單招1類(lèi)測(cè)試題庫(kù)及答案

單項(xiàng)選擇題:1.函數(shù)\(f(x)=x^2-1\)的定義域是(）A.\(R\)B.\([0,+\infty)\)C.\((-\infty,0]\)D.\(\{x|x\neq0\}\)答案：A2.直線(xiàn)\(y=2x+1\)的斜率是()A.1B.2C.-1D.-2答案：B3.已知\(\sin\alpha=\frac{1}{2}\),且\(\alpha\)是銳角,則\(\alpha\)等于()A.\(30^{\circ}\)B.\(60^{\circ}\)C.\(120^{\circ}\)D.\(150^{\circ}\)答案：A4.不等式\(x-1\gt0\)的解集是()A.\((-\infty,1)\)B.\((1,+\infty)\)C.\((-\infty,-1)\)D.\((-1,+\infty)\)答案：B5.若\(a\gtb\),則下列不等式一定成立的是()A.\(a-1\gtb-1\)B.\(a+1\ltb+1\)C.\(a-1\ltb-1\)D.\(a+1\gtb+1\)答案：A6.圓\(x^2+y^2=4\)的圓心坐標(biāo)是()A.\((0,0)\)B.\((1,1)\)C.\((2,2)\)D.\((-2,-2)\)答案：A7.函數(shù)\(f(x)=\lnx\)的定義域是()A.\((0,+\infty)\)B.\([0,+\infty)\)C.\((-\infty,0)\)D.\((-\infty,+\infty)\)答案：A8.向量\(\overrightarrow{a}=(1,2)\),\(\overrightarrow=(2,-1)\),則\(\overrightarrow{a}\cdot\overrightarrow\)等于()A.0B.1C.2D.3答案：A9.已知\(a\gt0\),\(b\gt0\),且\(a+b=1\),則\(ab\)的最大值是()A.\(\frac{1}{2}\)B.\(\frac{1}{4}\)C.\(\frac{1}{8}\)D.1答案：B10.函數(shù)\(f(x)=2^x\)的圖象是()A.一條直線(xiàn)B.一條射線(xiàn)C.一條拋物線(xiàn)D.一條指數(shù)曲線(xiàn)答案：D多項(xiàng)選擇題:1.下列函數(shù)中是奇函數(shù)的有(）A.\(f(x)=x^3\)B.\(f(x)=x+1\)C.\(f(x)=\frac{1}{x}\)D.\(f(x)=|x|\)答案:AC2.直線(xiàn)\(y=kx+b\)(\(k\neq0\))的性質(zhì)有()A.斜率為\(k\)B.恒過(guò)點(diǎn)\((0,b)\)C.當(dāng)\(k\gt0\)時(shí),函數(shù)單調(diào)遞增D.當(dāng)\(k\lt0\)時(shí),函數(shù)單調(diào)遞減答案:ABCD3.下列不等式成立的有(）A.\(a^2+1\gt0\)B.\(|a|\geq0\)C.\(a^2\geq2a\)D.\(a^2+a+1\gt0\)答案:ABD4.圓的方程\(x^2+y^2+Dx+Ey+F=0\)(\(D^2+E^2-4F\gt0\)）表示圓的條件有(）A.\(D\)、\(E\)、\(F\)為常數(shù)B.\(D^2+E^2-4F\gt0\)C.\(D\)、\(E\)不同時(shí)為零D.\(F\neq0\)答案:ABC5.向量\(\overrightarrow{a}\)、\(\overrightarrow\)滿(mǎn)足\(\overrightarrow{a}\cdot\overrightarrow=0\),則（）A.\(\overrightarrow{a}\perp\overrightarrow\)B.\(\overrightarrow{a}+\overrightarrow=\overrightarrow{0}\)C.\(\overrightarrow{a}-\overrightarrow=\overrightarrow{0}\)D.\((\overrightarrow{a}+\overrightarrow)\perp(\overrightarrow{a}-\overrightarrow)\)答案:AD6.已知\(a\gt0\),\(b\gt0\),且\(a+b=1\),則（）A.\(ab\leq\frac{1}{4}\)B.\(a^2+b^2\geq\frac{1}{2}\)C.\(\frac{1}{a}+\frac{1}\geq4\)D.\(\sqrt{a}+\sqrt\leq\sqrt{2}\)答案:ABCD7.函數(shù)\(f(x)=\log_ax\)(\(a\gt0\)且\(a\neq1\))的性質(zhì)有()A.定義域?yàn)閈((0,+\infty)\)B.恒過(guò)點(diǎn)\((1,0)\)C.當(dāng)\(a\gt1\)時(shí),函數(shù)單調(diào)遞增D.當(dāng)\(0\lta\lt1\)時(shí),函數(shù)單調(diào)遞減答案:ABCD8.下列函數(shù)在定義域上是增函數(shù)的有(）A.\(f(x)=x\)B.\(f(x)=x^2\)C.\(f(x)=2^x\)D.\(f(x)=\log_2x\)答案:ACD9.