2017年韩山师范学院本科插班生考试《高等代数》A卷

（A卷）第1 页共7 页韩山师范学院2016年本科插班生考试试卷汉语言文学专业现代汉语试卷（A卷）分）分，共16一. 填空（每空1 得分评卷人它是一种即从结构上说，汉语作为一种语言，具有一切语言共有的性质。

1. 。

；从功能上说，它是______________________ _________个辅音声母。

2. 声母是音节开头的_________，普通话中共有 _________。

e实际是单韵母中的_________，发音条件是3. ie、üe中的。

从现行汉字楷书字形角度对汉字进行汉字字体演变的主流是_________4._________。

分析，汉字的构件包括_________和是词_________所表达的内容。

词义是语言中词的含义，是词的_________5.义中的主要部分。

和___________6. 对句子结构分析，经常采用三种方法：句子成分分析法、。

___________ 。

“现在”则是___________，7. 就词性来说，“正在”是___________ 的不同上。

语气的不同主要表现在语调和___________8.分，共20分）二. 选择（每题1 评卷人得分（请将答案填入下面的表格中）1（A卷）第2 页共7 页1. 现代汉语常用词中以双音节为主的是（）A.代词B.量词C.名词D.动词2. 下列几项表述中属于口语特点的是（）A.用词精审B.结构严谨C.句子简短D.逻辑性强3. 语音的本质属性是（）A.物理属性B.社会属性C.生理属性D.心理属性4. 属于开口呼韵母的是（）A.强B.而C.主D.远5. 韵头、韵腹、韵尾俱全的是（）A.鸟B.娃C.句D.生6. pa、pai、pan、pang、pian中的a在实际发音中（）A.有差异，能区别词义B.有差异，不能区别词义D.没有差异，能区别词义 C.没有差异，不能区别词义7. 从汉字跟汉语的关系来看，汉字是（）A.语素文字B.音节文字C.音位文字D.音素文字8. “六书”中，促使汉字字量大大增加的结构方式是（）A.会意字B.形声字C.象形字D.假借字9. 属于一个语素的是（）A.蜓B.葡C.民D.柠檬汁儿10. 属于音译词的是（）A.伏特加B.美德C.心疼D.深浅11. “我们热爱伟大的祖国”中包含（）A.4个词、8个语素B.5个词、9个语素D.7 个词、 8个语素个语素C.6个词、712. 下列词语符合“平平仄仄”模式的是（）A.光明磊落B.师出有名C.喜笑颜开D.满载而归13. 属于偏正短语的是（）A.群众的智慧B.暗下去C.吃、穿、用D.喜欢游泳2（A卷）第3 页共7 页14. 属于谓词性短语的是（）A.十年前B.妈妈的微笑C.有资格晋升D.一百个15. 下列句子中含补语的句子是（）A.腐烂变质的食物吃不得。

韩山师范学院2013年专升本插班生模拟试卷数学与应用数学 专业 高等代数 考试 （A 卷）一、 选择题（每小题3分，共15分）1、设()n x x x f ,,,21 为n 元实二次型，则()n x x x f ,,,21 负定的充要条件为（ B ）（A ）负惯性指数=f 的秩 （B ）正惯性指数=0； （C ）符号差=n - （D ）f 的秩=n 。

2、设{}m ααα,,,21 是线性空间V 的一个向量组，它是线性无关的充要条件为（ A ）（A ）任一组不全为零的数m k k k ,,,21 ，都有∑=≠mi i i k 10α（B ）任一组数m k k k ,,,21 ，有∑==mi i i k 10α；（C ）当021====m k k k 时，有∑==mi i i k 10α；（D ）任一组不全为零的数m k k k ,,,21 ，都有∑==mi i i k 10α。

3、设E 1E 2…E s A E s +1…E t =I ,其中E i 为初等矩阵，i = 1,2,…, t , 则A -1等于( C ). （A ）E 1 E 2 …E t （B ）E t …E 2 E 1（C ）E s+1 …E t E 1 …E s （D ）E t …E s +1E 1 …E s .4、欧氏空间3R 中的标准正交基是（A ）（A ）()0,1,0;21,0,21;21,0,21⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛ （B ）()1,0,0;21,21;0,21,21⎪⎭⎫⎝⎛-⎪⎭⎫ ⎝⎛（C ）()0,0,0;31,31,31;31,31,31⎪⎪⎭⎫⎝⎛-⎪⎪⎭⎫ ⎝⎛ （D ）()()()1,1,1;1,1,1;1,1,1---5. 在欧氏空间C[0, 2π]中，向量x 2的长度等于 ( B )。

（A ）5325π （B （C ）383π （D 二、判断题（每小题2分，共10分。

你认为正确的，在题后圆括号内打“√”，错误的打“×”。

韩山师范学院2011年专升本插班生考试样卷数学与应用数学专业高等代数 A卷题号一二三四五六七八九十总分评卷人得分一、选择题(每小题3分，共15分)题号 1 2 3 4 5 答案1．m个方程n个未知量的线性方程组中，若其系数矩阵的秩等于m, 则( )成立。

（A）方程组一定有解; （B）方程组一定有无穷多解;（C）方程组一定无解; （D）方程组一定有唯一解.2. 设E1E2…E s A E s+1…E t =I,其中E i为初等矩阵，i = 1,2,…, t , 则A-1等于( ).（A）E1E2…E t；（B）E t…E2E1；（C）E s+1…E t E1…E s；（D）E t…E s+1E1…E s .3. 设A1, A2,…, A s都是n阶方阵，则对角线分块矩阵12sAAA⎛⎫⎪⎪⎪⎪⎝⎭的秩等于( ).（A）秩(A1A2…A s)；（B）秩A1×秩A2×…×秩A s；（C）秩(A1+A2+…+A s)；（D）秩A1+秩A2+…+秩A s .4. 设α1 , α2 ,…, αs与β1 , β2 ,…, βs均为线性相关的向量组，则下列结论正确的是（）.（A）α1+β1, α2+β2,…,αs+βs线性相关；（B）α1+β1,α2+β2,…,αs+βs线性无关；（C）α1,α2,…,αs,β1,β2,…,βs线性相关；（D）α1, α2,…,αs,β1,β2,…,βs线性无关.5.1221 , , 333α⎛⎫=-⎪⎝⎭，2212, ,333α⎛⎫=-⎪⎝⎭是R3的规范正交组，添加( )可以扩充为R 3的规范正交基.（A ）122 , , 333⎛⎫- ⎪⎝⎭； （B ）122 , , 333⎛⎫-- ⎪⎝⎭；（C ）221 , , 333⎛⎫-- ⎪⎝⎭； （D ）212 , , 333⎛⎫-- ⎪⎝⎭.二、填空题（把答案填在题中横线上。

每小题3分，共15分）1. 在n 元排列中，反序数最大的排列的反序数为 .2. 实数域上的不可约多项式的次数只能是 .3. 5432()2101616146f x x x x x x =-+-+-在Q [x ]内的典型分解式为. 4. 复数域C 作为实数域R 上的向量空间, 维数是 . 5. m ×n 矩阵A 的行向量组所生成的F n 的子空间叫做A 的 .三、判断题(每小题2分，共14分. 你认为正确的，在题后圆括号内打“√”，错误的打“×”。

