上海大学插班生部分试题
上海大学插班生考试高数范围
上海大学插班生考试高数范围Prepared on 21 November 2021上海大学插班生考试高数范围1、函数、极限、连续(1)、理解函数的概念，掌握函数的表示方法(2)了解函数的奇偶性、单调性、周期性和有界性(3)理解复合函数的概念，了解反函数及隐函数的概念。
会建立简单函数关系式(4)掌握基本初等函数的性质和图形(5)理解极限的概念,了解分段函数的极限(6)掌握极限四则运算法则，掌握利用两个重要极限求极限的方法。
(7)掌握极限存在的二个准则，并会利用它们求极限(8)理解无穷小、无穷大以及无穷小的阶的概念，会利用等价无穷小求极限1(9)理解函数连续性的概念，会判断函数间断点的类型(10)了解初等函数的连续性和闭区间上的连续函数的性质，并会应用这些性质2、导数与微分(1)理解导数的概念导数的几何意义和物理意义，函数的可导性与连续性之间的关系(2)掌握导数的四则元算法则和复合函数的求导法，掌握基本初等函数的导数公式。
会求分段函数的一阶二阶导数(3)了解高阶函数的概念，会求简单的函数的n阶导数，掌握初等函数的二阶导数的求法(4)会求隐函数和参数方程所确定的函数的一、二阶导数。
(5)了解微分的概念和四则运算(6)会用导数描述一些简单的物理量3、中值定理与导数的应用(1)理解并会应用罗尔定理、拉格朗日定理，利用定理能求方程的根、证明不等式。
了解柯西定理(2)理解函数的极值概念，掌握用导数判别函数的单调性和求函数极值的方法(3)会用导数描绘图形(4)会求MAX、MIN的应用问题(5)掌握洛必达法则求未定式极限的方法(6)了解曲率，曲率半径的概念，并会计算(7)了解求方程近似解的二分法和切线法4、不定积分(1)理解原函数的概念，理解不定积分的概念及性质(2)掌握不定积分的基本公式、换元法、分部积分法5、定积分及其应用(1)理解定积分的基本概念，定积分的中值定理(2)理解变限函数及其求导定理，掌握牛顿—莱布尼兹公式(3)掌握定积分的性质及换元积分法和分部积分法(4)了解定积分的近似计算方法(5)掌握定积分在几何上的应用，和物理上的应用(6)了解广义积分的概念，会计算广义积分6、级数(1)理解常数项级数收敛与发散的概念、收敛级数和的概念，掌握级数的基本性质及收敛的必要条件(2)掌握几何级数、P—级数的收敛性(3)掌握正向级数的判别法(4)会用交错级数的莱布尼兹判别法(5)了解无穷级数绝对收敛与条件收敛的概念，及两者之间的关系(6)了解函数项级数的收敛域和函数的概念(7)掌握幂级数的收敛半径，收敛区间及收敛域的求法(8)了解幂级数在收敛区间内的一些基本性质，会求一些幂级数在收敛区间内的和函数，并会由此求出某些数的项级数的和(9)了解泰勒公式、泰勒级数，掌握的麦克劳林展开式，会用它们将一些简单函数展开幂级数(10)了解幂级数在近似计算中得到简单应用(11)了解傅立叶级数的概念及函数展开成傅立叶级数的狄利克莱定理(12)会将定义在上函数展开为傅立叶级数，会将定义在上的函数展开为正弦与余弦级数、会些出傅立叶级数的和表达式7、向量代数与空间解析几何(1)理解向量的概念及其表示(2)掌握向量的运算，了解两向量垂直、平行的条件。
上海交大插班生考试真题2021
上海交大插班生考试真题2021第一部分：单项选择题1. I’m Sarah. I’m ________ journalist. [单选题] *A. anB. a(正确答案)C. theD. /2. Sorry, I ________ speak English. I speak a little Italian. [单选题] *A. don’t(正确答案)B. am notC. doesn’tD. do3. These are my ________, Sam and Anna. [单选题] *A. childs(正确答案)B. childrenC. childrensD. child4. I go ________ every morning. [单选题] *A. swimB. swimming(正确答案)C. swimedD. swimming5. My mother ________ the piano very well. We loved to listen to her. [单选题] *A. played(正确答案)B. playC. is playingD. plays6. A fridge is ________ than a freezer. [单选题] *A. more important(正确答案)B. importanterC. most importantD. much important7. ________ up, please. [单选题] *A. Stand(正确答案)B. StandingC. To standD. To standing8. Maria spends hours ________ the shopping center. [单选题] *A. in(正确答案)B. onD. for9. You may use my pen. I will use ________. [单选题] *A. hers(正确答案)B. herC. sheD. herself10. I drink ________ water every day. [单选题] *A. a fewB. a lot of(正确答案)C. fewD. a little of第二部分：完形填空Daniel Radcliffe 1________ born in 1990, the year when J.K. Rowling first thought of the now famous Harry Potter. He always wanted to be 2________ actor, but his parents didn’t like the idea. But when he had the opportunity to 3________Harry Potter his parents agreed and they were very proud 4________him when the first film came out.The success of the films 5________ Daniel both rich and famous. But he still enjoys the simple pleasures of life. He 6________playing guitar and 7________ his favourite football team, Fulham. 8________present he is working on several stage and film projects. Daniel says that he 9________ to work as an actor for as long 10________he can.1. [单选题] *B. was(正确答案)C. were2. [单选题] *A.an(正确答案)B. aC. the3. [单选题] *A. takeB. doC. play(正确答案)4. [单选题] *A. of(正确答案)B. inC. for5. [单选题] *A. makeB. have madeC. has(正确答案)6. [单选题] *B. loves(正确答案)C. is loving7. [单选题] *A. supportB. to supportC. supporting(正确答案)8. [单选题] *A. OnB. InC. At(正确答案)9. [单选题] *A. is going to continue(正确答案)B. continuesC. is continuing10. [单选题] *A. suchB. as(正确答案)C. like第三部分：判断题We had a great time last weekend. We decided to camp on Mount Olympus. You know, the mountain with flames that burn in the rock? It was really good!We travelled from Antalya by bus and arrived in Çirali at 6. The bus stopped on the main road and we walked a couple of kilometres to the village. We had a cup of tea and then we started the walk up the mountain. We arrived at the flames just as the sun started to go down.What a view! We watched the sky turn red and then the stars started to come out. It was really beautiful. The flames are incredible too. Some of them are really big. We cooked our food over one of them. We stayed awake all night. We passed the time playing cards and telling stories. One of my friends had a guitar and he played all our favourite songs. Next time you visit we can go there together. But for now — have a look at our fantastic photos!Take care,Orich1. They went camping on Mount Olympus last weekend. [单选题]T(正确答案)F2. They drove all the way to the village. [单选题]TF(正确答案)3. They arrived at the flames at midnight. [单选题]TF(正确答案)4. They didn’t sleep all that night. [单选题]T(正确答案)F5. Orich didn’t go with them. [单选题]TF(正确答案)第五部分阅读理解I'm Michael Bush, Managing Director of Hoogle Engineering. I am pleased to welcome you here to our website and I'd like to tell you a little about the company and its organization. Hoogle Engineering was set up in 1960. It was divided into several departments at that time, such as the sales department, marketing department, and production department. Lots of managers were employed to manage it all.Fortunately things are different now. Sixty people are employed by Hoogle and communication between departments is considered to be one of the most important aspects of the business. The market is global so we need to make contact with customers worldwide, not just locally.But in the old days we were all in different departments and never spoke to each other. We had a tall structure. Traditionally we had people at the first level on the shop floor, manufacturing products according to the instructions which they were given. Then you had a supervisory level of people who supervised them every day. Then you moved up to the middle management, who were doing the tasks of getting new business, and then you had the senior management team, and then you had the board, who decided the business strategy. So there were a lot of levels in the company in the old days actually.The structure today is that we form teams within teams to place people who can manufacture a product. Each team has members that can manufacture different products. The actual teams now are self-managing, so we don't even have team leaders. You've gotthe teams, and then you’ve got two people, only two people, who are what you think of as management. This is generally called flat structure.1. Hoogle Engineering was set up in ________. [单选题] *A. the nineteenth centuryB. the twentieth century(正确答案)C. the twenty first century2. There are many different ________ of management in a tall structure. [单选题] *A. kinds(正确答案)B. levelsC. functions3. People in a flat structure usually work in ________. [单选题] *A. departmentsB. families(正确答案)C. teams4. All of the following statements are true according to the passage EXCEPT that________. [单选题] *A. communication in the company is becoming more and more importantB. the author thinks the two structures have the same functionsC. there are more individual responsibilities in the flat structure(正确答案)5. The best title for the passage is ________. [单选题] *A. Organization Structure in Hoogle EngineeringB. History of Hoogle EngineeringC. Success in Hoogle engineering(正确答案)第四部分：翻译1. 经验是最好的老师。
