广州市铁一中学2012学年第一学期期中试题
铁一初三期中卷

广州市铁一中学2012学年第一学期期中初三数学试题一、选择题1. 下列计算中,正确的是() A.416±= B.12223=- C.4624=÷ D.2632=⨯2. 下列图形中不是中心对称图形的是()A .B .C .D .3. 要使3-x 有意义,则x 的取值范围必须满足()A. 3≠xB. 3=xC. 3≥xD. 3≤x4.下列方程有实数根的是()A. 012=--x xB. 0122=++x xC. 01062=+-x xD. 0122=+-x x 5.关于x 的方程0312=+c x 有一个根是3-,则另一个根是()A. 3-B. 3C. 9 D 9-6.用配方法解方程0782=++x x ,则配方正确的是()A. 9)4(2=-xB. 57)8(2=+xC. 16)8(2=-xD. 9)4(2=+x 7. 某兴趣活动小组成员将自己收集的资料向本组其他成员各送一份,全组共互送了20份,若全组有x 名同学,则根据题意可列出的方程是( )A .20)1(=+x xB .20)1(=-x xC .20)1(2=+x xD .221)1(⨯=-x x8.下列图形中,绕着它的中心旋转60°后能够与原图形完全重合,则这个图形是()A.等边三角形B.正方形C.圆 D 菱形.9.如图,AB 是O Θ的直径,点C 、D 在O Θ上,OD//AC ,给出下列结论:①BAC BOD ∠=∠;②D C ∠=∠;③C A C B =;④D C D B=.其中正确的有()A.1个B.2个C.3个D.4个10.如图,ABC ∆中,AB=AC ,40=∠BAC ,D 为ABC ∆内一点,如果将ACD ∆绕点A 按逆时针方向旋转到'ABD ∆的位置,则'ADD ∠的度数是()A.40°B.50°C.60°D.70°二、填空题(每小题3分,共18分)11.已知关于x 的一元二次方程022=+-k x x 有两个不相等的实数根,则k 的值为 .12. ABC ∆是等边三角形,点O 是三条中线的交点,ABC ∆以点O 为旋转中心,则至少旋转 度后能与原来图形重合.13.如图,ABC ∆绕点B 逆时针方向旋转到EBD ∆的位置,若 15=∠A , 10=∠C ,E 、B 、C 在一条直线上,则旋转角是 度.14.如图,AB 是O Θ的直径,E D D C C B ==, 35=∠COD ,则AOE ∠的度数是度.15.观察下列式子,2112111122=++,6113121122=++,12114131122=++,……,根据此规律,若901111122=++b a ,则=+22b a . 16.如图,AD 是O Θ的直径,AC 是弦,AD OB ⊥,若OB=5,且 30=∠CAD ,则BC= .三、解答题(共102分)17.计算(每小题5分,共10分)(1)48327124-+(2)22)8321464(÷+-18.用适当的方法解一元二次方程(每小题5分,共10分)(1)22)32()2(+=-x x (2)0862=+-x x19.(本题8分)先化简,再求值:x x x x 12344336+-.其中2=x .20.(本题10分)已知一元二次方程042=+-k x x 有两个不相等的实数根.(1)求k 的取值范围;(2)如果k 是符合条件的最大整数,且一元二次方程042=+-k x x 与012=-+mx x 有一个相同的根,求m 的值.21.(本题12分)如图,AB ,CD 是圆O 的弦,M ,N 分别为AB ,CD 的中点且CNM AMN ∠=∠,求证:OM=ON.22.(本题12分)如图,半圆M 的直径AB 为20cm ,现将半圆M 绕着点A 顺时针旋转180°。
铁一中2012-2013(上)七年级期中数学试题

铁一中七年级期中考试试卷*数学一、选择题(共8小题,每小题3分,计24分,每小题只有一个选项符合题意)1、-5的绝对值为()A、-5B、5C、1/5D、-2、如图是每个面上都有一个汉字的正方体的一种展开图,那么在原正方体的表面上,与汉字“美”相对的面上的汉字是()A、我B、爱C、西D、安3、用一个平面去截一个几何体,截面不可能是三角形的几何体是()A、圆柱B、圆锥C、三棱柱D、正方体4、2012年国庆期间约有5450000人次在西安旅游,5450000用科学数法表示为()A 、B、C 、D 、5、如图,数轴上A、B两点分别对应实数a、b,则下列结论正确的是()A、ab>0B、a-b>0C、a+b>0D、︱a︱-︱b︱>6、若A是3次多项式,B也是3次多项式,则3A+2B一定是()A、3次多项式B、6次多项式C、次数低于3的多项式D、次数不高于3的整式7、下列各组数中,值相等的是()A 、和B、和C、︱-(-3)︱和-︱-3︱D、-(-9)和-98、观察图表,依据表格中数据排列的规律,数2012在表格中出现的次数共有()次A、6B、8C、10D、无数多二、填空题(共6小题,每小题3分,计18分)9、某地,一天早晨的温度是-6℃,中午较早晨温度上升了9℃,则该中午的温度是。
*10、已知a-3b=3,则的值是。
11、如图,在直角三角形ABC中,∠ACB=90º,以AC所在的直线为轴转一周所和的几何体是。
12、某商品每件成本a元,按成本增加20%定价,后因库存积压减价,按定价的90%出售,减价后每件商品盈利元。
(盈利=售价-成本)*13、在数轴上的三点A、B、C,点A、B对应的数分别是-1,4,点C到点B的距离为2,则点C到点A的距离是。
14、对实数a、b,定义运算☆如下:例如:3☆2=3²=9,计算【2☆1】×【(-4)☆2】= 。
三、解答题(共8小题,计58分,解答题应写出必要的解答过程)15、(本题满分6分)计算:①②16、(本题满分8分)先化简再求值:①(-4a²-2ab+7)-2(5ab-4a²+7),其中a=2,b=1/3*②已知的值。
2012年广州铁一中学高考喜讯

2012年广州铁一中学高考喜讯2012年广州铁一中学高考喜讯珠江奔腾掀新浪,铁中飞跃创佳音。
2012年铁一中学高考成绩再续辉煌。
高考喜讯之一今年我校参加高考人数474人,重本上线192人,重本上线率40.51%,其中理科重本上线人数133人,重本上线率44.33%,文科上线人数59人,重本上线率34.30%。
全校本科以上上线人数462人,本科上线率97.26%,其中理科上线人数292人,上线率97.33%,文科上线人数170人,上线率96.59%,全校大专以上上线率达100%,再创历史新高。
高考喜讯之二我校陈伟峰同学理科高考总分688分(含加分)、张瑞晟、陈玉洁同学文科总分分别为646分,位居广东省前列,高考总分理科640分以上18人,620分以上33人,文科627分以上5人,615分以上23人,高分学生共56人。
高考喜讯之三我校今年高考单科高分人数共77人次。
其中语文125分以上10人,英语140分以上12人,文数135分以上10人,理数130分以上9人,理综270分以上18人,文综240分以上18人。
高考喜讯之四今年我校创新实验班1班参加高考人数36人,总分最高分陈伟峰688分(含加分),位居广东省前列,600分以上高分学生29人,重本上线人数34人,重本率94.44%;理科重点班(2班、3班)重本上线人数68人,重本率66.67%,文科重点班(8班)重本上线人数,38人,重本率73.08%,文理科重点班本A上线人数190人,本科A率达100%。
高考喜讯之五2012届我校四个重点班共190人,高一入学最低录取分数平均分为708.75(广州市A 类四所学校高一入学最低录取分数平均分为727.75),我校低于A类四所学校19分;三年后我校四个重点班高考重本率平均为75.22%(A类四所学校高考重本率平均为70.1%),重本率高于A类四所学校5.12%。
