初三期中考試數(shù)學(xué)試題

初三月考數(shù)學(xué)試題/r/n說明：本試卷分為第/r/nI/r/n卷（選擇題）和第/r/nII/r/n卷（非選擇題）兩部分，共/r/n8/r/n頁,滿分/r/n120/r/n分，考試時間/r/n120/r/n分鐘。/r/n注意事項：/r/n要作圖（含輔助線）或畫表，先用鉛筆進行畫線、繪圖，再用黑色字跡的鋼筆或簽字等描黑。（否則卷面成績成績?yōu)?r/n0/r/n分）/r/n一、精心選一選（本大題共/r/n10/r/n小題，每小題/r/n3/r/n分，共/r/n30/r/n分．每小題給出四個答案，其中/r/n只有一個是正確的）/r/n1/r/n．/r/n4－/r/n1/r/n的結(jié)果是（/r/nC/r/n）/r/nC/r/n./r/n3/r/nD/r/n./r/nC/r/n./r/n3/r/n2/r/n.位于環(huán)水東灣新城區(qū)的茂名市第一中學(xué)新校區(qū)占地面積約為/r/n536.5/r/n畝.將/r/n536.5/r/n用科學(xué)記數(shù)法可表示為（/r/nB/r/n）/r/nA/r/n./r/n0.5365/r/nx/r/n10/r/n3/r/nB/r/n./r/n5.365/r/nx/r/nl0/r/n2/r/nC/r/n./r/n53.65/r/nx/r/n10/r/nD/r/n./r/n536.5/r/n3/r/n.如圖，/r/nAB/r/n是/r/nO/r/nO/r/n的直徑，/r/nAB/r/n3/r/n.如圖，/r/nAB/r/n是/r/nO/r/nO/r/n的直徑，/r/nAB/r/n丄/r/nCD/r/n于點/r/nE/r/n,/r/n若/r/nCD=8/r/n,/r/n則/r/nDE=/r/n（/r/nB/r/n）/r/nA/r/n./r/n3/r/nB/r/n./r/n4/r/nC/r/n./r/n5/r/nD/r/n./r/n6/r/n4/r/n.方程組/r/n7=1/r/n的解為（/r/nD/r/n）/r/n5/r/n．/r/n在下列正方體的表面展開圖中，剪掉/r/n1/r/n個正方形（陰影部分），剩余/r/n5/r/n個正方形組成軸對稱圖形的是（/r/nC/r/n）/r/n

/r/n—個/r/nn/r/n邊形的內(nèi)角和為/r/n360/r/n度，則/r/nn/r/n的值是/r/n（/r/nB/r/n）/r/nA/r/n．/r/n3/r/nB/r/n．/r/n4/r/nC/r/n．/r/n5/r/nD/r/n．/r/n6/r/n下列調(diào)查中，適宜采用全面調(diào)查（普查）方式的是（/r/nD/r/n）/r/n對一批圓珠筆使用壽命的調(diào)查/r/n對全國九年級學(xué)生身高現(xiàn)狀的調(diào)查/r/n對某品牌煙花爆竹燃放安全的調(diào)查/r/n對一枚用于發(fā)射衛(wèi)星的運載火箭各零部件的檢查/r/n甲乙兩名射擊運動員各進行/r/n10/r/n次射擊練習(xí)，成績均為/r/n95/r/n環(huán)，這兩名運動員成績的方差/r/n分別是：￡侖/r/n=0.6/r/n,/r/n￡務(wù)/r/n=0.4/r/n,/r/n則下列說法正確的是（/r/nB/r/n）/r/nA/r/n./r/n甲比乙的成績穩(wěn)定/r/nB/r/n./r/n乙比甲的成績穩(wěn)定/r/nC/r/n./r/n甲乙兩人的成績一樣穩(wěn)定/r/nD/r/n./r/n無法確定誰的成績更穩(wěn)定/r/n如果/r/nx/r/n>/r/n0/r/n,/r/ny/r/n</r/n0/r/n,/r/nx+/r/ny/r/nV/r/n0/r/n,/r/n那