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北京市西城区2009届高三第二次模拟考试数学文科试题 2009.5

北京市西城区2009届高三第二次模拟考试数学文科试题 2009.5

题号分数一二三总分151617181920北京市西城区 2009年抽样测试高三数学试卷(文科)2009.5本试卷分第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40分)一、本大题共 8 小题,每小题 5 分,共 40 分. 在每小题列出的四个选项中,选出符合题目要求的一项.1. 已知集合A、B满足,那么下列各式中一定成立的是()A. B. B AC. D.2. 函数的反函数是()A. B.C. D.3. 设向量a=(1, x-1),b=(x+1,3),则“x=2”是“a//b”的()A. 充分但不必要条件B. 必要但不充分条件C. 充要条件D. 既不充分也不必要条件4. 抛物线的顶点在坐标原点,焦点是椭圆的一个焦点,则此抛物线的焦点到其准线的距离等于()A. 8B. 6C. 4D. 25.已知一个平面,那么对于空间内的任意一条直线a,在平面内一定存在一条直线b,使得a与b()A. 平行B. 相交C. 异面D. 垂直6.数列对任意满足,且,则等于( )A.24B. 27C. 30D. 327.某校要从高三的六个班中选出8名同学参加市中学生英语口语演讲,每班至少选1人,则这8个名额的分配方案共有()A.21B. 27C. 31D. 368.根据程序设定,机器人在平面上能完成下列动作:先从原点O沿正东偏北()方向行走一段时间后,再向正北方向行走一段时间,但的大小以及何时改变方向不定. 如右图. 假定机器人行走速度为10米/分钟,设机器人行走2分钟时的可能落点区域为S,则S可以用不等式组表示为()A. B.O x(m)yP(x, y)东北.C. D.北京市西城区 2009年抽样测试高三数学试卷(文科)2009.5第Ⅱ卷( 共110分)二、填空题:本大题共 6 小题,每小题 5 分,共 30 分. 把答案填在题中横线上 .9. 为了了解在一个水库中养殖的鱼的有关情况,从这个水库的不同位置捕捞出n条鱼. 将这n个样本分成若干组,若某组的频数和频率分别为30和0.25,则n=___________.10. 设,则的内角A=_________.11. 若的展开式中常数项为672,则a=___________.12. 设函数,则=__________;若,则x的取值范围是___________.13. 已知一个球的表面积为,球面上有两点P、Q,且球心O到直线PQ的距离为,那么此球的半径r=___________;P、Q两点间的球面距离为__________.14. 已知三个函数:; ; .其中满足性质:“对于任意R,若,则有成立”的函数是______________.(写出全部正确结论的序号)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)甲,乙两人射击,每次射击击中目标的概率分别是. 现两人玩射击游戏,规则如下:若某人某次射击击中目标,则由他继续射击,否则由对方接替射击. 甲、乙两人共射击3次,且第一次由甲开始射击. 假设每人每次射击击中目标与否均互不影响.(Ⅰ) 求3次射击的人依次是甲、甲、乙,且乙射击未击中目标的概率;(Ⅱ) 求乙至少有1次射击击中目标的概率.16.(本小题满分12分)已知函数.(Ⅰ)求的值域和最小正周期;(Ⅱ)设,且,求的值.17.(本小题满分14分)如图,在直三棱柱中,,D、E分别是AA1、B1C的中点.C BC1 B1AA1DE(Ⅰ) 求证:平面;(Ⅱ) 求异面直线与所成角的大小;(Ⅲ) 求二面角C-B1D-B的大小.18.(本小题满分14分)已知函数R).(Ⅰ) 若a=3,试确定函数的单调区间;(Ⅱ) 若函数在其图象上任意一点处切线的斜率都小于2a2,求a的取值范围.19.(本小题满分14分)已知的顶点A在射线上, A, B两点关于x轴对称,O为坐标原点,且线段AB上有一点M满足. 当点A在l1上移动时,记点M的轨迹为W.(Ⅰ) 求轨迹W的方程;(Ⅱ) 设N(2,0),过N的直线l与W相交于P、Q两点. 求证:不存在直线l,使得.20.(本小题满分14分)已知f是直角坐标平面xOy到自身的一个映射,点在映射f下的象为点,记作.设,,. 如果存在一个圆,使所有的点都在这个圆内或圆上,那么称这个圆为点的一个收敛圆. 特别地,当时,则称点为映射f下的不动点.若点在映射f下的象为点.(Ⅰ) 求映射f下不动点的坐标;(Ⅱ) 若的坐标为(2,2),求证:点存在一个半径为2的收敛圆.北京市西城区 2009年抽样测试参考答案高三数学试卷(文科)2009.5题号12345678答案C D A C D B A B一、选择题:本大题共 8 小题,每小题 5 分,共 40 分.二、填空题:本大题共 6 小题,每小题 5 分,共 30 分.9. 120 10. 11. 2 12. , 13. 6, 14.注:两空的题目,第一个空2分,第二个空3分.三、解答题:本大题共 6 小题,共 80 分.15.(本小题满分12分)(Ⅰ)解:记“3次射击的人依次是甲、甲、乙,且乙射击未击中目标” 为事件A. -----------1分由题意,得事件A的概率; ---------------------------5分(Ⅱ)解:记“乙至少有1次射击击中目标”为事件B, ---------------------------6分事件B包含以下两个互斥事件:事件三次射击的人依次是甲、甲、乙,且乙击中目标,其概率为;---------------------------8分事件三次射击的人依次是甲、乙、乙,其概率为. --------------10分所以事件B的概率为.所以事件“乙至少有1次射击击中目标”的概率为. ----------------------12分16.(本小题满分12分)(Ⅰ)解:---------------------------2分, ---------------------------4分因为,所以,即函数的值域为. ---------------------------6分函数的最小正周期为. ---------------------------8分(Ⅱ)解:由(Ⅰ)得,所以, ----------------------------9分因为,所以, ----------------------------10分所以,所以 . ---------------------------12分17.(本小题满分14分)方法一:(Ⅰ)证明:如图,设G为BC的中点,连接EG,AG,C G BC1 B1AA1DEF在中,,,且,又,且,,四边形为平行四边形,, ---------------------------2分又平面ABC,平面ABC,平面. ---------------------------4分(Ⅱ)解:如图,设F为BB1的中点,连接AF,CF,直三棱柱,且D是AA1的中点,,为异面直线与所成的角或其补角. ---------------------------7分在Rt中,,AB=1,BF=1,,同理,在中,,在中,,.异面直线与所成的角为. ---------------------------9分(Ⅲ)解:直三棱柱,,又,平面. ---------------------------10分如图,连接BD,在中,,,即,是CD在平面内的射影,,为二面角C-B1D-B的平面角. ---------------------------12分在中, , BC=1, ,,二面角C-B1D-B的大小为. ---------------------------14分方法二:(Ⅰ)同方法一. ---------------------------4分(Ⅱ)如图,以B为原点,BC、BA、BB1分别为x、y、z轴,建立空间直角坐标系O-xyz,则,, ---------------------------6分,异面直线与所成的角为. ---------------------------9分(Ⅲ)解:直三棱柱,,C BC1 B1AA1DxyzEG又,平面. ---------------------------10分如图,连接BD,在中,,,即,是CD在平面内的射影,,为二面角C-B1D-B的平面角. ----------------------------12分,,二面角C-B1D-B的大小为. -----------------------------14分18.(本小题满分14分)(Ⅰ)解:因为,所以, ---------------------------2分由,解得,由,解得或, ---------------------------4分所以函数的单调增区间为,减区间为,.-----------------6分(Ⅱ)解:因为,由题意,得对任意R成立, ---------------------------8分即对任意R成立,设,所以,所以当时,有最大值1, ---------------------------10分因为对任意R,成立,所以,解得或,所以,实数的取值范围为或 . ---------------------------14分19.(本小题满分14分)(Ⅰ)解:因为A, B两点关于x轴对称,所以AB边所在直线与y轴平行.设M(x, y),由题意,得, ----------------------------2分所以,因为,所以,即, ----------------------------5分所以点M的轨迹W的方程为. -----------------------------6分(Ⅱ)证明:设或,,当直线时:由题意,知点P,Q的坐标是方程组的解,消去y得,所以,且,, ------------------------8分因为直线l与双曲线的右支(即W)相交两点P、Q,所以,即. -------------9分因为,所以,,, -------------------------11分要使,则必须有,解得,代入不符合. -----12分所以不存在l,使得.当直线时,P(2, 3),,,不符合题意.综上:不存在直线l使得. --------------------------14分20.(本小题满分14分)(Ⅰ)解:设不动点的坐标为,由题意,得,解得,所以此映射f下不动点为. ---------------------------4分(Ⅱ)证明:由,得, ---------------------------6分所以,因为,所以,所以, ---------------------------8分由等比数列定义,得数列N*)是公比为-1,首项为的等比数列,所以,则. ---------------------------10分同理 .所以 . ---------------------------11分设,则, --------------------------12分因为,所以,所以.故所有的点都在以为圆心,2为半径的圆内,即点存在一个半径为2的收敛圆. --------------------------14分。

