浙江省杭州市翠苑中学2013-2014学年上学期10月质量检测九年级数学试卷浙教版
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一.选择题1. 【浙江省温州市苍南县龙港镇第二中学第一学期初中九年级期中试题】已知⊙1O 的半径为3cm ,⊙2O 的半径8cm .且1O 2O =5cm ,则两圆的位置关系正确的是( )A .外切B .内切C .相交D .外离2.【海宁市初中第三教研片2013-2014学年第一学期期中调研测试九年级数学试题】已知⊙O 的半径r =3,PO =10,则点P 与⊙O 的位置关系是( )A 、点P 在⊙O 内;B 、点P 在⊙O 上;C 、点P 在⊙O 外;D 、不能确定3.【海宁市初中第三教研片2013-2014学年第一学期期中调研测试九年级数学试题】如图O 是圆心,半径OC ⊥弦AB 于点D ,AB =8,OB=5,则OD 等于 ( )A 、2B 、3C 、4D 、54.【海宁市初中第三教研片2013-2014学年第一学期期中调研测试九年级数学试题】下列三个命题:①圆既是轴对称图形,又是中心对称图形;②垂直于弦的直径平分这条弦;③相等圆心角所对的弧相等.其中是真命题的是()A、②③B、①②C、①③D、①②③5.【湛师附中、东方实验学校2013-2014学年度上学期第一次月考九年级数学试题】如图4,⊙O的半径为5cm,弦AB的长为8cm,则圆心O到AB的距离为 cm.6.【湛师附中、东方实验学校2013-2014学年度上学期第一次月考九年级数学试题】如图,点C在以AB为直径的半圆上,∠BAC=20°,则∠BOC等于()A.20° B.30° C.40° D.50°7.【湛师附中、东方实验学校2013-2014学年度上学期第一次月考九年级数学试题】已知两圆的半径分别为5和3,圆心距为7,则两圆的位置关系是()A.内含 B.内切 C.相交 D.外切8.【杭州市翠苑中学2013-2014学年上学期10月质量检测九年级数学试卷】已知圆锥的母线为10,底面圆的直径为12,则此圆锥的侧面积是()A.24π B.30π C.48π D.60π9、【杭州市翠苑中学2013-2014学年上学期10月质量检测九年级数学试卷】如图,△ABC 内接于⊙O,∠C=30°,AB=2,则⊙O的半径为()A B. C.2 D.4考点:圆周角定理.10、【题文】下列三个命题:①圆既是轴对称图形,又是中心对称图形;②垂直于弦的直径平分这条弦;③平分弦的直径垂直于这条弦;④相等的圆心角所对的弧相等。
13-14学年度第一学期九年级数学期中水平测试卷一、选择题: 1.若点P(2,)是反比例函数图象上一点,则的值是( )A . 1B .2C .3D .42.抛物线3)2(2++=x y 的顶点坐标是( ) A .(2,-3) B . (2,3) C .(-2,3) D .(-2,-3)3.把抛物线2y x =-向左平移1个单位,然后向上平移3个单位,则平移后抛物线的解析式为( ) A. 2(1)3y x =--- B. 2(1)3y x =-+- C. 2(1)3y x =--+ D.2(1)3y x =-++ 4.如图,圆锥的底面半径为3cm ,母线长为5cm ,则它的侧面积为( ) A. 60πcm 2B. 45πcm 2C. 30πcm 2D15πcm25.已知111222333()()()P x y P x y P x y ,,,,,是反比例函数 的图象上的三点,且1230x x x <<<,则123y y y ,,的大小关系是( )A.321y y y <<B.123y y y << C.213y y y << D.231y y y <<6. 小明从图所示的二次函数2y ax bx c =++的图象中,观察得出了下面五条信息:①0c <;②0abc >;③0a b c -+>;④230a b -=;你认为其中正确信息的个数有( ) A .1个B .2个C .3个D .4个7.若一个三角形的外心在这个三角形的边上,那么这个三角形是( ) A .锐角三角形 B .直角三角形C .钝角三角形D .不能确定8.已知函数2y ax bx c =++的图象如图所示,那么函数y ’=23ax bx c +++ 的图像与x 轴的交点个数有( ) A .0个B .1个C .3个D .无法确定 9.如图,圆周角∠A =300,弦BC =3,则⊙O 的直径是 ()第6题4y x=yxO4第12题A .3B .33 C .6 D .3610.已知:如图,动点P 在函数的图像上运动,PM ⊥轴于点M ,PN ⊥轴于点N ,线段PM 、PN 分别与直线AB :交于点E 、F ,则AF ・BE 的值是( ) A .4 B .2C .1D .二、填空题:11.已知⊙O 的半径为5厘米,当OP =6厘米时,点p 在⊙O (填“内”或“外”或“上”) 12.已知二次函数y= -x 2+2x+m 的部分图象如图所示,则关于x 的一元二次方程-x 2+2x+m=0的解为________.13.圆的弦与直径相交成30度角,并且分直径为8㎝和2㎝两部分,则弦心距是 cm 。
浙江省杭州地区2013-2014学年第一学期期中练习九年级数学试卷一. 仔细选一选:1.如图,点、、为⊙上的三点,°,则的度数为()A.110°B.140°C.145°D.220°2. 以下命题:(1)同圆中等弧对等弦;(2)圆心角相等,它们所对的弧长也相等;(3)三点确定一个圆;(4)平分弦的直径必垂直于这条弦;(5)三角形的外心到三角形各顶点的距离都相等;(6)相等的圆周角所对的弧相等.其中正确的命题的个数是………()A. 2个B. 3个C. 4个D. 5个3.当时,下列函数:①;②;③;④,函数值随自变量增大而增大的有()。
A. 1个B. 2 个C. 3个D. 4个4.如图,P(x,y)是以坐标原点为圆心,5为半径的圆周上的点,若x、y都是整数,则这样的点共有()。
A. 4个B. 8个C. 12个D. 16个5.如图,直线是二次函数的图象的对称轴,则有()。
A. B. C. D.第4题第5题第6题6.如图,是⊙的直径,弦于点,是弧AC上任意一点,延长,与的延长线相交于点,连结,,,则图中与相等的角有()。
A. 5个B. 4个C. 3个D. 2个7.如图,⊙O的半径OB和弦AC相交于点D,∠AOB=90°,则下列结论错误..的是()A.∠C=45°B.∠OAB=45°C.OB∶AB=1∶D.∠ABC=4∠CAB8.已知是抛物线上的点,则()A.B.C.D.9.在同一直角坐标系中,函数y =mx +m 和函数y =-mx 2+2x +2(m 是常数,且m ≠0)的图象可能..是( ).10.若反比例函数y 1=的图象和一次函数 y 2 = ax + b 的图象如图所示,则当y 1﹤y 2时,相应的x 的取值范围是( )A .-5﹤x ﹤-1B .x ﹤-5或x ﹥-1C .-5﹤x ﹤-1或x ﹥0D .x ﹤-5或-1﹤x ﹤011.如图,边长为1的菱形ABCD 绕点A 旋转,当B 、C 两点恰好落在扇形AEF 的EF ︵上时,BC ︵的长度等于 ( )A .B .C .D .12.如图所示,P 是菱形ABCD 的对角线AC 上一动点,过P 垂直于AC的直线交菱形ABCD 的边于M 、N 两点,设AC=2,BD=1,AP=,△AMN 的面积为,则关于的函数图象的大致形状是( )A.B. C.A B C D二. 认真填一填:13.将抛物线先左平移动2个单位,再向下平移7个单位后得到一个新的抛物线,那么新的抛物线的解析式是 . 14.若抛物线与坐标轴有且只有两个交点,则的值是 . 15、 对于反比例函数,当时,x 的取值范围为 ;当时, y 的取值范围为 。
