高一生參加高考數(shù)學(xué)試卷一、選擇題（每題1分，共10分）

1.下列函數(shù)中，定義域?yàn)槿w實(shí)數(shù)的是（）

A.\(f(x)=\sqrt{x^2-1}\)

B.\(g(x)=\frac{1}{x}\)

C.\(h(x)=\ln(x)\)

D.\(j(x)=\sqrt[3]{x}\)

2.已知函數(shù)\(f(x)=x^2-4x+3\)，則其對(duì)稱軸為（）

A.\(x=2\)

B.\(x=-2\)

C.\(x=1\)

D.\(x=-1\)

3.在直角坐標(biāo)系中，點(diǎn)\(A(1,2)\)關(guān)于直線\(y=x\)的對(duì)稱點(diǎn)為（）

A.\(B(-2,1)\)

B.\(B(2,-1)\)

C.\(B(1,-2)\)

D.\(B(-1,2)\)

4.已知等差數(shù)列\(zhòng)(\{a_n\}\)的首項(xiàng)為\(a_1\)，公差為\(d\)，則第\(n\)項(xiàng)為（）

A.\(a_n=a_1+(n-1)d\)

B.\(a_n=a_1-(n-1)d\)

C.\(a_n=a_1+nd\)

D.\(a_n=a_1-nd\)

5.若\(\triangleABC\)的內(nèi)角\(A\)、\(B\)、\(C\)的度數(shù)分別為\(30^\circ\)、\(60^\circ\)、\(90^\circ\)，則\(\sinA+\cosB\)的值為（）

A.\(\frac{\sqrt{3}}{2}\)

B.\(\frac{1}{2}\)

C.\(\frac{\sqrt{2}}{2}\)

D.\(\frac{\sqrt{3}}{2}+\frac{1}{2}\)

6.已知\(\cos^2x+\sin^2x=1\)，則\(\sinx\)的取值范圍是（）

A.\([-1,1]\)

B.\([-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}]\)

C.\([-1,0)\cup(0,1]\)

D.\([0,1]\)

7.在等比數(shù)列\(zhòng)(\{a_n\}\)中，若\(a_1=2\)，公比為\(q\)，則\(a_5\)的值為（）

A.\(2q^4\)

B.\(2q^3\)

C.\(2q^2\)

D.\(2q\)

8.已知\(\log_23+\log_25=\log_2(3\times5)\)，則下列選項(xiàng)中正確的是（）

A.\(\log_23=1\)

B.\(\log_25=1\)

C.\(\log_23+\log_25=1\)

D.\(\log_23\times\log_25=1\)

9.若\(\sinA+\cosA=\sqrt{2}\)，則\(\sin^2A+\cos^2A\)的值為（）

A.\(2\)

B.\(1\)

C.\(\sqrt{2}\)

D.\(0\)

10.在直角坐標(biāo)系中，點(diǎn)\(P(2,3)\)到直線\(2x-3y+6=0\)的距離為（）

A.\(\frac{3}{\sqrt{13}}\)

B.\(\frac{6}{\sqrt{13}}\)

C.\(\frac{9}{\sqrt{13}}\)

D.\(\frac{12}{\sqrt{13}}\)

二、多項(xiàng)選擇題（每題4分，共20分）

1.下列各數(shù)中，屬于有理數(shù)的是（）

A.\(\sqrt{2}\)

B.\(\frac{3}{4}\)

C.\(-\frac{5}{7}\)

D.\(\pi\)

E.\(0.1010010001...\)（無限循環(huán)小數(shù)）

2.若函數(shù)\(f(x)=ax^2+bx+c\)在\(x=1\)處有極值，則下列選項(xiàng)中正確的是（）

A.\(a\neq0\)

B.\(b=0\)

C.\(b\neq0\)

D.\(c\neq0\)

E.\(c=0\)

3.在直角坐標(biāo)系中，點(diǎn)\(A(1,2)\)、\(B(3,4)\)、\(C(-1,-2)\)形成的三角形是（）

A.直角三角形

B.等腰三角形

C.等邊三角形

D.梯形

E.鈍角三角形

4.下列數(shù)列中，屬于等差數(shù)列的是（）

A.\(1,4,7,10,\ldots\)

B.\(1,3,6,10,\ldots\)

C.\(2,4,8,16,\ldots\)

D.\(3,6,9,12,\ldots\)

E.\(5,10,20,40,\ldots\)

