2008年河北省初中畢業生升學文化課考試數學試卷本試卷分卷和卷兩部分；卷為選擇題，卷為非選擇題本試卷滿分為120分，考試時間為120分鐘卷（選擇題，共20分）注意事項1答卷前，考生務必將自己的姓名、準考證號、科目填涂在答題卡上，考試結束，監考人員將試卷和答題卡一并收回2每小題選出答案后，用2B鉛筆把答題卡上對應題目的答案標號涂黑答在試卷上無效一、選擇題（本大題共10個小題；每小題2分，共20分在每小題給出的四個選項中，只有一項是符合題目要求的）1的倒數是（）8ABCD81182計算的結果是（）23AABCD2443A4A3把某不等式組中兩個不等式的解集表示在數軸上，如圖1所示，則這個不等式組可能是（）ABCD1X，1X，4X，4X，4據河北電視臺報道，截止到2008年5月21日，河北慈善總會已接受支援汶川地震災區的捐款15510000元將15510000用科學記數法表示為（）AB80540CD716155圖2中的兩個三角形是位似圖形，它們的位似中心是（）A點B點C點D點POMN6某縣為發展教育事業，加強了對教育經費的投入，2007年投入3000萬元，預計2009年投入5000萬元設教育經費的年平均增長率為，根據題意，下面所列方程正確的是X（）AB23010X2305CD52130150XX7如圖3，已知的半徑為5，點到弦的距離為3，則上OAAOA到弦所在直線的距離為2的點有（）B401圖1OPMN圖2OBA圖3A1個B2個C3個D4個8同時拋擲兩枚質地均勻的正方體骰子（骰子每個面上的點數分別為1，2，3，4，5，6）下列事件中是必然事件的是（）A兩枚骰子朝上一面的點數和為6B兩枚骰子朝上一面的點數和不小于2C兩枚骰子朝上一面的點數均為偶數D兩枚骰子朝上一面的點數均為奇數9如圖4，正方形的邊長為10，四個全等的小正方形的對稱中心分別在正方形AB的頂點上，且它們的各邊與正方形各邊平行或垂直若小正方形的邊長為BDAC，且，陰影部分的面積為，則能反映與之間函數關系的大致圖象是（X01YYX）XADCB圖4YX10O100AYX10O100BYX10O100C5YX10O100D10有一個四等分轉盤，在它的上、右、下、左的位置分別掛著“眾”、“志”、“成”、“城”四個字牌，如圖51若將位于上下位置的兩個字牌對調，同時將位于左右位置的兩個字牌對調，再將轉盤順時針旋轉，則完成一次變換圖52，圖53分別表示第1次變換90和第2次變換按上述規則完成第9次變換后，“眾”字位于轉盤的位置是（）眾志成城圖51成城眾志圖52志成城眾第1次變換城眾志成圖53成城眾志第2次變換A上B下C左D右2008年河北省初中畢業生升學文化課考試數學試卷卷（非選擇題，共100分）注意事項1答卷前，將密封線左側的項目填寫清楚2答卷時，將答案用藍色、黑色鋼筆或圓珠筆直接寫在試卷上二、填空題（本大題共8個小題；每小題3分，共24分把答案寫在題中橫線上）11如圖6，直線，直線與相交若，ABCAB，170則2_12當時，分式無意義X31X12BA圖6CCOAB圖713若互為相反數，則MN，5MN14如圖7，與相切于點，的延長線交于點，ABOBAOAC連結若，則C36_C15某班學生理化生實驗操作測試成績的統計結果如下表成績/分345678910人數1122891512則這些學生成績的眾數為16圖8所示的兩架天平保持平衡，且每塊巧克力的質量相等，每個果凍的質量也相等，則一塊巧克力的質量是G17點在反比例函數的圖象上，則231PM，YXM18圖91是我國古代著名的“趙爽弦圖”的示意圖，它是由四個全等的直角三角形圍成的若，將四個直角三角形中邊長為6的直角邊6AC5B分別向外延長一倍，得到圖92所示的“數學風車”，則這個風車的外圍周長是ABC圖91圖92三、解答題（本大題共8個小題；共76分解答應寫出文字說明、證明過程或演算步驟）19（本小題滿分7分）已知，求的值2X211X20（本小題滿分8分）某種子培育基地用A，B，C，D四種型號的小麥種子共2000粒進行發芽實驗，從中選出發芽率高的種子進行推廣通過實驗得知，C型號種子的發芽率為，根據實驗數據繪95制了圖101和圖102兩幅尚不完整的統計圖（1）D型號種子的粒數是；（2）請你將圖102的統計圖補充完整；（3）通過計算說明，應選哪一個型號的種子進行推廣；（4）若將所有已發芽的種子放到一起，從中隨機取出一粒，求取到B型號發芽種子的概率巧克力果凍50G砝碼圖8A35B20C20D各型號種子數的百分比圖101圖102ABCD型號8006004002000630370470發芽數/粒21（本小題滿分8分）如圖11，直線的解析表達式為，且與軸交于點，直線經過點，1L3YX1LXD2LAB，直線，交于點1L2C（1）求點的坐標；D（2）求直線的解析表達式；2L（3）求的