2020年山東省濰坊市中考數(shù)學試卷及答案

2020/r/n2020/r/n年中考/r/n2020/r/n年山東省濰坊市中考數(shù)學試卷/r/n一、選擇題（本大題共/r/n12/r/n小題，共/r/n36/r/n分．在每小題給出的四個選項中，只有一項是正確/r/n的，請把正確的選項選出來，每小題選對得/r/n3/r/n分，錯選、不選或選出的答案超過一個均記/r/n0/r/n分．）/r/nA/r/n./r/n2/r/na/r/n+3/r/nb/r/n=/r/n5/r/nab/r/nB/r/n./r/na/r/n3/r/n?/r/na/r/n2/r/n=/r/na/r/n5/r/nC/r/n.（/r/na/r/n+/r/nb/r/n）/r/n2/r/n=/r/na/r/n2/r/n+/r/nb/r/n2/r/nD/r/n.（/r/na/r/n2/r/nb/r/n）/r/n3/r/n=/r/na/r/n6/r/nb/r/n（/r/n3/r/n分）/r/n（/r/n2020/r/n?濰坊）今年的政府工作報告中指出：去年脫貧攻堅取得決定性成就，農(nóng)村/r/n貧困人口減少/r/n1109/r/n萬.數(shù)字/r/n1109/r/n萬用科學記數(shù)法可表示為（）/r/n1.109/r/nX/r/n10/r/n7/r/nB/r/n./r/n1.109/r/nX/r/n10/r/n6/r/nC/r/n./r/n0.1109/r/nX/r/n10/r/n8/r/nD/r/n./r/n11.09/r/nX/r/n10/r/n6/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）將一個大正方體的一角截去一個小正方體，得到的幾何體如圖所示，/r/n一分鐘跳繩個數(shù)/r/n141/r/n144/r/n145/r/n146/r/n（個）/r/n

/r/n學生人數(shù)（名）/r/n5212/r/n則關(guān)于這組數(shù)據(jù)的結(jié)論正確的是（/r/nA/r/n./r/n平均數(shù)是/r/n144/r/nB/r/n./r/n眾數(shù)是/r/n141/r/nD/r/n./r/n方差是/r/n5.4/r/n6/r/n./r/n（3/r/n分）（/r/n2020/r/n?濰坊）/r/n若/r/nm/r/n2/r/n+2/r/nm/r/n=/r/n1/r/n,/r/n則/r/nB/r/n./r/n眾數(shù)是/r/n141/r/nD/r/n./r/n方差是/r/n5.4/r/n6/r/n./r/n（3/r/n分）（/r/n2020/r/n?濰坊）/r/n若/r/nm/r/n2/r/n+2/r/nm/r/n=/r/n1/r/n,/r/n則/r/n4/r/nm/r/n2/r/n+8/r/nm/r/n-/r/n3/r/n的值是（/r/nA/r/n./r/n4/r/nB/r/n./r/n3/r/nC/r/n./r/n2/r/nD/r/n./r/n1/r/n7/r/n./r/n（3/r/n分）（/r/n2020/r/n?濰坊）/r/nDE/r/n1/r/n如圖，點/r/nE/r/n是/r/n「/r/nABCD/r/n的邊/r/nAD/r/n上的一點，且需/r/n=/r/n，連接/r/nBE/r/n并/r/nA/r/n./r/n21/r/nB/r/n./r/n28/r/nC/r/n./r/n34/r/nD/r/n./r/n42/r/n延長交/r/nCD/r/n的延長線于點/r/nF/r/n,/r/n若/r/nDE/r/n=/r/n3/r/n,/r/nDF/r/n=/r/n4/r/n,/r/n貝/r/nW/r/nABCD/r/n的周長為（/r/n）/r/n8/r/n./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）關(guān)于/r/nx/r/n的一元二次方程/r/nx/r/n2/r/n+/r/n（/r/nk/r/n-/r/n3/r/n）/r/nx/r/n+1/r/n-/r/nk/r/n=/r/n0/r/n根的情況，下列說法正確的是（）/r/nA/r/n./r/n有兩個不相等的實數(shù)根/r/nB/r/n./r/n有兩個相等的實數(shù)根/r/nC/r/n./r/n無實數(shù)根/r/nD/r/n./r/n無法確定/r/n9/r/n./r/n（3/r/n9/r/n./r/n（3/r/n分）（/r/n2020/r/n?濰坊）如圖，函數(shù)/r/ny/r/n=/r/nkx/r/n+/r/nb/r/n（/r/nkM/r/n0/r/n）/r/n與/r/ny/r/n=/r/n嚴/r/n（/r/nmM/r/n0/r/n）/r/n的圖象相交于點/r/nA/r/nA/r/n./r/nx/r/nA/r/n./r/nx/r/n>-/r/n2/r/nC/r/n./r/nx/r/n>/r/n1/r/n（-/r/n2/r/n,/r/n3/r/n），/r/nB/r/n（/r/n1/r/n，-/r/n6/r/n）兩點，則不等式/r/nkx/r/n+/r/nb/r/n＞/r/n號/r/n的解集為（/r/nB/r/n.-/r/n2/r/n</r/nx/r/n</r/n0/r/n或/r/nx/r/n>/r/n1/r/nD/r/n./r/nx/r/n<-/r/n2/r/n或/r/n0/r/n</r/nx/r/n</r/n1/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）如圖，在/r/nRt/r/nAAOB/r/n中，/r/nZAOB/r/n=/r/n90/r/n°，/r/nOA/r/n=/r/n3/r/n，/r/nOB/r/n=/r/n4/r/n，/r/n以點/r/nO/r/n為圓心，/r/n2/r/n為半徑的圓與/r/nOB/r/n交于點/r/nC/r/n,/r/n過點/r/nC/r/n作/r/nCD/r/n丄/r/nOB/r/n交/r/nAB/r/n于點/r/nD/r/n,/r/n點/r/nP/r/n是邊/r/nOA/r/n

/r/n上的動點.當/r/nPC/r/n上的動點.當/r/nPC/r/n+/r/nPD/r/n最小時，/r/nOP/r/n的長為（/r/n）/r/n'E/r/nTOC\o"1-5"\h\z/r/n1/r/n3/r/n3/r/nA/r/n./r/nB/r/n./r/nC/r/n./r/n1/r/nD/r/n./r/n-/r/n2/r/n4/r/n2/r/n3x/r/n—5/r/n二/r/n1/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）若關(guān)于/r/nx/r/n的不等式組/r/n｛/r/n2x—a<8/r/n有且只有/r/n3/r/n個整數(shù)解，則/r/na/r/n的取/r/n值范圍是（）/r/nA/r/n./r/n0/r/nWaW/r/n2/r/nB/r/n./r/n0/r/nWa</r/n2/r/nC/r/n./r/n0/r/n<aW/r/n2/r/nD/r/n./r/n0/r/n<a</r/n2/r/n（a/r/n—/r/nb（a>/r/n2b）/r/n（/r/n3/r/n分）/r/n（/r/n2020/r/n?濰坊）若定義一種新運算：/r/na/r/ng/r/nb/r/n=/r/n｛丄幾“<“、，例如：/r/n3/r/n0/r/n1/r/n=/r/n3/r/n（a/r/n+/r/nb—6（a/r/n</r/n2b）/r/n-/r/n1/r/n=/r/n2/r/n；/r/n5/r/n0/r/n4/r/n=/r/n5+4/r/n-/r/n6/r/n=/r/n3/r/n.貝/r/nV/r/n函數(shù)/r/ny/r/n=（/r/nx/r/n+2/r/n）/r/n0/r/n（/r/nx/r/n-/r/n1/r/n）的圖象大致是（/r/n）/r/n二、填空題（本大題共/r/n6/r/n小題，共/r/n18/r/n分.