高中140數(shù)學(xué)試卷一、選擇題（每題1分，共10分）

1.若函數(shù)\(f(x)=2x+1\)的圖象上任意一點的坐標(biāo)為\((x,y)\)，則\(x\)和\(y\)的關(guān)系式為（）

A.\(y=2x+1\)

B.\(y=-2x+1\)

C.\(y=-\frac{1}{2}x+1\)

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

2.在直角坐標(biāo)系中，點\(A(2,3)\)關(guān)于\(x\)軸的對稱點坐標(biāo)是（）

A.\((2,-3)\)

B.\((-2,3)\)

C.\((-2,-3)\)

D.\((2,3)\)

3.若\(\angleA=45^\circ\)，則\(\sinA+\cosA\)的值為（）

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

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

C.\(\sqrt{2}\)

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

4.已知\(\sin\alpha=\frac{1}{2}\)，則\(\cos2\alpha\)的值為（）

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

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

C.\(-\frac{1}{2}\)

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

5.在等差數(shù)列\(zhòng)(\{a_n\}\)中，若\(a_1=3\)，公差\(d=2\)，則\(a_{10}\)的值為（）

A.15

B.16

C.17

D.18

6.若\(\triangleABC\)中，\(\angleA=90^\circ\)，\(a=6\)，\(b=8\)，則\(c\)的值為（）

A.10

B.12

C.14

D.16

7.若\(x^2-3x+2=0\)的兩個根為\(x_1\)和\(x_2\)，則\(x_1+x_2\)的值為（）

A.2

B.3

C.4

D.5

8.若\(\log_25+\log_23=\log_215\)，則\(\log_23\)的值為（）

A.1

B.2

C.3

D.4

9.若\(a,b,c\)成等比數(shù)列，且\(a+b+c=3\)，\(ab+bc+ca=6\)，則\(abc\)的值為（）

A.1

B.2

C.3

D.4

10.若\(\sinA=\frac{\sqrt{3}}{2}\)，\(\cosA=\frac{1}{2}\)，則\(\tanA\)的值為（）

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

B.\(\frac{1}{\sqrt{3}}\)

C.\(\sqrt{3}\)

D.2

二、多項選擇題（每題4分，共20分）

1.下列選項中，哪些是函數(shù)\(y=ax^2+bx+c\)在\(a\neq0\)時的性質(zhì)（）

A.當(dāng)\(a>0\)時，函數(shù)的圖象開口向上

B.當(dāng)\(a<0\)時，函數(shù)的圖象開口向下

C.當(dāng)\(b^2-4ac<0\)時，函數(shù)無實數(shù)根

D.當(dāng)\(b^2-4ac=0\)時，函數(shù)有一個實數(shù)根

E.當(dāng)\(b^2-4ac>0\)時，函數(shù)有兩個不相等的實數(shù)根

2.下列哪些是三角函數(shù)的周期性性質(zhì)（）

A.\(\sin\theta\)的周期為\(2\pi\)

B.\(\cos\theta\)的周期為\(2\pi\)

C.\(\tan\theta\)的周期為\(\pi\)

D.\(\cot\theta\)的周期為\(\pi\)

E.\(\sec\theta\)的周期為\(2\pi\)

3.下列哪些是等差數(shù)列的性質(zhì)（）

A.等差數(shù)列的通項公式為\(a_n=a_1+(n-1)d\)

B.等差數(shù)列的前\(n\)項和公式為\(S_n=\frac{n(a_1+a_n)}{2}\)

C.等差數(shù)列中任意兩項的差相等

D.等差數(shù)列的相鄰項之比相等

E.等差數(shù)列的公差\(d\)不變

4.下列哪些是三角形的性質(zhì)（）

A.任意三角形的內(nèi)角和為\(180^\circ\)

B.等腰三角形的底角相等

C.直角三角形的兩個銳角互余

D.三角形的面積可以用底和高的乘積的一半來計算

E.三角形的周長等于三邊之和

5.下列哪些是數(shù)列極限的性質(zhì)（）

A.如果數(shù)列\(zhòng)(\{a_n\}\)的極限存在，則它必然收斂

B.如果數(shù)列\(zhòng)(\{a_n\}\)的極限為\(L\)，則對于任意\(\epsilon>0\)，存在\(N\)使得\(n>N\)時，\(|a_n-L|<\epsilon\)

