洋浦中学学年九年级上期末考试试卷

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吉林省长春市长春经济技术开发区洋浦学校2022-2023学年九年级上学期期末数学试题

吉林省长春市长春经济技术开发区洋浦学校2022-2023学年九年级上学期期末数学试题学校:___________姓名：___________班级：___________考号：___________A ．0abc >B ．0a b c ++<C ．20a b +>D ．当0y <时，1x <二、填空题三、解答题15．解方程：2432x x -+=．16．一个不透明的口袋中有三个小球，上面分别标有数字2、3、4，每个小球除数字不同外其余均相同．(1)若融融同学从口袋中随机摸出一个小球，小球上的数字是奇数的概率是______．(2)若融融同学从口袋中随机摸出一个小球，记下数字后放回，再随机摸出一个小球，记下数字．请用画树状图（或列表）的方法，求两次摸出的小球上的数字都是偶数的概率． 17．长泰大桥是长春市最高的双塔斜拉式高架桥，大桥属于双塔双索面混凝土特大斜拉桥桥型，图①是大桥的实物图，图②是大桥的示意图．假设你站在桥上点A 处测得拉索AB 与水平桥面的夹角是39︒，点A 处距离大桥立柱CD 底端D 的距离AD 为97米，已知大桥立柱上B 点距立柱顶端C 点的距离BC 为5米，求大桥立柱CD 的高．(结果精确到1米)[参考数据：390.63sin ︒≈，390.78cos ︒≈，390.81]tan ︒≈18．图①、图②均是4×4的正方形网格，每个小正方形的顶点称为格点，线段AB 的端点均在格点上．在图①、图②给定的网格中按要求画图．(1)在图①中，在线段AB 上画出点M ，使AM ＝3BM ．(2)在图②中，在线段AB 上画出点P ，使AP ＝2BP ．（保留作图痕迹，要求：借助网格，只用无刻度的直尺，不要求写出画法）．19．哈市某展览馆计划将长60米，宽40米的矩形场馆重新布置，展览馆的中间是个1500平方米的矩形展览区，四周留有等宽的通道．求通道的宽为多少米？20．如图，二次函数的图象顶点坐标为()12--，，且过()10，．(1)求该二次函数解析式；(2)当33x -≤<时，则函数值y 的取值范围是．21．如图，Rt ABC △中，90ACB ∠=︒，CD AB ⊥于点D ．猜想：如图，在ABC V 中，点D 、E 分别是AB 与AC 的中点．根据画出的图形，可以猜想：DE BC ∥，且12DE BC =对此，我们可以用演绎推理给出证明．23．如图，在ABC V 中，90ACB ∠=︒，10AB =，6BC =，动点P 从点A 出发，沿AC 以每秒5个单位长度的速度向终点C 匀速运动，设点P 的运动时间为t 秒（0t >），过点P 作AB 的垂线交AB 于点M ．（1）AC =________．（2）求PM 的长，（用含有t 的代数式表示）（3）若将点P 绕点M 逆时针旋转90︒于点N ．①求BN 的长（用含t 的代数式表示）②在点P 运动的同时，作点B 关于点N 的对称点Q ，连结PQ ．当AQP △为等腰三角形时，直接写出t 的值．24．如图所示，在平面直角坐标系xOy 中，已知二次函数223y ax ax =++的图象与x 轴交于点()30A -,，与y 轴交于点B ．(1)求该函数的表达式及顶点坐标；(2)当3m x m ≤≤+时，该二次函数有最大值2，请根据图象求出m 的值；(3)将该二次函数图象在点A ，B 之间的部分（含A ，B 两点）记为图象W ． ①点Q 在图象W 上，连接QA ，QB ，求ABQ V 面积的最大值；②若直线y c =与图象W 只有一个公共点，结合函数图象，直接写出c 的取值范围．。

