北京市朝陽區(qū)2019~2020學(xué)年度第一學(xué)期期末檢測九年級數(shù)學(xué)

D/r/n)/r/n1/r/n6/r/nD/r/n)/r/n1/r/n6/r/n./r/n如圖，在正方形網(wǎng)格中，/r/nA/r/nMPN/r/n繞某一點旋轉(zhuǎn)某一角度得到/r/n△/r/nMPN'，/r/n則旋轉(zhuǎn)中心可能/r/n北京市朝陽區(qū)/r/n2019~2020/r/n學(xué)年度第一學(xué)期期末檢測/r/n九年級數(shù)學(xué)試卷(選用)/r/n(/r/n考試時間/r/n120/r/n分鐘滿分/r/n100/r/n分/r/n)/r/n一、選擇題(本題共/r/n16/r/n分，每小題/r/n2/r/n分)/r/n第/r/n1—8/r/n題均有四個選項，符合題意的選項只/r/n．/r/n有/r/n．/r/n一個．/r/n1/r/n．下列事件中，隨機事件是/r/n通常溫度降到/r/n0°/r/nC/r/n以下，純凈的水結(jié)冰/r/n隨意翻到一本書的某頁，這頁的頁碼是偶數(shù)/r/n明天太陽從東方升起/r/n三角形的內(nèi)角和是/r/n360/r/n°/r/n拋物線/r/ny/r/n=/r/n(/r/nx/r/n-/r/n2)/r/n2/r/n+1/r/n的頂點坐標(biāo)是/r/n(/r/nA/r/n)/r/n(2/r/n，/r/n1)/r/n(/r/nB/r/n)/r/n(-2/r/n，/r/n1)/r/n(/r/nC/r/n)/r/n(-2/r/n，/r/n-1)/r/n(/r/nD/r/n)/r/n(1/r/n，/r/n2)/r/n只有/r/n1/r/n和它本身兩個因數(shù)且大于/r/n1/r/n的自然數(shù)叫做素數(shù)，我國數(shù)學(xué)家陳景潤在有關(guān)素數(shù)/r/n的/r/n“/r/n哥德巴赫猜想/r/n”/r/n的研究中取得了世界領(lǐng)先的成果.從/r/n5/r/n，/r/n7/r/n，/r/n11/r/n這/r/n3/r/n個素數(shù)中隨機抽取一/r/n個，則抽到的數(shù)是/r/n7/r/n的概率是/r/n1/r/n11/r/n1/r/n(/r/nA/r/n)/r/n7/r/n(/r/nB/r/n)/r/n5/r/n把/r/nRt/r/nA/r/nABC/r/n三邊的長度都擴大為原來的/r/n3/r/n倍，則銳角/r/nA/r/n的余弦值/r/n1/r/n(/r/nA/r/n)/r/n不變/r/n(/r/nB/r/n)/r/n縮小為原來的/r/n3/r/n(/r/nC/r/n)/r/n擴大為原來的/r/n3/r/n倍/r/n(/r/nD/r/n)/r/n擴大為原來的/r/n9/r/n倍/r/n5/r/n.如圖，/r/n△/r/nABC/r/n中，點/r/nD/r/n,/r/nE/r/n分另/r/nIJ/r/n在/r/nAB/r/n,/r/nAC/r/n上,/r/nDEllBC/r/n./r/n若/r/nAD/r/n=1/r/n，/r/nBD/r/n=2/r/n，貝/r/n^△/r/nADE/r/n與/r/n△/r/nABC/r/n的面積之比為/r/n(/r/nA/r/n)/r/n1:2/r/n(/r/nB/r/n)/r/n1:3/r/nD/r/n)/r/n1:9/r/nC/r/n)/r/n1:4/r/n