【上海插班生】心彼心插班生——微积分的物理应用+傅里叶级数补充内容+答案解析
1、已知高温物体置于低温介质中，任一时刻该物体温度对时间的变化率与该时刻物体和介质的温差成正比，现将一初始温度为120C ︒的物体在20C ︒的恒温介质中冷却，30min 后该物体降至30C ︒，若要将该物体的温度继续降至21C ︒，还需冷却多长时间？【分析】本题考查微分方程的物理应用.【答案解析】设t 时刻物体温度为()x t ，比例常数为(0)k >，介质温度为m ，则()dx k x m dt=--，从而()kt x t Ce m -=+，(0)120,20x m ==，所以100C =，即()10020kt x t e -=+，又1()30,2x =所以2ln10k =，所以11()20100t x t -=+，当21x =时，t =１，所以还需要冷却30min .2、有一平底容器，其内侧壁是由曲线)0)((≥=y y x ϕ绕y 轴旋转而成的旋转曲面(如图)，容器的底面圆的半径为2m .根据设计要求，根据设计要求，当以min /33m 的速率向容器内注入液体时，液面的面积将以min /2m π的速率均匀扩大(假设注入液体前，容器内无液体).(1)根据t 时刻液面的面积，写出t 与)(y ϕ之间的关系式；(2)求曲线)(y x ϕ=的方程.(注：m 表示长度单位米，min 表示时间单位分.)【分析】液面的面积将以min /2m π的速率均匀扩大，因此t 时刻液面面积应为：t ππ+22，而液面为圆，其面积可直接计算出来，由此可导出t 与)(y ϕ之间的关系式；又液体的体积可根据旋转体的体积公式用定积分计算，已知t 时刻的液体体积为3t ，它们之间也可建立积分关系式，求导后转化为微分方程求解即可.【答案解析】(1)设在t 时刻，液面的高度为y ，则由题设知此时液面的面积为t y πππϕ+=4)(2，从而.4)(2-=y t ϕ(2)液面的高度为y 时，液体的体积为.12)(33)(022-==⎰y t du u yϕϕπ上式两边对y 求导，得)()(6)(2y y y ϕϕπϕ'=，即).(6)(y y ϕπϕ'=解此微分方程，得y Ce y 6)(πϕ=，其中C 为任意常数，由2)0(=ϕ知2C =，故所求曲线方程为62y x eπ=.3、某种飞机在机场降落时，为了减少滑行距离，在触地的瞬间，飞机尾部张开减速伞，以增大阻力，使飞机迅速减速并停下.现有一质量为9000kg 的飞机，着陆时的水平速度为700/km h .经测试，减速伞打开后，飞机所受的总阻力与飞机的速度成正比（比例系数为).100.66⨯=k 问从着陆点算起，飞机滑行的最长距离是多少？【评注】kg 表示千克，/km h 表示千米/小时.【分析】本题是标准的牛顿第二定理的应用，列出关系式后再解微分方程即可.【答案解析】解法一：由题设，飞机的质量9000m kg =，着陆时的水平速度h km v /7000=.从飞机接触跑道开始记时，设t 时刻飞机的滑行距离为()x t ，速度为()v t .根据牛顿第二定律，得kv dt dv m-=.又dxdv v dt dx dx dv dt dv =⋅=，由以上两式得dv k m dx -=，积分得.)(C v k m t x +-=由于0)0(,)0(0==x v v ，故得0v k m C =，从而)).(()(0t v v km t x -=当0)(→t v 时，).(05.1100.67009000)(60km k mv t x =⨯⨯=→所以，飞机滑行的最长距离为1.05km .解法二：根据牛顿第二定律，得kv dt dv m-=，所以.dt m k v dv -=两端积分得通解t m k Cev -=，代入初始条件00t v v ==，解得0v C =，故.)(0t m k e v t v -=飞机滑行的最长距离为).(05.1)(0000km k mv e k mv dt t v x t m k ==-==∞+-∞+⎰或由t m k e v dt dx -=0，知)1()(000--==--⎰t m k t t m k e mkv dt e v t x ，故最长距离为当∞→t 时，).(05.1)(0km mkv t x =→解法三：根据牛顿第二定律，得dt dx k dt x d m -=22，所以022=+dt dx m k dtx d ，其特征方程为02=+λλm k ，解之得mk -==21,0λλ，故.21t m k e C C x -+=由002000,0v e m kC dt dx v x t t m k t t t =-====-===，得,021kmv C C =-=于是).1()(0t m k e k mv t x --=当+∞→t 时，).(05.1)(0km kmv t x =→所以，飞机滑行的最长距离为1.05km .【评注】本题求飞机滑行的最长距离，可理解为+∞→t 或0)(→t v 的极限值，这种条件应引起注意.x 4、一容器的内侧是由图中曲线绕y 轴旋转一周而成的曲面，该曲线由2212()2x y y y +=≥与2211()2x y y +=≤连接而成的．(I)求容器的容积；(II)若将容器内盛满的水从容器顶部全部抽出，至少需要做多少功？(长度单位：m ，重力加速度为2/gm s ，水的密度为3310/kg m )．【分析】本题考查定积分的物理应用.【答案解析】(I)如图：容器的容积即旋转体体积分为两部分12V V V =+()()1222211221y y dy y dy ππ-=-+-⎰⎰232123y y π⎛⎫=- ⎪⎝⎭+13213y y π-⎛⎫- ⎪⎝⎭=π1534⎛⎫+- ⎪⎝⎭=94π．(II)所做的功为22(2)(1)(2)(2)dw g y y dy g y y y dyπρπρ=--+--12222112(2)(1)(2)(2)w g y y dy g y y y dyπρπρ-=--+--⎰⎰1232322112(22)44)g y y y dy y y y dy πρ-⎛⎫=--+++-+ ⎪⎝⎭⎰⎰111224322312222221111211122242243243y y y y y g y y πρ----⎛⎫ ⎪=--++-+ ⎪ ⎪⎝⎭3271033758g g ππ⨯==．5、有一平底容器，其内侧壁是由曲线)0)((≥=y y x ϕ绕y 轴旋转而成的旋转曲面(如图)，容器的底面圆的半径为2m .根据设计要求，根据设计要求，当以min /33m 的速率向容器内注入液体时，液面的面积将以min /2m π的速率均匀扩大(假设注入液体前，容器内无液体).(1)根据t 时刻液面的面积，写出t 与)(y ϕ之间的关系式；(2)求曲线)(y x ϕ=的方程.(注：m 表示长度单位米，min 表示时间单位分.)【分析】液面的面积将以min /2m π的速率均匀扩大，因此t 时刻液面面积应为：t ππ+22，而液面为圆，其面积可直接计算出来，由此可导出t 与)(y ϕ之间的关系式；又液体的体积可根据旋转体的体积公式用定积分计算，已知t 时刻的液体体积为3t ，它们之间也可建立积分关系式，求导后转化为微分方程求解即可.【答案解析】(1)设在t 时刻，液面的高度为y ，则由题设知此时液面的面积为t y πππϕ+=4)(2，从而.4)(2-=y t ϕ(2)液面的高度为y 时，液体的体积为.12)(33)(022-==⎰y t du u yϕϕπ上式两边对y 求导，得)()(6)(2y y y ϕϕπϕ'=，即).(6)(y y ϕπϕ'=解此微分方程，得y Ce y 6)(πϕ=，其中C 为任意常数，由2)0(=ϕ知2C =，故所求曲线方程为62y x e π=.6、某建筑工程打地基时，需用汽锤将桩打进土层.汽锤每次击打，都将克服土层对桩的阻力而作功.设土层对桩的阻力的大小与桩被打进地下的深度成正比(比例系数为,0k k >).汽锤第一次击打将桩打进地下am .根据设计方案，要求汽锤每次击打桩时所作的功与前一次击打时所作的功之比为常数(01)r r <<.问(1)汽锤击打桩3次后，可将桩打进地下多深？(2)若击打次数不限，汽锤至多能将桩打进地下多深？(注：m 表示长度单位米.)【分析】本题考查用定积分的物理应用以及数列极限的计算.【答案解析】本题属变力做功问题，可用定积分进行计算，而击打次数不限，相当于求数列的极限.(1)设第n 次击打后，桩被打进地下n x ，第n 次击打时，汽锤所作的功为),3,2,1( =n W n .由题设，当桩被打进地下的深度为x 时，土层对桩的阻力的大小为kx ，所以22101221a k k kxdx W x ===⎰，).(2)(22222122221a x k x x k kxdx W x x -=-==⎰由12rW W =可得2222ra a x =-，即.)1(222a r x +=].)1([2)(22232223332a r x k x x k kxdx W x x +-=-==⎰由1223W r rW W ==可得22223)1(a r a r x =+-，从而a r r x 231++=，即汽锤击打3次后，可将桩打进地下am r r 21++.(2)由归纳法，设a r r r x n n 121-++++= ，则)(222111n n x x n x x k kxdx W n n -==++⎰+=].)1([22121a r r x k n n -++++- 由于1121W r W r rW W n n n n ====-+ ，故得22121)1(a r a rr x n n n =+++--+ ,从而.11111a r r a r r x n nn --=+++=++ 于是a r x n n -=+∞→11lim 1，即若击打次数不限，汽锤至多能将桩打进地下a r-11m .傅里叶级数(1)周期为2l 的傅里叶级数设函数)(x f 是周期为2l 的周期函数，且在[,]l l -上可积，则称1()cos (0,1,2,)l n l n a f x xdx n l l π-==⎰ ,1()sin )l n l n b f x xdx n l l π-= (=1,2,3,⎰ 为)(x f 的傅里叶系数；称级数01(cos sin )2n n n a n n a x b x l l ππ∞=++∑为)(x f 的傅里叶级数，记作01()(cos sin )2n n n a n n f x a x b x l lππ∞=++∑ ．(2)收敛定理设)(x f 是周期为2l 的周期函数，如果它满足：(1)在一个周期内连续或只有有限个第一类间断点;(2)在一个周期内至多只有有限个极值点．则)(x f 的傅立叶级数收敛，并且当x 是)(x f 的连续点时，级数收敛于)(x f ；当x 是)(x f 的间断点时，级数收敛于[])0()0(21++-x f x f ．(3)正弦级数和余弦级数()f x 在[,]l l -上是可积奇函数，则称其傅里叶级数为正弦级数1()sin.n n n x f x b lπ∞=∑ ()f x 在[,]l l -上是可积偶函数，则称其傅里叶级数为余弦级数01()cos .2n n a n x f x a lπ∞=+∑ (4)定义在[0,]l 上的函数的傅里叶级数展开要先对)(x f 进行奇(或偶)延拓，再周期延拓可将)(x f 展开成正弦级数(或余弦级数)．1)正弦级数展开1()~sin n n n f x b l π∞=∑，[0,]x l ∈，其中02()sin l n n b f x xdx l l π=⎰，(1,2,...)n =2)余弦级数展开01()cos ,[0,]2n n a n f x a x x l l π∞=+∈∑ ，其中02()cos ,(0,1,2,...)l n n a f x xdx n l l π==⎰【题型点拔】对于傅里叶级数，主要考查以下三个方面的内容．【点拨一】求函数()f x 的傅里叶级数与傅里叶系数，先确定()f x 的周期2l ，利用公式求出傅里叶系数．11111()cos (0,1,2,)1()sin (0,1,2,)n n n x a f x dx n l l n x b f x dx n l l ππ--====⎰⎰ 再由傅里叶系数得到傅里叶级数：01()~(cos sin 2n n n a n x n x f x a b l lππ∞=++∑．【点拨二】求傅里叶级数的和．这类问题主要考查傅里叶级数的收敛定理，即狄利克雷定理，设()f x 在[,]l l -上满足狄利克雷定理的条件，则()f x 的以2l 为周期的傅里叶级数01()~(cos sin 2n n n a n x n x f x a b l lππ∞=++∑的和函数为：(),(),(,)1()[(0)(0)],(),(,)21[(0)(0)],2f x x f x x l l S x f x f x x f x x l l f l f l x l ⎧∈-⎪⎪⎪=-++∈-⎨⎪⎪-++-=±⎪⎩为的连续点为的间断点.【点拨三】求函数()f x 的傅里叶级数展开式．设()f x 在[,]l l -上有定义，且满足狄利克雷定理的条件．(1)若()f x 在(,)l l -内连续，则有：01()(cos sin ),()2n n n a n x n x f x a b l x l l lππ∞==++-<<∑；(2)若()f x 在[,]l l -上连续，且()()f l f l -=，则有：01()(cos sin )2n n n a n x n x f x a b l x l l lππ∞==++-≤≤∑．除以上三个方面的内容外，本部分还会考查将函数()f x 展开成正弦级数或余弦级数的方法．【例1】设101(),2()sin (1,2,)2n f x x b f x n xdx n π=-==⎰ ．令1()sin n n s x b n x ∞==π∑，则9()4s -=()(A)34(B)14(C)14-(D)34-【解析】答案为(C)因为11,0,221()==211,,122x x f x x x x ⎧⎡⎤-∈⎪⎢⎥⎪⎣⎦-⎨⎡⎤⎪-∈⎢⎥⎪⎣⎦⎩，将()f x 作奇延拓，得周期函数()F x ，周期2T =．则()F x 在点9=4x -处连续，从而991111()()(((444444s F F F f -=-=-=-=-=-，故选(C)．【例2】设函数()sin ()f x x x x ππ=+-≤≤的傅里叶级数展开式为01(cos sin )2n n n a a nx b nx ∞=++∑，则其中系数3a =．【解析】直接代入公式可得：()30124=cos3cos39a f x xdx x xdx ππππππ-==-⎰⎰．【例3】设)(cos 02ππ≤≤-=∑∞=x nx ax n n ，则2a =．