宁德市2019-2020学年九(上)期末数学试卷及答案

宁德市2019-2020学年度第一学期期末九年级质量检测数学一、选择题（本题共10小题：每小题4分，共40分）1.sin30°＝A.21B.22C.23D.332.已知一个几何体如图所示，则该几何体的左视图是A.B.C.D.3.在一个不透明的袋子中放有若干个球，其中有6个白球，其余是红球，这些球除颜色外完全相同.每次把球充分搅匀后，任意摸出一个球记下颜色再放回袋子，通过大量重复试验后，发现模到白球的频率稳定在0.25左右，则红球的个数约是A.2B.12C.18D.244.如图，在Rt△ABC中，∠C=90°，BC=4，AB=5，则sinB的值是A.32B.53C.43D.545.如图，四边形ABCD与四边形GBFF是位似图形，则位似中心是A.点AB.点BC.点CD.点D6.如图,在四边形ABCD中，对角线AC、BD相交点O，且OA＝OC，OB=OD：若要使四边形ABCD为菱形，则可以添加的条件是A.AC=BDB.AB⊥BCC.∠AOB=60°D.AC⊥BD7.对于反比例函数y=－x4，下列说法正确的是A.y的值随x的增大而增大B.y的值随x值的增大而减小C.当x0时，y的值随x值的增大而增大D.当x0时，y的值随x值的增大而诚小8.若方程x2－4x+m=0有两个不相等的实数棖，则实数m的值可能是A.3B.4C.5D.69.己知抛物线y=ax2+bx+c经过点(－4，m)，(－3，n)，若x1，x2是关于x的一元二次方程ax2+bx+c=0的两个根，且－4－3，0，则下列结论一定正确的是A.m+n0B.m－n0C.m·n0D.nm010.如图，一根电线杆PO垂直于地面，并用两根拉线PA、PB固定，量得∠PAO=，PBD=，则拉线PA、PB的长度之比正面POBAODCBA(第6题)GFEDCBA(第5题)CBA(第4题)A.tantanB.coscosC.sinsinD.sinsin二、填空题（本颗共6小题，每小题4分，共24分）11.若3x=2y，则yx=________.12.已知一个几何体的主视图与俯视图如图所示，则该几何体可能是________.l3.如图，公路AC与BC互相垂直，公路AB的中点M与点C被潮湖隔开.若测得AB的长为24km，则M、C两点间的距离为________.14.中国古代数学著作《九章算术》中记载：“今有户高多于广六尺八寸，两隅相去适一丈.问户高、广各几何?”译文为：知长方形门的高比宽多6.8尺，门的对角线长为10尺，那么门的高和宽各是多少尺？设长方形门的宽为x尺，则可列方程为________.15.如图，E、F分别为矩形ABCD的边AD，BC的中点，若矩形ABCD与矩形EABF相似，则相似比等于________.16.如图，正方形的顶点A，C分别在y轴和x轴上，边BC的中点F在y轴上，若反比例函数y=x12的图象恰好经过CD的中点E，则OA的长为________.三、解答题（本题有9小题，共86分）17.(本题满分8分)解方程：x2+6x－5=018.(本趣满分8分)如图，D、E分别是△ABC的边AB、AC上的点，DE∥BC，AB=7，BD=2，AE=6，求AC的长.19.(本题满分8分)如图，点A在y轴正半轴上，点B(4，2)是反比例函数图象上的一点且tan∠OAB=1，过点A作AC⊥y轴，交反比例函数图象于点C.FEDCBA(第15题)MCBA(第13题)俯视图主视图(第12题)EDCBAyxFEDCBA(第16题)OyxOCBA（1）求反比例函数的表达式；（2）求点C的坐标.20.(本题满分8分)如图，在菱形ABCD中，点E在对角线AC上，延长BE交AD于点F.（1）求证：EBEF＝BCFA；（2）已知点P在边CD上，请以CP为边，用尺规作一个△CPQ与△AEF相似，并使得点Q在AC上.(只须作出个△CPQ，保留作图痕迹，不写作法)21.(本题满分8分)某化肥厂2019生产氮肥4000吨，现准备通过改走技术提开生产效率，计划到2021年生产氮肥4840吨.现技术攻关小组按要求给了，；；甲、乙两种技术改进方案，其中运用甲方案能使每年产量增长的百分率相同，运用乙方案能使每年增长的产量相同.问运用哪一种方案能使2020年氮肥的产量更高?高多少?22.(本题满分10分)某地要建造一个园形喷水池，在水池中央垂直于水面安装一个柱子OA，点O恰好在水面中心，安装在柱子顶端A处的圆形头向外喷水，水流在各个方向上沿形状相同的抛物线路径落下，且在过OA的任意平面上，水流喷出的高度y(m)与水平距离x(m)之间的关系如图所示，建立平面PFEDCBA直角坐标系.右边抛物线的关系式为y=－x2+2x+3.请完成下列问题：（1）将y=－x2+2x+3化为y=a(x－h)2+k的形式，并写出喷出的水流距水平面的最大高度是多少米；（2）写出左边那条抛物线的表达式；（3）不计其他因素，若要使喷出的水流落在池内，水池的直径至少要多少米?23.(本题满分10分)4月23日，为迎接“世界读书日”，某书城开展购书有奖活动.顾客每购书满100元获得一次摸奖机会，规则为：一个不透明的袋子中装有4个小球，小球上分别标有数字1，2，3，4，们除所标数字外完全相同，摇匀后同时从中随机摸出两个小球，则两球所标数字之和与奖励的购书券金额的对应关系如下：两球所标数字之和34567奖励的购书券金额(元)00306090（1）通过列表或画树状图的方法计算摸奖一次获得90元购书券的概率；（2）书城规定：如果顾客不愿意参加摸奖，那么可以直接获得30元的购书券，在“参加摸奖”和“直接获得胸书券”两种方式中，你认为哪种方式对顾客更合算?请通过求平均数的方法说明理由.24.(本题满分I2分)如图，已知□ABCD中，sin∠DBC=，BD=24，∠BDC=60°.□MPNQ的顶点P、Q在线段BD上(点P在Q的左边)，顶点M、N分别在线段AD和BC上.