/r/nD/r/n)/r/n1:9/r/n7/r/n.已知/r/no/r/no/r/n1/r/n,/r/no/r/no/r/n2/r/n,/r/n7/r/n.已知/r/no/r/no/r/n1/r/n,/r/no/r/no/r/n2/r/n,/r/no/r/no/r/n3/r/n是等圓，/r/n△/r/nabp/r/n內(nèi)接于/r/no/r/no/r/n1/r/n，/r/n點/r/nC/r/n,/r/nE/r/n分別在/r/no/r/no/r/n2/r/n,/r/no/r/no/r/n3/r/n上.如圖，/r/n以/r/nC/r/n為圓心，/r/nAP/r/n長為半徑作弧交。/r/n0/r/n2/r/n于點/r/nD/r/n,/r/n連接/r/nCD/r/n；/r/n以/r/nE/r/n為圓心，/r/nBP/r/n長為半徑作弧交/r/nO/r/n0/r/n3/r/n于點/r/nF/r/n,/r/n連接/r/nEF/r/n；/r/nF/r/n面有四個結(jié)論:/r/nCD/r/n+/r/nEF/r/n=/r/nAB/r/nCd/r/n+/r/nEf/r/n=/r/nAb/r/n-/r/n-/r/n-/r/nZ/r/nCO/r/n2/r/nD/r/n+/r/nZ/r/nEO/r/n3/r/nF/r/n=/r/nZ/r/nAO/r/n1/r/nB/r/nz/r/ncdo/r/n2/r/n+/r/nz/r/nefo/r/n3/r/n=/r/nZ/r/nP/r/n所有正確結(jié)論的序號是/r/n（/r/nA/r/n）/r/n①②③④/r/n（/r/nB/r/n）/r/n①②③/r/n（/r/nC/r/n）/r/n②④/r/n（/r/nD/r/n）/r/n②③④/r/n8/r/n如圖，拋物線/r/ny/r/n=/r/n1/r/nx/r/n2/r/n-/r/n1/r/n與/r/nx/r/n軸交于/r/nA/r/n，/r/nB/r/n兩點，/r/nD/r/n是以/r/n./r/n點/r/nC/r/n（/r/n0/r/n，/r/n4/r/n）為圓心,/r/nAD/r/n的中點，連接/r/nOE,/r/n1/r/n為半徑的圓上的動點，/r/nE/r/n是線段/r/nBD/r/n，/r/n則線段/r/nOE/r/n的最小值是/r/n(A/r/n)/r/n2/r/nD/r/n)/r/n3/r/n二、填空題（本題共/r/n16/r/n分，每小題/r/n2/r/n分）/r/n9/r/n．點（/r/n-1/r/n，/r/n-3/r/n）關(guān)于原點的對稱點的坐標(biāo)為/r/n．/r/n如圖，在平面直角坐標(biāo)系/r/nxOy/r/n中，射線/r/nl/r/n的端點為（/r/n0/r/n,/r/n1/r/n）,/r/n//r/n〃/r/nx/r/n軸，請寫出一個圖象/r/n第/r/n12/r/n題圖/r/n第/r/n13/r/n題圖/r/n第/r/n10/r/n題圖/r/n第/r/n12/r/n題圖/r/n第/r/n13/r/n題圖/r/n第/r/n10/r/n題圖/r/n第/r/n11/r/n題/r/n圖/r/n[5_/r/n1/r/n如果一個矩形的寬與長的比等于黃金數(shù)/r/n止/r/n1/r/n（約為），就稱這個矩形為黃金矩形/r/n./r/n如/r/n圖，矩形/r/nABCD/r/n為黃金矩形，寬/r/nAD/r/n=/r/n^/r/n5/r/n-/r/n1/r/n，則長/r/nAB/r/n為/r/n./r/n如圖，線段/r/nAB/r/n經(jīng)過/r/n0/r/nO/r/n的圓心，/r/nAC/r/n，/r/nBD/r/n分別與/r/n0/r/nO/r/n相切于點/r/nC/r/n，/r/nD/r/n./r/n若/r/nAC/r/n=/r/nBD/r/n=/r/n1,/r/nZ/r/nA/r/n=/r/n45°/r/n,/r/n則/r/nCD/r/n的長度為/r/n./r/n如圖，在正方形網(wǎng)格中，點/r/nA/r/n,/r/nB/r/n,/r/nC/r/n在/r/n0/r/n0/r/n上，并且/r/n都是小正方形的頂點，/r/nP/r/n是/r/nACB/r/n上/r/n任意一點，則/r/nZ/r/nP/r/n的正切值為/r/n./r/n拋物線/r/ny/r/n=/r/nax/r/n2/r/n-2/r/nax/r/n-3/r/n與/r/nx/r/n軸交于兩點，分別是是/r/n（/r/nm/r/n,/r/n0/r/n）,（/r/nn/r/n,/r/n0/r/n）,則/r/nm/r/n+/r/nn/r/n的值/r/n為/r/n./r/n為了打贏脫貧攻堅戰(zhàn)，某村計劃將該村的特產(chǎn)柑橘運到/r/nA/r/n地進行銷售/r/n./r/n由于受道路條件的限制，需要先將柑橘由公路運到火車站，再由鐵路運到/r/nA/r/n地/r/n?