對(duì)于向量\(\overrightarrow{a}\)、\(\overrightarrow\)、\(\overrightarrow{c}\),下列運(yùn)算正確的有（）A.\(\overrightarrow{a}\cdot(\overrightarrow+\overrightarrow{c})=\overrightarrow{a}\cdot\overrightarrow+\overrightarrow{a}\cdot\overrightarrow{c}\)B.\((\overrightarrow{a}\cdot\overrightarrow)\cdot\overrightarrow{c}=\overrightarrow{a}\cdot(\overrightarrow\cdot\overrightarrow{c})\)C.\(\overrightarrow{a}\cdot\overrightarrow=\overrightarrow\cdot\overrightarrow{a}\)D.\(\overrightarrow{a}\cdot\overrightarrow{a}=|\overrightarrow{a}|^2\)答案:ACD10.已知\(a\gtb\gt0\),則（）A.\(\frac{1}{a}\lt\frac{1}\)B.\(a^2\gtb^2\)C.\(\sqrt{a}\gt\sqrt\)D.\(a^3\gtb^3\)答案:ABCD判斷題：1.空集是任何集合的子集。()答案：對(duì)2.若兩個(gè)角的終邊相同,則這兩個(gè)角相等。()答案：錯(cuò)3.直線(xiàn)\(x=1\)的斜率不存在。()答案：對(duì)4.若\(a\gtb\),則\(ac^2\gtbc^2\)。()答案：錯(cuò)5.圓的標(biāo)準(zhǔn)方程是\((x-a)^2+(y-b)^2=r^2\)。()答案：對(duì)6.向量\(\overrightarrow{a}\)與\(\overrightarrow{a}\)的模相等。()答案：對(duì)7.函數(shù)\(f(x)=\frac{1}{x}\)在\((-\infty,0)\)和\((0,+\infty)\)上都是減函數(shù)。()答案：對(duì)8.若\(a\perpb\),則\(\overrightarrow{a}\cdot\overrightarrow=0\)。()答案：對(duì)9.不等式\(x^2-2x+1\lt0\)的解集為空集。()答案：對(duì)10.函數(shù)\(f(x)=x^2-2x+1\)的圖象與\(x\)軸有兩個(gè)交點(diǎn)。()答案：錯(cuò)簡(jiǎn)答題：1.簡(jiǎn)述函數(shù)的單調(diào)性定義。答案:設(shè)函數(shù)\(f(x)\)的定義域?yàn)閈(I\),區(qū)間\(D\subseteqI\)。如果對(duì)于任意的\(x_1\),\(x_2\inD\),當(dāng)\(x_1\ltx_2\)時(shí),都有\(zhòng)(f(x_1)\ltf(x_2)\)(或\(f(x_1)\gtf(x_2)\)),那么就稱(chēng)函數(shù)\(f(x)\)在區(qū)間\(D\)上是增函數(shù)(或減函數(shù))。2.求直線(xiàn)\(y=2x-1\)與\(x\)軸的交點(diǎn)坐標(biāo)。答案:令\(y=0\),則\(2x-1=0\),解得\(x=\frac{1}{2}\),所以交點(diǎn)坐標(biāo)為\((\frac{1}{2},0)\)。3.計(jì)算\(\sin30^{\circ}+\cos60^{\circ}\)的值。答案:\(\sin30^{\circ}=\frac{1}{2}\),\(\cos60^{\circ}=\frac{1}{2}\),所以\(\sin30^{\circ}+\cos60^{\circ}=\frac{1}{2}+\frac{1}{2}=1\)。4.簡(jiǎn)述圓的一般方程。答案:圓的一般方程為\(x^2+y^2+Dx+Ey+F=0\)(\(D^2+E^2-4F\gt0\))。討論題：1.討論一次函數(shù)\(y=kx+b\)(\(k\neq0\))中\(zhòng)(k\)、\(b\)的取值對(duì)函數(shù)圖象的影響。答案：當(dāng)\(k\gt0\)時(shí),函數(shù)圖象從左到右上升；當(dāng)\(k\lt0\)時(shí),函數(shù)圖象從左到右下降。\(b\)決定函數(shù)圖象與\(y\)軸的交點(diǎn),當(dāng)\(b\gt0\)時(shí),交點(diǎn)在\(y\)軸正半軸；當(dāng)\(b\lt0\)時(shí),交點(diǎn)在\(y\)軸負(fù)半軸。2.討論二次函數(shù)\(y=ax^2+bx+c\)(\(a\neq0\))的圖象特征與\(a\)、\(b\)、\(c\)的關(guān)系。答案：\(a\)決定圖象開(kāi)口方向,\(a\gt0\)開(kāi)口向上,\(a\lt0\)開(kāi)口向下。對(duì)稱(chēng)軸為\(x=-\frac{2a}\),\(b\)影響對(duì)稱(chēng)軸位置。\(c\)決定圖象與\(y\)軸交點(diǎn),交點(diǎn)為\((0,c)\)。3.討論指數(shù)函數(shù)\(y=a^x\)(\(a\gt0\)且\(a\neq1\))的性質(zhì)與\(a\)的取值關(guān)系。