)Between0and100.Which is the bestestimate of326x279?a)900b)9,000c)90,000d)900,000?The winningnumberin a contestwas lessthan50.It wasa multipleof3,5,and6.What was the number?a)14b)15c)30d)It cannot be determined.Convert fractionsto decimalsand percentsand use these representationsin estimations,putations,and applications.Convert78Convert56237?There is a20%off saleon sweaters.The listprice is$25.00.Find the sales price.?If Freyamakes4of her5free throwsin a basketball game,what isher freethrow shootingpercentage?a)20%b)40%c)80%d)90%?Some studentsattend school180of the365days ina year.About whatpart of the yeardo theyattend school?a)18%b)50%c)75%d)180%?A pairof jeansregularly sells for$24.00.They areon salefor25%off.What is the saleprice of the jeans?a)$6.00b)$18.00c)$20.00d)$30.00?What is the fractionalequivalent of60%?16363523?A CDplayer regularlysellsfor$80.It ison salefor20%off.What is thesaleprice of the CD1.3?to a decimal.?to apercent.?is betweenwhich twowhole numbers?a)b)c)d)player?a)b)$60c)$64d)$96$161.4*Differentiate betweenrational andirrational numbers.?Define rational numbers.?Define irrationalnumbers.?Label the following numberswith an“R”for rationalor an“I”for irrational:8?916?22525?1.271.212112111?9.85?1.5*Know thatevery rationalnumber iseither aterminating orrepeating decimaland beable toconvert terminatingdecimals intoreduced fractions.?Convert the following into adecimal:1256511?Convert the following into a fraction:?0.27?1.45?0.27271.6Calculate the percentage of increases anddecreases of a quantity.?Calculate the percent ofincrease:?From1to1.2?From3to6?From5to18?Calculate the percent of decrease:?From1to0.8?From14to7?From15to4?The costof an afternoon movie ticket last year was$4.00.This yearanafternoonmovieticketcost$5.00.What isthepercent ofincreaseof theticket fromlastyearto thisyear?a)10%b)20%c)25%d)40%?The price of a calculator hasdecreased from$12.00to$9.00.What isthepercentof decrease?a)b)25%c)33%d)75%3%1.7*Solve problemsthat involvediscounts,markups,missions,and profitand putesimple andpound interest.?What is15%of36?16is whatpercentof64?A realestate agentearned5%mission on a$200,000house.What isher mission?If ashirt ison salefor$25and itoriginally soldfor$30,what isthepercentof decrease?Sally puts$200.00ina bank aount.Each yearthe aountearns8%simple interest.How muchinterest will be earnedin threeyears?a)$16.00b)$24.00c)$48.00d)$160.00?Sally puts$200ina bank at8%interest poundedyearly.How muchpound interestwillbeearning in3years?*STUDENTS NEEDTO BEABLE TOESTIMATE PERCENTS(MULTIPLES OFTEN)WITHOUT ACALCULATOR.2.1Understand negative whole-number exponents.Multiply and divide expressionsinvolving exponentswith amon base.?Simplify:?2?212?33?655266?210102.2*Add andsubtract fractionsby usingfactoring to find mon denominators.?Simplify:112849116399243272?24?322?4?3?4?Which of the followingistheprime factoredform of the lowestmondenominatorof781015a)5x1b)2x3x5c)2x5x3x5d)10x152.3*Multiply,divide,and simplifyrationalnumbersby usingexponent rules.c)3d)33222.4Use theinverse relationshipbetween raisingtoapower and extracting theroot of a perfectsquare integer;for aninteger thatis notsquare,determine withoutacalculatorthe two integers betweenwhich itssquare rootlies andexplain why.?25?Evaluate forx=2,y=?3,and z=5?2333?3223?a)b)10x3y2z2+y(x3)2?283=436316?5?169100?Find theside of a squarewith anarea of81units2.Determine whichtwointegersthe radicalis in between:37?99?12814?The squareroot of150is between a)10and11b)11and12c)12and13d)13and14The squareof awhole numberis between1,500and1,600.The numbermust bebetweena)30and35?b)35and40c)40and45d)45and502.5*Understand themeaning of the absolute value of a number;interpret the absolutevalueas thedistance of the numberfrom zero on anumber line;and determihe absolutevalue ofreal numbers.?Simplify|9|,|83|?True orfalse?1919?49?5?If|x|=3,what isthe value of x?a)?3or0b)?3or3c)0or3d)?9or9What istheabsolutevalue of?4?a)?414c)14d)4ALGEBRA ANDFUNCTIONSe orinequalities thatrepresent averbal description(e.g.,three lessthan anumber,half aslarge asarea A).Use variableand