2024-2025学年湖北省武汉市第六中学高一下学期第3次月考数学试题及答案.docVIP

2024-2025学年湖北省武汉市第六中学高一下学期第3次月考数学试题及答案

2024-2025学年湖北省武汉市第六中学高一下学期第3次月考数学试题

一、选择题（本大题共12小题，每小题5分，共60分）

1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{1,2,3\}\)，则\(A\capB=(\)\()\)

A.\(\{1,2\}\)B.\(\{1,3\}\)C.\(\{2,3\}\)D.\(\{1,2,3\}\)

2.函数\(f(x)=\sqrt{x-1}+\frac{1}{x-2}\)的定义域为\((\)\()\)

A.\([1,2)\cup(2,+\infty)\)B.\((1,2)\cup(2,+\infty)\)

C.\([1,2)\)D.\((1,2]\)

3.下列函数中，既是奇函数又在区间\((0,+\infty)\)上单调递增的是\((\)\()\)

A.\(y=x^3\)B.\(y=\lnx\)C.\(y=x^{\frac{1}{2}}\)D.\(y=2^{-x}\)

4.已知\(\sin\alpha=\frac{3}{5}\)，且\(\alpha\)为第二象限角，则\(\cos\alpha=(\)\()\)

A.\(-\frac{4}{5}\)B.\(\frac{4}{5}\)C.\(-\frac{3}{5}\)D.\(\frac{3}{5}\)

5.已知向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow{b}=(2,-2)\)，则\(\overrightarrow{a}\cdot\overrightarrow{b}=(\)\()\)

A.\(-2\)B.\(2\)C.\(-6\)D.\(6\)

6.已知直线\(l\)：\(ax+y-2=0\)与圆\(C\)：\(x^2+y^2=1\)相切，则\(a=(\)\()\)

A.\(\pm1\)B.\(\pm\sqrt{3}\)C.\(\pm2\)D.\(\pm\sqrt{5}\)

7.已知\(\sin(\alpha+\frac{\pi}{3})=\frac{1}{3}\)，则\(\cos(2\alpha-\frac{\pi}{3})=(\)\()\)

A.\(-\frac{7}{9}\)B.\(\frac{7}{9}\)C.\(-\frac{1}{3}\)D.\(\frac{1}{3}\)

8.已知函数\(f(x)=\sin(2x+\varphi)\)，\(|\varphi|\lt\frac{\pi}{2}\)，若\(f(x)\)在\([-\frac{\pi}{6},\frac{\pi}{3}]\)上单调递增，则\(\varphi\)的取值范围为\((\)\()\)

A.\([-\frac{\pi}{3},\frac{\pi}{6}]\)B.\([-\frac{\pi}{6},\frac{\pi}{3}]\)

C.\([-\frac{\pi}{2},\frac{\pi}{2}]\)D.\([-\frac{\pi}{2},\frac{\pi}{6}]\)

9.已知直线\(l\)：\(x+y+m=0\)与圆\(C\)：\(x^2+y^2-2x+4y-4=0\)相交于\(A\)、\(B\)两点，若\(|AB|=2\sqrt{2}\)，则\(m=(\)\()\)

A.\(-1\)或\(3\)B.\(1\)或\(-3\)C.\(-2\)或\(6\)D.\(2\)或\(-6\)

10.已知\(a=\log_23\)，\(b=\log_34\)，\(c=\log_45\)，则\(a\)、\(b\)、\(c\)的大小关系为\((\)\()\)

A.\(a\gtb\gtc\)B.\(b\gta\gtc\)C.\(c\gtb\gta\)D.\(a\gtc\gtb\)

11.已知函数\(f(x)=\begin{cases}2^x,x\leq0\\\log_2x,x\gt0\end{cases}\)，若\(f(a)=\frac{1}{2}\)，则\(a=(\)