一.选择题1【江苏省泰兴市济川中学初三数学阶段试题】下列图形中,既是轴对称图形又是中心对称图形的有()A.4个B. 3个C. 2个D. 1个2【湛师附中、东方实验学校2013-2014学年度上学期第一次月考九年级数学试题】下列图形中,是中心对称图形的是()3.【湛师附中、东方实验学校2013-2014学年度上学期第一次月考九年级数学试题】下列图形中,对称轴最多的是()A .等边三角形B .矩形C .正方形D .圆4.【湛师附中、东方实验学校2013-2014学年度上学期第一次月考九年级数学试题】点M (3,2-)关于原点对称的对称点的坐标是( )A.(3-,2)B.(3,2)C.(3-,2-)D.(2,3)5 【温州市七校2013-2014学年上学期12月联考九年级数学试题】按如下方法,将△ABC 的三边缩小到原来的21,如图,任取一点O ,连接AO 、BO 、CO ,并取它们的中点D 、E 、F ,得到△DEF,则下列说法错误的是( )A.△ABC 与△DEF 是位似图形B.△ABC 与△DEF 是相似图形C.△ABC 与△DEF 的面积之比为4:1D.△ABC 与△DEF 的周长之比为1:2考点:位似图形的性质.6.【湛师附中、东方实验学校2013-2014学年度上学期第一次月考九年级数学试题】某几何体的三视图如图2所示,那么该几何体是()A.棱柱 B.圆锥 C.圆柱 D.长方体7 【云南省临沧区云县后箐中学2014届九年级10月综合练习数学试题】如图,A、B、C三点在正方形网格线的交点处.若将△ACB绕着点A逆时针旋转得到△AC′B′,则tan B′的值为( )A.14B.13C.12D.1【答案】B.【解析】试题分析:如图,过C点作CD⊥AB,垂足为D,根据旋转性质可知,∠B′=∠B.8.【云南省临沧区云县后箐中学2014届九年级10月综合练习数学试题】直角三角形纸片的两直角边长分别为6,8,现将△ABC 如图那样折叠,使点A 与点B 重合,折痕为DE ,则tan∠CBE 的值是( )A .247 B C .724 D .139.【北京市海淀区九年级第一学期期中测评数学试题】如图所示的图案绕旋转中心旋转一定角度后能够与自身重合,那么这个旋转角可能是( ) A .60 B .72 C .90D .12010.【浙江省桐乡市实验中学2013-2014学年上学期基础调研九年级数学试卷】对下图的对称性表述,正确的是().(A)轴对称图形(B)中心对称图形(C)既是轴对称图形又是中心对称图形(D)既不是轴对称图形又不是中心对称图形11.【诸暨市陶朱中学2013-2014学年第一学期10月月考九年级数学试卷】如图,矩形纸片ABCD 中,BC=4,AB=3,点P是BC边上的动点(点P不与点B、C重合).现将△PCD沿PD翻折,得到△PC’D;作∠BPC’的角平分线,交AB于点E.设BP= x,BE= y,则下列图象中,能表示y与x的函数关系的图象大致是( )12.【北京市海淀区九年级第一学期期中测评数学试题】在角、等边三角形、平行四边形、圆中,既是中心对称图形又是轴对称图形的是( )A.角 B.等边三角形 C.平行四边形 D.圆13、【江苏省无锡市惠山六校联考2014届九年级上学期期中考试数学试题】如图所示,把一个长方形纸片沿EF折叠后,点D,C分别落在D′,C′的位置.若∠EFB=65°,则∠AED′等于()A. 70°B.65°C.50°D.25°14.【广东省温州地区2013-2014学年八年级上学期第三次月考数学试卷】右图中几何体的左视图是()A B C D二.填空题15.【温州市七校2013-2014学年上学期12月联考九年级数学试题ABCD 绕点A 逆时针方向旋转30o 后得到正方形AB 'C 'D ',则图中阴影部分面积为【解析】试题分析:设CD 与B'C'的交点是M ,连结AM ,则 ∠DAM=30° ∴AM=2DM 由勾股定理得DM=1考点:1.旋转的性质;2.正方形的性质.正面14题16.【广东省温州地区2013-2014学年八年级上学期第三次月考数学试卷】如图所示,用一根长度足够的长方形纸带,先对折长方形得折痕l,再折纸使折线过点B,且使得A在折痕l上,这时折线CB与DB所成的角为:。
杭州市余杭区崇贤中学2013-2014学年上学期10月阶段质量检测九年级数学试卷班级: 姓名: 学号:试题卷一. 仔细选一选 (本题有10个小题, 每小题3分, 共30分) 1.若反比例函数ky x=的图象经过点(-3,2),则k 的值为 ( ) A .-5 B .5 C .-6 D .6 2.抛物线3)2(2--=x y 的顶点坐标是( )A .(2,—3)B .(—2,—3)C .(2,3)D .(—2,3) 3.已知点(-3,1y ),(-2,2y ),(2,3y )在函数xy 1-=的图像上,则( ) A .321y y y << B .312y y y << C .123y y y << D .213y y y <<4.⊙O 的半径为6,圆心O 的坐标为(0,0),点P 的坐标为(3,4),则点P 与⊙O 的位置关系是( )A .点P 在⊙O 内B .点P 在⊙O 上C .点P 在⊙O 外D .不能确定 5.抛物线23x y =的图象向上平移3个单位,再向右平移4个单位所得的解析式为( ) A .4)3(32+-=x y B .3)4(32-+=x yC .3)4(32--=x y D . 3)4(32+-=x y 6.一条排水管的截面如图所示.已知排水管的水深CD =4, 水面宽 AB =16,则截面圆半径OB 是( )A .8B .10C .12D .387.如图,AB 为⊙O 的直径,CD 为弦,AB ⊥ CD ,如果∠BOC = 70°,则∠ABD 的度数为( )A .35°B .45°C .55°D .70° 8.已知二次函数2y ax bx c =++的图像如图所示,那么一次函数y bx c =+和反比例函数ay x=在同一平面直角坐标系中的图像大致是( )A .B .C .D .9.正比例函数y 1=k 1x 的图像和反比例函数y 2=2k x的图像交于A (-1,3)、B (1,-3)两点,若y 1 <y 2,则x 的取值范围是( )A .x <-1或x >1B .-1<x <0或x >1C .x <-1或0<x <1D .-1<x <0或 0<x <110.小明从图所示的二次函数c bx ax y ++=2的图象中,观察得出了下面五条信息:①0<c ;②0>abc ;③0>+-c b a ;④032=-b a ; ⑤04>-b c ,你认为其中正确..信息的个数有( ) A .2 B .3 C .4 D .5 二. 认真填一填 (本题有6个小题, 每小题4分, 共24分) 11.如果反比例函数xmy 31-=的图象位于第二、四象限,那么m 的取值范围是 . 12.已知二次函数62--=x x y ,则与x 轴的交点坐标是 .13.