appropriateoperations towrite anexpression,an equation,an inequality,or asystem ofequations orinequalities thatrepresent averbal description(e.g.,three lessthan anumber,half aslarge asarea A).?Five lessthan3times anumber.?The length of a rectangle isfour more than thewidth.If the perimeter is20,find thewidth.?Four timesan unknownis lessthan12.?Which of the followinginequalities representthe statement,“A number,x,decreased by13is lessthan orequal to39”?a)1339x?b)1339x?c)1339x?d)1339x?A shopkeeperhas xkilograms oftea instock.He sells15kilograms and then receivesa newshipment weighting2y kilograms.Which expressionrepresents theweight of the teahe nowhas?a)152xy?b)152xy?c)152xy?d)152xy?Divide anumber by5and add4to theresult.The answeris9.Which of the followingequations matches these statements?b)?1.1a)495n?b)4955n?n?n?c)4d)495?In acertain room,the number of chairs,c,is equalto3times the number oftables,t.Which equationmatchestheinformation?a)3?c=tb)3?t=c c)3?c=3?t d)c?t=3Use thecorrect orderof operationsto evaluatealgebraic expressionssuch as3(2x+5)2.?If x=2,y=3and z=1,evaluate:a.x5b.3x+2yz3yx?1.2c.4d.e.8(x2y)3(2x+5)2Simplify:?(5y)+(4)+(x)+(2y)(7y)?4b9b+7b?3x5+4x2?2(2x+1)3(x4)?(2x?4)?If h=3,and k=4,then422hk?a)b)7c)d)10681.3*Simplify numericalexpressions by applying propertiesof rationalnumbers(e.g.,identity,inverse,distributive,associative,mutative)and justifythe processused.?Name theproperty illustratedby eachof the following:o x(y+?y)=x (0)o x(y+?y)=xy+x(?y)o x(y+?y)=(y+?y)(x)o x(y+?y)=x(?y+y)1() (1)x yxy?1.4Use algebraicterminology(e.g.,variable,equation,term,coefficient,inequality,expression,constant)correctly.o?1.5?Embedded Representquantitative relationshipsgraphically andinterpret themeaning of a specificpart of a graphin thesituation representedby the graph.?Consider thecircle graph shown below.How manyhours aday doesRamon spendin school?a)2hours b)4hours c)6hours d)8hours?After threehours of travel,Car Ais abouthow manykilometers aheadof CarB?a)2b)10c)20d)25?The graph above showsthe timeoftravelby pupilsfrom hometo school.How manypupils musttravel for morethan10minutes?a)2b)5c)7d)8?The costofalong distancecall chargedby eachof twotelephone paniesis shownon the graph below.Company Ais lessexpensive thanCompany Bfor a)All callsb)3minutes callonly c)calls lessthan3minutes d)calls longerthan3minutes?The graphbelow showsthe value of Whistler Company stock at the end ofevery otheryear from1994to2000.From thisgraph,which of the followingwas themost probablevalueofWhistlerCompanystockat theendof1992?a)?$10b)$1c)$10d)$20Interpret positivewhole-number powersas repeatedmultiplication andnegativewhole-number powersas repeateddivision ormultiplication bythe multiplicativeinverse.Simplify andevaluate expressionsthat includeexponents.?Simplify:o(x3)4(3x4)2(2xy2)(3x4y)m3m2m6?Simplify:2x3?x y?a)9xy2.1ooo33b)(xy)6c)3xy d)xxxyyy3?5XXx y?325x y?Simplify theexpression shown below. (5)(8x z2640x zb)40x zc)40x zd)40x z?Simplify (6)(7a bc4313a bc b)13abc c)42abc d)42abc Multiplyanddividemonomials;extend theprocess oftaking powersandextractingroots tomonomials when the latterresults ina monomialwith aninteger exponent.223)xz a)35365543)ab ca)542435422.2?44x?2b)2x c)4x d)2x2?3 (4)x?(2xya)x xy2)?2(3x x?2105x?21215xx3.1Graph functionsin theform y=nx2and y=nx3and usein solvingproblems.?Which of the followingcould be thegraphof3yx?n=counting number?Plot the values from the volumesof three-dimensional shapesfor variousvalues of the edgelengths(e.g.,cubes withvarying edgelengths ora triangleprism with a fixedheight andan equilateraltriangle baseof varyinglengths).3.3*Graph linearfunctions,noting that the verticalchange(change iny-value)per unitof horizontalchange(change in x-value)is always the sameand knowthat the ratio(“rise overrun”)is calledthe slope of thegraph.?Graph:y=2x4?Identify slope.y=nx2y=nx33.2?What isthe slope of the line shownin thegraphabove:a)?21212b)?c)d)2The slopeof theline shownbelow is2?3.What isthe valueofd?a)3b)4c)6d)932?Graph.y?Graph.2yx?313x11x?Graph.yx?Graph.?Graph.?Graph.43yy?x?Graph a line goingthrough