【解析】根据余弦级数的定义，有x d x xdx x a 2sin 12cos 202022⎰⎰=⋅=ππππ=⎰⋅-πππ002]22sin 2sin [1xdx x x x =⎰⎰-=πππππ000]2cos 2cos [12cos 1xdx x x x xd 1=．【例4】设,0()1,0x e x f x x ππ⎧-≤<=⎨≤<⎩则其以2π为周期的傅里叶级数在x π=处收敛于，在2x π=处收敛于．【解析】根据狄利克雷定理可知，()f x 的以2π为周期的傅里叶级数在x π=处收敛于()()001()=22f f e S ππππ--+++=；()f x 的以2π为周期的傅里叶级数在2x π=处收敛于(00)(00)11(2)(0)122f f S S π-+++====．【例5】设21,0()1,0x f x x x ππ--<≤⎧=⎨+<≤⎩，则其以2π为周期的傅里叶级数在点x π=处收敛于_______．【解析】由狄利克雷定理可得，傅里叶级数在x π=处收敛于22111[(0)(0)][11]222f f ππππ-++-=-++=．【例6】将函数2()1(0)f x x x π=-≤≤展开成余弦级数，并求级数11(1)n n n -∞=-∑的和．【解析】将()f x 作偶周期延拓，则有0,1,2,n b n == ．22002(1)213a x dx πππ⎛⎫=-=- ⎪⎝⎭⎰．02()cos n a f x nxdx ππ=⎰20002cos cos nxdx x nxdx ππππ⎡⎤=-⎢⎥⎣⎦⎰⎰22000022sin 2sin 0cos x nx x nx x nxdx dx n n ππππππ⎡⎤⎡⎤=-=--⎢⎥⎢⎥⎣⎦⎢⎥⎣⎦⎰⎰112222(1)4(1)n n n n ππ---⋅-=⋅=．所以2120211(1)()1cos 14cos ,023n n n n a f x x a nx nx x n ππ-∞∞==-=-=+=-+≤≤∑∑．令0x =，有2121(1)(0)143n n f n π-∞=-=-+∑，又(0)1f =，所以1221(1)12n n n π-∞=-=∑．【例7】将函数()2(11)f x x x =+-≤≤展开成以2为周期的傅里叶级数，并由此求级数211n n ∞=∑的和．【解析】按傅里叶级数公式，先求()f x 的傅里叶系数n a 与n b .因()f x 为偶函数，所以1()sin 0(1,2,3,)l n l n b f x xdx n l l π-== =⎰ 012()cos ()cos l l n l n n a f x xdx f x xdx l l l lππ-==⎰⎰11100022(2)cos 4cos sin x n xdx n xdx xd n x n ππππ=+=+⎰⎰⎰122022(cos 1)sin (1,2,3,)n n xdx n n n ππππ-=-= =⎰ 1002(2)5a x dx =+=⎰因为()2||f x x =+在区间(11)x -≤≤上满足狄利克雷收敛定理的条件，所以01()2||cos sin 2n n n a n n f x x a x b x l l ππ∞=⎛⎫=+=++ ⎪⎝⎭∑22152(cos 1)cos 2n n n x n πππ∞=-=+∑221541cos(21)(11)2(21)n n x x n ππ∞==-- -≤≤-∑令0x =，有221541(0)2002(21)n f n π∞==+=--∑所以，2211(21)8n n π∞==-∑，又222221*********(21)(2)(21)4n n n n n n n n n ∞∞∞∞====⎡⎤=+=+⎢⎥--⎣⎦∑∑∑∑所以，2213148n n π∞==∑，即22116n nπ∞==∑.【例8】设()f x 在[,]ππ-上可积，n n b a ,为()f x 的傅里叶系数，试证：()()∑⎰=-≤++N n n n dx x f b a a 12222012πππ.【解析】只需证明对任意正整数N 都有()()∑⎰=-≤++N n n n dx x f b a a 12222012πππ．令()()∑=++=N n n n N nx b nx a a x S 10sin cos 2，则有：()()[]()⎰⎰--=-≤ππππdx x f dx x S x f N 220()()()⎰⎰--+-ππππdx x S dx x S x f N N 22()()()⎥⎦⎤⎢⎣⎡+++⎥⎦⎤⎢⎣⎡++-=∑∑⎰==-N n n n N n n n b a a b a a dx x f 12220122202222ππππ．()()∑⎰=-≤++∴N n n n dx x f b a a 12222012πππ．。
【上海插班生】心彼心插班生——插班真题选
2017-2018插班生强化班真题选集(14~16)一：极限及其应用(2016华师大)以下哪个极限存在 【 D 】:lim sin 2n n A π→∞; 21:lim 2n n B n →∞+; 1:lim(1)n n n C n →∞+-; 11:lim (sin )n n D e n--→∞.(2016华师大)1lim(23)3nn nn →∞+=(2014海事)设1032n n n n a x-+=⎰, 求lim n n na →∞. [321(1)1e+-](2016华师大)222121lim(]122n nn n n n →∞+++=+++(2014东华)222333212lim()122n n n n n n n n n →∞+++++++++. [13](2015东华)1112120,(),()22n n na a a a a a a +>=+=+.证明{}n a 收敛，并求极限。
】(2015华师大)()f x 在R 上连续，210'()f x x <<，数列{}:()(1,2,3,)n n x x f n n ==。
证明数列{}n x 收敛。
【11(),(())'0,()(1)1f x f x f n f x n+<+≤+】(2016同济)已知221'()()f x x f x =+，1)0(=f ，证明：lim ()x f x A →+∞=存在，且 122211+≤≤++ππA 。
【22211;'()()1;'()()1122f f x f x A f x A f x x x A Aππ≤⇒≤≤+≥⇒≥≥+⇒++】(2014同济)1lim1cosn n →∞++. [π](2016复旦)1limn n→∞21ln nk k n=∑，计算并证明其合理性。
【2】(2016华理)求1lim1k nnn k en k→∞=+∑。
【上海插班生】心彼心插班生法学模拟卷三(答案版)
2022上海插班生法律专业课考试模拟试卷（3）一、单项选择题（每题1分，共15分）1.我国婚姻法规定，“子女可以随父姓，也可以随母姓”。
这一规范属于（）A.强行性规范B.任意性规范C.非确定性规范D.准用性规范2.某省会城市的人大常委会根据相关法律制定了《城市桥梁隧道安全管理条例》。
从我国法律渊源角度看，该规范性法律文件属于（）A.行政法规B.部门规章C.地方性法规D.地方政府规章3.在对人的效力方面，我国法律所采用的原则是A.以属地主义为主，以属人主义为补充B.以属人主义为主，以属地主义为补充C.以保护主义为主，以属人主义和属地主义为补充D.以属地主义为主，以属人主义和保护主义为补充4.贾某与甄某酒后斗殴，分别被科以200元罚款和5天拘留。
这类处罚属于()。
A.行政处分B.行政制裁C.刑事制裁D.民事制裁5.我国的国家性质是（）A.社会主义国家B.无产阶级专政C.人民代表大会D.人民民主专政6.根据我国宪法规定，现阶段我国社会主义分配制度的基本原则是（）。
A.平均分配为主，多种分配方式并存B.按需分配为主，多种分配方式并存C.按资分配为主，多种分配方式并存D.按劳分配为主，多种分配方式并存7.公民因飞机失事失踪的,利害关系人申请宣告其死亡的时间要件是()。
A.飞机失事发生之日起满2年B.政府公布失踪人员名单之日起满2年C.飞机失事发生之日起满4年D.政府公布失踪人员名单之日起满4年8.根据《民法典》的规定,诉讼时效中止后,从中止时效的原因消除之日起,诉讼时效期间()。
A.届满B.还有六个月即届满C.重新计算D.继续计算9.甲喜新厌旧,欲杀害妻子乙后与情妇结婚，虽然明知其儿子丙有与乙在同一饭碗里吃饭的习惯，由于杀乙心切而不顾丙的死活，仍在乙的饭碗里投放毒药。
结果乙、丙均中毒身亡。
本案中甲对丙死亡的心理态度是()。
A.直接故意B.间接故意C.过于自信的过失D.疏忽大意的过失10.下列各项中，属于行政处罚的是()A.罚金B.拘役C.罚款D.管制11.逮捕的执行机关是()A.公安机关B.人民检察院C.人民法院D.国家安全机关12.在民事诉讼中，对第一审判决和裁定的上诉期限是（）：A.10日、5日B.15日、10日C.15日、5日D.10日、10日13.刘某欲买“全聚德”牌烤鸭,临上火车前购买了商标不同但外包装十分相似的显著标明名称为“仝聚德”牌烤鸭,遂向“全聚德”公司投诉。
复旦大学插班生真题文科英语
复旦大学插班生真题文科英语1、95--Where and when _______ you _______ it? [单选题] *A. did; buy(正确答案)B. do; buyC. have; boughtD. will; buy2、( ) My mother told me _____ in bed. [单选题] *A. not readB. not readingC. don’t readD. not to read(正确答案)3、It is an online platform _____ people can buy and sell many kinds of things. [单选题] * A．whenB. where(正确答案)C．thatD．which4、--Jenny, what’s your favorite _______?--I like potatoes best. [单选题] *A. fruitB. vegetable(正确答案)C. drinkD. meat5、The notice put _______ on the wall says “No Smoking”. [单选题] *A. up(正确答案)B. offC. awayD. out6、—It’s too noisy outside. I can’t fall asleep.—I can’t, either. We have to ______ new ways to solve the problem.（）[单选题] *A. come up with(正确答案)B. get on withC. make up withD. catch up with7、39．—What do you ________ my new dress?—Very beautiful. [单选题] *A．look atB．think aboutC．think of(正确答案)D．look through8、She _______ so much _______ her mother. [单选题] *A. looks; like(正确答案)B. looks; forC. looks; afterD. looks forwards; to9、The Titanic is a nice film. I _______ it twice. [单选题] *A. sawB. seeC. have seen(正确答案)D. have saw10、It is reported（）three people were badly injured in the traffic accident. [单选题] *A. whichB. that(正确答案)C.whileD.what11、My home is about _______ away from the school. [单选题] *A. three hundred metreB. three hundreds metresC. three hundred metres(正确答案)D. three hundreds metre12、77．You can watch TV when you finish________ your homework. [单选题] * A．to doB．doC．to doingD．doing(正确答案)13、He studied harder to _______ his reading skills. [单选题] *A. improve(正确答案)B. rememberC. memorizeD. forget14、He always ______ the teacher carefully in class. [单选题] *A. listensB. listens to(正确答案)C. hearsD. hears of15、____ father is a worker. [单选题] *A.Mike's and Mary'sB. Mike and Mary's(正确答案)C. Mike's and MaryD. Mike and Marys'16、—Why is Mary asking Bob about the school trip? —Because she wants to know ______.（）[单选题] *A. how does he think of the tripB. what does he think of the tripC. what he likes the tripD. how he likes the trip(正确答案)17、Neither she nor her friends ______ been to Haikou. [单选题] *A. have(正确答案)B. hasC. hadD. having18、He _______ getting up early. [单选题] *A. used toB. is used to(正确答案)C. is usedD. is used for19、Can you give her some ______ ? [单选题] *A. advice(正确答案)B. suggestionC. advicesD. suggest20、Where have you _______ these days? [单选题] *A. been(正确答案)B. beC. isD. are21、They lost their way in the forest, and _____ made matters worse was night began to fall. [单选题] *A. thatB. itC. what(正确答案)D. which22、62．--There is? ? ? ? ? sale on in the shop today. Let’s go together.--Please wait? ? ? ? ? ?minute. I’ll finish my homework first. [单选题] *A．a; theB．a; a(正确答案)C．the; aD．the; the23、I run out of money. Could you _______ me some？[单选题] *A. lend(正确答案)B. sellC. borrowD. buy24、With all the work on hand, he _____ to the cinema last night. [单选题] *A.should goB.must have goneC.might goD..shouldn’t have gone(正确答案)25、I like this house with a beautiful garden in front, but I don't have enough money to buy _____. [单选题] *A. it(正确答案)B. oneC. thisD. that26、She talks too much; you’ll be glad when you’re free of her. [单选题] *A. 与她自由交谈B. 离开她(正确答案)C. 受她的控制D. 与她在一起27、I got caught in the rain and my suit____. [单选题] *A. has ruinedB. had ruinedC. has been ruined(正确答案)D. had been ruined28、The bookshop is far away. You’d better _______. [单选题] *A. by the busB. by busC. take busD. take?the bus(正确答案)29、Reading（）the lines, I dare say that the government are more worried than they admitted. [单选题] *A. behindB. between(正确答案)C. alongD. among30、We got up early this morning and took a long walk after breakfast. We walked _____ the business section of the city. [单选题] *A. amongB. betweenC. through(正确答案)D. upon。