北京市09年五校联考期末模块考试高一年级语文科试题及参考答案

北京市09年五校联考期末模块考试高一年级语文科试题及参考答案

09 年五校联考期末模块考试高一年级语文科试题2009 年1 月试题说明:本试卷分为第Ⅰ卷和第Ⅱ卷两部分。

共150 分,考试时间150 分钟。

注意事项:1.答卷前,考生务必用黑色字迹的钢笔或签字笔将自己的姓名和考生号填写在答题卡上。

2.选择题每小题选出答案后,用2B铅笔把答题卡上对应题目的答案标号涂黑;如需改动,用橡皮擦干净后,再选涂其他答案;不能答在试卷上。

3.非选择题必须用黑色字迹钢笔或签字笔作答,答案必须写在答卷各题目指定区域内;如需改动,先划掉原来的答案,然后再写上新的答案;不准使用铅笔和涂改液。

不按以上要求作答,答案无效。

第Ⅰ卷(共57 分)一、本大题 3 小题,每小题 3 分,共9 分。

1.下列加点字读音错.误.的一项(3 分)A.惦.(diàn)念B.舂.(chōnɡ)粮鸟窠.(kē)兽窟偃仰啸.(xiāo)歌长篙.(ɡāo)蓬蒿.(hāo)逦.(lǐ)迤一恸.(dònɡ)C.匏.(páo)尊百舸.(ɡě)争流锱.(zī)铢眼眸.(móu)D.笙.(shēnɡ)箫酾.(shī)酒临江潜蛟.(jiāo)颓圮.(pǐ)2.下列各句中,加点成语使用恰当的一句是(3 分)A.读研究生那几年,欧阳立都身在国外,现在终于学成归国了,也终于与相恋多年的女友破.镜.重.圆.了。