/r/n村里負責(zé)銷售的人員從該村運到火車站的所有柑橘中隨機抽取若干柑橘，進行了“柑橘完好率”統(tǒng)計，獲得的數(shù)據(jù)記錄如下表：/r/n柑橘總質(zhì)/r/n量/r/nn/r/n/kg/r/n100/r/n150/r/n200/r/n250/r/n300/r/n350/r/n400/r/n450/r/n500/r/n完好柑橘質(zhì)量/r/nm/r/n/kg/r/n柑橘完好/r/nm/r/n的頻率一/r/nn/r/n①估計從該村運到火車站柑橘完好的概率為/r/n（結(jié)果保留小數(shù)點后三位）;/r/n②若從該村運到/r/nA/r/n地柑橘完好的概率為/r/n，/r/n估計從火車站運到/r/nA/r/n地柑橘完好的概率為./r/n16/r/n．/r/n如圖，分別過第二象限內(nèi)的點/r/nP/r/n作/r/nx/r/n,/r/ny/r/n軸的平行線，與/r/ny/r/n,/r/nx/r/n軸分別交于點/r/nA/r/n,/r/nB/r/n,/r/n與/r/n③存在無數(shù)個點/r/nP/r/n使/r/nS/r/n=/r/nS/r/n四邊形/r/nOAPB/r/n△/r/nACD/r/n所有正確結(jié)論的序號是/r/n三、解答題（本題共/r/n68/r/n分，第/r/n1722/r/n題，每小題/r/n5/r/n分，第/r/n2326/r/n題，每小題/r/n6/r/n分，第/r/n27/r/n28/r/n題，每小題/r/n7/r/n分）/r/n17/r/n.計算：/r/nsin60/r/no/r/n—/r/ncos30/r/n。/r/n+/r/ntan45/r/n。/r/n./r/n4/r/n如圖，在/r/nA/r/nABC/r/n中/r/n，Z/r/nB/r/n=30/r/n°,/r/ntan/r/nC/r/n=/r/n3/r/n，/r/nAD/r/n丄/r/nBC/r/n于點/r/nD/r/n./r/n若/r/nAB/r/n=8/r/n，求/r/nBC/r/n的長./r/n

/r/n19./r/n如圖，/r/n△/r/nABC/r/n為等邊三角形，將/r/nBC/r/n邊繞點/r/nB/r/n順時針旋轉(zhuǎn)/r/n30/r/n°，得到線段/r/nBD/r/n,/r/n連接/r/nAD/r/n,/r/n20./r/n已知一次函數(shù)/r/ny/r/n=/r/nkx/r/n+/r/nm/r/n(/r/nk/r/n工/r/n0)/r/n和二次函數(shù)/r/ny/r/n=/r/nax/r/n2/r/n+/r/nbx/r/n+/r/nc/r/n(/r/na/r/nH/r/nO)/r/n部分自變量和對應(yīng)的函/r/n1/r/n2/r/n數(shù)值如下表：/r/nx/r/n?…/r/n-2/r/n-1/r/n0/r/n1/r/n2/r/n?…/r/n???/r/n0/r/n1/r/n2/r/n3/r/n4/r/n???/r/ny/r/n???/r/n0/r/n-1/r/n0/r/n3/r/n8/r/n???/r/n求/r/ny/r/n2/r/n的表達式；/r/n關(guān)于/r/nx/r/n的不等式/r/nax/r/n2/r/n+/r/nbx/r/n+/r/nc/r/n>/r/nkx/r/n+/r/nm/r/n的解集是/r/n./r/n筒車是我國古代發(fā)明的一種水利灌溉工具，彰顯了我國古代勞動人民的智慧，圖/r/n1/r/n,點/r/nP/r/n表示筒車的一個盛水桶.