只要求填寫最后結(jié)果，每小題填對得/r/n3/r/n分.）/r/nTOC\o"1-5"\h\z/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）因式分解：/r/nx/r/n2/r/ny/r/n-/r/n9/r/ny=/r/n./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）若/r/nl/r/na/r/n-/r/n21/r/n+Vb/r/n—3=/r/n0/r/n,則/r/na/r/n+/r/nb=/r/n./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）如圖，在/r/nRt/r/nAABC/r/n中，/r/nZC/r/n=/r/n90/r/n°,/r/nZB/r/n=/r/n20/r/n°,/r/nPQ/r/n垂直平分/r/nAB/r/n,/r/n垂足為/r/nQ/r/n，/r/n交/r/nBC/r/n于點/r/nP/r/n./r/n按以下步驟作圖：/r/n①/r/n以點/r/nA/r/n為圓心，以適當?shù)拈L為半徑作弧，/r/n1/r/n分別交邊/r/nAC/r/n，/r/nAB/r/n于點/r/nD/r/n，/r/nE/r/n；/r/n②/r/n分別以點/r/nD/r/n，/r/nE/r/n為圓心，以大于/r/nyDE/r/n的長為半徑作弧,兩弧相交于點/r/nF/r/n；/r/n③/r/n作射線/r/nAF/r/n./r/n若/r/nAF/r/n與/r/nPQ/r/n的夾角為/r/na/r/n,/r/n則/r/na/r/n=/r/n°/r/n./r/n

/r/n1/r/n有增根，則/r/nm/r/n1/r/n有增根，則/r/nm/r/n=/r/n（/r/n3/r/n分）（/r/n2°/r/n2/r/n°/r/n?濰坊）若關(guān)于/r/nx/r/n的分式方程才=嬴/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）如圖，矩形/r/nABCD/r/n中，點/r/nG/r/n,/r/nE/r/n分別在邊/r/nBC/r/n,/r/nDC/r/n上，連接/r/nAC/r/n,/r/n記為點/r/nF/r/n./r/n若/r/nCE/r/n=/r/n3/r/n,/r/nCG/r/n=/r/n4/r/n,/r/n則/r/nsin/r/nZDAE=/r/nEG/r/n,/r/nAE/r/n，/r/n將/r/n△/r/nABG/r/n記為點/r/nF/r/n./r/n若/r/nCE/r/n=/r/n3/r/n,/r/nCG/r/n=/r/n4/r/n,/r/n則/r/nsin/r/nZDAE=/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）如圖，四邊形/r/nABCD/r/n是正方形，曲線/r/nDA/r/n1/r/nB/r/n1/r/nC/r/n1/r/nD^A/r/n2/r/n…是由一段段/r/n90/r/n度的弧組成的.其中：丙］的圓心為點/r/nA/r/n,/r/n半徑為/r/nAD/r/n；/r/n可/r/n行的圓心為點/r/nB/r/n,/r/n半徑為/r/nBA/r/n1/r/n；/r/n瓦/r/n-/r/n的圓心為點/r/nC/r/n,/r/n半徑為/r/nCB/r/n1/r/n；/r/n:耳/r/n的圓心為點/r/nD/r/n,/r/n半徑為/r/nDC/r/n］/r/n；/r/n…/r/n圧町，/r/n可/r/n行，/r/nB/r/n1/r/nC/r/n1/r/n,/r/n?q,/r/n…的圓心依次按點/r/nA,B,C,D/r/n循環(huán).若正方形/r/nABCD/r/n的邊長為/r/n1,/r/n則/r/n^/r/n20/r/n^/r/n2020/r/n的長是/r/n./r/n三、解答題（本大題共/r/n7/r/n小題,共/r/n66/r/n分.解答應與出文字說明、證明過程或演算步驟.）/r/n咒/r/n三、解答題（本大題共/r/n7/r/n小題,共/r/n66/r/n分.解答應與出文字說明、證明過程或演算步驟.）/r/n咒/r/n1/r/nX/r/n2/r/n2X1/r/nx3/r/nX1/r/n19/r/n./r/n（/r/n2020/r/n?濰坊）先化簡，再求值：（/r/n1/r/n其中/r/nx/r/n是/r/n16/r/n的算術(shù)平方根./r/n（/r/n2020/r/n?濰坊）某?！熬C合與實踐”小組采用無人機輔助的方法測量一座橋的長度.如圖,/r/n橋/r/nAB/r/n是水平并且筆直的，測量過程中，小組成員遙控無人機飛到橋/r/nAB/r/n的上方/r/n120/r/n米的點/r/nC/r/n處懸停，此時測得橋兩端/r/nA/r/n，/r/nB/r/n兩點的俯角分別為/r/n60/r/n°和/r/n45/r/n°，求橋/r/nAB/r/n的長度./r/n(/r/n2020/r/n?濰坊)在/r/n4/r/n月/r/n23/r/n日“世界讀書日”來臨之際，某校為了了解學生的課外閱讀情況，從全校隨機抽取了部分學生，調(diào)查了他們平均每周的課外閱讀時間“單位：小時).把調(diào)查結(jié)果分為四檔，/r/nA/r/n檔：/r/ntV/r/n8/r/n；/r/nB/r/n檔：/r/n8/r/nWtV/r/n9/r/n；/r/nC/r/n檔：/r/n9/r/nWtV/r/n10/r/n；/r/nD/r/n檔：/r/n&10/r/n./r/n根據(jù)調(diào)查情況，給出了部分數(shù)據(jù)信息：/r/nA/r/n檔和/r/nD/r/n檔的所有數(shù)據(jù)是：/r/n7/r/n，/r/n7/r/n，/r/n7.5/r/n，/r/n10/r/n，/r/n7/r/n，/r/n10/r/n，/r/n7/r/n，/r/n7.5/r/n，/r/n7/r/n，/r/n7/r/n，/r/n10.5/r/n，/r/n10.5/r/n；/r/n圖/r/n1/r/n和圖/r/n2/r/n是兩幅不完整的統(tǒng)計圖./r/n圖/r/n1/r/n圉/r/n3/r/n根據(jù)以上信息解答問題：/r/n(/r/n1/r/n)求本次調(diào)查的學生人數(shù)，并將圖/r/n2/r/n補充完整；/r/n已知全校共/r/n1200/r/n名學生，請你估計全校/r/nB/r/n檔的人數(shù)；/r/n學校要從/r/nD/r/n檔的/r/n4/r/n名學生中隨機抽取/r/n2/r/n名作讀書經(jīng)驗分享，已知這/r/n4/r/n名學生/r/n1/r/n名來自七年級，/r/n1/r/n名來自八年級，/r/n2/r/n名來自九年級，請用列表或畫樹狀圖的方法，求抽到的/r/n2/r/n名學生來自不同年級的概率./r/n(/r/n2020/r/n?濰坊)如圖，/r/nAB/r/n為/r/nO/r/nO/r/n的直徑，射線/r/nAD/r/n交/r/nO/r/nO/r/n于點/r/nF/r/n，/r/n點/r/nC/r/n為劣弧麗的中點，過點/r/nC/r/n作/r/nCE/r/n丄/r/nAD/r/n,/r/n垂足為/r/nE/r/n,/r/n連接/r/nAC/r/n./r/n求證：/r/nCE/r/n是/r/nO/r/nO/r/n的切線；/r/n若/r/nZBAC/r/n=/r/n30/r/n°,/r/nAB/r/n=/r/n4/r/n，/r/n求陰影部分的面積./r/n

