2018年河南省中考數(shù)學(xué)試卷

-/r/n.z./r/n2018/r/n年河南省中考數(shù)學(xué)試卷/r/n（滿分/r/n120/r/n分，考試時(shí)間/r/n100/r/n分鐘）/r/n一、選擇題（每小題/r/n3/r/n分，共/r/n30/r/n分）/r/n的相反數(shù)是（）/r/nA/r/n．/r/nB/r/n．/r/nC/r/n．/r/nD/r/n．/r/n今年一季度，河南省/r/n對(duì)/r/n"/r/n一帶一路/r/n”/r/n沿/r/n線國家進(jìn)出口總額達(dá)/r/n214.7/r/n億元．?dāng)?shù)據(jù)/r/n"/r/n214.7/r/n億/r/n”/r/n用/r/n科學(xué)記數(shù)法表示為（）/r/nA/r/n．/r/n2.147×10/r/n2/r/nB/r/n．/r/n0.2147×10/r/n3/r/nC/r/n．/r/n2.147×10/r/n10/r/nD/r/n．/r/n0.2147×10/r/n11/r/n*正方體的每個(gè)面上都有一個(gè)漢字，如圖是它的一種展開圖，則在原正方體中，/r/n與/r/n"/r/n國/r/n”/r/n字/r/n所在面相對(duì)的面上的漢字是（）/r/nA/r/n．厲/r/nB/r/n．害/r/nC/r/n．了/r/nD/r/n．我/r/n下列運(yùn)算正確的是（）/r/nA/r/n．/r/nB/r/n．/r/nC/r/n．/r/nD/r/n．/r/n河南省游資源豐富，/r/n2013/r/n～/r/n2017/r/n年旅游收入不斷增長，同比增速分別為：/r/n15.3%/r/n，/r/n12.7%/r/n，/r/n15.3%/r/n，/r/n14.5%/r/n，/r/n17.1%/r/n．關(guān)于這組數(shù)據(jù)，下列說法正確的是（）/r/nA/r/n．中位數(shù)是/r/n12.7%B/r/n．眾數(shù)是/r/n15.3%/r/nC/r/n．平均數(shù)是/r/n15.98%D/r/n．方差是/r/n0/r/n《九章算術(shù)》中記載：/r/n"/r/n今有共買羊，人出五，不足四十五；人出七，不足三．問人數(shù)、羊價(jià)各幾何？/r/n”/r/n其大意是：今有人合伙買羊，若每人出/r/n5/r/n錢，還差/r/n45/r/n錢；若每人出/r/n7/r/n錢，還差/r/n3/r/n錢．問合伙人數(shù)、羊價(jià)各是多少？設(shè)合伙人數(shù)為/r/n*/r/n人，羊價(jià)為/r/ny/r/n錢，根據(jù)題意，可列方程組為（）/r/nA/r/n．/r/nB/r/n．/r/nC/r/n．/r/nD/r/n．/r/n下列一元二次方程中，有兩個(gè)不相等實(shí)數(shù)根的是（）/r/nA/r/n．/r/nB/r/n．/r/nC/r/n．/r/nD/r/n．/r/n現(xiàn)有/r/n4/r/n張卡片，其中/r/n3/r/n張卡片正面上的圖案是/r/n"/r/n?/r/n”/r/n，/r/n1/r/n張卡片正面上的圖案是/r/n"/r/n?/r/n”/r/n，它們除此之外完全相同．把這/r/n4/r/n張卡片背面朝上洗勻，從中隨機(jī)抽取兩張，則這兩張卡片正面圖案相同的概率是（）/r/nA/r/n．/r/nB/r/n．/r/nC/r/n．/r/nD/r/n．/r/n如圖，已知/r/n□/r/nAOBC/r/n的頂點(diǎn)/r/nO/r/n(0/r/n，/r/n0)/r/n，/r/nA/r/n(/r/n-/r/n1/r/n，/r/n2)/r/n，點(diǎn)/r/nB/r/n在/r/n*/r/n軸正半軸上．按以下步驟作圖：/r/n①/r/n以點(diǎn)/r/nO/r/n為圓心，適當(dāng)長度為半徑作弧，分別交邊/r/nOA/r/n，/r/nOB/r/n于點(diǎn)/r/nD/r/n，/r/nE/r/n；/r/n②/r/n分別以點(diǎn)/r/nD/r/n，/r/nE/r/n為圓心，大于/r/nDE/r/n的長為半徑作弧，兩弧在/r/n∠/r/nAOB/r/n內(nèi)交于點(diǎn)/r/nF/r/n；/r/n③/r/n作射線/r/nOF/r/n，交邊/r/nAC/r/n于點(diǎn)/r/nG/r/n．