2014年真题分析
- 格式:docx
- 大小:32.86 KB
- 文档页数:9
2014 年普通高等学校招生全国统一考试(天津卷)第一部分:英语知识运用(共两节,满分45分)第一节:单项填空(共15小题;每小题1分,满分15分)1.Give me a chance, ________ I’ll give you a wonderful surprise.A.ifB. orC. andD. while【考点】考察特殊句式和连词辨析【答案】C【解析】本题考察的是“祈使句+连词+陈述句”的特殊句式。
该句型相当于:If条件句,+主句;本句相当于:If you give me a chance, I’ll give you a wonderful surprise.在变成条件句时,如果是一个肯定句,就使用连词and;如果成为一个否定句,就使用or;如:Hurry up, or we will be late.相当于:If you don’t hurry up, you will be late.句义:给我一个机会,我就会给你一个惊喜。
故C正确。
【试题延伸】本题中含有特殊句式:祈使句+连词+陈述句=If引导的条件句+主句。
这个句型进一步转换成:名词短语+连词+陈述句。
如果原句中的连词是and,那么可以转换成一个肯定的条件句;如果原句中的连词是or,可以转换成一个否定的祈使句。
【举一反三】and I’ll get the work finished.A.Have one more hourB.One more hourC.Given one more hourD.If I have one more hour〖答案〗B〖考点〗本题考查“祈使句+and+简单句”的用法,〖解析〗本题考查“祈使句+and+简单句”的用法, 其中祈使句可转换成名词短语, 如One more word and I’ll beat you flat.因此B项正确。
如果选C, D两项, 要去掉and。
2.---Ok, I’ll fix your computer right now. ---Oh, take your time. __________.A.I can’t stand itB. I’m in no hurryC. That’s a great ideaD. It’s not my cup of tea【考点】考察交际用语【答案】B【解析】本句考察的是交际用语。
2014年山东高考真题解析结构变化多试题创新多时代特性强6月8日,随着最后一门英语考试的结束,2014年山东省夏季高考也宣告结束。
今年山东高考试题有多个变化,取消基本能力测试、取消英语听力、综合科目考试分值增高到300分等。
下午,省招考院请专家就今年的高考试题进行点评,专家们普遍认为,今年试题难易适中,有不少创新,考题命制更加贴近现实生活。
透过专家的点评,刚刚参加完考试的考生们或许也能对自己考试中的表现有一个初步判断。
语文>>>取消现代文阅读选做题今年的高考语文,考生普遍反映难度不大,题目比较新颖。
据专家分析,从总体上看,今年语文试卷结构保持相对稳定,注重对考生语文应用能力和审美、探究能力的考查,选材典雅唯美,设题新颖别致,卷面清新自然,试题难易适中,具有较好的区分度。
今年的语文试卷在保持试卷结构相对稳定的基础上,在考试内容和形式上也有所变化。
第六大题现代文阅读,取消了选做题的形式,直接给出了一篇文学类文本让考生阅读答题,减轻了考生的阅读量,可以使考生快速答题。
试卷结构的相对稳定,可以使考生迅速进入考试状态,对试卷没有陌生感,从而更好地发挥考试水平。
今年试卷最突出的特点是在选材上具有传统性与时代性相结合的特点,典雅唯美,清新自然,使整个试卷充满了语文的美感,让人眼前一亮,耳目一新。
如第二大题论述类阅读材料选取了梁漱溟《朝话》中关于“心理调整”的一段文字,语言平实,口语化强,逻辑清楚,条理性强,而且内容与考生贴近,读起来极具有亲切感和现实感,改变了以往选材局限于文化、历史及哲学类的文章,避免了语言晦涩、概念缠绕的毛病,是一个大的突破。
除此之外,第4小题成语的考查涉及到先秦诸子名家的文章风格;第5小题病句的考查涉及房地产和商品房价格的现实问题;第16小题概括信息涉及24字社会主义核心价值观的内容;尤其是第18小题,要求考生组合两副有关春节和端午的对联,对联具有浓郁的中国传统文化的特色,这就要求考生既要了解春节和端午的节日特点,还要懂得对联的特点,更加突出了命题者对传统文化的重视,具有良好的价值导向。
2014年高考真题题型分析——椭圆一、椭圆的几何性质1.(2014辽宁,5分)(2014•辽宁)已知椭圆C :+=1,点M 与C 的焦点不重合,若M 关于C 的焦点的对称点分别为A 、B ,线段MN 的中点在C 上,则|AN|+|BN|= _________ .二、椭圆与参数方程2.(2014福建,5分)设P ,Q 分别为圆x 2+(y ﹣6)2=2和椭圆+y 2=1上的点,则P ,Q5 + 三、椭圆与直线(交点、比例、向量)3.(2014安徽,5分)设21,F F 分别是椭圆)10(1:222<<=+b by x E 的左、右焦点,过点1F 的直线交椭圆E 于B A ,两点,若x AF BF AF ⊥=211,3轴,则椭圆E 的方程为__________ 4.(2014江西,5分)设椭圆C :+=1(a >b >0)的左右焦点为F 1,F 2,过F 2作x轴的垂线与C 相交于A ,B 两点,F 1B 与y 轴相交于点D ,若AD ⊥F 1B ,则椭圆C 的离心率等于 _________ .5. (2014新课标全国卷Ⅱ,12分)设1F ,2F 分别是椭圆C:()222210y x a b a b+=>>的左,右焦点,M 是C 上一点且2MF 与x 轴垂直,直线1MF 与C 的另一个交点为N.(Ⅰ)若直线MN 的斜率为34,求C 的离心率;(Ⅱ)若直线MN 在y 轴上的截距为2,且15MN F N =,求a,b .6.(2014江苏,14分)如图,在平面直角坐标系xOy 中,21,F F 分别是椭圆)0(12322>>=+b a b y a x 的左、右焦点,顶点B 的坐标为),0(b ,连结2BF 并延长交椭圆于点A ,过点A 作x 轴的垂线交椭圆于另一点C ,连结C F 1.(1)若点C 的坐标为)31,34(,且22=BF ,求椭圆的方程;(2)若,1AB C F ⊥求椭圆离心率e 的值.四、椭圆与直线(韦达定理)7.(2014江西,5分)过点M (1,1)作斜率为﹣的直线与椭圆C :+=1(a >b >0)相交于A ,B 两点,若M 是线段AB 的中点,则椭圆C 的离心率等于 _________ .8.(2014河南,12分)已知点A (0,﹣2),椭圆E :+=1(a >b >0)的离心率为,F 是椭圆E 的右焦点,直线AF 的斜率为,O 为坐标原点.(Ⅰ)求E 的方程; (Ⅱ)设过点A 的动直线l 与E 相交于P ,Q 两点,当△OPQ 的面积最大时,求l 的方程.9.(2014辽宁,12分)圆x2+y2=4的切线与x轴正半轴,y轴正半轴围成一个三角形,当该三角形面积最小时,切点为P(如图),双曲线C1:﹣=1过点P且离心率为.(Ⅰ)求C1的方程;(Ⅱ)若椭圆C2过点P且与C1有相同的焦点,直线l过C2的右焦点且与C2交于A,B两点,若以线段AB为直径的圆过点P,求l的方程.10.(2014•山东,14分)在平面直角坐标系xOy中,椭圆C:+=1(a>b>0)的离心率为,直线y=x被椭圆C截得的线段长为.(Ⅰ)求椭圆C的方程;(Ⅱ)过原点的直线与椭圆C交于A,B两点(A,B不是椭圆C的顶点).点D在椭圆C 上,且AD⊥AB,直线BD与x轴、y轴分别交于M,N两点.(i)设直线BD,AM的斜率分别为k1,k2,证明存在常数λ使得k1=λk2,并求出λ的值;(ii)求△OMN面积的最大值.。