/r/n(/r/n2020/r/n?濰坊)因疫情防控需要，消毒用品需求量增加.某藥店新進一批桶裝消毒液，每桶進價/r/n50/r/n元，每天銷售量/r/ny/r/n(桶)與銷售單價/r/nx/r/n(元)之間滿足一次函數(shù)關(guān)系，其圖象如圖所示./r/n求/r/ny/r/n與/r/nx/r/n之間的函數(shù)表達式；/r/n每桶消毒液的銷售價定為多少元時，藥店每天獲得的利潤最大，最大利潤是多少元？(利潤=銷售價-進價)/r/n伸/r/n(桶/r/n)/r/n100/r/n80/r/nO/r/n~/r/n/元)/r/n(/r/n2020/r/n?濰坊)如圖/r/n1/r/n,在/r/n△/r/nABC/r/n中，/r/nZA/r/n=/r/n90/r/n°，/r/nAB/r/n=/r/nAC/r/n=V2+/r/n1/r/n,/r/n點/r/nD/r/n，/r/nE/r/n分別在邊/r/nAB/r/n，/r/nAC/r/n上，且/r/nAD/r/n=/r/nAE/r/n=/r/n1/r/n，/r/n連接/r/nDE/r/n./r/n現(xiàn)將/r/nAADE/r/n繞點/r/nA/r/n順時針方向旋轉(zhuǎn)，旋轉(zhuǎn)角為/r/na/r/n(/r/n0/r/n°V/r/na/r/nV/r/n360/r/n°),/r/n如圖/r/n2/r/n,/r/n連接/r/nCE/r/n，/r/nBD/r/n，/r/nCD/r/n./r/n當/r/n0/r/n°V/r/na/r/nV/r/n180/r/n°/r/n時，求證：/r/nCE/r/n=/r/nBD/r/n；/r/n如圖/r/n3/r/n,當/r/na/r/n=/r/n90/r/n。時，延長/r/nCE/r/n交/r/nBD/r/n于點/r/nF/r/n,/r/n求證：/r/nCF/r/n垂直平分/r/nBD/r/n；/r/n在旋轉(zhuǎn)過程中，求/r/nABCD/r/n的面積的最大值，并寫出此時旋轉(zhuǎn)角/r/na/r/n的度數(shù)./r/n(/r/n2020/r/n?濰坊)如圖，拋物線/r/ny/r/n=/r/nax/r/n2/r/n+/r/nbx/r/n+8/r/n(/r/naM/r/n0/r/n)/r/n與/r/nx/r/n軸交于點/r/nA/r/n(-/r/n2,0/r/n)和點/r/nB/r/n(/r/n8,/r/n0/r/n),與/r/ny/r/n軸交于點/r/nC/r/n,/r/n頂點為/r/nD/r/n,/r/n連接/r/nAC/r/n,/r/nBC/r/n,/r/nBC/r/n與拋物線的對稱軸/r/nl/r/n交于點/r/nE/r/n./r/n(/r/n1/r/n)求拋物線的表達式；/r/n3/r/n點/r/nP/r/n是第一象限內(nèi)拋物線上的動點，連接/r/nPB/r/n,/r/nPC/r/n,/r/n當/r/nS/r/n^/r/nPBC/r/n=/r/n5/r/nS/r/n^/r/nabc/r/n時，求點/r/nP/r/n的坐標；/r/n點/r/nN/r/n是對稱軸/r/nl/r/n右側(cè)拋物線上的動點，在射線/r/nED/r/n上是否存在點/r/nM/r/n,/r/n使得以點/r/nM/r/n，/r/nN/r/n，/r/nE/r/n為頂點的三角形與/r/nAOBC/r/n相似？若存在，求點/r/nM/r/n的坐標；若不存在，請說明理由./r/n2020/r/n年山東省濰坊市中考數(shù)學試卷/r/n參考答案與試題解析/r/n一、選擇題（本大題共/r/n12/r/n小題，共/r/n36/r/n分．在每小題給出的四個選項中，只有一項是正確的，請把正確的選項選出來，每小題選對得/r/n3/r/n分，錯選、不選或選出的答案超過一個均記/r/n0/r/n分．）/r/n是軸對稱圖形，不是中心對稱圖形，故此選項不符合題意;/r/n是軸對稱圖形，也是中心對稱圖形，故此選項符合題意；/r/n是軸對稱圖形，不是中心對稱圖形，故此選項不符合題意;/r/n故選：/r/nC/r/n./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）下列運算正確的是（/r/n）/r/nB/r/n./r/na/r/n3/r/n?/r/na/r/n2/r/n=/r/nB/r/n./r/na/r/n3/r/n?/r/na/r/n2/r/n=/r/na/r/n5/r/nC/r/n.（/r/na/r/n+/r/nb/r/n）/r/n2/r/n=/r/na/r/n2/r/n+/r/nb/r/n2/r/nD/r/n.（/r/na/r/n2/r/nb/r/n）/r/n3/r/n=/r/na/r/n6/r/nb/r/n【解答】/r/n解：/r/nA/r/n、/r/n不是同類項，不能合并，故選項/r/nA/r/n計算錯誤；/r/nB/r/n、/r/na/r/n3/r/n?/r/na/r/n2/r/n=/r/na/r/n5/r/n，故選項/r/nB/r/n計算正確；/r/nC/r/n、/r/n（/r/na/r/n+/r/nb/r/n）/r/n2/r/n=/r/na/r/n2/r/n+2/r/nab/r/n+/r/nb/r/n2/r/n，故選項/r/nC/r/n計算錯誤；/r/nD/r/n、/r/n（/r/na/r/n2/r/nb/r/n）/r/n3/r/n=/r/na/r/n6/r/nb/r/n3/r/n，故選項/r/nD/r/n計算錯誤./r/n故選：/r/nB/r/n./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）今年的政府工作報告中指出：去年脫貧攻堅取得決定性成就，農(nóng)村/r/n貧困人口減少/r/n1109/r/n萬.數(shù)字/r/n1109/r/n萬用科學記數(shù)法可表示為（/r/n）/r/n1.109/r/nX/r/n10/r/n7/r/nB/r/n./r/n1.109/r/nX/r/n10/r/n6/r/nC/r/n./r/n0.1109/r/nX/r/n10/r/n8/r/nD/r/n./r/n11.09/r/nX/r/n10/r/n6/r/n【解答】/r/n解：/r/n?.?1109/r/n萬=/r/n11090000/r/n,/r/n

/r/n???11090000/r/n=/r/n1.109/r/nX/r/n10/r/n7/r/n./r/n故選：/r/nA/r/n./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）將一個大正方體的一角截去一個小正方體，得到的幾何體如圖所示,/r/n故選：/r/nD/r/n./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）為調(diào)動學生參與體育鍛煉的積極性，某校組織了一分鐘跳繩比賽活/r/n動，體育組隨機抽取了/r/n10/r/n名參賽學生的成績，將這組數(shù)據(jù)整理后制成統(tǒng)計表：/r/n平均數(shù)為：/r/n壬/r/n=/r/n14/r/n平均數(shù)為：/r/n壬/r/n=/r/n14/r/n^/r/n5+4/r/n4^+^/r/n1+46/r/n^/r/n=143,/r/n5+2+1+2/r/n故/r/nA/r/n選項錯誤；/r/n一分鐘跳繩個數(shù)/r/n141/r/n144/r/n145/r/n146/r/n（個）/r/n學生人數(shù)（名）/r/n5/r/n21/r/n2/r/n則關(guān)于這組數(shù)據(jù)的結(jié)論正確的是（/r/n)/r/nA/r/n./r/n平均數(shù)是/r/n144/r/nB/r/n./r/n眾數(shù)是/r/n141/r/nC/r/n./r/n中位數(shù)是/r/n144.5/r/nD/r/n./r/n方差是/r/n5.4/r/n解答】/r/n解：根據(jù)題目給出的數(shù)據(jù)，可得：/r/n眾數(shù)是：/r/n141/r/n,故/r/nB/r/n選項正確；/r/n141+144/r/n中位數(shù)是：一/r/n2/r/n=/r/n142.5/r/n，故/r/nC/r/n選項錯誤；/r/n2/r/nA/r/n．