B.我们教育工作者应该懂得:发展学生的智力,必须与培养学生的非智力因素结合起来,因为二者是休.戚.相.关.,紧密相连的。

C.听到门铃声响,八岁的他抢着跑去开门迎接客人,还彬.彬.有.礼.地做出“请”的手势,逗得大家都笑了。

D.为了纪念“邓小平诞辰一百周年”,新落成的“小平故居”于“十·一”向游人开放,前往参观的人不.绝.如.缕.。

3.下列各句中没有语病的一句是(3 分)A.现在,我又看到了那阔别多年的乡亲,那我从小就住惯了的山区所特有的用石头和茅草搭成的小屋,那崎岖的街道,那熟悉的可爱的乡音。

09年高考模拟试题北京市西城区2009届高三5月抽样测试1150

09年高考模拟试题北京市西城区2009届高三5月抽样测试1150

09年高考模拟试题北京市西城区2009届高三5月抽样测试测试题 2019.91,下图表示的是某物质所发生的A.取代反应 B.水解反应 C.中和反应 D.电离过程2,下列叙述正确的是A.直径介于1 nm ~ 100 nm之间的微粒称为胶体B.电泳现象可证明胶体带电C.用盐析法可分离皂化反应后所得的产物D.用含1 mol FeCl3的溶液可制得6.02×1023个Fe(OH)3胶体粒子3,将液体Y滴加到盛有固体X的试管中,并在试管口对生成的气体进行检验。

下表中固体X、液体Y及检测方法对应关系错误的是S O、Al3+和X四种离子以物质的量之比2:4:1:1大量共存于同一4,Fe3+、2-4溶液中,X 可能是A .Na +B .OH -C .2-3CO D .Cl - 5,X 、Y 、Z 、W 四种短周期元素在周期表中相对位置如表所示,Y 、Z 质子数之和为21,下列说法中不正确的是A .X 、Y 、Z 、W 均为非金属元素B .X 、Y 、W 的氢化物中,Y 的氢化物沸点最高C .Z 的阳离子与Y 的阴离子电子层结构相同D .W 元素的简单离子半径大于Z 元素的简单离子半径6,某新型可充电电池,能长时间保持稳定的放电电压。

该电池的总反应为:A .放电时负极反应为:Zn-2e -+2OH -=Zn(OH)2B .放电时正极反应为:2-4FeO +4H 2O+3e -=Fe(OH)3+5OH - C .放电时每转移3 mol 电子,正极有1 molK 2FeO 4被氧化 D .充电时阳极附近溶液的碱性减弱7,一定温度下,1 molX 和n molY 在容积为2 L 的密闭容器中发生如下反应:X(g)+Y(g) Z(g)+M(s),5 min 后达到平衡,此时生成a molZ 。

下列说法正确的是A.向平衡后的体系中加入1 molM,平衡向逆反应方向移动B.用X表示此反应的反应速率是(0.1-0.1a) mol•(L•min)-1C.向上述平衡体系中再充入1 molX,U (正)增大,U (逆)减小,平衡正向移动D.当混合气体的质量不再发生变化时,说明反应达到平衡状态8,分子式为C8H8O3的芳香族化合物有多种不同的结构,这些物质在食品、化妆品等行业有广泛用途。

自主招生考试试题——北京大学(2009年)

自主招生考试试题——北京大学(2009年)

2009年北京大学保送生考试试题(P龙独家回忆)鏖战两个月,终于等到了今天……我把我能回忆起的试题发到这里给有志于参加北大保送的学弟学妹们看看吧~就当我为贴吧做点贡献~我一个多小时的心血啊~手好痛……语文一、举出两个被人们曲解了意思的成语,并学着曲解其意思。

二、修改病句:(1)我们都有一个家,名字叫中国。

(2)素胚勾勒出青花笔锋浓转淡三、对对联:上联——博雅塔前人博雅对出下联四、翻译文言文:给出一大段不加标点的文言文,要求通篇翻译。

具体内容肯定记不清了,大概是讲做人不能太高调吧!五、现代文阅读:鲁迅的《求乞者》我顺着剥落的高墙走路,踏着松的灰土。

另外有几个人,各自走路。

微风起来,露在墙头的高树的枝条带着还未干枯的叶子在我头上摇动。

微风起来,四面都是灰土。

一个孩子向我求乞,也穿着夹衣,也不见得悲戚,而拦着磕头,追着哀呼。

我厌恶他的声调,态度。

我憎恶他并不悲哀,近于儿戏;我烦厌他这追着哀呼。

我走路。

另外有几个人各自走路。

微风起来,四面都是灰土。

一个孩子向我求乞,也穿着夹衣,也不见得悲戚,但是哑的,摊开手,装着手势。

我就憎恶他这手势。

而且,他或者并不哑,这不过是一种求乞的法子。

我不布施,我无布施心,我但居布施者之上,给与烦腻,疑心,憎恶。

我顺着倒败的泥墙走路,断砖叠在墙缺口,墙里面没有什么。

微风起来,送秋寒穿透我的夹衣;四面都是灰土。

我想着我将用什么方法求乞:发声,用怎样声调?装哑,用怎样手势?……另外有几个人各自走路。

我将得不到布施,得不到布施心;我将得到自居于布施之上者的烦腻,疑心,憎恶。

我将用无所为和沉默求乞……我至少将得到虚无。

微风起来,四面都是灰土。

另外有几个人各自走路。

灰土,灰土,……………………灰土……1、“高墙”、“灰土”、“各自走路的人”各象征什么?2、“乞求”和“布施”个象征什么?这象征着人与人之间什么样的关系?3、前面一个问记不清了。