在⊙O 中,AB ,CD 为⊙O 的弦,且AB //CD ,AB =24,CD =10,弦AB 的弦心距为5,则AB 和CD 之间的距离是 .14.给出下列命题:①平分弦的直径必垂直于弦,并且平分弦所对的两条弧;②圆周角相等,则它们所对的弧也相等;③三角形的外心是三角形各边中垂线的交点;④若半径为5的圆中,有一条长为5的弦,则这条弦所对的圆周角等于30°;⑤平面上有A ,B ,C ,D 四个点,若任意三点不共线,则过其中三点可作4个圆.其中错误..的命题有 .(请填序号)15.已知二次函数322+-=x x y ,当0≤x ≤3时,y 的最大值是 ,y 的最小值是 . 16.如图,点A (x 1,y 1)、B (x 2,y 2)都在双曲线y =kx(x >0)上,且x 2-x 1=4,y 1-y 2=2.分别过点A 、B 向x 轴、y 轴作垂线段,垂足分别为C 、D 、E 、F , AC 与BF 相交于G 点,四边形FOCG 的面积 为2,五边形AEODB 的面积为14,那么双曲 线的解析式为______________. 三. 全面答一答 (本题有8个小题, 共66分)解答应写出文字说明, 证明过程或推演步骤. 17.(本题6分)已知⊙O 的两条弦AB ,AC 的位置如图,作⊙O .(要求尺规作图,保留作图痕迹,不写作法)BAC18.(本题8分)已知函数12y y y =-,其中1x y 与成正比例,22x y -与成反比例,且当x =1时,y =1;当3=x 时,y =5.求y 关于x 的函数解析式.19.(本题8分) 如图,在平面直角坐标系中,反比例函数y =kx (x >0)的图象经过点A (1, 2),B (m ,n )(m >1), 过点B 作y 轴的垂线,垂足为C . (1)求该反比例函数解析式;(2)当△ABC 面积为2时,求点B 的坐标.20.(本题10分) 某商场将进价为2000元的冰箱以2400元售出,平均每天能售出8台,为了配合国家“家电下乡”政策的实施,商场决定采取适当的降价措施,调查表明:这种冰箱的售价每降低50元,平均每天就能多售出4台.问每台冰箱售价为多少元时,商场每天销售这种冰箱的利润最高?最高利润是多少?21.(本题10分) 如图所示,AB =AC ,AB 为⊙O 的直径,AC 、BC 分别交⊙O 于E 、D ,连结ED 、BE . (1)试判断DE 与BD 是否相等,并说明理由; (2)如果BC =6,AB =5,求BE 的长.22.(本题12分) 已知A (1,0),B (0,-1),C (-1,2),D (2,-1),E (4,2)五个点,抛物线)0()1(2>+-=a k x a y 经过其中三个点.(1)求证:C 、E 两点不可能同时在抛物线)0()1(2>+-=a k x a y 上; (2)点A 在抛物线)0()1(2>+-=a k x a y 上吗?为什么? (3)求a 与k 的值.23.(本题12分) 如图,在平面直角坐标系中,已知矩形ABCD 的三个顶点B (1,0),C (3,0),D (3,4).以A 为顶点的抛物线c bx ax y ++=2过点C .动点P 从点A 出 发,沿线段AB 向点B 运动.同时动点Q 从点C 出发,沿线段CD 向点D 运动.点P ,Q 的运动速度均为每秒1个单位.运动时间为t 秒.过点P 作PE ⊥AB 交AC 于点E .(1)直接写出点A 的坐标,并求出抛物线的解析式; (2)过点E 作EF ⊥AD 于F ,交抛物线于点G , 当t 为何值时,△ACG 的面积最大?最大值为多少? (3)在动点P ,Q 运动的过程中,当t 为何值时, 在矩形ABCD 内(包括边界)存在点H ,使以 C ,Q ,E ,H 为顶点的四边形为菱形?请直接 写出t 的值.九年级数学 评分标准一、选择题(本题有10小题,每小题分,共30分.请选出各题中一个符合题意的正确选项,三、解答题(本题有8小题,共66分) 17.(本题6分)(结论没写扣1分) 18. (本题8分)解:2,2211-==x k y x k y 设 则221--=x k x k y ………………(2分) ⎩⎨⎧=-=+5312121k k k k ………………(2分)解得:21,2321-==k k ………………(2分) 42123-+=x x y ………………(2分)19. (1)xy 2=………………(4分)(2)⎪⎩⎪⎨⎧=-=2)2(212n m mn ………………(2分))32,3(B ………………(2分)20.解:设降了50X 元。
2014学年第一学期杭州市翠苑中学九年级10月阶段性测试一、单项填空16.--We’ve learned “bookstore”,”fork”,so can you get the sound of the underlined letters in the word “horn”---Yes,it pronounces________.A./i:/B./e/C./ei/D./ɔ:/17.--You’re doing much better in your writing.____can you improve it so quickly.--Well,I started keeping diaries in English two months ago.A.WhenB.WhereC.HowD.What18.I find_____ difficult to keep my room clean.A.itB.thisC.thatD.one19.--What fruit would you like? ---Some_____,please.They are my favorite.A.dessertB.grapesC.juiceD.biscuits.20.When you come across new words in reading,it is not a good idea to ____in a dictionary at once.A.make up them.B.look up themC.make them upD.look them up21.--We will have a 7-day holiday from Oct.7 for our Chinese National Day.---Wow,______ exciting news it is!A.WhatB.What anC.HowD.How an22.My father wants to know______ next week.A.when my uncle leavesB.when will my uncle leaveC.when my uncle will leaveD.when does my uncle leave.23.--Does my question sound ____enough?--I don’t think so.You can ask more____by using “could”instead of “can”A.politely;politelyB.politely;politeC.polite;politelyD.polite;polite24.I won’t go to the party unless I_____.A.inviteB.am invitingC.am invitedD.will be invited25.