2014年普通高等学校招生全国统一考试(全国大纲卷)语文试题第Ⅰ卷一、(12分,每小题3分)1.下列词语中加点的字,读音全都正确的一组是(B)A.龃龉.(yǔ) 系.鞋带(xi) 舐.犊情深(shi) 曲.意逢迎(qū)B.倜傥.(tǎng) 纤.维素(xiān) 羽扇纶.巾(guān ) 针砭.时弊(biān)C.感喟.(kuì) 揭疮.疤(chuāng) 按捺.不住(nài) 大相径.庭(jing)D.霰.弹(xiàn ) 涮.羊肉(shuàn) 以儆.效尤(jǐng) 纵横捭.阖必(bì)2.下列各句中,加点的成语使用恰当的一项是(A)A.在评价某些历史人物时,我们不能只是简单地对他们盖棺论定....,,还应该学科网特别注意研究他们的人生经历和思想变化轨迹。
B.这把吉他是我最要好的朋友出国前存在我这里的,本来说存一年,结果朋友一直没回来,这吉他到现在巳经由我敝帚自珍....了十年。
C.最美的是小镇的春天,草长莺飞,风声鹤唳....,走进小镇就如同置身于世外桃源,来此旅游的人一定会被这里的美丽景色深深吸引。
D.这个剧院的大型话剧、歌剧等演出票价不菲,让许多有艺术爱好而又收入不高的普通人叹为观止....,无法亲临现场享受艺术大餐。
3.下列各句中,没有语病的一句是答:DA.有的人看够了城市的繁华,喜欢到一些人迹罕至的地方去游玩,但这是有风险的,近年来已经发生了多次背包客被困野山的案情。
B.他家离铁路不远,小时候常常去看火车玩儿,火车每当鸣着汽笛从他身边飞驰而过时,他就很兴奋,觉得自己也被赋予了一种力量。
学科网C.新“旅游法”的颁布实施,让很多旅行社必须面对新规定带来的各种新问题,不少旅行社正从过去拼价格向未来拼服务转型的阵痛。
D.哈大高铁施行新的运行计划后,哈尔滨至北京、上海等地的部分列车也将进一步压缩运行时间,为广大旅客快捷出行提供更多选择。
4.依次填人下面一段文字横线处的语句,衔接最恰当的一组是答:C信息时代给人们带来了一种新的极其便捷的阅读方式,那就是网络阅读。
2014年内蒙古公务员考试行测真题答案及解析1.【答案】A。
铅笔芯的主要成分是铅解析:铅笔芯的主要成分是石墨和黏土,这些物质按照不同的比例加以混合、压制,就可以制成铅笔芯。
故本题答案选A。
2.【答案】A。
古埃及:“0”的发现解析:数字“0”是由印度人发明的。
故本题答案选A。
3.【答案】D。
页岩是最常见的岩浆岩解析:常见的岩浆岩有:花岗岩、橄榄岩、玄武岩、安山岩、流纹岩。
页岩是沉积岩。
故本题答案选D。
4.【答案】C。
波罗的海是世界上盐度最高的海域解析:红海是世界上盐度最高的海域;波罗的海是世界上盐度最低的海域。
故本题答案选C。
5.【答案】D。
“烈火焚烧若等闲”指熟石灰的高温煅烧解析:“烈火焚烧若等闲”是指高温煅烧石灰石。
石灰石的主要成分是碳酸钙,熟石灰的主要成分是氢氧化钙,二者是有区别的。
故本题答案选D。
6.【答案】A。
九寨沟国家地质公园以雅丹地貌闻名解析:雅丹地貌是一种典型的风蚀性地貌。
我国的雅丹地貌面积约2万多平方公里,主要分布于青海柴达木盆地西北部,疏勒河中下游和新疆罗布泊周围。
九寨沟国家地质公园主要是喀斯特地貌。
故本题答案选A。
8.【答案】C。
沥青、松香解析:A项属于液体;B项油漆属于液体;D项属于气体。
故本题答案选C。
9.【答案】D。
巴颜喀拉山解析:我国一二级阶梯的分界线是:昆仑山—祁连山—青藏高原东缘;二三级阶梯的分界线是:大兴安岭—太行山—巫山—雪峰山;A、B、C三项位于第二阶梯上。
巴颜喀拉山是庞大的昆仑山脉南支的一部分,位于第一阶梯上。
故本题答案选D。
10.【答案】A。
硝石:加拿大解析:加拿大地域辽阔,森林和矿产资源丰富。
矿产有60余种,镍、锌、铂、石棉的产量居世界首位,铀、金、镉、铋、石膏居世界第二位。
铜、铁、铅、钾、硫磺、钴、铬、钼及鱼类等产量相当丰富。
故本题答案选A。
11.【答案】AD。
中国是最早栽培大豆的国家印度是世界上最大的稻米出口国解析:中国是大豆的原产地,也是最早驯化和种植大豆的国家,栽培历史至少已有4000年,A项正确;中国种植玉米的时间较晚,明末清初(新航路开辟后,大致是1620-1690)从美洲传入欧洲再传入中国,B项错误;世界四大主要油料作物为大豆、油菜、花生、向日葵,作为油料作物,大豆是世界上最主要的植物油和蛋白饼粕的提供者。
第一部分言语理解与表达本部分包括选词填空与语句理解两方面的内容,请根据题目要求,在四个选项中选出一个最恰当的答案。
1.罗斯福的《正义论》被誉为20世纪最重要的政治哲学著作,_____着整个当代政治哲学的发展。
罗斯福说,正义是社会制度的首要德性,一如真理是思想体系的最高价值。
因此,当我们评价制度时,最重要的是看它是否合乎公正。
如果不公正,我们便有责任改变甚至_____它。
依次填入划横线部分最恰当的一项是()A.推动淘汰B.影响推翻C.激励颠覆D.指导优化2.如果你的生活中没有伟大、高贵的人和有智慧的人怎么办?请不要变得麻木,不_____,不要放弃向生活学习的机会,因为至少在你的周围还有树,特别是大树,它会教会你许多东西。
一棵大树,就是你的亲人和老师,而且也可以毫不夸张地说,它就是伟大、高贵和有智慧的人。
依次填入划横线部分最恰当的一项是()A.自以为是B.茫然失措C.随波逐流D.自暴自弃3.“凑足一群人就可以走了,和红绿灯无关”,略带自嘲和无奈的“中国式过马路”,_____着集体漠视规则的人们,_____了城市交通管理的软肋。
依次填入划横线部分最恰当的一项是()A.嘲弄戳痛B.挖苦打中C.调侃戳中D.讥讽击中4.条纹,作为最简洁而又生机勃勃的视觉设计语言,自石器时代起便被广泛运用。
彩色条纹依旧不断_____于当今时装界,新锐设计师们拒绝了浮华,但同样_____着高调。
依次填入划横线部分最恰当的一项是()A.风靡保持B.时兴延续C.流行维持D.活跃蕴含5. 石油峰值论认为,石油产量会达到最高点,之后不可避免地开始下降。
石油峰值几乎是确定的事,但仍然存在两个问题:它究竟何时出现?世界是否能够及时研发出替代能源?________的观察家并不相信石油峰值会在2020年前出现,但一些石油公司承认他们此前夸大了地下的石油储量。
因此,这更引起人们的________:我们可能已经过了这个峰值。
依次填入划横线部分最恰当的一项是()A.乐观担忧B.激进争议C.冷静怀疑D.理智恐慌6. 一年以来,欧美国家示威、罢工活动________,暴力事件频发,社会乱象________,显示出在经济持续不景气的背景下西方发达国家内部矛盾激化,社会危机加剧。
2014年考研数学三真题与解析一、选择题 1—8小题.每小题4分,共32分.1.设0≠=∞→a a n n lim ,则当n 充分大时,下列正确的有( )(A )2a a n >(B )2a a n <(C )n a a n 1-> (D)na a n 1+< 【详解】因为0≠=∞→a a n n lim ,所以0>∀ε,N ∃,当N n >时,有ε<-a a n ,即εε+<<-a a a n ,εε+≤<-a a a n ,取2a =ε,则知2a a n >,所以选择(A )2.下列曲线有渐近线的是(A )x x y sin += (B )x x y sin +=2(C )xx y 1sin+= (D )x x y 12sin +=【分析】只需要判断哪个曲线有斜渐近线就可以. 【详解】对于xx y 1sin +=,可知1=∞→x y x lim 且01==-∞→∞→x x y x x sin lim )(lim ,所以有斜渐近线x y =应该选(C )3.设32dx cx bx a x P +++=)(,则当0→x 时,若x x P tan )(-是比3x 高阶的无穷小,则下列选项中错误的是( )(A )0=a (B )1=b (C )0=c (D )61=d 【详解】只要熟练记忆当0→x 时)(tan 3331x o x x x ++=,显然31010====d c b a ,,,,应该选(D ) 4.设函数)(x f 具有二阶导数,x f x f x g )())(()(110+-=,则在],[10上( )(A )当0≥)('x f 时,)()(x g x f ≥ (B )当0≥)('x f 时,)()(x g x f ≤ (C )当0≥'')(x f 时,)()(x g x f ≥ (D )当0≥'')(x f 时,)()(x g x f ≤ 【分析】此题考查的曲线的凹凸性的定义及判断方法.