韩山师范学院2017年本科插班生考试试卷旅游管理专业市场营销学试卷（A卷）一、单项选择题（每题1分, 共20分）1. 市场营销的核心是（）。

A. 生产B. 分配C. 交换D. 促销2.体育明星和电影明星是其崇拜者的（）。

A. 成员群体B. 直接参照群体C. 厌恶群体D. 向往群体3．在复杂的购买行为中, 消费者购买决策过程的第三个阶段是（）。

A. 确认B. 收集信息C. 备选产品评估D. 决定购买4. 收集第一手资料的主要工具是（）。

A. 计算机B. 乱数表C. 调查表D. 统计年鉴5．某工程机械公司专门向建筑业用户供应推土机、打桩机、起重机、水泥搅拌机等建筑工程中所需要的机械设备, 这是一种（）策略。

A. 市场集中化B. 市场专业化C. 全面市场覆盖D. 产品专业化6. 市场定位是（）在细分市场的位置。

A. 塑造一家企业B. 塑造一种产品C. 确定目标市场D. 分析竞争对手7. （）差异的存在是市场细分的客观依据。

A. 产品B. 价格C. 需求偏好D. 细分8. 产品组合的宽度是指产品组合中所拥有（）的数目。

A. 产品项目B. 产品线C. 产品种类D. 产品品牌9．丽兰化妆品公司决定对其现有市场上销售的润肤霜进行升级换代, 这种密集增长战略是（）。

A.市场渗透B.产品开发C.市场开发D.多元化发展10. 某服装店售货员把相同的服装以800元卖给顾客A, 以600元卖给顾客B, 该服装店的定价属于( )。

A. 顾客差别定价B. 产品形式差别定价C. 产品部位差别定价D. 销售时间差别定价11.汽车制造厂增加了拖拉机生产, 叫( )。

A. 前向一体化B. 水平一体化C. 同心多元化D. 水平多元化12. 品牌中可以用语言称呼、表达的部分是( )。

A.品牌B.商标C.品牌标志D.品牌名称13. （）是最常见的市场营销组织形式。

A. 职能型组织B. 产品型组织C. 地区型组织D. 管理型组织14. 生产消费品中的便利品的企业通常采取（）的策略。

韩山师范学院2017年本科插班生考试试卷计算机科学与技术专业 高级语言程序设计试卷（A 卷）一、填空题（每空2分，共10分）1．C 程序的基本组成单位是 函数 。

2．当a=1,b=35,c=5时，表达式a!=b>c 的值是 _____ 0 __。

3. 一个C 文件是一个__字节流__流或二进制流。

4. 一个字符数据既可以以字符形式输出，也可以以_ 整形 _形式输出。

5. 若a 是int 型变量，且a 的初值为6，则执行表达式a+=a-=a*a 后，a 的值为 -24 。

二、单项选择题（每题2分，共30分）1.下述程序段的输出结果是（D）。

int x=10;int y=x--;printf("%d,%d",(y++,x),y++);A、9，10B、11，10C、10，9D、9，11逗号运算符：表达式用逗号分开，所以最终的值应该是最后一个表达式的值2.下面各选项中，均是C语言标识符的选项组是（C）。

A、for china toB、void union _342C、long_123 short56 _doD、text.txt _075 _3ew 3．若int k=10；则执行下列程序后，变量k的正确结果是（B）。

main( ){ int k=10；switch(k){ case 9: k+=1；case 10: k+=1；break；case 11: k+=1；default: k+=1}printf(″%d\n″，k)；}A、12B、11C、10D、94．在位运算中，操作数每右移一位,其结果相当于（A）。

A、操作数除以2B、操作数乘以16C、操作数除以16D、操作数乘以2左移乘二，右移除以2，都是整除5．以下能对二维数组c进行正确的初始化的语句是（B）。

A、int c[][5]={{1},{},{4}};B、int c[][5]={{1},{2},{4}};C、int c[5][]={{2},{8},{4},{5}};D、int c[5][]={{6},{6},{9}};6、以下程序执行后，sum的值是（A）。

韩山师范学院2019年本科插班生招生考试数学与应用数学 专业 高等代数 试卷（B 卷）一、填空（每空3分，共30分）1. 一个素数p 有 个因数.2. 最小的数域是 .3. 方阵001020300A ⎛⎫ ⎪= ⎪ ⎪⎝⎭的逆矩阵A –1＝ .4. 多项式)(x f 无重因式的充要条件是)(x f 与()f x '满足条件 .5．n 阶行列式D 中等于零的元素的个数大于n n -2，则此行列式的值为 ．6. 次数大于零的多项式在复数域C 中只能有 次的不可约因式.7. 一个向量组的极大线性无关组所含向量的个数叫做该向量组的 .8．数域 F 上的向量空间V 的非空子集W 是V 的子空间的充要条件是． 9. 已知A 为⨯m n 矩阵, ≠m n ，则方程组θ=AX 只有零解的充要条件是 ．10. 两个复二次型等价的充分必要条件是 .二、是非题（对的打“√”，错的打“×”，每题3分，共30分）1.若111221221,a a a a =则11211112222212,b a a b x x b a a b ==是方程组111122121122220,0.++=⎧⎨++=⎩a x a x b a x a x b 的解. ( ) 2．任一个向量组空间都有基 . ( ) 3. 已知欧氏空间R 3的线性变换(,,)(,,)x y z x y y y z σ=++，则σ 是正交变换，也是对称变换. ( ) 4. 523146879 是奇排列. ( ) 5. 在欧氏空间C [-1，1]中，向量1与2x 正交. ( ) 6. 2是多项式1415623-+-x x x 的二重根. ( )7. 若两个向量组等价，则它们所包含的向量的个数相同。

( )8. 多项式432810-+-x x x 在有理数域上是不可约的. ( ) 9．奇数阶反对称矩阵的行列式值为零． ( ) 10. C 为复数域，则C 构成C 上的向量空间. ( ) 三、证明题（共10分）设)(x f 是一个整系数多项式，求证：若)1(),0(f f 都是奇数，那么)(x f 不可能有整数根.四、证明题（共10分）如果矩阵A 满足A T = A ，那么称A 是对称的. 设P 是可逆矩阵，证明：A 是对称矩阵⇔P T AP 是对称矩阵.五、证明题（共10分）设V 为数域P 上的n 维线性空间，且),,,(21n L V αααΛ=，证明：},,,{21211n αααααα++++ΛΛ是V 的一组基.六、计算题（共10分）设数域F 上三维向量空间的线性变换σ关于{α1 , α2 , α3}的矩阵是⎪⎪⎪⎭⎫ ⎝⎛--201120101，假设11232123312323,34,22βαααβαααβααα=++=++=++求σ关于基321,,βββ的矩阵.。