如圖/r/n2/r/n,當(dāng)筒車工作時，盛水桶的運行路徑是以軸心/r/n0/r/n為圓心，/r/n5/r/nm/r/n為半徑的圓，且圓心在水面上方.若圓被水面截得的弦/r/nAB/r/n長為/r/n8m/r/n,/r/n求筒車工作時，盛水桶在水面以下的最大深度．/r/n圖/r/n1/r/n圖/r/n2/r/n在平面內(nèi)，/r/n0/r/n為線段/r/nAB/r/n的中點，所有到點/r/n0/r/n的距離等于/r/n0A/r/n的點組成圖形/r/nW/r/n./r/n取/r/n0A/r/n的中點/r/nC/r/n,/r/n過點/r/nC/r/n作/r/nCD/r/n丄/r/nAB/r/n交圖形/r/nW/r/n于的點/r/nD/r/n，/r/nD/r/n在直線/r/nAB/r/n的上方，連接/r/nAD/r/n，/r/nBD/r/n./r/n求/r/nZ/r/nABD/r/n的度數(shù)；/r/n若點/r/nE/r/n在線段/r/nCA/r/n的延長線上，且/r/nZ/r/nADE/r/n=/r/nZ/r/nABD/r/n，求直線/r/nDE/r/n與圖形/r/nW/r/n的公共點個數(shù)/r/n./r/n備用圖/r/n23/r/n．閱讀下面材料：/r/n請回答：/r/n?.?AB/r/n=/r/nAC/r/n,/r/nAZ/r/nABC/r/n=/r/nZ/r/nACB/r/n./r/n?：Z/r/nPCB/r/n=/r/nZ/r/nPBA/r/n,/r/n:./r/n上/r/nPCA/r/n=/r/n./r/nVZ/r/nPAC/r/n=/r/nZ/r/nPCB/r/n,/r/n?/r/n?/r/n?△/r/nACP/r/ns^/r/nCBP/r/n./r/n?/r/nAP/r/n_/r/nPC/r/n_/r/nAC'PB~CB/r/nVZ/r/nACB/r/n=45/r/n°,/r/n.??Z/r/nBAC/r/n=90/r/n°/r/n./r/n?/r/nAC/r/n??/r/n=/r/n■/r/nCB/r/nV/r/nAP/r/n=1/r/n,/r/n./r/n\/r/nPC/r/n=</r/n2/r/n./r/n:./r/nPB/r/n=/r/n./r/n參考小軍的思路，解決問題：/r/nAP/r/n如圖/r/n1/r/n,在/r/n△/r/nABC/r/n中，/r/nAB/r/n=/r/nAC/r/n,/r/nP/r/n是/r/n△/r/nABC/r/n內(nèi)一點，/r/nZ/r/nPAC/r/n=/r/nZ/r/nPCB/r/n=/r/nZ/r/nPBA/r/n./r/n若/r/nZ/r/nACB/r/n=30°/r/n,/r/n求竺/r/nBP/r/n的值；/r/n點/r/nA/r/n是反比例函數(shù)/r/ny/r/n_/r/n—(/r/nx/r/n>/r/n0)/r/n的圖象/r/n1/r/n1/r/n上一點，直線/r/nAB/r/n〃/r/nx/r/n軸，交反比例函數(shù)/r/nx/r/n3/r/n3/r/ny/r/n=/r/n—(/r/nx/r/n>/r/n0)/r/n的圖象/r/nl/r/n2/r/n于點/r/nB/r/n,/r/n直線/r/nAC/r/n,/r/n軸，交/r/nl/r/n2/r/n于點/r/nC/r/n,/r/n直線/r/nCCD/r/nIIx/r/n軸，交/r/nI/r/nx/r/n于點/r/nD/r/n．/r/n(1)/r/n若點/r/nA/r/n(1/r/n,/r/n1)/r/n,/r/n求線段/r/nAB/r/n和/r/nCD/r/n的長度；/r/n⑵對于任意的點/r/nA/r/n(/r/na/r/n,/r/nb/r/n)/r/n,/r/n判斷線段/r/nAB/r/n和/r/nCD/r/n的大小關(guān)系，并證明./r/n如圖，在矩形/r/nABCD/r/n中，/r/nE/r/n是/r/nBA/r/n延長線上的定點，/r/nM/r/n為/r/nBC/r/n邊上的一個動點，連接/r/nME/r/n,/r/n將射線/r/nME/r/n繞點/r/nM/r/n順時針旋轉(zhuǎn)/r/n76/r/n。