則點(diǎn)/r/nG/r/n的坐標(biāo)為（）/r/nA/r/n．/r/nB/r/n．/r/nC/r/n．/r/nD/r/n．/r/n如圖/r/n1/r/n，點(diǎn)/r/nF/r/n從菱形/r/nABCD/r/n的頂點(diǎn)/r/nA/r/n出發(fā)，沿/r/nA/r/n→/r/nD/r/n→/r/nB/r/n以/r/n1cm/s/r/n的速度勻速運(yùn)動(dòng)到點(diǎn)/r/nB/r/n．圖/r/n2/r/n是點(diǎn)/r/nF/r/n運(yùn)動(dòng)時(shí)，/r/n△/r/nFBC/r/n的面積/r/ny/r/n（/r/ncm/r/n2/r/n）隨時(shí)間/r/n*/r/n（/r/ns/r/n）變化的關(guān)系圖象，則/r/na/r/n的值為（）/r/nA/r/n．/r/nB/r/n．/r/n2C/r/n．/r/nD/r/n．/r/n圖/r/n1/r/n圖/r/n2/r/n二、填空題（每小題/r/n3/r/n分，共/r/n15/r/n分）/r/n計(jì)算：/r/n__________/r/n．/r/n如圖，直線/r/nAB/r/n，/r/nCD/r/n相交于點(diǎn)/r/nO/r/n，/r/nEO/r/n⊥/r/nAB/r/n于點(diǎn)/r/nO/r/n，/r/n∠/r/nEOD/r/n=50°/r/n，則/r/n∠/r/nBOC/r/n的度數(shù)為/r/n____________/r/n．/r/n不等式組/r/n的最小整數(shù)解是/r/n___________/r/n．/r/n如圖，在/r/n△/r/nABC/r/n中，/r/n∠/r/nACB/r/n=90°/r/n，/r/nAC/r/n=/r/nBC/r/n=2/r/n，將/r/n△/r/nABC/r/n繞/r/nAC/r/n的中點(diǎn)/r/nD/r/n逆時(shí)針旋轉(zhuǎn)/r/n90°/r/n得到/r/n△/r/nA′B′C′/r/n，其中點(diǎn)/r/nB/r/n的運(yùn)動(dòng)路徑為/r/nEQ\o\ac(/r/nBB'/r/n,\s\up9(/r/n︵/r/n))/r/n，則圖中陰影部分的面積為/r/n____________/r/n．/r/n如圖，/r/n∠/r/nMAN/r/n=90°/r/n，點(diǎn)/r/nC/r/n在邊/r/nAM/r/n上，/r/nAC/r/n=4/r/n，點(diǎn)/r/nB/r/n為邊/r/nAN/r/n上一動(dòng)點(diǎn)，連接/r/nBC/r/n，/r/n△/r/nA′BC/r/n與/r/n△/r/nABC/r/n關(guān)于/r/nBC/r/n所在直線對(duì)稱．/r/nD/r/n，/r/nE/r/n分別為/r/nAC/r/n，/r/nBC/r/n的中點(diǎn)，連接/r/nDE/r/n并延長交/r/nA′B/r/n所在直線于點(diǎn)/r/nF/r/n，連接/r/nA′E/r/n．當(dāng)/r/n△/r/nA′EF/r/n為直角三角形時(shí)，/r/nAB/r/n的長為/r/n____________/r/n．/r/n三、解答題（本大題共/r/n8/r/n個(gè)小題，滿分/r/n75/r/n分）/r/n（/r/n8/r/n分）共化簡，再求值：/r/n，其中/r/n．/r/n（/r/n9/r/n分）每到春夏交替時(shí)節(jié)，雌性楊樹會(huì)以滿天飛絮的方式來傳播下一代，漫天飛舞的楊絮易引發(fā)皮膚病，呼吸道疾病等，給人們?cè)斐衫_．為了解市民對(duì)治理?xiàng)钚醴椒ǖ馁澩闆r，*課題小組隨機(jī)調(diào)查了部分市民（問卷調(diào)查表如圖所示），并根據(jù)調(diào)查結(jié)果繪制了如下尚不完整的統(tǒng)計(jì)圖．/r/n治理?xiàng)钚?r/n——/r/n您選哪一項(xiàng)？