韩山师范学院本科三年级插班生考试 数学与应用数学 专业 高等代数 试卷一、 填空题（每题2分，共12分）1、设)(x p 是)(x f 的导数)(x f '的1-k 重因式，则)(x p 是)(x f 的k 重因式的充要条件是 ．2、设 A 是 n 阶方阵，则det(3A)= ．3、设 A 都是 n 阶可逆方阵, 满足aA 2+bA+I=0，则A -1= ． 4、n 元齐次线性方程组的系数矩阵的秩为r ，那么其基础解系含 个解向量． 5、欧氏空间中向量α的长度 α=2，则><αα,= ．6、复数域上两个n 元二次型等价的充要条件是它们____ _____． 二、 判断题（每题2分，共10分；在题后括号内打“√”或“×”） 1．A 、B 都为n 阶实方阵，detA = detB ，则A = B ．( ) 2．等价的向量组含有相同个数的向量．( )3．设δ，τ是n 维向量空间V 的两个线性变换．A ，B 分别是δ，τ关于V 的基n ααα,,,21 的矩阵，当δ≠τ时，必有 B ≠A ．（ ） 4．两个不同矩阵的特征根一定不同．（ ）5．在欧氏空间中V 中，对任何实数 k 都有 k k αα=．（ ） 三、 选择题（每题3分，共18分；将正确的选项序号填在题中括号内）1．下列命题正确的是：（ ） A 、如果)()()()(x h x f x g x f =，那么)()(x h x g =； B 、如果)()()(x g x f x h ，那么)()(x f x h 或)()(x g x h ； C 、如果)()(x f x p ，那么)())(),((x f x p x f =； D 、若既约分数sr为整系数多项式)(x f 的有理根，则)1(f r s -而且)1(-+f r s ． 2．n 阶行列式D 的元素ij a 的余子式ij M 与ij a 的代数余子式ij A 的关系是：（ ） A ．ij ij M A =； B 、ij ij M A -=； C 、ij ji ij M A +-=)1(； D 、ij ij M A ≠3、设0λ是可逆矩阵A 的非零特征根，则10-λ是（ ）的一个特征根．A ．—A ；B ．A ' ；C ．2A ； D ．1-A ．4．若m ααα,,,21 与n βββ,,,21 都线性无关,则向量组m αα,,,1 ,n ββ,,,1 ( )．A.一定线性无关；B.不一定线性无关；C.一定线性相关；D.以上结论都不对. 5、设A=)(ij a , detA=0, b=),,,(21'n b b b , X=),,,(21'n x x x ．其中A ，b 为已知，则线性方程组AX=b( )．A.无解；B.有无穷多解；C.有唯一解；D.无解或有无穷多解． 6、设A 、B ∈)(F M n ，则A 的列向量组与B 的列向量等价当且仅当( )． A.A ＝B ； B.detA ＝detB ； C.det(AB)≠0； D.秩A=秩B四、（8分）计算行列式D ＝y y x x -+-+1111111111111111．五、（8分）判断方程组⎪⎩⎪⎨⎧=+=+=+=+242131243121b x x b x x a x x a x x （其中2121b b a a +=+）是否有解，有解时求其一般解．六、（10分）证明：),(),(222g f g f =． 七、（8分）证明：秩AB ＝秩B 的充分必要条件是(AB)X=0与BX=0有相同的解．八、(8分)设 n 阶方阵 A 满足A 2=A ，证明I+A 可逆，且 (I+A)-1 = I －A ． 九、（8分）设V 是数域F 上的向量空间，()1 , λδV L ∈ 和 2λ 是δ的两个不同的本征值，i α是δ的属于i λ的本征向量，2 , 1=i ．证明：021≠+αα，但它却不再是δ的本征向量，即F ∈∀λ，()() 2121ααλαασ+≠+．十、（10分）判定二次型ơ()32312123222132128632,,x x x x x x x x x x x x -++++=是否正定．。