/r/n，交射線/r/nCD/r/n于點/r/nF/r/n,/r/n連接/r/nMD/r/n./r/nB/r/nA//r/nC/r/n小東根據(jù)學(xué)習(xí)函數(shù)的經(jīng)驗，對線段/r/nBM/r/n,/r/nDF/r/n,/r/nDM/r/n的長度之間的關(guān)系進行了探究/r/n./r/n下面是小東探究的過程，請補充完整：/r/n(/r/n1/r/n)對于點/r/nM/r/n在/r/nBC/r/n上的不同位置，畫圖、測量，得到了線段/r/nBM/r/n,/r/nDF/r/n,/r/nDM/r/n的長度的/r/n幾組值，如下表：/r/n位置/r/n1/r/n位置/r/n2/r/n位置/r/n3/r/n位置/r/n4/r/n位置/r/n5/r/n位置/r/n6/r/n位置/r/n7/r/n位置/r/n8/r/n位置/r/n9/r/nBM/r/n/cm/r/nDF/r/n/cm/r/nDM/r/n/cm/r/n在/r/nBM/r/n,/r/nDF/r/n,/r/nDM/r/n的長度這三個量中，確/r/n的長度是自變量，/r/n的長度/r/n和/r/n的長度都是這個自變量的函數(shù)；/r/n在同一平面直角坐標(biāo)系/r/nxOy/r/n中，畫出(/r/n1/r/n)中所確定的函數(shù)的圖象；/r/n結(jié)合畫出的函數(shù)圖象，解決問題：當(dāng)/r/nDF=/r/n2cm/r/n時，/r/nDM/r/n的長度約為/r/ncm./r/n26/r/n.在平面直角坐標(biāo)系/r/nxOy/r/n中，拋物線/r/ny/r/n二/r/nax/r/n2/r/n+/r/nbx/r/n經(jīng)過點/r/n(3/r/n,/r/n3)/r/n./r/n(1)/r/n用含/r/na/r/n的式子表示/r/nb/r/n；/r/n⑵直線/r/ny/r/n二/r/nx/r/n+/r/n4/r/na/r/n+4/r/n與直線/r/ny/r/n二/r/n4/r/n交于點/r/nB/r/n,/r/n求點/r/nB/r/n的坐標(biāo)(用含/r/na/r/n的式子表示)；/r/n在/r/n(2)/r/n的條件下，已知點/r/nA/r/n(1/r/n，/r/n4)/r/n，若拋物線與線段/r/nAB/r/n恰有一個公共點，直接寫出/r/na/r/n(/r/na/r/nV/r/nO)/r/n的取值范圍/r/n./r/n27/r/n./r/n已知/r/nZ/r/nMON/r/n=120/r/n°,/r/n點/r/nA,/r/nB/r/n分別在/r/nON/r/n,/r/nOM/r/n邊上，且/r/nOA/r/n=/r/nOB/r/n,/r/n點/r/nC/r/n在線段/r/nOB/r/n上(不與點/r/nO/r/n,/r/nB/r/n重合)，連接/r/nCA/r/n./r/n將射線/r/nCA/r/n繞點/r/nC/r/n逆時針旋轉(zhuǎn)/r/n120/r/n°得到射線/r/nCA/r/nZ/r/n,/r/n將射線/r/nBO/r/n繞點/r/nB/r/n逆時針旋轉(zhuǎn)/r/n150/r/n°與射線/r/nCA，/r/n交于點/r/nD/r/n./r/n(1)/r/n根據(jù)題意補全圖/r/n1/r/n；/r/n(2/r/n)/r/n求證：①/r/nZ/r/nOAC/r/n=/r/nZ/r/nDCB/r/n；/r/n②/r/nCD/r/n=/r/nCA/r/n(提示：可以在/r/nOA/r/n上截取/r/nOE/r/n=/r/nOC/r/n,/r/n連接/r/nCE/r/n)；/r/n⑶點/r/nH/r/n在線段/r/nAO/r/n的延長線上，當(dāng)線段/r/nOH/r/n,/r/nOC/r/n,/r/nOA/r/n滿足什么等量關(guān)系時，對于任意的點/r/nC/r/n都有/r/nZ/r/nDCH/r/n=2/r/nZ/r/nDAH/r/n,/r/n寫出你的猜想并證明/r/n./r/n備用圖/r/n28/r/n.