--I wonder if I can learn English well. --___.All things are difficult before they are easy.A.I am afraid so.B.You’re slow.C.It takes time.D.It’s a piece of cake.二.完形填空A family far from home finds kindness in a bag of fruits.Two years ago we were at a turning point in our lives in New Zealand.So we left our jobs,said__26__ to friends,and went to live in Switzerland.Our daughters,who were 11 and 15 at the time,__27__the local school.They couldn’t speak the local language,so we know their school life would be__28__.But after only a few months,the girls were doing really__29__,and trying their best to join in the Swiss(瑞士)way of life.The local newspaper then wrote a story__30__ them.When the article,complete with photos,__31__ in the newspaper,the girls were happy.But what happened next still makes us__32__.A teacher from the school__33__ the article to friends of his,a Swiss family who was nearing the end of their 12-month stay in __34__.When they__35__how wemissed feijoas(费约果),a fruit unknown in Switzerland,they quickly looked out of the window at the huge feijca tree.__36__they picked two kilograms of feijcas and brought them back with them to Switzerland--especially for __37__.They gave the fruit to their friend,the teacher who then drove two hours to__38__send these special gifts to us.Later that day,we found a big bag of feijoas outside the door.A note in the bag helped us__39__ how it got there.It was from the __40__,wishing us all the best and happy eating.26.A.hello B.sorry C.thanks D.goodbye27.A.joined B.left C.found D.refused28.A.happy B.relaxing C.hard D.colorful29.A.badly B.well C.strangely D.fast30.A.with B.against C.to D.about31.A.came B.appeared y D.went32.A.angry B.silent C.surprised D.sad33.A.threw B.sold C.showed D.carried34.A.New Zealand B.France C.Switzerland D.Australia35.A.wrote B.asked C.read D.dreamed36.A.But B.So C.Or D.Though37.A.him B.her D.them38.A.secretly B.angrily C.politely D.easily39.A.work out B.try out C.point out D.find out40.A.newspaper B.school C.family D.magazine三、阅读理解A_________________________________We are glad to announce the results of our competition to create a new school festival for students to celebrate this year.This competition,which we have had twice,has been a huge success.But this year,we have had more entries(参赛作品)than ever before.We have got many wonderful suggestions,including one that suggested there should be a festival of shoes!This was certainly a creative idea,but not surprisingly,our judges liked other suggestions more!The winning suggestion was from Henry Chan,who suggested that there should be a festival of bicycles.It was the judge’ s favorite.Henry,who is in G rade Nine,said that he went to school by bike every day and enjoyed taking bike trips very much.He added that so many public bikes were in use in our city that it would be a shame not to celebrate them.As part of the festival,a bike trip will be organized in the city.Then students will hold a ten-meter bike riding competition,in which anyone who can ride