/r/n4/r/nB/r/n．/r/n3/r/nC/r/n．/r/n2/r/nD/r/n．/r/n1/r/n【解答】/r/n解：/r/n???m/r/n2/r/n+2m/r/n=/r/nl/r/n,/r/n4/r/nm/r/n2/r/n+8/r/nm/r/n-/r/n3/r/n=/r/n4/r/n（/r/nm/r/n2/r/n+2/r/nm/r/n）-/r/n3/r/n=/r/n4/r/nX/r/n1/r/n-/r/n3/r/n=/r/nl/r/n．/r/n故選：/r/nD/r/n．/r/nDE/r/n1/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）如圖，點/r/nE/r/n是/r/n「/r/nABCD/r/n的邊/r/nAD/r/n上的一點，且需=；，連接/r/nBE/r/n并/r/n延長交/r/nCD/r/n的延長線于點/r/nF/r/n,/r/n若/r/nDE/r/n=/r/n3/r/n,/r/nDF/r/n=/r/n4/r/n,/r/n貝/r/nW/r/nABCD/r/n的周長為（/r/n）/r/nA/r/n./r/n21/r/nB/r/n./r/n28/r/nC/r/n./r/n34/r/nD/r/n./r/n42/r/n【解答】/r/n解：/r/n?/r/n?四邊形/r/nABCD/r/n是平行四邊形，/r/n.??AB/r/n〃/r/nCF/r/n,/r/nAB/r/n=/r/nCD/r/n，/r/n.?.△ABE/r/nsA/r/ndfe/r/n，/r/nDEFD1/r/n''AE~AB~2^/r/n，/r/n?/r/nDE/r/n=/r/n3/r/n，/r/nDF/r/n=/r/n4/r/n，/r/n./r/nAE/r/n=/r/n6/r/n，/r/nAB/r/n=/r/n8/r/n，/r/n./r/nAD/r/n=/r/nAE/r/n+/r/nDE/r/n=/r/n6+3/r/n=/r/n9/r/n，/r/n???/r/n平行四邊形/r/nABCD/r/n的周長為：/r/n（/r/n8+9/r/n）X/r/n2/r/n=/r/n34/r/n./r/n故選：/r/nC/r/n./r/n（/r/n3/r/n分）/r/n（/r/n2020/r/n?濰坊）關(guān)于/r/nx/r/n的一元二次方程/r/nx/r/n2/r/n+/r/n（/r/nk/r/n-/r/n3/r/n）/r/nx/r/n+1/r/n-/r/nk/r/n=/r/n0/r/n根的情況，下列說法正確的是（）/r/nA/r/n./r/n有兩個不相等的實數(shù)根/r/nB/r/n./r/n有兩個相等的實數(shù)根/r/nC/r/n./r/n無實數(shù)根/r/nD/r/n./r/n無法確定/r/n【解答】/r/n解：/r/n△=（/r/nk/r/n-/r/n3/r/n）/r/n2/r/n-/r/n4/r/n（/r/n1/r/n-/r/nk/r/n）/r/n=/r/nk/r/n2/r/n-/r/n6/r/nk/r/n+9/r/n-/r/n4+4/r/nk/r/n

/r/n=/r/nk/r/n3/r/n3/r/nA/r/n./r/nB/r/n./r/n3/r/n3/r/nA/r/n./r/nB/r/n./r/nC/r/n./r/n1/r/nD/r/n./r/n-/r/n4/r/n2/r/n【解答】/r/n解：如圖，延長/r/nCO/r/n交/r/nO/r/nO/r/n于點/r/nE/r/n,/r/n連接/r/nED/r/n,/r/n交/r/nAO/r/n于點/r/nP/r/n,/r/n此時/r/nPC/r/n+/r/nPD/r/n的值最小./r/n=(/r/nk/r/n-/r/n1/r/n)/r/n2/r/n+4/r/n,/r/n?/r/n\(/r/nk/r/n-/r/n1/r/n)/r/n2/r/n+4/r/n>/r/n0/r/n,即厶/r/n>/r/n0/r/n,/r/n???/r/n方程總有兩個不相等的實數(shù)根./r/n故選：/r/nA/r/n./r/n(/r/n3/r/n分)(/r/n2020/r/n?濰坊)如圖，函數(shù)/r/ny/r/n=/r/nkx/r/n+/r/nb/r/n(/r/nkM/r/n0/r/n)/r/n與/r/ny/r/n=/r/n^/r/n(/r/nmM/r/n0/r/n)/r/n的圖象相交于點/r/nA/r/n(-/r/n2/r/n,/r/n3/r/n(-/r/n2/r/n,/r/n3/r/n),/r/nB/r/n(/r/n1/r/n,-/r/n6/r/n)兩點，則不等式/r/nkx/r/n+/r/nb/r/n>/r/n號/r/n的解集為(/r/n)/r/nA/r/n./r/nx/r/n>-/r/n2/r/nB/r/n.-/r/n2/r/nVxV/r/n0/r/n或/r/nx>/r/n1/r/nC/r/n./r/nx/r/n>/r/n1/r/nxV-/r/n2/r/nC/r/n./r/nx/r/n>/r/n1/r/n【解答】/r/n解：/r/n??/r/n?函數(shù)/r/ny/r/n=/r/nkx/r/n+/r/nb/r/n(/r/nkM/r/n0/r/n)/r/n與/r/ny=/r/n^/r/n(mH0)/r/n的圖象相交于點/r/nA/r/n(-/r/n2/r/n,/r/n3/r/n),/r/nB/r/n(/r/n1/r/n，-/r/n6/r/n)兩點，/r/n???/r/n不等式/r/nkx+b/r/n>/r/n￥/r/n的解集為：/r/nxV-/r/n2/r/n或/r/n0/r/nVxV/r/nl/r/n,/r/n故選：/r/nD/r/n./r/n(/r/n3/r/n分)(/r/n2020/r/n?濰坊)如圖，在/r/nRt/r/nAAOB/r/n中，/r/nZAOB/r/n=/r/n90/r/n°,/r/nOA/r/n=/r/n3/r/n,/r/nOB/r/n=/r/n4/r/n,/r/n以點/r/nO/r/n為圓心，/r/n2/r/n為半徑的圓與/r/nOB/r/n交于點/r/nC/r/n,/r/n過點/r/nC/r/n作/r/nCD/r/n丄/r/nOB/r/n交/r/nAB/r/n于點/r/nD/r/n,/r/n點/r/nP/r/n是邊/r/nOA/r/n上的動點.當/r/nPC/r/n+/r/nPD/r/n最小時，/r/nOP/r/n的長為(/r/n)/r/n

/r/n:/r/n.Z/r/n:/r/n.Z/r/nDCB/r/n=/r/n90/r/n°/r/n又/r/nZ/r/nAOB/r/n=/r/n90/r/n°/r/n//r/nDCB/r/n=//r/nAOB/r/n,/r/nCD/r/n〃/r/nAO/r/nBCCD/r/nBOAO/r/nOC/r/n=/r/n2/r/n,/r/nOB/r/n=/r/n4/r/n,/r/nBC/r/n=/r/n2/r/n,/r/n2/r/nCD/r/n2/r/nCD/r/n,/r/n4/r/n=/r/nT/r/n'解得'/r/ncD/r/n=2/r/n；/r/nCD/r/nH/r/nAO/r/n,/r/nEOPO2/r/nECDC/r/nEOPO2/r/nECDC/r/n'即/r/n2/r/nP0/r/n,/r/n3/r/n=T/r/n'解得’/r/nPO/r/n=/r/n3/r/n故選：/r/nB/r/n./r/n（/r/n3x/r/n—5/r/nn/r/n1/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）若關(guān)于/r/nx/r/n的不等式組/r/n｛/r/n2/r/n%_/r/na/r/n</r/n8/r/n有且只有/r/n3/r/n個整數(shù)解，則/r/na/r/n的取/r/n值范圍是（/r/nA/r/n./r/n0/r/nWaW/r/nA/r/n./r/n0/r/nWaW/r/n2/r/n0/r/nWaV/r/n2/r/n0/r/nVaW/r/n2/r/nD/r/n./r/n0/r/n</r/na/r/n</r/n2/r/n解答】解：/r/n解不等式/r/n解答】解：/r/n解不等式/r/n3/r/nx/r/n-/r/n5/r/n2/r/n1/r/n得：/r/nx/r/n±/r/n2/r/n./r/n解不等式/r/n2/r/nx/r/n-/r/na/r/n</r/n8/r/n得：/r/nx/r/n</r/n警,/r/n???