[数学] 2014数学sub回忆题（造福后人，考完的都来回忆一下把） [复制链接]

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发表于 2014-10-25 12:07:52 |只看该作者 |正序浏览

本帖最后由 rainystarwow 于 2014-10-25 14:15 编辑

2014数学sub回忆题（造福后人，大家都来回忆一下把），最好是简单说下做法和答案，顺便祝福大家都考个好成绩。以下题目为寄托网友回忆，感谢以下楼层所有人。据说跟11年4月回忆题类似，大家补充一下没有的题。

1. 11^100-1结尾有几个连续的零？

2.  p, q为不同的质数群g的阶为pq 问该群是否交换是否和pq阶变换群的子群同构是否有四个子群？

3. S是圆柱x^2+y^2=1 与z=0 ，x+y+z=2所夹出的部分。n是单位外法向量。求  曲面积分 ∫∫（x,y,z)·n dS

4. dy/dt - y/t = t e^(-t) ,y(1) =1 ,求当t趋向∞， lim y/t

5. 1,2……，12 中取两个数（可重复），求加起来为12的概率

6. v1.v2.v3.v4.v5 是V中的5个向量当a1,a2,a3,a4,a5均不等于0时 sigma(viai) 不等于0 求V可能的最小维数

7. n趋向于正无穷时 sigma k=1..n(k/(n^2+k^2)

8. cos (bx)=1+sin^2(x) ，除了X=0外还别的解时，b的集合

9. f是R-R上的函数,求不连续点不可能的集合是什么A、空集 B、有理数集 C、无理数集 D、正R  E、R

10. 3x+4=e^t ,(3x+4)^2 (Yx)'' + 4(3x+4)(Yx)' - 6y=0 ,将上式用(Yt)''与(Yt)'表达

11. u,v 是平行四边形两条对角线的向量,求平行四边形的面积等于几倍|uXv|

12. 190条边的完全图有几个点

13.  A^2=I  A为二阶方阵，问A这样的A有多少个 A、1 B、2 C、4 D、8  E、infinite

14. f在[0,1]上有定义  f(0)=0 f‘（0）=0 0<=f''(x)<=1，当x属于(0,1)  求f(1)的取值范围 A、[0,1/2) B、[0,1/2]

15. k=1
S=1
I=1
WHILE K<100
PRINT I
K=K+2
I=I*K/S
S=I
END
问第10个输出的值等于多少

16. O1 的半径为1  O2的半径为2 O1与O2圆心之间的距离是4 求到圆O1与圆O2等距的点的轨迹  的形状

17. 求原点到平面 x+2y-z=14 的距离

18.  f(x) g(x) 的图像如图所示  D8640A6E-0121-4C3C-B677-AB62433488FE.png （好丑。。）
求f (f+g)的图像

19. a是  2X2方阵A中的一个未知数（方阵具体数值与a的位置不记得了）求Ax=b 至少有一个解  时  a 的解集

以下是11年4月的回忆题：

1. Four points ABCD are on a circle arranged clockwise, AB intersects DC atP,AP=9, BP=4, CP=3, what is the length of DP? 

2. Surface S is part of x^2+y^2=1between planes Z=0 and x+y+z=2, a vector field F=(xi, yj, zk), what is the value of integration ∬F ndS, n is the unit normal vector of dS?  

3. f: [0, +∞)->[0, +∞) strictly increasing, I(a)=int(0->a)f(x)dx,J(b)=int(0->b)f^(-1) (x)dx   which are correct:  I.  J(b) equal to the area bounded by x=0, y=b, f(x)  II. a>0, 0<b<f(a), I(a)+J(b)<ab  III. a>0, b>f(a), I(a)+J(b)>ab  

4. Linear transformation T:V->V, exist v in V that T^2v≠0, T^3v=0, S=span{ v, Tv, T^2v}, which conclusions are right ..... 

5. lim(x→0)(e^(sin^2 x)-cosx)/x^3

6. Area of region bounded by y=x^2 and y=2-x^2 7. The distance of origin to the plane x+2y-z=14     

8. How many zeros are at the end of 11^100-1? 

9. Partial sum from n=1 to 100 of series n*2^(n-1)  

10. A pulley with radius 2cm, rotated in speed of 1round per second. What is the speed of the object relative to the center of the pulley when it drops 4cm? 