2022-2023学年海南省儋州市洋浦中学数学九上期末学业质量监测模拟试题含解析

2022-2023学年九上数学期末模拟试卷考生请注意：1．答题前请将考场、试室号、座位号、考生号、姓名写在试卷密封线内，不得在试卷上作任何标记。

2．第一部分选择题每小题选出答案后，需将答案写在试卷指定的括号内，第二部分非选择题答案写在试卷题目指定的位置上。

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考试结束后，请将本试卷和答题卡一并交回。

一、选择题（每题4分，共48分）1．如图，线段CD两个端点的坐标分别为C（4，4）、D（6，2），以原点O为位似中心，在第一象限内将线段CD缩小为线段AB，若点B的坐标为（3，1），则点A的坐标为（）A．（0，3）B．（1，2）C．（2，2）D．（2，1）2．如图，在⊙O中，分别将AB、CD沿两条互相平行的弦AB、CD折叠，折叠后的弧均过圆心，若⊙O的半径为4，则四边形ABCD的面积是（）A．8 B．163C．32 D．3233．在下面四个选项的图形中，不能由如图图形经过旋转或平移得到的是（）A．B．C．D．4．如图，⊙O 的弦AB ＝8，M 是AB 的中点，且OM ＝3，则⊙O 的半径等于（）A ．8B ．4C ．10D ．55．已知当x ＞0时，反比例函数y ＝k x 的函数值随自变量的增大而减小，此时关于x 的方程x 2﹣2（k +1）x +k 2﹣1＝0的根的情况为（）A ．有两个相等的实数根B ．没有实数根C ．有两个不相等的实数根D ．无法确定6．将一元二次方程2473x x +=化成一般式后，二次项系数和一次项系数分别为（）A ．4，3B ．4，7C ．4，-3D ．24 3x x7．一元二次方程x 2－2x ＝0根的判别式的值为( )A ．4B ．2C ．0D ．－48．下列说法正确的是（）A ．打开电视机，正在播放广告是必然事件B ．天气预报明天下雨的概率为90％，说明明天一定会下雨C ．买一张体育彩票会中奖是可能事件D ．长度分别为3，5，9厘米的三条线段不能围成一个三角形是随机事件9．在平面直角坐标系xOy 中，点()A a,b 在双曲线2y x =-上，点A 关于y 轴的对称点B 在双曲线k y x=上，则k 2-的值为A ．4-B ．0C ．2D ．4 10．在Rt △ABC 中，∠C ＝90°，若AC ＝4，AB ＝5，则cos B 的值（）A ．45B ．35C ．34D ．4311．下列长度的三条线段能组成三角形的是（）A ．1，2，3B ．2，3，4C ．3，4，7D ．5，2，812．在平面直角坐标系xOy 中，将一块含有45°角的直角三角板如图放置，直角顶点C 的坐标为（1，0），顶点A 的坐标为（0，2），顶点B 恰好落在第一象限的双曲线上，现将直角三角板沿x 轴正方向平移，当顶点A 恰好落在该双曲线上时停止运动，则此时点C 的对应点C ′的坐标为（）A ．（32，0）B ．（2，0）C ．（52，0）D ．（3，0）二、填空题（每题4分，共24分）13．如图，BD 是⊙O 的直径，∠CBD ＝30°，则∠A 的度数为_____．14．在一个不透明的盒子里有2个红球和n 个白球，这些求除颜色外其余完全相同，摇匀后随机摸出一个，摸出红球的概率是15，则n 的值为__________． 15．飞机着陆后滑行的距离s （单位：m ）关于滑行的时间t （单位：s ）的函数解析式是2200.5s t t =-，飞机着陆后滑行______m 才能停下来.16．已知在正方形ABCD 中，点E 、F 分别为边BC 与CD 上的点，且∠EAF=45°，AE 与AF 分别交对角线BD 于点M 、N ，则下列结论正确的是_____.①∠BAE+∠DAF=45°；②∠AEB=∠AEF=∠ANM ；③BM+DN=MN ；④BE+DF=EF17．汉代数学家赵爽在注解《周髀算经》时给出的“赵爽弦图”是我国古代数学的瑰宝.如图所示的弦图中，四个直角三角形都是全等的，它们的两直角边之比均为2:3，现随机向该图形内掷一枚小针，则针尖落在阴影区域的概率为__________.18．如图，菱形的ABCD 边长为4，60DAB ∠=︒，E 为BC 的中点，在对角线AC 上存在一点P ，使PBE ∆的周长最小，则PBE ∆的周长的最小值为__________．三、解答题（共78分）19．（8分）如图，已知O 是坐标原点，B 、C 两点的坐标分别为()3,1-，()2,1，将BOC ∆绕点O 逆时针旋转90度，得到11B OC ∆，画出11B OC ∆，并写出B 、C 两点的对应点1B 、1C 的坐标，20．（8分）已知二次函数()21y a x k =-+的图像与y 轴交于点()0,8C -，与x 轴的一个交点坐标是()2,0A -．（1）求二次函数的解析式；（2）当x 为何值时，0y <．21．（8分）如图，AB 为O 的直径，AE 平分BAF ∠，交O 于点E ，过点E 作直线ED AF ⊥，交AF 的延长线于点D ，交AB 的延长线于点C（1）求证：CD 是O 的切线（2）若2CB =，4CE =，求AB 的长22．（10分）一只不透明的袋子中，装有2个白球，1个红球，1个黄球，这些球除颜色外都相同．请用列表法或画树形图法求下列事件的概率：(1)搅匀后从中任意摸出1个球，恰好是白球．(2)搅匀后从中任意摸出2个球，2个都是白球．(3)再放入几个除颜色外都相同的黑球，搅匀后从中任意摸出1个球，恰好是黑球的概率为57，求放入了几个黑球？ 23．（10分）如图，在某广场上空飘着一只气球P ，A 、B 是地面上相距90米的两点，它们分别在气球的正西和正东，测得仰角∠PAB=45°，仰角∠PBA=30°，求气球P 的高度（精确到0.1米）．24．（10分）已知：如图，△ABC 中，∠BAC ＝90°，AB ＝AC ＝1，点D 是BC 边上的一个动点(不与B ， C 点重合)，∠ADE ＝45°．（1）求证：△ABD ∽△DCE ；（2）设BD＝x，AE＝y，求y关于x的函数关系式；（3）当△ADE是等腰三角形时，请直接写出AE的长．25．（12分）某校根据课程设置要求，开设了数学类拓展性课程，为了解学生最喜欢的课程内容，随机抽取了部分学生进行问卷调查（每人必须且只选中其中一项），并将统计结果绘制成如下统计图（不完整），请根据图中信息回答问题：（1）求m，n的值．（2）补全条形统计图．（3）该校共有1200名学生，试估计全校最喜欢“数学史话”的学生人数．26．文具店有三种品牌的6个笔记本，价格是4，5，7（单位：元）三种，从中随机拿出一个本，已知P（一次拿到7元本）23 ．（1）求这6个本价格的众数．（2）若琪琪已拿走一个7元本，嘉嘉准备从剩余5个本中随机拿一个本．①所剩的5个本价格的中位数与原来6个本价格的中位数是否相同？并简要说明理由；②嘉嘉先随机拿出一个本后不放回，之后又随机从剩余的本中拿一个本，用列表法．．．求嘉嘉两次都拿到7元本的概率．参考答案一、选择题（每题4分，共48分）1、C【解析】直接利用位似图形的性质得出对应点坐标乘以12得出即可．【详解】解：∵在第一象限内将线段CD缩小为线段AB，点B的坐标为（3，1），D（6，2），∴以原点O为位似中心，在第一象限内将线段AB缩小为原来的12后得到线段CD，∵C（4，4），∴端A点的坐标为：（2，2）．故选：C．【点睛】本题考查位似图形的性质，熟练掌握位似图形的性质是解题的关键.2、B【分析】过O作OH⊥AB交⊙O于E，延长EO交CD于G，交⊙O于F，连接OA，OB，OD，根据平行线的性质得到EF⊥CD，根据折叠的性质得到OH=12OA，进而推出△AOD是等边三角形，得到D，O，B三点共线，且BD为⊙O的直径，求得∠DAB=90°，同理，∠ABC=∠ADC=90°，得到四边形ABCD是矩形，于是得到结论．【详解】过O作OH⊥AB交⊙O于E，延长EO交CD于G，交⊙O于F，连接OA，OB，OD．∵AB∥CD，∴EF⊥CD．∵分别将AB、CD沿两条互相平行的弦AB、CD折叠，折叠后的弧均过圆心，∴OH=12OA，∴∠HAO=30°，∴∠AOH=60°，同理∠DOG=60°，∴∠AOD=60°，∴△AOD是等边三角形．∵OA=OB，∴∠ABO=∠BAO=30°，∴∠AOB=120°，∴∠AOD+∠AOB=180°，∴D，O，B三点共线，且BD为⊙O的直径，∴∠DAB=90°，同理，∠ABC=∠ADC=90°，∴四边形ABCD是矩形，∴AD=AO=4，AB=3AD=43，∴四边形ABCD的面积是163．故选B．【点睛】本题考查了垂径定理，圆周角定理，矩形的判定和性质，正确的作出辅助线是解答本题的关键．3、C【分析】由题图图形，旋转或平移，分别判断、解答即可．【详解】A 、由图形顺时针旋转90°，可得出；故本选项不符合题意；B 、由图形逆时针旋转90°，可得出；故本选项不符合题意；C 、不能由如图图形经过旋转或平移得到；故本选项符合题意；D 、由图形顺时针旋转180°，而得出；故本选项不符合题意；故选：C ．【点睛】本题考查了旋转，旋转是围绕一点旋转一定的角度的图形变换，因而旋转一定有旋转中心和旋转角，且旋转前后图形能够重合，这时判断旋转的关键．4、D【详解】解：∵OM ⊥AB ，∴AM=12AB=4，由勾股定理得：；故选D ．5、C 【分析】由反比例函数的增减性得到k ＞0，表示出方程根的判别式，判断根的判别式的正负即可得到方程解的情况．【详解】∵反比例函数y k x=，当x ＞0时，y 随x 的增大而减小，∴k ＞0，∴方程()222110x k x k -++-=中，△＝224(1)4(1)k k +--=8k +8＞0，∴方程有两个不相等的实数根．故选C ．【点睛】本题考查了根的判别式，以及反比例函数的性质，熟练掌握反比例函数的性质是解答本题的关键．6、C【分析】一元二次方程的一般形式是：ax 2+bx+c=0（a ，b ，c 是常数且a≠0）特别要注意a≠0的条件．这是在做题过程中容易忽视的知识点．在一般形式中ax 2叫二次项，bx 叫一次项，c 是常数项．其中a ，b ，c 分别叫二次项系数，一次项系数，常数项．【详解】解：2473x x +=化成一元二次方程一般形式是4x 2-1x+7=0，则它的二次项系数是4，一次项系数是-1．故选：C ．【点睛】本题主要考查了一元二次方程的一般形式，关键把握要确定一次项系数，首先要把方程化成一般形式．7、A【解析】根据一元二次方程判别式的公式24b ac =-△进行计算即可.【详解】解:在这个方程中，a ＝1，b ＝－2，c ＝0，∴224(2)4104b ac =-=--⨯⨯=，故选：A.【点睛】本题考查一元二次方程判别式，熟记公式24b ac =-△正确计算是本题的解题关键.8、C【分析】根据必然事件，随机事件发生的可能性逐一判断即可．【详解】A.打开电视机，正在播放广告是随机事件，故错误；B.天气预报明天下雨的概率为90％，明天也不一定会下雨，故错误；C.买一张体育彩票会中奖是可能事件，故正确；D.长度分别为3，5，9厘米的三条线段不能围成一个三角形是必然事件，故错误；故选：C ．【点睛】本题主要考查随机事件和必然事件，掌握随机事件和必然事件发生的可能性是解题的关键．9、B【分析】由点A （a ，b ）在双曲线2y x =-上，可得ab=-2，由点A 与点B 关于y 轴的对称，可得到点B 的坐标，进而求出k ，然后得出答案．【详解】解：∵点A （a ，b ）在双曲线2y x =-上， ∴ab=-2；又∵点A 与点B 关于y 轴对称，∴B （-a ，b ）∵点B 在双曲线k y x=上， ∴k=-ab=2；∴2k -=2-(-2)=4；故选：D ．【点睛】本题考查反比例函数图象上的点坐标的特征，关于y轴对称的点的坐标的特征．10、B【分析】根据勾股定理计算出BC长，再根据余弦定义可得答案．【详解】如图所示：∵AC＝4，AB＝5，∴BC22AB AC-2516-3，∴cos B＝CBAB＝35．故选：B．【点睛】考查了锐角三角函数，解题关键是掌握余弦：锐角A的邻边b与斜边c的比叫做∠A的余弦，记作cosA．11、B【解析】根据三角形三边关系定理得出：如果较短两条线段的和大于最长的线段，则三条线段可以构成三角形，由此判定即可．【详解】A．1+2=3，不能构成三角形，故此选项错误；B．2+3＞4，能构成三角形，故此选项正确；C．3+4=7，不能构成三角形，故此选项错误；D．5+2＜8，不能构成三角形，故此选项错误．故选：B．