/r/n不等式組的解集為：/r/n2/r/nWx/r/n</r/n8/r/n+/r/n￡/r/n,/r/n?/r/n??不等式組/r/n?/r/n??不等式組/r/n｛2x/r/n-/r/na/r/n</r/n8/r/n3x/r/n—5/r/nn/r/n1/r/n有三個整數(shù)解,/r/n?/r/n??三個整數(shù)解為：/r/n2/r/n,/r/n3/r/n,/r/n4/r/n,/r/n4/r/n</r/n8+/r/n^/r/n<5,/r/n解得：/r/n0/r/nVaW/r/n2/r/n,/r/n故選：/r/nC/r/n./r/nfa/r/n一/r/nb(a/r/n>/r/n2b)/r/n(/r/n3/r/n分)(/r/n2020/r/n?濰坊)若定義一種新運算：/r/na/r/ng/r/nb/r/n=｛/r/n丄幾“孑”、，例如：/r/n3/r/n0/r/n1/r/n=/r/n3/r/na+b—6(a<2b)/r/n-/r/n1/r/n=/r/n2/r/n；/r/n5/r/n0/r/n4/r/n=/r/n5+4/r/n-/r/n6/r/n=/r/n3/r/n.貝/r/nV/r/n函數(shù)/r/ny/r/n=(/r/nx/r/n+2/r/n)/r/n0/r/n(/r/nx/r/n-/r/n1/r/n)的圖象大致是(/r/n)/r/n【解答】/r/n解：/r/n??/r/n?當/r/nx/r/n+2/r/n2/r/n2/r/n(/r/nx/r/n-/r/n1/r/n)時，/r/nxW/r/n4/r/n,/r/n當/r/nxW/r/n4/r/n時，/r/n(/r/nx/r/n+2/r/n)/r/n0/r/n(/r/nx/r/n-/r/n1/r/n)=(/r/nx/r/n+2/r/n)-(/r/nx/r/n-/r/n1/r/n)=/r/nx/r/n+2/r/n-/r/nx/r/n+1/r/n=/r/n3/r/n,/r/n即：/r/ny/r/n=/r/n3/r/n，/r/n當/r/nx/r/n>/r/n4/r/n時，/r/n(/r/nx/r/n+2/r/n)/r/n0/r/n(/r/nx/r/n-/r/n1/r/n)=(/r/nx/r/n+2/r/n)/r/n+/r/n(/r/nx/r/n-/r/n1/r/n)-/r/n6/r/n=/r/nx/r/n+2+/r/nx/r/n-/r/n1/r/n-/r/n6/r/n=/r/n2/r/nx/r/n-/r/n5/r/n,/r/n即：/r/ny/r/n=/r/n2/r/nx/r/n-/r/n5/r/n，/r/n./r/nk/r/n=/r/n2/r/n>/r/n0/r/n，/r/n?/r/n?.當/r/nx/r/n>/r/n4/r/n時，/r/ny/r/n=/r/n2/r/nx/r/n-/r/n5/r/n，函數(shù)圖象向上，/r/ny/r/n隨/r/nx/r/n的增大而增大，/r/n綜上所述，/r/nA/r/n選項符合題意./r/n故選：/r/nA/r/n./r/n二、填空題(本大題共/r/n6/r/n小題，共/r/n18/r/n分.只要求填寫最后結(jié)果，每小題填對得/r/n3/r/n分.)/r/n(/r/n3/r/n分)(/r/n2020/r/n?濰坊)因式分解：/r/nx/r/n2/r/ny/r/n-/r/n9/r/ny/r/n=/r/ny/r/n(/r/nx/r/n+3/r/n)(/r/nx/r/n-/r/n3/r/n)/r/n./r/n【解答】/r/n解：/r/nx/r/n2/r/ny/r/n-/r/n9/r/ny/r/n，/r/n=/r/ny/r/n(/r/nx/r/n2/r/n-/r/n9/r/n)，/r/n=/r/ny/r/n(/r/nx/r/n+3/r/n)(/r/nx/r/n-/r/n3/r/n)./r/n(/r/n3/r/n分)/r/n(/r/n2020/r/n?濰坊)若/r/nl/r/na/r/n-/r/n21/r/n+Vb/r/n—3=/r/n0/r/n,則/r/na/r/n+/r/nb/r/n=/r/n5/r/n./r/n【解答】/r/n解：根據(jù)題意得，/r/na/r/n-/r/n2/r/n=/r/n0/r/n，/r/nb/r/n-/r/n3/r/n=/r/n0/r/n，/r/n解得/r/na/r/n=/r/n2/r/n，/r/nb/r/n=/r/n3/r/n，/r/n?/r/na/r/n+/r/nb/r/n=/r/n2+3/r/n=/r/n5/r/n./r/n故答案為：/r/n5/r/n./r/n

/r/n15./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）如圖，在/r/nRt/r/nAABC/r/n中，/r/nZC/r/n=/r/n90/r/n°,/r/nZ/r/nB/r/n=/r/n20/r/n。，/r/nPQ/r/n垂直平分/r/nAB/r/n,/r/n垂足為/r/nQ/r/n,/r/n交/r/nBC/r/n于點/r/nP/r/n./r/n按以下步驟作圖：/r/n①/r/n以點/r/nA/r/n為圓心，以適當?shù)拈L為半徑作弧，/r/n1/r/n分別交邊/r/nAC/r/n，/r/nAB/r/n于點/r/nD/r/n，/r/nE/r/n；/r/n②/r/n分別以點/r/nD/r/n，/r/nE/r/n為圓心，以大于/r/nyDE/r/n的長為半徑作弧,兩弧相交于點/r/nF/r/n；/r/n③/r/n作射線/r/nAF/r/n./r/n若/r/nAF/r/n與/r/nPQ/r/n的夾角為/r/na/r/n,/r/n則/r/na/r/n=/r/n55/r/n°/r/n./r/n解答】解：如圖，/r/n???△/r/nABC/r/n是直角三角形/r/n，/r/nZC/r/n=/r/n90/r/n°,/r/n.?/r/n?/r/nZB/r/n+/r/nZBAC=/r/n90/r/n°,/r/nVZB=/r/n20/r/n°/r/n，/r/nAZBAC=/r/n90/r/n°-ZB=/r/n90/r/n°-/r/n20/r/n°=/r/n70/r/n°,/r/n?/r/nAM/r/n是/r/nZ/r/nBAC/r/n的平分線，/r/n11/r/nA/r/nZ/r/n2=/r/nI/r/n^BAC/r/n=/r/n2/r/nx70°=35°/r/n,/r/nPQ/r/n是/r/nAB/r/n的垂直平分線，/r/n???△/r/nAMQ/r/n是直角三角形，/r/nAZAMQ/r/n+/r/nZ/r/n2/r/n=/r/n90/r/n°,/r/nZAMQ=/r/n90/r/n°-Z/r/n2/r/n=/r/n90/r/n°-/r/n35/r/n°=/r/n55°,/r/nZ/r/na/r/n與/r/nZ/r/nAMQ/r/n是對頂角，/r/n?