the silweat wins.What’s more,you students are called on to ride bikes to school as often as possible.The Bicycle Festival will start on October 28th and last two days.We hope you will take part in the festival and do your bit to protect our environment.41.This announcement is made to______.A.judgesB.parentsC.teachersD.students42.We can learn that_______ from the passage.A.Henry is the judge of the competitionB.Henry suggested a festival of shoesC.Henry rides a bike to schoolD.Henry doesn’t like the idea of using public bikes43.The underlined word “them” in paragraph3 refer to______.A.ideasB.shoesC.bicyclespetitions44.After this year’s Bi cycle Festival,what will happen most probably?A.Fewer people will use public bicyclesB.More students will ride bicycles to schoolC.The Bicycle Festival will be held every dayD.Bicycle to other cities will be organized.45.What is the title of the announcement?A.Care For The EnvironmentB.Entries Form Creative StudentsC.Suggestions To The StudentsD.Results of New Festival CompetitionBSomething caught my eyes when I was walking down the street. Two silver coins were shining in a melting(溶化) snow bank, so I dug(挖dig的过去式) through the snow looking for more. Of course, I just ended up with really cold hands. I slipped the two coins into my pocket and went home, colder but richer. I began to think about how to spend the money...Two days later, Mary and her little sister were searching the snow banks. "Finders are keepers" was my first thought. I didn't want to hand them out even though Susy was already crying. " I dropped them right here," she said between tears. Her hands were cold and red for digging in the snow. Maybe they slid down the street with the melting snow. Let's dig over here." Mary's voice sounded confident."They'll never know" was my second thought, and I walked past them. " Phil, have you seentwo sliver coins?" asked Mary. Susy looked up from digging. Her eyes were hopeful."Tell a lie" was my third thought. "As a matter of fact," I hesitated(犹豫),“I dug two coins out of that snow bank just a few days ago. I wondered who might have lost them." Susy hugged me with a big smile, "Oh, thank you, thank you."46. How did Phil feel when he was going home?A. Unhappy.B. Excited.C. Nervous.D. Confident.47. The underlined word "they" in the 2nd paragraph refers to ________ .A. Susy and MaryB. Mary and PhilC. Snow banksD. Two coins.48. Which of the following is the right order of the things that happened?a. Phil found two silver coins in the snow.b. Susy dropped two silver coins.c. Phil dug throngh the snow.d. Susy kept digging in the snow for her lost coins.A. a-b-c-dB. a-c-d-bC. b-a-c-dD. b-c-d-a49. What does the sentence"Her eyes were hopeful." in the 3rd paragragh suggest?A. Susy expected Phil to dig together.B. Susy expected Phil to return the coins.B. Susy hoped to dig out the lost coins. D. Susy hoped to get some useful information.50. What might Phil do with the two coins in the end?A. He would give them back to Susy.B. He would give them away.C. He might keep them for himself.D. He might give them to his