这篇文章体现了鲁迅什么样的世界观和思想命题?4、评价本文的艺术特点六、翻译:吴人之妇有绮其衣者衣数十袭届时而易之而特居于盗乡盗涎而妇弗觉犹日炫其华绣于丛莽之下盗遂杀而取之盗不足论而吾甚怪此妇知绮其衣而不知所以置其身夫使托身于荐绅之家健者门焉严扃深居盗乌得取唯其濒盗居而复炫其装此其所以死耳天下有才之士不犹吴妇之绮其衣乎托非其人则与盗邻盗贪利而耆杀故炫能于乱邦匪有全者杜袭喻繁钦曰子若见能不已非吾徒也钦卒用其言以免于刘表之祸呜呼袭可谓善藏矣钦亦可谓善听矣不尔吾未见其不为吴妇也七、作文。

2009年北京大学自主招生考试数学试题及解答

2009年北京大学自主招生考试数学试题及解答

2009年北京大学自主招生考试数学试题第一题:已知圆的内接四边形ABCD,其中AB=1,BC=2,CD=3,DA=4。

求圆的半径。

第二题:已知一无穷等差数列中有3项:13,25,41,求证:2009为数列中的一项。

第三题:是否存在实数x,使tanx+3与cotx+3为有理数?第四题:已知对任意x均有acosx+bcos2x>=-1恒成立,求a+b的最大值第五题:某次考试共有333名学生做对了1000道题。

做对3道及以下为不及格,6道及以上为优秀,问不及格和优秀的人数哪个多?2009年北京大学自主招生考试数学试题参考解答若a+b非零,除过来就矛盾了。

所以必有a+b=0,此时ab+2也是0.显然与a,b是有理数矛盾。

第四题:acosx+bcos2x>=-1b=0的时候可知得有|a|≤1此时a+b≤1.下面考虑b不等于0的情况。

代入+1和-1后得出的式子可以化成|a|≤b+1.....(1)(必有b≥-1)对称轴的位置是x=-a/4b.当对称轴在[-1,1]外的时候那么1≤|-a/4b|≤(b+1)/4|b|.分类讨论后就可以得出b≤1/3此时a+b≤b+1+b≤5/3.若对称轴在[-1,1]内,则可得a^2≤8(b-b^2) (2)这里注意到(b+1)^2-8(b-b^2)=(3b-1)^2≥0.故只需要(2)式成立,就必有(1)式也成立。

此时用柯西不等式(a+b-1/2)^2≤(a^2+8(b-1/2)^2)(1+1/8)≤9/4那么就有了a+b≤2.等号成立的充要条件是a=4/3,b=2/3,易验证这是成立的.比较三种情况,显然2是a+b的最大值第五题:设优秀有a人,及格b人,不及格c人。

则a+b+c=333 ①6a+4b+0c≤1000(这里都取各层次里的最少人,故用小于等于)即6a+4b≤1000即3a+2b≤500由①得2a+2b=666-2c即a+666-2c≤500即a+166≤2c若a≥167则这167人至少共解出167*6=1002道题,矛盾故a≤166故a+166≤166+166≤2c即c≥166所以c≥166≥a即不及格的人数大于等于优秀的人数。

北京大学2009年数学分析试题及解答

北京大学2009年数学分析试题及解答

因此 又因为 故
∫A
∫A
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A
A f (x)
4
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1
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A→+∞ A
2
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A→+∞
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注 此题与北京大学 2011 年数学分析第 9 题本质上相同.
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hn = c − an > 0, F (c − hn) > m, 同时 F (c + hn) ⩽ m, 于是 F (c + hn) − F (c − hn) < 0, 故 D+F (c) ⩽ 0.
3
下面来证明原命题.
∀ε > 0, F (x) = f (x)+εx 在 (a, b) 上应该单调不减. 事实上, 若前一句话不成立, 则 ∃x1, x2 ∈ (a, b), x1 < x2, 但 F (x1) > F (x2). 由上面证得的引理, ∃ξ ∈ (x1, x2), 使得 D+F (ξ) ⩽ 0. 而 D+F (ξ) = D+f (ξ) + ε > 0, 矛 盾.

5.2009年普通高等学校招生全国统一考试理科综合能力测试(北京卷)

5.2009年普通高等学校招生全国统一考试理科综合能力测试(北京卷)

2009年普通高等学校招生全国统一考试理科综合能力测试(北京卷)本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,第Ⅰ卷1至4页,第Ⅱ卷5至13页,共300分。

考试时间150分钟。

考试结束后,将本试卷和答题卡一并交回。

注意事项:1.考生务必将答案答在答题卡上,在试卷上作答无效。

2.答题前考生务必用黑色字迹的签字笔在答题卡上填写姓名、准考证号,然后再用2B 铅笔将与准考证号对应的信息点涂黑。

3.答题卡上第Ⅰ卷必须用2B铅笔作答,将选中项涂满涂黑,黑度以盖住框内字母为准,修改时用橡皮擦除干净。

第Ⅱ卷必须用黑色字迹的签字笔按照题号顺序在各题目的答题区域内作答,未在对应的答题区域内作答或超出答题区域作答的均不得分。

以下数据可供解题时参考:可能用到的相对原子质量:H 1 C 12 N 14 O 16 F 19Na 23 Al 27 Si 28 P 31 S 32第Ⅰ卷(选择题共120分)本卷共20小题,每小题6分,共120分。