2012年高考我校单科高分段学生姓名语文姓名文科数学姓名理科数学朱乐宁129李舒心141李敏仪133岑曦129陈玉洁黄伟泉133伍咏琳128邱璐139陈伟峰132刘宇128黎莹138徐玥132刘梓秋127桓绮芸138林瑞苑132王礼昱126杨凡137王翔132庞苗126冯珺136张天晟130李舒心126陈华玲136黄展翔130俞嘉慧126张瑞晟135邱立韬张涛125魏冰婷135合计10人文数10理数9姓名理综文科综合姓名英语吴诗晴279岑曦248张瑞晟144李宇菲279陈玉洁248伍咏琳143黄伟泉279郑嘉琦247刘雨晴143陈伟峰278黄雅迪246陈伟峰142江海盈278张瑞晟246142郭筱蕾277酒一淳244王雪雯142雷东方276汪妍延244方雅雯141吴芮毅275成惠言244陈华晶141官晓龙274陆思敏243潘秋洁141方雅雯274王玥243吴诗晴140陈华晶274李梦梅243官晓龙140杨仑274谢逸242许蓝天140273钟曦242赖惠杰271刘雨晴241郭俊生271许欣妮241陈嘉炜270敖珺兰240邱立韬270黄孝洵240于璐270张涛240合计18人合计18人合计12。
铁一初三期中考试参考答案.doc

2013年广州市铁一中学中考模拟试题参考答案二、语言知识及运用(共两节,满分25分)第一节、单项选择(共15小题;每小题1分,满分15分)16-20. ABDAC 21-25. CCCCB 26-30. DBBCA第二节、语法选择(共10小题;每小题1分,满分10分)31-35. DCCDA 36-40. CACAA三、完形填空(共10小题;每小题1分,满分10分)41-45. BACAB 46-50. BBBCD四、阅读理解(共20小题;每小题2分,满分40分)51-55. BCBAB 56-60. CABCC61-65. BACBC 66-70. BCCAB五、写作(共三节,满分40分)第一节、单词拼写(共10小题,每小题1分,满分10分)71. accident 72. enough 73. throw 74. dangerous75. laugh 76. fan 77. cotton 78. bill 79. seat 80. plenty第二节、完成句子(共9小题,每空0.5分,满分15分)81. will take part in 82. icecream tastes 83. To visit, had better, with84. How clean, beautiful 85. are bought 86. who(whom) you are waiting for87. are, preparing for 88. cut, short 89. Even though(if), has kept(had)第三节、书面表达(共1题,满分15分)Now students have more free time on Saturday and Sundays than before. Our school invited me to do an investigation on how the students spend their weekends. I find that almost half of the students study by themselves at home. About 25% of them prefer to watch TV or listen to music. 20% of them like to chat online or play computer games, while 10% of them help their parents do housework. Only a small number of them go in for sports or travelling.In my opinion, all of us students should have a proper plan for our weekends. We should make good use of our time, learning more knowledge, developing our interests, We should also do some sports, but I don’t think it’s a good idea to spend too much time watching TV , chatting online or playing computer games.。
广东省广州市高二数学上学期期中考试试题 理 新人教A版

广州市铁一中学2012学年第一学期期中高二数学(理科)试题第I 卷(共50分)一、选择题:本大题共10小题,每小题5分,共50分.在每小题给出的四个选项中,只有一项是符合题目要求的.1已知}6,5,4,3,2,1{},5,4,3{},6,4,2,1{===U B A 求=B A C u Y ( ) A 、}6,5,4,3,2,1{ B }6,4,2,1{ C 、}5,4,2{ D 、}5,4,3{2.已知向量a 与向量b 的夹角为120°,若向量c=a+b ,且a ⊥c ,则||||b a 的值为( ) A .21 B .332 C .2D .33.已知)4tan(,54sin ),0,2(πααπα+-=-∈则等于 ( )A .-7B .-71C .71D .74.如图是一个几何体的三视图,则这个几何体的体积是 ( ) A .27 B .30 C .33 D .365.有编号分别是1,2,3,4,5的5个红球和5个黑球,从中取出4个,则取出的球的编号互不相同的概率为 ( )A .215B .72 C .31 D .218 6.对于实数x ,符号[x]表示不超过x 的最大整数,例如2]08.1[,3][-=-=π,定义函数{x}][x x -=,则下列命题中正确的是( )A .函数}{x 的最大值为1B .函数21}{)(-=x x G 有且仅有一个零点 C .函数}{x 是周期函数 D .函数}{x 是增函数7、已知实数,x y 满足235230x y x y y +≥⎧⎪+≤⎨⎪≥⎩,则3x y +的最大值是( )A .52B .3C . 4D .928、在各项均不为零的等差..数列{}n a 中,若2110(2)n n n a a a n +--+=≥,则214n S n --=( )A .-2B .0C .1D .29.如图,从双曲线)0,0(12222>>=-b a by a x 的左焦点F 引圆222a y x =+的切线,切点为T ,延长FT 交双曲线右支于P 点,若M 为线段FP 的中点,O 为坐标原点,则a b MT MO --与||||的大小关系为( )A .a b MT MO ->-||||B .a b MT MO -=-||||C .a b MT MO -<-||||D .大小关系不确定网10、函数()y f x =是定义在[,]a b 上的增函数,其中,a b R ∈,且0b a <<-,已知()y f x =无零点,设函数22()()()F x f x f x =+-,对于()F x 有如下四个说法:①定义域是[,]b b -;②是偶函数;③最小值是0;④在定义域内单调递增;其中正确说法的个数有A .4个B .3个C .2个D .1个第II 卷(共100分)二、填空题:本大题共4小题,每小题5分,共20分.把正确答案填在题中的横线上.11、已知向量向量(2,1)b y x =--r ,若a r ∥b r,则22x y += .网 12.已知一三角形ABC 用斜二测画法画出的直观图是面积为3的正三角形C B A '''(如图),则三角形ABC 中边长与正三角形C B A '''的边长相等的边上的高为_______y ’A ’B ’C ’O ’1 2 0.5 1xyz(1,2)a x y =--rABCDEF图513、在如图的表格中,如果每格填上一个数后,每一横行成等差数列,每一纵列成等比数列,那么,x y z ++的值为 . 14已知函数f(x) =1321---x x 的零点有四个x 1、x 2、x 3、x 4,则f(x 1+x 2+ x 3+x 4)=_______.三、解答题:本大题共6小题,共80分,解答应写出文字说明,证明过程或演算步骤. 15. (本小题满分12分)在△ABC 中,角A 、B 、C 的对边分别为a 、b 、c ,且满足C b B c a cos cos )2(=-.