韩山师范学院2017年本科插班生考试试卷英语 专业 英语语法 试卷（A 卷）一、Choose the correct answer （每题1分，共40分）Direction: Complete the following sentences and then blacken the corresponding letter on the ANSWER SHEET.1.______ can get a better view of the game than the participants.A. Looker-onB. Lookers-onC. Looker-onsD. Lookers-ons2. My mother cut the cloth with ______ scissors.A. aB. twoC. a couple ofD. a pair of3.______ receives only a small portion of the total amount of the sun’s energy.A . The earth’s surface B. The surface earthC. The surface of earthD. The earth surface4. Little boys are easily ______.A. taken outB. taken awayC. taken inD. taken over5. The thief ran away as fast as he could ______ the policeman.A. in sightB. within the sight ofC. within sightD. at the sight of6. Prior ______ his departure, he wrote a letter to his mother.A. ofB. fromC. toD. in7. ______ classical music, which follows formal European traditions, jazz is a spontaneous and free form.A. In comparison withB. In connection withC. In regard toD. In contrast to8. The investigators found that more should be done for ______ in India.A. the poorB. a poorC. poorD. those poor9. A man suffering from a chock should be given ______.A. hot sweet teaB. a hot sweet teaC. the hot sweet teaD. one hot sweet tea10. Under no circumstances will there be wage control while I am ______ of the government.A. the headB. headC. a headD. that head11. We have produced ______ this year as we did in 1993.A. as much cotton twiceB. as twice much cottonC. much as twice cottonD. twice as much cotton12. With the miniaturization of the structural components the weight of these electric devices has decreased ______ 30%.A. byB. withC. inD. as13. Most English people go to Spain for the sea, the sun and all the ______ things associated with a relaxing holiday.A. any b. another C. other D. some14. I cannot invited ______ of you, since I’ve got only one extra ticket.A. eitherB. bothC. someD. one15. The little baby was left alone, with ______ to look after it.A. someoneB. anyoneC. not oneD. no one16. Frank admired his friends Tom and David. He imitated ______.A. theirs every actionB. every action of theirsC. every of their actionD. every action of their one17. The modern machine proved ______ in heart surgery.A. high valuableB. highly valuableC. valuable highD. valuable highly18. Tuition at American university runs ______ one thousand dollars a semester.A. so high asB. as high toC. as high asD. as higher than19. If negotiations for the new trade agreements take ______, critical food shortages will develop in several countries.A. too much longerB. much too longC. the longestD. the longer20. Many scientists ______ their own eyes and ears than the theories of the ancients.A. would rather to believeB. will rather believeC. rather would believeD. would rather believe21. “We didn’t see him at the lecture yesterday.” “He ______ it.”A. mustn’t attendB. cannot have attendedC. would have not attendedD. needn’t have attended22. ______ that bad weather was on the way, the climbers decided to put off their attempt on Eiger until the following week.A. Having toldB. Being toldC. TellingD. Having been told23. You must follow the directions exactly and if you become ______, you must take the time to go back again and reread them.A. to confuseB. confusingC. confusedD. confuse24. What’s the use ______ extra leisure time if you don’t know what to do?A. of knowingB. to haveC. being haveD. have25. I have tried _______ worrying about it.A. to stop consciouslyB. to consciously stopC. to conscious stoppingD. to stopping consciously26. Now that you _______ , what are you going to do?A. are being returnedB. have been returningC. have been returnedD. have returned27. The little girl ______ by the drug-pusher to carry drugs into the country.A. was made useB. was made usedC. was made use ofD. was made used of28. ______ a meeting this afternoon.A. There going to beB. There will be going to beC. There is going to beD. There will going to be29. By the time the course ends,______ a lot about Britain.A. we’ll learntB. we are learningC. we have learntD. we’ll have learnt30. I suppose you’re not going today, ______?A. are youB. do youC. don’t youD. aren’t you31. ______ that this region was so rich in natural resources.A. Little he knewB. Little did he knowC. Little he did knowD. Little he had known32. ______ was wrong.A. Not the teacher but the studentsB. Both the students and the teacherC. Neither the teacher not the studentsD. Not the students but the teacher33. The Smiths ______ their breakfast when the morning post came.A. were havingB. has been havingC. are havingD. had34. Were it not for the adoption of the open policy, things ______ they are today.A. would never beB. could have beenC. would never have beenD. didn’t have35. Einstein’s theory of relativity seemed hard to believe at the time ______.A. when he first introducedB. that he first introduced itC. he first introducedD. which he first introduced it36. The time will surely come ______ ordinary people could operate computers as well.A. whileB. whenC. asD. on which37. _____ human beings depend to a great extent on forests, every effort must be made to preserve trees and wildlife.A. IfB. UnlessC. UntilD. Since38. No one has _____ been able to trace the author of the poem.A. stillB. yetC. alreadyD. just39. Will all those _____ the proposal raise their hands?A. in relation toB. in excess ofC. in contrast toD. in favor of40. I used to be able to play well but I'm _____ now.A. out of dateB. out of touchC. out of practiceD. out of place二、Correct the errors in the following sentences.（每题1分，共20分）Directions: Identify the one that would not be acceptablein standard written English. Mark out the incorrect one and correct it. And then write down your answers on the ANSWER SHEET.1. He had joined the Party for ten years before he was transferred to the city.A B C D2. Because radio communication had failed once before, I was afraid the men inA Bthe crew on the plane might be lost touch with the control tower.C D3. From the measure adopted by the committee, higher retirement age will notA Bgo into effect for two years.C D4. It is this marvelous continuity found in the human condition in any centuryA Bthat make the reading of masterpieces so fascinating.C D5. The president mentioned to the cabinet members he was going to negotiate aA B Cnew treaty with the foreign minister.D6. My brother doesn’t care how much does the car cost because he is going to buyA B C Dit anyway.7. Having finished high school, the village education board appointed him to aA B C teaching post in the primary school.D8. He sold the vegetables at half price, therefore they would go bad.A B C D9. Doctors often study film records of complex operations for improvingA B Ctheir own knowledge and skill.D10. If a crisis was to occur, those unfamiliar with the proceduresA Bwould not know how to handle the situation.C D11. The harder she tried, the more badly she danced before such a large audience.A B C D12. It was not until very recent times that had the theory of “probability” beenA B Clooked upon as hardly more than a curiosity.D13. He had trouble finding out that the capital of that country lay on the coast or inA B C Dthe mountains.14. As a result from hearing from the radio announcement, Peter has written toA Boffer himself as a member of the panel for next week.C D15. Learning a foreign language is especially difficult for those who had neverA B Clearned one before.D16. It often mistakenly supposed that the most expensive things are always the best.A B C D17. Some international students use a cassette recorder to make tapes of theirA Bclasses so that they can repeat the lecture again.C D18. To become a member of the civic association, one need only attend threeA Bmeetings and to pay his fees regularly.C D19. Thomas was a real friend, for he advised me as well as helping me with myA B C Arabic.D20. Some find swimming more enjoyable than to sit at home reading.A B C D三、Put the verbs in brackets in the correct form.（每空1分，共20分）1. The boy, who had remained silent and deep in thought on the journey home, _____(reply) in a way that shocked his father.2. For example, the proverb, “plucking a crop _____ (help) it grow”, is based on the following story.3. They use computers to keep the traffic _____ (run) smoothly.4. Up to now, the program _____ (save) thousands of children who would otherwise have died.5. The Group of Eight, or G8, _____ (form) by eight o f the world’s wealthiestnations in 1998.6. Barbara is easy to recognize as she’s the only one of the women who _____ (wear) an evening dress.7. Liuxiang was the first Asian _____ (win) the men’s 110m hurdles at the Olympics in Athens.8. When the first English settlers arrived in the New World, the Indians wearing jewelry made of animal bones ___(greet) them warmly.9. Do you believe that there is a _____ (connect) between smoking and heart disease?10. She stared at the painting, wondering where she _____ (see) it.11. By the end of next year they _______(complete) the task.12. A good deal of British car manufacture _______ (closely tie with) the continental industry.13. He held out a suggestion that the working part ________ (machine) in a more efficient way.14. Part of the light _______ (strike) the surface will be reflected from it.15. ____(remind) not to miss the flight at 15:30, the manager set out for the airport in a hurry.16. They ______(build) a new bridge over the river since May.17. Their letters ______ (not arrive) when they ______(leave) home this morning.18. She _________ (not want) to stay in bed while the others _________ (all,四、Fill in the blanks with proper prep., adv.,determiner, coordinator or subordinator.（每空1分，共10分）1.Mr. Brown showed his dissatisfaction ______your delay.2.The two companies are completely independent. There is no connection______ them.3.Don’t blame him for this; I am responsible ______that has happened.4.We managed to keep the fire in check, but we couldn’t put it _____.5.Medical research has shown that the widespread use of cigarettes contributes______the increase of cancers.6.He decided to make further improvements on the computer’s design ______the light of the requirements of customers.7.Finding a job in such a big company has always been ______ his wildestdreams.8.He was not conscious ______ what an important discovery he had made.9.He stood there with his back _______ the wall.10.That mountain is about two thousand feet _____ sea level.五、Rewrite the following sentences according to therequirements. （每题1分，共10分）1. Combine the sentence by using infinitive “to”She is so excited that she can’t utter one word.2. Use “there be” structure to rewrite the following sentence:Three accidents have occurred at this crossroads this week.3. Rewrite the following sentence with anticipatory “it”:How she came to have such a valuable painting is a mystery.4. Rewrite the given situation into subjunctive mood:I did not bring enough money with me, so I can’t take a taxi now.5. Put the following sentence into indirect speech:“I’ll be waiting for you in the office tonight,” David said.6. Join the sentences by changing the second into a non-restrictive attributive clause:The postman came to the back door. He is new in the district.7. Rewrite the following sentence so that it contains an adverbial clause.Hearing the news they immediately set off for Shanghai.8. Rewrite the underlined parts by using inversion.A temple stands at the foot of the mountain.9. Rewrite the underlined sentence with the emphasized pattern “it is …that/who/which”.She didn’t know her mother was ill in bed until she came home from work.10. Combine the following sentences by using an absolute construction (独立主格结构)There was no way for me to cross. I walked upstream on the south side.。