（1）求证：DM=BN；（2）如图1，将△BCD沿直线BD折叠得到△BC'D，当BC'恰好经过点M时，求证四边形AMPNQ是菱形；（3）如图2，若四边形MPNQ是矩形，且MP∥AB，求BP的长.(结果中的分母可保留根式)25.(本题满分14分)已知二次函数y=ax2+bx+c(a0)的图象经过点A(1，2)（1）当c＝4时，若点B(3，10)在该二次函数的图象上，求该二次函数的表达式；（2）已知点M(t－3，5)，N(t+3，5)在该二次函数的图象上，求t的取值范围；（3）当a＝1时，若该二次函数的图象与直线y=3x－1交于点P、Q，且PQ＝10，求b的值宁德市2019-2020学年度第一学期期末九年级质量检测数学试题参考答案及评分标准一、选择题：ABCBBDACD二、填空题：C'QNMPDCBA(图1)QNMPDCBA(图2)11．23；12．三棱柱；13．1.2；14．222(6.8)10xx；15．2∶1(或2)；16．26．三、解答题17．解：265xx．1分26+959xx．·················································································3分2(3)14x．····················································································5分∴314x．················································································7分即1314x，2314x．·································································8分18．解：∵AB=7，BD=2，∴AD=AB-BD=5．·················································································1分∵//DEBC，∴ADAEABAC．·····················································································5分∵AE=6∴567AC．························································································6分∴425AC．························································································8分19．解：（1）设反比例函数的表达式为kyx，∵点B(4，2)在反比例函数图象上，∴24k．··························································································2分解得8k．·······················································································3分∴反比例函数的表达式为xy8．·································································4分（2）过点B作BD⊥AO于点D．∵点B的坐标为(4，2)，∴BD＝4，DO＝2．·······································5分在Rt△ABD中，OABtan=ADBD=1，∴AD=BD=4．··························································································6分∴AO=AD+DO=6．∵AC⊥y轴，∴点C的纵坐标为6．··········································································7分将y=6代入xy8，得x=34．∴点C的坐标为（34，6）．·······································································8分20．解：（1）∵四边形ABCD是菱形，∴AD∥BC．∴∠FAE＝∠ACB．又∵∠AEF＝∠CEB，··········································································2分DyABOxC∴△AEF∽△CEB．·············································································3分∴EFFAEBBC．····················································································4分（2）尺规作图如图所示：或········································································································7分∴△CPQ就是所求作的三角形．·····························································8分21．解：设甲方案的平均增长率为x，依题意得1分24000(1)4840x．······