°.Z/r/na/r/n=ZAMQ=/r/n55/r/n°./r/n故答案為：/r/n55/r/n°./r/n中考數(shù)學試題/r/n中考數(shù)學試題/r/n中考數(shù)學試題/r/n中考數(shù)學試題/r/n2020/r/n2020/r/n年中考/r/n7/r/n25/r/n3/r/n2020/r/n7/r/n25/r/n3/r/n2020/r/n年中考/r/n3x/r/n加/r/n＜3/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）若關(guān)于/r/nx/r/n的分式方程/r/n=/r/n1/r/n有增根，則/r/nm/r/n=/r/n3/r/nX2x2/r/n【解答】/r/n解：去分母得：/r/n3/r/nx/r/n=/r/nm/r/n+3+/r/n（/r/nx/r/n-/r/n2/r/n）,整理得：/r/n2/r/nx/r/n=/r/nm/r/n+1/r/n,/r/nT/r/n關(guān)于/r/nx/r/n的分式方程/r/nT/r/n關(guān)于/r/nx/r/n的分式方程/r/n3x/r/nX2/r/nm3/r/nX2/r/n1/r/n有增根，即/r/nx/r/n-/r/n2/r/n=/r/n0/r/n,/r/n?/r/n.x/r/n=/r/n2/r/n./r/n把/r/nx/r/n=/r/n2/r/n代入到/r/n2/r/nx/r/n=/r/nm/r/n+1/r/n中得：/r/n2/r/nX/r/n2/r/n=/r/nm/r/n+1/r/n,/r/n解得：/r/nm/r/n=/r/n3/r/n；/r/n故答案為：/r/n3/r/n./r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）如圖，矩形/r/nABCD/r/n中，點/r/nG/r/n,/r/nE/r/n分別在邊/r/nBC/r/n,/r/nDC/r/n上，連接/r/nAC,/r/nEG/r/n,/r/nAE/r/n,/r/n將/r/n△/r/nABG/r/n和/r/nAECG/r/n分別沿/r/nAG/r/n,/r/nEG/r/n折疊，使點/r/nB/r/n,/r/nC/r/n恰好落在/r/nAE/r/n上的同一點,/r/n記為點/r/nF/r/n./r/n記為點/r/nF/r/n./r/n若/r/nCE/r/n=/r/n3/r/n,/r/nCG/r/n=/r/n4/r/n,/r/n則/r/nsin/r/nZDAE/r/n=/r/n7/r/n25/r/n【解答】/r/n解：矩形/r/nABCD/r/n中，/r/nGC/r/n=/r/n4/r/n,/r/nCE/r/n=/r/n3/r/n,ZC/r/n=/r/n90/r/n°,/r/n?/r/nGE/r/n=VGC2~CEi=/r/nV42~3/r/n2/r/n=5/r/n,/r/n根據(jù)折疊的性質(zhì)：/r/nBG/r/n=/r/nGF/r/n,/r/nGF/r/n=/r/nGC/r/n=/r/n4/r/n,/r/nCE/r/n=/r/nEF/r/n=/r/n3/r/n,ZAGB=ZAGF,ZEGC=Z/r/nEGF/r/n,//r/nGFE/r/n=//r/nC/r/n=/r/n90/r/n°,//r/nB/r/n=//r/nAFG/r/n=/r/n90/r/n°,/r/nBG=GF=GC=/r/n4/r/n,ZAFG/r/n+/r/nZEFG=/r/n90/r/n°,/r/nBC/r/n=/r/nAD/r/n=/r/n8/r/n,/r/n點/r/nA/r/n,/r/n點/r/nF/r/n,/r/n點/r/nE/r/n三點共線,/r/nVZAGB/r/n+/r/nZAGF/r/n+/r/nZEGC/r/n+/r/nZEGF=/r/n180/r/n°,/r/n?ZAGE=/r/n90/r/n°,/r/n???RtAEGFs/r/nRt/r/n^EAG,/r/nEGEF/r/n5/r/n3/r/n云=云/r/n，即石/r/n=/r/n5/r/n?/r/n?/r/n?/r/nEA=/r/n2/r/n5/r/n.*.DE=/r/n』/r/nAE/r/n2/r/nAD/r/ni/r/n=/r/nV/r/n（/r/n2/r/n3/r/n5/r/n）/r/n2/r/n8/r/n2/r/n=/r/n7/r/n,/r/nsinZDAE=/r/n芻￡/r/n7/r/nsinZDAE=/r/n芻￡/r/n7/r/n25/r/n,/r/n7/r/n故答案為：/r/n25/r/n*/r/n（/r/n3/r/n分）（/r/n2020/r/n?濰坊）如圖，四邊形/r/nABCD/r/n是正方形，曲線/r/nDA/r/n1/r/nB/r/n1/r/nC/r/n1/r/nD^A/r/n2/r/n…是由一段段/r/n90/r/n度的弧組成的.其中：/r/n圧/r/n町的圓心為點/r/nA/r/n,/r/n半徑為/r/nAD/r/n；/r/n可/r/n耳的圓心為點/r/nB/r/n,/r/n半徑為/r/nBA/r/n1/r/n；/r/n瓦/r/n-/r/n的圓心為點/r/nC/r/n，/r/n半徑為/r/nCB/r/n］/r/n；/r/n:/r/nq/r/n的圓心為點/r/nD/r/n，/r/n半徑為/r/nDC/r/n］/r/n；/r/n…可行，/r/nB/r/n1/r/nC/r/n1/r/n，/r/n?q,/r/n…的圓心依次按點/r/nA,B,C,D/r/n循環(huán).若正方形/r/nABCD/r/n的邊長為/r/n1,/r/n則/r/n^/r/n20/r/n^/r/n2020/r/n的長是/r/n4039/r/nn/r/n./r/n【解答】/r/n解：由圖可知，曲線/r/nDA/r/n1/r/nB/r/n1/r/nC/r/n1/r/nD^A/r/n2/r/n…是由一段段/r/n90/r/n度的弧組成的，半徑每次比前一段弧半徑/r/n+1/r/n,/r/nAD/r/n=/r/nAA/r/n1/r/n=/r/n1/r/n,/r/nBA/r/n1/r/n=/r/nBB/r/n1/r/n=/r/n2/r/n,/r/n,/r/nAD/r/nn/r/n_/r/n1/r/n=/r/nAA/r/nn/r/n=/r/n4/r/n(/r/nn/r/n-/r/n1/r/n)/r/n+1/r/n,/r/nBA/r/nn/r/n=/r/nBB/r/nn/r/n=/r/n4/r/n(/r/nn/r/n-/r/n1/r/n)/r/n+2/r/n,/r/n故/r/nA/r/n2o2/r/n?/r/nB/r/n2020/r/n的半徑為/r/nBA/r/n2020/r/n=/r/nBB/r/n2020/r/n=/r/n4/r/n(/r/n2020/r/n-/r/n1/r/n)/r/n+2/r/n=/r/n8078/r/n,/r/n^/r/n20^2020/r/n的弧長/r/n=/r/n90/r/n-90/r/nX8078/r/n兀/r/n=4039/r/n兀/r/n./r/n180/r/n故答案為：/r/n4039/r/nn/r/n./r/n三、解答題（本大題共/r/n7/r/n小題,共/r/n66/r/n分.解答應與出文字說明、證明過程或演算步驟.）/r/n19/r/n*（/r/n202°/r/n?濰坊）先化簡，再求值：/r/n（/r/n1/r/n-占/r/n1/r/n）一三，其中/r/nx/r/n是/r/n16/r/n的算術(shù)平方根./r/n解答】/r/n解：/r/n原式/r/n=/r/n嚴一/r/n解答】/r/n解：/r/n原式/r/n=/r/n嚴一/r/n2%+1/r/n(/r/n%/r/n2/r/n-2%+1/r/n%+1/r/n%/r/n2/r/n-2%+1/r/n%—3/r/n%-1/r/n，/r/n-/r/n%/r/n2/r/n—3x/r/n)/r/nx/r/n%_1/r/n%/r/n2/r/n—2%+1/r/n%_3/r/n%(%_3)/r/nx/r/n%_1/r/n(/r/n%_1/r/n)/r/n2/r/n%_/r/n3/r/n%/r/n1/r/n*/r/n???x/r/n是/r/n16/r/n的算術(shù)平方根,/r/n.