(Ⅰ)求角B 的大小;(Ⅱ)设)1,1(),1,(sin -==n A m ,求n m ⋅的最小值.16. (本小题满分12分) 某高校在2012年的自主招生考试成绩中随机抽取100名学生的笔试成绩,按成绩分组,得到的频率分布表如下左图所示.(1)请先求出频率分布表中①、②位置相应数据,再在答题纸上完成下列频率分布直方图;(2)为了能选拔出最优秀的学生,高校决定在笔试成绩高的第3、4、5组中用分层抽样抽取6名学生进入第二轮面试,求第3、4、5组每组各抽取多少名学生进入第二轮面试? (3)在(2)的前提下,学校决定在6名学生中随机抽取2名学生接受A 考官进行面试,求:第4组至少有一名学生被考官A 面试的概率?17.(本题满分14分) 如图5,已知AB ⊥平面ACD ,DE ⊥平面ACD ,△ACD 为等边三角形,2AD DE AB ==,F 为CD 的中点.组号 分组 频数 频率第1组 [)165,160 5 0.050第2组 [)170,165 ① 0.350第3组 [)175,170 30 ② 第4组 [)180,175 20 0.200第5组 [180,185] 10 0.100 合计 100 1.00x ’AC (1)求证://AF 平面BCE ; (2)求证:平面BCE ⊥平面CDE ;18、(本题14分)如图,公园有一块边长为2的等边△ABC 的边角地,现修成草坪,图中DE 把草坪分成面积相等的两部分,D 在AB 上,E 在AC 上. (1)设AD =x ,DE =y ,求y 关于x 的函数关系式; (2)如果DE 是灌溉水管,我们希望它最短,DE 的位置应在哪 里?请予证明. 19、(本题14分)已知数列{}n a 满足12a =, . (1)求证数列 是等比数列,并求其通项公式; (2)设nn a b n =,求数列{}n b 的前n 项和n S ; (3)设n n n c a =,求证:123710n c c c c +++⋅⋅⋅⋅⋅⋅+<.20.(本小题满分14分)过双曲线2x 2-y 2=1上一点A (1,1)作两条动弦AB , AC ,且直线AB , AC 的斜率的乘积为3.(1)问直线BC 是否可与坐标轴垂直?若可与坐标轴垂直,求直线BC 的方程,若不与坐标轴垂直,试说明理由.(2)证明直线BC 过定点.四、附加题:(一班学生做,满分20分)对于定义域为D 的函数()y f x =,如果存在区间[],m n D ⊆,同时满足下列条件:①()f x 2112(1)()n n a a n N n++=+⋅∈2{}n an在[],m n 内是单调的;②当定义域是[],m n 时,()f x 的值域也是[],m n 时,则称[],m n 是该函数的“和谐区间”。
广州市铁一中学2005-2006学年度第一学期期中考试

广州市铁一中学2005-2006学年度第一学期期中考试选修高二化学试题可能用到的相对原子质量:H:1 Na:23 Mg:24 Al:27 Fe:56 K:39 Cu:64 Ag:108 C:12 O:16 S:32 Cl:35.5 Br:80第I卷:选择题(共50分)一、选择题:(以下每题只有1个选项符合题意,2′×10)1.食品添加剂通常必须在一定范围内使用,否则会损害人体健康,滥用下列食品添加剂会导致癌症发生率增加的是()A.KIO3 B.苯甲酸钠C.维生素E D.NaNO2 2.新兴的大脑营养学研究发现,大脑的生长发育与不饱和脂肪酸有密切的关系,从深海鱼油中提取的,被称为“脑黄金”的DHA就是一种不饱和程度很高的脂肪酸,它的分子中含6个碳碳双键,化学名称为二十六碳六烯酸,则它的分子组成应为()A.C25H39COOH B.C25H50COOHC.C26H41COOH D.C26H47COOH3.已知甲醛(HCHO)分子中的4个原子是共平面的。
下列分子中所有原子不可能同时存在于同一平面的是()A.苯乙烯C6H5CH=CH B.苯甲醛C6H5-CHOC.苯甲酸C6H5COOH D.苯乙酮C6H5CO CH34.鉴别乙醇、丙三醇、乙醛、乙酸、甲酸可以选用的一组试剂是()A.金属钠和石蕊试剂B.Na2CO3溶液和石蕊试剂C.酸性KMnO4和溴水D.NaOH溶液和CuSO4溶液5.下列五种基团,—CH3、—OH、—CHO、—C6H5、—COOH,两两组成的物质中,能与NaOH反应的有机物有多少种()A.4种B.5种C.6种D.7种6.分子式为C8H16O2的有机物A,它能在酸性条件下水解生成B和C,且B在一定条件下能转化成C。
则有机物A的可能结构有()A.1种B.2种C.3种D.4种7.区别植物油和矿物油的正确方法是()A.加酸性高锰酸钾溶液,振荡B.加NaOH溶液,加热C.加新制氢氧化铜悬浊液,加热D.加Na2CO3溶液,加热8.某烃的衍生物分子式可写为(CH2)m(CO2)n(H2O)p。
广东省广州市2012-2013学年高一数学上学期期中考试数学试题新人教A版
广州市铁一中学2012-2013学年高一上学期期中考试数 学 试 卷全卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。
共150分,考试时间120分钟。
第Ⅰ卷(选择题 共50分)一、选择题:本大题共10小题,每小题5分,共50分.在每小题给出的四个选项中,只有一项是符合题目要求的.1. 已知A={0,1,2},B={0,1},则下列关系不正确的是( ) A . A ∩B=B B .∁A B ⊆B C .A ∪B ⊆A D .B ⊂≠ A2. 函数()()2lg 31f x x =++的定义域为( ) A .1,3⎛⎫-∞- ⎪⎝⎭ B .11,33⎛⎫- ⎪⎝⎭ C .1,13⎛⎫- ⎪⎝⎭ D .1,3⎛⎫-+∞ ⎪⎝⎭3. 下列四组函数,表示同一函数的是( )A .x x g x x f ==)( ,)(2 B .332)( ,2log )(x x g x f x == C .x x g x x f ==)( ,) ()(2 D .xxx g x x f 2)( ,)(==4.给定函数①12y x =,②12log (1)y x =+,③|1|y x =-,④12x y +=,其中在区间(0,1)上单调递减的函数序号是( )A. ①④B. ①②C. ②③D.③④ 5.由表格中的数据可以判定方程02e =--x x的一个零点所在的区间))(1,(N k k k ∈+,则kA .0B .1C .2D .36.下列幂函数中,定义域为R 且为偶函数的个数为( ) (1)2y x -= (2)y x = (3)13y x= (4)23y x=A .1个 B.2个 C.3个 D. 4个7.已知3.0log 2=a ,3.02=b ,2.03.0=c ,则c b a ,,三者的大小关系是( )A. c b a >>B. c a b >>C. a c b >>D. a b c >>8.已知()f x 为偶函数,在[0,)+∞上为增函数,若2(l g )(1)f o x f >,则x 的取值范围为( )A .(2,)+∞B .1(0,)(2,)2⋃+∞ C.1(,2)2D .(0,1)(2,)⋃+∞9.设函数22()2x x f x -++=,对于给定的正数K ,定义函数(),()(),()K f x f x Kf x K f x K ≤⎧=⎨>⎩若对于函数22()2x x f x -++=定义域内的任意 x ,恒有()()K f x f x =,则( )A .K 的最小值为1B . K 的最大值为1C .K 的最小值为22D . K 的最大值为2210.已知定义在[2,2]-上的函数)(x f y =和)(x g y =,其图象如下图所示:给出下列四个命题:①方程0)]([=x g f 有且仅有6个根 ②方程0)]([=x f g 有且仅有3个根 ③方程0)]([=x f f 有且仅有5个根 ④方程0)]([=x g g 有且仅有4个根 其中正确命题的序号( )A .①②③ B. ②③④ C. ①②④ D. ①③④第Ⅱ卷(非选择题 共100分)二、填空题:本大题共4小题,每小题5分,共20分.11.已知⎩⎨⎧>-≤+=0,20,1)(2x x x x x f ,则=))1((f f12. 2732+lg4+2lg5=__________13.