韩山师范学院2017年本科插班生考试试卷英语专业基础英语试卷（ A卷）nguage knowledge. Choose one word, phrase or statementthat best completes the sentence. （每空1分，共20分）1. Agriculture is the country’s chief source of wealth, wheat ______ by far the biggest cereal crop.A. isB. beenC. beD. being2. Jack _____ from home for two days now, and I am beginning to worry about his safety.A. has been missingB. has been missedC. had been missingD. was missed3. Above the trees are the hills, ____ magnificence the river faithfully reflects on the surface.A. whereB. of whoseC. whoseD. which4. Who ______ was coming to see me in my office this afternoon?A. you saidB. did you sayC. did you say thatD. you did say5. Does Alan like hamburgers?Yes. So much ____ that he eats them almost every day.A.forB. asC. toD. so6. Your ideas, ______ seem unusual to me.A. like herB. like hersC. similar to herD. similar to herself7. The opening ceremony is a great occasion. It is essential _____ for that.A. for us to be preparedB. that we are preparedC. of us to be preparedD. our being prepared8. Time _____, the celebration will be held as scheduled.A. permitB. permittingC. permittedD. permits9. The bus moved slowly in the thick fog. As a result, we arrived at our _____ almost two hours late.A. designationB. destinyC. destinationD. dignity10. He demonstrated his _____ for music by the ease with which he picked out melodies by ear.A. attitudeB. ability C aptitude D. wisdom11. Many modern language teachers make occasional use of teaching aids such as computers and tape recorders, but only a few use then systematically as an ______part of their work.A. incredibleB. individualC. integralD. associate12. Living in the countryside has its _____ as well as advantages.A. inferiorityB. setbacksC. drawbacksD. validity13. The air that holds a maximum amount of water vapor is _____, like s sponge unable to hold any more water.A. immersedB. saturatedC. quantifiedD. ventilated14. Electric wires in your house are_____ with poor conductors like rubber or silk.A. segregatedB. insulatedC. isolatedD. severed15. The enemy are now in a very difficult situation; they can neither advance nor ____ .A. resignB. retreatC. retrieveD. repel16. Reading is an active thinking process ______ the interaction between the reader and the print.A. containingB. indulgingC. involvingD. resolving17. In some cases, a sentence may be grammatically acceptable, but ______ in implication.A. ambitiousB. affirmativeC. approximateD. ambiguous18. For Europeans, life is a career; for Americans, it is a _______ of hazards.A. successB. recessionC. successionD. procession19. Reading efficiency means the ______ of a reading task within an appropriate time frame and with appropriate comprehension.A. accomplishmentB. commitmentC. contentmentD. complement20. In the past, major disasters, such as wars, plagues and earthquakes, could destroy only a _____ of the human race and environment.A. fractionB. fragmentC. frictionD. fictionII.Derivative. Write down the correct word to complete each sentence. （每题1分，共10分）A.Breathe1. It is so hot in this small kitchen that I can hardly ________.2. When I answered the telephone, there was an unknown and _____ voice on other end, which was really irritating.3. There was a ______ silence during the last world table-tennis championship game.4. You are wasting your ______ trying to persuade him to quit smoking. He’ll only stop when he wants to.5. During the last convention, there were so many items on the agenda that there was hardly any ____ space.B. express6. Being an advanced student of English, you should be able to _____ yourself freely in English.7. A cat’s mewing may be _______ of hunger, cold or pain.8. _______, impressionism and romanticism are different movements in art, music and literature.9. The shop assistant was a middle-aged man with an ______ face.10. The beauty of the cave, with its stalagmites and stalactites and dripping water, was beyond _______.III.Match each word in Column A with the phrase in Column B that is similar in meaning. (每题1分，共10分）IV.Fill in each blank with a preposition from the box.（每题1分，共10分）1. The “quality”newspapers are often held ___ as an example ofimpartial journalism.2. I don’t think our food suppliers will hold ___ much longer.3. Do you think the editors of the magazines will hold ____ our taking sides on political questions?4. During the enemy’s offensive, the village people refused to surrender but held ___ until the rescue troops arrived.5. The football match was held ____ till further notice on account of the continual rain.6. We are not surprised at the young man’s enrollment in that university because it is not their policy to hold a person’s past bad behavior _____ him.7. Any teacher is inclined to hold ___ any excellent work of the students for his or her class to imitate.8. If we think what we are doing is good and beneficial to the people we should try to hold ____ it and never give up.9. Before the rainy season, the authorities had already had the banks of earth built to hold _____ the potential flood.10. It was a place of romance. I felt I had just to hold ____ my hand to touch it.V.Reading comprehension. Choose the one that you think is the best answer and mark your answers on Answer Sheet.（每题2分，共10分）Passage OneToday, more and more people are using credit cards instead of money to buy the things they need. Almost anyone who has a steady income and a continuous work record can apply for a credit card. If you have a credit card, you can buy a car, have a dinner, take a trip, and even get a haircut by charging the cost to your account. In this way you canpay for purchases a month or two later, without any extra charge. Or you may choose to spread out your payments over several months and pay only part of the total amount each month. If you do this, the credit card company or the bank who sponsors the credit card will add a small service charge to you total bill. This is very convenient for the customer. With the credit card in your wallet or purse, you don’t have to carry much cash. This saves you trips to the bank to cash checks or draw cash. Also if you carry credit cards instead of a lot of cash, you don’t have to be concerned about losing your money through carelessness or theft. The card user only has to worry about paying the final bill. This of course can be a problem if you charge more than you can pay for.Credit cards are big business. Americans spend 16 billion dollars a year on credit cards and there are already 590 million of them in circulation. Many banks sponsor their own credit companies and issue cards free to their customers. Other credit card companies charge their members annual dues. The stores that accept credit cards must pay a small fee to the credit card company – a percentage of purchase price of the merchandise or service. In return, the credit card company promptly pay the store for the merchandise or service. Credit card companies make a profit from the fees they charge the stores and also from the fees collected from customers who pay for their charges in monthly installments.However, credit card companies sometimes have problems collecting overdue payments from unreliable customers. Also the use of stolen, lost, or counterfeit credit cards by criminals has become a big headache for the credit card companies which are responsible for the goods and services illegally charged to their customers’ account.1. What is the biggest worry for credit card users?A. Their credit cards may get stolen.B. They will be charged for the credit card service by the bank.C. The time allowed for them to pay back the money is not long enough.D. They may have spent more money than they can pay back.2. According to the passage, which of the following is Not a channel for the credit card company to make a profit?A. Membership fees for credit card users.B. A heavy fine for overdue payments.C. Service charges for stores that accept credit cards.D. Service charges for card users who pay back over period.3. The author’s purpose of writing this article is to _____.A. persuade people to use credit cardsB. warn people of the danger of using credit cardsC. explain how credit card business worksD. explain how to use credit cardsPassage TwoSome 2,400 miners were on the day shift last Tuesday morning at the Kinross gold mine, 65 miles from Johannesburg. A welding team was repairing a broken track for one of the trains that help carry gold ore to the surface. Suddenly, an acetylene tank sparked and flared. Flames swept through the tunnel, igniting plastic-covered wiring, which in turn set fire to polyurethane foam that keeps the walls dry and solid. Within minutes the mine shaft filled with thick black smoke containing toxic fumes from the burning plastic. Choking miners immediately fell and died of asphyxiation.When the initial 9 ½ -hour rescue operation ended, 177 were dead, one was missing, and 235 were injured, making Kinross the worst gold-mine disaster in South African history. All but five of the victims were black, and the black-dominated National Union of Mineworkers denounced the “unacceptably low safety standards” in the mines. In fact, Kinross last year lost its top safety rating. But the mine’s generalmanager said the plastics that burned had been considered safe. A government investigation is now under way.4. Which of the following statements is true?A. Many miners were burnt to death.B. Many miners choked and died.C. Many miners fell into the mine and were killed.5. Which of the following statements is not mentioned in the text?A. Kinross gold mine is the only gold mine in South Africa.B. Kinross gold mine disaster was worse than any other disaster that has taken place in South Africa.C. Kinross gold mine used to have a high safety rating.VI.Cloze. Decide which of the words given in the box below would best complete the passage if inserted in the corresponding blanks.The words can be used ONCE ONLY. Mark the letter for eachword on Answer Sheet.（每题1分，共10分）In the recent past, medical research has shown that heart disease is associated with certain factors in our day-to-day lives: with smoking, with poor nutrition, and with a lack of exercise.Doctors and other health experts have been 1____ the fact that we can often reduce the risk of heart disease by paying more attention to these factors.More and more people are realizing that there is a 2_____ betweenheart disease and the way they live. As a result of this new awareness, attitudes towards health are changing. In the past, people tend to think that it was 3____ for good health to have a good doctor who could be relied on to know exactly what to do when they become ill. Now they are realizing that merely receiving the best treatment 4_____ illness and injury is not enough. They are learning that they must 5____ more responsibility for their own health.Today many people are changing their dietary 6_____ and eating food with less fat and cholesterol. Many are paying more attention to reducing 7 ____ in their lives. The number of smokers in the US is now far below the level of a lot of years ago 8______ many people succeed in breaking the habit and as fewer people take it up.More and more are aware of the 9______ of regular exercise like walking, running or swimming, some have begun to walk or ride bicycles to work instead of driving. Millions have become members of health clubs and have 10 ____ health club one of the fastest growing businesses in the US today.e the words given in parentheses to translate the following sentences. Change the forms if necessary.（每题3分，共15分）1. 我们原无须自己预定雅虎因特网服务。