【详解1】如果对曲线在区间],[b a 上凹凸的定义比较熟悉的话,可以直接做出判断.如果对区间上任意两点21x x ,及常数10≤≤λ,恒有())()()()(212111x f x f x x f λλλλ+-≥+-,则曲线是凸的. 显然此题中x x x ===λ,,1021,则=+-)()()(211x f x f λλ)()())((x g x f x f =+-110,而())()(x f x x f =+-211λλ,故当0≥'')(x f 时,曲线是凹的,即())()()()(212111x f x f x x f λλλλ+-≤+-,也就是)()(x g x f ≤,应该选(D )【详解2】如果对曲线在区间],[b a 上凹凸的定义不熟悉的话,可令x f x f x f x g x f x F )())(()()()()(110---=-=,则010==)()(F F ,且)(")("x f x F =,故当0≥'')(x f 时,曲线是凹的,从而010==≤)()()(F F x F ,即0≤-=)()()(x g x f x F ,也就是)()(x g x f ≤,应该选(D )5.行列式dcd c b a b a000000等于(A )2)(bc ad - (B )2)(bc ad -- (C )2222c bd a - (D )2222c bd a +- 【详解】2000000000000000)()()(bc ad bc ad bc bc ad ad dc b a bcd cb a add c cba b d c d b a a dc dc b a b a --=-+--=+-=+-=应该选(B ).6.设321ααα,, 是三维向量,则对任意的常数l k ,,向量31ααk +,32ααl +线性无关是向量321ααα,,线性无关的(A )必要而非充分条件 (B )充分而非必要条件 (C )充分必要条件 (D ) 非充分非必要条件 【详解】若向量321ααα,,线性无关,则(31ααk +,32ααl +)K l k ),,(),,(3213211001αααααα=⎪⎪⎪⎭⎫ ⎝⎛=,对任意的常数l k ,,矩阵K 的秩都等于2,所以向量31ααk +,32ααl +一定线性无关.而当⎪⎪⎪⎭⎫⎝⎛=⎪⎪⎪⎭⎫ ⎝⎛=⎪⎪⎪⎭⎫ ⎝⎛=000010001321ααα,,时,对任意的常数l k ,,向量31ααk +,32ααl +线性无关,但321ααα,,线性相关;故选择(A ).7.设事件A ,B 想到独立,3050.)(,.)(=-=B A P B P 则=-)(A B P ( )(A )0.1 (B )0.2 (C )0.3 (D )0.4【详解】)(.)(.)()()()()()(.)(A P A P A P B P A P A P AB P A P B A P 505030=-=-=-==-. 所以60.)(=A P ,=-)(A B P 205050.)(..)()(=-=-A P AB P B P .故选择(B ). 8.设321X X X ,,为来自正态总体),(20σN 的简单随机样本,则统计量3212X X X S -=服从的分布是(A )),(11F (B )),(12F (C ) )(1t (D ))(2t 【详解】232132122XX X X X X S -=-=,显然),(~10221N X X σ-,)(~12223χσX ,且),(~10221N X X σ-与)(~12223χσX 相互独立,从而)(~1222223212321321t X X X XX X X X X S σσ-=-=-=故应该选择(C ).二、填空题(本题共6小题,每小题4分,满分24分. 把答案填在题中横线上)9.设某商品的需求函数为p Q 240-=(p 为商品的价格),则该商品的边际收益为 . 【详解】2240p p pQ p R -==)(,边际收益p p R 440-=)('.10.设D 是由曲线01=+xy 与直线0=+y x 及2=y 所围成的有界区域,则D 的面积为 . 【详解】22112101ln +=+=⎰⎰⎰⎰--yydx dy dx dy S11.设412=⎰ax dx xe ,则=a . 【详解】411241244120202+-=-==⎰)(|)(a e x e dx xe a ax ax.所以.21=a12.二次积分=⎪⎪⎭⎫ ⎝⎛-⎰⎰dx e xe dy y y x 11022.【详解】)()(12111010101010100110101102222222222-==+-=--=-=⎪⎪⎭⎫ ⎝⎛-⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰e dy ye dy ye dy e e dy y e dy x e x d dx e dy dy x e dx dx e x e dy y y y dxx x y xx y y x y y x 13.设二次型3231222132142x x x ax x x x x x f ++-=),,(的负惯性指数是1,则a 的取值范围是 .【详解】由配方法可知232232231323122213214242xa x x ax x x x x ax x x x x x f )()()(),,(-+--+=++-=由于负惯性指数为1,故必须要求042≥-a ,所以a 的取值范围是[]22,-.14.设总体X 的概率密度为⎪⎩⎪⎨⎧<<=其它,,),(02322θθθθx xx f ,其中θ是未知参数,n X X X ,,, 21是来自总体的简单样本,若∑=ni iXC12是2θ的无偏估计,则常数C = .【详解】22222532θθθθ==⎰2dx x x X E )(,所以21225θCn X C E n i i =⎪⎪⎭⎫ ⎝⎛∑=,由于∑=ni i X C 12是2θ的无偏估计,故125=Cn,nC 52=. 三、解答题15.(本题满分10分)求极限)ln())((limxx dt t e t x tx 1112112+--⎰+∞→.【分析】.先用等价无穷小代换简化分母,然后利用洛必达法则求未定型极限. 【详解】21121111111222121122112=⎪⎭⎫ ⎝⎛-++=--=--=+--∞→∞→+∞→+∞→⎰⎰x x o x x x x e x xdtt e t xx dt t e t x xx xtx x tx )((lim ))((lim ))((lim)ln())((lim16.(本题满分10分)设平面区域{}004122≥≥≤+≤=y x y x y x D .,|),(.计算⎰⎰++Ddxdy y x y x x )sin(22π 【详解】由对称性可得432112121212022222222-==+=+++=++=++⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰DD DD dr r r d dxd y x dxdy y x y x y x dxd y x y x y dxd y x y x x πθπππππsin )sin()sin()()sin()sin(17.(本题满分10分)设函数)(u f 具有二阶连续导数,)cos (y e f z x=满足x x e y e z yzx z 222224)c o s (+=∂∂+∂∂.若0000==)(',)(f f ,求)(u f 的表达式.【详解】设y e u xcos =,则)cos ()(y e f u f z x==,y e u f y e u f xze uf xzx x y x cos )('cos )(",)('cos +=∂∂=∂∂2222; y e u f y e u f yz y e u f y z xx x cos )('sin )(",sin )('-=∂∂-=∂∂2222; x x x e y e f e u f yzx z 222222)cos (")("==∂∂+∂∂ 由条件xx e y e z yz x z 222224)cos (+=∂∂+∂∂, 可知u u f u f +=)()("4这是一个二阶常用系数线性非齐次方程.