在每小题列出的四个选项中,选出符合题目要求的一项。

1.在植物细胞中,吲哚乙酸主要由色氨酸经一系列酶催化生成。

下列相关叙述正确..的是A.吲哚乙酸可在胚芽鞘中大量合成B.色氨酸至少含有一个氨基和一个羧基C.吲哚乙酸是一种具有调节作用的蛋白质D.过量的色氨酸可抑制吲哚乙酸的合成2.细胞膜在细胞的生命活动中具有重要作用。

下列相关叙述不正确...的是A.细胞膜的糖被在细胞间具有识别作用B.细胞膜对膜两侧物质的进出具有选择性C.细胞膜内外两侧结合的蛋白质种类有差异D.载体蛋白是镶在细胞膜内外表面的蛋白质3.真核生物进行有性生殖时,通过减数分裂和随机受精使后代A .增加发生基因突变的概率B .继承双亲全部的遗传性状C .从双亲各获得一半的DNAD .产生不同于双亲的基因组合4.小麦和玉米的CO 2固定量随外界CO 2浓度的变化而变化(如下图)。

下列相关叙述不正确...的是A .小麦的CO 2固定量与外界CO 2浓度呈正相关B .CO 2浓度在100 mg·L -1时小麦几乎不固定CO 2C .CO 2浓度大于360 mg·L -1后玉米不再固定CO 2D .C 4植物比C 3植物更能有效地利用低浓度CO 25.化学与人类生活密切相关。

2009年普通高等学校招生全国统一考试(北京卷)(数学理)有答案

2009年普通高等学校招生全国统一考试(北京卷)(数学理)有答案

2009年普通高等学校招生全国统一考试数 学(理工农医类)(北京卷)本试卷分第I 卷(选择题)和第Ⅱ卷(非选择题)两部分,第I 卷1至2页,第Ⅱ卷3至9页,共150分。

考试时间120分钟。

考试结束后,将本试卷和答题卡一并交回。

第I 卷(选择题 共40分)注意事项:1.答第I 卷前,考生务必将答题卡上的姓名、准考证号用黑色字迹的签字笔填写,用2B 铅笔将准考证号对应的信息点涂黑。

2.每小题选出答案后,将答题卡上对应题目的答案选中涂满涂黑,黑度以盖住框内字母为准,修改时用橡皮擦除干净。

在试卷上作答无效。

一、本大题共8小题,每小题5分,共40分。

在每小题列出的四个选项中,选出符合题目要求的一项。

1在复平面内,复数(12)z i i =+对应的点位于 ( ) A .第一象限 B .第二象限 C .第三象限 D .第四象限 【答案】B2.已知向量a 、b 不共线,c k =a +b (k ∈R ),d =a -b ,如果c //d ,那么 ( ) A .1k =且c 与d 同向 B .1k =且c 与d 反向 C .1k =-且c 与d 同向 D .1k =-且c 与d 反向 【答案】D3.为了得到函数3lg10x y +=的图像,只需把函数lg y x =的图像上所有的点 ( ) A .向左平移3个单位长度,再向上平移1个单位长度 B .向右平移3个单位长度,再向上平移1个单位长度 C .向左平移3个单位长度,再向下平移1个单位长度 D .向右平移3个单位长度,再向下平移1个单位长度 【答案】C4.若正四棱柱1111ABCD A BC D -的底面边长为1,1AB 与面ABCD 成60°角,则11AC 到底面ABCD 的距离为 ( )A .3B .1C D 【答案】D 5.“2()6k k Z παπ=+∈”是“1cos 22α=”的 ( )A .充分而不必要条件B .必要而不充分条件C .充分必要条件D .既不充分也不必要条件 【答案】A6.若5(1,a a b =+为有理数),则a b += ( ) A .45 B .55 C .70 D .80 【答案】C7.用0到9这10个数字,可以组成没有重复数字的三位偶数的个数为 ( ) A .324 B .328 C .360 D .648 【答案】B8.点P 在直线:1l y x =-上,若存在过P 的直线交抛物线2y x =于,A B 两点,且|||PA AB =,则称点P 为“点”,那么下列结论中正确的是 ( )A .直线l 上的所有点都是“点”B .直线l 上仅有有限个点是“点”C .直线l 上的所有点都不是“点”D .直线l 上有无穷多个点(点不是所有的点)是“点”【答案】A2009年普通高等学校招生全国统一考试 数 学(理工农医类)(北京卷)第Ⅱ卷(共110分)注意事项:1.用钢笔或圆珠笔将答案直接写在试卷上。

