福建去年高考數(shù)學(xué)試卷一、選擇題（每題1分，共10分）

1.下列哪個(gè)選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的選擇題？

A.\(1+1=2\)

B.\(\sin60^\circ=\frac{\sqrt{3}}{2}\)

C.\(a^2+b^2=c^2\)

D.\(\sqrt[3]{-27}=-3\)

2.在福建去年高考數(shù)學(xué)試卷中，下列哪個(gè)方程組的解為\((x,y)=(1,1)\)？

A.\(\begin{cases}x+y=2\\2x-y=1\end{cases}\)

B.\(\begin{cases}x+y=1\\2x-y=2\end{cases}\)

C.\(\begin{cases}x+y=2\\2x-y=3\end{cases}\)

D.\(\begin{cases}x+y=3\\2x-y=1\end{cases}\)

3.以下哪個(gè)選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的立體幾何題目？

A.解一元二次方程\(x^2-5x+6=0\)

B.求圓的面積\(S=\pir^2\)

C.已知正方體邊長(zhǎng)為2，求其表面積

D.解對(duì)數(shù)方程\(\log_2{x}=3\)

4.在福建去年高考數(shù)學(xué)試卷中，下列哪個(gè)選項(xiàng)表示平面直角坐標(biāo)系中的一個(gè)點(diǎn)？

A.\((x,y)=(0,0)\)

B.\((x,y)=(1,1)\)

C.\((x,y)=(-1,-1)\)

D.\((x,y)=(\frac{1}{2},\frac{1}{2})\)

5.以下哪個(gè)選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的數(shù)列題目？

A.已知數(shù)列\(zhòng)(\{a_n\}\)中\(zhòng)(a_1=1\)，\(a_n=2a_{n-1}\)，求\(a_2\)

B.已知數(shù)列\(zhòng)(\{b_n\}\)中\(zhòng)(b_1=2\)，\(b_n=3b_{n-1}-2\)，求\(b_2\)

C.已知數(shù)列\(zhòng)(\{c_n\}\)中\(zhòng)(c_1=3\)，\(c_n=4c_{n-1}-1\)，求\(c_2\)

D.已知數(shù)列\(zhòng)(\{d_n\}\)中\(zhòng)(d_1=4\)，\(d_n=5d_{n-1}+2\)，求\(d_2\)

6.在福建去年高考數(shù)學(xué)試卷中，下列哪個(gè)選項(xiàng)表示函數(shù)\(y=\frac{1}{x}\)的圖象？

A.雙曲線

B.拋物線

C.直線

D.橢圓

7.以下哪個(gè)選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的統(tǒng)計(jì)題目？

A.已知某班有40名學(xué)生，其中男生20名，女生20名，求班級(jí)性別比例

B.已知某市去年高考平均分為500分，今年平均分為550分，求去年與今年的平均分之差

C.已知某學(xué)校去年有10名學(xué)生參加高考，今年有12名學(xué)生參加高考，求去年與今年的考生人數(shù)之比

D.已知某地區(qū)去年出生人口為5萬，今年出生人口為6萬，求去年與今年的出生人口之比

8.以下哪個(gè)選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的解析幾何題目？

A.求圓\(x^2+y^2=1\)與直線\(y=2x-1\)的交點(diǎn)坐標(biāo)

B.求拋物線\(y=x^2\)的焦點(diǎn)坐標(biāo)

C.求橢圓\(x^2+4y^2=1\)的頂點(diǎn)坐標(biāo)

D.求雙曲線\(x^2-4y^2=1\)的漸近線方程

9.在福建去年高考數(shù)學(xué)試卷中，下列哪個(gè)選項(xiàng)表示向量的坐標(biāo)表示法？

A.\(\vec{a}=(x_1,y_1)\)

B.\(\vec{a}=(x_1,x_2,x_3)\)

C.\(\vec{a}=(y_1,y_2,y_3)\)

D.\(\vec{a}=(x_1,y_1,z_1)\)

10.以下哪個(gè)選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的極限題目？

A.求極限\(\lim_{x\to0}\frac{\sinx}{x}\)

B.求極限\(\lim_{x\to0}(3x^2-2x+1)\)

C.求極限\(\lim_{x\to\infty}\frac{x}{x+1}\)

D.求極限\(\lim_{x\to0}(x^2-1)^{\frac{1}{2}}\)

二、多項(xiàng)選擇題（每題4分，共20分）

1.下列哪些選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的函數(shù)題目？

A.求函數(shù)\(f(x)=x^2-4x+3\)的零點(diǎn)

B.已知函數(shù)\(f(x)=\frac{1}{x}\)，求\(f(x)\)的反函數(shù)