parents.CTeens don’ t want to be seen with their parents, much less talk to them or do anything with them. That’s what we hear all the time. I don’t believe it. Oh,sure, when my daughter and my son were in their teens, they wanted to spend most of their free time with their friends. But there were always those special times planned when we enjoyed being alone with each other, when we connected deeply, and when we were reminded again how much we loved one another.for a date to see a movie. It was a bittersweet Italian movie, Cinema Paradiso, and I wanted this story to give her a sense of how I grew up as an Italian boy in a small town, where life was simple and where everyone knew one another. I wanted her to know how her father had been brought up and shaped.We both laughed and cried during the same scenes in the movie. She was attached to the movie. I decided we should complete our evening with some lively conversation at a nearby bakery. I told her the movie was now so much more special for me because I had shared it with her. She smiled. She understood. We made a memory that night.From our living room window, I saw my 13-year-old son, Jason, tearfullysearching our vegetable garden for a place to bury his pet boa constrictor (蟒蛇). Because my son had suffered from asthma (哮喘) and allergies, he could never have a dog, a faithful friend that he wanted so much. Every pet he owned—lizards, fish, or snakes—had died.I was at his side as we searched for the best gravesite (墓地). We dug the grave, said our goodbyes and then he cried. He cried hard and he asked me why every pet he had owned died so soon. I could feel his heart break against my chest. I just held him close. He let me hold his aching soul. He needed me while he was confused. Share your heart with your teens. Show them repeatedly that you know and love who they really are. There are tender memories waiting to be made.51. What can we learn from the passage?A. Children would like to spend time with parents.B.Parents have trouble in getting along with children.C.The author always spent time with children in a planned way.D.The family should help each other at the important moment.52. Why did the author choose to see Cinema Paradiso with his daughter?A. To make his daughter laugh.B.To give his daughter encouragement.C.To let his daughter love movies.D.To make his daughter know him better.53. What do the underlined words “was attached to” in Paragraph 3 mean? A.Disliked. B.Loved.C.Missed. D.Hated54. It can be inferred that________.A. at some moments, children want to be with parentsB.the author’s children cannot take care of th emselvesC.it is hard for parents to know the inside of their childrenD.the author’s son is cruel to cold blooded animals55. From the last paragraph we know that________.A.setting a good example to children is importantB.the author advises people to make memories with their teensC.the son was touched by what his father had doneD.knowing children’s daily activities is necessary借鉴别人好的学习方法,是提高学习成效的途径之一。