在平面直角坐標(biāo)系/r/nxOy/r/n中，已知點/r/nA/r/n(0/r/n,/r/n2)/r/n,點/r/nB/r/n在/r/nx/r/n軸上，以/r/nAB/r/n為直徑作。/r/nC/r/n,/r/n點/r/nP/r/n在/r/ny/r/n軸上，且在點/r/nA/r/n上方，過點/r/nP/r/n作/r/n0/r/nC/r/n的切線/r/nPQ/r/n,/r/nQ/r/n為切點，如果點/r/nQ/r/n在第一象限,/r/n則稱/r/nQ/r/n為點/r/nP/r/n的離點/r/n./r/n例如，圖/r/n1/r/n中的/r/nQ/r/n為點/r/nP/r/n的一個離點/r/n./r/n⑴已知點/r/nP/r/n(0/r/n,/r/n3)/r/n,/r/nQ/r/n為/r/nP/r/n的離點/r/n./r/n如圖/r/n2/r/n,若/r/nB/r/n(0/r/n,/r/n0)/r/n,則圓心/r/nC/r/n的坐標(biāo)為/r/n，線段/r/nPQ/r/n的長為/r/n若/r/nB/r/n(2/r/n，/r/n0)/r/n，求線段/r/nPQ/r/n的長；/r/n⑵已知/r/n1/r/nW/r/nPA/r/nW/r/n2,/r/n直線/r/nI/r/n：/r/ny/r/n二/r/nkx/r/n+/r/nk/r/n+/r/n3/r/n(/r/nk/r/nM/r/n0/r/n)/r/n./r/n當(dāng)/r/nk/r/n=1/r/n時，若直線/r/nI/r/n上存在/r/nP/r/n的離點/r/nQ/r/n,/r/n則點/r/nQ/r/n縱坐標(biāo)/r/nt/r/n的最大值為/r/n；/r/n記直線/r/nI/r/n：/r/ny/r/n二/r/nkx/r/n+/r/nk/r/n+/r/n3/r/n(/r/nk/r/nM/r/n0/r/n)/r/n在/r/nTWxW/r/nl/r/n的部分為圖形/r/nG/r/n,/r/n如果圖形/r/nG/r/n上存在/r/nP/r/n的離點，直接寫出/r/nk/r/n的取值范圍/r/n./r/n九年級數(shù)學(xué)試卷參考答案及評分標(biāo)準(zhǔn)/r/n一、選擇題（本題共/r/n16/r/n分，每小題/r/n2/r/n分）/r/n題號/r/n1/r/n2/r/n3/r/n4/r/n5/r/n6/r/n7/r/n8/r/n答案/r/nB/r/nA/r/nC/r/nA/r/nD/r/nB/r/nD/r/nA/r/n二、填空題（本題共/r/n16/r/n分，每小題/r/n2/r/n分）/r/n題號/r/n9/r/n10/r/n11/r/n12/r/n答案/r/n(1,3)/r/n答案不唯一.如：/r/n1/r/ny=-/r/nx/r/n2/r/n兀/r/n題號/r/n13/r/n14/r/n15/r/n16/r/n答案/r/n1/r/n2/r/n2/r/n答案不唯一./r/n__22/r/n如：①；②/r/n23/r/n①②③/r/n三、解答題（本題共/r/n68/r/n分，第/r/n17-22/r/n題，每小題/r/n5/r/n分，第/r/n23-26/r/n題，每小題/r/n6/r/n分，第/r/n27/r/n，/r/n28/r/n題，每小題/r/n7/r/n分）/r/nV3V3,/r/n17/r/n./r/n解：原式/r/n二飛/r/n—丁+/r/n1/r/n=1/r/n．/r/n18/r/n.