上海大学模拟试题及答案
上海大学模拟试题及答案一、选择题（每题2分，共20分）1. 以下哪个选项是上海大学的标志建筑？A. 东方明珠塔B. 上海中心大厦C. 复旦大学光华楼D. 上海大学图书馆答案：D2. 上海大学成立于哪一年？A. 1922年B. 1923年C. 1924年D. 1925年答案：A3. 上海大学位于中国的哪个城市？A. 北京B. 上海C. 广州D. 深圳答案：B4. 上海大学的主要学科领域包括以下哪些？A. 工程学B. 医学C. 法学D. 所有以上答案：D5. 上海大学的学生人数大约是多少？A. 10000人B. 20000人C. 30000人D. 40000人答案：C6. 上海大学的校训是什么？A. 求实创新B. 厚德载物C. 自强不息D. 博学笃志答案：A7. 上海大学在哪个校区举办了2019年的国际文化节？A. 宝山校区B. 延长校区C. 嘉定校区D. 闵行校区答案：A8. 上海大学的校花是什么？A. 牡丹B. 玫瑰C. 桂花D. 荷花答案：C9. 上海大学提供哪些类型的学位？A. 学士B. 硕士C. 博士D. 所有以上答案：D10. 上海大学在以下哪个领域获得了国家科技进步奖？A. 材料科学B. 信息技术C. 生物医学D. 环境工程答案：A二、填空题（每空1分，共20分）11. 上海大学是中国教育部直属的一所________大学。
答案：重点12. 上海大学拥有________个学院，涵盖了多个学科领域。
答案：2913. 上海大学的校徽以________色为主色调，象征学术的严谨与纯洁。
答案：蓝14. 上海大学在________年首次跻身QS世界大学排名前500。
答案：201915. 上海大学的学生社团活动丰富，其中包括学术科研、文化艺术、志愿服务等________类。
答案：六16. 上海大学的校歌是《________》，歌词表达了对知识的渴望和对未来的憧憬。
答案：上海大学校歌17. 上海大学注重国际交流与合作，与________个国家的高校建立了合作关系。
上海插班生——心彼心插班生法学模拟卷一
2022上海插班生法律专业课考试模拟试卷（1）一、单项选择题（每题1分，共15分）1.下列哪些不属于法的基本特征()A.法的普遍性B.法的规范性C.法的国家强制性D.法的正义性2.我国宪法规定：“中华人民共和国公民有宗教信仰自由”。
该规定属于法律规范中的()A.授权性规范B.禁止性规范C.义务性规范D.命令性规范3.下列关于法律效力的表述，能够成立的是()。
A.法律应使人知晓，不知者不为罪B.法律不经公布，就不具有效力C.在现代社会，法律完全不具有溯及力D.法律效力高低取决于它的强制性程度4.根据我国现行宪法，中国人民政治协商会议的性质是（）。
A.爱国统一战线组织B.国家权力机关C.一般人民团体D.群众自治组织5.下列社会关系中,属于民事关系的是()。
A.用人单位与劳动者之间的关系B.税务机关与纳税人之间的关系C.发包人与设计单位之间的关系D.专利授权机关与专利申请人之间的关系6.下列行为中,属于可撤销民事行为的是()。
A.甲(8周岁)接受远房亲戚馈赠的现金1万元B.乙(14周岁)用压岁钱购买价值2800元的金项链C.丙从某公司购买一辆无牌照的走私车D.丁因受对方欺诈买回一部不能使用的手机7.下列行为中,已满14周岁不满16周岁的人应当负刑事责任的是()。
A.故意伤害致人重伤或者死亡、强奸、抢劫、拐卖儿童B.强奸、抢劫、抢夺、放火、爆炸C.强奸、抢劫、贩卖毒品、放火、爆炸D.抢劫、绑架、放火、爆炸8.犯罪分子为日后向甲勒索财物，用枪威逼甲杀死一名路人并录像。
甲的杀人行为属于（）。
A.正当防卫B.紧急避险C.自救行为D.犯罪行为9.下列哪些属于抽象行政行为？（）A.行政许可B.行政立法C.行政强制D.行政征收10.《中华人民共和国刑事诉讼法》规定:“刑事案件由()的人民法院管辖。
”A.犯罪地B.被告人居住地C.被告人户口所在地D.受害人户口所在地11.因不动产纠纷提起的诉讼，由()人民法院管辖；A.侵权行为地B.被告住所地C.不动产所在地D.原告住所地12.经济法产生的原因是()A.政府失灵B.垄断C.不正当竞争D.市场失灵13．所谓“最惠国待遇”是指()的待遇。
复旦大学插班生英语真题
复旦大学插班生英语真题1、40．Star wars is ______ adventure film and it is very interesting. [单选题] * A．aB．an (正确答案)C．theD．/2、In winter, animals have a hard time_____anything to eat. [单选题] *A.to findB.finding(正确答案)C.foundD.to finding3、Li Jing often helps me ______ my geography.（）[单选题] *A. atB. inC. ofD. with(正确答案)4、—Whose book is it? Is it yours?—No, ask John. Maybe it’s ______.（）[单选题] *A. hersB. his(正确答案)C. he’sD. her5、--Don’t _______ too late, or you will feel tired in class.--I won’t, Mum. [单选题] *A. call upB. wake upC. stay up(正确答案)D. get up6、The car is _______. It needs washing. [单选题] *A. cleanB. dirty(正确答案)C. oldD. new7、—Why is Mary asking Bob about the school trip? —Because she wants to know ______.（）[单选题] *A. how does he think of the tripB. what does he think of the tripC. what he likes the tripD. how he likes the trip(正确答案)8、There _____ wrong with my radio. [单选题] *A. are somethingB. are anythingC. is anythingD. is something(正确答案)9、He has made a lot of films, but ____ good ones. [单选题] *A. anyB. someC. few(正确答案)D. many10、28．The question is very difficult. ______ can answer it. [单选题] * A．EveryoneB．No one(正确答案)C．SomeoneD．Anyone11、11．________ big furniture shop it is! [单选题] *A．HowB．WhatC．What a (正确答案)D．What an12、The traffic jams often happen in _______ hours. [单选题] *A. lunchB. workC. leisureD. rush(正确答案)13、50．—The sweater is not the right ________ for me.—Well, shall I get you a bigger one or a smaller one? [单选题] *A．priceB．colorC．size(正确答案)D．material(材料)14、The green shorts are _______ sale for ＄[单选题] *A. forB. on(正确答案)C. atD. with15、We _______ swim every day in summer when we were young. [单选题] *A. use toB. are used toC. were used toD. used to(正确答案)16、--How is your friend coming?--I’m not sure. He _______ drive here. [单选题] *A. may(正确答案)B. canC. mustD. will17、You should stick to your（）and tell him you won' t do the thing. [单选题] *A. principle(正确答案)B. qualityC. contactD. influence18、______this story, and you will realize that not everything can be bought with money. [单选题] *A. ReadingB. ReadC. To readD.Being read(正确答案)19、A healthy life is generally thought to be（）with fresh air, clean water, and homegrown food. [单选题] *A. joinedB. boundC. lackingD. associated(正确答案)20、There is a popular belief _____schools don’t pay any attention to spelling. [单选题] *A.that(正确答案)B.whichC.whatD.whose21、We should have breakfast every day to keep ______. [单选题] *A. healthB. healthy(正确答案)C. healthilyD. the healthy22、6．Hi, boys and girls. How are you ________ your posters for the coming English Festival at school? [单选题] *A．getting onB．getting offC．getting with (正确答案)D．getting23、The young man had decided to give up the chance of studying abroad, _____ surprised his parents a lot. [单选题] *A. whenB. whereC. which(正确答案)D. that24、He always ______ the teacher carefully in class. [单选题] *A. listensB. listens to(正确答案)C. hearsD. hears of25、Catherine has two cousins. One is quiet, and _______ is noisy. [单选题] *A. anotherB. the other(正确答案)C. othersD. other26、24．I often ask my English teacher some questions ________ e-mail. [单选题] *A．by(正确答案)B．inC．forD．with27、Mary wanted to travel around the world all by herself, but her parents did not _______ her to do so. [单选题] *A. forbidB. allowC. follow(正确答案)D. ask28、39．__________ he was very tired, he didn’t stop working. [单选题] * A．Although (正确答案)B．WhenC．AfterD．Because29、—What can I do for you? —I ______ a pair of new shoes.（）[单选题] *A. likeB. would lookC. would like(正确答案)D. take30、You can ask（）is on duty there tonight. [单选题] *A. WhatB. whomC. whoever(正确答案)D. whomever。
上海理工大学插班生《英语》考试大纲
上海理工大学插班生《英语》考试大纲本考试是专为有志到上海理工大学继续本科学习的上海市其他高校本科一年级学生设计的一种考试，其主要目的是测试考生是否达到《大学英语课程教学要求》中相应级别所规定的的英语水平。
它每年在上海理工大学举行一次。
一、本试卷组成部分及题型：第一部分听力理解 (Part I Listening Comprehension) (30分)本部分测试考生听力理解的能力。
这一部分由三种题型组成：1．短对话，共10题，只听一遍。
每题1分；2．短文，共10题，只听一遍。
每题1分；3．复合听写，听三遍，要求考生写出所听文章中空缺的8个单词和3个句子。
其中每个单词0.5分，每个句子2分。
第二部分阅读理解 (Part II Reading Comprehension)（40分）本部分测试考生阅读能力。
阅读材料的题材包括：科普、社会、文化、史地、人物、日常生活等；体裁有议论文、叙事文、描写文、应用文等。
具体要求是：1．掌握所读材料的主旨和大意；2．了解用以说明主旨的事实或细节；3．根据所读材料进行一定的判断和推断；4．理解个别句子或词的意思和上下文的逻辑关系。
本题共有四篇文章组成，每篇文章后有5个问题，每个题目后有四个选项供考生选择。