thepoint(?3,2)having aslopeof12m?.?Find thex andy interceptsof4?Graph theline3x+2y=8.?What isthe slopeof theline to the right?520.xy?3.4*Plot thevalues ofquantities whoseratios arealwaysthesame(e.g.,cost tothe number of anitem,feet toinches,circumference todiameter ofa circle).Fit aline tothe plotand understandthat theslopeof thelineequals thequantities.?3223?2332?Given:?Write arule for the table.?Graph theabove charton acoordinate plane.?Best Burgersells cheeseburgersfor$1.75each.Part of the tablerepresenting the number ofcheeseburgers purchased and theircost isshownbelow.Which of the followingisaportion of thegraphof the data in the table?4.1*Solve two-step linearequations andinequalities inone variableover therationalnumbers,interpret the solution orsolutions in the contextfrom whichthey arose,and verifythe reasonableness of the results.?3?3x+1=7?4x+3.24=0.72m18=72x=8?3?Solve andgraph thesolution on anumberline:?P86?10x+7?3x108In theinequality2$10,000x?district.Which phrasemost auratelydescribes theemployees salary?a)At least$30,000b)At most$30,000c)Less than$30,000?70,000?,x representsthe salaryof anemployee ina schoolx y1210313416074d)More than$30,000Solve forx:2x3=7a)?5b)?2c)2d)5Solve forn.2n+317a)n2b)n3c)n5d)n7?A flowershop deliveryvan traveledthese distancesduring oneweek:104.4,117,8,92,3,168,7,and225.6miles.How manygallons ofgas wereused bythe deliveryvan duringthis week?What otherinformation is needed in order informationisneededinorderto solvethis problem?a)The average speed traveledin miles per hour b)The costof gasolineper gallonc)The averagenumberofmiles pergallon for the vand)The numberof differentdeliveries thevan made4.2*Solve multi-step problemsinvolving rate,average speed,distance,and timeoradirect variation.?2(x+1)3=22?6y4+3y=19?3(2w1)=15?5n10=4n+23x+6=12x?4?Before eachgame,the HarborHigh Mudcatssell programsfor$1.00per program.To printthe programs,the printercharges$60plus$0.20per program.How manyprograms doesthe teamhave tosell tomake aprofit of$200?A)250programs B)300programs C)325programs D)350programs Aperson drovefor6hours at an averagespeed of45miles per hour(mph)and for9hours atan averagespeed of55mph.Find the averagespeedfortheentire trip.A)50mph C)52mph B)51mph D)53mph d=rt Thediameter ofa treetrunk variesdirectly withthe ageof thetree.A45-year-old treehas atrunk diameterof18inches.What isthe ageofatree thathas atrunk diameterof20inches?a)47years b)50years c)63years d)90years Stephanieis readinga456-page book.During thepast7days,she hasread168pages.If shecontinues readingatthesame rate,how manymore dayswill ittake herto pletethe book?a)12b)14c)19d)24?Tina isfilling a45gallon tubatarate of1.5gallons owater perminute.At thisrate,how longwill ittake tofill thetub?a)30.0minutes b)43.5minutes c)46.5minutes d)67.5minutes Anairplane flies678miles fromSeattle toSan Francisco.The triptakes anhour anda half.What isthe airplanes averagespeed?a)402miles per hourb)422miles perhour c)432miles perhour d)452miles perhour MEASUREMENTAND GEOMETRYCompare weights,capacities,geometric measures,times,and temperatureswithin and between measurementsystems(e.g.,miles perhour andfeet persecond,cubic inchesto cubic centimeters).?How many square feetare in5square yards?Order thefollowing threespeeds fromfastest toslowest:3,100yd/hr,160ft/min,9,200ft/hr.?A boyis twometers tall.About howtall isthe boyin feet(ft)and inches(in)?(1meter?39inches)a)5ft0inb)5ft6in c)6ft0in d)6ft6in?Juanita exercisedfor onehour.How manyseconds didJuanita exercise?a)60b)120c)360d)3,600?One cubic inch isapproximately equalto16.38cubic centimeters.Approximately how many cubientimeters arethere in3cubic inches?a)5.46b)13.38c)19.38d)49.14?The tablebelow showsthe flighttimes fromSan Francisco(S.F.)to NewYork(N.Y.).?1.1Which flighttakes thelongest?a)The flightleaving at8:30A.M.b)The flightleaving at12:00noon c)The flightleaving at3:30P.M.d)The flightleaving at9:45P.M.Construct andread drawingsand modelsmade toscale.?If ahalf-inch representsa mileon amap,3?inches representshowmanymiles?The actualwidth(w)ofarectangle is18centimeters(cm).Use thescale