对应齐次方程的通解为:u u e C e C u f 2221-+=)(其中21C C ,为任意常数.对应非齐次方程特解可求得为u y 41-=*. 故非齐次方程通解为u e C e C u f u u 412221-+=-)(. 将初始条件0000==)(',)(f f 代入,可得16116121-==C C ,. 所以)(u f 的表达式为u e e u f u u 4116116122--=-)(. 18.(本题满分10分) 求幂级数∑∞=++031n nxn n ))((的收敛域、和函数.【详解】 由于11=+∞→nn n a a lim,所以得到收敛半径1=R .当1±=x 时,级数的一般项不趋于零,是发散的,所以收敛域为()11,-. 令和函数)(x S =∑∞=++031n nxn n ))((,则3211121112131111234)('"'")())(()()(x xx x x x x x x n x n n x n n x S n n n n n nn nn n--=⎪⎭⎫ ⎝⎛-+⎪⎪⎭⎫ ⎝⎛-=⎪⎪⎭⎫ ⎝⎛+⎪⎪⎭⎫ ⎝⎛=++++=++=∑∑∑∑∑∞=+∞=+∞=∞=∞=19.(本题满分10分)设函数)(),(x g x f 在区间[]b a .上连续,且)(x f 单调增加,10≤≤)(x g ,证明: (1) []b a x a x dt t g xa,,)(∈-≤≤⎰0;(2)⎰⎰≤⎰+ba dtt g a adx x g x f dx x f ba )()()()(.【详解】(1)证明:因为10≤≤)(x g ,所以[]b a x dt dt t g dx xax axa,)(∈≤≤⎰⎰⎰10.即[]b a x a x dt t g xa,,)(∈-≤≤⎰0.(2)令⎰⎰⎰-=+xa dtt g a axadu u f du u g u f x F )()()()()(,则可知0=)(a F ,且⎪⎭⎫ ⎝⎛+-=⎰xa dt t g a f x g x g x f x F )()()()()(',因为,)(a x dt t g xa-≤≤⎰0且)(x f 单调增加,所以)()()(x f a x a f dt t g a f xa=-+≤⎪⎭⎫ ⎝⎛+⎰.从而0=-≥⎪⎭⎫ ⎝⎛+-=⎰)()()()()()()()()('x f x g x g x f dt t g a f x g x g x f x F xa , []b a x ,∈也是)(x F 在[]b a ,单调增加,则0=≥)()(a F b F ,即得到⎰⎰≤⎰+badtt g a adx x g x f dx x f ba )()()()(.20.(本题满分11分)设⎪⎪⎪⎭⎫⎝⎛---=302111104321A ,E 为三阶单位矩阵. (1) 求方程组0=AX 的一个基础解系; (2) 求满足E AB =的所有矩阵.【详解】(1)对系数矩阵A 进行初等行变换如下:⎪⎪⎪⎭⎫ ⎝⎛--→⎪⎪⎪⎭⎫ ⎝⎛----→⎪⎪⎪⎭⎫ ⎝⎛----→⎪⎪⎪⎭⎫ ⎝⎛---=310020101001310011104321134011104321302111104321A ,得到方程组0=AX 同解方程组⎪⎩⎪⎨⎧==-=43424132xx x x x x 得到0=AX 的一个基础解系⎪⎪⎪⎪⎪⎭⎫⎝⎛-=13211ξ.(2)显然B 矩阵是一个34⨯矩阵,设⎪⎪⎪⎪⎪⎭⎫⎝⎛=444333222111z y x z y x z y x z y x B 对矩阵)(AE 进行进行初等行变换如下:⎪⎪⎪⎭⎫⎝⎛-------→⎪⎪⎪⎭⎫⎝⎛------→⎪⎪⎪⎭⎫⎝⎛-----→⎪⎪⎪⎭⎫⎝⎛---=141310013120101621001141310001011100014321101134001011100014321100302101011100014321)(AE由方程组可得矩阵B 对应的三列分别为⎪⎪⎪⎪⎪⎭⎫ ⎝⎛-+⎪⎪⎪⎪⎪⎭⎫ ⎝⎛--=⎪⎪⎪⎪⎪⎭⎫ ⎝⎛1321011214321c x x x x ,⎪⎪⎪⎪⎪⎭⎫ ⎝⎛-+⎪⎪⎪⎪⎪⎭⎫ ⎝⎛--=⎪⎪⎪⎪⎪⎭⎫ ⎝⎛1321043624321c y y y y ,⎪⎪⎪⎪⎪⎭⎫⎝⎛-+⎪⎪⎪⎪⎪⎭⎫ ⎝⎛-=⎪⎪⎪⎪⎪⎭⎫ ⎝⎛1321011134321c z z z z , 即满足E AB =的所有矩阵为⎪⎪⎪⎪⎪⎭⎫⎝⎛++-+-++-+-----=321321321321313431212321162c c cc c c c c c c c c B 其中321c c c ,,为任意常数. 21.(本题满分11分)证明n 阶矩阵⎪⎪⎪⎪⎪⎭⎫⎝⎛111111111与⎪⎪⎪⎪⎪⎭⎫⎝⎛n 00200100 相似. 【详解】证明:设=A ⎪⎪⎪⎪⎪⎭⎫⎝⎛111111111,=B ⎪⎪⎪⎪⎪⎭⎫⎝⎛n 00200100 . 分别求两个矩阵的特征值和特征向量如下:1111111111--=---------=-n n A E λλλλλλ)(,所以A 的n 个特征值为0321====n n λλλλ ,;而且A 是实对称矩阵,所以一定可以对角化.且⎪⎪⎪⎪⎪⎭⎫⎝⎛00 λ~A ;1002010--=---=-n n nB E λλλλλλ)(所以B 的n 个特征值也为0321====n n λλλλ ,;对于1-n 重特征值0=λ,由于矩阵B B E -=-)(0的秩显然为1,所以矩阵B 对应1-n 重特征值0=λ的特征向量应该有1-n 个线性无关,进一步矩阵B 存在n 个线性无关的特征向量,即矩阵B 一定可以对角化,且⎪⎪⎪⎪⎪⎭⎫⎝⎛00 λ~B 从而可知n 阶矩阵⎪⎪⎪⎪⎪⎭⎫⎝⎛111111111与⎪⎪⎪⎪⎪⎭⎫⎝⎛n 00200100 相似. 22.(本题满分11分)设随机变量X 的分布为2121====)()(X P X P ,在给定i X =的条件下,随机变量Y 服从均匀分布210,),,(=i i U .(1) 求Y 的分布函数; (2) 求期望).(Y E 【详解】(1)分布函数())/()/()()/()()/(),(),()()(2121221121=≤+=≤===≤+==≤==≤+=≤=≤=X y Y P X y Y P X P X y Y P X P X y Y P X y Y P X y Y P y Y P y F 当0<y 时,0=)(y F ;当10<≤y 时,y y y y F 4322121=+=)(; 当21<≤y 时,214122121+=+=y y y F )(; 当2≥y 时,1=)(y F . 所以分布函数为⎪⎪⎪⎩⎪⎪⎪⎨⎧≥<≤+<≤<=2121421104300y y y y y y y F ,,,,)((2)概率密度函数为⎪⎪⎪⎩⎪⎪⎪⎨⎧<<<<==其它,,,)(')(021411043y y y F y f ,434432110=+=⎰⎰dy y ydy Y E )(. 23.(本题满分11分)设随机变量X ,Y 的概率分布相同,X 的概率分布为321310====)(,)(X P X P ,且X ,Y 的相关系数21=XY ρ. (1) 求二维随机变量),(Y X 的联合概率分布; (2) 求概率)(1≤+Y X P .[详解]由于X ,Y 的概率分布相同,故321310====)(,)(X P X P ,321310====)(,)(Y P Y P , 显然32==EY EX ,92==DY DX 相关系数()929421-=-===XY E DYDX EXEY XY E DY DX Y X COV XY )(),(ρ,所以95=)(XY E . 而),()(1111==⨯⨯=Y X P XY E ,所以9511===),(Y X P ,从而得到),(Y X 的联合概率分布:11 9511===),(Y X P ,9110===),(Y X P ,9101===),(Y X P ,9200===),(Y X P (2).),()()(94111111===-=>+-=≤+Y X P Y X P Y X P。