【点睛】本题考查了三角形的三边关系，在运用三角形三边关系判定三条线段能否构成三角形时并不一定要列出三个不等式，只要两条较短的线段长度之和大于第三条线段的长度即可判定这三条线段能构成一个三角形．12、C【分析】过点B作BD⊥x轴于点D，易证△ACO≌△BCD（AAS），从而可求出B的坐标，进而可求出反比例函数的解析式，根据解析式与A的坐标即可得知平移的单位长度，从而求出C的对应点．【详解】解：过点B作BD⊥x轴于点D，∵∠ACO+∠BCD＝90°，∠OAC+∠ACO＝90°，∴∠OAC＝∠BCD，在△ACO与△BCD中，OAC BCDAOC BDC AC BC∠=∠⎧⎪∠=∠⎨⎪=⎩∴△ACO≌△BCD（AAS）∴OC＝BD，OA＝CD，∵A（0，2），C（1，0）∴OD＝3，BD＝1，∴B（3，1），∴设反比例函数的解析式为y＝kx，将B （3，1）代入y＝kx，∴k＝3，∴y＝3x，∴把y＝2代入y＝3x，∴x＝32，当顶点A恰好落在该双曲线上时，此时点A移动了32个单位长度，∴C也移动了32个单位长度，此时点C的对应点C′的坐标为（52，0）故选：C．【点睛】本题考查反比例函数的综合问题，涉及全等三角形的性质与判定，反比例函数的解析式，平移的性质等知识，综合程度较高，属于中等题型．二、填空题（每题4分，共24分） 13、60°【解析】解：∵BD 是⊙O 的直径， ∴∠BCD=90°（直径所对的圆周角是直角）， ∵∠CBD=30°，∴∠D=60°（直角三角形的两个锐角互余）， ∴∠A=∠D=60°（同弧所对的圆周角相等）；故答案是：60° 14、1【分析】根据红球的概率结合概率公式列出关于n 的方程，求出n 的值即可【详解】解：∵摸到红球的概率为15∴2125n =+ 解得n=1．故答案为：1．【点睛】本题考查概率的求法与运用，根据概率公式求解即可：如果一个事件有n 种可能，而且这些事件的可能性相同，其中事件A 出现m 种结果，那么事件A 的概率()m P A n= 15、200【分析】要求飞机从滑行到停止的路程就，即求出函数的最大值即可.【详解】解：()()222200.50.5404002000.520200s t t t t t =-=--++=--+所以当t=20时，该函数有最大值200. 故答案为200. 【点睛】本题主要考查了二次函数的应用，掌握二次函数求最值的方法，即公式法或配方法是解题关键. 16、①②④【分析】由∠EAF=45°，可得∠BAE+∠DAF=45°，故①正确；如图，把△ADF 绕点A 顺时针旋转90°得到△ABH ，根据三角形的外角的性质得到∠ANM=∠AEB ，于是得到∠AEB=∠AEF=∠ANM ；故②正确；由旋转的性质得，BH=DF ，AH=AF ，∠BAH=∠DAF ，由已知条件得到∠EAH=∠EAF=45°，根据全等三角形的性质得到EH=EF ，∴∠AEB=∠AEF ，求得BE+BH=BE+DF=EF ，故④正确；BM 、DN 、MN 存在BM 2+DN 2=MN 2的关系，故③错误.【详解】解：∵∠EAF=45°，∴∠BAE+∠DAF=45°，故①正确；如图，把△ADF 绕点A 顺时针旋转90°得到△ABH ，由旋转的性质得，BH=DF ，AH=AF ，∠BAH=∠DAF ， ∵∠EAF=45°，∴∠EAH=∠BAH+∠BAE=∠DAF+∠BAE=90°-∠EAF=45°， ∴∠EAH=∠EAF=45°，在△AEF 和△AEH 中，45AH AF EAH EAF AE AE =⎧⎪∠=∠=︒⎨⎪=⎩， ∴△AEF ≌△AEH （SAS ）， ∴EH=EF ， ∴∠AEB=∠AEF ，∴BE+BH=BE+DF=EF ，故④正确； ∵∠ANM=∠ADB+∠DAN=45°+∠DAN ， ∠AEB=90°-∠BAE=90°-（∠HAE-∠BAH ）=90°-（45°-∠BAH ）=45°+∠BAH ， ∴∠ANM=∠AEB ，∴∠AEB=∠AEF=∠ANM ；故②正确；BM 、DN 、MN 满足等式BM 2+DN 2=MN 2，而非BM+DN=MN ，故③错误. 故答案为①②④.【点睛】本题考查了正方形的性质，全等三角形的判定与性质，等腰直角三角形的性质，勾股定理，熟记各性质并利用旋转变换作辅助线构造成全等三角形是解题的关键． 17、1213【解析】分析：设勾为2k ，则股为3k 13，由此求出大正方形面积和阴影区域面积，由此能求出针尖落在阴影区域的概率．详解：设勾为2k，则股为3k，弦为13k，∴大正方形面积S=13k×13k=13k2，中间小正方形的面积S′=（3−2）k•（3−2）k=k2，故阴影部分的面积为：13 k2-k2=12 k2∴针尖落在阴影区域的概率为:221212 1313kk=．故答案为12 13．点睛：此题主要考查了几何概率问题，用到的知识点为：概率=相应的面积与总面积之比．18、23+2【分析】连接DE，因为BE的长度固定，所以要使△PBE的周长最小，只需要PB+PE的长度最小即可．【详解】解：连结DE．∵BE的长度固定，∴要使△PBE的周长最小只需要PB+PE的长度最小即可，∵四边形ABCD是菱形，∴AC与BD互相垂直平分，∴P′D=P′B，∴PB+PE的最小长度为DE的长，∵菱形ABCD的边长为4，E为BC的中点，∠DAB=60°，∴△BCD是等边三角形，又∵菱形ABCD的边长为4，∴BD=4，BE=2，DE=23∴△PBE的最小周长=DE+BE=232，故答案为：232．【点睛】本题考查了菱形的性质、轴对称以及最短路线问题、直角三角形斜边上的中线性质；熟练掌握菱形的性质，并能进行推理计算是解决问题的关键．三、解答题（共78分）19、详见解析；点1B ，1C 的坐标分别为()1,3，()1,2-【分析】利用网格特点和旋转的性质画出B 、C 的对应点B 1、C 1即可．【详解】解：如图，11B OC ∆为所作，点1B ，1C 的坐标分别为()1,3，()1,2-【点睛】本题考查了画图−性质变换：根据旋转的性质可知，对应角都相等都等于旋转角，对应线段也相等，由此可以通过作相等的角，在角的边上截取相等的线段的方法，找到对应点，顺次连接得出旋转后的图形． 20、（1）y = (x-1)2-9 ；（2）-2<x<4【分析】（1）将点A 和点C 的坐标代入抛物线的解析式可求得 a ，k 的值，从而得到抛物线的解析式；（2）根据对称性求出抛物线与x 轴的另一个交点B 的坐标，最后依据y ＜1可求得x 的取值范围．【详解】解：（1）∵y =a (x-1)2+k 的图像与y 轴交于点C （1，﹣8），与x 轴的一个交点坐标是A （﹣2，1）．∴809a k a k -=+⎧⎨=+⎩，解得，19a k =⎧⎨=-⎩，∴该函数的解析式为y = (x-1)2-9；（2）令y =1，则(x-1)2-9=1，解得：122,4x x =-=， ∴点B 的坐标为（4，1）． ∴当-2<x<4时，y <1．【点睛】本题主要考查的是抛物线与x 轴的交点、待定系数法求二次函数的解析式，掌握相关知识是解题的关键．21、（1）证明见解析；（2）6【分析】（1）要证CD 是⊙O 的切线，只要连接OE ，再证OE ⊥CD 即可．（2）由勾股定理求得AB 的长即可．【详解】证明：（1）如图，连接OE ，∵OA=OE ， ∴∠OAE=∠OEA ． ∵AE 平分∠CAD ， ∴∠OAE=∠DAE ． ∴∠OEA=∠DAE ． ∴OE ∥AD ． ∵DE ⊥AD ， ∴OE ⊥DE ． ∵OE 为半径， ∴CD 是⊙O 的切线．（2）设⊙O 的半径是r ， ∵CD 是⊙O 的切线， ∴∠OEC=90°．由勾股定理得：OE 2 +CE 2 =OC 2 ，即222r 4(2)r +=+ ，解得r=3，即AB 的长是6 【点睛】本题综合性较强，既考查了切线的判定，要证某线是圆的切线，已知此线过圆上某点，连接圆心与这点（即为半径），再证垂直即可．同时考查了勾股定理，作出辅助线是本题的关键． 22、（1）12；（2）16；（3）n ＝1【分析】（1）摸到白球的可能为2种，根据求概率公式即可得到答案；（2）利用树状图法，即可得到概率；（3）设放入黑球n 个，根据摸到黑球的概率，即可求出n 的值. 【详解】解：（1）根据题意，恰好摸到白球有2种， ∴将“恰好是白球”记为事件A ，P (A )＝2142=；（2）由树状图，如下：∴事件总数有12种，恰好抽到2个白球有2种，∴将“2个都是白球”记为事件B ，P (B )＝21126=；（3）设放入n 个黑球，由题意得：4nn +＝57，解得：n ＝1．【点睛】此题考查了列表法与树状图法，用到的知识点为：概率=所求情况数与总情况数之比．解题的关键是掌握求概率的方法. 23、气球P 的高度约是32.9米．【分析】过点P 作PC ⊥AB 于C 点，由PC 及∠A 、∠B 的正切值表示出AB ，即AB=tan tan PC PCA B+∠∠，求得PC 即可．【详解】过点P 作PC ⊥AB 于C ，设PC = x 米，在Rt △PAC 中，∠PAB=45°， ∴ AC =" PC" = x 米，在Rt △PBC 中，∠PBA=30°， ∵ tan ∠PBA =PCBC， ∴333BC x==（米）又∵ AB = 90米，∴ AB = AC + CB =390x x =米 ∴31x =+≈32.9（米），答：气球P 的高度约是32.9米．24、（1）证明见解析；（2）y=x 2-x+1=（）2+12；（3）AE 的长为或 12．【分析】（1）根据等腰直角三角形的性质及三角形内角与外角的关系，易证△ABD ∽△DCE ．（2）由△ABD ∽△DCE ，对应边成比例及等腰直角三角形的性质可求出y 与x 的函数关系式；（3）当△ADE 是等腰三角形时，因为三角形的腰和底不明确，所以应分AD=DE ，AE=DE ，AD=AE 三种情况讨论求出满足题意的AE 的长即可．【详解】（1）证明： ∵∠BAC=90°，AB=AC ∴∠B=∠C=∠ADE=45°∵∠ADC=∠B+∠BAD=∠ADE+∠CDE ∴∠BAD=∠CDE ∴△ABD ∽△DCE ；（2）由（1）得△ABD ∽△DCE ， ∴BD EC =ABCD， ∵∠BAC=90°，AB=AC=1，∴，，EC=1-y ， ∴1x y∴y=x 2-x+1=（x-2）2+12；（3）当AD=DE 时，△ABD ≌△CDE ， ∴BD=CE ，∴x=1-y ，即 x-x 2=x ，∵x ≠0，∴等式左右两边同时除以x 得：-1∴，当AE=DE 时，DE ⊥AC ，此时D 是BC 中点，E 也是AC 的中点，所以，AE=12；当AD=AE 时，∠DAE=90°，D 与B 重合，不合题意；综上，在AC 上存在点E ，使△ADE 是等腰三角形， AE 的长为2-2或 12．【点睛】本题考查相似三角形的性质、等腰直角三角形的性质、等腰三角形的判定和性质、二次函数的性质等知识，解题的关键是学会构建二次函数解决最值问题，学会用分类讨论的思想思考问题，属于中考压轴题． 25、（1）15%m =，15%n =；（2）见解析；（3）300人.【分析】（1）用选A 的人数除以其所占的百分比即可求得被调查的总人数，然后根据百分比＝其所对应的人数÷总人数分别求出m 、n 的值j 即可；（2）用总数减去其他各小组的人数即可求得选D 的人数，从而补全条形统计图；（3）用样本估计总体即可确定全校最喜欢“数学史话”的学生人数．【详解】（1）抽取的学生人数为1220%60÷=人，所以156025%,96015%m n =÷==÷=．（2）最喜欢“生活应用”的学生数为6030%18⨯=（人）．条形统计图补全如下：（3）该要校共有1200名学生，可估计全校最喜欢“数学史话”的学生有；120025%300⨯=人．【点睛】本题考查了条形统计图与扇形统计图的应用，从条形统计图、扇形统计图中获取必要的信息是解决问题的关键． 26、（1）众数是7；（2）①相同；见详解；②310【分析】(1)由概率公式求出7元本的个数，由众数的定义即可得出答案； (2)①由中位数的定义即可得出答案；②用列表法得出所有结果，嘉嘉两次都拿到7元本的结果有6个，由概率公式即可得出答案．【详解】解:（1）∵P （一次拿到7元本）23=，∴7元本的个数为6×23=4(个)，按照从小到大的顺序排列为4，5，7，7，7,7,∴这6个本价格的众数是7. （2）①相同；∵原来4、5、7、7、7、7，∴中位数为777 2+=，5本价格为4、5、7、7、7，中位数为7，∴77=，∴相同.②见图∴P（两次都为7）2010==.【点睛】本题考查了众数、中位数以及列表法求概率；熟练掌握众数、中位数的定义，列表得出所有结果是解题的关键．。