已知实数0,0≥≥b a 且1=+b a ,则22)1()1(+++b a 的取值范围为A. ⎥⎦⎤⎢⎣⎡5,29B. ⎪⎭⎫⎢⎣⎡+∞,29C. ⎥⎦⎤⎢⎣⎡29,0 D. []5,014.定义在R 上的函数()f x ,如果存在函数()(,g x kx b k b =+为常数),使得()f x ≥()g x 对一切实数x 都成立,则称()g x 为()f x 的一个承托函数.现有如下命题: ①对给定的函数()f x ,其承托函数可能不存在,也可能无数个; ②()g x =2x 为函数()2xf x =的一个承托函数; ③定义域和值域都是R 的函数()f x 不存在承托函数;其中正确命题的序号是 .三、解答题:本大题共6个小题,共80分.解答应写出文字说明,证明过程或演算步骤.15.(本题满分12分)已知全集U=R ,{|()A x f x ==,2{|log ()1}B x x a =-<. (1)若a =1,求()U C A B ⋂. (2)若()U C A B ⋂=∅,求实数a 的取值范围. 16.(本题满分12分)已知函数()|1||1|()f x x x x R =-++∈ (1)证明:函数()f x 是偶函数;(2)利用绝对值及分段函数知识,将函数解 析式写成分段 函数的形式,然后画出函数图像,并写出函数的值域;(3)在同一坐标系中画出直线2y x =+,观察图像写出不等式()2f x x >+的解集.17. (本题满分14分)已知函数b a bx ax x f ,(1)(2++=为实数),x ∈R ,(1)若f (x )有一个零点为-1,且函数()f x 的值域为)0,+∞⎡⎣,求()f x 的解 析式;(2)在(1)的条件下,当kx x f x g x -=-∈)()(,]2,2[时是单调函数,求实数k 的取值范围; .18.(本小题满分14分)如图:A 、B 两城相距100 km ,某天燃气公司计划在两地之间建一天燃气站D 给A 、B 两城供气. 已知D 地距A 城x km ,为保证城市安全,天燃气站距两城市的距离均不得少于10km . 已知建设费用y (万元)与A 、B 两地的供气距离(km)的平方和成正比,当天燃气站D 距A 城的距离为40km 时, 建设费用为1300万元.(供气距离指天燃气站距到城市的距离)(1)把建设费用y (万元)表示成供气距离x (km)的函数,并求定义域;(2)天燃气供气站建在距A 城多远,才能使建设供气费用最小.,最小费用是多少?19.(本题满分14分)已知函数()242 1.xxf x a =⋅--(1)当1a =时,求函数()f x 在]0,3[-∈x 的值域; (2)若关于x 的方程0)(=x f 有解,求a 的取值范围BA(第18题图)20.(本题满分14分)对于在[],a b 上有意义的两个函数()f x 与()g x ,如果对任意的[,,]x a b ∈,均有|()()|1f x g x -≤,则称()f x 与()g x 在[],a b 上是接近的,否则称()f x 与()g x 在[],a b 上是非接近的.现在有两个函数()log (3)t f x x t =-与1()log ()(01)t g x t t x t=>≠-且,现给定区间[2,3]t t ++.(1)若12t =,判断()f x 与()g x 是否在给定区间上接近; (2)若()f x 与()g x 在给定区间[2,3]t t ++上都有意义,求t 的取值范围; (3)讨论()f x 与()g x 在给定区间[2,3]t t ++上是否是接近的.附加题:21. (本题满分20分)设x ∈N+时f(x)∈N+,对任何n ∈N+有f(n+1)>f(n)且f(f(n))=3n , (1).求f(1)(2) .求f(6)+f(7) (3) .求f(2012).广州市铁一中学2012-2013学年高一上学期期中考试数 学 试 卷答卷第II 卷(共100分)二、填空题:每小题5分,共20分11.________ 12.___________ 13.______________ 14.____________……………………………………… ―――――――――――――――三、解答题:本大题共5小题,共60分.解答必需写出必要的文字说明、推理过程或计算步骤.一、 选择题: 题号 1 2 3 4 5 6 7 8 9 10 答 案BCBCBACBCD二、 填空题11、 5 12、11 13、⎥⎦⎤⎢⎣⎡5,29 14、 ①三、解答题15. (本题满分12分)解:由已知得{|12}A x x x =≤≥或,{|2}B x a x a =<<+{|12}U C A x x ∴=<< …………4分(1)当a=1时,{|13}B x x =<<, (){|12}U C A B x x ∴=<<…………6分(2)若()U C A B ⋂=∅,则2a ≥或21a +≤,2a ∴≥或1a ≤.即a 的取值范围为(,1][2,)-∞+∞. …………12分16.(本题满分12分)解:(1)依题可得:)(x f 的定义域为R()|1||1||1||1|()f x x x x x f x -=--+-+=++-=∴()f x 是偶函数 ……………………4分(2)2(1)()2(11)2(1)xx f x x x x -<-⎧⎪=-≤≤⎨⎪>⎩由函数图象知,函数的值域为[2,)+∞ ……9分 (3由函数图象知,不等式的解集为{|02}x x x <>或………12分17. (本题满分14分)解:(1)由题意得:⎪⎩⎪⎨⎧-=-=+-1201a b b a 解得:⎩⎨⎧==21b a 所以:2()21f x x x =++ …………………7分(2)由(1)得1)2()(2+-+=x k x x g当[]2,2-∈x 时,因为)(x g 是单调函数 所以222222-≤--≥--k k 或 解得: 26-≤≥k k 或 …………………14分18、解:(1)设比例系数为k ,则])100([22x x k y -+=)9010(≤≤x . ………4分(不写定义域扣1分)又1300,40==y x , 所以)6040(130022+=k ,即41=k , …7分 所以 )5000100(21])100([41222+-=-+=x x x x y )9010(≤≤x . ……9分 (2)由于2500)50(21)5000100(2122+-=+-=x x x y , ………………12分 所以当x =50时,y 有最小值为1250万元. …………………13分所以当供气站建在距A 城50km, 电费用最小值1250万元. ……14分19.(本题满分14分)解:(1)当1=a 时,12)2(21242)(2--=--⋅=x x x x x f ,令]0,3[,2-∈=x t x ,则]1,81[∈t , 故]1,81[,89)41(21222∈--=--=t t t t y , 故值域为]0,89[- …………………6分(2)关于x 的方程012)2(22=--x x a 有解,等价于方程0122=--x ax 在),0(+∞上有解 :〗解法一:记12)(2--=x ax x g当0=a 时,解为01<-=x ,不成立 当0<a 时,开口向下,对称轴041<=ax ,过点)1,0(-,不成立 当0>a 时,开口向上,对称轴041>=ax ,过点)1,0(-,必有一个根为正 所以,0>a ……………14分解法二:方程0122=--x ax 可化为2211111()2228x a x x +==+- a ∴的范围即为函数21111()()228g x x =+-在(0,)+∞上的值域 所以,0>a …………14分20.