2014年学考试题分析及变式训练一、单项填空1. More and more people now travel by _____ bike to reduce _______ pollution.A. a ; theB. the ; theC. / ; /D. the ; /2. ---Excuse me , could you tell me the way to the library?---Sorry. I’m stranger here.---______.A. Thanks , anywayB. It’s a pleasur eC. Forget itD. Go ahead3. Tom is _____ to help you because he is a warm-hearted man.A. lovelyB. thankfulC. likelyD. careful4. Work harder , ________ you will make greater progress in English .A. asB. soC. yetD. and5. –Where did you buy your Longman Dictionary?--I bought ______ at Taobao . It’s cheaperA. thisB. itC. oneD. that6. Every year Beijing ______ a great many visitors from all over the world.A. respectsB. prefersC. employsD. attracts7. They raised money and ______ a new school in the town.A. set offB. set upC. set outD. set aside8. I like listening to music while my brother is fond _____collecting stamps.A. forB. ofC. toD. with9. _______ black and white people equal , Nelson Mandela struggled all his life .A. MadeB. MakingC. MakeD. To make10. Jack, ______ is crazy about table tennis, got the first place in that competition .A. whichB. thatC. whoD. whom11. Mary, together with her friends, ______ paying a visit to Sanya next Saturday. A. is B. has been C. are D. have been12. It’s raining _____ outside, so we’ll have to put off the sports meet.A. heavilyB. greatlyC. BadlyD. seriously13. When he was a boy, he ______ in three different schools.A. Will be educatedB. has been educatedC. was educatedD. is educated14. --______ I keep the book till next month?--I’m afraid not . You can only keep it for one week.A. MustB. MayC. DareD. Need15._____ the boy is only ten years old, he knows a lot about history .A. BecauseB. WhenC. SinceD. Although(变式训练)Mother : Bill _1__ (graduate) from high school soon . What do you think he is going to do ?1Father : I think he should go to college. But I haven’t decided where he should go yet . In my opinion, I want him _2__(go) to a small university , _3__ the classes woul dn’t be so large.Mother : He ought to go to a public school where the student’s are _4__(serious) about study than those in a private school.Father : Yes , I agree with you. And I suggest that he should go to a collage out of the state , where he can widen his knowledge and _5__ (broad) his view. Mother : But that will be too far for him to come home on weekends . I can only see him in summer and winter vacations. I _6__ miss him.Father : He is old enough to depend on _7__. You cannot take care of himfo rever. It’s time _8__ him to be independent.Mother : OK. But the most important thing is where Bill wants to go . _9__ we discussed now is just a suggestion. And Bill should make the final _10__ (decide) by himself.Father : That’s right . We will talk to him about this after he comes home .二、完形填空My Mom and Dad’s relationship became worse. However , I was not prepared __16__ the day that Dad would decided to leave . All that I could _17__ was that I would become a product of a broken family . It was something I never thought possible , and it _18__ me greatly .The night before my Dad _19__, I wrote a long _20__ to him. I told him how _21__ I loved him and how much I would _22__ him . I told him that I would always and _23__ be his Krissie. As I folded my letter, I put in a _24__ of me with a saying “ Anyone can be a father , but it takes someone _25__ to be a daddy “. Early the next morning , As