海南省洋浦中学2024届九年级数学第一学期期末质量跟踪监视模拟试题含解析

海南省洋浦中学2024届九年级数学第一学期期末质量跟踪监视模拟试题注意事项1．考生要认真填写考场号和座位序号。

2．试题所有答案必须填涂或书写在答题卡上，在试卷上作答无效。

第一部分必须用2B 铅笔作答；第二部分必须用黑色字迹的签字笔作答。

3．考试结束后，考生须将试卷和答题卡放在桌面上，待监考员收回。

一、选择题（每题4分，共48分）1．用直角三角板检查半圆形的工件，下列工件合格的是（）A ．B ．C ．D ．2．为了解某地区九年级男生的身高情况，随取了该区100名九年级男生，他们的身高x （cm ）统计如根据以上结果，抽查该地区一名九年级男生，估计他的身高不高于180cm 的概率是（）组别（cm ）x ≤160 160＜x ≤170 170＜x ≤180 x ＞180 人数15 42 38 5 A ．0.05 B ．0.38 C ．0.57 D ．0.953．如图，点O 是五边形ABCDE 和五边形A 1B 1C 1D 1E 1的位似中心，若OA ：OA 1＝1：3，则五边形ABCDE 和五边形A 1B 1C 1D 1E 1的面积比是（）A ．1：2B ．1：3C ．1：4D ．1：9 4．如图，O 是ABC ∆的外接圆，AD 是O 的直径，若O 的半径是32，2AC =，则sin B =（）A．23B．53C．32D．3555．如图，△ABC的顶点均在⊙O上，若∠A＝36°，则∠OBC的度数为( ) A．18°B．36°C．60°D．54°6．已知反比例函数y＝kx的图象如图所示，则二次函数y＝k2x2+x﹣2k的图象大致为（）A．B．C．D．7．某种工件是由一个长方体钢块中间钻了一个上下通透的圆孔制作而成，其俯视图如图所示，则此工件的左视图是（）A．B．C．D．8．在同一平面直角坐标系中，一次函数y＝ax+b和二次函数y＝ax2+bx+c的图象可能为（）A．B．C．D．9．如图，过⊙O上一点C作⊙O的切线，交⊙O直径AB的延长线于点D．若∠D＝40°，则∠A的度数为（）A．20°B．25°C．30°D．40°10．如图，螺母的一个面的外沿可以看作是正六边形，这个正六边形ABCDEF的半径是23cm，则这个正六边形的周长是（）A．12 B．3C．36 D．311．一人乘雪橇沿如图所示的斜坡（倾斜角为30°）笔直滑下，滑下的距离为24米，则此人下滑的高度为（）A．24 B．123C．12 D．612．有n支球队参加篮球比赛，共比赛了15场，每两个队之间只比赛一场，则下列方程中符合题意的是( )A．n(n﹣1)＝15 B．n(n+1)＝15C．n(n﹣1)＝30 D．n(n+1)＝30二、填空题（每题4分，共24分）13．如图，在4×4的正方形网络中，已将部分小正方形涂上阴影，有一个小虫落到网格中，那么小虫落到阴影部分的概率是____.14．某品牌手机六月份销售400万部，七月份、八月份销售量连续增长，八月份销售量达到576万部，则该品牌手机这两个月销售量的月平均增长率为_________.15．二次函数y＝（x﹣1）2﹣5的顶点坐标是_____．16．已知二次函数y =ax2－bx＋2(a≠0) 图象的顶点在第二象限，且过点（1，0），则a的取值范围是_________；若a＋b 的值为非零整数，则b 的值为_________．17．比较大小：10_____1．（填“＞”、“=”或“＜”）18．如图，矩形ABCD中，AB=4，BC=5，AF平分∠DAE，EF⊥AE，则CF=______．三、解答题（共78分）19．（8分）为提升学生的艺术素养，某校计划开设四门选修课程：声乐、舞蹈、书法、摄影．要求每名学生必须选修且只能选修一门课程，为保证计划的有效实施，学校随机对部分学生进行了一次调查，并将调查结果绘制成如下不完整的统计表和统计图．学生选修课程统计表课程人数所占百分比声乐14 %b 舞蹈8 16% 书法16 32% 摄影a 24% 合计 m 100%根据以上信息，解答下列问题：（1）m = ，b = ．（2）求出a 的值并补全条形统计图．（3）该校有1500名学生，请你估计选修“声乐”课程的学生有多少名．（4）七（1）班和七（2）班各有2人选修“舞蹈”课程且有舞蹈基础，学校准备从这4人中随机抽取2人编排“舞蹈”在开班仪式上表演，请用列表法或画树状图的方法求所抽取的2人恰好来自同一个班级的概率．20．（8分）某商场试销一种成本为每件60元的服装，规定试销期间销售单价不低于成本单价，且获利不得高于45%，经试销发现，销售量y （件）与销售单价x （元）符合一次函数y kx b =+，且65x =时，55y =；75x =时，45y =．（1）求一次函数y kx b =+的表达式；（2）若该商场获得利润为W 元，试写出利润W 与销售单价x 之间的关系式；销售单价定为多少元时，商场可获得最大利润，最大利润是多少元？（3）若该商场获得利润不低于500元，试确定销售单价x 的范围．21．（8分）（问题情境）（1）古希腊著名数学家欧几里得在《几何原本》提出了射影定理，又称“欧几里德定理”：在直角三角形中，斜边上的高是两条直角边在斜边射影的比例中项，每一条直角边又是这条直角边在斜边上的射影和斜边的比例中项．射影定理是数学图形计算的重要定理．其符号语言是：如图1，在Rt △ABC 中，∠ACB=90°，CD ⊥AB ，垂足为D ，则：（1）AC²=AB·AD ；(2)BC²=AB·BD ；(3)CD² = AD·BD ；请你证明定理中的结论（1）AC² = AB·AD ．（结论运用）（2）如图2，正方形ABCD的边长为3，点O是对角线AC、BD的交点，点E在CD上，过点C作CF⊥BE，垂足为F，连接OF，①求证：△BOF∽△BED；BE ，求OF的长．②若1022．（10分）某鱼塘中养了某种鱼5000条，为了估计该鱼塘中该种鱼的总质量，从鱼塘中捕捞了3次，取得的数据如下：数量/条平均每条鱼的质量/kg第1次捕捞20 1.6第2次捕捞15 2.0第3次捕捞15 1.8（1）求样本中平均每条鱼的质量；（2）估计鱼塘中该种鱼的总质量；（3）设该种鱼每千克的售价为14元，求出售该种鱼的收入y（元）与出售该种鱼的质量x（kg）之间的函数关系，并估计自变量x的取值范围．23．（10分）武汉市某中学进行九年级理化实验考查，有A和B两个考查实验，规定每位学生只参加一个实验的考查，并由学生自己抽签决定具体的考查实验，小孟、小柯、小刘都要参加本次考查．（1）用列表或画树状图的方法求小孟、小柯都参加实验A考查的概率；（2）他们三人中至少有两人参加实验B的概率（直接写出结果）．24．（10分）解方程：（1）x（2x﹣1）+2x﹣1＝0（2）3x2﹣6x﹣2＝025．（12分）请回答下列问题．（1）计算：()()20180612cos30212tan 60113-+︒+-+⨯︒-- （2）解方程：2320x x --=26．如图，在ABC ∆中，90BAC ∠=，AB AC =，点,D E 均在边BC 上，且45DAE ∠=．（1）将ABD ∆绕A 点逆时针旋转90，可使AB 与AC 重合，画出旋转后的图形ACG ∆，在原图中补出旋转后的图形．（2）求DAG ∠和ECG ∠的度数．参考答案一、选择题（每题4分，共48分）1、C【分析】根据直径所对的圆周角是直角逐一判断即可．【题目详解】解：A 、直角未在工件上，故该工件不是半圆，不合格，故A 错误；B 、直角边未落在工件上，故该工件不是半圆，不合格，故B 错误；C 、直角及直角边均落在工件上，故该工件是半圆，合格，故C 正确；D 、直角边未落在工件上，故该工件不是半圆，不合格，故D 错误，故答案为： C ．【题目点拨】本题考查了直径所对的圆周角是直角的实际应用，熟知直径所对的圆周角是直角是解题的关键．2、D【分析】先计算出样本中身高不高于180cm的频率，然后根据利用频率估计概率求解．【题目详解】解：样本中身高不高于180cm的频率＝1005100-＝0.1，所以估计他的身高不高于180cm的概率是0.1．故选：D．【题目点拨】本题考查了概率，灵活的利用频率估计概率是解题的关键.3、D【分析】由点O是五边形ABCDE和五边形A1B1C1D1E1的位似中心，OA：OA1=1：3，可得位似比为1：3，根据相似图形的面积比等于相似比的平方，即可求得答案．【题目详解】∵点O是五边形ABCDE和五边形A1B1C1D1E1的位似中心，OA：OA1＝1：3，∴五边形ABCDE和五边形A1B1C1D1E1的位似比为1：3，∴五边形ABCDE和五边形A1B1C1D1E1的面积比是1：1．故选：D．【题目点拨】此题考查了位似图形的性质．此题比较简单，注意相似图形的周长的比等于相似比，相似图形的面积比等于相似比的平方．4、A【分析】连接CD，得∠ACD=90°，由圆周角定理得∠B=∠ADC，进而即可得到答案．【题目详解】连接CD，∵AD是直径，∴∠ACD=90°，∵O的半径是32，∴AD=3，∵∠B=∠ADC，∴sin B=2 sin3ACADCAD∠==，故选A．【题目点拨】本题主要考查圆周角定理以及正弦三角函数的定义，掌握圆周角定理以及正弦三角函数的定义，是解题的关键． 5、D【解题分析】根据圆周角定理，由∠A=36°，可得∠O=2∠A =72°，然后根据OB=OC ，求得∠OBC=（180°-∠O ）=（180°-72°）=54°. 故选：D点睛：此题主要考查了圆周角定理，解题时，根据同弧所对的圆周角等于圆心角的一半，求出圆心角，再根据等腰三角形的性质和三角形的内角和定理求解即可，解题关键是发现同弧所对的圆心角和圆周角，明确关系进行计算. 6、A【分析】先根据已知图象确定反比例函数的系数k 的正负，然后再依次确定二次函数的开口方向、对称轴、与y 轴的交点坐标确定出合适图象即可.【题目详解】解：∵反比例函数图象位于第一三象限，∴k ＞0，∴k 2＞0，﹣2k ＜0，∴抛物线与y 轴的交点（0，－2k ）在y 轴负半轴，∵k 2＞0，∴二次函数图象开口向上，∵对称轴为直线x ＝212k ＜0，∴对称轴在y 轴左边，纵观各选项，只有A 选项符合．故选：A ．【题目点拨】本题考查了二次函数和反比例函数的图象特征，根据反比例函数图象确定k 的正负、熟知二次函数的性质是解题的关键.7、A【解题分析】从左面看应是一长方形，看不到的应用虚线，由俯视图可知，虚线离边较近，故选A ．8、A【分析】本题可先由二次函数y=ax 2+bx+c 图象得到字母系数的正负，再与一次函数y=ax+b 的图象相比较看是否一致．【题目详解】A 、由抛物线可知，a ＜0，x=﹣2b a＜0，得b ＜0，由直线可知，a ＜0，b ＜0，故本选项正确； B 、由抛物线可知，a ＞0，由直线可知，a ＜0，故本选项错误；C 、由抛物线可知，a ＞0，x=﹣2b a＞0，得b ＜0，由直线可知，a ＞0，b ＞0，故本选项错误； D 、由抛物线可知，a ＞0，由直线可知，a ＜0，故本选项错误．故选A ．9、B【分析】直接利用切线的性质得出∠OCD=90°，进而得出∠DOC=50°，进而得出答案．【题目详解】解：连接OC ，∵DC 是⊙O 的切线，C 为切点，∴∠OCD=90°，∵∠D=40°，∴∠DOC=50°，∵AO=CO ，∴∠A=∠ACO ，∴∠A=12∠DOC=25°．故选：B ．【题目点拨】此题主要考查了切线的性质，正确得出∠DOC=50°是解题关键．10、D【分析】由正六边形的性质证出△AOB 是等边三角形，由等边三角形的性质得出AB=OA ，即可得出答案【题目详解】设正六边形的中心为O ，连接AO ，BO ，如图所示：∵O 是正六边形ABCDEF 的中心，∴AB=BC=CD=DE=EF=FA ，∠AOB=60°，3，∴△AOB 是等边三角形，∴3，∴正六边形ABCDEF 的周长3故选D【题目点拨】此题主要考查了正多边形和圆、等边三角形的判定与性质；根据题意得出△AOB 是等边三角形是解题关键. 11、C【分析】由题意运用解直角三角形的方法根据特殊三角函数进行分析求解即可.【题目详解】解：因为斜坡（倾斜角为30°），滑下的距离即斜坡长度为24米，所以下滑的高度为0124sin 3024122⨯=⨯=米. 故选：C.【题目点拨】本题考查解直角三角形相关，结合特殊三角函数进行求解是解题的关键，也可利用含30°的直角三角形，其斜边是30°角所对直角边的2倍进行分析求解.12、C 【解题分析】由于每两个队之间只比赛一场，则此次比赛的总场数为：1(1)2n n -，场．根据题意可知：此次比赛的总场数=15场，依此等量关系列出方程即可．【题目详解】试题解析：∵有n 支球队参加篮球比赛，每两队之间都比赛一场， ∴共比赛场数为1(1)2n n -， ∴共比赛了15场，1(1)152n n ∴-=，即()130.n n -=故选C.二、填空题（每题4分，共24分）13、716【解题分析】本题应分别求出正方形的总面积和阴影部分的面积，用阴影部分的面积除以总面积即可得出概率．【题目详解】解：小虫落到阴影部分的概率＝774416=⨯，故答案为：716．【题目点拨】本题考查的是概率的公式，用到的知识点为：概率＝相应的面积与总面积之比．14、20%【分析】根据增长（降低）率公式()21a x b ±=可列出式子.【题目详解】设月平均增长率为x.根据题意可得:()24001+576x=. 解得:0.2x =.所以增长率为20%.故答案为:20%.【题目点拨】本题主要考查了一元二次方程的应用，记住增长率公式很重要.15、（1，﹣5）【分析】已知解析式为抛物线的顶点式，根据顶点式的坐标特点，直接写出顶点坐标．【题目详解】解：因为y ＝（x ﹣1）2﹣5是抛物线的顶点式，根据顶点式的坐标特点，顶点坐标为（1，﹣5）．故答案为：（1，﹣5）．【题目点拨】本题考查了二次函数的性质，根据二次函数的顶点式找出抛物线的对称轴及顶点坐标是解题的关键．16、20a -<< 3CAB π∠=【分析】根据题意可得a <0，再由02b a>可以得到b >0，把（1，0）函数得a −b +2=0，导出b 和a 的关系，从而解出a 的范围，再根据a ＋b 的值为非零整数的限制条件，从而得到a,b 的值.【题目详解】依题意知a <0,02b a> ，a −b +2=0，故b >0，且b =a +2，a =b −2，a +b =a +a +2=2a +2，∴a +2>0，∴−2<a <0，∴−2<2a +2<2，∵a +b 的值为非零实数，∴a +b 的值为−1，1，∴2a +2=−1或2a +2=1，32a ∴=- 或12a =- ， ∵b =a +2，12b ∴= 或32b = 17、＞．【解题分析】先求出【题目详解】∵12=9＜10，＞1，故答案为＞．【题目点拨】本题考查了实数的大小比较和算术平方根的应用，用了把根号外的因式移入根号内的方法． 18、32【解题分析】试题分析：证△AEF ≌△ADF ，推出AE=AD=5，EF=DF ，在△ABE 中，由勾股定理求出BE=3，求出CE=2，设CF=x ，则EF=DF=4-x ，在Rt △CFE 中，由勾股定理得出方程（4-x ）2=x2+22，求出x 即可．试题解析：∵AF 平分∠DAE ，∴∠DAF=∠EAF ，∵四边形ABCD 是矩形，∴∠D=∠C=90°，AD=BC=5，AB=CD=4，∵EF ⊥AE ，∴∠AEF=∠D=90°，在△AEF 和△ADF 中，{?D AEFDAF EAF AF AF∠=∠∠=∠=，∴△AEF≌△ADF（AAS），∴AE=AD=5，EF=DF，在△ABE中，∠B=90°，AE=5，AB=4，由勾股定理得：BE=3，∴CE=5-3=2，设CF=x，则EF=DF=4-x，在Rt△CFE中，由勾股定理得：EF2=CE2+CF2，∴（4-x）2=x2+22，x=32，CF=32．考点：矩形的性质．三、解答题（共78分）19、（1）50、28；（2）12a=，补全图形见解析；（3）估计选修“声乐”课程的学生有420人；（4）所抽取的2人恰好来自同一个班级的概率为13．【分析】（1）由舞蹈人数及其所占百分比可得m的值，声乐人数除以总人数即可求出b的值；（2）总人数乘以摄影对应百分比求出其人数，从而补全图形；（3）利用样本估计总体思想求解可得；（4）画树状图展示所有12种等可能的结果数，再找出抽取的2名学生恰好来自同一个班级的结果数，然后根据概率公式求解．【题目详解】（1）816%50m=÷=，14%100%28%50b=⨯=，即28b=，故答案为50、28；（2）5024%12a=⨯=，补全图形如下：（3）估计选修“声乐”课程的学生有150028%420⨯=（人）．（4）七（1）班的学生记作1，七（2）班的学生记作2，画树状图为：∴共有12种等可能的结果数，其中抽取的2名学生恰好来自同一个班级的结果数为4，则所抽取的2人恰好来自同一个班级的概率为41123=．【题目点拨】本题考查了统计表、条形统计图、样本估计总体、列表法与树状图法求概率：利用列表法或树状图法展示所有等可能的结果n ，再从中选出符合事件A 或B 的结果数目m ，然后利用概率公式计算事件A 或事件B 的概率．20、解：（3）一次函数的表达式为120y x =-+（4）当销售单价定为4元时，商场可获得最大利润，最大利润是893元（3）销售单价x 的范围是7087x ≤≤．【解题分析】（3）列出二元一次方程组解出k 与b 的值可求出一次函数的表达式．（4）依题意求出W 与x 的函数表达式可推出当x=4时商场可获得最大利润．（3）由w=500推出x 4﹣380x+7700=0解出x 的值即可．【题目详解】(3)根据题意得：65557545k b k b +=⎧⎨+=⎩，解得k=﹣3，b=3．所求一次函数的表达式为120y x =-+；（4）2(60)(120)1807200w x x x x =--+=-+-=2(90)900x --+，∵抛物线的开口向下，∴当x ＜90时，W 随x 的增大而增大，而销售单价不低于成本单价，且获利不得高于45%，即60≤x≤60×（3+45%），∴60≤x≤4，∴当x=4时，W=2(8790)900--+=893，∴当销售单价定为4元时，商场可获得最大利润，最大利润是893元．（3）令w=500，解方程21807200500x x -+-=，解得170x =，2110x =，又∵60≤x≤4 ，所以当w≥500时，70≤x≤4．考点：3．二次函数的应用；4．应用题．21、（1）见解析；（235 【分析】（1）证明△ACD ∽△ABC ，即可得证；（2）①BC 2=BO•BD ，BC 2=BF•BE ，即BO•BD=BF•BE ，即可求解；②在Rt△BCE中，BC=3，BE=10，利用△BOF∽△BED，即可求解．【题目详解】解：（1）证明：如图1，∵CD⊥AB，∴∠BDC=90°，而∠A=∠A，∠ACB=90°，∴△ACD∽△ABC，∴AC：AB=AD：AC，∴AC² = AB·AD；（2）①证明：如图2，∵四边形ABCD为正方形，∴OC⊥BO，∠BCD=90°，∴BC2=BO•BD，∵CF⊥BE，∴BC2=BF•BE，∴BO•BD=BF•BE，即BO BFBE BD=，而∠OBF=∠EBD，∴△BOF∽△BED；②∵在Rt△BCE中，BC=3，10，∴221BE BC-=，∴DE=BC-CE=2；在Rt △OBC 中，， ∵△BOF ∽△BED ，∴OF BO DE BE =，即2OF =，∴. 【题目点拨】本题为三角形相似综合题，涉及到勾股定理运用、正方形基本知识等，难点在于找到相似三角形，此类题目通常难度较大．22、（1）1.78kg ；（2）1kg ；（3）y ＝14x ，0≤x ≤1．【分析】（1）根据平均数的公式求解即可；（2）根据每条鱼的平均质量×总条数＝总质量即可得答案；（3）根据收入=单价×质量，列出函数表达式即可．【题目详解】（1）样本中平均每条鱼的质量为20 1.615 2.015 1.8 1.78201515⨯+⨯+⨯=++（kg ）．（2）∵样本中平均每条鱼的质量为1.78kg ，∴估计鱼塘中该种鱼的总质量为1.78×5000＝1（kg ）．（3）∵每千克的售价为14元，∴所求函数表达式为y ＝14x ，∵该种鱼的总质量约为1kg ，∴估计自变量x 的取值范围为0≤x≤1．【题目点拨】本题考查一次函数的应用、用样本估计总体，明确题意，写出相应的函数关系式，利用平均数的知识求出每条鱼的质量是解题关键．23、（1）14；（2）12 【分析】（1）先画出树状图，得出所有等情况数和小孟、小柯都参加实验A 考查的情况数，再根据概率公式即可得出答案；（2）根据每人都有2种选法，得出共有8种等情况数，他们三人中至少有两人参加实验B 的有4种，再根据概率公式即可得出答案．【题目详解】解：（1）画树状图如图所示：∵两人的参加实验考查共有四种等可能结果，而两人均参加实验A考查有1种，∴小孟、小柯都参加实验A考查的概率为14．（2）共有8种等情况数，他们三人中至少有两人参加实验B的有4种，所以他们三人中至少有两人参加实验B的概率是41 82 =.故答案为：12．【题目点拨】本题考查了数据统计的知识，中考必考题型，重点需要掌握树状图的画法.24、（1）x1＝12，x2＝﹣1；（2）x1315+，x2315-【分析】（1）先分解因式，即可得出两个一元一次方程，求出方程的解即可；（2）求出b2-4ac的值，再代入公式求出即可．【题目详解】（1）x（2x﹣1）+2x﹣1＝0，（2x﹣1）（x+1）＝0，2x﹣1＝0，x+1＝0，x1＝12，x2＝﹣1；（2）3x2﹣6x﹣2＝0，这里a=3，b=-6，c=-2b2﹣4ac＝（﹣6）2﹣4×3×（﹣2）＝60，x 660±x1315+，x2315-【题目点拨】本题考查了解一元二次方程的应用，能选择适当的方法解方程是解此题的关键．25、（1）-4；（2）1317x+=，2317x-=.【分析】（1）先把特殊角的三角函数值代入，再计算乘方，再进行二次根式的运算即可；（2）用公式法解方程即可.【题目详解】解：（1）原式= 36(13)1223212(13)(13)++⨯+-+⨯-+ = 13232333++---=-4；（2）2(3)41(2)∆=--⨯⨯-=17 ∴13172x +=，23172x -=，【题目点拨】本题考查了特殊角的三角函数值及二次根式的混合运算、一元二次方程的解法，牢记特殊角的三角函数值是解题的关键.26、（1）见解析；（2）=90DAG ∠︒，=90ECG ∠︒.【分析】（1）以C 为圆心BD 为半径作弧，与以A 为圆心AD 为半径作弧的交点即为G 点，然后连线即可得解；（2）根据旋转的性质可得∠CAG=∠BAD ，∠ACG=∠ABD ，然后根据题意即可得各角的大小.【题目详解】（1）△ACG 如图：（2）∵90BAC ∠=，45DAE ∠=，∴∠B+∠ACB=90°，∠BAD+∠CAE=45°，又∵ACG ∆为ABD ∆绕A 点逆时针旋转90所得，∴∠CAG=∠BAD ，∠ACG=∠ABD ，∴=90DAG DAE EAC GAC ∠=++︒∠∠∠，==90ECG ECA ACG ∠+︒∠∠.【题目点拨】本题主要考查画旋转图形，旋转的性质，解此题的关键在于熟练掌握其知识点.。