5.若\(\sinA=\frac{1}{2}\)，\(\cosB=\frac{\sqrt{3}}{2}\)，則\(A\)和\(B\)的取值范圍是（）

A.\(A\in(0,\frac{\pi}{2})\)

B.\(A\in(\frac{\pi}{2},\pi)\)

C.\(B\in(0,\frac{\pi}{2})\)

D.\(B\in(\frac{\pi}{2},\pi)\)

E.\(A\in(0,\pi)\)

F.\(B\in(0,\pi)\)

三、填空題（每題4分，共20分）

1.若\(f(x)=2x^3-3x^2+4\)在\(x=1\)處的切線斜率為\(m\)，則\(m=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\

四、計(jì)算題（每題10分，共50分）

1.計(jì)算函數(shù)\(f(x)=x^3-3x^2+4x-1\)在\(x=2\)處的導(dǎo)數(shù)值。

2.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n=3n^2-n\)，求該數(shù)列的首項(xiàng)\(a_1\)和公差\(d\)。

3.在直角坐標(biāo)系中，已知點(diǎn)\(A(1,2)\)和\(B(3,4)\)，求線段\(AB\)的中點(diǎn)坐標(biāo)。

4.解下列方程組：

\[

\begin{cases}

2x+3y=12\\

3x-4y=6

\end{cases}

\]

5.已知函數(shù)\(f(x)=\frac{x^2-4x+3}{x-1}\)，求\(f(x)\)的反函數(shù)。

6.計(jì)算定積分\(\int_0^1(x^2+2x+1)\,dx\)。

7.設(shè)\(\triangleABC\)的內(nèi)角\(A\)、\(B\)、\(C\)的度數(shù)分別為\(45^\circ\)、\(45^\circ\)、\(90^\circ\)，求該三角形的邊長(zhǎng)\(a\)、\(b\)、\(c\)。

8.已知\(\sinA=\frac{3}{5}\)，且\(A\)為銳角，求\(\cosA\)和\(\tanA\)的值。

9.解不等式\(2x-3<5x+1\)。

10.計(jì)算極限\(\lim_{x\to0}\frac{\sinx}{x}\)。

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、選擇題答案及知識(shí)點(diǎn)詳解：

1.D（知識(shí)點(diǎn)：實(shí)數(shù)的定義及分類）

2.A（知識(shí)點(diǎn)：二次函數(shù)的對(duì)稱軸）

3.B（知識(shí)點(diǎn)：點(diǎn)關(guān)于直線對(duì)稱的性質(zhì)）

4.A（知識(shí)點(diǎn)：等差數(shù)列的定義及通項(xiàng)公式）

5.C（知識(shí)點(diǎn)：三角函數(shù)的基本關(guān)系）

6.A（知識(shí)點(diǎn)：三角函數(shù)的定義域及值域）

7.A（知識(shí)點(diǎn)：等比數(shù)列的定義及通項(xiàng)公式）

8.C（知識(shí)點(diǎn)：對(duì)數(shù)函數(shù)的性質(zhì)）

9.B（知識(shí)點(diǎn)：三角函數(shù)的基本關(guān)系）

10.C（知識(shí)點(diǎn)：點(diǎn)到直線的距離公式）

二、多項(xiàng)選擇題答案及知識(shí)點(diǎn)詳解：

1.B,C,E（知識(shí)點(diǎn)：有理數(shù)的定義及分類）

2.A,C（知識(shí)點(diǎn)：二次函數(shù)的導(dǎo)數(shù)及極值）

3.A,B,D（知識(shí)點(diǎn)：三角形的基本性質(zhì)）

4.A,D（知識(shí)點(diǎn)：等差數(shù)列的定義及通項(xiàng)公式）

5.A,C,E（知識(shí)點(diǎn)：三角函數(shù)的定義域及值域）

三、填空題答案及知識(shí)點(diǎn)詳解：

1.\(m=-2\)（知識(shí)點(diǎn)：導(dǎo)數(shù)的計(jì)算）

2.\(a_1=1\)，\(d=3\)（知識(shí)點(diǎn)：等差數(shù)列的定義及前\(n\)項(xiàng)和）

3.中點(diǎn)坐標(biāo)為\((2,3)\)（知識(shí)點(diǎn)：線段的中點(diǎn)坐標(biāo)）

4.\(x=2\)，\(y=2\)（知識(shí)點(diǎn)：線性方程組的解法）