要求考生从中选出最佳答案。
每题2分。
第三部分词汇与语法 (Part III Vocabulary and Structure)（10分）本部分测试考生的语言知识，包括语法结构和词汇。
这一部分由20道题组成，其中词汇15题，语法结构5题。
每题为一个不完整的句子，句子下面列有四个选择项，要求考生从中选出最佳答案。
每题0.5分。
第四部分完形填空 (Part IV Cloze)（10分）本部分测试考生的理解和综合运用语言能力。
在一篇题材熟悉、难度适中的短文内留有20个空格，每一个空格为一题，每题有四个选择项。
考生应通读全文，在理解文章大意的基础上选择最佳答案，使文章的意思和结构完整。
六年级插班考试题及答案
六年级插班考试题及答案一、选择题（每题2分，共20分）1. 下列哪个选项是正确的？A. 地球是平的B. 太阳是宇宙的中心C. 地球围绕太阳转D. 月球是地球的卫星答案：C2. 以下哪个是化学元素的符号？A. H2OB. CO2C. NaClD. 以上都是答案：D3. 以下哪个是数学中的基本概念？A. 长度B. 面积C. 体积D. 以上都是答案：D4. 以下哪个是英语中表示“我”的单词？A. YouC. SheD. I答案：D5. 以下哪个是中国古代四大发明之一？A. 指南针B. 火药C. 造纸术D. 以上都是答案：D6. 以下哪个是人体最大的器官？A. 心脏B. 肺C. 皮肤D. 肝脏答案：C7. 以下哪个是计算机的输入设备？A. 键盘B. 鼠标C. 显示器D. 以上都是答案：A8. 以下哪个是植物的组成部分？B. 茎C. 叶D. 以上都是答案：D9. 以下哪个是动物的分类？A. 哺乳动物B. 爬行动物C. 鸟类D. 以上都是答案：D10. 以下哪个是水的三态变化？A. 固态B. 液态C. 气态D. 以上都是答案：D二、填空题（每题2分，共20分）1. 地球的自转周期是______小时。
答案：242. 光年是长度单位，表示光在一年内通过的距离，其数值是______公里。
答案：约9.46万亿3. 人体中最大的细胞是______。
答案：卵细胞4. 英语中“Hello”的中文意思是______。
答案：你好5. 世界上最大的海洋是______。
答案：太平洋6. 计算机的CPU是______的缩写。
答案：中央处理器7. 植物通过______进行光合作用。
答案：叶绿体8. 哺乳动物的特点是______。
答案：胎生哺乳9. 鸟类的特点是______。
答案：卵生，有羽毛10. 水的三态变化分别是______、液态和气态。
答案：固态三、简答题（每题5分，共30分）1. 请简述牛顿的三大运动定律。
答案：牛顿的三大运动定律包括：第一定律（惯性定律）、第二定律（加速度定律）和第三定律（作用与反作用定律）。
上海大学插班生高等数学a基本要求
上海大学插班生高等数学A基本要求上海大学插班生高等数学A基本要求1、函数、极限、连续（1）、理解函数的概念，掌握函数的表示方法（2）了解函数的奇偶性、单调性、周期性和有界性（3）理解复合函数的概念，了解反函数及隐函数的概念。
会建立简单函数关系式（4）掌握基本初等函数的性质和图形（5）理解极限的概念,了解分段函数的极限（6）掌握极限四则运算法则，掌握利用两个重要极限求极限的方法。
（7）掌握极限存在的二个准则，并会利用它们求极限（8）理解无穷小、无穷大以及无穷小的阶的概念，会利用等价无穷小求极限1（9）理解函数连续性的概念，会判断函数间断点的类型（10）了解初等函数的连续性和闭区间上的连续函数的性质，并会应用这些性质2、导数与微分（1）理解导数的概念导数的几何意义和物理意义，函数的可导性与连续性之间的关系（2）掌握导数的四则元算法则和复合函数的求导法，掌握基本初等函数的导数公式。
会求分段函数的一阶二阶导数（3）了解高阶函数的概念，会求简单的函数的n阶导数，掌握初等函数的二阶导数的求法（4）会求隐函数和参数方程所确定的函数的一、二阶导数。
（5）了解微分的概念和四则运算（6）会用导数描述一些简单的物理量3、中值定理与导数的应用（1）理解并会应用罗尔定理、拉格朗日定理，利用定理能求方程的根、证明不等式。
了解柯西定理（2）理解函数的极值概念，掌握用导数判别函数的单调性和求函数极值的方法（3）会用导数描绘图形（4）会求MAX、MIN的应用问题（5）掌握洛必达法则求未定式极限的方法（6）了解曲率，曲率半径的概念，并会计算（7）了解求方程近似解的二分法和切线法4、不定积分（1）理解原函数的概念，理解不定积分的概念及性质（2）掌握不定积分的基本公式、换元法、分部积分法5、定积分及其应用（1）理解定积分的基本概念，定积分的中值定理（2）理解变限函数及其求导定理，掌握牛顿—莱布尼兹公式（3）掌握定积分的性质及换元积分法和分部积分法（4）了解定积分的近似计算方法（5）掌握定积分在几何上的应用，和物理上的应用（6）了解广义积分的概念，会计算广义积分6、级数（1）理解常数项级数收敛与发散的概念、收敛级数和的概念，掌握级数的基本性质及收敛的必要条件（2）掌握几何级数、P—级数的收敛性（3）掌握正向级数的判别法（4）会用交错级数的莱布尼兹判别法（5）了解无穷级数绝对收敛与条件收敛的概念，及两者之间的关系（6）了解函数项级数的收敛域和函数的概念（7）掌握幂级数的收敛半径，收敛区间及收敛域的求法（8）了解幂级数在收敛区间内的一些基本性质，会求一些幂级数在收敛区间内的和函数，并会由此求出某些数的项级数的和（9）了解泰勒公式、泰勒级数，掌握的麦克劳林展开式，会用它们将一些简单函数展开幂级数（10）了解幂级数在近似计算中得到简单应用（11）了解傅立叶级数的概念及函数展开成傅立叶级数的狄利克莱定理（12）会将定义在上函数展开为傅立叶级数，会将定义在上的函数展开为正弦与余弦级数、会些出傅立叶级数的和表达式7、向量代数与空间解析几何（1）理解向量的概念及其表示（2）掌握向量的运算，了解两向量垂直、平行的条件。
【上海插班生】心彼心插班生——各高校插班生数学历年真题(1)
4 (1 x)5
(2019复旦)求 y
的渐近线
4x
(2019同济)求
y
arctan
e2
x2的渐近线
(2019华师)求 y 1 x10ex2 的渐近线
(2019复旦)设 xk 为 x tan x
的正根从小到大排列的数列，
求 A, B, C ，使得：
lim
k
k
(
xk
(2019华师大)已知
1(x) 2x 2 , f (x) ln x
x 1
求 f ((x))
(2019华师大)
lim
x0
x
1 x
(2019同济)
e
1 x2
lim
x x0 100
1
(2019上理工) lim(x e2x )sin x x0
(2019华理)
lim[1 n 1 n] n2
n
z exy arctan y , 求 dz
x
(2019上大) f (x) 可导，且
g(x, y) yf (x2 y2 )
求：y
g x
x
g y
(2019海洋)设 z z(x, y) 由方程
x mz ( y nz) 确定，
其中 m, n为常数， 可微，
则 m z n z x y
(2019海洋)设方程x mz ( y nz)
( A) f (0) 是极小值； (B) f (0) 是极大值；
(C) (0, f (0)) 是拐点；
(D) 以上均不对。
(2019华师大)求
f (x) sin4 x cos4 x, (x [0, ])
4
的拐点.
上海插班生考试英语基础班资料
10th day理解下列句子并准确翻译出带有标记部分的中文意思：1.Chin a's environment authorities have stepped up efforts to en sure a blue sky and clean air for war commemoration activities centering on a military parade to be staged in Tian'anmen Square on Sept memor ate ---celebrate ---celebrity Activ ateAuthentic ---autonomous ----automatic ---authoritative//official ----automobileParade ---process ---process ion ---cruise ---patro l /patro nCruise throughPatron //patrol Sponsor2.The Ministry of Environment ordered Beijing and its six surroundingprovincial regions to "swiftly take action"to ensure a soundenvironment during the events,its statement said Friday.Swift ---shift –promptSound ---healthy ---san itary ---sane //insane ---fitness /fit Sane ---in sane ProvinceAdminis ter ---implement ----execute ---enforce同达插班生孔老师英语复习资料Ministry ----minister---administer /administration /administrative3.Beijing,Tianjin,Hebei,Shanxi,Inner Mongolia,Shandong and Henan authorities were given a deadline of Aug 28for monitoring various industries and shutting down companies with excessive emissions .Heads of the seven local governments will take the major responsibilities for the mission.Industrious ---diligent Major---majority//anoverwhelmingmajorityof …..---specialize/specialization ----minor ///minorityMaximum ---maximize ----maximal Minimum Miniature Deadline //headlineEmit ---transmit //communicate //contract //infect //infectious ---commit///commitmentInter mit tentExcessive ---excess ---exceed /proceed ---succeed //success /succession //successive ---precede /recede ---procedure //proceedings Surplus ----redundant同达插孔老师英语复习资4.More than 12,200coal-fired boilers and factories in polluting industries in these regions will suspend production starting Aug 28.More than ----not only Other thanRather than --instead of Better thanSus pend ---suspension ---suspense Im pend ---impending //imminentSuspect ---suspicious //skeptical//dubiousCease /ease ---pause ---halt ---terminate ---expire ///--abort ---abolish5.Motor vehicles,especially trucks from out of town,will be restricted from entering the capital.Cars with excess emissions will not beallowed to enter.Constrict ---coil ///curl //curve //carve //craveConstrain ---constraintStrict ---restrict ---restriction/iveStrain ---restrain ---restraint Store ---restore Cover ---recoverCollect ----recollect //retrospect Call ---recall同达插班生孔老师英语复习资料Retrieve ---to retrieve the information6.Beijing started to restrict the number of private vehicles on its roads on Thursday to ensure blue skies.Vehicles will be allowed on the roads based on odd or even license plate numbers up to and including Sept 3.Even ---get even withOdd ---temporary ----tentative ---provisional ----occasional ---interim ---transitionalPrivate ---privatize ---privacy ---PirateIntrude on the privacy –protrude //protract Invasion of the privacyPervade ---penetrate ---leak ///waterproof //watertightVulnerable to ---invulnerable7.The ban does not apply to ambulanc es ,fire engines,roadmaintenance vehicles,those carrying foodstuffs,or electric vehicles.Training baseMaintain ---disdain ---sustain –detain –attain ---retain8.It has been estimated by the transportation authority that the restrictions will cut the use of vehicles by 35to 50percent.