°.x=4,/r/n4/r/n當/r/nx/r/n=/r/n4/r/n時，原式/r/n=/r/n3/r/n?/r/n（/r/n2020/r/n?濰坊）某?！熬C合與實踐”小組采用無人機輔助的方法測量一座橋的長度.如圖，橋/r/nAB/r/n是水平并且筆直的，測量過程中，小組成員遙控無人機飛到橋/r/nAB/r/n的上方/r/n120/r/n米的點/r/nC/r/n處懸停，此時測得橋兩端/r/nA/r/n，/r/nB/r/n兩點的俯角分別為/r/n60/r/n°和/r/n45/r/n°，求橋/r/nAB/r/n的長度./r/n【解答】解：如圖示：過點/r/nC/r/n作/r/nCD/r/n丄/r/nAB/r/n,/r/n垂足為/r/nD/r/n，/r/n由題意得/r/n，/r/nZMCA=ZA=/r/n60/r/n°,ZNCB=ZB=/r/n45/r/n°,CD=/r/n120/r/n,/r/n在/r/nRtG/r/nCD/r/n中,/r/nAD/r/n=/r/n島=揣/r/n=/r/n4"/r/n（米），/r/n在/r/nRt/r/nABCD/r/n中，/r/nVZCBD=/r/n45/r/n°,/r/n.??BD/r/n=/r/nCD/r/n=/r/n120/r/n（米），/r/n.??AB/r/n=/r/nAD/r/n+/r/nBD/r/n=（/r/n40/r/n^3+/r/n120/r/n）（米）/r/n./r/n答：橋/r/nAB/r/n的長度為（/r/n40/r/n^3+/r/n120/r/n）米./r/n（/r/n2020/r/n?濰坊）在/r/n4/r/n月/r/n23/r/n日“世界讀書日”來臨之際，某校為了了解學生的課外閱讀情況，從全校隨機抽取了部分學生，調(diào)查了他們平均每周的課外閱讀時間（單位：小時）.把調(diào)查結(jié)果分為四檔，/r/nA/r/n檔：/r/ntV/r/n8/r/n；/r/nB/r/n檔：/r/n8/r/nWtV/r/n9/r/n；/r/nC/r/n檔：/r/n9/r/nWtV/r/n10/r/n；/r/nD/r/n檔：/r/n&10/r/n./r/n根據(jù)調(diào)查情況，給出了部分數(shù)據(jù)信息：/r/nA/r/n檔和/r/nD/r/n檔的所有數(shù)據(jù)是：/r/n7/r/n,/r/n7/r/n,/r/n7.5/r/n,/r/n10/r/n,/r/n7/r/n,/r/n10/r/n,/r/n7/r/n,/r/n7.5/r/n,/r/n7/r/n,/r/n7/r/n,/r/n10.5/r/n,/r/n10.5/r/n；/r/n圖/r/n1/r/n和圖/r/n2/r/n是兩幅不完整的統(tǒng)計圖./r/n根據(jù)以上信息解答問題：/r/n求本次調(diào)查的學生人數(shù)，并將圖/r/n2/r/n補充完整；/r/n已知全校共/r/n1200/r/n名學生，請你估計全校/r/nB/r/n檔的人數(shù)；/r/n學校要從/r/nD/r/n檔的/r/n4/r/n名學生中隨機抽取/r/n2/r/n名作讀書經(jīng)驗分享，已知這/r/n4/r/n名學生/r/n1/r/n名來自七年級，/r/n1/r/n名來自八年級，/r/n2/r/n名來自九年級，請用列表或畫樹狀圖的方法，求抽到的/r/n2/r/n名學生來自不同年級的概率．/r/n【解答】解：(/r/n1/r/n)由于/r/nA/r/n檔和/r/nD/r/n檔共有/r/n12/r/n個數(shù)據(jù)，而/r/nD/r/n檔有/r/n4/r/n個，/r/n因此/r/nA/r/n檔共有：/r/n12/r/n-/r/n4/r/n=/r/n8/r/n人，/r/n8/r/n三/r/n20%/r/n=/r/n40/r/n人，/r/n補全圖形如下：/r/n(2/r/n)/r/n1200/r/nx/r/n40/r/n=/r/n480/r/n(人),/r/n答：全校/r/nB/r/n檔的人數(shù)為/r/n480/r/n．/r/n(/r/n3/r/n)用/r/nA/r/n表示七年級學生，用/r/nB/r/n表示八年級學生，用/r/nC/r/n和/r/nD/r/n分別表示九年級學生，畫/r/n樹狀圖如下，/r/n開始/r/nA/r/nB/r/nC/r/nD/r/nB/r/nCDACD/r/nABI>AB/r/nc/r/n因為共有/r/n12/r/n種等可能的情況數(shù)，其中抽到的/r/n2/r/n名學生來自不同年級的有/r/n10/r/n種，/r/n所以/r/nP/r/n2/r/n名學生來自不同年級）/r/n10/r/n所以/r/nP/r/n2/r/n名學生來自不同年級）/r/n10/r/n12/r/n5/r/n6/r/n*/r/n（/r/n2020/r/n?濰坊）如圖，/r/nAB/r/n為/r/nO/r/nO/r/n的直徑，射線/r/nAD/r/n交/r/nO/r/nO/r/n于點/r/nF/r/n,/r/n點/r/nC/r/n為劣弧麗的中點,/r/n過點/r/nC/r/n作/r/nCE/r/n丄/r/nAD/r/n,/r/n垂足為/r/nE/r/n,/r/n連接/r/nAC/r/n./r/n（1/r/n）求證：/r/nCE/r/n是/r/nO/r/nO/r/n的切線;/r/n（2/r/n）若/r/n（2/r/n）若/r/nZBAC/r/n=/r/n30/r/n°,/r/nAB/r/n=/r/n4/r/n,/r/n求陰影部分的面積./r/n【解答】解：（/r/n1/r/n）連接/r/nBF/r/n,/r/n*//r/nAB/r/n是/r/nO/r/nO/r/n的直徑，/r/nAZAFB=/r/n90/r/n°/r/n，即/r/nBF/r/nL/r/nAD,/r/n?.?CE/r/n丄/r/nAD/r/n,/r/n:./r/nBF//CE/r/n,/r/n連接/r/nOC/r/n,/r/n??/r/n?點/r/nC/r/n為劣弧麗的中點，/r/n.?.OC/r/n丄/r/nBF/r/n,/r/n?:/r/nBF//CE/r/n,/r/n：./r/nOC/r/nICE,/r/nVOC/r/n是/r/nO/r/nO/r/n的半徑，/r/n???CE/r/n是/r/nOO/r/n的切線；/r/n(/r/n2/r/n)連接/r/nOF/r/n,/r/nVOA=OC,ZBAC=/r/n30°/r/n,/r/nZBOC=/r/n60/r/n°,/r/n??/r/n?點/r/nC/r/n為劣弧麗的中點，/r/nFC/r/n=/r/nBC/r/n,/r/nZFOC=ZBOC=/r/n60/r/n°,/r/n

/r/nVAB=/r/n4/r/n,/r/n：?/r/nF0/r/n=/r/n0C/r/n=/r/n0B/r/n=/r/n2/r/n,/r/n.c/r/n60/r/n?兀/r/nx2/r/n2/r/n=/r/n2/r/n,,S/r/n扇形/r/nOC/r/n=/r/n360/r/n=/r/n3/r/nn/r/n，/r/n2/r/n即陰影部分的面積為：/r/n3/r/n“/r/nD/r/nD/r/n（/r/n2020/r/n?濰坊）因疫情防控需要，消毒用品需求量增加.某藥店新進一批桶裝消毒液，每桶進價/r/n50/r/n元，每天銷售量/r/ny/r/n（桶）與銷售單價/r/nx/r/n（元）之間滿足一次函數(shù)關(guān)系，其圖象如圖所示./r/n1/r/n）/r/n求/r/ny/r/n與/r/nx/r/n之間的函數(shù)表達式；/r/n2/r/n）/r/n每桶消毒液的銷售價定為多少元時，藥店每天獲得的利潤最大，最大利潤是多少元？/r/n（利潤=銷售價-進價）/r/n100/r/n80/r/nO/r/n6070/r/n頂元/r/n（利潤=銷售價-進價）/r/n100/r/n80/r/nO/r/n6070/r/n頂元/r/n）/r/n【解答】解：（/r/n1/r/n）設(shè)/r/ny/r/n與銷售單價/r/nx/r/n之間的函數(shù)關(guān)系式為：/r/ny/r/n=/r/nkx/r/n+/r/nb/r/n，/r/n

