整式综合测试(一)

一.选择题

1.当a=3/4,b=－1/4时a²－2ab+4(a+1)+b²－4b的值为(        )

A.3                           B.6                               C.9                                      D.10

2.若二次三项式x²+mx－12在整数范围内可以再分则整数m有(        )个

A.3                           B.6                               C.7                                       D.8

3.若6x²－13xy+6y²=0,y≠0,则x/y的值为(         )

A.3/2                        B.2/3                          C.－3/2                                   D.3/2或2/3

4.设A=(x－3)(x－7)﹑B=(x－2)(x－8),则A﹑B的大小关系为(           )

A.A=B                     B.A＞B                     C.A＜B                                  D.不确定

5.已知m﹑p﹑q为正整数满足(x+p)(x+q)=x²+mx+36则有(          )个m值

A.2                           B.3                             C.4                                           D.5

6.下列乘积中结果是(b+c)²－a²的是(          )

A.(a+b+c)(a+b－c)                                  B.(b+c－a)(b－c－a)

C.(c+b+a)(c－b－a)                                 D.(－a+b+c)(a+b+c)

7.若3(a²+b²+c²)=(a+b+c)²则a﹑b﹑c的大小关系为(           )

A.a=b＜c                           B.a＜b＜c                           C.a=b=c                            D.a＞b＞c

8.计算(2+1)(2²+1)(2⁴+1)……(2ⁿ+1)=(          )

A.4ⁿ－1                             B.4²ⁿ+1                              C.4ⁿ+1                                D.4²ⁿ－1

 9.若ax²+bx+c=(2x+1)(x－2),则a－b+c=(            )  

A.1                                  B.3                                 C.5                                     D.9

10.下列各式中计算正确的是(           )

A.(2a+1)(2a－1)=4a²－a－1                      B.(a－b)(a+b)=a²－ab+b²

C.(x－2y)(3x+y)=3x²－5xy－2y²             D.(m+2)(3m+6)=3m²+6m+12

二.填空题11.如果a^x－3·a^x=a²,那么x=_____.

12.若x﹑y都是正整数,且2^x·2^y=2^5,则x+y=_______;x﹑y的值有_______对.

13.已知a=2⁵⁵,b=3⁴⁴,c=5³³,d=6²²则a﹑b﹑c﹑d的大小关系为_______.

14.(x²+x+1)(x²－2x+1)展开式中x项的系数是_______.

15.若x³+y³=100,x+y=10,则x²+y²=_____.

16.已知x+1/x=3,求x²/x⁴+x²+1的值是______________.

17.同时出现a﹑b﹑c且系数为1的5次单项式一共有_______个.

18.若x+2y+3z=10,4x+3y+2z=15,则x﹑y﹑z的和是___________.

19.已知x/a－b=y/b－c=z/c－a,则x+y+z=__________.

20.求81⁷－27⁹－9¹³被135整除的商是__________.

三.解答题

21.解方程:(x－4)²－(x－3)(x+4)=2(3x－1).

22.解不等式:(x－3)(x+4)－(x+4)²＜2(1－3x).

23.分解下列各式

     ①(ax+by)²+(bx－ay)²;                                 ②(x²+2x+3)(x²+2x－2)－6.

24.计算:①1×3×4+2×6×8……n·3n·4n/1×4×5+2×8×10……n·4n·5n.

    ②若(2x2－x－1)3=a0x6+a1x5+a2x4+a3x3+a4x2+a5x+a6  ,求a1+a3+a5的值.

25.若x+y+z=a,xy+xz+yz=b,xyz=c.

    ①求x²+y²+z²,②求(x－1)(y－1)(z－1).

[参考答案]

一.选择题

1.C     2.B       3.D        4.B         5.D         6.D        7.C          8.A          9.B                   10.C

二.填空题

11.5/2             12.5     4                13.(c＞b＞d＞a)               14.0            15.40                  16.8/1

17.6               18.5                    19.0                      20.3²³

三.解答题

21.x=2        22.x＜2         23.(1)(a²+b²)(x²+y²)      (2)(x－1)(x+3)(x²+2x+4)        

24.(1)3/5          (2)－4          25.(1)a^2＿2b      (2)c－b+a－1