高三佛山二模數(shù)學(xué)試卷一、選擇題（每題1分，共10分）

1.已知函數(shù)$f(x)=ax^2+bx+c$，其中$a\neq0$，若$f(1)=3$，$f(2)=5$，$f(3)=7$，則$3f(1)+2f(2)+f(3)$的值為（）

A.21B.22C.23D.24

2.若等差數(shù)列$\{a_n\}$的公差為$d$，且$a_1+a_4=5$，$a_2+a_5=7$，則$a_3+a_6$的值為（）

A.5B.6C.7D.8

3.已知函數(shù)$f(x)=\sqrt{x^2-2x+2}$，則函數(shù)的定義域?yàn)椋ǎ?/p>

A.$[1,+\infty)$B.$(-\infty,1]\cup[2,+\infty)$C.$(-\infty,2]\cup[2,+\infty)$D.$(-\infty,1)\cup(1,+\infty)$

4.若直線$y=kx+b$與圓$x^2+y^2=1$相切，則$k^2+b^2$的最小值為（）

A.1B.2C.3D.4

5.已知數(shù)列$\{a_n\}$滿足$a_1=1$，$a_n+a_{n+1}=2^n$，則$a_{100}$的值為（）

A.$2^{99}$B.$2^{100}$C.$2^{101}$D.$2^{102}$

6.若$\triangleABC$的邊長分別為$a$、$b$、$c$，且滿足$a^2+b^2=c^2$，則$\triangleABC$的形狀為（）

A.直角三角形B.等腰三角形C.等邊三角形D.梯形

7.已知函數(shù)$f(x)=x^3-3x^2+4x$，則$f'(x)$的零點(diǎn)為（）

A.1B.2C.3D.4

8.若$\log_2(x+1)=\log_2(2x-1)$，則$x$的值為（）

A.1B.2C.3D.4

9.已知數(shù)列$\{a_n\}$滿足$a_1=1$，$a_{n+1}=2a_n$，則$\lim_{n\to\infty}\frac{a_n}{2^n}$的值為（）

A.0B.1C.2D.無窮大

10.若函數(shù)$f(x)=\frac{1}{x^2+1}$在$x=0$處的導(dǎo)數(shù)為$f'(0)$，則$f'(0)$的值為（）

A.0B.1C.$-\frac{1}{2}$D.$\frac{1}{2}$

二、多項(xiàng)選擇題（每題4分，共20分）

1.下列哪些是實(shí)數(shù)域上的多項(xiàng)式函數(shù)？（）

A.$f(x)=x^3-2x^2+5x-3$B.$g(x)=\sqrt{x^2-4}$C.$h(x)=\frac{1}{x^2+1}$D.$j(x)=\log_2(x+1)$

2.已知函數(shù)$f(x)=ax^2+bx+c$，若$f(1)=2$，$f'(2)=0$，則下列哪些條件能確定$a$、$b$、$c$的值？（）

A.$f(0)=3$B.$f(-1)=0$C.$f'(0)=0$D.$f(3)=6$

3.下列哪些數(shù)列是等差數(shù)列？（）

A.$\{a_n\}=\{2n-1\}$B.$\{a_n\}=\{n^2\}$C.$\{a_n\}=\{\frac{n}{n+1}\}$D.$\{a_n\}=\{n\}$

4.下列哪些函數(shù)在其定義域內(nèi)是增函數(shù)？（）

A.$f(x)=x^2$B.$g(x)=\frac{1}{x}$C.$h(x)=\lnx$D.$j(x)=e^x$

5.下列哪些結(jié)論是正確的？（）

A.平行四邊形的對角線互相平分B.相似三角形的面積比等于相似比的平方

C.任意三角形的外心是三角形三邊中點(diǎn)的交點(diǎn)D.任意三角形內(nèi)角和等于180度

三、填空題（每題4分，共20分）

1.函數(shù)$f(x)=x^3-3x+1$的導(dǎo)數(shù)$f'(x)=\boxed{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\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四、計(jì)算題（每題10分，共50分）

1.已知函數(shù)$f(x)=x^3-6x^2+9x+1$，求$f'(x)$，并求出函數(shù)的極值點(diǎn)。

2.在直角坐標(biāo)系中，已知點(diǎn)$A(1,2)$，$B(3,4)$，$C(5,1)$，求$\triangleABC$的面積。

3.已知等差數(shù)列$\{a_n\}$的前$n$項(xiàng)和為$S_n=3n^2-2n$，求該數(shù)列的通項(xiàng)公式。

4.解下列不等式組：

\[

\begin{cases}

2x-3y<6\\

x+y>1

\end{cases}

\]

并在坐標(biāo)系中表示出解集。

5.已知函數(shù)$f(x)=\frac{x^2-3x+2}{x-1}$，求$f(x)$的導(dǎo)數(shù)$f'(x)$，并求出函數(shù)的單調(diào)區(qū)間。

6.解下列方程組：

\[

\begin{cases}

2x+y=5\\

3x-2y=1

\end{cases}

\]

并用矩陣形式表示解法。

本專業(yè)課理論基礎(chǔ)試卷答案及知識(shí)點(diǎn)總結(jié)如下：

一、選擇題答案：

1.A

2.A

3.B

4.B

5.A

6.A

7.A

8.B

9.B

10.A

二、多項(xiàng)選擇題答案：

1.A,C

2.A,B,C

3.A,C

4.C,D

5.A,B,D

三、填空題答案：

1.$f'(x)=3x^2-6x+9$

2.$\triangleABC$的面積為$\frac{1}{