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第8课Choose the best answer to each of the following questions:1. According to the author, being an author is a gainful occupation only __________.A. in a broad senseB. in a mental senseC. in a limited senseD. in a profitable sense2. It can be inferred from the first three paragraphs that “this failure”(L21) refers to ____________.A. WrathB. EnvyC. PrideD. Sloth3. The sentence “it is Acedia which has claimed you for its own ” (L 44 ) means ___________.A. you are guilty of AcediaB. you are losing touch with AcediaC. you have become physically sluggish because of AcediaD. you have overcome Acedia4. What does the phrase “sense of proportion ” (L48 ) mean?A. The ability to judge what is most important in a situation.B. The capacity to keep one‟s balance with the increasing age.C. The possibility of feeling nothing at all.D. The feeling of being troubled or wounded in one‟s youth.5. If “one lives at all times under a mental and spiritual cloud ”(L57), it shows that ____________.A. he has begun to feel painB. he has ceased to feel joyC. he has gained wisdom and become more matureD. he has abandoned satisfactions and delights of life6. According to the context, the word “bias” ( L. 83) may stand for __________.A. feelingB. prejudiceC. preferenceD. training7. One of the reasons why we have to do things we detest sometimes is ___________.A: we are not free to discuss it with our own wishesB: we are not free to do whatever we likeC: we are free to act according to our wishesD: we are victims of Acedia8. It seems that people are afraid of joy because _____________.A. being religious, they dread the passing of JesusB. they want to escape the pain brought by joyC. they do not want to become the victims of AcediaD. they care too much about looking dignified9. Which of the following is Not true of Acedia?A. Acedia reaches people gradually and silently without people‟s knowledge.B. Acedia discourages and kills the spirit.C. Acedia causes people to feel pain.D. Acedia means intellectual and spiritual torpor, indifference and lethargy.10. The author concludes his speech by ___________.A. calling on the audience to break the padlock of their hearts in order to gain new freedomB. encouraging the audience to release their feelings of pleasure on receiving their degreesC. warning the audience against the danger of AcediaD. telling the audience the real purpose of education泛读第10课Choose the best answer to each of the following questions:1.The author recounts her meeting with the Russian linguist in order to .A.introduce the constant topic of America as a melting potB.introduce boiling potters in contrast to the main courseC.show the latter‟s earnestness in pursuing his professionD.show the positive relationship between one‟s accent and one‟s ancestry2.The word “blurred” (L 27) most probably means .A.indefiniteB. unrealC. rootedD. displaced3.“I suppose I‟ve always known that my uninterest in it contains a large component of thewilled: I am American, and those places purport to be my history. But they are not mine” (L.29--31). From these two sentences, we can infer that .A. American history is, to a certain degree, beyond the author‟s understandingB. those places are special symbols of American historyC. the author thought she had a different historyD.the author is going through an identity crisis4.In the author‟s eyes, Ellis Island is not a place of honor because .A. once it was in a state of dereliction for quite some timeB.immigrants received many mistreatments when they landed thereC. the pictures taken by Louis Hine reflect the dark realities thereD.three thousand people couldn‟t help but commit suicide5.Which of the following choices best explains this sentence fragment “…the machinery ofimmigration nearly collapsed under its own weight” (L108--109) ?A. The immigration institutions had a strong bias against immigrants.B. The medical examinations were too strict to be good.C. The immigration system failed to function properly.D.The machinery concerned with immigration became too complicated.6. The meaning of the word “air” (L 82) is .A. mixture of gasesB. an artificial mannerC. sentimentD. mood7.According to the passage, which of the following statement is NOT true?A. World War I made America dislike people from other countries.B. Immigrants came to the United States in order to take part in a classy party.C. Ellis Island has a strong hold on the author‟s imagination.D.Ellis Island does not reflect the bright side of American immigration history.8.“It is part of being an American to be engaged in a somewhat tiresome but alwaysself-absorbing process of national definition” (L159--161). According to this sentence, which of the following statements would the author most likely agree to?A. It has been a trying task for the immigrants to maintain their identity.B. American national definition is somewhat hard to come by.C. In order to survive, immigrants had to meet the challenge of new circumstances.D.Immigrants have been trying to assimilate themselves and become Americans.9.What does the word “accidents” (L159) mean?A. incidental qualitiesB. misfortunesC. unforeseen circumstancesD. properties10.Besides paying her respect to the ghost of Ellis Island, the author‟s purpose in writing thispassage is to .A. criticizeB. entertainC. persuadeD. fight back泛读第11课Choose the best answer to each of the following questions:1. At the end of the first paragraph, the author says “the more we learn about the two captains …the more powerful becomes their pull on our imagination.”The word “pull”probably means .A.sympathyB. influenceC. resistanceD. clarity2. What is true about the journals of the expedition?A. Lewis edited part of the journals.B. It was Lewis‟s work to write the journals of the expedition.C. William Clark edited the raw journals into the two-volume final form.D. It was William Clark who published the whole editions of the journals.3. According to the article, which of the following statement is true?A. Lewis and Clark treated each other as if they were both captains.B. Clark had a higher military rank than Lewis.C. Lewis and Clark both held the rank of captain.D. Clark had never thought about his commission.4. In Line 58 the word “anticipated” means .A. opposedB. looked forward toC. shared inD. agreed5. What made Lewis and Clark popular again a century later?A. The exploration led by John Charles Fremont.B. The Exploration led by John Wesley Powell.C. The republication of