Dad left our _26__ , I sneaked (偷偷地走) out to the car and put my letter _27__ one of his bags.Two weeks went by , _28__ there was not a word from my father . Then , one afternoon, I came home from school to _29__ my Mom sitting at the table ,_30___ to talk to me . She told me Dad had been there and they had talked for a long time. They decided there were thing that _31___ of them could share and that their _32__ was worth saving.Mom then turned her focus to my eyes , “Krissie , Dad told me you wrote him a letter and that when reading your letter , __33__ cried . It meant a lot to him . after that , he called to ask _34__ he could come over to talk . Whatever you side really made a __35__ to your Dad.”16. A. with B. for C. by D. in17. A. look for B. hear of C. think of D. ask for18. A. worried B. interested C. satisfied D. excited19. A. left B. arrived C. ran D. came20. A. report B. note C. story D. letter21. A. many B. much C. little D. few22. A. hate B. hurt C. meet D. miss23. A. never B. often C. forever D. seldom24. A. photo B. diary C. dream D. record25. A. rude B. foolish C. special D. boring26. A. house B. city C. village D. country227. A. through B. into C. besides D. off28. A. or B. until C. but D. unless29. A. learn B. accept C. feel D. find30. A. failing B. waiting C. begging D. refusing31. A. some B. neither C. all D. both32. A. chance B. belief C. marriage D. company33. A. he B. she C. I D. we34. A. how B. which C. that D. if35. A. research B. difference C. question D. promise(变式训练)A teacher let her class play a game. The teacher told each__1__ to bring a bag __2__a few potatoes. Each potato will be given a name of a(n)__3__that the child hates, so the number of potatoes that a child will put into his/her bagwill__4__ the number of people the child__5__.Some children had two potatoes ; some had three and others had__6__five potatoes. The teacher then told the children to__7__ the bag wherever they go for a week.As the days __8__, the children started to complain (抱怨) because of theunpleasant __9__ coming from the rotten(腐烂的) potatoes. And the students with five potatoes also had to carry __10__ bags.After __11__ , the teacher asked ,”How did you feel ?” The children started complaining about the __12__ they had to go through , when they had to carry the heavy and __13__ potatoes everywhere they went.__14__the teacher said, ”This is the situation __15__ you carry hate for__16__inside your heart. The smell of hate will __17__ your heart and you will carry__18__with you everywhere you go. If you cannot __19__ the smell of rotten potatoes for __20__ one week, can you imagine what it is like to have the smell of hate in your heart fo r your lifetime?”1. A. child B. headmaster C. teacher D. classmate2. A. including B. taking C. containing D. providing3. A. animal B. toy C. book D. person4. A. lead to B. depend on C. belong to D. consist of5. A. spots B. hates C. loves D. misses6. A. up to B. or rather C. at least D. less than7. A. fetch B. offer C. carry D. bring8. A. went away B. went down C. went up D. went on9. A. shape B. smell C. color D. taste10. A. smaller B. lighter C. brighter D. heavier11. A. a week B. an evening C. a month D. an hour12. A. success B. quarrel C. trouble D. pleasure13. A. smell B. pleasant C. fresh D. lively14. A. Tues B. Then C. Anyhow D. However15. A. until B. unless C. since D. when16. A. somebody B. something C. everybody D. everything17. A. prevent B. protect C. pollute D. produce18. A. them B. it C. us D. that319. A. allow B. admit C. bear D. breathe20. A. ever B. still C. once D. just阅读AA man was sitting in the park watching the ducks on the pond when a woman approached him with a while poodle .she sat down on a bench, took out a magazine and began to read.The poodle was sitting between her and the man.After it had been sitting quietly for about ten minutes, the poodle turned and looked up the man.