江苏省常州市2023-2024学年高三上学期期末学业水平监测数学试卷 无答案

江苏省常州市20232024学年高三上学期期末学业水平监测数学试卷考试时间：120分钟满分：150分一、选择题（每题5分，共25题，计125分）1.已知函数\(f(x)=\frac{1}{x^2+1}\)，则函数\(f(x)\)的值域为：A.\((0,1]\)B.\([0,1)\)C.\([0,1]\)D.\((0,1)\)2.设\(a,b,c\)是等差数列的三个连续项，且\(a+b+c=12\)，则\(a\cdotb\cdotc\)的值为：A.16B.18C.20D.243.已知\(\cos\alpha=\frac{1}{2}\)，则\(\sin^2\alpha+\cos^2\alpha\)的值为：A.1B.\(\frac{3}{4}\)C.\(\frac{5}{4}\)D.24.函数\(y=2x^24x+1\)的对称轴方程是：A.\(x=1\)B.\(x=2\)C.\(x=1\)D.\(x=0\)5.已知数列\(\{a_n\}\)满足\(a_1=1\)，\(a_{n+1}=2a_n+1\)，则\(a_5\)的值为：A.31B.32C.33D.346.若\(\log_2x=3\)，则\(x\)的值为：A.8B.9C.10D.117.已知\(\tan\theta=1\)，则\(\sin\theta\)的值为：A.\(\frac{1}{\sqrt{2}}\)B.\(\frac{1}{\sqrt{2}}\)C.\(\frac{\sqrt{2}}{2}\)D.\(\frac{\sqrt{2}}{2}\)8.函数\(y=\sqrt{x^24}\)的定义域为：A.\(x\leq2\)或\(x\geq2\)B.\(2<x<2\)C.\(x\leq2\)D.\(x\geq2\)9.已知\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow{b}=(2,1)\)，则\(\overrightarrow{a}\cdot\overrightarrow{b}\)的值为：A.0B.1C.2D.310.若\(\sin\alpha=\frac{1}{2}\)，则\(\cos2\alpha\)的值为：A.\(\frac{3}{4}\)B.\(\frac{1}{4}\)C.\(\frac{3}{4}\)D.\(\frac{1}{4}\)11.函数\(y=\frac{1}{x1}\)在\(x=2\)时的导数为：A.1B.1C.0D.不存在12.已知\(a\cdotb=0\)，且\(a^2+b^2=1\)，则\(a+b\)的最大值为：A.1B.\(\sqrt{2}\)C.2D.\(\sqrt{3}\)13.函数\(y=\ln(x^2+1)\)的图像在\(x>0\)时：A.单调递增B.单调递减C.先增后减D.先减后增14.已知\(\overrightarrow{a}=(1,1)\)，\(\overrightarrow{b}=(2,2)\)，则\(\overrightarrow{a}+\overrightarrow{b}\)的模长为：A.\(\sqrt{2}\)B.2C.\(\sqrt{8}\)D.415.函数\(y=\frac{1}{x}\)在\(x<0\)时的图像是：A.上升的B.下降的C.水平的D.折线型的16.已知\(a,b,c\)是等差数列的三个连续项，且\(a+b+c=12\)，则\(a\cdotb\cdotc\)的值为：A.16B.18C.20D.2417.函数\(y=2x^24x+1\)的对称轴方程是：A.\(x=1\)B.\(x=2\)C.\(x=1\)D.\(x=0\)18.已知数列\(\{a_n\}\)满足\(a_1=1\)，\(a_{n+1}=2a_n+1\)，则\(a_5\)的值为：A.31B.32C.33D.3419.若\(\log_2x=3\)，则\(x\)的值为：A.8B.9C.10D.1120.已知\(\tan\theta=1\)，则\(\sin\theta\)的值为：A.\(\frac{1}{\sqrt{2}}\)B.\(\frac{1}{\sqrt{2}}\)C.\(\frac{\sqrt{2}}{2}\)D.\(\frac{\sqrt{2}}{2}\)21.函数\(y=\sqrt{x^24}\)的定义域为：A.\(x\leq2\)或\(x\geq2\)B.\(2<x<2\)C.\(x\leq2\)D.\(x\geq2\)22.已知\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow{b}=(2,1)\)，则\(\overrightarrow{a}\cdot\overrightarrow{b}\)的值为：A.0B.1C.2D.323.若\(\sin\alpha=\frac{1}{2}\)，则\(\cos2\alpha\)的值为：A.\(\frac{3}{4}\)B.\(\frac{1}{4}\)C.\(\frac{3}{4}\)D.\(\frac{1}{4}\)24.函数\(y=\frac{1}{x1}\)在\(x=2\)时的导数为：A.1B.1C.0D.不存在25.已知\(a\cdotb=0\)，且\(a^2+b^2=1\)，则\(a+b\)的最大值为：A.1B.\(\sqrt{2}\)C.2D.\(\sqrt{3}\)二、填空题（每题5分，共5题，计25分）26.已知\(\cos\alpha=\frac{1}{2}\)，则\(\sin^2\alpha+\cos^2\alpha\)的值为______。27.函数\(y=2x^24x+1\)的对称轴方程是______。28.已知数列\(\{a_n\}\)满足\(a_1=1\)，\(a_{n+1}=2a_n+1\)，则\(a_5\)的值为______。29.若\(\log_2x=3\)，则\(x\)的值为______。30.已知\(\tan\theta=1\)，则\(\sin\theta\)的值为______。三、解答题（共3题，计50分）31.（15分）已知函数\(f(x)=x^33x+2\)，求证：函数\(f(x)\)在\(x>1\)时单调递增。32.（15分）在直角坐标系中，已知点