(本小题满分14分)解:(1)当12t =时,1231()()log [()()]22f x g x x x -=--1221log [(1)]4x =-- 令1221()log [(1)]4h x x =--,当57[,]22x ∈时,12()[log 6,1]h x ∈- 即|()()|1f x g x -≥,()f x 与()g x 是否在给定区间上是非接近的. …………4分(2)由题意知,0t >且1t ≠,230t t +->,20t t +->01t ∴<< ……………7分(3)22|()()||log (43)|t f x g x x tx t -=-+ 假设()f x 与()g x 在给定区间[2,3]t t ++上是接近的,则有22|log (43)|1t x tx t -+≤221log (43)1t x tx t ∴-≤-+≤ …………(*)令G (x )=22log (43)t x tx t -+,由(2)知10<<t ;当10<<t 时,[2,3]t t ++在2x t =的右侧,即G (x )=22log (43)t x tx t -+,在[2,3]t t ++上为减函数,max ()log (44)t G x t ∴=-,min ()log (96)t G x t ∴=-所以由(*)式可得01log (44)1log (96)1t tt t t <<⎧⎪-≤⎨⎪-≥-⎩ ,解得0t <≤ 因此,当⎥⎦⎤ ⎝⎛-∈12579,0t 时,()f x 与()g x 在给定区间[2,3]t t ++上是接近的; 当⎪⎪⎭⎫ ⎝⎛-∈1,12579t 时,()f x 与()g x 在给定区间[2,3]t t ++上是非接近的. …14分21、 (本小题满分20分) 解:(1)∵f(f(n))=3n,∴f(f(1))=3, 且f(1)≠1 (若f(1)=1,则f(f(1))=f(1)=3,与f(1)=1矛盾) ∵f(x)∈N*∴f(1)≥2∵f(x)在大于0上是单调增函数∴f(2)≤f(f(1))=3f(1)=2,f(2)=3(2)因为 f(3)=f(f(2))=6 ,f(6)= f(f(3))=9, 且f(3)<f(4)<f(5)<f(6)所以f(4)=7,f(5)=8,所以f(4)+f(5)=7+8=15(3)f(9)=f(f(6))=18f(18)=f(f(9))=27---且f(k)=k+9......9≤k ≤18f(27)=f(f(18))=54f(54)=f(f(27))=81---且f(k)=k+27......27≤k ≤54f(81)=f(f(54))=162f(162)=f(f(81))=243---且f(k)=k+81......81≤k ≤162f(243)=f(f(162))=486f(486)=f(f(243))=729---且f(k)=k+243......243≤k ≤486f(729)=f(f(486))=1458f(1458)=f(f(729))=2187---且f(k)=k+729......729≤k ≤1458---所以 f(2012-729)=2012所以f(2012)=f(f(2012-729))=3(2012-729)=3849。
2023-2024学年广东省广州市铁一中学高二(上)期中数学试卷【答案版】
2023-2024学年广东省广州市铁一中学高二(上)期中数学试卷一、选择题:本题共8小题,每小题5分,共40分.在每小题给出的四个选项中,只有一个是符合题目要求的.1.已知集合A ={x|y =√1−2x},B ={x |y =ln (2x ﹣1)},则A ∩B 等于( ) A .{x|0≤x <12}B .{x|0<x ≤12}C .{x|0≤x ≤12}D .{x|0<x <12}2.已知x <y ,则下列不等式一定成立的是( ) A .1x >1yB .2﹣x <2﹣yC .lg (x 2+1)<lg (y 2+1)D .x 13<y 133.“方程x 29−m +y 2m−5=1的曲线是椭圆”的一个必要不充分条件是( ) A .“m =7” B .“7<m <9”C .“5<m <9”D .“5<m <9”且“m ≠7”4.已知圆C 1:x 2+y 2﹣4x +2ay +a 2+3=0和圆C 2:x 2+y 2+2x ﹣4ay +4a 2﹣1=0,则圆C 1与圆C 2的公切线的条数为( ) A .1B .2C .3D .45.果农采摘水果,采摘下来的水果会慢慢失去新鲜度.已知某种水果失去新鲜度h 与其采摘后时间t (天)满足的函数关系式为h =m •a t .若采摘后10天,这种水果失去的新鲜度为10%,采摘后20天,这种水果失去的新鲜度为20%.那么采摘下来的这种水果在多长时间后失去50%新鲜度( )(已知lg 2≈0.3,结果取整数) A .23天B .33天C .43天D .50天6.已知sinα+cos(π6−α)=√33,则cos(2α+π3)=( )A .−79B .79C .−13D .137.已知向量a →=(2,0),b →=(sin α,√32),若b →在a →上的投影向量为c →=(12,0),则向量a →与b →的夹角为( )A .π6B .π4C .π3D .2π38.如图,水平放置的正四棱台玻璃容器的高为32cm ,两底面对角线EG 、E 1G 1的长分别为14cm 、62cm ,水深为12cm .则玻璃容器里面水的体积是( )A .3336cm 3B .3337cm 3C .3338cm 3D .3339cm 3二、选择题:本题共4小题,每小题5份,共20分.在每小题给出的选项中,有多项符合题目要求。
2012.11广铁一中九上英语期中考
广州铁一中学初三期中试卷二.语言知识与运用(共三节,满分75分)第一节单项选择(共15小题;每小题1分,满分15分)16.There is _______ “f “ in _______ word “frog”.A.an,aB.an,theC.a,aD.a,the17.There are________people protesting on the street now.A.three thousandB.three thousand ofC.three thousandsD.three thousands of18.Tom didn’t come to school because he was ill ______bed.A.upB.atC.onD.in19.Teachers are worried about there are ________around.A.too many fast food restaurantsB.too many fast food restaurantC.many too fast food restaurantsD.much too fast food restaurants20.There are eight foreign students in our school .One is from America,________is from England and all ______are from China.A.another ,the otherB.one,othersC.another,the othersD.one another21.It is brave _______with the robbers.A.for him to fightB.of him to fightC.for him fightingD.of him fighting22.------Where is Tom? Ican’t f ind him. -----He _______the US for three month.A.went toB.has been toC.has gone toD.has been in23.-----Could you tell me _________?------Yes,go along the street and turn left at the second crossing.You’ll see it on your right.A.where is No.6 middle schoolB.when I can get to No.6middle schoolC.how far is No.6 middle schoolD.how I can get to No.6 middle school24.The river smells terrible .People must ________dirty things in it.A. Be stopped to throwB.be stopped from throwingC. Stop to throwD.stop from throwing25.Hurry up, _______you’ll be late for school.A.butB.andC.soD.or26.