“Excuse me.” the dog whispered, ”but you look like a kind man. Please buy me from this bad woman.The man could hardly believe his ears. A dog was whispering to him .In English!“She is no mean to me,” the dog continued. she ne ver pets me or plays with me. She doesn’t feed me properly and she often beats me when she is unhappy, which is most of the time.”The man was amazed to hear the dog say all this. He was even more surmised when the dog added, “And I’m really a very good dog . I’m quite famous, too. I won a medal in the last war and was twice wounded in action. I’ve saved three children---two from drowning and one from a fire.”The man decided that he would try to buy the dog from woman .He would pay a lot of money if necessary. The dog would soon earn tens of thousands of dollars on television. It would be the world’s first talking dog.“Excuse me,” he said to the woman, “but I love you little dog. would you sell him to me?”“I’ll be delighted to sell him, ” the woman said .“you can have him for ten dollars.”“Ten dollars !” the man said. “Only ten dollars ? why so little ? ”“because, ” the woman said, “ he tell lies and is always making trouble.”36. The underlined word “people” is a kind of ______.A. dogB. tigerC. monkeyD. duck37. The man was surprised to know that ________.A. the woman was so famous.B. the dog could talk in English .C. the woman was always happy.D. the woman fed the dog properly.38. The man wanted to buy the dog to _______.A. feed itB. play with itC. make monkeyD. punished the women39. What does the women think of the dog?A. It’s a very good dogB. It always pleases her.C. It’s often tells the truthD. It is a trouble-maker40. The passage is probably a _______.A. funny storyB. poemC. book reportD. notice4BA have funB study for the future jobC kill timeD work in performing business42.Which course is for people who would like to work in sports centers?A Performing ArtsB Art and DesignC Basic Information TechnologyD Sports Students43. What can you learn in Art and Design ?A. Clothes design.B. Directing.C. Programming and software.D. Fitness and diet.44. If you have only one year to take a course , you can choose from_______.A. Performing Arts & Sports StudiesB. Sports Studies & Art and DesignC. Performing Arts & Basic Information TechnologyD. Basic Information Technology & Art and Design45. You must ______ if you take these course.A. be under 16B. finish high schoolC. learn full timeD. be strong and healthy5CTime Berners-Lee looks ordinary ---- he is middle-age and brown hair . His life is quite normal---he was born in England , but his home is now in Massachusetts, USA. However, in 1989 , Tim had a very important idea and invented the World Wide Web (www) later!Tim went to school in London . his parents both worked with computers , so it isn’t surprising that he loved computers from an early age, When he was eighteen , he left school and went to Oxford University , in which he studied Physics. At Oxford , he became more and more interested