么下列關(guān)系式中正確的是（/r/nB/r/n）/r/nA/r/n./r/nx/r/n>/r/ny/r/n>/r/n-/r/ny/r/n>/r/n_/r/nxB/r/n./r/n-/r/nx/r/n>/r/ny/r/nC/r/n./r/ny/r/n>-/r/nA/r/n./r/nx/r/n>/r/ny/r/n>/r/n-/r/ny/r/n>/r/n_/r/nxB/r/n./r/n-/r/nx/r/n>/r/ny/r/n10/r/n./r/n如圖，四邊形/r/nABCD/r/n四邊的中點分別為/r/nE/r/n,/r/nF/r/n,/r/nG/r/n,/r/nH/r/n,/r/n對角線/r/nAC/r/n與/r/nBD/r/n相交于點/r/nO,/r/n若四邊形/r/nEFGH/r/n的面積是/r/n3/r/n,則四邊形/r/nABCD/r/n的面積是/r/n（/r/nB/r/nA/r/n./r/n3/r/nB/r/n./r/n6/r/nC/r/n./r/n9/r/nD/r/n./r/n12/r/n二、細(xì)心填一填（本大題共/r/n5/r/n小題,每小題/r/n3/r/n分,共/r/n15/r/n分.請你把答案填在橫線的上方）./r/n分解因式：/r/na/r/n2/r/ny/r/n-/r/nay=/r/n./r/n如圖所示,建高樓常需要用塔吊來吊建筑材料,而塔吊的上部是三角形結(jié)構(gòu),這是應(yīng)用/r/n了三角形的哪個性質(zhì)？答：—穩(wěn)定/r/nf/r/n./r/n（填/r/n"/r/n穩(wěn)定性/r/n”/r/n或/r/n"/r/n不穩(wěn)定性/r/n”/r/n）/r/n丿/r/n■/r/nn/r/n高樓/r/n塔吊/r/na/r/n+/r/n4/r/n若分式/r/n的值為/r/n0/r/n則/r/na/r/n的值是/r/n-4/r/n./r/na/r/n-/r/n5/r/n如圖，在/r/n3/r/nx/r/n3/r/n的方格中（共有/r/n9/r/n個小格），每個小方格都是邊長為/r/n1/r/n的正方形，/r/nO/r/n、/r/nB/r/n、/r/n5/r/n兀/r/nC/r/n是格點，則扇形/r/nOBC/r/n的面積等于—/r/n（結(jié)果保留/r/nn/r/n）/r/n4/r/nS/r/n0/r/nS/r/n0/r/n15/r/n?在平直的鐵路上行駛的火車的車輪與鐵軌的位置關(guān)系是：/r/n相切/r/n三、用心做一做（本大題共/r/n3/r/n小題，每小題/r/n7/r/n分，共/r/n21/r/n分）/r/n16/r/n.計算：/r/n解：原式=上二/r/n|/r/n=/r/n1/r/na/r/n—/r/n2/r/nI/r/nx/r/n+/r/n3/r/nn/r/n1/r/n17/r/n?求不等式組仁/r/n—/r/n5/r/n./r/n1/r/n的整數(shù)解?/r/n解：由/r/nx+/r/n32/r/n1/r/n得/r/nx±-2;/r/n由/r/n2x-5W/r/n1/r/n得/r/nxW3/r/n所以原不等式組的解集是/r/n-2WxW3/r/n所以原不等式組的整數(shù)解是：-/r/n2/r/n、-/r/n1/r/n、/r/n0/r/n、/r/n1/r/n、/r/n2/r/n、/r/n3/r/n。/r/n如圖，圖中的小方格都是邊長為/r/n1/r/n的正方形，/r/nA/r/nABC/r/n的頂點坐標(biāo)分別為/r/nA/r/n（-/r/n3/r/n,/r/n0/r/n）,/r/nB/r/n（-/r/n1/r/n,-/r/n2/r/n）,/r/nC/r/n（-/r/n2/r/n，/r/n2/r/n）./r/n請在圖中畫出/r/n△/r/nABC/r/n繞/r/nB/r/n點順時針旋轉(zhuǎn)/r/n180/r/n°后的圖/r/n形；/r/n解：畫圖如下（/r/nA/r/nA^C/r/n］/r/n即為所求）：/r/n

