廣東的高職高考數(shù)學(xué)試卷一、選擇題（每題1分，共10分）

1.下列函數(shù)中，屬于一次函數(shù)的是（）

A.\(y=\sqrt{x}\)

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

C.\(y=2x-3\)

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

2.若\(a>0\)，\(b<0\)，則下列不等式中，正確的是（）

A.\(a+b>0\)

B.\(a-b<0\)

C.\(ab>0\)

D.\(a^2>b^2\)

3.在直角坐標(biāo)系中，點(diǎn)P的坐標(biāo)為\((2,3)\)，則點(diǎn)P關(guān)于x軸的對稱點(diǎn)坐標(biāo)是（）

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

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

C.\((2,3)\)

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

4.下列各式中，正確的是（）

A.\(x^2-4=(x+2)(x-2)\)

B.\(a^2-b^2=(a+b)(a-b)\)

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

D.\((a-b)^2=a^2-2ab+b^2\)

5.若\(a,b,c\)是等差數(shù)列，且\(a+b+c=18\)，\(ab+bc+ca=42\)，則\(abc\)的值為（）

A.24

B.18

C.14

D.6

6.下列關(guān)于函數(shù)\(y=\frac{1}{x}\)的說法，正確的是（）

A.函數(shù)在x=0處無定義

B.函數(shù)在x=1處有最大值

C.函數(shù)的圖像是一條拋物線

D.函數(shù)在x>0時(shí)單調(diào)遞增

7.在等腰三角形ABC中，\(AB=AC=6\)，\(BC=8\)，則該等腰三角形的底角\(A\)的大小為（）

A.\(30^\circ\)

B.\(45^\circ\)

C.\(60^\circ\)

D.\(75^\circ\)

8.若\(x,y\)滿足方程組

\[

\begin{cases}

x+2y=6\\

3x-4y=2

\end{cases}

\]

則\(x\)的值為（）

A.2

B.1

C.\(-1\)

D.\(-2\)

9.在\(\triangleABC\)中，\(a=5\),\(b=6\),\(c=7\)，則\(\cosA\)的值為（）

A.\(\frac{7}{25}\)

B.\(\frac{6}{25}\)

C.\(\frac{5}{25}\)

D.\(\frac{4}{25}\)

10.下列關(guān)于圓的說法，正確的是（）

A.圓是平面上所有與給定點(diǎn)距離相等的點(diǎn)的集合

B.圓的直徑是圓上任意兩點(diǎn)之間的最長距離

C.圓的周長是圓的直徑的\(\pi\)倍

D.圓的面積是圓的半徑的\(\pi\)倍

二、多項(xiàng)選擇題（每題4分，共20分）

1.下列關(guān)于一元二次方程的根的判別式\(\Delta\)的說法，正確的是（）

A.當(dāng)\(\Delta>0\)時(shí)，方程有兩個(gè)不相等的實(shí)數(shù)根

B.當(dāng)\(\Delta=0\)時(shí)，方程有兩個(gè)相等的實(shí)數(shù)根

C.當(dāng)\(\Delta<0\)時(shí)，方程無實(shí)數(shù)根

D.\(\Delta\)的值與方程的系數(shù)成正比

2.下列關(guān)于三角函數(shù)的說法，正確的是（）

A.正弦函數(shù)的值域?yàn)閈([-1,1]\)

B.余弦函數(shù)在第一象限是增函數(shù)

C.正切函數(shù)的周期為\(\pi\)

D.余弦函數(shù)在第二象限是減函數(shù)

3.下列關(guān)于數(shù)列的說法，正確的是（）

A.等差數(shù)列的通項(xiàng)公式為\(a_n=a_1+(n-1)d\)

B.等比數(shù)列的通項(xiàng)公式為\(a_n=a_1\cdotr^{n-1}\)

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

D.等比數(shù)列的前n項(xiàng)和公式為\(S_n=a_1\cdot\frac{1-r^n}{1-r}\)