in computer , and he made his first computer from a old television . He graduated in 1976 and got a job with a computer company in Dorset ,English.In 1989 ,he went to work in Switzerland ,where he first had the idea of an international information network linked by computer…and he decided to call it the World Wide Web. In 1994, he went to live in the United States, where he now works. In 1995, he wrote an article in the New York Times where he said “the Web is a universe of information: it is for everyone.” His idea of a web, where people from all over the world can exchange information, is now real. The Interest has created thousands of millionaires, but Berners-Lee is not one of them.46. Where does Tom Berners-Lee live now?A. In LondonB. In DorsetC. In New YorkD. in Massachusetts.47.He loved computers from an early age beca use of his___A. parents B teachers C friends D classmates48.He first has the idea of the World Wide Web in__A 1976B 1989C 1994D 199549.Which the following is true?A. Tim was a millionaire.B. Tim studied chemistry at Oxford.C. Tim made his first computer using an old television.D. Tim got a job with a computer company in Switzerland.50. What’s the passage mainly about?A The World Wide WebB Tim Berners-LeeC The importance of the webD The information age.DIt’s said that one can know the nature of both man and women by their behaviors at table. Indeed table manners are closely related to one’s life and one’s job. As the saying goes“When in Rome ,do as the Romans do”, English learners should knows what the proper table manners are in western countries if invites to a dinner party. The followings are some suggestions that may be helpful to you .The first important thing you need to know is when to begin eating. Before dinner, the hostess usually serves guests first and herself last. So do not eat as soon as served but wait until the hostess has also has been served and has picked up her fork as the signal to begin. But at a large dinner party where there are many guests, the hostess may ask everyone to begin eating as soon as they are served.If you want to talk while eating ,your mouth should certainly not be full of food because it is considered very bad manners . but it is possible to speak with6a little food in the mouth . When you have to answer a question , naturally you must wait until the food in your mouth in eaten.When a dish is passed to you with a fork in the plate , you should use it to take your food. Do not take too much at a time and make sure that the other guests can have enough food.Anyway , good table manners are very important and they are not so simple as we thought. But it is necessary for one to know what good table manners are because they can help one succeed in his life!51. Table manners are closely related to one’s ______ in paragraph 1.A. life and nameB. job and ageC. job and nameD. life and job52. What is the first important thing to know at a dinner party?A. What to eatB. Whether to talkC. When to begin eatingD. How to use forks53. If you have to answer a question while eating, you should _______.A. refuse to answer itB. answer it immediatelyC. tell him/her to ask it laterD. wait until the food in your mouth is eaten54. The author suggests that you use the_____ to take food.A. forkB. knifeC. chopsticksD. spoon55. In which section (栏目) of a newspaper can you find such a passage ?A. SportsB. CultureC. MusicD. News.书面表达假如你是高二学生李华,最近收到了外国朋友Tom 的 E-mail 。