C.求函數(shù)\(f(x)=\sqrt{x^2-1}\)的定義域

D.求函數(shù)\(f(x)=\log_2{x}\)的值域

E.求函數(shù)\(f(x)=x^3-3x+2\)的單調(diào)區(qū)間

2.以下哪些選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的概率題目？

A.拋擲一枚公平的硬幣，求至少出現(xiàn)一次正面的概率

B.從一副52張的撲克牌中隨機(jī)抽取一張，求抽到紅桃的概率

C.某班級(jí)有30名學(xué)生，其中有18名男生和12名女生，隨機(jī)選擇3名學(xué)生參加比賽，求選出的3名學(xué)生都是女生的概率

D.從1到10這10個(gè)自然數(shù)中隨機(jī)選擇一個(gè)數(shù)，求選擇的數(shù)是偶數(shù)的概率

E.某城市有1000戶家庭，其中有500戶家庭有電腦，隨機(jī)調(diào)查10戶家庭，求調(diào)查的家庭中至少有1戶有電腦的概率

3.下列哪些選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的立體幾何題目？

A.求長(zhǎng)方體的對(duì)角線長(zhǎng)度

B.求球的體積

C.求圓錐的表面積

D.求正四面體的體積

E.求圓柱的側(cè)面積

4.以下哪些選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的數(shù)列題目？

A.已知數(shù)列\(zhòng)(\{a_n\}\)中\(zhòng)(a_1=2\)，\(a_n=3a_{n-1}-2\)，求\(a_2\)

B.已知數(shù)列\(zhòng)(\{b_n\}\)中\(zhòng)(b_1=1\)，\(b_n=2b_{n-1}+1\)，求\(b_2\)

C.已知數(shù)列\(zhòng)(\{c_n\}\)中\(zhòng)(c_1=3\)，\(c_n=4c_{n-1}-3\)，求\(c_2\)

D.已知數(shù)列\(zhòng)(\{d_n\}\)中\(zhòng)(d_1=4\)，\(d_n=5d_{n-1}+3\)，求\(d_2\)

E.已知數(shù)列\(zhòng)(\{e_n\}\)中\(zhòng)(e_1=2\)，\(e_n=e_{n-1}+3\)，求\(e_2\)

5.以下哪些選項(xiàng)是福建去年高考數(shù)學(xué)試卷中的三角函數(shù)題目？

A.求角\(\theta\)的正弦值，已知\(\cos\theta=\frac{1}{2}\)

B.求角\(\alpha\)的余弦值，已知\(\sin\alpha=\frac{\sqrt{3}}{2}\)

C.求角\(\beta\)的正切值，已知\(\tan\beta=-\sqrt{3}\)

D.求角\(\gamma\)的余切值，已知\(\cot\gamma=\frac{1}{2}\)

E.求角\(\delta\)的正割值，已知\(\sec\delta=2\)

三、填空題（每題4分，共20分）

1.已知函數(shù)\(f(x)=2x^3-3x^2+4\)，則\(f'(x)=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\

四、計(jì)算題（每題10分，共50分）

1.計(jì)算下列極限：

\[\lim_{x\to\infty}\frac{\sqrt{x^2+1}-\sqrt{x^2-1}}{x}\]

2.解下列一元二次方程：

\[2x^2-5x+3=0\]

3.求函數(shù)\(f(x)=x^3-6x^2+11x-6\)的導(dǎo)數(shù)，并求其極值。

4.已知三角形的三邊長(zhǎng)分別為\(a=3\)，\(b=4\)，\(c=5\)，求該三角形的面積。

5.在平面直角坐標(biāo)系中，點(diǎn)\(A(2,3)\)關(guān)于直線\(y=x\)對(duì)稱的點(diǎn)\(B\)的坐標(biāo)是多少？請(qǐng)給出計(jì)算過程。

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（基礎(chǔ)知識(shí)，實(shí)數(shù)的性質(zhì)）

2.A（方程組的解法，代入法）

3.C（立體幾何，正方體的性質(zhì)）

4.B（平面直角坐標(biāo)系，點(diǎn)的坐標(biāo)）

5.A（數(shù)列，等比數(shù)列的定義）

6.A（函數(shù)，反函數(shù)的定義）

7.C（概率，組合概率的計(jì)算）

8.A（立體幾何，對(duì)角線的長(zhǎng)度）

9.A（向量，坐標(biāo)表示法）

10.A（極限，極限的定義）

二、多項(xiàng)選擇題答案及知識(shí)點(diǎn)詳解

1.A、B、C、E（函數(shù)，函數(shù)的基本性質(zhì)和定義域、值域）

2.A、B、C、D（概率，概率的基本性質(zhì)和計(jì)算方法）

3.