/r/n四、沉著冷靜，縝密思考（本大題共/r/n2/r/n小題，每小題/r/n7/r/n分，共/r/n14/r/n分）/r/n（/r/n7/r/n分）（/r/n2012/r/n?/r/n茂名）某校計劃組織學(xué)生到市影劇院觀看大型感恩歌舞劇，為了解學(xué)生如何去影劇院的問題，學(xué)校隨機抽取部分學(xué)生進行調(diào)查，并將調(diào)查結(jié)果制成了表格、條形統(tǒng)計圖和扇形統(tǒng)計圖（均不完整）./r/n（/r/n2/r/n）將表格填充完整；/r/n步行騎自行車坐公共汽車其他/r/n50/r/n150/r/n225/r/n75/r/n（/r/n3/r/n）將條形統(tǒng)計圖補充完整./r/n解：（/r/n1/r/n）/r/n50/r/n=/r/n10%=500/r/n（位）/r/n答：此次共調(diào)查了/r/n500/r/n位學(xué)生/r/n（/r/n2/r/n）填表如下：/r/n騎自行車：/r/n500/r/nx/r/n30%=150/r/n人，坐公共汽車：/r/n500/r/nx/r/n45%=225/r/n人，其他：/r/n500/r/n-/r/n50/r/n-/r/n150/r/n-/r/n225=75/r/n人.故答案為：/r/n150/r/n，/r/n225/r/n，/r/n75/r/n./r/n

/r/n宣傳講座，小青同學(xué)不知該如何聽課，最后他決定通過擲硬幣來確定，擲硬幣規(guī)則如下：連續(xù)拋擲硬幣三次，如果三次正面朝上或三次反面朝上，則小青聽兩堂講座；如果兩次正面朝上一次反面朝上，則小青去聽有關(guān)“地溝油”的講座；如果兩次反面朝上一次正面朝上，則小青去聽有關(guān)“瘦肉精”的講座。/r/n（1）/r/n用畫樹狀圖的方法表示三次拋擲硬幣的所有結(jié)果；/r/n（2）/r/n小青聽兩堂知識講座的概率有多大？/r/n（3）/r/n小青用這個游戲規(guī)則去選擇聽“地溝油”或“瘦肉精”的講座是否合理？為什么？/r/n???/r/n三次拋擲硬幣的所有結(jié)果有：正正正，正正反，正反正，正反反，反正正，反正反，反反正，反反反/r/n8/r/n種。/r/n（2）7/r/n由（/r/n1）/r/n可知，三次拋擲硬幣共有/r/n8/r/n種等可能結(jié)果，三次正面朝上或三次反面朝上的有/r/n2/r/n種，/r/n21/r/n???/r/n小青聽兩堂知識講座的概率為-二/r/n-/r/n。/r/n84/r/n3）/r/n這個游戲規(guī)則合理。/r/n??/r/n?兩次正面朝上一次反面朝上的結(jié)果有/r/n3/r/n種：正正反，正反正，反正正,/r/n3/r/n.??/r/n小青去聽有關(guān)“地溝油”的講座概率為―。/r/n8/r/n?兩次反面朝上一次正面朝上的結(jié)果有/r/n3/r/n種：正反反,反正反,反反正,/r/n3/r/n.??/r/n小青去聽有關(guān)“瘦肉精”的講座概率為一。/r/n8/r/n.小青去聽有關(guān)“地溝油”的講座概率=小青去聽有關(guān)“瘦肉精”的講座/r/n概率。/r/n.這個游戲規(guī)則合理。