2023届海南省儋州市洋浦中学英语九年级第一学期期末统考试题含解析

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Ⅰ. 单项选择1、I love the weekend because I_______ get up early to go to school.A．can't B．mustm't C．needn't D．shouldn't2、—Julia shines at every turn in the company. And her boss pays her well.--Yeah. I hear she makes a ________ $90000 every year.A．extra B．clear C．clean D．mean3、—I’m sorry. I broke your tea cup.—________. I have another one at home.A．It’s too bad B．My pleasure C．It doesn’t matter D．Y ou’d better not4、Don’t be afraid of new wo rds. Y ou can ________ in a dictionary.A．look at them B．look for them C．look them up5、—Have you watched “ Avengers: Endgame” (《复仇者联盟：终局之战》)recently?—Of course, action movies like this usually have quite a few funny ____ and an unexpected ending.A．conversation B．dialogues C．communication6、It ________ them about one hour to get to the center of the city by underground.A．used B．paid C．spent D．took7、-Must I stay here with you? -No, you_____. You may go home now, but you_____ go to the net-bar.A．mustn't, needn't B．needn’t, mustn’tC．must, need D．need, must8、—I called you several times last night, but there was no answer.—Oh, I’m really sorry. I ____ my mobile phone at the office yesterday.A．have left B．was leaving C．left9、It's better for us to stay indoors, when PM 2.5 reaches dangerous levels.A．properly B．possibly C．generally D．especially10、_______riding shared bikes is an easy way to travel, it also causes some problems.A．Although B．If C．UntilⅡ. 完形填空11、We began our hunt for the treasure. At the top of the hill, we sat down to rest. Suddenly, a 1 from trees started singing: “Fifteen men on the dead man’s chest—Yo-ho-ho, and a bottle of rum!”The pirates were 2 . Their faces turned white, and some of them jumped up.“It’s Flint!”cr ied one.“Someone is playing the 3 on us,” said Silver.The men started to feel better at these words. 4 the voice called out again.“Darby McGraw,” it called out several times. “Fetch the rum, Darby!”The pirates 5 where they were, looking around in fear.“Those were Flint’s last words before he died,” whispered one.“ 6 here except us knows about Darby,” said Silver. “I’m here to get the treasure. I was never afraid of Flint when he was 7 , and I’m not afraid of him now. There’s 700,000 pounds a quarter of a mile from here. I’m not going to 8 .”“You’re right, John,” said one of the pirates. “And that voice 9 like Flint’s voice. It was more like…”“Ben Gunn!!” shouted Silver.“Yes!” cried another10 . “It was Ben Gunn! And nobody is afraid of Ben Gunn, dead or alive.”With this, the men’s spirit returned. They picked up their things and we carried 11 walking.We were now close to the tall trees. I was worried about Silver. I was sure he could easily kill everyone to keep the treasure for 12 .“Hooray!” shouted one of the pirates and they all started running. Suddenly they stopped. When Silver and I reached them we saw 13 .In front of us there was a very big hole. At the 14 of the hole there was a broken wooden box. On one of the sides I saw the word Walrus—the 15 of Flint’s ship.It was clear that the treasure was not there.1．A．woman B．voice C．bird D．child2．A．angry B．frightened C．happy D．excited3．A．joke B．music C．piano D．toy4．A．If B．Or C．And D．But5．A．remained B．received C．rested D．relaxed6．A．Nobody B．Somebody C．Anybody D．Everybody7．A．dead B．young C．alive D．live8．A．pick it up B．give it up C．put it up D．open it up9．A．was B．sounded C．wasn’t D．didn’t10．A．softly B．sadly C．quietly D．loudly11．A．out B．with C．on D．to12．A．himself B．myself C．themselves D．ourselves13．A．what B．why C．where D．which14．A．end B．front C．top D．bottom15．A．weight B．colour C．name D．sizeⅢ. 语法填空12、Diet and way of life are often a problem for teenagers. However, 1．you eat the right food and exercise more, you can feel better, look better and have more energy. So healthy eating along with regular exercise is 2．( probable) the only way to become fit.As a teenager, it is important to give your body the energy 3．needs. For a healthy diet, you should eat mostly rice, bread, vegetables and fruit. You also need to drink a lot of water — six to eight glasses a day.4．(drink) enough water will improve your skin and give you 5．(health) hair.Exercise is something 6．can help to make you look good, feel good and be healthy. Teenagers should spend at least 30 minutes exercising, five times a week. Walking and riding your bike count, and so do school 7．(sport). When you exercise, your body produces some things that make you feel peaceful and 8．(relax) and increase your ability to concentrate when you study. These things can even help you sleep better at night. A good amount of sleep every night 9．(be) also important for your health. Teenagers need eight to ten hours of sleep each night.If you follow the suggestions above, you will look and feel much 10．(good) in no time at all.Ⅳ. 阅读理解A13、A 7-magnitude（震级）earthquake hit Ya'an,Sichuan at 8:02 on April 20, 2013, and it killed at least 196 people and injured more than 11,000.Together with other students, Yang Xuelan ran out to the playground. She was safe. But all her textbooks and exercise books were buried（埋）in the teaching building.What can we do when an earthquake happens? In fact, there's little we can do to stop naturaldisasters, such as earthquakes happening. But, some methods can reduce the harm they cause.◆ Drop down onto your hands and knees. This way can protect you from falling.◆ Cover your head under a strong table or desk. You can also stay along a wall, and cover your head with your arms and hands.◆ Hold on to(守住,抓牢) your shelter(遮蔽物) until the shaking stops. Be prepared to move with your shelter if the shaking continues.Schools can normally take the earthquake drills（演练）to help student stay alive.1．Ho w many people lost their lives in the earthquake in Ya’an?A．At least 196. B．More than 11,000C．Less than 196. D．About 11,196.2．When the earthquake happened in Ya'an, Y ang Xuelan was______________.A．at home B．playing on the playgroundC．on her way to school D．at school3．What does the underlined word “disasters” mean in Chinese?A．祸患B．现象C．灾害D．事故4．According to the writer, we can _________ to reduce the harm natural disasters cause.A．do nothing B．take some methodsC．stay at home D．run out of the house5．Which of the following can help you stay alive in an earthquake?A．Dropping down onto your hands and knees.B．Covering your head under a strong table or desk.C．Holding on to your shelter until the shaking stopsD．A, B and C．B14、Have you ever heard of a famous charity called Operation Smile? We hope we can help you understand how we are trying to help children all over the world.Operation Smile was started by a doctor and his wife. In 1982, together with some volunteers, they went to Philippines to help children who had holes in their lips or inside their mouths. It was very difficult for them to eat and drink. These volunteers worked very hard. But they worried that they could not carry on with the work because they were short of money. Then they decided to start a charity so that they could help these needy children. They called it Operation Smile. Operation Smile works in more than twenty developing countries and has cured over 10,000 children who have problems with their mouths. Operation Smile has won many prizes for its work and in 1999 they even started a special event called“The World Journey of Hope”. 5,000 children in 18 countries are cured during the event.On the other hand, Operation Smile trains local doctors and nurses in developing countries so that they can continue to help children when Operation Smile has left. As to the children with much more serious problems, they will send them to America for further treatment.So show your kindness and generosity to the needy children now. You can send your donation to Operation Smile at local banks. Many thanks from the children who can smile now will come to you.1．Operation Smile is a famous _____, which was started by a doctor and his wife.A．school B．charity C．building D．person2．Operation Smile helps the children by _____.A．curing the children who have problems with their mouthsB．helping poor children go back to schoolC．helping blind children to see againD．offering houses to homeless children3．Five thousand children from _____ countries are cured during the event “The World Journey of Hope”.A．ten B sixteen B．eighteen C．twenty4．Why did they worry that they could not carry on with the work?Because _____.A．there were no more volunteersB．they went to America for further studyC．they didn’t have enough moneyD．the doctors were too busy5．What does the writer ask us to do to show our kindness and generosity to the needy children? A．To donate money at local banks.B．To be a volunteer in Philippines.C．To send cards to the needy children.D．To be a doctor of Operation Smile.C15、1．Who is this form above most probably written for?A．Parents. B．Doctor.C．Students. D．Teachers.2．According to the information given in the form, why don’t students like to study?A．Becauseoftoomuchhomework.B．Becausetheydon’tknowhowtogetonwellwithclassmat es.C．Becausetheydon’tliketodoexercise.D．Becausecomputers have a bad influence on them.3．_______ can help you avoid becoming short-sighted.A．Doingeyeexercisesregularly B．ReadinginbedC．Readinginthesun D．Readingtoolong4．If you feel stressed, you should ________.A．dolesshomeworkB．makeplansforyourstudy,hobbiesandrelaxationC．fightwithothersD．havesomesnacks5．Peter is very fat. Maybe he ________.A．playscomputergamestoomuchB．hastoomanysnacksC．B or DD．doesn’tliketodoexerciseD16、We learn not only different subjects at school, but also some other lessons that may change our world view.When I was in primary school, I got into a big argument (争论) with a boy in my class. I forgot what the argument was about, but I will never forget the lesson I learned that day.I thought that I was right and he was wrong, and he thought I was wrong and he was right. The teacher decided to teach us a very important lesson without criticizing (批评) both of us.She brought us to the front of the class and asked him to stand on one side of her desk and me on the other. In the middle of her was a large, round ball. I could clearly see that it was black. She asked the boy what color the ball was. "White", he answered.I couldn't believe it. The ball was obviously black! Another argument started between us, this time about the color of the ball.The teacher told us to change places and then asked me what color the ball was. I answered, “White.”It was a ball with two differently colored sides, and from one side it was white. Only from my side it was black.Sometimes we need to look at problems from other person's view in order to truly understand his or her idea.1．In the beginning, the writer ______.A．didn't get along with boys B．fought with a boy in her classC．taught the boy a lesson D．had a big argument with a boy2．When the writer was in the boy's place, she changed her answer because ______.A．the boy changed his answer, too B．the ball had two differently colored sidesC．she wanted to say sorry to the boy D．the teacher said the boy was right3．From what the teacher did, we know that she was ______.A．wise B．polite C．kind D．strict4．The passage mainly tells us that ______.A．teachers shouldn’t punish students B．seeing is believingC．we should put ourselves in others’ shoes D．nobody can always be rightE17、Everyone needs friends. Friends bring us happiness and hope in our lives. But the ability (能力)to make friends changes from person to person. To some people, making friends is easy, and to others it’s very difficult.Making friends is a skill, and the first thing is to know how to get along with others.If you have trouble in making friends, maybe I can tell you how to do it.★Realize your own good points. You have skills and talents that others will like.★Believe that you are a good person and have something nice to share with others.★Be humorous. Learn to laugh at yourself and your weakness. Remember to smile to others.★Respect the others. Everyone has his own idea. Learn how to listen to others’ ideas without trying to make them accept yours.★Be kind. If you are kind to others, they will usually be kind to you. There are hundreds of little things you can do to show kindness. Open the door for someone. Wave to a friend and so on.★Don’t complain. Learn to accept what you can’t change, and work hard to change what you can. No one is willing to hear your complaining all the time.★Never give up. Even if you are faced with some closed-minded people, never give up. And try to find someone who will understand you.1．Why do we need friends according to the passage?A．Friends can do everything for us.B．Friends can bring us happiness.C．Friends accept our ideas all the time.D．Without friends we could not live.2．What’s the first thing we should learn in order to make friends?A．To help others.B．To smile to others.C．To get along with others.D．To listen to others’ complaints.3．. Which of the following shows a sense of humour?A．Opening the door for someone.B．Complaining to others all the time.C．Laughing at ourselves and our weakness.D．Finding someone who will understand us.4．How many pieces of advice does the writer offer when we have trouble in making friends?A．Five. B．Seven. C．Nine. D．Eleven.5．I you don’t want to complain, you are supposed to according to the passage.A．Learn to help your parentsB．Learn to make lots of friendsC．Learn to change yourselfD．Learn to accept what you can’t changeF18、An Englishman, a Frenchman and a Russian were discussing happiness. "Happiness," said the Englishman, "Happiness is when you return home tired after work, yet find your slippers(拖鞋) warming by the fire.""You English have no romance," said the Frenchman. "Happiness is when you go on a business trip, find a pretty girl who entertains you －then afterwards you part(道别) without regrets（遗憾）.""You are both wrong," said the Russian. "True happiness is when you are at home in bed and at 4 a.m., you hear a ring at the door and outside stand the secret police, who say to you, 'Ivanovitch, you are under arrest', and you say, 'Sorry, Ivanovitch lives next door.'"1．The Englishman's happiness suggests that _______.A．he should have no time to warm his slippersB．he enjoys the warmth of the familyC．he thinks it the most important to have slippersD．he wants someone to warm his slippers2．What the Frenchman said means that _______.A．a man can be free to play with any pretty girl when possibleB．he wants to marry a girl he lovesC．he is interested in going on a business tripD．the Englishman should have more romance3．The meaning of the Russian's words is that _______.A．he would like to have a good sleep at nightB．he will feel happy if his neighbour is arrestedC．he thinks it happiness to feel safeD．he will feel afraid if anyone knocks at his door at nightⅤ.书面表达19、书面表达（本题20分）根据要求完成短文写作，请将作文写在答题卡指定的位置上。

吉林省长春市经开区洋浦学校2022-2023学年九年级上学期期末英语试卷(含解析)

2022-2023学年吉林省长春市经开区洋浦学校九年级（上）期末英语试卷Ⅰ、单项选择（10 分）1．（1分）Everyone should try their best to create___clean and peace world.（）A．a B．an C．the D．/2．（1分）Linda is preparing the clothes _______ she will need during the school trip.（）A．whom B．whose C．who D．which3．（1分）_______valuable gift it is!It reminds me of my childhood.（）A．What B．What a C．What an D．How4．（1分）1 find necessary to learn to manage our time and make full use of every minute.（）A．that B．this C．its D．it5．（1分）Today Chinese by more and more people in the world．（）A．was spoken B．is spoken C．spoke D．speak6．（1分）Our teacher always explains to us whenever we ask her questions.（）A．patiently B．widely C．especially D．politely7．（1分）﹣﹣﹣Do you have any plans for the winter vacation？﹣﹣﹣I'm not sure.I work as a volunteer.（）A．must B．can C．may D．should8．（1分）I didn't understand my mom's love_______we had a long talk.（）A．until B．if C．since D．because9．（1分）Your bicycle is so nice．Could you tell me ________？Of course．At the shop near my home．（）A．where you buy it B．where do you buy itC．where you bought it D．where did you buy it10．（1分）— I don't think teenagers should be allowed to drive cars.— ________ They are not serious enough.（）A．I agree with you.B．I'm afraid so.C．I hope so.D．No problem.Ⅱ、交际运用。

九年级化学上学期期末考试试题试题 2_1_1

洋浦中学2021届九年级化学上学期期末考试试题新人教版可能用到的相对原子质量：C~12 H~1 O~16 K~39 Mn~55一、选择题〔本大题一一共14小题，每一小题只有一个选项符合题意，每一小题3分，一共42分〕1、以下变化中，属于物理变化的是〔〕A、米饭变馊B、火药爆炸C、湿衣服晾干D、铁锅生锈2、以下实验操作正确的选项是〔〕A．验满氧气 B．倾倒液体 C．读取液体体积 D．点燃酒精灯3、营养学家提出“每天一杯牛奶，强壮一个民族〞，我们认为这应该归功于牛奶中含有丰富的钙、镁等。