韩山师范学院2017年本科插班生考试试卷数学与应用数学 专业 数学分析 试卷（A 卷）一、 填空题（每小题3分，共30分）1. 设函数)(x f 在 [a,b ] 上连续，则21()x d f t dt dx⎰= . 2. 设)(x f 具有连续的导数, 则=+⎰dx x f x f x f )(1)()(2' .3. 设=)(x f sin , 0,, 0, (2, 0,kxx x k x k x x ⎧<⎪⎪=⎨⎪+>⎪⎩为常数）, 若()f x 在0x =在右连续，则k =_________ _ ____.4. 设∈+=x x n xn x f n , ||1sin )(2) , (∞+∞-.则=∞→)(lim x f n n . 5. 函数3ln 3)(--=x x x f 全部间断点是 .6.343()41032f x x x ⎡⎤=-+⎢⎥⎣⎦设 ，则其在，上的最小值为 .7. 二重积分23Dx y dxdy ⎰⎰ (其中D ：0≤y ≤x 2,0≤x ≤1)的值为 ． 8. 设(,)z f x y xy =+，(,)f u v 具有连续偏导数，则偏导数zy∂=∂ . 9. 交换积分dx y x f dyy⎰⎰-101),(的次序成为 .10. 设dy hh x f x f x f y h 36)2()(lim),(0则且=+-=→等于 .二、 计算题（每小题6分，共30分）1. 设⎪⎩⎪⎨⎧=+≠++=0 ,0 0 ,1sin ),(222222y x y x yx y y x f ,考察函数f 在原点(0,0)的偏导数。

2. 求cos 2x 的幂级数展开式.3. 计算极限 2n 11lim(1)nn n→∞++.4．求曲面z y x =+22，4:22=+y x D 及xoy 平面所围成的立体体积.5．求由曲线y 2 = 2x 及直线y = x-4所围成的图形的面积。

韩山师范学院专升本插班生考试样卷数学与应用数学 专业 高等代数 样卷一、填空题(每小题2分，共12分) 1．最小的数域是 。

2．能整除任意多项式的多项式是 。

3．－1是5432()614113f x x x x x x =+----的 重根。

4．六阶行列式D 的一项233142561465a a a a a a 的符号为 。

5．二次型12312(,,)6f x x x x x =-的矩阵是 。

6．设(1,1,1),(1,1,)αβλ=-=是欧氏空间R 3的两个向量，则当λ= 时，有αβ⊥。

二、判断题(每小题2分，共10分)1．设:f A B →是一个映射，若对12,x x A ∀∈，只要12x x =，就有12()()f x f x =，那么f 是A 到B 的一个单射．( ) 2．次数大于1的奇次实系数多项式在实数域上一定可约． ( ) 3．若5整除三阶行列式D 的每一个元素，则53整除D ．( )4．n 阶行列式D 的元素ij a 的代数余子式A ij ，当i 与j 的奇偶性相同时一定等于余子式M ij ．( ) 5．(A+B)(A －B )=A 2－B 2．( )三、选择题(每小题3分，共18分)1．010002000010n n-=( )．(A) n!； (B) (-1)n-1n! ； (C )－n! ； (D) (-1)n n! 2．m 个方程n 个未知量的线性方程组有无穷多解的充要条件是( )． (A)m n <； (B) 系数矩阵的秩<n ； (C ) 系数矩阵的秩等于增广矩阵的秩； (D)系数矩阵的秩等于增广矩阵的秩且小于n 3．n 阶矩阵A 不可逆的充要条件是( )． (A)对数域F 上任意n 阶矩阵B ，都有AB ≠BA ； (B)存在数域F 上的一个n 阶矩阵B ，使得AB ≠I ； (C)对数域F 上任意n 阶矩阵B ，都有AB ≠I ； (D)对数域F 上任意n 阶矩阵B ，都有AB =04．当λ满足条件( )时，二次型222123123121323(,,)5422f x x x x x x x x x x x x λ=+++-- 为正定二次型．(A)2λ>； (B)2λ<； (C)2λ≥ ； (D)2λ≤5．设σ是n 维欧氏空间V 的线性变换，12,,,n ααα 为V 的规范正交基，则( )使σ为正交变换．(A)12,,,n V βββ∀∈ ，有(),1,2,,i i i n σαβ== ；(B)12,,,n βββ 为V 中线性无关的向量，且(),1,2,,i i i n σαβ== ； (C)12,,,n βββ 两两正交，有(),1,2,,i i i n σαβ== ； (D)12,,,n βββ 为V 的规范正交基，且(),1,2,,i i i n σαβ==6．设β可由12,,,n ααα 线性表示，但β不能由121,,,n ααα- 线性表示，则( ) (A)121,,,,n αααβ- 线性无关； (B)121,,,,n αααβ- 线性相关；(C)n α不能由121,,,,n αααβ- 线性表示；(D)n α可由121,,,,n αααβ- 线性表示四、计算题(共30分)1．(7分)计算n 阶行列式D=1221100001000001nn n x x x a a a a x a -----+．2．(8分)设A=112224336⎛⎫⎪⎪ ⎪⎝⎭，求齐次线性方程组AX=0的一个基础解系，并求一个秩为2的方阵B ，使AB=0．3．(7分)判断c 满足何条件时，线性方程组1212212212x x x x c x x c +=⎧⎪-=⎨⎪+=⎩有解？4．(8分)设线性变换σ在基123,,ααα下的矩阵为A=001010100⎛⎫⎪⎪ ⎪⎝⎭，求σ的本征值与本征向量。