/r/n五、滿懷信心，再接再厲（本大題共/r/n3/r/n小題，每小題/r/n8/r/n分，共/r/n24/r/n分）/r/n21./r/n如圖，已知矩形/r/nABCD/r/n中，/r/nF/r/n是/r/nBC/r/n上一點，且/r/nAF=BC,DE/r/n丄/r/nAF,/r/n垂足是/r/nE/r/n,/r/n連接/r/nDF./r/n求證：/r/n（/r/n1/r/n）/r/n△/r/nABF/r/n9A/r/nDEA/r/n；/r/n（4/r/n分/r/n）/r/n（/r/n2/r/n）/r/nDF/r/n是/r/nZ/r/nEDC/r/n的平分線./r/n（3/r/n分/r/n）/r/n證明：(/r/n1/r/n)/r/nT/r/n四邊形/r/nABCD/r/n是矩形,/r/n:/r/n丄/r/nB=90/r/n°/r/n,/r/nAD=BC/r/n,/r/nAD/r/nII/r/nBC/r/n,/r/nAZ/r/nDAE=/r/nZ/r/nAFB/r/n,/r/n???DE/r/n丄/r/nAF/r/n,/r/nAZ/r/nDEA=/r/nZ/r/nB=90/r/n°/r/n,/r/n???AF=BC/r/n,/r/nA/r/nAF=AD/r/n,/r/n在/r/n厶/r/nABF/r/n和/r/n厶/r/nDEA/r/n中/r/nr/r/nZDAB=ZAFB/r/n??rZ/r/n怔/r/nD/r/n二工/r/nB,/r/n，蚯二/r/nAF/r/nA/r/n△/r/nABF/r/n竺/r/n△/r/nDEA/r/n(/r/nAAS/r/n)；/r/n(/r/n2/r/n)/r/n?/r/n由(/r/n1/r/n)知/r/n厶/r/nABF/r/n竺/r/n△/r/nDEA/r/n,/r/nA/r/nDE=AB/r/n,/r/n?/r/n四邊形/r/nABCD/r/n是矩形,/r/nAZ/r/nC=90/r/n°/r/n,/r/nDC=AB/r/n,/r/n

/r/n???DC=DE/r/n./r/n???Z/r/nC=/r/nZ/r/nDEF=90/r/n°/r/n?/r/n在/r/nRt/r/nA/r/nDEF/r/n和/r/nRt/r/nA/r/nDCF/r/n中/r/nr/r/nDF=DF/r/n1de=dc/r/n△/r/nRtDEF/r/n竺/r/nRt/r/nA/r/nDCF/r/n(/r/nHL/r/n)/r/nZ/r/nEDF=/r/nZ/r/nCDF/r/n，/r/nDF/r/n是/r/nZ/r/nEDC/r/n的平分線./r/n22/r/n.大潤發(fā)超市進了一批成本為/r/n8/r/n元/r/n//r/n個的文具盒。調(diào)查發(fā)現(xiàn)：這種文具盒每個星期的銷售量/r/ny/r/n（個）與它的定價/r/nx/r/n（元/r/n//r/n個）的關(guān)系如圖所示：/r/n第/r/n24/r/n題圖/r/n（/r/n1/r/n）求這種文具盒每個星期的銷售量/r/ny/r/n（個）與它的定價/r/nx/r/n（元/r/n//r/n個）之間的函數(shù)關(guān)系式（不/r/n必寫出自變量/r/nx/r/n的取值范圍）；/r/n（4/r/n分/r/n）/r/n（/r/n2/r/n）每個文具盒定價是多少元時，超市每星期銷售這種文具盒（不考慮其他因素）可獲得/r/n的利潤最高？最高利潤是多少？/r/n（4/r/n分/r/n）/r/n解：（/r/n1/r/n）設(shè)/r/ny/r/n=/r/nkx/r/n+/r/nb/r/n。。。。。。。。。。。。。。。。/r/n1/r/n分/r/n。。。。/r/n3/r/n分/r/n「/r/n10/r/nk/r/n+/r/nb/r/n二/r/n200/r/n由題意得：/r/n|/r/n14/r/nk/r/n+/r/nb/r/n二/r/n160/r/n。。。。/r/n3/r/n分/r/n解之得：/r/nk/r/n=－/r/n10/r/n；/r/nb/r/n=/r/n300/r/n。