江蘇省常州市2023-2024學(xué)年高三上學(xué)期期末學(xué)業(yè)水平監(jiān)測數(shù)學(xué)試卷 無答案

江蘇省常州市20232024學(xué)年高三上學(xué)期期末學(xué)業(yè)水平監(jiān)測數(shù)學(xué)試卷考試時間：120分鐘滿分：150分一、選擇題（每題5分，共25題，計125分）1.已知函數(shù)\(f(x)=\frac{1}{x^2+1}\)，則函數(shù)\(f(x)\)的值域為：A.\((0,1]\)B.\([0,1)\)C.\([0,1]\)D.\((0,1)\)2.設(shè)\(a,b,c\)是等差數(shù)列的三個連續(xù)項，且\(a+b+c=12\)，則\(a\cdotb\cdotc\)的值為：A.16B.18C.20D.243.已知\(\cos\alpha=\frac{1}{2}\)，則\(\sin^2\alpha+\cos^2\alpha\)的值為：A.1B.\(\frac{3}{4}\)C.\(\frac{5}{4}\)D.24.函數(shù)\(y=2x^24x+1\)的對稱軸方程是：A.\(x=1\)B.\(x=2\)C.\(x=1\)D.\(x=0\)5.已知數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_1=1\)，\(a_{n+1}=2a_n+1\)，則\(a_5\)的值為：A.31B.32C.33D.346.若\(\log_2x=3\)，則\(x\)的值為：A.8B.9C.10D.117.已知\(\tan\theta=1\)，則\(\sin\theta\)的值為：A.\(\frac{1}{\sqrt{2}}\)B.\(\frac{1}{\sqrt{2}}\)C.\(\frac{\sqrt{2}}{2}\)D.\(\frac{\sqrt{2}}{2}\)8.函數(shù)\(y=\sqrt{x^24}\)的定義域為：A.\(x\leq2\)或\(x\geq2\)B.\(2<x<2\)C.\(x\leq2\)D.\(x\geq2\)9.已知\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(2,1)\)，則\(\overrightarrow{a}\cdot\overrightarrow\)的值為：A.0B.1C.2D.310.若\(\sin\alpha=\frac{1}{2}\)，則\(\cos2\alpha\)的值為：A.\(\frac{3}{4}\)B.\(\frac{1}{4}\)C.\(\frac{3}{4}\)D.\(\frac{1}{4}\)11.函數(shù)\(y=\frac{1}{x1}\)在\(x=2\)時的導(dǎo)數(shù)為：A.1B.1C.0D.不存在12.已知\(a\cdotb=0\)，且\(a^2+b^2=1\)，則\(a+b\)的最大值為：A.1B.\(\sqrt{2}\)C.2D.\(\sqrt{3}\)13.函數(shù)\(y=\ln(x^2+1)\)的圖像在\(x>0\)時：A.單調(diào)遞增B.單調(diào)遞減C.先增后減D.先減后增14.已知\(\overrightarrow{a}=(1,1)\)，\(\overrightarrow=(2,2)\)，則\(\overrightarrow{a}+\overrightarrow\)的模長為：A.\(\sqrt{2}\)B.2C.\(\sqrt{8}\)D.415.函數(shù)\(y=\frac{1}{x}\)在\(x<0\)時的圖像是：A.上升的B.下降的C.水平的D.折線型的16.已知\(a,b,c\)是等差數(shù)列的三個連續(xù)項，且\(a+b+c=12\)，則\(a\cdotb\cdotc\)的值為：A.16B.18C.20D.2417.函數(shù)\(y=2x^24x+1\)的對稱軸方程是：A.\(x=1\)B.\(x=2\)C.\(x=1\)D.\(x=0\)18.已知數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_1=1\)，\(a_{n+1}=2a_n+1\)，則\(a_5\)的值為：A.31B.32C.33D.3419.若\(\log_2x=3\)，則\(x\)的值為：A.8B.9C.10D.1120.已知\(\tan\theta=1\)，則\(\sin\theta\)的值為：A.\(\frac{1}{\sqrt{2}}\)B.\(\frac{1}{\sqrt{2}}\)C.\(\frac{\sqrt{2}}{2}\)D.\(\frac{\sqrt{2}}{2}\)21.函數(shù)\(y=\sqrt{x^24}\)的定義域為：A.\(x\leq2\)或\(x\geq2\)B.\(2<x<2\)C.\(x\leq2\)D.\(x\geq2\)22.已知\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(2,1)\)，則\(\overrightarrow{a}\cdot\overrightarrow\)的值為：A.0B.1C.2D.323.若\(\sin\alpha=\frac{1}{2}\)，則\(\cos2\alpha\)的值為：A.\(\frac{3}{4}\)B.\(\frac{1}{4}\)C.\(\frac{3}{4}\)D.\(\frac{1}{4}\)24.函數(shù)\(y=\frac{1}{x1}\)在\(x=2\)時的導(dǎo)數(shù)為：A.1B.1C.0D.不存在25.已知\(a\cdotb=0\)，且\(a^2+b^2=1\)，則\(a+b\)的最大值為：A.1B.\(\sqrt{2}\)C.2D.\(\sqrt{3}\)二、填空題（每題5分，共5題，計25分）26.已知\(\cos\alpha=\frac{1}{2}\)，則\(\sin^2\alpha+\cos^2\alpha\)的值為______。27.函數(shù)\(y=2x^24x+1\)的對稱軸方程是______。28.已知數(shù)列\(zhòng)(\{a_n\}\)滿足\(a_1=1\)，\(a_{n+1}=2a_n+1\)，則\(a_5\)的值為______。29.若\(\log_2x=3\)，則\(x\)的值為______。30.已知\(\tan\theta=1\)，則\(\sin\theta\)的值為______。三、解答題（共3題，計50分）31.（15分）已知函數(shù)\(f(x)=x^33x+2\)，求證：函數(shù)\(f(x)\)在\(x>1\)時單調(diào)遞增。32.（15分）在直角坐標(biāo)系中，已知點