同达插班生孔老师英语复习资料---------------------------------------------------------------------------------9.The Beijing Commission of Transportation said on Thursday that traffic was mildly c ongested and had been reduced by 30percent from average levels.Mild ---wild ---moderate ---modest ---intermediateTransit ---transition /transitional ---transparent ---transfuse ---transplant ---transferable ---transmission ---translation10.In the environment ministry's latest inspections ,it checked andregulated 241companies,45construct ion sites and a large number ofoutdoor barbecue stalls .It also secretly visited some factories inDingzhou City,Hebei Province,saying the environment situation there is "not optimistic."Stall ---stance //false stance ---stalk ---stable //staple ---stack ---stake11.Now the Chinese approach to education is not confined to strict andabsolute obe die nce ,because teachers also encourage different student's potential .ObeyFine ---confine ---refine//refinery Front ---confront ---confrontation Strict同达插班生孔老师英语复习资料Obey ---obedien ce //obedient //compliant Comply with Encourage –discouragePotential ---underlying –prospective client Potentiality12.The UK needs to promote the authority of teachers to make teaching more efficient and better exploit the potential of teachers.EfficientExploit ---explode ---exploreExploitationExplosionExploration----------------------------------------------------------13.More than ten foreign armies will participate in China's militaryparade scheduled for Sept.3in Beijing to mark the 70th anniversaryof China's victory in war against Japan aggression .Schedule –scheme ---timetable ---agenda ---itinerary ---route /chart/routine14.Foreign troops have already arrived to the parade's training base and are currently training with their Chinese counterpart s.Counterpart ---encounter //confront同达插班生孔老师英语复习资料15.Their participation in the parade is a clear indication of their attitude to jointly commemorate the victory in the world anti-fascist war ,and a symbol of the pursuit of and hope for lasting world peace .16.Their dormitories are equipped with laundry rooms,phone booths,foreign exchange services as well as football fields and swimming pools.17.China will also show its military sophistication by rolling out 27armament formations.About 84percent of the weaponry and equipment has never been shown to the public before./debutIntricate ---intricacyElusive18.They’re not the only ones paying huge prices for prestigious properties .Real estate19.Many argue the stability of the US dollar will keep New York as an同达插班生孔老师英语复习资料attractive destination for the foreseeable future .Destiny ---destination ---doom doomsdayStable ---stability ---stabilize ---instable //instability ---insecure //insecurity SteadyForesee ---predict ----forecast ---prophet20.The China -US relationship has achieved remarkable developmentdespite twists and turns since both countries established formaldiplomatic relations 36years ago.This relationship has become oneof the most important bilateral relationships in the world.Multilateral ---unilateralism Spin ---whirl –rotary Wither WhipWade ////Huddle/coddle/cuddle /fuddle /muddle /meddle21.We have conducted extensive exchanges and cooperation in nearly all areas including political,economic,educational,cultural,同达插班生孔老师英语复习资料people-to-people and international affairs .Event ///sound //parade //cruise //patrol //procession Extensive exchanges Extensive cooperation ConductSuspend production Participate Clear indication of A symbol Foreseeable futureProspect –prospective /potentialStall ---booth Laundry22.History has proved that China and the US both gain frompeaceful coexistence and cooperation ,and lose fromconflicts and confrontation .Peace ---stable and prosperous //prospective Collide --collisionClash ---confrontation ///confine //imprison ---constrain //constrictRestrict ---excessive emission同达插班生孔老师英语复习资料Odd and even license plate number Based on Knack –recipe EnsureDeadline ---headline MonitorInspection ---pessimistic AdministerMinistry ---suspend Bilateral23.China-US economic and trade relations is a critical pillar for our bilateral relations.It is mutually beneficial in nature.As the biggestdeveloping country and the biggest developed country respectively ,China and the US enjoy great complementarities in terms of naturaland human resources,market,capital and technology.Mutual ---reciprocal ---reproachComplementary //compliment Supplement ---Credit ---principal //installment //mortgage //loan24.In 1979,the annual trade volume between our two countries was just同达插班生孔老师英语复习资料2.45billion US st year,the figure exceeded 590billion US dollars,an increase of over 240times in 36years.Today,China and the US is each other’s 2nd largest trading partner,which brings tremendous benefits for the two peoples.25.At the same time,Chinese companies’invest ment in the US also witnessed remarkable increase .Investigate //scrutinize //inspect Witness ///The last decade witnessed rapid development in technology.Military sophistication26.Deepening economic ties have boost ed the growth of countries,creating more jobs and bringing tangible benefits to the people of both nations.Boost ---promote //exploitFosterWitness //launch ///initiate //involve //revolve around Intang ibl e ---invisible Tangle ---entangle Mutually beneficial Mildly congested同达插班生孔老师英语复习资料Reciprocal ---reproachBond –bound --bind ---band ---bandage ---badge ---slogan ---token ---bunch //punch /batch /ballot /ballet27.Since China and the US resumed contact 36years ago,the two sides have seen f requent high-level visits and improving dialogue mechanisms .Resume ----presume //presumptuous ProceedMechanical learning Flexible use ContinualEloquent ---innocentInstruction demand better response mechanismAssume ---consume ---presume ---resumeContact ---intact forest ---contract//engagement ///commitment28.Both sides also launched a series of initiatives in the fields of education,science and technology,culture,sports,women and youth exchanges.Promote ---boost ---foster ---facilitate同达插班生孔老师英语复习资料Witness ---launch29.Chinese universities hosted approximately 12,000American scholars,and 217symposiums were held jointly by China and the US.