/r/n.*./r/ny/r/n=/r/n—/r/n10/r/nX/r/n+/r/n300/r/n可彳丁/r/noooooooooooo/r/n4/r/n分/r/n（2/r/n）由上知超市每星期的利潤:/r/nw/r/n=（/r/nx/r/n—/r/n8/r/n）/r/n?/r/ny/r/n=（/r/nx/r/n—/r/n8/r/n）（—/r/n10X/r/n+/r/n300/r/n）/r/n。。。/r/n5/r/n分/r/n=－/r/n10/r/n（/r/nx/r/n－/r/n8/r/n）（/r/nx/r/n－/r/n30/r/n）=－/r/n10/r/n（/r/nx/r/n2/r/n－/r/n38/r/nx/r/n＋/r/n240/r/n）/r/n=—/r/n10/r/n（/r/nx/r/n—/r/n19/r/n）/r/n2/r/n＋/r/n1210/r/n。。。。。。。。。/r/n6/r/n分/r/n./r/n?.當(dāng)/r/nx/r/n=/r/n19/r/n即定價/r/n19/r/n元/r/n//r/n個時超市可獲得的利潤最高。。。。。。。。。。/r/n7/r/n分最高利潤為/r/n1210/r/n元。。。。。。。。。。。。/r/n8/r/n分/r/n23/r/n.如圖，點/r/nA/r/n,/r/nB/r/n,/r/nC/r/n,/r/nD/r/n在/r/n0/r/nO/r/n上，/r/nAB=AC/r/n,/r/nAD/r/n與/r/nBC/r/n相交于點/r/nE/r/n,/r/nAE/r/n=/r/n|eD/r/n，延長/r/nDB/r/n到點/r/nF/r/n,/r/n使/r/nFB/r/n=/r/n*BD/r/n，連接/r/nAF/r/n./r/n（/r/n1/r/n）/r/n證明：/r/nA/r/nBDE/r/nsA/r/nFDA/r/n；/r/n（4/r/n分/r/n）/r/n（/r/n2/r/n）/r/n試判斷直線/r/nAF/r/n與/r/n0/r/nO/r/n的位置關(guān)系，并給出證明./r/n（4/r/n分/r/n）/r/n

/r/n⑴/r/n證明：在沖和/r/nMDA/r/n中’?/r/n2/r/nBD/r/n,/r/nAE/r/n=/r/n2/r/ne/r/nD/r/n,/r/n???/r/n|g/r/n=黑=/r/n3/r/n又/r/n?.?z/r/nBDE/r/n=z/r/nFDA/r/n,./r/n?/r/n./r/nA/r/nBDE/r/nsA/r/nFDA/r/n。/r/nD/r/n(2/r/n)解：直線/r/nAF/r/n與相切。證明如下：/r/nD/r/n連接/r/nOA/r/n,/r/nOB/r/n,/r/n0C/r/n,/r/n?.?AB/r/n=/r/nAC/r/n,/r/nBO/r/n=/r/nCO/r/n,/r/nOA/r/n=/r/nOA/r/n,/r/n5/r/n.?.△/r/noab/r/n^a/r/noac/r/n(/r/nsss/r/n)o.z/r/nOAB/r/n=z/r/nOAC/r/no/r/n???AO/r/n是等腰三角形/r/nABC/r/n頂角/r/nZ/r/nBAC/r/n的平分線。/r/n?/r/nAO/r/n丄/r/nBe/r/n。/r/n△/r/nBDE/r/ns/r/nFDA/r/n,/r/n得/r/nz/r/nEBD/r/n=z/r/nAFD/r/n,/r/n?/r/n./r/nBE/r/n〃/r/nFA/r/no/r/nAO/r/n丄/r/nBE/r/n,/r/n./r/nAO/r/n丄/r/nFA/r/no./r/n直線/r/nAF/r/n與。/r/n0/r/n相切。