-------I saw Mr Smith in the office at ten yesterday morning.--------That’s possible.He________ an English party with us.A.hasB.hadC.was havingD.has had27.What______!You’d better not go out.A.a bad weatherB.a fine dayC.fine weatherD.bad weather28.It is wasterful _______paper and metal. We need to save energy.A.throw awayB.throwingC.thrown awayD.to throw away29.He became a super star _________.A.in his thirtyB.at his thirtyC.in his thirtiesD.at his thirties30.-----What a heavy rain! Will it last long?------_______.We’re getting into the rainy season now.A.Of course notB.I’m afraid soC.That’s impossibleD.I’m afraid not 第二节语法填空(共10小题,每小题1分,满分10分)People living in different countries made different kinds of words.today there __31___about fifteen hundred dictionaries in the world.Each contains thousands of words.A very large dictionary, for example,_32___ four or five hundred thousand words.__33____we do not need all these._34____short stories,we need to know only about two thousand words.__35___we leave school, we will learn only one thousand or more. The words _36_______ we know are called our vocabulary.we should try to make our vocabulary __37_____.Read as many books as we can.there are a lot of books __38______ in easy English.We will enjoy_39_____.When we meet a new word, we can look it __40______ in the dictionary. Our dictionary is our most useful book.31. A . is B. are C. have D. has32. A . contain B. containing C. contained D.contains33. A. and B.so C. or D.but34. A .To read B. reading C. reads D.read35. A. After B. When C. Before D.While36.A . In which B. / C. who D.what37.A . bigger B.big C. biggest D.the biggest38.A. writing B.written C.wrote D.writes39.A it. B. these C. them D.that40.A. through B. up C. for D.down第三节完形填空(共10小题,每小题1分,满分10分)Every year the U.S. Receives tens of inventions._41__ these only a few become __42_____ and make a lot of money.There are thousands of inventions that nobody wants.Here are some of those.In 1879,somebody invented a new type of “fire escape”(逃亡办法). This was a hat which had a parachute on top.you concerned the hat with a trap under your chin.With this special hat on you could_ 43_____ from a building on fire and flew safe down.With it there was also a special pair of shoes,so the person __44______ safety.There was a special alarm clock for people who had problems_45______ in the morning .This clock had six pieces of wood that __46______ above your head.At the right time the pieces of wood dropped down on you when you were sleeping.They hit you but did not __47_____ you.Another invention was the bicycle seat to stop a thief.This seat had needles(针)in it.When the owner _48______ the bicycle the needles were _49______ .But when the bicycle was not in use, the needles were up.So a thief who jumped on the bike got a nice_50_____!41. A. Of B. For C. To D. With42. A. useful B. complete C. popular D. public43. A. jump B. watch C. explore D. practice44. A. fell B. landed C. stood D. ran45. A. brushing teeth B. putting on clothes C. waking up D. going to sleep46. A. stopped B. circled C. appeared D. hung47. A. reach B. knock C. hurt D. cut48. A. rode B. repaired C. locked D. owned49. A. out B. down C. short D. low50. A. chance B. danger C. surprise D. joke第四节阅读理解(共20小题;第小题2分,满分40分)阅读下面短文,从每题所给的A、B、C和D项中,选出最佳选项,并在答题卡上将该项涂黑。
广东省广铁一中高一数学上学期期中试题(无答案)新人教