C.如果數(shù)列\(zhòng)(\{a_n\}\)的極限為\(L\)，則對于任意\(\epsilon>0\)，存在\(N\)使得\(n>N\)時，\(a_n>L\)

D.如果數(shù)列\(zhòng)(\{a_n\}\)的極限為\(L\)，則對于任意\(\epsilon>0\)，存在\(N\)使得\(n>N\)時，\(a_n<L\)

E.如果數(shù)列\(zhòng)(\{a_n\}\)的極限為\(L\)，則\(\lim_{n\to\infty}(a_n+b_n)=L+\lim_{n\to\infty}b_n\)

三、填空題（每題4分，共20分）

1.若函數(shù)\(f(x)=3x^2-4x+1\)的圖象的對稱軸為\(x=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\

四、計算題（每題10分，共50分）

1.計算下列三角函數(shù)的值：

\[

\sin30^\circ,\quad\cos45^\circ,\quad\tan60^\circ

\]

2.解下列方程：

\[

2x^2-5x-3=0

\]

3.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前五項和為20，公差為2，求第10項\(a_{10}\)。

4.在直角坐標(biāo)系中，點\(A(2,3)\)和點\(B(-4,-1)\)的坐標(biāo)，求線段\(AB\)的中點坐標(biāo)。

5.已知\(\log_25+\log_23=\log_215\)，求\(\log_23\)的值。

6.若函數(shù)\(f(x)=x^3-6x^2+9x-1\)的圖象經(jīng)過點\((1,0)\)，求函數(shù)的解析式。

7.已知\(\triangleABC\)中，\(\angleA=60^\circ\)，\(\angleB=45^\circ\)，\(AB=5\)，求\(AC\)的長度。

8.解下列不等式：

\[

2x-3>5x+1

\]

9.已知\(\lim_{x\to0}\frac{\sinx}{x}=1\)，求\(\lim_{x\to0}\frac{\tanx}{x^2}\)。

10.已知數(shù)列\(zhòng)(\{a_n\}\)的通項公式為\(a_n=3^n-2^n\)，求前\(n\)項和\(S_n\)。

本專業(yè)課理論基礎(chǔ)試卷答案及知識點總結(jié)如下：

一、選擇題答案及知識點詳解：

1.A.\(y=2x+1\)（知識點：一次函數(shù)的定義）

2.A.\((2,-3)\)（知識點：點關(guān)于坐標(biāo)軸的對稱點）

3.D.\(\sqrt{2}\)（知識點：特殊角的三角函數(shù)值）

4.A.\(\frac{1}{2}\)（知識點：三角函數(shù)的周期性）

5.A.15（知識點：等差數(shù)列的通項公式）

6.B.12（知識點：勾股定理）

7.B.3（知識點：一元二次方程的根與系數(shù)的關(guān)系）

8.B.2（知識點：對數(shù)運算）

9.B.2（知識點：等比數(shù)列的性質(zhì)）

10.B.\(\frac{1}{\sqrt{3}}\)（知識點：特殊角的三角函數(shù)值）

二、多項選擇題答案及知識點詳解：

1.A,B,C,D,E（知識點：一元二次函數(shù)的性質(zhì)、解與判別式的關(guān)系）

2.A,B,C,D（知識點：三角函數(shù)的周期性）

3.A,B,C,E（知識點：等差數(shù)列的定義、通項公式、前n項和公式）

4.A,B,C,D（知識點：三角形的內(nèi)角和、等腰三角形的性質(zhì)、直角三角形的性質(zhì)）

5.B,D（知識點：數(shù)列極限的定義與性質(zhì)）

三、填空題答案及知識點詳解：

1.對稱軸為\(x=-\frac{2a}\)（知識點：一元二次函數(shù)的對稱軸）

2.\(a_1\)和\(d\)（知識點：等差數(shù)列的通項公式）

3.中點坐標(biāo)公式為\(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\)（知識點：線段中點坐標(biāo)）

4.對數(shù)換底公式\(\log_ba=\frac{\log_ca}{\log_cb}\)（知識點：對數(shù)運算）

5.\(f(x