4.下列關(guān)于幾何圖形的說法，正確的是（）

A.平行四邊形的對角線互相平分

B.矩形的四個(gè)角都是直角

C.正方形的四條邊都相等

D.菱形的對角線互相垂直

5.下列關(guān)于函數(shù)圖像的說法，正確的是（）

A.函數(shù)\(y=ax^2+bx+c\)的圖像是一個(gè)拋物線

B.函數(shù)\(y=\frac{1}{x}\)的圖像是一個(gè)雙曲線

C.函數(shù)\(y=\sqrt{x}\)的圖像是一個(gè)開口向上的拋物線

D.函數(shù)\(y=\log_2x\)的圖像是一個(gè)在x軸右側(cè)的增函數(shù)

三、填空題（每題4分，共20分）

1.若一元二次方程\(x^2-4x+3=0\)的兩個(gè)根分別為\(x_1\)和\(x_2\)，則\(x_1+x_2=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\

四、計(jì)算題（每題10分，共50分）

1.計(jì)算下列一元二次方程的根：

\[x^2-5x+6=0\]

2.已知函數(shù)\(f(x)=2x^2-3x+1\)，求函數(shù)的頂點(diǎn)坐標(biāo)。

3.計(jì)算下列數(shù)列的前10項(xiàng)和：

\[1,3,5,7,\ldots\]

4.解下列三角形：

在\(\triangleABC\)中，\(a=8\),\(b=10\),\(c=6\)，求\(\angleA\)的大小。

5.已知\(\sinx=\frac{3}{5}\)，且\(x\)在第二象限，求\(\cosx\)和\(\tanx\)的值。

6.計(jì)算下列函數(shù)在\(x=2\)時(shí)的導(dǎo)數(shù)值：

\[f(x)=3x^3-2x^2+4x-1\]

7.已知\(\cos\theta=-\frac{1}{2}\)，且\(\theta\)在第四象限，求\(\sin\theta\)和\(\tan\theta\)的值。

8.解下列方程組：

\[\begin{cases}

2x+3y=8\\

3x-4y=-2

\end{cases}\]

9.計(jì)算下列極限：

\[\lim_{x\to2}\frac{x^2-4}{x-2}\]

10.已知\(\sinA=\frac{1}{2}\)，\(\cosB=\frac{\sqrt{3}}{2}\)，且\(A\)和\(B\)在第一象限，求\(\sin(A+B)\)的值。

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

一、選擇題答案及知識點(diǎn)詳解：

1.C.\(y=2x-3\)，因?yàn)橐淮魏瘮?shù)的一般形式是\(y=ax+b\)，其中\(zhòng)(a\)和\(b\)是常數(shù)，\(a\neq0\)。

2.B.\(a-b<0\)，因?yàn)閈(a>0\)，\(b<0\)，所以\(a-b\)為正數(shù)減去負(fù)數(shù)，結(jié)果為正數(shù)。

3.A.\((2,-3)\)，關(guān)于x軸對稱的點(diǎn)，橫坐標(biāo)不變，縱坐標(biāo)取相反數(shù)。

4.D.\((a-b)^2=a^2-2ab+b^2\)，這是完全平方公式。

5.A.24，由等差數(shù)列的性質(zhì)，\(a_1+a_n=2a_2\)，\(a_1+a_2+a_3=3a_2\)，解得\(a_2=6\)，\(a_1=2\)，\(a_3=10\)，所以\(abc=2\cdot6\cdot10=120\)。

6.A.函數(shù)在x=0處無定義，因?yàn)榉帜覆荒転榱恪?/p>

7.C.\(60^\circ\)，等腰三角形底角相等，利用余弦定理\(c^2=a^2+b^2-2ab\cosC\)，解得\(\cosA=\frac{1}{2}\)，即\(A=60^\circ\)。

8.C.\(-1\)，使用代入法或消元法解方程組。

9.A.\(\frac{7}{25}\)，利用余弦定理和三角形的邊長，求得\(\cosA=\frac{7}{25}\)。

10.A.圓是平面上所有與給定點(diǎn)距離相等的點(diǎn)的集合，這是圓的定義。

二、多項(xiàng)選擇題答案及知識點(diǎn)詳解：

1.A,B,C，一元二次方程的根的判別式\(\Delta=b^2-4ac\)，當(dāng)\(\Delta>0\)時(shí)，方程有兩個(gè)不相等的實(shí)數(shù)根；當(dāng)\(\Delta=0\)時(shí)，方程有兩個(gè)相等的