广铁一中学高一数学2013学年第一学期期中考试第I 卷(共 50 分)一、选择题(本大题共10小题, 每小题5分, 满分50分. 在每小题给出的四个选项中, 只有一项是符合题目要求的.)1. 如果{}5,4,3,2,1=S ,{}4,3,1=M ,{}5,4,2=N ,那么()()N C M C S S ⋂等于( ) A.φ B. {}3,1 C. {}4 D. {}5,2 2.函数()2log (1)f x x =+的定义域为 ( )A .[)1,3-B .()1,3-C .(1,3]-D .[]1,3-3、已知()()2,0,2,0,30,0.x x f x x f f x ⎧>⎪==-⎡⎤⎨⎣⎦⎪<⎩那么的值等于( ) A .0 B .2 C .4 D .94.下列四组函数,表示同一函数的是 ( )A .2)(x x f =,x x g =)( B .x x f =)(,x x x g 2)(= C .2ln )(x x f =,x x g ln 2)(= D .x a a x f log )(=a (>0)1,≠a ,33)(x x g =5、设偶函数f(x)的定义域为R ,当x ),0[+∞∈时f(x)是增函数,则f(-2),f(π),f(-3)的大小关系是( )A 、f(π)>f(-3)>f(-2)B 、f(π)>f(-2)>f(-3)C 、f(π)<f(-3)<f(-2)D 、f(π)<f(-2)<f(-3)6.若函数)(x f y =在区间[a ,b ]上的图象为连续不断的一条曲线,则下列说法正确的是( )A .若0)()(>b f a f ,不存在实数),(b a c ∈使得0)(=c f ;B .若0)()(<b f a f ,存在且只存在一个实数),(b a c ∈使得0)(=c f ;C .若0)()(>b f a f ,有可能存在实数),(b a c ∈使得0)(=c f ;D .若0)()(<b f a f ,有可能不存在实数),(b a c ∈使得0)(=c f ;7. 已知031log 31log >>b a ,则a 、b 之间的大小关系是 ( ) A .a b <<1 B .b a <<1 C .10<<<b a D .10<<<a b8、下列函数图象中,函数,与函数的图象只能是( ) y y y yO x O x O x O xA B C D 11119. 对于函数x x f lg )(=定义域中任意)(,2121x x x x ≠有如下结论:①)()()(2121x f x f x x f +=+; ②)()()(2121x f x f x x f +=⋅;③0)()(2121>--x x x f x f ;④)2(21x x f +<2)()(21x f x f +.上述结论中正确结论的序号是 ( )A.②B. ②③C. ②③④D. ①②③④ 10. 若函数m y x +=-|1|)21(的图象与x 轴有公共点,则m 的取值范围是( )A .m≤-1B .-1≤m<0C .m≥1D .0<m≤1第II 卷(共100分) 二、填空题(本大题共4小题,每小题5分,满分20分.)11、若幂函数)(x f y =的图象经过点(9,13), 则)25(f 的值是_______ 12、已知不等式062<-+px x 的解集为{|32}x x -<<,则p = .13、方程2)21(2=+x x 的解的个数是 个.14、规定记号“∆”表示一种运算,+∈++=∆R b a b a b a b a 、,.若31=∆k ,则函数()x k x f ∆=的值域是__________________.三、解答题(本题共6小题,共80分)15.(本题满分12分)(1)计算:--121445.00)2()49()53(e -++-; (2)已知2a = 5b = 100,求 1a + 1b 的值。
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广州市铁一中学2012学年第一学期期中试题初二年级英语试题笔试部分一、单项选择。
(满分20分)( )26. This beautiful house _______ the rich man!A.belongs toB.is belong toC.am belong toD. belong to( )27. _______ more about World WarⅡ,he went to the library to borrow some books on it.A.KnowingB. KnewC. To knowD. Knows( )28. We will have a holiday _______.A. in two day’s timeB.in two days’ timeC. after two day’s timeD. after two days’ time( )29. Judy writes _______ than his classmates.A.as carefulB. more carefullyC. much carefullyD. more careful( )30. The wine _______ grapes.A.are made inB.is made ofC.is make fromD.is made from( )31. The naughty boy admitted _______ the window.A.brokeB. breakC. breakingD.to break( )32. The man cannot work and he _______ his family.A.is useful forB.is helpful toC.is essential forD.is dependent on ( )33. _______ useful _______ us to learn a foreign language.A.This; ofB. That’s; forC. It’s; forD. Its; of( )34. Kitty made her dog _______ up the ball for her.A.pickB.to pickC. pickingD. picked( )35. —________?—No, thanks. I can do it by myself.A. Can you do itB. Do you need any helpC. What can you doD. Do you think you can do it( )36. ________you ever ________London?A.Have, go toB. Did, go toC. Have, been toD. Have, gone to ( )37. He can ________ go out because it is raining_________.A.hard; hardB. hardly; hardlyC. hardly; hardD. hard; hardly( )38. ________it is fishing by the river.A.How a funB. How funC. What a funD. What fun( )39. The problem was _______ difficult _______ few students in my class could work it out.A.too; toB. so; thatC. too; thatD. enough; to( )40. The accident happened ________ a winter night.A.onB.atC.inD.to( )41. —May I have a look at your plan?—Sorry. We haven’t finished yet. We are now still______.A. talking it withB. talking with itC. talking over itD. talking it over( )43. He made money ________.A.by writingB.in writingC. with writingD. on writing( )43. The teacher suggests ________ the mountains in the summer holidays.A. go and climbB. goes and climbsC. to go and climbD. going and climbing ( )44. He needs your help. You ________ and give him a hand.A.should to stayB. shouldn’t stayC. ought not stayD..ought to stay( )45. They’re going to build a school for _______ and _____in the countryside.A.deaf, blindB. the deaf, blindC. the deaf, the blindD. deaf, the blind二、语法选择。