2014年韩山师范学院本科插班生考试试卷小学教育专业课程与教学论试卷（A卷）一、填空（每空1分，共10分）1．1918年，美国著名教育家_________出版了《___________》一书，该著作被看作是课程成为一个独立研究领域的标志。

2．按照大课程论的理解，教学设计是_________的微观层次。

3．行为目标的优点是具有_________和_________，可以对目标进行分解，但是那些很难测评、很难被转化为行为、不易直接观测与衡量的内容就会从课程与教学中消失。

4．布鲁纳认为，人类信息加工系统，用三种方式来表征世界，它们分别是：_________、_________和_________。

5．课程组织的基本要素主要有：_________、原理、技能和_________。

二、选择（每题1分，共10分）得分评卷人12345678910（下面每道选择题的正确答案请填入表格中对应的小题题号的格子中。

）1．在教学理论发展史上，古罗马教育家的教育著作（）被誉为“西方第一本教学法”的专著。

A.《雄辩术原理》B.《大教学论》C.《爱弥儿》D.《普通教育学》2．下列说法不正确的是（）。

A.柏拉图在他的著作《理想国》中提出了自然教育的观点，主张使儿童从社会因袭的束缚与压抑下解放出来。

B.美国实用主义教育家杜威强调尊重儿童的兴趣与需要，发展儿童的个性，主张以儿童的生活经验为课程。

C.美国课程理论专家艾斯纳提出了用表现性目标来续写课程目标的主张。

D.系统理论、传播理论和学习理论是教学设计的重要理论基础。

3．课程与教学政策不属于中央集权型的国家是（）。

A.日本B.前苏联C.法国D.英国4．关于课程与教学目标的制定，需要具有一定的依据，下列说法不正确的是（）。

A.需要关注对学生的研究B.需要关注对学科的研究C.需要关注对教师的研究D.需要关注对社会的研究5．斯金纳的程序教学设计属于（）。

A.认知主义教学设计B.建构主义教学设计C.行为主义教学设计D.传统主义教学设计6．永恒主义课程流派认为真理具有普遍性和永恒性，在课程组织中重视（）。

韩山师范学院专升本插班生考试样卷数学与应用数学 专业 高等代数 A 卷一、填空题（每小题2分，共12分） 1. 一个素数p 有 个因数.2. 多项式)(x f 无重因式的充要条件是 .3. 两个实二次型等价的充分必要条件是它们有相同的秩和 .4. 最大的数域是 .5. 次数大于零的多项式在复数域C 中只能有 次的不可约多项式.6. 一个向量空间V 的基所含向量的个数叫做V 的 . 二、判断题（每小题2分，共10分） 1. 4267351 是奇排列.（ ）2. 2是多项式1415623-+-x x x 的二重根.（ ）3. 多项式3261614x x x -+-在有理数域上是不可约的.（ ）4. 任意一个齐次线性方程组都有基础解系.（ ）5. 在欧氏空间C [-1，1]中，向量1与x 正交.（ ） 三、选择题（每小题3分，共18分） 1．若111221221,a a a a = 则下列（ ）是方程组111122121122220,0.a x a x b a x a x b -+=⎧⎨-+=⎩ 的解. （A ）11211112222212,;b a a b x x b a a b ==（B ）11211112222212,;b a a b x x b a a b -==-（C ）11211112222212,;b a a b x x b a a b -==-（D ）11211112222212,.b a a b x x b a a b --==--2.000000200000300000101n n =-（ ）.（A ） (-1)n -3 n ! ; （B ） (-1) 2n n ! ; （C ） (-1)n -2 n ! ; （D ）n ! . 3. 设A ,B ,C 都是n 阶方阵，且ABC =I , 则（ ）成立.（A ）CAB = I （B ）BAC = I （C ）ACB = I （D ） CBA = I 4. 设A 是n 阶可逆矩阵，则下面推断正确的是（ ）（A ） 交换A 的i , j 两行得到B ，则交换A -1的i , j 两行就得到B -1. （B ） 交换A 的i , j 两行得到B ，则交换A -1的i , j 两列就得到B -1.（C ） 把A 的第 j 行的k 倍加到第i 行得到B ，则把A -1的第i 行的k 倍加到第j 行就得到B -1.（D ） 把A 的第 j 行的k 倍加到第i 行得到B ，则把A -1的第i 列的k 倍加到第j 列就得到B -1.5. 设Q 为有理数域，R 为实数域，C 为复数域，则下述结论正确的是（ ）. （A ）Q 构成R 上的向量空间； （B ）Q 构成C 上的向量空间； （C ）R 构成C 上的向量空间； （D ）C 构成R 上的向量空间.6. 已知欧氏空间R 3的线性变换(,,)(,,)x y z x y y y z σ=++，则（ ）成立. （A ）σ 是正交变换，但不是对称变换； （B ）σ 是对称变换，但不是正交变换； （C ）σ 是正交变换，也是对称变换； （D ）σ 不是正交变换，也不是对称变换. 四、计算题（共30分） 1．（7分）计算行列式ab b b b b a b b b D bb a b b b b b a b b b b b a=。

韩山师范学院专升本插班生考试样卷数学与应用数学专业高等代数 A卷一、选择题(每小题3分，共15分)1．m个方程n个未知量的线性方程组中，若其系数矩阵的秩等于m, 则( )成立。

（A）方程组一定有解; （B）方程组一定有无穷多解;（C）方程组一定无解; （D）方程组一定有唯一解.2. 设E1E2…E s A E s+1…E t =I,其中E i为初等矩阵，i = 1,2,…, t , 则A-1等于( ).（A）E1E2…E t；（B）E t…E2E1；（C）E s+1…E t E1…E s；（D）E t…E s+1E1…E s .3. 设A1, A2,…, A s都是n阶方阵，则对角线分块矩阵12sAAA⎛⎫⎪⎪⎪⎪⎝⎭的秩等于( ).（A）秩(A1A2…A s)；（B）秩A1×秩A2×…×秩A s；（C）秩(A1+A2+…+A s)；（D）秩A1+秩A2+…+秩A s .4. 设α1 , α2 ,…, αs与β1 , β2 ,…, βs均为线性相关的向量组，则下列结论正确的是（）.（A）α1+β1, α2+β2,…,αs+βs线性相关；（B）α1+β1,α2+β2,…,αs+βs线性无关；（C）α1,α2,…,αs,β1,β2,…,βs线性相关；（D）α1, α2,…,αs,β1,β2,…,βs线性无关.5.1221 , , 333α⎛⎫=-⎪⎝⎭，2212, ,333α⎛⎫=-⎪⎝⎭是R3的规范正交组，添加( )可以扩充为R3的规范正交基.（A）122, ,333⎛⎫-⎪⎝⎭；（B）122, ,333⎛⎫--⎪⎝⎭；（C）221, ,333⎛⎫--⎪⎝⎭；（D）212, ,333⎛⎫--⎪⎝⎭.二、填空题（把答案填在题中横线上。