（單選）/r/nA/r/n．減少楊樹新面積，控制楊樹每年的栽種量/r/nB/r/n．調(diào)整樹種結(jié)構(gòu)，逐漸更換現(xiàn)有楊樹/r/nC/r/n．選育無絮楊品種，并推廣種植/r/nD/r/n．對(duì)雌性楊樹注射生物干擾素，避免產(chǎn)生飛絮/r/nE/r/n．其他/r/n根據(jù)以上統(tǒng)計(jì)圖，解答下列問題：/r/n（/r/n1/r/n）本次接受調(diào)查的市民共有/r/n__________/r/n人；/r/n（/r/n2/r/n）扇形統(tǒng)計(jì)圖中，扇形/r/nE/r/n的圓心角度數(shù)是/r/n__________/r/n；/r/n（/r/n3/r/n）請(qǐng)補(bǔ)全條形統(tǒng)計(jì)圖；/r/n（/r/n4/r/n）若該市約有/r/n90/r/n萬人，請(qǐng)/r/n估計(jì)贊同/r/n"/r/n選育無絮楊品種，并推廣種植/r/n”/r/n的/r/n人數(shù)．/r/n（/r/n9/r/n分）如圖，反比例函數(shù)/r/n的圖象過格點(diǎn)（網(wǎng)格線的交點(diǎn)）/r/nP/r/n．/r/n（/r/n1/r/n）求反比例函數(shù)的解析式；/r/n（/r/n2/r/n）在圖中用直尺和/r/n2B/r/n鉛筆/r/n畫出兩個(gè)矩形（不寫畫法），要求每個(gè)矩形均需滿足下列兩個(gè)條件：/r/n①/r/n四個(gè)頂點(diǎn)均在格點(diǎn)上，且其中兩個(gè)頂點(diǎn)分別是點(diǎn)/r/nO/r/n，點(diǎn)/r/nP/r/n；/r/n②/r/n矩形的面積等于/r/nk/r/n的值．/r/n（/r/n9/r/n分）如圖，/r/nAB/r/n是/r/n⊙/r/nO/r/n的直徑，/r/nDO/r/n⊥/r/nAB/r/n于點(diǎn)/r/nO/r/n，連接/r/nDA/r/n交/r/n⊙/r/nO/r/n于點(diǎn)/r/nC/r/n，過點(diǎn)/r/nC/r/n作/r/n⊙/r/nO/r/n的切線交/r/nDO/r/n于點(diǎn)/r/nE/r/n，連接/r/nBC/r/n交/r/nDO/r/n于點(diǎn)/r/nF/r/n．/r/n（/r/n1/r/n）求證：/r/nCE/r/n=/r/nEF/r/n；/r/n（/r/n2/r/n）連接/r/nAF/r/n并延長，交/r/n⊙/r/nO/r/n于點(diǎn)/r/nG/r/n．填空：/r/n①/r/n當(dāng)/r/n∠/r/nD/r/n的度數(shù)為/r/n_________/r/n時(shí)，四邊形/r/nECFG/r/n為菱形；/r/n②/r/n當(dāng)/r/n∠/r/nD/r/n的度數(shù)為/r/n_________/r/n時(shí)，四邊形/r/nECOG/r/n為正方形．/r/n（/r/n9/r/n分）/r/n"/r/n高低杠/r/n”/r/n是女/r/n子體操特有的一個(gè)競技項(xiàng)目，其比賽器材由高、低兩根平行杠及若干支架組成，運(yùn)動(dòng)員可根據(jù)自已的身高和習(xí)慣在規(guī)定范圍內(nèi)調(diào)節(jié)高、低兩杠間的距離．*興趣小組根據(jù)高低杠器材的一種截面圖編制了如下數(shù)學(xué)問題，請(qǐng)你解答．/r/n如圖所示，底座上/r/nA/r/n，/r/nB/r/n兩點(diǎn)間的距離為/r/n90cm/r/n．低杠上點(diǎn)/r/nC/r/n到直線/r/nAB/r/n的距離/r/nCE/r/n的長為/r/n155cm/r/n，高杠上點(diǎn)/r/nD/r/n到直線/r/nAB/r/n的距離/r/nDF/r/n的長為/r/n234cm/r/n，已知低杠的支架/r/nAC/r/n與直線/r/nAB/r/n的夾角/r/n∠/r/nCAE/r/n為/r/n82.4°/r/n，高杠的支架/r/nBD/r/n與直線/r/nAB/r/n的夾角/r/n∠/r/nDBF/r/n為/r/n80.3°/r/n．