drawing of the rectangle tofind theactual length(l).1.2a)b)24cm c)36cm d)54cm6cm?The scaledrawingof the basketball court shownbelow isdrawn usinga scaleof1inch(in)=24feet(ft).What isthe length,in feet,of thebasketballcourt?a)90ft c)114ft b)104ft d)120ft1.3*Use measuresexpressed asrates(e.g.,speed,density)and measureexpressed asproducts(e.g.,person-days)to solveproblems;check the units of the solutions;and usedimensional analysis to check the reasonablenessof theanswer.?Sixty miles perhouristhesame rateas which of thefollowing?a)1mile perminute b)1mile persecond c)6milesperminute d)360milespersecond?Beverly ransix milesatthespeed offour milesperhour.How longdid ittake herto runthat distance?23a)hr b)1124hrs hrsc)d)6hrs Useformulas routinelyfor findingthe perimeterand area of basictwo-dimensional figuresand the surface areaand volume of basicthree-dimensional figures,including rectangles,parallelograms,trapezoids,squares,triangles,circles,prisms,and cylinders.?Find the perimeter ofa parallelogramwith length4.7cm and width27.2cm.?Find the area ofa squarewith sides16cm long.?Find the volume:?In thefigure below,the radiusoftheinscribed circleis6inches(in).What istheperimeterof squareABCD?2.1a)b)36?in c)24in d)48in12?in?What isthe area oftheshaded regionin thefigure shownbelow?(Area ofa triangle12bh?)a)b)c)d)4cm26cm28cm216cm21.7cm7cm14cm?The largestpossible circleistobe cutfrom a10-foot squareboard.What willbetheapproximate area,in squarefeet,ofthe remaining board(shaded region)?(3.14Ar and?)a)20b)30c)50d)802?What isthe area ofthetriangle shownabove?12()Abh?a)b)60square unitsc)88square unitsd)120square units44square units?The twocircles shownabove haveradii of3cm and6cm.What isCircumferenceof CirclexCircumference ofCircle y?()Cd?1412?a)b)c)4d)2?A rectangularpool42feet by68feet isonarectangular lot105feet by236feet.The restofthelot isgrass.Approximately howmanysquarefeet isgrass?a)2,100b)2,800c)21,000d)28,000?What isthevolumeoftheshoebox shownabove incubic inches(in3)?a)29b)75c)510d)675?was wrongbecause thecorrect answershould beabout a)4x4x4=64b)3x3x40=360c)31x4x4=496d)3x40x40=4800Estimate andpute the areaofmore plexor irregulartwo-and three-dimensional figuresby breakingthe figuresdown intomore basicgeometric objects.?One-inch cubesare stackedas shownin thedrawing below.Louis calculatedtheareaofthecircle aboveand gotan answerof50.769cm2.He knowhis answer2.2What isthe totalsurface area?a)19in2b)29in2c)32in2d)38in2?In thefigure shownbelow,all thecorners formright angles.What istheareaofthefigure insquare units?a)67b)73c)78d)91?A right triangle isremoved fromarectangleas shownin thefigure below.Find theareaoftheremainingpart oftherectangle.a)b)44in2c)48in2d)52in240in2Compute the length oftheperimeter,the surface areaofthe faces,and thevolumeofa three-dimensional objectbuilt fromrectangular solids.Understand thatwhenthe lengths ofall dimensionsare multiplied byascale factor,thesurfacearea ismultipliedbythe squareofthescale factorand thevolume ismultipliedbythe cubeofthescale factor.?In thefigure above,an edge ofthelarger cubeis3times theedgeofthe smaller cube.What istheratioofthesurfaceareaofthesmallercubeto thatofthelarger cube?a)1:3b)1:9c)1:12d)1:272.3?A cerealmanufacturer needsa boxthat canh oldtwice asmuch cerealas the box shownbelow.Which ofthefollowingchanges willresult in the desiredbox?(v=lwh)a)Double theheight only.b)Double boththe lengthandwidth.c)Double boththelengthand height.d)Double thelength,width,and height.?The clubmembers hiked3kilometers northand4kilometers east,but thenwent directlyhome asshown bythe dottedline.How fardid theytravel toget home?a)4km b)5km c)6km d)7km Relatethe changesin measurementwithachange ofscale totheunitsused(e.g.,square inches,cubic feet)and toconversions betweenunits.?Identify andconstruct basicelements ofgeometric figures(e.g.,altitudes,midpoints,diagonals,angle bisectors,and perpendicular bisectors;central angles,radii,diameters,and chordsof circles)by usinga passand straightedge.?2.41square foot=_square inchesor1ft2=_in2,1cubicinch?_cubientimetersor1in3=_cm33.1?Constr