每小题3分，共15分）1. 在n 元排列中，反序数最大的排列的反序数为 .2. 实数域上的不可约多项式的次数只能是 .3. 5432()2101616146f x x x x x x =-+-+-在Q [x ]内的典型分解式为.4. 复数域C 作为实数域R 上的向量空间, 维数是 .5. m ×n 矩阵A 的行向量组所生成的F n 的子空间叫做A 的 .三、判断题(每小题2分，共14分. 你认为正确的，在题后圆括号内打“√”，错误的打“×”。

韩山师范学院2017年本科插班生考试试卷数学与应用数学 专业 高等代数 试卷（A 卷）一、填空（每空3分，共30分）1．设A 、B 都是 n 阶方阵，AB = I ( I 为单位矩阵) ，则BA = ．2. 设1123A -⎫⎛=⎪-⎝⎭ ，则A 的特征多项式为 . 3．多项式32()325f x x x x =--+的三个根之和等于 ． 4. 已知n 元实二次型12(,,,)n q x x x 的秩为3, 符号差为1. 则此实二次型的典范形式为 ．5．四阶行列式1250238131241425------=6．设123A ⎫⎛⎪ =⎪ ⎪⎝⎭, 那么312(2)(3)T AD = . 7. 二次型2221231231223(,,)3224q x x x x x x x x x x =+-+-的矩阵A =.8. 一个向量空间V 的基所含向量的个数叫做V 的 .9．设A = { a , b }，B = { 1, 2, 3, 4 }，C = { x , y , z }，f 、g 分别是A 到B 、B 到C 的映射: f ：a → 1，b → 3. g ：1 → x ，2 → y ，3 → z ，4 → z . 则合成映射g o f ： ． 10. 已知12323ξααα=++，12322ηααα=-++，其中123,,ααα是欧氏空间V 的规范正交基，则内积,η= ． 二、是非题（每题3分，共30分。

你认为正确的，在题后括号内打“√”，错误的打“×”。

）1．若矩阵A 的秩为r ，由A 添加1行得到B ，再由B 添加1列得到C ，那么C 的秩为r +2. ( ) 2．若()()f x h x 且()()g x h x ，则()()()f x g x h x . ( ) 3. 多项式()f x 有重根当且仅当()f x 有重因式. ( ) 4．设A , B 都是n 阶方阵, 则det ( A +B ) = det A + det B ． ( ) 5．设A 、B 都是n 阶方阵，那么秩(AB ) ≤秩A ． ( ) 6. 实数集R 不是数域. ( ) 7．若A ，B 都是n 阶正交矩阵，则AB 也是正交矩阵． （ ） 8．线性变换变线性无关组为线性无关组． （ ） 9. 奇排列经过奇数次对换就变成奇排列. （ ） 10． 实对称矩阵的特征根都是实数． （ ） 三、证明题（共10分）设F 是数域，(),()[]f x g x F x ∈，且()|()g x f x . 证明：()g x 的根都是()f x 的根.四、证明题（共10分）设A是一个幂等矩阵（若2A A，则称A是幂等矩阵）, 而B与A相似. 证明：B是幂等矩阵.五、证明题（共10分）设12,W W 是向量空间V 的两个子空间, 证明12W W 也是V 的子空间.六、计算题（共10分）求线性方程组12341234123421,21,25 5.x x x x x x x x x x x x -++=⎧⎪-+-=-⎨⎪-++=⎩ 的一般解.。

韩山师范学院2014年本科插班生考试试卷数学与应用数学 专业 高等代数 试卷（A 卷）一、是非题（每题2分，共20分。

你认为正确的，在题后括号内打“√”，错误的打“×”。

）1． 设A , B 都是n 阶对称矩阵，AB 可交换，那么AB 也是对称矩阵. ( ) 2．设A , B 都是n 阶方阵，A , B 都不可逆，则A +B 不可逆. ( ) 3．设(),()[],f x g x F x ∈ A 是n 阶方阵, 那么()()()()f A g A g A f A =. ( ) 4. 在欧氏空间V 中，如果,ξη线性无关，那么2,,,ξηξξηη〈〉<〈〉〈〉. ( ) 5. 向量空间V 的一个基到另一个基的过渡矩阵不是可逆矩阵. ( ) 6．设V 是数域F 上的向量空间，而σ是V 的一个线性变换. 那么σ是单射Ker()σ⇔={0}. ( )7． 设D 为n （≥2）阶行列式, A ij 表示D 中第i 行第j 列元素的代数余子式, 又已知D 的第1行元素皆为1, 则21222n A A A +++=D . ( )8. 两个数环的并是一个数环. ( ) 9. 多项式3261614x x x -+-在有理数域上是不可约的. ( ) 10．设A 是一个n 阶实对称矩阵，那么A 一定可以对角化. ( ) 二、填空（每空3分，共30分）1．n 阶方阵 A 的秩等于 n 是A 为可逆矩阵的 条件． 2．设433()42,()21f x x x x g x x x =-++=-+, 那么((),())f xg x = . 3. 若一个线性方程组有解，增广矩阵的秩为r , 则系数矩阵的秩. 4．设 C = P A ，P 为可逆矩阵，则秩C 秩A ．5．如果映射:f A B →和映射:g B A →满足,.A B g f j f g j ==那么g 叫做f 的 .6. 复数域C 作为实数域R 上的向量空间, 维数是 .7. 实二次型2221231231223(,,)3224q x x x x x x x x x x =+-+-的矩阵A =.8. 在欧氏空间R 4中, 向量()() 1 , 5 , 1 , 3 , 3 , 2 , 2 , 1 ==βα的夹角等于 . 9. 实数域R 上两个n 元二次型等价，那么它们有相同的 和 . 三、计算题（每题10分，共20分）1． 计算行列式x y y y y yx y y y D yy x y y y y y x y yyyyx=2．求齐次线性方程组1234123412340,30,230.x x x x x x x x x x x x --+=⎧⎪-+-=⎨⎪--+=⎩ 的一个基础解系. 四、证明题（每题10分，共30分）1. 设(),()f x g x 是数域F 上多项式，且((),())1f x g x =，m 是正整数. 证明：((),())1m m f x g x =.2．令A *是n 阶可逆矩阵A 的伴随矩阵. 证明：det A * = (det A )n -1 .3．设σ是数域F 上向量空间V 的线性变换，12,αα是σ的分别属于本征值– 1, 1的本征向量，向量3α满足323()σααα=+. 证明：123,,ααα线性无关.。