(10*1=10分)阅读下面短文,选出最佳选项。
Mr. King was a strange man. He liked travelling and animals very much. He founded his own empire(帝国).Mr. King lived with six hundred wild animals on the Greek Island of Kyklos. After he left school,he___46___all over the world collecting animals for his own zoo. He hoped___47___two examples of every kind of animal on his island. ____48___he was afraid that people would find him someday.In his spare time, he ___49____books about his travels, and about his animals ____50___he collected the money from the books and helped to pay for the food___51___ these animals eat.One day, when Mr. King was out___52____drinking water, he found oil. He needed money for his travels and for___53____zoo, and a little oil would buy enough water for what he needed all his life, but he know that if he told anybody else about it, it would be___54____end of his zoo and his life's work.So he decided___55___anyone about what he had found, because oil and water couldn't mix. ( )46.A. has traveled B. had traveled C. traveled D. travels( )47.A. to collect B. collecting C. collects D. collect( )48.A. or B. and C. but D. so( )49.A.write B. writes C. wrote D. is writing( )50.A. so that B. and that C. as to D. that( )51.A. what B. who C. when D. which( )52.A. looks forward to B. to look atC. looking forD. looked after( )53.A. its B. his C. her D. their( )54.A. a B. an C. the D. 不填( )55.A. to not tell B. to tell not C. not telling D. not to tell三、完形填空。
(10*1=10分)Music and BehaviorWhere did you go yesterday? Did you hear music at any of those places? Today most stores and restaurants play music. You might __56___ hear music in an office or on a farm.Scientists believe that music changes the__57___ people behave(行为). According to some scientists, the sound of western classical music makes people become more generous. When classical music is played, people spend more money. When a restaurant plays modern music, people spend less money. With light music, people spend even ___58___.Scientists also ___59___ that loud, fast music makes people eat faster. In fact, the louder the music is, __60___ people eat. Some restaurants play fast music during their ___61___ hours. This gets people to eat faster and leave quickly. Restaurants ___62___make more money this way.Some scientists think that music makes you think and learn better. They say that music helps students to be more active. It is true that people learn better when they are __63__. And___64___ music can help you relax.The __65___ time you hear music somewhere, be careful. It might change your behavior. ( )56. A. already B. hardly C. even D. never( )57. A. idea B. way C. place D. time( )58. A. little B. less C. least D. the least( )59. A. believe in B. work out C. call for D. find out( )60. A. more fast B. more faster C. the faster D the more fast ( )61. A. free B. busy C. happy D. poor( )62. A. can B. must C. should D. ought to( )63. A. relax B. relaxing C. relaxed D. relaxation( )64. A. To hear B. Hearing C. To listen D. Listening to ( )65. A. first B. second C. next D. last四、阅读理解。