一.选择题1. 【浙江省三门县城关中学2013-2014学年第一学期10月月考九年级数学试卷】定义新运算“※”如下:当a≥b 时,a※b=a a b +,当a <b 时,a※b=a a b -,若()()2x 1x 20-+=※,则x 的值为 ( ▲ )A .121x 3x 2=-=, B .121x 1x 2=-=, C .1231x 3x x 12=-==-,, D . 以上答案均不正确2.【衢州市衢江区2013-2014学年第一学期九年级第三次联考数学试题】如图,将一个有45°角的三角板ABC 的直角顶点放在一张宽为3cm 的纸带边沿上.另一个顶点在纸带的另一边沿上,测得三角板的一边与纸带的一边所在的直线成30°角,则三角板的最大边AB 的长为( )A. 3 cmB.6cmC.二.填空题3.【温州市七校2013-2014学年上学期12月联考九年级数学试题】将一副三角尺如图拼接:含30°角的三角尺(△ABC)的长直角边与含45°角的三角尺(△ACD)的斜边恰好重合.已知AB=23,E是AC上的一点(AE>CE),且DE=BE,则AE的长为 .4.【浙江省杭州市翠苑中学2013-2014学年上学期10月质量检测九年级数学试题】(10分)如图,矩形ABCD为一本书,AB=12π,AD=2,当把书卷起时大致如图所示的半圆状(每张纸都是以O为圆心的同心圆的弧),如第一张纸AB对应为»AB,最后一张纸CD对应为»CD(»CD 为半圆),(1)连结OB,求钝角∠AOB=;(2)如果该书共有100张纸,求第40张纸对应的弧超出半圆部分的长.三.解答题5.【浙江省金华市聚仁教育集团2014九年级上学期第二阶段考试数学试题】将△ABC绕点A按逆时针方向旋转θ度,并使各边长变为原来的n倍,得△AB′C′,即如图①,我们将这种变换记为[θ,n].(1)如图①,对△ABC作变换[60°,]得△AB′C′,则S△AB′C′:S△ABC=____;直线BC 与直线B′C′所夹的锐角为______度;(2)如图②,△ABC中,∠BAC=30°,∠ACB=90°,对△ABC 作变换[θ,n]得△AB'C',使点B、C、C′在同一直线上,且四边形ABB'C'为矩形,求θ和n的值;(3)如图③,△ABC中,AB=AC,∠BAC=36°,BC=l,对△ABC作变换[θ,n]得△AB′C′,使点B、C、B′在同一直线上,且四边形ABB'C'为平行四边形,求θ和n的值.6.【浙江省桐乡市实验中学2013-2014学年上学期基础调研九年级数学试卷】(6分)(1)解方程:1x x2x136-+-=-(2)x,y表示两个数,规定新运算“*”及“”如下:x*y=mx+ny,x△y=kxy,其中m,n,k 均为自然数(零除外),已知1*2=5,(2*3)△4=64,求(1△2)*3的值.∴1△2=2×1×2=4.∴(1△2)*3=4*3=4+2×3=10.考点:1.解一元一次方程;2.新定义;3.简单推理.7.【衢州市衢江区2013-2014学年第一学期九年级第三次联考数学试题】(本题10分)数学课上,王老师出示了问题:如图1,四边形ABCD是正方形,点E是边BC的中点.∠AEF=90°,且EF交正方形外角∠DCG的平行线CF于点F,求证:AE=EF.经过思考,小明展示了一种正确的解题思路:取AB的中点M,连接ME,则AM=EC,易证△AME≌△ECF,所以AE=EF.在此基础上,同学们作了进一步的研究:(1)观点一:如图2,如果把“点E是边BC的中点”改为“点E是边BC上(除B,C外)的任意一点”,其它条件不变,那么结论“AE=EF”仍然成立.观点二:如图3,点E是BC的延长线上(除C点外)的任意一点,其他条件不变,结论“AE=EF”仍然成立.请从以上两个观点中选择一个观点判断是否正确,如果正确,写出证明过程;如果不正确,请说明理由.(2)拓展:如图4,当四边形ABCD是矩形,且AB=2AD时,点E是边BC上的任意一点(不与B、C重合),∠AEF=90°,且AE=2EF,连接CF,求tan∠FCG的值.试题解析:(1)观点一正确.证明:在AB上取一点M,使AM=EC,连接ME.∴BM=BE.∴∠BME =45°.∴∠AME=135°.∵CF是外角平分线,∴∠DCF=45°.∴∠ECF=135°.∴∠AME =∠ECF.8.【云南省临沧区云县后箐中学2014届九年级10月综合练习数学试题】当060α︒︒<<时,下列关系式中有且仅有一个正确.A. ()2sin 30sin αα+︒=+B. ()2sin 302sin αα+︒=C. ()2sin 30cos ααα+︒=+(1)正确的选项是 ;(2)如图1,△ABC 中, AC 1B 30A α=∠=︒∠=,,,请利用此图证明(1)中的结论;(3)两块分别含45︒ 和30︒的直角三角板如图2方式放置在同一平面内,BD =,求ADC S ∆.(3)由(2)证明的等式易得()sin 30α+︒= 如图2,过点A 作AG⊥CD 交CD 的延长线于点G .∵△ABD 和△BCD 是两个含45°和30°的直角三角形,BD =,∴∠ADG=75°,AD=8,CD =考点:1.解直角三角形;2.三角形外角性质;3. 锐角三角函数定义;4.特殊角的三角函数值;5.三角形面积.9.【江苏省无锡市惠山六校联考2014届九年级上学期期中考试数学试题】(10分)某数学兴趣小组开展了一次课外活动,过程如下:如图,正方形ABCD中,AB=6,将三角板放在正方形ABCD上,使三角板的直角顶点与D点重合。
浙江省杭州市翠苑中学2013-2014学年上学期10月质量检测九年级数学试卷浙教版一、选择题(每小题3分,共30分)1、在直线运动中,当路程s(千米)一定时,速度v(千米/小时)关于时间t(小时)的函数关系式的大致图象是( )A B C D2、已知圆锥的母线为10,底面圆的直径为12,则此圆锥的侧面积是( )A .24πB .30πC .48πD .60π3、二次函数y=x 2-2x-3,当y<0时,自变量x 的取值范围是( )A .-1<x <3B .x <-1C .x >3D .x <-1或x >34、下列函数:①y x =-;②1y x =-;③y x=;④()212024030y x x x =++<中,y随x 的增大而减小的函数有( )A .1个B .2个C .3个D .4个5、扇形OAB 的半径OA=1,圆心角∠AOB=90°,点C 是弧AB 上的动点,连结AC 和BC ,记弦AC ,CB 与弧AC 、CB 围成的阴影部分的面积为S ,则S 的最小值为( )A .142π- B .4π- C .1444π-- D .184π- 6、若点P 1(-1,y 1),P 2(-2,y 2),P 3(1,y 3),都在函数y=x 2-2x+3的图象上,则( )A .y 2<y 1<y 3B .y 1<y 2<y 3C .y 2>y 1>y 3D .y 1>y 2>y 37、如图,△ABC 内接于⊙O ,∠C=30°,AB=2,则⊙O 的半径为( )A B . C .2 D .48、下列三个命题:①圆既是轴对称图形,又是中心对称图形;②垂直于弦的直径平分这条弦;③平分弦的直径垂直于这条弦;④相等的圆心角所对的弧相等。
其中是真命题的是() A.①②B.①②③C.①②④D.①②③④9、若双曲线kyx=如下图所示,那么二次函数221y kx k x=--的图象大致为()A B C D10、如图,⊙O的半径OA,OB,且OA⊥OB,连结AB。