/r/n將點（/r/n60/r/n,/r/n100/r/n）、（/r/n70/r/n，/r/n80/r/n）代入一次函數(shù)表達式得：/r/n{101707+r/r/n解得：/r/n{/r/n解得：/r/n{/r/nk/r/n=/r/n—2/r/nb/r/n=/r/n220/r/n,/r/n故函數(shù)的表達式為：/r/ny/r/n=-/r/n2/r/nx/r/n+220/r/n；/r/n（2/r/n）設(shè)藥店每天獲得的利潤為/r/nW/r/n元，由題意得:/r/nw/r/n=(/r/nx/r/n-/r/n50/r/n)/r/n(-/r/n2/r/nx/r/n+220/r/n)=-/r/n2/r/n(/r/nx/r/n-/r/n80/r/n)/r/n2/r/n+1800/r/n,/r/n???-/r/n2/r/nV/r/n0/r/n,/r/n函數(shù)有最大值，/r/n??.當/r/nx/r/n=/r/n80/r/n時，/r/nw/r/n有最大值，此時最大值是/r/n1800/r/n,/r/n故銷售單價定為/r/n80/r/n元時，該藥店每天獲得的利潤最大，最大利潤/r/n1800/r/n元．/r/n(/r/n2020/r/n?濰坊)如圖/r/n1/r/n,在/r/n△/r/nABC/r/n中，/r/nZA/r/n=/r/n90/r/n°,/r/nAB/r/n=/r/nAC/r/n=V2+/r/n1/r/n,/r/n點/r/nD/r/n,/r/nE/r/n分別在邊/r/nAB/r/n,/r/nAC/r/n上，且/r/nAD/r/n=/r/nAE/r/n=/r/n1/r/n,/r/n連接/r/nDE/r/n./r/n現(xiàn)將/r/nAADE/r/n繞點/r/nA/r/n順時針方向旋轉(zhuǎn)，旋轉(zhuǎn)角為/r/na/r/n(/r/n0/r/n°V/r/na/r/nV/r/n360/r/n°),/r/n如圖/r/n2/r/n,/r/n連接/r/nCE/r/n,/r/nBD/r/n,/r/nCD/r/n./r/n當/r/n0/r/n°V/r/na/r/nV/r/n180/r/n°/r/n時，求證：/r/nCE/r/n=/r/nBD/r/n；/r/n如圖/r/n3/r/n,當/r/na/r/n=/r/n90/r/n。時，延長/r/nCE/r/n交/r/nBD/r/n于點/r/nF/r/n,/r/n求證：/r/nCF/r/n垂直平分/r/nBD/r/n；/r/n在旋轉(zhuǎn)過程中，求/r/nABCD/r/n的面積的最大值，并寫出此時旋轉(zhuǎn)角/r/na/r/n的度數(shù)./r/nC/r/nE/r/nE/r/nA/r/nA/r/nB/r/nA/r/nB/r/nD/r/nD/r/n圖/r/nC/r/nE/r/nE/r/nA/r/nA/r/nB/r/nA/r/nB/r/nD/r/nD/r/n圖/r/n3/r/n【解答】(/r/n1/r/n)證明：如圖/r/n2/r/n中，根據(jù)題意:/r/nAB/r/n=/r/nAC/r/n,/r/nAD/r/n=/r/nAE,ZCAB=ZEAD/r/n=/r/n90/r/n°,/r/nVZCAE/r/n+/r/nZBAE=ZBAD/r/n+/r/nZBAE=/r/n90/r/n°,/r/nAZCAE=ZBAD,/r/n在/r/nAACE/r/n和/r/nAABD/r/n中，/r/nAC=AB/r/n{/r/n^CAE=ABAD/r/n,/r/nAE=AD/r/n.?./r/n△/r/nACE9AABD(SAS),/r/n.??CE/r/n=/r/nBD/r/n；/r/n(/r/n2/r/n)/r/n證明：如圖/r/n3/r/n中，根據(jù)題意：/r/nAB/r/n=/r/nAC/r/n,/r/nAD/r/n=/r/nAE,ZCAB=ZEAD/r/n=/r/n90/r/n°,/r/n在/r/nAACE/r/n和/r/nAABD/r/n中，/r/nAC/r/n=/r/nAB/r/n{/r/naCAE/r/n=ABAD/r/n,/r/nAE=AD/r/n.?./r/n△/r/nACE9AABD(SAS),/r/n?.ZACE=ZABD,/r/n??ZACE/r/n+/r/nZAEC/r/n=/r/n90/r/n。，且/r/nZAEC=ZFEB/r/n,/r/nAZABD/r/n+/r/nZFEB=/r/n90/r/n°,/r/nAZEFB=/r/n90/r/n°,/r/n./r/nCF/r/n丄/r/nBD/r/n,/r/n

/r/nVAB=AC/r/n=V2+1/r/n,AD=AE=/r/n1/r/n,ZCAB=ZEAD=/r/n90°/r/n,/r/n:/r/n.bc/r/n=42/r/nab/r/n=42+2/r/n,/r/nCD=AC/r/n+/r/nAD/r/n=V2+2/r/n,/r/n:/r/n.BC/r/n=/r/nCD/r/n,/r/nVCF/r/n丄/r/nBD/r/n,/r/n???CF/r/n是線段/r/nBD/r/n的垂直平分線；/r/n解：/r/nABCD/r/n中，邊/r/nBC/r/n的長是定值，則/r/nBC/r/n邊上的高取最大值時/r/nABCD/r/n的面積有最/r/n大值,/r/n???/r/n當點/r/nD/r/n在線段/r/nBC/r/n的垂直平分線上時，/r/nABCD/r/n的面積取得最大值，如圖/r/n4/r/n中:/r/nD/r/nE/r/nD/r/nE/r/n@4/r/nWAB=AC/r/n=V2+1/r/n，/r/nAD=AE=/r/n1/r/n，/r/nZCAB=ZEAD=/r/n90/r/n°/r/n，/r/nDG/r/n丄/r/nBC/r/n于/r/nG/r/n,/r/n:/r/n.AG/r/n=/r/n|/r/nbc/r/n=/r/ny/r/n:/r/n.AG/r/n=/r/n|/r/nbc/r/n=/r/ny/r/n2+2/r/n2/r/n，/r/nZGAB=/r/n45/r/n:/r/n.DG/r/n=/r/nAG/r/n+/r/nAD/r/n=/r/ny/r/n2+2/r/n2/r/n+1=/r/n^/r/n2+/r/n4/r/n，/r/nZDAB=/r/n180°/r/n-45/r/n°=/r/n135/r/n°,/r/n1/r/n{64/r/n押弈/r/n8==/r/n0/r/no/r/n,/r/n解得仁一/r/n1/r/n1/r/n???/r/n拋物線解析式為：/r/ny=-/r/n—/r/nx2+3x+8/r/n；/r/n(/r/n2/r/n)當/r/nx/r/n=/r/n0/r/n時,/r/ny/r/n=/r/n8/r/n,/r/n?/r/nC/r/n(/r/n0/r/n,/r/n8/r/n),/r/n?直線/r/nBC/r/n解析式為：/r/ny/r/n=-/r/nx/r/n+8/r/n,/r/n11/r/n???s/r/n△亦/r/n=/r/n—/r/n如/r/n3/r/n=/r/n——°淞=/r/n4/r/n°/r/n，/r/n?S^pbc/r/n二/r/nl/r/nS/r/n△/r/nABC/r/n=/r/n-4/r/n，/r/n過點/r/nP/r/n作/r/nPG/r/n丄/r/nx/r/n軸，交/r/nx/r/n軸于點/r/nG/r/n,/r/n交/r/nBC/r/n于點/r/nF,/r/nP/r/n設(shè)/r/n1_2/r/nP/r/n設(shè)/r/n1_2/r/n???F/r/n(/r/nt/r/n,-/r/nt/r/n+8/r/n),/r/n1/r/nPF/r/n=/r/n一/r/n二代/r/n+4t/r/n,/r/n1/r/n???S/r/n△嘶