交大聯(lián)考數(shù)學(xué)試卷一、選擇題（每題1分，共10分）

1.設(shè)集合A={1,2,3},B={2,3,4},則集合A與B的并集為？

A.{1,2,3}

B.{2,3,4}

C.{1,2,3,4}

D.{1,4}

2.函數(shù)f(x)=|x-1|在區(qū)間[0,2]上的最小值為？

A.0

B.1

C.2

D.-1

3.已知等差數(shù)列的首項為2，公差為3，則該數(shù)列的前5項和為？

A.25

B.30

C.35

D.40

4.直線y=2x+1與直線y=-x+3的交點坐標(biāo)為？

A.(1,3)

B.(2,5)

C.(1,4)

D.(2,4)

5.函數(shù)f(x)=sin(x)在區(qū)間[0,π]上的積分值為？

A.0

B.1

C.π

D.2

6.設(shè)矩陣A為2x2矩陣，且A的行列式為2，則矩陣A的逆矩陣的行列式為？

A.1/2

B.2

C.4

D.-2

7.在復(fù)數(shù)域中，方程x^2+1=0的解為？

A.1+i

B.-1+i

C.1-i

D.-1-i

8.設(shè)函數(shù)f(x)在區(qū)間[a,b]上連續(xù)，則在[a,b]上至少存在一點ξ，使得f(ξ)等于該區(qū)間上函數(shù)值的平均值，這是？

A.中值定理

B.羅爾定理

C.拉格朗日中值定理

D.泰勒定理

9.設(shè)向量a=(1,2,3)，向量b=(4,5,6)，則向量a與向量b的點積為？

A.32

B.38

C.42

D.48

10.在空間解析幾何中，平面x+y+z=1在三維坐標(biāo)系中的位置是？

A.通過原點

B.平行于x軸

C.平行于y軸

D.平行于z軸

二、多項選擇題（每題4分，共20分）

1.下列函數(shù)中，在區(qū)間(-∞,+∞)上連續(xù)的函數(shù)有？

A.f(x)=x^2

B.f(x)=1/x

C.f(x)=sin(x)

D.f(x)=|x|

2.下列方程中，在復(fù)數(shù)域中有兩個不相等實數(shù)解的方程有？

A.x^2-4=0

B.x^2+1=0

C.x^2+x+1=0

D.x^2-2x+1=0

3.下列不等式正確的有？

A.log_2(3)>log_2(4)

B.e^2>e^3

C.(1/2)^(-3)<(1/2)^(-2)

D.sqrt(3)<sqrt(4)

4.下列向量中，線性無關(guān)的向量組有？

A.a=(1,0,0),b=(0,1,0),c=(0,0,1)

B.a=(1,1,1),b=(1,2,3),c=(2,3,4)

C.a=(1,2,3),b=(4,5,6),c=(7,8,9)

D.a=(1,0,0),b=(0,0,1),c=(0,1,0)

5.下列關(guān)于矩陣的說法正確的有？

A.單位矩陣的行列式為1

B.兩個可逆矩陣的乘積仍然是可逆矩陣

C.矩陣的秩等于其列向量組的秩

D.一個n階矩陣的伴隨矩陣的行列式等于該矩陣行列式的平方

三、填空題（每題4分，共20分）

1.設(shè)函數(shù)f(x)=x^3-3x^2+2，則f(x)的導(dǎo)函數(shù)f'(x)=？

2.極限lim(x→2)(x^2-4)/(x-2)的值為？

3.已知等比數(shù)列的首項為2，公比為3，則該數(shù)列的前4項和為？

4.在空間直角坐標(biāo)系中，點P(1,-2,3)到坐標(biāo)原點的距離為？

5.設(shè)矩陣A=|12|,B=|34|,則矩陣A與矩陣B的乘積AB=？

四、計算題（每題10分，共50分）

1.計算不定積分∫(x^2+2x+1)/(x+1)dx。

2.求解微分方程y'-y=x。

3.計算二重積分?_D(x^2+y^2)dA，其中D為圓域x^2+y^2≤1。

4.計算級數(shù)∑_{n=1}^∞(1/2^n)的和。

5.求解線性方程組：

x+2y+3z=1

2x+y+2z=3

3x+3y+5z=2

本專業(yè)課理論基礎(chǔ)試卷答案及知識點總結(jié)如下

一、選擇題答案

1.C

2.B

3.C

4.A

5.B

6.B

7.D

8.A

9.A

10.D

二、多項選擇題答案

1.A,C,D

2.A,D

3.C,D

4.A,D

5.A,B,C

三、填空題答案

1.3x^2-6x

2.4

3.26

4.sqrt(14)

5.|58|

四、計算題答案及過程

1.解：∫(x^2+2x+1)/(x+1)dx=∫(x+1)^2/(x+1)dx=∫(x+1)dx=(1/2)x^2+x+C

2.解：y'-y=x=>y'=y+x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x=>y'-y=x

=>y'-y=x