11.Area of parallelogram with diagonal vectors a and b  

12. Two persons select one number from integers 1to 12 individually, what is the probability that the sum is equal to 12? 

13. In ring Z/2Z, which polynomial is in the ideal generated by 1+x2 and 1+x3  1+x^4    x^5+x+1 1+x^6  

14. p, q are two prime numbers, for a group G with order pq, which is correct?  G has four subgroups  G is communicative  … 

15. Number of generators of cyclic group of order 36. 

16. f(z)=xy-ixy, where is the function differentiable? 

17. Newton's method, a quadratic function choose the equation between x(n+1) and x(n)

 18.Sequence {an}, all but finitely many  terms are not in [0,2], which is correct 

19. a(n+1)=(6+a(n))^1/2, a(1)=6^1/2, limit of the sequence?

 20. Two circles with radius 1 and 2 respectively, the distance between the two centers is 4. What is the curve formed by points with equal distances to the two circles? 

21. A complete graph has 190 edges, how many vertices does it have?

 22. A dodecagon labelled by 12 months at each edge is rolled in a game. One “turn” of the game is to roll it until one April appears, then the number of the rolls is recorded. What is the probability to have five consecutive turns with rolls no greater than 10? 

23. An closed associative operator # on set S, if a#b#a=b for any a,b in S, which is correct?  # is communicative  S is a group  S is finite

 24. S(f)={x: x>0, f(x)=x}, ∑(x∈S(f))(1/x) converges for which function in the following?  A. tanx B. tanx2 C. tan2x D. tan√x E. √|tanx| 

25. f is discontinuous on a subset of R, which one is impossible?  A. Φ B. Rational numbers C. Irrational numbers D. Positive real numbers  E.R 

26. Flow chart, ask about the result will be printed.

25. (3x+4)^2 (d^2 y)/(dx^2)+4(3x+4) dy/dx-6y=0, let 3x+4=et, what is the new form of the equation? 

26. cos(bx)=sin2x+1 only have solution at 0, what’s the value of b? 27. Continuous function f(x) on [0,1], f(0)=0, f’(0)=0, 0≤f’’(x)≤1, then the range of f(x):  A.[0,1/2] B. [0,1/2] C. [0,1] D. [0,1] E. 

28. Function from 5 element set to 3element set, the number of maps which are not onto 

29. Tangent plane equation of a surface at (1,1,10) 

30. The number of points on the complex plane with zz*=1 

31. Equations (x+2y=2, 2x+ay=2a/3) is consistent, then the set of a values:  A. Φ    B. R-{0} C. R-{4} D. R E. Not enough conditions 

32. Distance  function defined by int(1->t^3)e^(-1/u) du, what is the velocity when t=2? 

33. f,g continuous on [0,1], sup f=sup g, which is correct:  inf(-f)=inf(-g)  exist x in (0,1) that f(x)=g(x)  exist x that f(x)=sup g(x) 

34. lim(n→∞)∑(k=1->n)k/(k^2+n^2 ) 

35. y=e^2x, the tangent at x=c is parallel to y=3x, the value of  c?

 36. (log(logx2))’ 

37. int(0->+∞)(e^t/(1+e^2t ))dt 

38. Five nonzero vectors v1 to v5, a1v1+a2v2+a3v3+a4v4+a5v5≠0 if none of ai is zero. What is the minimum dimension of the space?  A.1 B.2  C.3  D.4  E.6 

39. Matrices X,Y, AX=YB, which is correct  A. A,B are square  B. X,Y are square  C. If A and X communicative…  D. If A and Y communicative…  E. … 

40. f(x)=ax2+bx+c, a≠0, f(2)=1, f(-2)=-1, which is correct:  a<0 B. -2b/a=0 C…. D. b2-4ac>0 E….

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[数学] 2014数学sub回忆题（造福后人，考完的都来回忆一下把） [复制链接]

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