面積；A（4）在直線上存在異于點的另一點，使得2LCP與的面積相等，請直接寫出點的坐標DP22（本小題滿分9分）氣象臺發布的衛星云圖顯示，代號為W的臺風在某海島（設為點）的南偏東方向的O45點生成，測得臺風中心從點以40KM/H的速度向正北方向移動，經B106KMOBB5H后到達海面上的點處因受氣旋影響，臺風中心從點開始以30KM/H的速度向北偏CC西方向繼續移動以為原點建立如圖12所示的直角坐標系60（1）臺風中心生成點的坐標為，臺風中心轉折點的坐標為C；（結果保留根號）（2）已知距臺風中心20KM的范圍內均會受到臺風的侵襲如果某城市（設為點）位于A點的正北方向且處于臺風中心的移動路線上，那么臺風從生成到最初侵襲該城要經過多O長時間23（本小題滿分10分）L1L2XYDO3BCA2（4，0）圖11X/KMY/KM北東AOBC6045圖12在一平直河岸同側有兩個村莊，到的距離分別是3KM和2KM，LAB，AB，LKMABA現計劃在河岸上建一抽水站，用輸水管向兩個村莊供水1ALP方案設計某班數學興趣小組設計了兩種鋪設管道方案圖131是方案一的示意圖，設該方案中管道長度為，且（其中于點）；圖132是方案二的示意圖，設1DKMPBABL該方案中管道長度為，且（其中點與點關于對稱，與2KDPALAB交于點）L觀察計算（1）在方案一中，KM（用含的式子表示）；1DA（2）在方案二中，組長小宇為了計算的長，作了如圖133所示的輔助線，請你按小宇2D同學的思路計算，KM（用含的式子表示）2探索歸納（1）當時，比較大?。ㄌ睢啊?、“”或“”）；4A12_D當時，比較大小（填“”、“”或“”）；6（2）請你參考右邊方框中的方法指導，就（當時）的所有取值情況進A1行分析，要使鋪設的管道長度較短，應選擇方案一還是方案二24（本小題滿分10分）如圖141，的邊在直線上，且；的邊也ABCLACBCEFP在直線上，邊與邊重合，且LEFEFP（1）在圖141中，請你通過觀察、測量，猜想并寫出與所滿足的數量關系和位A置關系；（2）將沿直線向左平移到圖142的位置時，交于點，連結，PLEQAABPLLABPC圖131圖132LABPC圖133K方法指導當不易直接比較兩個正數與的大小時，MN可以對它們的平方進行比較，2MN0與的符號相同當時，即；0當時，即；2NN當時，即；猜想并寫出與所滿足的數量關系和位置關系，請證明你的猜想；BQBAP（3）將沿直線向左平移到圖143的位置時，的延長線交的延長線于點EFLEPAC，連結，你認為（2）中所猜想的與的數量關系和位置關系還成立嗎BQA若成立，給出證明；若不成立，請說明理由A（E）BC（F）PLLLAABBQPEFFCQ圖141圖142圖143EPC25（本小題滿分12分）研究所對某種新型產品的產銷情況進行了研究，為投資商在甲、乙兩地生產并銷售該產品提供了如下成果第一年的年產量為（噸）時，所需的全部費用（萬元）與滿足關XYX系式，投入市場后當年能全部售出，且在甲、乙兩地每噸的售價，21590YXP甲（萬元）均與滿足一次函數關系（注年利潤年銷售額全部費用）P乙（1）成果表明，在甲地生產并銷售噸時，請你用含的代數式表示X1420PX甲X甲地當年的年銷售額，并求年利潤（萬元）與之間的函數關系式；W甲（2）成果表明，在乙地生產并銷售噸時，（為常數），且在乙地當年X1XN乙的最大年利潤為35萬元試確定的值；N（3）受資金、生產能力等多種因素的影響，某投資商計劃第一年生產并銷售該產品18噸，根據（1），（2）中的結果，請你通過計算幫他決策，選擇在甲地還是乙地產銷才能獲得較大的年利潤參考公式拋物線的頂點坐標是20YAXBC24BAC，26（本小題滿分12分）如圖15，在中，分別是RTABC905AB30CDEF，的中點點從點出發沿折線以每秒7個單位長ACB，PDEFCD的速度勻速運動；點從點出發沿方向以每秒4個單位長的速度勻速運動，過點QBA作射線，交折線于點點同時出發，當點繞行一周回QKCGPQ，P到點時停止運動，點也隨之停止設點運動的時間是秒（）D，T0（1）兩點間的距離是；F，（2）射線能否把四邊形分成面積相等的兩部分若能，求出的值若不能，DEFT說明理由；（3）當點運動到折線上，且點又恰好落在射線上時，求的值；PCPQKT（4）連結，當時，請直接寫出的值GABT2008年河北省初中畢業生升學文化課考試數學試題參考答案一、選擇題題號12345678910答案DBBCAACBDC二、選擇題1170；12，1；13；1427；159分（或9）；1620；172；1876三、解答題19解原式21X1X當時，原式2320解（1）500；（2）如圖1；（3）型號發芽率為，B型號發芽率為，A90925D型號發芽率為，C型號發芽率為4應選C型號的種子進行推廣圖