the journals of the Lewis and Clark expedition.D. The publicity of the exploration by Fremont and Powell.6. In Line 138 the word “aspiration” means .A. a love affairB. expulsion of breathC. a creative ideasD. a strong desire for high achievement7. Charles McKenzie did not like Lewis at Fort Mandan mainly because .A.Lewis talked too muchB.Lewis tended to dislike the BritishC.Lewis knew everything wellD.Lewis had an offensive character8. In Line 116 the word “unambiguous” means .A.unimaginableB. practicalC. clearD. tough9. Three years later after the expedition, Lewis died .A. because he had suffered the depressionB. because too much administrative work crushed him downC. because he had a writing problemD. but the cause of his death is not clear10. “But when the revelers got to the captains in the 18th and final toast, they seemed to be at aloss for words” (L180--3). The expression “at a loss for words” probably means ___________.A.lostB.not knowing where to goC.unable to winD.not knowing what to say泛读第15课Choose the best answer to each of the following questions:1.“To give freely, spontaneously, like nature in her abundance. (…How many are unworthy ofthe light, and yet the day rises to them.‟ Seneca also wrote.)” (L54--7). How to understand the sentence in the brackets?A.Many people are not aware of the light, yet they still live in the world.B.There are many people who are not worthy of the light, yet the sun still shines on them.C.There are many people who don‟t deserve the light, yet they are happy every day.D.When the sun rises every day, how many on earth don‟t deserve the light?2.Which count in the following sentences carries the same meaning as the one in “The niceties,of course, not the raw act of giving … are what count” (L32--3)?A.You can count on his help.B.They have 3 dogs, counting the puppies.C.She‟s count ed the best singer in this town.D.Every second counts when one is having an examination.3.“She told me how; she was explicit about it” (L 98). The meaning of the second sentence isthat she ________________.A.explained the reasonsB.expressed herself clearlyC.talked about it in detailD.had a sincere talk with me4.“Foundation executives talk about their gifts as …investment s‟ and look for a return of sorts,for the kind of success in a project or program they can point to and call …mine‟” (L153--6).Through this example, the author wants to argue that foundation executives ____________.A.are interested in big achievementsB.try to expand their investment to a great extentC.expect some rewards from the donationD.expect a larger amount of money back in return5.“Why not a broom? Why not a month‟s supply of Wonder Bread?” (ll. 88-9). Through thesetwo rhetorical questions, we can sense that the author __________________.A.wants to give suggestions on better giftsB.doesn‟t think practical gifts are always idealC.is wondering there may be some better choicesD.can‟t understand why they are not able to give an ideal gift6.The author mentions when gift-giving happened in his family, one didn‟t have to wrap them,and cards were unnecessary. Why?A.His mother thought decoration was frivolous.B.When the family was so poor, decoration was meaningless.C.Decoration was important only on some special occasions.D.One should form the habit of thrift since childhood.7.“But they‟re an ideal gift. Purely symbolic. Purely cliché” (L101--2). The word “cliché” heremeans _________.A.an over used wordB. a customC.an ordinary ideaD. a sound8.One of the purposes of the author is to prove _____________________.A.there is altruism, but most of time, we simply ignore itB.most people are not altruists, although there exists altruismC.even those altruists still expect something back in returnD.the philanthropic organization is the typical representative of altruism9. The word “tension” in the sentence “We who are not poets live in the tension for the mostpart” (L188--9) means the strain between _______________.A.egoism and social regulationsB.altruism and social needsC.altruism and egoismD.altruism and self-accomplishment10. At one university a department chairman even asked me to write a critique of his department,which he then distributed to his faculty. The reason is that _________________.A. the author was a famous criticB.there were some serious problems in this departmentC. as an altruist, the author was greatly respected by othersD. the chairman wanted to please the author in this way泛读第18课Choose the best answer to each of the following questions:1.In Line 2 of the text, “He was one, but not the other”, what does the expressions “one ” and“the other” respectively refer to?A. A beggar and a lunatic.B. A lunatic and a beggar.C. A beggar and a degenerate.D. A lunatic and a maniac.2.In the sentence “In order to procure a quantity of false, perishable goods he has sold the onlytrue, lasting good, his own independence” (L. 52--4), what does the expression “the only true, lasting good” mean?A.His expensive clothes.B.His own freedom.C.His big house.D.His bank accounts.3.What is the main difference between Diogenes and other philosopher like Plato?A.Diogenes lived in sanctuaries but others didn‟t.B.Diogenes lived in Athens or Cornth but others didn‟t.C.Diogenes talked about the unreality of this contingent existence but others didn‟t.D.Diogenes discoursed to ordinary people but others to a chosen few.4.Alexander would be interested in _________ according to the sentence “Jugglers and stuntartists and virtuosos of the absurd he dismissed with a shrug, but on reaching India he was to spend hours discussing the problems of life and death with naked Hindu mystics, and later to see one demonstrate Yoga self-command by burning himself impassively to death” (Lines 128--132).A. a jugglerB. a Hindu mysticC. a stunt artistD. a virtuoso5.Which of the following would Diogenes least do?A.To wear a blanket through out the year.B.To live like a beggar in a quiet village.C.To teach in a crowd of ordinary people.D.To shout at the people he disliked.6.In this narrative essay, the author‟s tone proves to be _______.A.sarcasticB.skepticalC.humorousD.paradoxical7.According to the text, what is the least likely reason that Alexander visited Diogenes?A.The curiosity to seek out anything strange yet instructive.B.The generosity taught by Aristotle.C.The desire to show his air of destiny.D.The fact that he was still young and civil.8.Diogenes could be best described as __________.A. a recluseB. a beggarC. a sober manD. a civil person9.In the sentence “He understood Cynicism as the others could not” (Lines 171--172) the word“as” could be replaced by _______.A.BecauseB. whileC. whenD. the way10.In the last sentence of the text, who does the pronoun “he” refer to?A.One of Diogenes‟ pupils.B. Diogenes.C. One of Alexander servants.D. Alexander.