这里的钙、镁是指：〔〕A．元素 B．原子 C．分子 D．离子4、“墙脚数枝梅，凌寒单独开。

遥知不是雪，为有暗香来。

〞(王安石?梅花?)诗人在远处就能闻到淡淡的梅花香味的原因是( )A．分子很小 B．分子可以再分C．分子之间存在间隙 D．分子在不断运动5、金属钛及钛的合金被认为是21世纪重要的金属材料，地壳中的钛矿石主要是金红石〔TiO2〕，TiO2中钛的化合价是〔〕A.+5B.+4C.+3D.+26以下各物质应用中，主要利用其化学性质的是〔〕A．用木炭进展烧烤B．活性炭吸附臭味C．HY石用于切割玻璃D．用石墨做干电池电极7、发射HY所用的燃料燃烧时的化学方程式：A + 2H2O2====N2+ 4H2O，那么A的化学式为( )A . N2 B. NO2C. NOD. N2H48、各物质组中，前者属于单质，后者属于混合物的是〔〕A.氮气蒸馏水B.海水木炭C.氧气石灰石D.矿泉水空气9、W、X、Y、Z四种物质在一定条件下充分反响后，测得反响前后各物质的质量如下：以下说法错误的选项是A.W在反响中可能是催化剂 40g10、火柴划着后，假如将火柴直立，是火焰在上，火柴就不易继续燃烧，其原因是〔〕A．氧气缺乏 B．火柴的着火点升高C．没有到达着火点D．空气缺乏11、图书档案室或者存放精细仪器的工作室失火，宜使用的灭火器为〔〕12、玻璃仪器洗干净的标志是( )A ．透明B ．内壁上有少量水珠C ．内壁上的水成股流下D ．内壁上附着的水既不聚成水滴，也不成股流下 13、以下各图是表示气体分子的示意图，图中“ 〞和“ 〞分别表示两种不同元素的原子，其中表示单质的是〔〕A 、、14、以下化学反响中既不是化合反响也不是分解反响的是〔〕A ．铁+氧气−−→−点燃四氧化三铁B ．二氧化碳+碳−−→−高温一氧化碳 C.氧化汞−−→−加热汞+氧气 D ．乙炔+氧气−−→−点燃二氧化碳+水二、填空题〔本大题一一共3小题，每个小空2分，一共20分〕15、请你从①氧气、②二氧化碳、③HY 石、④一氧化碳、⑤氮气、五种物质中，选出符合以下要求的物质填入相应空内：(用序号填写上)〔1〕可用于做制冷剂和人工降雨的是______；〔2〕能与血液中血红蛋白结合，使人中毒的是______；〔3〕可以供应呼吸的是______；〔4〕可以保护气的是_________；16、蔗糖〔C12H22O11〕是生活中常见的食品之一，它由____.种元素组成，各元素的原子个数比是__________，它的一个分子中一共有_________个原子，元素质量比m(C)：m(H)：m(O)为______________.17、完成以下表格三、简答〔本大题一一共2小题，每一小题6分，一共12分〕18、通常情况下，燃烧需要哪三个条件？19、很多科学家提出，全球气候变暖是如今面临的非常严重的环境问题之一。

2023届海南省洋浦中学英语九上期末综合测试试题含解析

2022-2023学年九上英语期末模拟试卷注意事项：1．答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。

2．选择题必须使用2B铅笔填涂；非选择题必须使用0．5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

4．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。

Ⅰ. 单项选择1、— Do you still remember ?—July, 15th,2015.A．when did BRT in the city start to runB．when BRT in the city started to runC．how BRT in the city started to runD．how did BRT in the city started to run2、Everyone knows that the sun in the east.A．rises B．falls C．stays D．lives3、﹣Can you catch what I said？﹣Sorry，I can ______understand it because you speak very quickly．A．almost B．probably C．mostly D．hardly4、Lily Lucy may go with you because one of them must stay at home.A．Not only; but also B．Neither; norC．Both; and D．Either; or5、Many kids in China are crazy about the Western culture. But I still can't understand to us Chinese.A．what does Christmas mean B．what Christmas does meanC．what mean Christmas does D．what Christmas means6、The boy doesn't speak his sister, but his written work is very good.A．as well as B．so good asC．more better than D．more worse than7、— Who is the girl under the tree?—She _______ be Tom’s sister. But it’s too far, I’m not sure.A．may B．can’t C．must D．shouldn’t8、Not only can the art bring happiness to others, but it also shows that even cold, hard iron can__________ to life with a little creativity.A．bring back B．be brought back C．bring out9、—We have 42 students in our class. of them are boys.—Yes. There are 28 boys and 14 girls.A．Two thirds B．One third C．A half D．A quarter10、Zhu Ting, one of volleyball players in China, has already led China to many victories and has been awarded many MVPs in the volleyball matches.A．excellent B．more excellent C．most excellent D．the most excellentⅡ. 完形填空11、Long ago there were no airplanes. It was 1 for men to fly because men had no wings. But a young man wanted to fly so much. Every day he looked at the 2 in the sky and hoped to fly like them. Then he had an idea. He wanted to 3 some wings. He tried many 4 that he could find and at last, he used feathers (羽毛) and wax (蜡). After he finished the wings, he 5 up to the top of a mountain and put on the wings. Then he jumped off the mountain. So he flew above the clouds and saw the sun. But he flew too 6 the sun and it was too hot. Suddenly the wax on his wings melted. The wings were 7 . He fell and fell and finally he fell into the sea. Luckily, he was alive and continued inventing wings which could make him fly. Of course, this is just a beautiful legend！1．A．easy B．hard C．important D．tired2．A．sun B．clouds C．birds D．winds3．A．buy B．make C．do D．take4．A．ways B．materials C．foods D．tools5．A．run B．jumped C．climbed D．walk6．A．close B．far C．next D．near7．A．on fire B．in fire C．at fire D．out fireⅢ. 语法填空12、In one’s life, one usually has little understanding of oneself. When you succeed, you may be very proud. When you 1．, you may lose heart. If you don’t get a thorough understanding of yourself, you may miss lots of 2．(chance) in life.To get a thorough understanding of yourself is to know well 3．yourself. Y ou may know your strong points and weak 4．(one). You may hope for a wonderful future, but be sure not to expect too much because not all dreams can 5．(realize). You may be confident enough to meet challenges, but first you should know what to do.To get a thorough understanding of yourself, you should have a real sense of self-appreciation. Maybe you think you are not a tall tree 6．just small grass, as long as you get full confidence, you are sure to face any trouble.To get a thorough understanding of yourself also 7．to look after yourself. When you are angry, find a quiet place so that you won’t be hurt. When you are sad, tell your friends about it to 8．the mood into a good one. When you are tired, g et a good sleep. If you don’t take good care of yourself, you won’t be able to stay away from 9．(ill).So if you get a thorough understanding of yourself, you 10．(get) a full control of yourself and find your life full ofcolor.Ⅳ. 阅读理解A13、It was the last day of the final examination in a college. On the steps of the building, a group of engineering students were waiting for the last exam .On their faces was confidence. They knew the exam would be easy. The professor (a teacher at a college) had said they could bring any books and notes during the test.Right after they came into the classroom,the professor handed out the papers.There are only five questions on it.Three hours passed. Then the professor began to collect the papers.The students no longer looked confident. On their faces was nervous expression. The professor watched the worried faces before him, and asked, “How many of you have completed all five questions?” No hand was raised. “How many of you have answered four?” Still no hands. Three? Two?” The students moved restlessly in their seats. “One, then?” Certainly someone has finished one. But the class kept silent. The professor said, “That is exactly I expected. I just want to make you know clearly that even though you have completed four years of engineering. There are still many things about the subject you don’t know. These questions you could not answer are common in everyday practice.” Then,smiling,he added, “You will all pass this course, your education has just begun.”The years haveobscuredthe name of this professor, but not the lesson he taught.1．（小题1）Why did the students think the exam was easy at first?A．Becouse it was their last exam in the college.B．Because they knew there were only five questions.C．Because they thought they were clever and talented.D．Because they were allowed to bring any books and notes during the test.2．（小题2）What does the underlined word “obscured” mean in the last paragraph?A．Make something not clear.B．Make somebody think of something.C．Remind somebody of something.D．Make something change.3．（小题3）What could the students learn from the last exam?A．He laughs best who laughs last.B．A good beginning is half done.C．One is never too old to learn.D．The early bird catches the worm.(虫子)4．（小题4）What’s the best title for the article?A．Some confident students.B．A difficult exam.C．An interesting professor.D．An unforgettable lesson.B14、I was waiting for a phone call from my agent last night. He had left a message the night before, telling me that my show was to be cancelled. I called him several times, but each time his secretary told me that he was in a meeting and that he would call me later. So I waited and waited, but there was still no call. Three hours passing by, I became more and more impatient. I was certain that my agent didn't care about my work, and he didn't care about me. That thought beat me. I started to shout at the phone, "Let me wait, will you? Who do you think you are?"At that time I didn't realize my wife was looking on. Without showing her surprise, she rushed in, took away the phone and pulled the lines out of the phone, and shouted at the phone, "Yeah! Who do you think you are? Bad telephone! Bad telephone!" And she swept it into the wastebasket.I stood watching her, speechless. What on earth...?She stepped to the doorway and shouted at the rest of the house, "Now hear this! All objects in this room - if you do anything to upset my husband, out you go!"Then she turned to me, kissed me, and said quietly, "Dear, you just have to learn how to take control." With that, she left the room.After watching a crazy woman rushing in and out, shouting at everything in sight, I noticed that something in my feelings had changed. I was laughing. How could I have trouble with that phone?Her unusual actions helped me realize I had been driven crazy by small things. Twenty minutes later my agent did call. I was able to listen to him and talk to him quietly.1．（小题1）Why did the writer shout at the telephone?A．He was mad at the telephone.B．He was worried about his wife.C．He was angry with his agent.D．He was impatient with the secretary.2．（小题2）What did the writer's wife do after she heard his shouting?A．She said nothing. B．She threw the phone away.C．She shouted at him. D．She called the agent.3．（小题3）What made the writer laugh?A．His wife's sweet kiss.B．His own behavior.C．His changeable feelings.D．His wife's suggestion.C15、People drink alcohol(酒) in many parts of the world. Some medical scientists say light drinking may even be good for your health, especially for the heart. But they say such health benefits(好处) should be compared to the many health risks connected with alcohol use.Some research suggests that having one to two drinks of alcohol a day may be good for your health. Several large studies have shown that this type of drinking may lower the risk of heart disease and other diseases.A study last year suggested that drinking a little red wine may help lower the risk of breast cancer(乳腺癌) in women. Researchers at Medical Center in California studied 36 women. Each woman drank a glass of red or white wine every day for almost a month. Researchers collected blood samples(样本) from the women two times a month to test their hormone(激素) levels. The next month these women were told to exchange their wine. The researchers found that the women who drank red wine had lower levels of the female hormone than the white wine drinkers. They said red grapes have chemicals that may help to lower the risk of breast cancer.However, recent studies suggested that even a little alcohol may generally increase the risk of breast cancer in women. They found that women who drink four small glasses of wine a week increase their risk of breast cancer by 15 percent.Many studies have examined the harmful effects of alcohol use on the body. Alicia Ann Kowalchuk serves as medical director, saying “Healthy use for adults --- that's men under age 65 --- is no more than 4 drinks in a day and no more than 14 drinks in a week. And for women of all ages, it's no more than 7 drinks in a week and no more than 2 drinks in a day.” She says too much alcohol use has something to do with liver (肝脏) diseases, and many other cancers.1．How did the researchers carry out their study?A．By following an example. B．By listing facts.C．By collecting information worldwide. D．By comparing tested objects.2．Which of the following shows the structure of the passage?A．B．C ．D ．3．What is the best title of this passage?A．Alcohol drinking may do harm to your healthB．Alcohol drinking can be both good and bad for youC．Drinking alcohol is popular in many parts of the worldD．Drinking alcohol a day may give your health some benefits.D16、BBC News on TV, radio and online often brings you stories from across the world. Today we can hear “Life in China”. Have you got a story about life in China today? If you do, please put your stories here.Wu Peng, Anhui I am a 14-year-old boy from a poor village in Anhui Province. Like many other left-behind children in China, I live with my grandparents now. My parents went to work in Shanghaiseveral years ago. They call me twice a month to ask about my study. I really miss my parentsand I hope I can go to school in Shanghai. I think every child needs parents’ love and care.Cindy, Shenzhen I like traveling and I have traveled a lot around China. During the trip, I often find that anumber of Chinese often break the rules in public. For example, when I traveled in Hong Kongthis year, I saw a kid eating noodles on the underground, which was against the rules. However,the kid’s mother didn’t think she did wrong. Can you believe it? Let’s improve our publicmanners.Mike, Shanghai These days, w e’re asked to “clear our plates” when having our meals and say no to wasting.Some of us used to order more than what we could eat. That was a big waste of food. Now weneed to finish the food we order. We should also stop wasting in some other ways. For example,we should turn off the lights when we leave the classroom.1．How does Wu Peng contact his parents according to the passage?A．By writing letters. B．On the telephone.C．On the Internet. D．By sending text messages.2．Who thought it was not right to eat on the underground?A．Cindy. B．Mike. C．Wu Peng. D．The kid’s mother3．What does Mike want people to do?A．Care about left-behind children B．Obey the rules in public.C．Improve their public manners D．Stop wastingE17、Doctors, psychologists(心理学家), economists(经济学家) and other experts have recently got together to find out what makes us happy and have come to surprising results.One of the main topics is how to measure(衡量)happiness. Although some experts say that there are many ways to measure happiness, li ke recording a person’s feelings, satisfaction in life or being healthy, others say that you can’t really measure happiness, but you can see it.Money is really important in most people’s lives. Once people have enough money to support their living, they p ay more attention to other meaningful things. In many cases, friends and a close family are more important. Some people also need meaningful and creative work to find happiness.Studies find that there is a connection between happiness and health. Most of the time, people who are happier have better health. They work better and they are not as stressed as others. Besides, happier people may be able to live longer and enjoy their happiness. Studies also show that those who laugh a lot and those who are in good moods are also happier.Is there a way of achieving happiness? Some experts say that if people express their thanks, they can become happier. Joining pleasant conversations can also bring more satisfaction and happiness. Not surprisingly, people feel that a good relationship is important in being happy. Happiness is alsocontagious. The results show that if you happen to have a member of your family or a friend near you who is happy, you’ll happy, too.1．What plays a more important role in most people’s d aily life, according to the passage?A．Health. B．Money. C．Satisfaction. D．Friendship.2．Some people will feel happy if they have ____________ work.A．popular and free B．meaningful and creativeC．well-paid and hard. D．relaxing and interesting3．What can make people happier according to the passage?A．Working harder. B．Making more money.C．Having more children. D．Being thankful.4．What does the underlined word “contagious” mean in Chinese?A．纯洁的B．持续的C．传染性的D．可转换的5．What can we learn from the passage?A．Happiness influences our health.B．Money makes us live longer.C．How to find good jobs.D．How to work better.F18、They tell us when to get up or when we’re running late for work and whether we are in danger of missing our favourite TV programme. But while our daily activities depend on clocks that tell us the time science is discovering that our well-being is influenced by a very different kind of timepiece. Circadian rhythms---the human body’s own internal(体内的) clock—have a powerful influence on our health and behaviour. They are programmed from birth and control functions ranging from temperature and blood pressure to sleep patterns.In recent years researchers have also discovered that this built-in mechanism (内在机制) can influence everything from the way we react to medicines to how well we learn music.The latest example, from experts at Harvard University in the US, shows that the human body clock can even influence whether or not we are likely to tell the truth. Researchers found it was easier for people to tell lies in the afternoon because as they were tired, the self control that would normally prevent them from lying started to break down. Tiredness made it easier for them to tell lies ---especially if it meant they got a financial reward at the end.“The body clock has a great effect on us all,” says Professor Jim Horne from the Sleep Research Centre at Loughborough University. “Most people tend to feel good around late morning and then decline in the early afternoon. But the time most of us will feel ou r sharpest is between 6pm and 8pm. That’s because sleepiness tends to build up throughout the day. By early evening our body clock kicks in to wake us up. One reason may be to ensure we get home safely. When our ancestors (祖先) were coming home after hunting all day, their internal clocks kicked in to get themhome in one piece.”So what effects do circadian rhythms have and what’s the best time of day to take advantage of them? 1．The underlined word “They” in the first paragraph refers to_____ .A．our health and behaviour B．scientists and expertsC．our daily routines D．circadian rhythms2．The research referred to in Paragraph 3 found that people would rather ______ .A．tell lies when they are tired B．tell lies if they are rewardedC．get angry as they become tired D．break down because they are tired3．According to the passage, when are people most quick-thinking?A．In the morning. B．Around midday.C．In the late afternoon. D．In the early evening.4．What information will the writer probably give following the last paragraph?A．An explanation of how the human body clock controls the body.B．Examples of how the human body clocks control the body.C．Examples of the most suitable time to do different activities.D．Some practical suggestions to prevent people from lying.Ⅴ.书面表达19、根据要求完成大作文“孝敬长辈” 是中华民族的传统美德，请结合你的情况和提示谈谈：1.在你的长辈（family members）中你最爱的人是谁？2. 他或她是怎么对你的（对学习要求严格但和蔼可亲；鼓励你努力学习将来上大学）？3. 你是如何孝敬长辈的（做些家务；努力学习）？要求：1. 语言正确，行文流畅，书写规范；2. 词数80词左右；3. 文中不能出现真实的姓名、学校或所在地名等。