1ABCD型號8006004002000630370470發芽數/粒380AECDFGBQK圖15P（4）3701B6845P取到型號發芽種子21解（1）由，令，得3YXYXX10D，（2）設直線的解析表達式為，由圖象知2LKB，；，4X0YX2Y直線的解析表達式為32KB，6K，2L362YX（3）由解得YX，3Y，C，AD192ADCS（4）63P，22解（1），；103B，10203，（2）過點作于點，如圖2，則COACD在中，RTD3COS02A0，26351臺風從生成到最初侵襲該城要經過11小時23觀察計算（1）；A（2）24探索歸納（1）；（2）22240DAA當，即時，；40512D12D12D當，即時，；X/KMY/KMAOBC6045圖2D當，即時，420A5A210D120D12D綜上可知當時，選方案二；當時，選方案一或方案二；5當（缺不扣分）時，選方案一124解（1）；ABPA（2）；Q證明由已知，得，EFFP45E又，ACB45CQC在和中，RTQT，90APP，TTBCBQ如圖3，延長交于點M，RTTQAP12在中，又，BC3903424190QMAAP（3）成立證明如圖4，45EF45CQ又，CBP在和中，RTQTAP，90CQTTBB如圖4，延長交于點，則QAPNCB，RTTCAP在中，B90CBLABFCQ圖3M1234EPLABQPEF圖4NC90APCBN90PBQ25解（1）甲地當年的年銷售額為萬元；2140X2390WX甲（2）在乙地區生產并銷售時，年利潤222111590590NXXXN乙由，解得或24905311N經檢驗，不合題意，舍去，N5（3）在乙地區生產并銷售時，年利潤，2109WX乙將代入上式，得（萬元）；將代入，18X2乙82390WX甲得（萬元），應選乙地24W甲乙甲26解（1）25（2）能如圖5，連結，過點作于點，DFHAB由四邊形為矩形，可知過的中點時，CEQKDFO把矩形分為面積相等的兩部分QK（注可利用全等三角形借助割補法或用中心對稱等方法說明），此時由，得125HOF20BHCBA16H故6748T（3）當點在上時，如圖6PE5T，QBTD由，得CA720453TTAECDFOBQK圖5HPGAECDFBQK圖6PGAECDFBQK圖7PG214T當點在上時，如圖7PFC657T已知，從而，QBT由，得73203520T解得12T（4）如圖8，；如圖9，T74T（注判斷可分為以下幾種情形當時，PGAB6027T點下行，點上行，可知其中存在的時刻，如圖PGAB8；此后，點繼續上行到點時，而點卻在下行到FT點再沿上行，發現點在上運動時不存在EE；當時，點均在上，也不存657T，FC在；由于點比點先到達點并繼續沿下PGABD行，所以在中存在的時刻，如圖9；當時，點均在8TPGAB810TPG，上，不存在）CDAECDFBQK圖8PGHAECDFBQK圖9PG（英文版）EASILYBLAME,TOPREVENTTHEBROKENWINDOWEFFECTSUPERVISETHELEADINGCADRESTOPLAYANEXEMPLARYROLE,TAKETHELEADINTHESTRICTIMPLEMENTATIONOFTHEAND,LEADTOSAFEGUARDTHESOLEMNITYANDAUTHORITYOFTHEPARTYDISCIPLINE,ENSURETHATTHEPARTYDISCIPLINEANDTHELAWSANDREGULATIONSFORIMPLEMENTATIONINPLACETHROUGHOUTTHEDISCIPLINEINTHEDAILYSUPERVISIONANDMANAGEMENT,STRENGTHENSUPERVISIONANDINSPECTION,FROMTHETHOROUGHINVESTIGATIONOFVIOLATIONSOFDISCIPLINEBEHAVIORSTRENGTHENTOKEYAREAS,KEYDEPARTMENTSANDKEYPROJECTSASWELLASTHEMASSESREFLECTTHECONCENTRATIONOFTHEUNITSANDDEPARTMENTSFORSUPERVISIONSTRENGTHENINGSUPERVISION,DISCIPLINEINSPECTIONANDSUPERVISIONOFCADRESTOSETANEXAMPLEFORCOMPLIANCEWITHTHEANDISAMANMUSTBEHEXYL,BLACKSMITHNEEDSITSOWNHARDWAREDISCIPLINEINSPECTIONORGANSASTHEEXECUTOROFTHEPARTYDISCIPLINE,ANDSUPERVISOROFTHEDEFENDERS,FORITSSUPERVISIONMUSTBEMORESTRICTLY,DISCIPLINEINSPECTIONANDSUPERVISIONOFCADRESTOFIRMLYESTABLISHTHEAWARENESSOFPARTYCONSTITUTION,SENSEOFDISCIPLINEANDRULESCONSCIOUSNESS,POLITICSLOYALTY,SENSEOBEYACTIONSPEAKJIORDINANCETOSETANEXAMPLEOFTHEREGULATIONSOFTHERULEOFLAW,STRENGTHENSUPERVISIONANDACCEPTTHESUPERVISIONOFTHEFIRMNESSANDCONSCIOUSNESS,DOCOMPLYWITHANDTOFIRMLYESTABLISHTHEDISCIPLINEMUSTFIRSTBEDISCIPLINED,THESUPERVISORWILLBESUBJECTTOTHESUPERVISIONOF“CONCEPT,ANDCONSCIOUSLYSAFEGUARDANDIMPLEMENTPARTYCOMPASSESPARTY,TAKETHELEADINPRACTICING“THREESTRICTREALSTRICT,SOLOYAL,CLEAN,PLAYTOBEGOODATLEARNING,THECONSTITUTIONANDTHEASMORALITY,POLITICSANDBROUGHTTOFRUITIONTOIMPLEMENT,DONOTWANTTO,DARENOT,NOTWITHDISCIPLINARYRULERTOSUPERVISIONTODISCIPLINEARULER,OFTENTHECONTROLINSPECTION,ANDCONSCIOUSLYINTHEIDEOLOGICALREDLINETODRAWTHEROWMINGGOODACCUMULATIONISINDEEDTHEBOTTOMLINE,SOTHATTHEHEARTHASFEAR,SAIDTOHAVEQUIT,THELINEHASENDEDATTACHEDINDIFFERENTTOHEART,CALMLYTOTHETABLEINOURLIFE,THEREAREMANYUNPREDICTABLETHINGSWILLHAPPEN,SOMEGOOD,SOMEBADTHINGS,WECANNOTCONTROLISPOWERLESSTOSTOP,BUTWITHTIME,YOUWILLFINDINLIFESOMETIMESTURNSOUTTOBENOTGOOD,SOMEBADTHINGSFINALLYTURNEDOUTTOBEAGOODTHING,BUTTHENWEMUDDYHOWEVERDIDNOTKNOW,THISISTHELIFETEACHUSTHINGS1,LIFECANBECOMPLEX,CANALSOBESIMPLEWANTSIMPLELIFEOFPRECIPITATION,TOHAVEENOUGHTIMETOREFLECT,TOMAKEBECOMEMOREPERFECTLIFEISTHEMOSTIMPORTANTTHINGISNOTTOWIN,BUTTHESTRUGGLENOTTOHAVECONQUERED,BUTTOHAVEFOUGHTWELL2,THEPLAINISTHEBACKGROUNDOFLIFELIVEAPLAINLIFE,GIVEUPONTHEMSELVESISNOTACOWARD,BUTTHEWISEANSWERSNOTDISILLUSIONEDAFTERTHEHEART,SUCHASASHES,BUTEXPERIENCETHESTORMAFTERTHEENLIGHTENMENTNOTUNREWARDINGPERFUNCTORILY,BUTCALMATTITUDEOFLIFEOFUNRESTRAINEDSELFCONFIDENCEPLAINLIVING,THEREISNONOISENOISY,NOEARTHLYTROUBLES,MOREDIDNOTFILLINTHEDISCONTENTOFDESIRE,SOMEJUSTACALM,ACALM3,MEMORYOFHEARTWILLNOTGOODTHINGSTOERASETHE,LIFEISAWHENNOMOVIE,PAINISABEGINNING,THESTRUGGLEISAKINDOFPROCESS,DEATHISAKINDOFENDINGGIVEUPTHISGIVINGUPISTHEHELPLESS,DONOTGIVEUPTHEABANDONED,DONOTGIVEUPTHISGIVINGUPISIGNORANCE,DONOTGIVEUPSHOULDNOTGIVEUPISPERSISTENT4,ATHINGFIGUREDISHEAVEN,THINKIMPASSABILITYISHELLSINCETHELIVING,TOLIVEBETTERSOMETIMESWEBECAUSEOFTOONARROWMINDED,TOOCAREAROUNDTHECHORESANDPENNYWISEANDPOUNDFOOLISH,NOTWORTHTHECANDLESOMETHINGSTOATTRACTTROUBLEANDWORRY,COMPLETELYDEPENDSONHOWWELOOKATANDDEALWITHITDONTALWAYSTAKEEVERYTHINGBACKTOTHINGS,ANDDONTGETINTOABLINDALLEY,DONTWANTTOFACE,DONTBENARROWMINDEDPOKETOCARE,ISAKINDOFOPENMINDED,AFREEANDEASY5,IAMNOTAFRAIDOFOTHERSBEHINDMEAKNIFE,IAFRAIDTOLOOKBACKANDSEESTABME,ISMYINTENTIONTOTREATPEOPLEIAMNOTAFRAIDOFTHETRUTHTOTELLTHEBESTFRIEND,IMAFRAIDHETURNEDTOITASAJOKETOTELLDONT6,WHENWEAREINAPOSITIVEFRAMEOFMIND,YOUWILLFINDMANYGOODTHINGSANDWHENWEAREINANEGATIVESTATEOFMIND,YOUWILLFINDMANYDEPRESSEDTHINGSLIFEHAPPYANDWORRY,ALLISYOUOFLIFEATTITUDE,OPTIMISTIC,GOODLUCKLOSSOFSINK,ERITREACOMPANYWHENYOUAREINADVERSITY,MAYWISHTOCHANGEAPOINTOFVIEWTOTHINKEVERYTHINGOVERTOTHEGOODTHINK,BECAUSEGOODMENTALITYDECIDEDTHEFATEOFTHE7,PEOPLEARETIRED,RESTHEARTTIRED,CALMGROWUP,MATURE,THISSOCIETYREADTIREDANDSAD,SQUATDOWN,TOTHEIRAHUGBECAUSETHEWORLDNOONECANSYMPATHIZEWITHYOU,HAVEMERCYONYOUYOUCRY,TEARSISYOUROWNYOUPAIN,NOONECANUNDERSTANDTHENYOUONLYTEARSTOSMILE8,EACHPEOPLEHAVEYOUTH,EACHYOUTHAREASTORY,THELIFEOFTHEWORLDNEVERGETSEASIER,IWANTWHAT,WISHTHEWORLDALLKNOW,ASHASBEENTHESAMENOWWANTANYTHING,FORFEARTHATOTHERSKNOW,ORLIKETOLOSETHESAME9,THEHEARTMOVE,EVERYTHINGINTHEWORLDISFOLLOWEDBYBIRTH,RANGRANG,IMPORTANTTHINGISOFTENTHEMOSTDIFFICULTTOOPENONESMOUTH,BECAUSEWORDSWILLREDUCEITSIMPORTANCETOLETSTRANGERSPEOPLECAREABOUTYOURLIFEINTHEGOODTHINGS,THEORIGINALISNOTEASY10,DONOTBLAME,DONOTLAUGHATWHO,ALSODONTENVYWHOLIKEAPERSONISAKINDOFFEELING,NOTLIKEAPERSONISTRUETHETRUTHISEASYTOEXPLAIN,IFEELISUNSPEAKABLETHEBESTTRAVELLIFEISTHATYOUINASTRANGEPLACEFOUNDALONGLOSTTOUCHED11,HAPPYLIFENOTINTHEBUSTLINGIN,ANDINTHEPEACEOFMINDNOMATTERHOWMANYGRIEVANCES,HOWUNCOMFORTABLE,ANDULTIMATELYTOHEALTHEMSELVESORTHEIROWN,OTHERSMAYGOTYOUTOCOMFORT,BUTNEVERKNOWYOURHEARTISHOWWANJIANCHUA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