现在⊙O上找一点C,使OA2+AB2=BC2,则∠OAC的度数为()A.15°或75°B.20°或70°C.20° D.30°二、填空题(每小题4分,共24分)11、在平面直角坐标系中,已知点A(3,2),B(-2,-3),则经过A,B两点函数图象的解析式可以为 (写出一个即可)12、把球放在长方体纸盒内,球的一部分露出盒外,其截面如图所示,已知EF=CD=16厘米,则球的半径为厘米.13、如图,已知点C在双曲线2kyx=上,点E在双曲线kyx=上,过点C分别作x轴和y轴的垂线,垂足为B,G,过点E分别作x轴和y轴的垂线,垂足为A,F,CG与AE交于点D,四边形ABCD与四边形DEFG的面积分别为88与28,则△ADG的面积为14、如图是小明制作的一个圆锥形纸帽的示意图,围成这个纸帽的纸(圆锥侧面)的面积为cm2.若从纸帽的底面圆周上点A处用一条红线绕纸帽的侧面一圈,那么这样的红线至少要cm.(红线的接头长度忽略不计)第14题 第15题15、如图,在矩形ABCD 中,BC=1,现将矩形ABCD 绕点C 顺时针旋转90°得到矩形A 'B 'CD ',则AD 边扫过的面积(阴影部分)为16、如图,AB 为⊙O 的直径,AB=AC ,BC 交⊙O 于点D ,AC 交⊙O 于点E ,∠BAC=45°。
给出以下五个结论:①∠EBC=22.5°;②BD=DC ;③AE=2EC ;④劣弧»AE 是劣弧»DE的2倍;⑤AE=BC .其中正确结论的序号是 .三、解答题(共66分,解答需写出必要的文字说明、演算步骤或证明过程)17、(6分)(1)尺规作图:作出⊙O 的内接正方形ABCD ,使正方形ABCD 的对边AD ,BC 都垂直于EF(见示意图);(说明:不要求写作法,但须保留作图痕迹)(2)连接EA 、EB ,求出∠EAD 、∠EBC 的度数.18、(8分)已知:正比例函数1y k x =的图象于反比例函数()20k y x x=>的图象交于点M(a,1),MN ⊥x 轴于点N(如图),若△OMN 的面积等于2,求这两个函数的解析式。
19、(8分)如图,已知直线l与y轴、x轴交于点A(0,8)、B(6,0)两点,直线y=4x-8与y轴、直线l分别交于点C、D,求△ACD绕y轴旋转一周所围成几何体的表面积。
20、(10分)如图,点A、B、C是⊙O上的三点,AB∥OC(1)求证:AC平分∠OAB.(2)过点O作OE⊥AB于点E,交AC于点P.若AB=2,∠AOE=30°,求PE的长.21、(10分)如图,足球场上守门员在O处开出一高球,球从离地面1米的A处飞出(A在y 轴上),运动员乙在距O点6米的B处发现球在自己头的正上方达到最高点M,距地面约4米高,球落地后又一次弹起.据实验测算,足球在草坪上弹起后的抛物线与原来的抛物线形状相同,最大高度减少到原来最大高度的一半.(1)求足球开始飞出到第一次落地时,该抛物线的表达式.(2)足球第一次落地点C 距守门员多少米?(取7=)(3)运动员乙要抢到第二个落点D ,他应再向前跑多少米?(取5=)22、(10分)如图,矩形ABCD 为一本书,AB=12π,AD=2,当把书卷起时大致如图所示的半圆状(每张纸都是以O 为圆心的同心圆的弧),如第一张纸AB 对应为»AB ,最后一张纸CD 对应为»CD (»CD 为半圆),(1)、连结OB ,求钝角∠AOB= ;(2)、如果该书共有100张纸,求第40张纸对应的弧超出半圆部分的长。
23、(12分)如图,在直角坐标系中,以点为圆心,以x 轴相交于点B ,C ,与y 轴相交于点D ,E.(1)若抛物线y=13x 2+bx+c 经过点C ,D 两点,求抛物线的解析式,并判断点B 是否在该抛物线上。
(2)在(1)中的抛物线的对称轴上有一点P ,使得△PBD 的周长最小,求点P 的坐标。
(3)设Q 为(1)中的抛物线的对称轴上的一点,在抛物线上是否存在这样的点M ,使得四边形BCQM 是平行四边形?若存在,求出点M 的坐标;若不存在,说明理由.参考答案一、选择题1.D 2.D 3.A 4.A 5.B 6.C 7.C 8.A 9.B 10.A二、填空题11、6y x =(答案不唯一) 12、20 13、16 14、300π, 15、14π 16、①②④ 三、解答题17、解:(1)如图所示:(2)由作图可知:∠EOD=45°,∠EOC=135°,∵∠EOC=135°,∴∠∵∠EOD=45°, ∴∠EAD=18、解:∵MN ⊥x 轴,点M (a ,1) ∴S △OMN=a 21=2 ∴a=4∴M(4,1)∵正比例函数y=k 1x 的图象与反比例函数xk y 2=(x>0)的图象交于点M (4,1) ∴414121k k == 解得 44121==∴正比例函数的解析式是x y 41=,反比例函数的解析式是xy 4=19、解:l 与y 轴、x 轴交于A(0,8)B(6,0)两点 AB:y=-43x+8 与直线y=4x-8的交点为D 解之得,D(3,4)线段AD 、CD 绕Y 轴旋转一轴所围成几何体是两个三棱锥组成因为D(3,4),C(0,-8)则AD=5,CD=AD 为母线三棱锥的表面积:πrl=15πCD 为母线三棱锥的表面积:πrl=围成几何体的表面积=3(π20、(1)∵AB ∥OC , ∴∠C=∠BAC ;∵OA=OC ,∴∠C=∠OAC ∴∠BAC=∠OAC 即AC 平分∠OAB.(2)∵OE ⊥AB ∴AE=BE=12AB=1 又∵∠AOE=30°,∠PEA=90°∴∠EAO=60°∴∠EAP=12∠OAE=30°, ∴PE=12PA ,设PE=x ,则PA=2x ,根据勾股定理得2221(2)x x +=,解得3x =(或者用tan PE EAP AE ∠=)即PE 的长是3. 21、(1)y=-4)6(1212+-x (2)y=0, x=6+43︽13(3)设y=2)(1212+-m x m=13+26︽18 y=0, x=18±26︽23 ∴ 再向前跑10米22、(1) ∠AOB= 144° (2) 65π23、解:(1)OA =∵AB AC ==(B ∴,C又在Rt AOD △中,AD =OA =3OD =∴D ∴的坐标为(03)-,又D,C 两点在抛物线上,23103c c =-⎧⎪⎨⋅++=⎪⎩∴解得3b c ⎧=⎪⎨⎪=-⎩ ∴抛物线的解析式为:2133y x x =-当x =0y =∴点(B 在抛物线上 (2)2133y x x =-∵21(43x =-- ∴抛物线2133y x x =-的对称轴方程为x = 在抛物线的对称轴上存在点P ,使PBD △的周长最小.BD ∵的长为定值 ∴要使PBD △周长最小只需PB PD +最小. 连结DC ,则DC 与对称轴的交点即为使PBD △周长最小的点. 设直线DC 的解析式为y mx n =+.由30n n =-⎧⎪⎨+=⎪⎩得3m n ⎧=⎪⎨⎪=-⎩∴直线DC的解析式为3y x =-由3y x x ⎧=-⎪⎨⎪=⎩得2x y ⎧=⎪⎨=-⎪⎩ 故点P的坐标为2)-(3)存在,设)Q t为抛物线对称轴x =M 在抛物线上要使四边形BCQM 为平行四边形,则BC QM ∥且BC QM =,点M 在对称轴的左侧. 于是,过点Q 作直线L BC ∥与抛物线交于点()m M x t ,由BC QM =得QM =从而m x =-12t =故在抛物线上存在点(M ,使得四边形BCQM 为平行四边形.。