2022年海南省儋州市洋浦中学数学九上期末质量检测模拟试题含解析

2022-2023学年九上数学期末模拟试卷注意事项1．考生要认真填写考场号和座位序号。

2．试题所有答案必须填涂或书写在答题卡上，在试卷上作答无效。

第一部分必须用2B 铅笔作答；第二部分必须用黑色字迹的签字笔作答。

3．考试结束后，考生须将试卷和答题卡放在桌面上，待监考员收回。

一、选择题（每题4分，共48分）1．若关于x 的方程29(2)40x k x -++=有两个相等的根，则k 的值为（）A ．10B ．10或14C ．-10或14D ．10或-142．已知点(2,)A a -，(2,)B b ，(4,)C c 是抛物线24y x x =-上的三点，则a ，b ，c 的大小关系为（） A ．b c a >> B ．b a c >> C ．c a b >> D ．a c b >>3．如图，AB 是⊙O 的直径，BC 与⊙O 相切于点B ，AC 交⊙O 于点D ，若∠ACB=50°，则∠BOD 等于（）A ．40°B ．50°C ．60°D ．80°4．若关于x 的方程220x x a --=，它的一根为3，则另一根为（）A ．3B ．3-C ．1-D ．c5．下列两个变量成反比例函数关系的是（）①三角形底边为定值，它的面积S 和这条边上的高线h ；②三角形的面积为定值，它的底边a 与这条边上的高线h ；③面积为定值的矩形的长与宽；④圆的周长与它的半径．A ．①④B ．①③C ．②③D ．②④6．如图，在△ABC 中，M ，N 分别为AC ，BC 的中点．则△CMN 与△CAB 的面积之比是( )A ．1:2B ．1:3C ．1:4D ．1:9 7．反比例函数2k y x -=的图象，当x ＞0时，y 随x 的增大而减小，则k 的取值范围是（） A ．2k < B ．k 2≤ C ．2k > D ．2k ≥8．反比例函数y ＝(k≠0)的图象经过点(2，-4)，若点(4，n)在反比例函数的图象上，则n 等于( )A ．﹣8B ．﹣4C ．﹣D ．﹣29．如图，抛物线y=ax 2+bx+c （a≠0）的对称轴是直线x=1，与x 轴交于A 、B （-1,0），与y 轴交于C ．下列结论错误的是（）A ．二次函数的最大值为a+b+cB ．4a-2b+c ﹤0C ．当y ＞0时，-1﹤x ﹤3D ．方程ax 2+bx+c=-2解的情况可能是无实数解，或一个解，或二个解.10．对于不为零的两个实数a ，b ，如果规定a ★b ()()211,42.a b a b b a b a⎧+>⎪⎪=⎨⎪-≤⎪⎩，那么函数2y x =★的图象大致是（） A ． B ． C ． D ．11．一次函数y=kx+k （k≠0）和反比例函数()0k y k x=≠在同一直角坐标系中的图象大致是（） A ． B ． C ． D ．12．一个口袋中有红球、白球共10个，这些球除颜色外都相同，将口袋中的球搅拌均匀，从中随机模出一个球，记下它的颜色后再放回口袋中，不断重复这一过程，共摸了100次球，发现有80次摸到红球，则口袋中红球的个数大约有（）A ．8个B ．7个C ．3个D ．2个二、填空题（每题4分，共24分）13．在一个布袋中装有四个完全相同的小球，它们分别写有“美”、“丽”、“罗”、“山”的文字．先从袋中摸出1个球后放回，混合均匀后再摸出1个球，求两次摸出的球上是含有“美”“丽”二字的概率为_____．14．如图所示，1n +个边长为1的等边三角形，其中点A ，1C ，2C ，3C ，…n C 在同一条直线上，若记111B C D ∆的面积为1S ，222B C D ∆的面积为2S ，333B C D ∆的面积为3S ，…，n n n B C D ∆的面积为n S ，则n S =______.15．已知抛物线y ＝2x 2﹣5x +3与y 轴的交点坐标是_____．16．二次函数y ＝ax 2＋bx ＋c （a ≠0）的图像如图所示，当y ＜3时，x 的取值范围是____．17．如图，直线y =x +2与反比例函数y =k x的图象在第一象限交于点P ．若OP =10，则k 的值为________．18．如图,ABC ∆是正三角形，D 、E 分别是BC 、AC 上的点，当ADE ∠=_______时，ABD ∆~DCE ∆.三、解答题（共78分）19．（8分）（1）解方程2980x x +-=．（2）计算：21028sin 452(3.14)π--+-+-．20．（8分）已知正比例函数y ＝x 的图象与反比例函数y ＝k x （k 为常数，且k ≠0）的图象有一个交点的纵坐标是1．（Ⅰ）当x ＝4时，求反比例函数y ＝k x的值；（Ⅱ）当﹣1＜x ＜﹣1时，求反比例函数y ＝k x的取值范围． 21．（8分）某果园有果树80棵，现准备多种一些果树提高果园产量，但是如果多种树，那么树之间的距离和每棵树所受光照就会减少，单棵树的产量随之降低，若该果园每棵果树产果y （千克），增种果树x （棵），它们之间的函数关系如图所示．（1）求y 与x 之间的函数关系式；（2）在投入成本最低的情况下，增种果树多少棵时，果园可以收获果实6750千克？22．（10分）如图1，AB 、CD 是圆O 的两条弦，交点为P.连接AD 、BC ．OM ⊥ AD ，ON ⊥BC ，垂足分别为M 、N.连接PM 、PN.图1 图2（1）求证：△ADP ∽△CBP ；（2）当AB ⊥CD 时，探究∠PMO 与∠PNO 的数量关系，并说明理由；（3）当AB ⊥CD 时，如图2，AD=8,BC=6, ∠MON=120°，求四边形PMON 的面积.23．（10分）已知函数y ＝mx 1﹣（1m +1）x +1（m ≠0），请判断下列结论是否正确，并说明理由．（1）当m ＜0时，函数y ＝mx 1﹣（1m +1）x +1在x ＞1时，y 随x 的增大而减小；（1）当m ＞0时，函数y ＝mx 1﹣（1m +1）x +1图象截x 轴上的线段长度小于1．24．（10分）我县寿源壹号楼盘准备以每平方米5000元均价对外销售，由于国务院有关房地产的新政策出台，购房者持币观望，房地产开发商为了加快资金周转，对价格进行两次下调后，决定以每平方米4050元的均价开盘销售．（1）求平均每次下调的百分率．（2）某人准备以开盘均价购买一套120平方米的住房，开发商给予以下两种优惠方案供选择：①打9.8折销售；②不打折，一次性送装修费每平方米70元．试问哪种方案更优惠？25．（12分）如图，四边形ABCD 中，AB AC AD ==，AC 平分BAD ∠，点P 是AC 延长线上一点，且PD AD ⊥.（1）证明：BDC PDC ∠=∠；（2）若AC 与BD 相交于点E ，1,:2:3AB CE CP ==，求AE 的长.26．甲、乙两个不透明的袋子中，分别装有大小材质完全相同的小球，其中甲口袋中小球编号为1、2、3、4，乙口袋中小球编号分别是2、3、4，先从甲口袋中任意摸出一个小球，记下编号为m ，再从乙袋中摸出一个小球，记下编号为n ．（1）请用画树状图或列表的方法表示(),m n 所有可能情况；（2）规定：若m 、n 都是方程2560x x -+=的解时，小明获胜；若m 、n 都不是方程2560x x -+=的解时，小刚获胜，请说明此游戏规则是否公平？参考答案一、选择题（每题4分，共48分）1、D【分析】根据题意利用根的判别式，进行分析计算即可得出答案.【详解】解：∵关于x 的方程29(2)40x k x -++=有两个相等的根， ∴[]2224(2)49441400b ac k k k ∆=-=-+-⨯⨯=+-=，即有(10)(14)0k k -+=，解得k = 10或-14.故选：D.【点睛】本题考查的是根的判别式，熟知一元二次方程20(a 0)++=≠ax bx c 中，当0∆=时，方程有两个相等的两个实数根是解答此题的关键．2、D【分析】将A ，B ，C 三点坐标分别代入抛物线24y x x =-，然后化简计算即可.【详解】解：∵点(2,)A a -，(2,)B b ，(4,)C c 是抛物线24y x x =-上的三点，∴()()224212a =--⨯-=， 22424b =-⨯=-，24440c =-⨯=.∴a c b >>故选：D ．【点睛】本题考查二次函数图象上点的坐标，将点坐标分别代入关系式，正确运算，求出a ，b ，c 是解题的关键．3、D【分析】根据切线的性质得到∠ABC=90°，根据直角三角形的性质求出∠A ，根据圆周角定理计算即可．【详解】∵BC 是⊙O 的切线，∴∠ABC=90°， ∴∠A=90°-∠ACB=40°，由圆周角定理得，∠BOD=2∠A=80°，故选D ．【点睛】本题考查的是切线的性质、圆周角定理，掌握圆的切线垂直于经过切点的半径是解题的关键．4、C【分析】设方程的另一根为t ，根据根与系数的关系得到3+t=2，然后解关于t 的一次方程即可．【详解】设方程的另一根为t ，根据题意得：3+t=2，解得：t=-1，即方程的另一根为-1．故选：C ．【点睛】本题主要考查了一元二次方程根与系数的关系：12x x 、是一元二次方程20x px q ++=的两根时，12x x p +=-，12x x q =．5、C【分析】根据反比例函数的定义即可判断．【详解】①三角形底边为定值，它的面积S 和这条边上的高线h 是成正比例关系，故不符合题意；②三角形的面积为定值，它的底边a 与这条边上的高线h 是反比例函数关系；故符合题意；③面积为定值的矩形的长与宽；是反比例函数关系；故符合题意；④圆的周长与它的半径，是成正比例关系，故不符合题意．故选：C ．【点睛】本题考查了反比例函数的解析式，解答本题的关键是根据题意列出函数关系式来进行判断，本题属于基础题型． 6、C【解析】由M 、N 分别为AC 、BC 的中点可得出MN ∥AB ，AB ＝2MN ，进而可得出△ABC ∽△MNC ，根据相似三角形的性质即可得到结论．【详解】∵M 、N 分别为AC 、BC 的中点，∴MN ∥AB ，且AB ＝2MN ，∴△ABC ∽△MNC ，∴MNC ABC S S =（MN AB ）2＝14．故选C ．【点睛】本题考查了相似三角形的判定与性质以及三角形中位线定理，根据三角形中位线定理结合相似三角形的判定定理找出△ABC ∽△MNC 是解题的关键．7、C【分析】根据反比例函数的性质直接判断即可得出答案．【详解】∵反比例函数y =2k x -中，当x ＞0时，y 随x 的增大而减小， ∴k -1＞0，解得k ＞1．故选C ．【点睛】本题考查的是反比例函数的性质，熟知反比例函数y =k x（k ≠0）中，当k ＞0时，双曲线的两支分别位于第一、第三象限，在每一象限内y 随x 的增大而减小是解答此题的关键．8、D【解析】利用反比例函数图象上点的坐标特征得到4n=1×(-4)，然后解关于n 的方程即可．【详解】∵点（1，-4）和点（4，n ）在反比例函数y=的图象上，∴4n=1×(-4)， ∴n=-1．故选D ．【点睛】本题考查了反比例函数图象上点的坐标特征：反比例函数y=（k 为常数，k≠0）的图象是双曲线，图象上的点（x ，y ）的横纵坐标的积是定值k ，即xy=k ．9、D【分析】A. 根据对称轴为1x =时，求得顶点对应的y 的值即可判断；B. 根据当2x =-时，函数值小于0即可判断；C. 根据抛物线与x 轴的交点坐标即可判断．D. 根据抛物线与直线2y =-的交点情况即可判断.【详解】A.∵当1x =时，y a b c =++，根据图象可知，0a b c ++=，正确．不符合题意；B.∵当2x =-时，42y a b c =-+，根据图象可知，420a b c -+<，正确．不符合题意；C.∵抛物线是轴对称图形，对称轴是直线1x =，点()10B -，，所以与x 轴的另一个交点A 的坐标为()30，，根据图象可知：当0y >时，13x ，正确．不符合题意；D. 根据图象可知：抛物线与直线2y =-有两个交点，∴关于x 的方程22ax bx c ++=-有两个不相等的实数根，本选项错误，符合题意．故选：D ．【点睛】本题考查了二次函数与系数的关系、根的判别式、抛物线与x 轴的交点，掌握二次函数的性质、二次函数图象与系数的关系是解题的关键．10、C【分析】先根据所给新定义运算求出分段函数解析式，再根据函数解析式来判断函数图象即可.【详解】解：∵a ★b ()()211,42.a b a b b a b a⎧+>⎪⎪=⎨⎪-≤⎪⎩， ∴2y x =★()()2112,422.x x x x⎧+>⎪⎪=⎨⎪-≤⎪⎩ ∴当x>2时，函数图象在第一象限且自变量的值不等于2，当x ≤2时，是反比例函数，函数图象在二、四象限. 故应选C.【点睛】本题考查了分段函数及其图象，理解所给定义求出分段函数解析式是解题的关键.11、C【解析】A、由反比例函数的图象在一、三象限可知k＞0，由一次函数的图象过二、四象限可知k＜0，两结论相矛盾，故选项错误； B、由反比例函数的图象在二、四象限可知k＜0，由一次函数的图象与y轴交点在y轴的正半轴可知k ＞0，两结论相矛盾，故选项错误；C、由反比例函数的图象在二、四象限可知k＜0，由一次函数的图象过二、三、四象限可知k＜0，两结论一致，故选项正确；D、由反比例函数的图象在一、三象限可知k＞0，由一次函数的图象与y 轴交点在y轴的负半轴可知k＜0，两结论相矛盾，故选项错误，故选C．12、A【分析】根据利用频率估计概率可估计摸到红球的概率，即可求出红球的个数．【详解】解：∵共摸了100次球，发现有80次摸到红球，∴摸到红球的概率估计为0.80，∴口袋中红球的个数大约10×0.80=8（个），故选：A．【点睛】本题考查了利用频率估计概率的知识，属于常考题型，掌握计算的方法是关键．二、填空题（每题4分，共24分）13、1 8【分析】画树状图展示所有16种等可能的结果数，再找出两次摸出的球上是写有“美丽”二字的结果数，然后根据概率公式求解．【详解】（1）用1、2、3、4别表示美、丽、罗、山，画树形图如下：由树形图可知，所有等可能的情况有16种，其中“1，2”出现的情况有2种，∴P（美丽）21 168 ==．故答案为：18．【点睛】本题考查了用列表法或树状图法求概率．列表法可以不重复不遗漏的列出所有可能的结果，适合于两步完成的事件；树状图法适合两步或两步以上完成的事件；解题时要注意是放回实验还是不放回实验．用到的知识点为：概率=所求情况数与总情况数之比．14、344n n + 【分析】由n+1个边长为1的等边三角形有一条边在同一直线上，则B,B 1，B 2，B 3，…B n 在一条直线上，可作出直线BB 1．易求得△ABC 1的面积，然后由相似三角形的性质，易求得S 1的值，同理求得S 2的值，继而求得S n 的值．【详解】如图连接BB 1，B 1B 2，B 2B 3；由n+1个边长为1的等边三角形有一条边在同一直线上，则B,B 1, B 2，B 3，…B n 在一条直线上．∴S △ABC1=12×1×32=34 ∵B B 1∥AC 1，∴△ BD 1B 1∽ △ AC 1D 1，△BB 1C 1为等边三角形则C 1D 1=BD 1=12；，△C 1B 1D 1中C 1D 1边上的高也为32； ∴S 1=12×12×32=38；同理可得21221221==D 2C AC BD B B ；则22C D =23, ∴S 2=12×23×32=36；同理可得：n-1n n-1n n n n 1==D nC AC BD B B ； ∴n n C D =n 1n +， S n =12×n 1n +×32=344n n +．【点睛】此题考查了相似三角形的判定与性质以及等边三角形的性质．此题难度较大，属于规律性题目，注意辅助线的作法，注意数形结合思想的应用．15、（0,3）【分析】要求抛物线与y 轴的交点，即令x=0，解方程即可．【详解】解：令x=0，则y=3，即抛物线y=2x 2-5x+3与y 轴的交点坐标是（0，3）．故答案为（0，3）．【点睛】本题考查了抛物线与y 轴的交点．求二次函数y=ax 2+bx+c （a ，b ，c 是常数，a≠0）与y 轴的交点坐标，令x=0，即可求得交点纵坐标．16、－1＜x ＜3【分析】根据图象，写出函数图象在y=3下方部分的x 的取值范围即可．【详解】解：如图，根据二次函数的对称性可知，－1＜x ＜3时，y ＜3，故答案为：－1＜x ＜3.【点睛】本题考查了二次函数与不等式和二次函数的对称性，此类题目，利用数形结合的思想求解更简便．17、3【分析】已知直线y=x+2与反比例函数y=k x的图象在第一象限交于点P ，设点P 的坐标为(m,m+2)，根据，列出关于m 的等式，即可求出m ，得出点P 坐标，且点P 在反比例函数图象上，所以点P 满足反比例函数解析式，即可求出k 值．【详解】∵直线y=x+2与反比例函数y=k x 的图象在第一象限交于点P ∴设点P 的坐标为(m,m+2)∵=解得m 1=1，m 2=-3∵点P 在第一象限∴m=1∴点P 的坐标为(1,3)∵点P 在反比例函数y=k x 图象上 ∴31k = 解得k=3故答案为：3【点睛】本题考查了一次函数与反比例函数交点问题，交点坐标同时满足一次函数和反比例函数解析式，根据直角坐标系中点坐标的性质，可利用勾股定理求解．18、60°【分析】由△ABC 是正三角形可得∠B=60°，又由△ABD ∽△DCE ，根据相似三角形的对应角相等，即可得∠EDC=∠BAD ，然后利用三角形外角的性质，即可求得∠ADE 的度数【详解】∵△ABC 是正三角形，∴∠B=60°，∵△ABD ∽△DCE ，∴∠EDC=∠BAD ，∵∠ADC 是△ABD 的外角，∴∠ADE+∠EDC=∠B+∠BAD ，∴∠ADE=∠B=60°，【点睛】此题考查了相似三角形的判定与性质、等边三角形的性质以及三角形外角的性质．此题难度适中．三、解答题（共78分）19、（1）192x -+=，292x -=；（2）112-．【分析】（1）根据题意直接运用公式法解一元二次方程即可；（2）根据题意运用幂的运算以及特殊锐角三角函数进行计算即可.【详解】解：（1）由题意可知1,9,8a b c ===-，1922b x a -+-+==，2922b x a --==.（2）()02122 3.14π---+-14122=-+-+ 112=-．【点睛】本题考查解一元二次方程以及实数的运算，熟练掌握实数运算法则以及解一元二次方程的解法是解本题的关键．20、（Ⅰ）1；（Ⅱ）﹣4＜y ＜﹣1．【解析】（Ⅰ）首先把y ＝1代入直线的解析式，求得交点坐标，然后利用待定系数法求得反比例函数的解析式，最后把x ＝4代入求解；（Ⅱ）首先求得当x ＝﹣1和x ＝﹣1时y 的值，然后根据反比例函数的性质求解．【详解】解：（Ⅰ）在y ＝x 中，当y ＝1时，x ＝1，则交点坐标是（1，1），把（1，1）代入y ＝k x，得：k ＝4，所以反比例函数的解析式为y ＝4x，当x ＝4，y ＝4k ＝1；（Ⅱ）当x ＝﹣1时，y ＝2k -＝﹣1；当x ＝﹣1时，y ＝1k -＝﹣4，则当﹣1＜x ＜﹣1时，反比例函数y ＝k x 的范围是：﹣4＜y ＜﹣1．【点睛】此题考查了反比例函数与一次函数的交点问题，以及反比例函数的增减性，两函数的交点即为同时满足两函数解析式的点，其中用待定系数法确定函数的解析式，是常用的一种解题方法．同学们要熟练掌握这种方法．21、（1）1802y x =-+；（2）增种果树10棵时，果园可以收获果实6750千克. 【分析】（1）设(0)y kx b k =+≠，将点（12，74）、（28，66）代入即可求出k 与b 的值，得到函数关系式；（2）根据题意列方程，求出x 的值并检验即可得到答案.【详解】（1）设(0)y kx b k =+≠，将点（12，74）、（28，66）代入，得12742866k b k b +=⎧⎨+=⎩，解得1280k b ⎧=-⎪⎨⎪=⎩， ∴y 与x 的函数关系式为1802y x =-+；（2）由题意得： 1(80)(80)67502x -++=，解得： 110x =， 270x =，∵投入成本最低，∴x=10，答：增种果树10棵时，果园可以收获果实6750千克.【点睛】此题考查待定系数法求一次函数解析式，一元二次方程的实际应用，正确理解题意中的x、y的实际意义是解题的关键.22、（1）证明见解析；（2）∠PMO=∠PNO，理由见解析；（3）S平行四边形PMON=63【分析】（1）利用同弧所对的圆周角相等即可证明相似,（2）由OM⊥ AD，ON⊥BC得到M、N为AB、CD的中点，再由直角三角形斜边中线等于斜边一半即可解题,（3）由三角形中位线性质得∠QBC=90°,进而证明∠QCB=∠PBD,得到四边形MONP为平行四边形即可解题.【详解】（1）因为同弧所对的圆周角相等，所以∠A=∠C, ∠D=∠B,所以△ADP∽△CBP.（2）∠PMO=∠PNO因为OM⊥ AD，ON⊥BC，所以点M、N为AB、CD的中点，又AB⊥CD，所以PM=12AD,PN=12BC，所以，∠A=∠APM，∠C=∠CPN，所以∠AMP=∠CNP,得到∠PMO与∠PNO. （3）连接CO并延长交圆O于点Q，连接BD.因为AB⊥CD，AM=12AD,CN=12BC，所以PM=12AD,PN=12BC.由三角形中位线性质得，ON=1BQ 2.因为CQ为圆O直径，所以∠QBC=90°，则∠Q+∠QCB=90°，由∠DPB=90°，得∠PDB+∠PBD=90°，而∠PDB=∠Q，所以∠QCB=∠PBD,所以BQ=AD，所以PM=ON.同理可得，PN=OM.所以四边形MONP为平行四边形.S平行四边形【点睛】本题考查了相似三角形的判定和性质,圆的基本知识,圆周角的性质,直角三角形的性质,平行四边形的判定,综合性强,熟悉圆周角的性质是求解（1）的关键,利用斜边中线等于斜边一半这一性质是求解（2）的关键,证明四边形MONP为平行四边形是求解（3）的关键.23、（1）详见解析；（1）详见解析．【分析】（1）先确定抛物线的对称轴为直线x＝1+12m，利用二次函数的性质得当m＞1+12m时，y随x的增大而减小，从而可对（1）的结论进行判断；（1）设抛物线与x轴的两交的横坐标为x1、x1，则根据根与系数的关系得到x1+x1＝21mm+，x1x1＝2m，利用完全平方公式得到|x1﹣x1|＝|1﹣1m|，然后m取15时可对（1）的结论进行判断．【详解】解：（1）的结论正确．理由如下：抛物线的对称轴为直线(21)1122-+=-=+mxm m，∵m＜0，∴当m＞1+12m时，y随x的增大而减小，而1＞1+12m，∴当m＜0时，函数y＝mx1﹣（1m+1）x+1在x＞1时，y随x的增大而减小；（1）的结论错误．理由如下：设抛物线与x轴的两交的横坐标为x1、x1，则x1+x1＝21mm+，x1x1＝2m，|x1﹣x1|＝|1﹣1m|，而m＞0，若m 取15时，|x 1﹣x 1|＝3， ∴当m ＞0时，函数y ＝mx 1﹣(1m +1)x +1图象截x 轴上的线段长度小于1不正确．【点睛】本题考查了二次函数的增减性问题，与x 轴的交点问题，熟练掌握二次函数的性质是解题的关键．24、（1）10%；（2）选择方案①更优惠．【分析】（1）此题可以通过设出平均每次下调的百分率为x ，根据等量关系“起初每平米的均价(1⨯-下调百分率）(1⨯-下调百分率）=两次下调后的均价”，列出一元二次方程求出．（2）对于方案的确定，可以通过比较两种方案得出的费用：①方案：下调后的均价1000.98⨯⨯+两年物业管理费②方案：下调后的均价100⨯，比较确定出更优惠的方案．【详解】解：（1）设平均每次降价的百分率是x ，依题意得25000(1)4050x -=，解得：110%x =，21910x =（不合题意，舍去）．答：平均每次降价的百分率为10%．（2）方案①购房优惠：4050×120×(1-0.98)=9720(元) 方案②购房优惠：70×120=8400(元) 9720(元)＞8400(元)答：选择方案①更优惠．【点睛】本题结合实际问题考查了一元二次方程的应用，根据题意找准等量关系从而列出函数关系式是解题的关键．25、（1）详见解析；（2）23AE = 【分析】（1）直接利用等腰三角形的性质结合互余的定义得出∠BDC=∠PDC ；（2）首先过点C 作CM ⊥PD 于点M ，进而得出△CPM ∽△APD ，求出EC 的长即可得出答案．【详解】解：（1）：∵AB AD =，AC 平分BAD ∠，∴AC BD ⊥，∴90ACD BDC ∠+∠=︒，∵AC AD =，∴ACD ADC ∠=∠，∴90ADC BDC ∠+∠=︒，∴BDC PDC ∠=∠；（2）过点C 作CM PD ⊥于点M ，∵BDC PDC ∠=∠，∴CE CM =，∵90,CMP ADP P P ∠=∠=︒∠=∠，∴CPM APD ∆∆∽， ∴CM PC AD PA =，设CM CE x ==， ∵:2:3CE CP =，∴32PC x =， ∵1AB AD AC ===，∴323112x x x =+，解得：13x =， ∴12133AE =-=. 【点睛】此题主要考查了相似三角形的判定与性质以及等腰三角形的性质等知识，正确得出△CPM ∽△APD 是解题关键．26、（1）见解析；（2）两人获胜机会不均等，此游戏规则不公平【分析】（1）根据画树形图即可表示出所有可能出现的结果；（2）先解方程，再分别求出两个人赢的概率，再进行判断即可．【详解】（1）列出树状图：（2）解方程2560x x -+=可得12x =，23x =．∴P（m、n都是方程的根）41 123 ==．P（m、n都不是方程的根）21 126 ==．∴两人获胜机会不均等，此游戏规则不公平．【点睛】本题考查的是游戏公平性的判断，判断游戏公平性就要计算每个事件的概率，概率相等就公平，否则就不公平．。