解：/r/n?.F/r/nD/r/n丄/r/nBC/r/n,/r/n:/r/n.Z/r/nADB/r/n=/r/nZ/r/nADC/r/n=90/r/n°./r/n在/r/nRt/r/n^/r/nADB/r/n中，/r/nVZ/r/nB/r/n=30/r/n°,/r/nAB/r/n=8/r/n,/r/n.?.AD/r/n=4/r/n,/r/nBD/r/n=/r/n4/r/n、./r/n3/r/n./r/n在/r/nRt/r/nA/r/nADC/r/n中,/r/n4/r/n?/r/ntan/r/nC/r/n==/r/n,/r/n3/r/nCD/r/ntan/r/nCD/r/ntan/r/nC/r/n./r/nCD/r/n=3/r/n./r/n19/r/n.解：/r/n?△/r/nABC/r/n為等邊三角形,/r/n

/r/n.??AB=BC/r/n,Z/r/nABC=/r/n60/r/n°./r/n根據(jù)題意可知/r/nBD/r/n=/r/nBC/r/n,Z/r/nDBC=/r/n30/r/n°./r/n./r/nAB=BD/r/n./r/n?/r/n??Z/r/nABD=/r/n90/r/n°,Z/r/nBDC=/r/n75/r/n°./r/n.??Z/r/nBDA=/r/n45/r/n°./r/n?\Z/r/nADC=/r/n30/r/n°./r/n20/r/n?解：/r/n（/r/n1/r/n）/r/n根據(jù)題意設(shè)/r/ny/r/n2/r/n的表達式為/r/n:/r/ny/r/n2/r/n=/r/na/r/n（/r/nx/r/n+l）/r/n2/r/n-/r/n1/r/n./r/n把（/r/n0/r/n,/r/n0/r/n）代入得/r/na/r/n=1/r/n./r/n./r/ny/r/n=/r/nx/r/n2/r/n+2/r/nx/r/n．/r/n2/r/n（/r/n2/r/n）/r/nx/r/nV/r/n-2/r/n或/r/nx/r/n>/r/n1/r/n./r/n解：作/r/nOD/r/n丄/r/nAB/r/n于/r/nE/r/n,/r/n交/r/n0/r/n0/r/n于點/r/nD/r/n,/r/n.?/r/nAE/r/n=/r/n1/r/nAB/r/n./r/nV/r/nAB/r/n=8/r/n,/r/n.??AE/r/n=4/r/n./r/n在/r/nRt/r/nA/r/nAEO/r/n中，/r/nA0/r/n=5/r/n,/r/n0E=\/r/nOA/r/n2/r/nAE/r/n2/r/n=3/r/n./r/n???ED/r/n=2/r/n./r/n???/r/n筒車工作時，盛水桶在水面以下的最大深度為/r/n2m./r/n解：（/r/n1/r/n）根據(jù)題意，圖形/r/nW/r/n為以/r/n0/r/n為圓心，/r/n0A/r/n為直徑的圓/r/n./r/n連接/r/n0D/r/n,/r/n./r/n0A/r/n=/r/n0D/r/n./r/n??/r/n?點/r/nC/r/n為/r/n0A/r/n的中點，/r/nCD/r/n丄/r/nAB/r/n,/r/n?/r/n\/r/nAD/r/n=/r/n0D./r/n???0A/r/n=/r/n0D/r/n=/r/nAD/r/n./r/n:./r/n△/r/nOAD/r/n是等邊三角形/r/n./r/n?/r/n\Z/r/nA0D/r/n=60/r/n°/r/n./r/n?/r/n\Z/r/nABD/r/n=30/r/n°/r/n./r/n3/r/n3/r/n),．/r/n8/r/n8/r/n(2/r/n)VZ/r/nADE/r/n=/r/nZ/r/nABD/r/n,/r/n23/r/n．解：/r/nZ/r/nPBC/r/n；/r/n遼/r/n；/r/n2./r/n2/r/n\D/r/n\D/r/nV/r/nAB/r/n=/r/nAC/r/n,/r/n:/r/n.Z/r/nABC/r/n=/r/nZ/r/nACB/r/n./r/n?：//r/nPCB/r/n=/r/n//r/nPBA/r/n,/r/n???