泛读第21课Choose the best answer to each of the following questions:1. The reason that people with more confidence are less immune to flattery is that____________________.A.they are not shrew enoughB.they haven‟t got enough praiseC.they posses more wisdomD.they think they deserve more praise2.According to the author, flattery was regarded as dangerous in the Renaissance becausepeople at the time believed that ________________.A.they would go to hell if they flattered othersB.flattery would disturb the existing social hierarchyC.flattery was a serious offence against GodD.only those in power had the rights to flatter3.“And we believed him because it was a pleasing fiction” (L47--8). The word “fiction”probably means _________.A. a storyB. a theoryC. an untrue statementD. flattery4.The author uses the example of Clinton to show _______________.A.how the flattery of the people is exploited by politiciansB.that most people have difficulty in judging what is the truthC.how flattery will damage people‟s trust in the governmentD.people always know who is speaking the truth and who can be trusted5.“Once social mobility became a good, flattery lost its moral stigma and became just anothertool of social advancement”(L53--4). The expression “s ocial mobility”probably means ________________.A.moving from one social group to anotherB.moving from one place to anotherC.changing jobs from time to timeD.flattering those wealthy and powerful people6.What was the attitude of the American Puritans toward flattery?A.They hated flattery and considered it as evil as people in the Old world did.B.They were more direct in flattering and didn‟t mind being absurd.C.They believed that flattery should not be too direct and sincere.D.They thought flattery would be more effective if it was done sincerely.7.According to the author, flattery becomes more effective for modern Americans. It is because______________________.A.they believe that others‟ views are more correct than their ownB.they need others to direct the way of their lifeC.they have begun to consider it as noble to flatter others and themselvesD.they need others to convince them how good they are8.“It is the tactical omissions of everyday life that make society possible”(L92--3). Theexpression “the tactical omission” probably refers to _________________.A.the flattery directed at oneselfB.the ignoring of other people‟s flatteryC.not questioning other people‟s self-flatteryD.contesting other people‟s depictions of us9.The author believes that too much undeserving public praise would ___________.A.be a serious threat to the stability of society and the governmentB.cheapen the value of private flattery and personal appreciationC.make the language we speak phony and clichédD.make people distrust those great figures like Darwin and Martin Luther king10.According to the author, to make flattery more authentic, we can ____________.A.share our secrets with others, the more the betterB.talk in general when flattering othersC.flatter people when they are not presentD.mix a bit of criticism with flattery泛读第24课Choose the best answer to each of the following questions:1.The author believes that creativity is ______________.A.only the gift of God to a chosen fewB.not a suitable topic for a television seriesC. a power that each of us has to a certain degreeD.defined by people like Picasso and Michelangelos2.Newton failed to develop a comprehensive theory for chemistry, because the science itself hadnot developed to the point __________ he could see the new order.A. whenB. whereC. whichD. why3.The author uses the case of Newton to ____________________________.A.illustrate the relationship between convergent thinking and divergent thinkingB.show that even a genius cannot break through without the shoulders of giantsC.prove that overconfidence does no good in scientific studyD.exemplify what a real genius can achieve in science4.Which of the following best explains the sentence “creative thinking is discontinuous within acontext of continuity (L 49--50)?”A.Creative thinking is a discontinuous process.B.Creative thinking is a continuous process.C.Creative thinking is based on what has preceded and at the same time breaks from thepast.D.Creative thinking comes up with unpredictable conclusions through breaking from thepast.5.That “Maya Angelou had everything against her (L 169) ” means that _________.A.Maya objected herB.everybody objected MayaC.nothing is favorable to MayaD.Maya owned everything which helped her6.One characteristic that the author does not say about the creative people is their______________________.A.powerful egosB. disciplineC.childlike wonderD. reliability7.Which of the following statements is NOT true about convergent and divergent thinking?A.Both kinds of thinking are characteristic of human thinking.B.Divergent thinking is directly related to creative thinking.C.Convergent thinking tends toward an unpredictable answer.D.They are fundamentally different but related.8.Which of the following would the author disagree?A.We need to think more about why some people are creative than why others are usingtheir creative power.B.We‟d better avoid making judgments in order to keep creative thinking.C.Creative people keep their childlike wonder alive long into life.D.Peer prejudice is something to kill original thinking.9.According to the text, which of the following is inconsistent with creativity?A.Conformity to other people.B.Novel use of a familiar object.C.Metaphors and similes.D.Tolerance of ambiguity.10. By saying that “my heart leaps at the consensus emerging among some scientists that creativeability can be learned”(L192--3), the author means that he is ________________ the possibility that creativity can be learned.A.suspicious ofB. willing to acceptB.surprised to hear aboutC. at a loss as toKey to Lesson 81.C2.D3.A4.A5.B6.C7.B8.D9.C 10.BKey to Lesson 101.B2. A3.C4.B5.C6.D7.B8.D9.C 10.AKey to Lesson 111.B2.C3.A4.B5.C6.D7.B8.C9.D 10.DKey to Lesson 151.B2.D3.B4.C5.B6.A7.B8.B9.C 10.DKey to Lesson 181.A2.B3.D4.B5.B6.C7.C8.C9.B 10.DKey to Lesson 211. D2.B3.C4.A5.A6.D7.D8.C9.B 10.DKey to Lesson 241.C2.B3.A4.C5.C6.D7.C8.A9.A 10.B11。

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