---symposium---syndromeSym---symmetric ---sym ptom --syndrome Eu phon ious/pathetic /a pathetic //typical /atypical //analytical ----symposiumAffinity ---vicinity------------------------------------------------------------------------------------30.China has pledged "Three Ten-thousand Programs",that is ,to providescholarships for 10,000US students to study in Chinese universities,to sponsor 10,000scholarships under the “Chinese Bridge”program,and to send 10,000Chinese to pursue doctor ate degrees in the US.Pledge ---promise ---swear ---oathCommitment ---guaranteeSponsor ---patron /patrol//cruise ---fund /refund ---spontaneous31.China and the US maintain close and effective communication and coordination on major regional and international issues ,including同达插班生孔老师英语复习资料the Korean Peninsula,Iranian nuclear,Afghanistan,counter terrorism ,energy security,public health and climate change.Maintain the relationship between …and …/.Close communicationEffective coordination //counter part /encounter /confront ///confrontation ///confine32.Through close coordination in fighting various challenges,China and the US are t remendously contributing to regional and global peace,stability and prosperity .33.Since its economic reform and opening-up policy,China has step by step transformed from an isolated poor country into a new engine of the world economy.Transform –transformationTransmit ---transmissionShiftSwiftly take action34.The gear of growth is shifting from high speed to medium-to-high speed,and China's focus of development is more on quality instead of同达插班生孔老语复习资料quantity .Quant ify Quanti ta tiveQuot a ---quote/quotationTransform ---convert ---shift ---adapt ---gear Be geared to35.We will let the market play a decisive role in resource allocation .China stock market drop reflects the adjustment of China's economy .The so-called 'China economy collapse 'is entirely groundless.36.In the face of complex and ever-changing international situation,our two countries should seize the correct direction to avoid zero-sumgame .37.History has proved that China’s success lies in its commitment to peaceful development.Consist in38.The blasts rocking Tianjin last Wednesday has captured both domestic and international media attention over the past several days.同达插班生孔老师英语复习资料Fascinate ---captivate ---capture39.As of August 18,Tianjin Municipal has held in total 8press conferences with regard to the incident.Regard ---disregardIncident ---incidence ---subsequent //sequence ---consequent //consequence//result ant ---ensue from40.Upon closer scrutiny ,when sudden tragic incidents involvingcasualties and treasure loss happen in Western countries,theinformation first releasedsituation more seriously than it actually is,rather than vice versa .Subsequently,as more accurate information is learned through investigation,thegovernment will revise earlier data to a “better than expected”one.Inthis way,the consequences of such incidents are more easily acceptedby the general public,thus relieving the tension and emotional stress .41.For example,15days after the September 11attacks in the United States in 2001,the ernment announced that 6,398people were missing.On November 11of that year,two months after the attacks,the authorities changed the number to 3,748based on newly同达插班生孔老师英语习资料acquired data .Then on September 11,2002,exactly one year after,the U.S.Department of Defense said that the total number of the people killed and missing was 3,025.And eventually,the total number of deaths was confirmed to be 2,996.42.The U.S.handled the information regarding Hurricane Katrina that hit New Orleans in 2005in a similar manner .Right after the hurricane,Louisiana Governor Kathleen Babineaux Blanco revealed that “thousands of people”could have died from this natural disaster,officials from the federal government estimated the number to be “tensof thousands”,while the mayor of New Orleans said that“Ten-thousand is not an unrealistic estimation”during interview.The death toll was confirmed to be 1,836,much smaller than previouslyestimated .43.We always want to play down the disaster,with the motivation to notarouse panic ,whereas in fact,with the death toll rising,the public’s fear and tension will be inevitably upgraded .44.People instinctivel y want to know exactly what has happened.45.When such demands are not met,panic and anxiety would be同达插班生孔老师英语复习资料cultivated and further inquiry and doubts ensue .46.Generally speaking,these mindset and actions are not malicious ,and they can be easily assuaged by acquisition of demanded information.47.A well-trained spokesperson can only be forged by several scorching times under the flashlight and in front of the microphone.48.Just like the old Chinese saying goes,no clever housewife can cook a meal without rice .49.The US media falsely accused China of using Operation Fox Hunt to deploy secret agents on US soil.The US is providing shelter to those on the run.We have reason to suspect that the US wants to divertattention and regain the moral high ground.Deploy ---assuageFlank FoilPlausibleLoquacious–eloquent同达插班生孔老师英语复习资料HilariousDay 10TEST 12试完成下列题目；并根据选项尽力想出所学过的同根、同缀、同型、同意、近型、近义、反义等相关单词2.Black hair is a sharp ______to white skin.A.contact B.contrastC.contractD.contradiction 同与不同Assess/access/process //assetSwarm/school/herd /flock Superlative Contradict CompatibleCommit a foulDefinitelyDefinite --define //indefinite //infinite6.The fundamental ______,which govern all physical processes,are alsorelated to many everyday occurrences.同达插班生孔老师英语复习资料A.principalsB.rulesC.principlesD.Regulations9.It is impossible to ______with a person whose methods are completely opposed to your own.A.cooperateB.correspondC.operatepete11.When replying to this advertisement,please ______a stamped addressed envelope.A.discloseB.containC.encloseD.Mention13.The beauty of the sight nearly took my ______away.A.sighB.breathC.mindD.Soul14.The general manager of the company ______why the other membersof the committee hadn’t been informed of this important news.A.requiredB.acquiredC.inquiredD.Requested15.Anyone who is ______thinks before speaking and considers thefeelings of others.A.considerateB.considerableC.moderateD.Talkative16.As income tax has ______steadily,it seems that the richer you get,theless rich you are than you think you ought to be.A.de creased B.diminished C.increasedD.reduced同达插班生孔老师英语复习资料21.Children are ______to have some accidents as they grow up.A.obviousB.indispensableC.boundD.doubtful22.For the child to be brought up in such a comfortable environment isnot necessarily ______to his future.A.favorableB.availableC.respectableD.capable23.The government ______regulations that put this arch a eological site under protection.A.publishedB.issuedC.dischargedD.released27.Sometimes Professor ______his students’poor comprehension to alack of intelligence.A.distributesB.attributesC.contributesD.devotes28.What we achieved in our research might ______what we had beenexpecting.A.exceedB.expandC.enlargeD.extend31.It is believed that the moon contains all the ______found on theearth.ponentsB.elementsC.factorsD.ingredients近义词：36.He ______this book could be of great help to whoever took over thejob.A.encounteredB.condemnedC.classifiedD.claimedpetition,we believe,______the national character rather than同达插班生孔老师英语复习资料corrupt it.A.enforcesB.confirmsC.intensifiesD.strengthens42.She ______her mother in appearance but not in height and