求高、低杠間的水平距離/r/nCH/r/n的長．/r/n（結(jié)果精確到/r/n1cm/r/n．參考數(shù)據(jù)：/r/nsin82.4°≈0.991/r/n，/r/ncos82.4°≈0.132/r/n，/r/ntan82.4°≈7.500/r/n，/r/nsin80.3°≈0.983/r/n，/r/ncos80.3°≈0.168/r/n，/r/ntan80.3°≈5.850/r/n）/r/n（/r/n10/r/n分）*公司推出一款產(chǎn)品，經(jīng)市場調(diào)查發(fā)現(xiàn)，該產(chǎn)品的日銷售量/r/ny/r/n（個(gè)）與銷售單價(jià)/r/n*/r/n（元）之間滿足一次函數(shù)關(guān)系．關(guān)于銷售單價(jià)、日銷售量、日銷售利潤的幾組對(duì)應(yīng)值如下表：/r/n銷售單價(jià)/r/n*/r/n（元）/r/n85/r/n95/r/n105/r/n115/r/n日銷售量/r/ny/r/n（個(gè)）/r/n175/r/n125/r/n75/r/nm/r/n日銷售利潤（元）/r/n875/r/n1875/r/n1875/r/n875/r/n注：日銷售利潤/r/n=/r/n日銷售量/r/n×/r/n（銷售單價(jià)/r/n-/r/n成本單價(jià)）/r/n（/r/n1/r/n）求/r/ny/r/n關(guān)于/r/n*/r/n的函數(shù)解析式（不要求寫出/r/n*/r/n的取值范圍）及/r/nm/r/n的值；/r/n（/r/n2/r/n）根據(jù)以上信息，填空：/r/n該產(chǎn)品的成本單價(jià)是/r/n_______/r/n元．當(dāng)銷售單價(jià)/r/n*/r/n=_______/r/n元時(shí)，日銷售利潤/r/nw/r/n最大，最大值是/r/n_________/r/n元；/r/n（/r/n3/r/n）公司計(jì)劃開展科技創(chuàng)新，以降低該產(chǎn)品的成本．預(yù)計(jì)在今后的銷售中，日銷售量與銷售單價(jià)仍存在（/r/n1/r/n）中的關(guān)系．若想實(shí)現(xiàn)銷售單價(jià)為/r/n90/r/n元時(shí)，日銷售利潤不低于/r/n3750/r/n元的銷售目標(biāo)，該產(chǎn)品的成本單價(jià)應(yīng)不超過多少元？/r/n（/r/n10/r/n分）（/r/n1/r/n）問題發(fā)現(xiàn)/r/n如圖/r/n1/r/n，在/r/n△/r/nOAB/r/n和/r/n△/r/nOCD/r/n中，/r/nOA/r/n=/r/nOB/r/n，/r/nOC/r/n=/r/nOD/r/n，/r/n∠/r/nAOB/r/n=/r/n∠/r/nCOD/r/n=40°/r/n，連接/r/nAC/r/n，/r/nBD/r/n交于點(diǎn)/r/nM/r/n．填空：/r/n①/r/n的值為/r/n_____________/r/n；/r/n②∠/r/nAMB/r/n的度數(shù)為/r/n_____________/r/n．/r/n（/r/n2/r/n）類比探究/r/n如圖/r/n2/r/n，在/r/n△/r/nOAB/r/n和/r/n△/r/nOCD/r/n中，/r/n∠/r/nAOB/r/n=/r/n∠/r/nCOD/r/n=90°/r/n，/r/n∠/r/nOAB/r/n=/r/n∠/r/nOCD/r/n=30°/r/n，連接/r/nAC/r/n交/r/nBD/r/n的延長線于點(diǎn)/r/nM/r/n．請(qǐng)判斷/r/n的值及/r/n∠/r/nAMB/r/n的度數(shù)，并說明理由．/r/n（/r/n3/r/n）拓展延伸/r/n在（/r/n2/r/n）的條件下，將/r/n△/r/nOCD/r/n繞點(diǎn)/r/nO/r/n在平面內(nèi)旋轉(zhuǎn)，/r/nAC/r/n，/r/nBD/r/n所在直線交于點(diǎn)/r/nM/r/n．若/r/nOD/r/n=1/r/n，/r/nOB/r/n=/r/n，請(qǐng)直接寫