/PCA/r/n=/r/n/PBC./r/n?:/r/n"AC/r/n=/r/n//r/nPCB/r/n,/r/n:./r/n△/r/nACP/r/n^^/r/nCBP/r/n./r/n.APPCAC/r/n??/r/n=/r/n=/r/n./r/nPCPBBC/r/nVZ/r/nACB/r/n=30°/r/n,/r/nAP/r/n_/r/nPC/r/n_/r/n竺/r/n_/r/n也/r/n…/r/nPC_PB_BC_/r/n3/r/n設(shè)/r/nAP/r/n=/r/na/r/n，貝/r/n9/r/nPC/r/n=/r/n\/r/n：3/r/na/r/n,/r/nPB/r/n=3/r/na/r/n．/r/nAP/r/n1/r/n?/r/n=/r/n./r/nBP3/r/n3/r/n24/r/n.解：/r/n(/r/n1/r/n)T/r/nAB/r/n〃/r/nx/r/n軸，/r/nA(1/r/n,/r/n1)/r/n,/r/nB/r/n在反比例函數(shù)/r/ny/r/n=/r/n(/r/nx/r/n>/r/n0)/r/n的圖象上,/r/nx/r/ny./r/n?/r/nB/r/n(3/r/n,/r/n1)/r/n./r/n同理可求：/r/nC/r/n(1/r/n,/r/n3)/r/n,/r/nD/r/n(/r/n1/r/n,/r/n3)/r/n2/r/n?/r/nAB/r/n=/r/n2/r/n,/r/nCD=/r/n3/r/n

/r/n(2/r/n)/r/nAB/r/n>/r/nCD/r/n./r/n證明：/r/n???A/r/n(/r/na/r/n,/r/nb),A/r/n在反比例函數(shù)/r/ny/r/n=/r/n1/r/n(/r/nx/r/n>/r/n0)/r/n的圖象上，/r/nx/r/n1/r/n?'?A(/r/na/r/n,/r/n)./r/na/r/n3/r/n?/r/nAB/r/n^/r/nx/r/n軸，/r/nB/r/n在反比例函數(shù)/r/ny/r/n=/r/n—(/r/nx/r/n>/r/n0)/r/n的圖象上,/r/nx/r/n1/r/nTOC\o"1-5"\h\z/r/nB/r/n(3/r/na/r/n,/r/n)/r/n./r/na/r/n/r/n3/r/na/r/n3/r/n同理可求：/r/nC/r/n(/r/na/r/n,/r/n)/r/n,/r/nD/r/n(二/r/n,/r/n)/r/n./r/na/r/n3/r/na/r/n2/r/n.*.AB/r/n=2/r/na/r/n,/r/nCD/r/n=/r/n—/r/na./r/n3/r/n?/r/na/r/n>/r/n0/r/n，/r/n2/r/n2/r/na/r/n>/r/na/r/n./r/n3/r/n./r/nAB/r/n>/r/nCD/r/n./r/n25/r/n?解：答案不唯一./r/n(1)/r/nBM/r/n,/r/nDF/r/n,/r/nDM/r/n./r/n2/r/n）如圖所示．/r/n26/r/n．解：(/r/n1/r/n)將點(/r/n3/r/n，/r/n3/r/n)代入/r/ny/r/n=/r/nax/r/n2/r/n+/r/nbx/r/n，得/r/n9/r/na/r/n+3/r/nb/r/n=3./r/nb/r/n=_/r/n3/r/na/r/n+1/r/n./r/n(/r/n2/r/n)令/r/nx/r/n+/r/n4/r/na/r/n+4=4/r/n，得/r/nx/r/n=/r/n-/r/n4/r/na/r/n./r/n,/r/nB/r/n(-/r/n4/r/na/r/n,4)/r/n./r/n(/r/n3/r/n)/r/na/r/n=-/r/n1/r/n或/r/na/r/nV-/r/n2/r/n./r/n27/r/n．（/r/n1/r/n）解：補全圖形，如圖/r/n./r/n(2/r/n)/r/n證明：①根據(jù)題意/r/nZ/r/nACD/r/n=120/r/n°/r/n./r/n.??Z/r/nDCB/r/n+/r/nZ/r/nACO