/r/n六、靈動智慧,超越自我(本大題共/r/n2/r/n小題,每小題/r/n8/r/n分,共/r/n16/r/n分)/r/nk/r/n如圖，一次函數(shù)/r/ny=x+l/r/n與反比例函數(shù)/r/ny=—/r/n的圖象相交于點/r/nA(2/r/n,/r/n3)/r/n和點/r/nB./r/nx/r/n求反比例函數(shù)的解析式；/r/n(3/r/n分/r/n)/r/n過點/r/nB/r/n作/r/nBC/r/n丄/r/nx/r/n軸于/r/nC/r/n,/r/n過點/r/nB/r/n作/r/nBC/r/n丄/r/nx/r/n軸于/r/nC/r/n,/r/n求/r/nS/r/n.(2/r/n分/r/n)/r/n△/r/nABC/r/n解：(/r/n1/r/n)將/r/nA/r/n點坐標(biāo)代入反比例函數(shù)/r/ny/r/n=/r/n—得/r/nk/r/n=6/r/no/r/nx/r/n6/r/n???反比例函數(shù)的解析式為/r/ny=—/r/no/r/nx/r/ny=x+1/r/n(2/r/n)/r/n由題意得方程組：/r/n］/r/n6/r/n，/r/ny=-/r/n

/r/nl/r/nx/r/n得：/r/nx(x+1)=6/r/n,/r/n即/r/nx/r/n2/r/n+x/r/n-/r/n6=0,/r/n解得/r/nx/r/n=/r/n-/r/n3,/r/nx/r/n=2/r/n。/r/n1/r/n2/r/n?*.B/r/n點坐標(biāo)為（/r/n一/r/n3/r/n,—/r/n2/r/n）。/r/n（/r/n3/r/n）在厶/r/nABC/r/n中，以/r/nBC/r/n為底邊，則高為/r/n2/r/n—（—/r/n3/r/n）/r/n=5/r/n。/r/n?/r/n?/r/n?/r/nS/r/n=丄/r/nx/r/n2/r/nx/r/n5/r/n=/r/n5/r/n。/r/nA/r/nABC/r/n2/r/n如圖，在平面直角坐標(biāo)系中，二次函數(shù)/r/ny=x/r/n2/r/n+bx+c/r/n的圖象與/r/nx/r/n軸交于/r/nA/r/n、/r/nB/r/n兩點，/r/nA/r/n點在原點的左側(cè)，/r/nB/r/n點的坐標(biāo)為（/r/n3/r/n,/r/n0/r/n），與/r/ny/r/n軸交于/r/nC/r/n（/r/n0/r/n,-/r/n3/r/n）點，點/r/nP/r/n是直線/r/nBC/r/n下方的拋物線上一動點．/r/n（/r/n1/r/n）/r/n求這個二次函數(shù)的表達(dá)式．/r/n（3/r/n分/r/n）/r/n（/r/n2/r/n）/r/n連接/r/nPO/r/n、/r/nPC/r/n，/r/n并把/r/n△/r/nPOC/r/n沿/r/nCO/r/n翻折，得到四邊形/r/nPOPC/r/n，那么是否存在點/r/nP/r/n,/r/n使/r/n四邊形/r/nPOP'C/r/n為菱形？若存在，請求出此時點/r/nP/r/n的坐標(biāo)；若不存在，請說明理由./r/n（3/r/n分/r/n）/r/n（/r/n3/r/n）/r/n當(dāng)點/r/nP/r/n運動到什么位置時，四邊形/r/nABPC/r/n的面積最大并求出此時/r/nP/r/n點的坐標(biāo)和四邊形/r/nABPC/r/n的最大面積./r/n（2/r/n分/r/n）/r/n解：（/r/n1/r/n）將/r/nB/r/n、/r/nC/r/n兩點的坐標(biāo)代入得（/r/n2/r/n分）/r/n%=-2/r/n解得§；/r/n所以二次函數(shù)的表達(dá)式為：/r/ny=x/r/n2/r/n-/r/n2x/r/n-/r/n3/r/n（/r