intelligent.A.repeatsB.assemblesC.resemblesD.appears44.The concerns with the origins of the earth ______their study.A.motivatedB.advisedC.excitedD.exceeded46.This ruler has one ______in centimeters and another in inches.A.portionB.rateC.scaleD.base53.He pointed out that the living standard of urban and ______peoplecontinued to improve.A.remoteB.municipalC.ruralD.provincial57.The employees want to ______the number of working hours and toincrease pay.A.diminishB.decreaseC.depressD.delete63.For the past two years,Audi cars have ______Germany’s TouringCar Championship.A.dominatedB.conqueredC.determinedD.Contested同达插班生孔老师英语复习资料66.Our company decided to ______the contract because a number of theconditions in it had not been met.A .concealB.cancelC.concedeD.consult78.Of all the soldiers they had the ______of being the fiercest,the mostpatriotic and the toughest.A.recognitionB.reservationC.reputationD.recreation85.He was ______enough to understand my question from the gestures I made.A.intelligentB. C.proficient D.diligent86.We may be able to ______you in some way if you cannot finish yourwork on time.A.resistB.insistC.assistD.consist91.All parts of this sewing machine are ______so that it is very simpleto get replacements for them.A.mechanizedB.minimizedC.D.standardized99.Controlled exposure to the object of fear is the best key to ______anormal state of mind.A.resumeB.consumeC.restrictD.imagineTEST 131.In writing the investigation report,I have ______all unnecessary details so as to make it clearer.同达生孔老师英语复习资料A.omittedB.left outC.forgotD.neglected3.Accuracy is ______to the programming of computers.A.B.elementaryC.fundament alD.characteristic5.Even though I have lived in Australia for many years,I still can not______myself to the Australia customs.A.adoptB.adjustC.adaptD .accept6.The explorers had ______much suffering in the recent exploration.A.unde rgoneB.underl inedC.u nder takenD.un done7.This home-made car is by no means ______to that one made in Japan.A.inferiorB.interiorC.exteriorD.senior19.Mary didn’t hear the bell because she was completely ______in herreading.A.confirmedB.concernedC.absorbedD.performed32.I’d like to ______a special seat for the concert of October 12.A.preserveB.reserveC.serveD.conserve39.The strike has been on for ten months;______there is a severedecline in production.A.accordinglyB.subsequentlyC.consequentlyD.frequently40.The professor can hardly find ______grounds on which to base hisargument in favor of the new theory.A.efficientB.sufficientC.effectiveD.同达插班生孔老师英语复习资料durable45.China is a(n)______great power though she is still backward in many respects.A.remoteB.curiousC.effic ientD.potential48.The population ______will be so great that men will fight for standing room in the future.A.densityB.tensionC.crisisD.danger53.A real poet is a master of words and can ______his meaning in wordswhich sing like music and move men to tears.A.conveyB.interpretC.explainD.transfer54.There is always excitement at the Olympic Games when a ______record is surpassed.A.previousB.preciousC.valuableD.primitive56.I ______you that I had no intention of offending you.A.convinceB.guaranteeC.persuadeD.assure72.Even as a child Tom showed an inclination to ______the otherchildren.A.dominateB.ruleernD.inspect74.We ______our journey after a short rest.A.cancelled B.interruptedC.renewedD.resumed75.A person doesn’t always ______his human form or qualities.A.remainB.retainC.resignD.retail同达插班生孔老师英语复习资料79.Poor people can’t always live in ______conditions.A.accentB.decentC.recentD.dense80.The sports meeting has been ______because of the bad weather.A.abolished B.abandonedC.concealedD.cancelled86.The older generation have always ______on some of the ideas of the young.A.frownedB.flowedC.relievedD.released90.While studying at Cambridge University,Mr.Smith _______his oldfriend,whom he has not seen for nearly twenty years.A.encounteredB.whisperedC.anticipatedD.disturbed92.The _______production of cars in our factory has doubled this year.A.manualB.annualD.negative97.Can you think of a ______excuse for our being late?A.flexibleB.reliableC.reasonableD.favorable100.The former,U.S.President Clinton,made an excellent _______onthe current international situation.mitteemandmentmissionTEST 141.To ______the circumstances thoroughly requires more specificmeasures than have been taken thus far.同达插班生孔老师英语复习资料A.abuseB.clarifyC.civilizeD.circulate3.What’s the best way to ______the problem of unemployment?A.tackleB.createC.presentD.rescue4.We _______cattle mainly for the international market.A.breezeB.greetC.gripD.breed15.The failure of the project might be ______to the ineffective management.A.distributedB.contributedC.attributedD.retreated19.She will probably be awarded a Nobel Prize on account of her ______achievements in chemistry.A.obviousB.outstandingprehensiveD.distinct20.The local police made an ______into the accident which causedtwenty deaths.A.interferenceB.investigationC.interruptionD.interaction21.He is an hour late.He may have been ______by fog.Of course,that’sonly a possibility.A.delayedB.releasedC.detectedD.devised22.These desks and chairs can be ______to the height of any child.A.appointedB.adjustedC.addressedD.adopted32.The report of her sudden death on the plane to New York was not______until yesterday evening.A.in form edB.con form edC.confirmedD.affirmed同达插班生孔老师英语复习资料38.Professor Smith made such a ______contribution to the universitythat they are naming one of the new buildings after him.A.minimumB.modestC.genuineD.generous42.To ______wildlife in this area,the government has set up a huge national forest park.A.reserveB.retainC.preserveD.provide48.We moved into Chang Jiang Hotel because it is ______in its prices.A.cheapB.expensiveC.moderateD.inexpensive95.Apart from those three very cold weeks in January,it has been a very______.A.plainB.paleC.softd同达插班生孔老师英语复习资料。
上海大学模拟试题及答案
上海大学模拟试题及答案一、单项选择题（每题2分，共20分）1. 上海大学位于中国的哪个城市？A. 北京B. 上海C. 广州D. 深圳答案：B2. 上海大学成立于哪一年？A. 1922年B. 1923年C. 1924年D. 1925年答案：A3. 上海大学的校训是什么？A. 厚德博学B. 求实创新C. 笃学致远D. 明德新民答案：B4. 上海大学的主要校区位于哪个区？A. 浦东新区B. 黄浦区C. 静安区D. 徐汇区5. 上海大学是否为“211工程”和“985工程”重点建设的大学？A. 是B. 否答案：B6. 上海大学图书馆藏书量超过多少万册？A. 100万B. 200万C. 300万D. 400万答案：C7. 上海大学开设的学科门类有多少个？A. 10个B. 12个C. 14个D. 16个答案：C8. 上海大学是否拥有博士学位授予权？A. 是B. 否答案：A9. 上海大学的学生人数大致在哪个范围内？A. 1万以下B. 1万至2万C. 2万至3万D. 3万以上10. 上海大学是否设有海外交流项目？A. 是B. 否答案：A二、多项选择题（每题3分，共15分）1. 下列哪些是上海大学的知名校友？（）A. 钱学森B. 陈省身C. 张爱玲D. 马寅初答案：C2. 上海大学提供哪些类型的学位教育？（）A. 学士B. 硕士C. 博士D. 博士后答案：A B C3. 上海大学在哪些领域有较强的研究实力？（）A. 工程学B. 管理学C. 人文社会科学D. 自然科学答案：A B C D4. 下列哪些是上海大学的特色项目？（）A. 创新创业教育B. 国际交流与合作C. 学生社团活动D. 校园文化建设答案：A B C D5. 上海大学的学生可以参加哪些类型的竞赛？（）A. 学术竞赛B. 体育竞赛C. 艺术竞赛D. 科技竞赛答案：A B C D三、填空题（每题2分，共10分）1. 上海大学的主要教学语言是______。
答案：中文2. 上海大学的校徽颜色以______为主色调。