成人考試?yán)砜票乜碱}目及答案

一、單項(xiàng)選擇題（每題2分，共10題）1.函數(shù)\(y=\sinx\)的最小正周期是（）A.\(\frac{\pi}{2}\)B.\(\pi\)C.\(2\pi\)D.\(4\pi\)2.拋物線\(y^2=8x\)的焦點(diǎn)坐標(biāo)是（）A.\((2,0)\)B.\((0,2)\)C.\((4,0)\)D.\((0,4)\)3.已知向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(-1,m)\)，若\(\overrightarrow{a}\parallel\overrightarrow\)，則\(m\)的值為（）A.\(2\)B.\(-2\)C.\(\frac{1}{2}\)D.\(-\frac{1}{2}\)4.等差數(shù)列\(zhòng)(\{a_{n}\}\)中，\(a_{1}=1\)，\(a_{3}=5\)，則\(a_{5}\)的值為（）A.\(9\)B.\(10\)C.\(11\)D.\(12\)5.已知\(\cos\alpha=\frac{1}{3}\)，且\(\alpha\)是第四象限角，則\(\sin\alpha\)的值為（）A.\(\frac{2\sqrt{2}}{3}\)B.\(-\frac{2\sqrt{2}}{3}\)C.\(\frac{\sqrt{2}}{3}\)D.\(-\frac{\sqrt{2}}{3}\)6.函數(shù)\(y=\log_{2}(x+1)\)的定義域是（）A.\((-1,+\infty)\)B.\((-\infty,-1)\)C.\((0,+\infty)\)D.\((1,+\infty)\)7.已知\(x\)，\(y\)滿足約束條件\(\begin{cases}x+y\geqslant1\\x-y\leqslant1\\y\leqslant1\end{cases}\)，則\(z=2x+y\)的最大值是（）A.\(1\)B.\(2\)C.\(3\)D.\(4\)8.圓\(x^{2}+y^{2}-2x+4y-4=0\)的圓心坐標(biāo)和半徑分別是（）A.\((1,-2)\)，\(3\)B.\((1,-2)\)，\(9\)C.\((-1,2)\)，\(3\)D.\((-1,2)\)，\(9\)9.已知\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x\gt0\)時(shí)，\(f(x)=x^{2}-2x\)，則\(f(-1)\)的值為（）A.\(-1\)B.\(1\)C.\(3\)D.\(-3\)10.直線\(x+\sqrt{3}y-5=0\)的傾斜角是（）A.\(30^{\circ}\)B.\(60^{\circ}\)C.\(120^{\circ}\)D.\(150^{\circ}\)答案1.C2.A3.B4.A5.B6.A7.C8.A9.A10.D二、多項(xiàng)選擇題（每題2分，共10題）1.下列函數(shù)中，是偶函數(shù)的有（）A.\(y=x^{2}\)B.\(y=\cosx\)C.\(y=\sinx\)D.\(y=|x|\)2.已知直線\(l_{1}:A_{1}x+B_{1}y+C_{1}=0\)，\(l_{2}:A_{2}x+B_{2}y+C_{2}=0\)，則\(l_{1}\parallell_{2}\)的條件是（）A.\(A_{1}B_{2}-A_{2}B_{1}=0\)B.\(A_{1}C_{2}-A_{2}C_{1}\neq0\)C.\(A_{1}B_{2}-A_{2}B_{1}=0\)且\(A_{1}C_{2}-A_{2}C_{1}\neq0\)D.\(A_{1}A_{2}+B_{1}B_{2}=0\)3.下列關(guān)于橢圓的說法正確的有（）A.橢圓\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a\gtb\gt0)\)的長(zhǎng)軸長(zhǎng)為\(2a\)B.橢圓\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a\gtb\gt0)\)的離心率\(e=\frac{c}{a}\)（\(c\)為半焦距）C.橢圓\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a\gtb\gt0)\)的焦點(diǎn)在\(x\)軸上D.橢圓\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a\gtb\gt0)\)與\(\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1(a\gtb\gt0)\)的焦距相等4.已知\(\alpha\)，\(\beta\)是兩個(gè)不同的平面，\(m\)，\(n\)是兩條不同的直線，則下列命題正確的有（）A.若\(m\parallel\alpha\)，\(n\parallel\alpha\)，則\(m\paralleln\)B.若\(m\perp\alpha\)，\(m\paralleln\)，則\(n\perp\alpha\)C.若\(m\subset\alpha\)，\(n\subset\beta\)，\(\alpha\parallel\beta\)，則\(m\paralleln\)D.若\(\alpha\perp\beta\)，\(\alpha\cap\beta=l\)，\(m\subset\alpha\)，\(m\perpl\)，則\(m\perp\beta\)5.下列運(yùn)算正確的有（）A.\(a^{m}\cdota^{n}=a^{m+n}\)B.\((a^{m})^{n}=a^{mn}\)C.\((ab)^{n}=a^{n}b^{n}\)D.\(a^{m}\diva^{n}=a^{m-n}(a\neq0)\)6.已知\(a\)，\(b\)，\(c\)為\(\triangleABC\)的三邊，且滿足\(a^{2}+b^{2}-c^{2}=ab\)，則（）A.\(\cosC=\frac{1}{2}\)B.\(\cosC=-\frac{1}{2}\)C.\(\angleC=60^{\circ}\)D.\(\angleC=120^{\circ}\)7.已知函數(shù)\(f(x)=x^{3}-3x\)，則（）A.\(f(x)\)是奇函數(shù)B.\(f(x)\)的單調(diào)遞增區(qū)間是\((-\infty,-1)\)和\((1,+\infty)\)C.\(f(x)\)的單調(diào)遞減區(qū)間是\((-1,1)\)D.\(f(x)\)的極大值為\(2\)，極小值為\(-2\)8.已知數(shù)列\(zhòng)(\{a_{n}\}\)是等比數(shù)列，公比為\(q\)，則下列說法正確的有（）A.若\(q\gt1\)，則\(\{a_{n}\}\)是遞增數(shù)列B.若\(a_{1}\gt0\)，\(0\ltq\lt1\)，則\(\{a_{n}\}\)是遞減數(shù)列C.若\(a_{1}\lt0\)，\(0\ltq\lt1\)，則\(\{a_{n}\}\)是遞增數(shù)列D.若\(q\lt0\)，則\(\{a_{n}\}\)是擺動(dòng)數(shù)列9.已知\(A(1,2)\)，\(B(3,4)\)，則（）A.\(\overrightarrow{AB}=(2,2)\)B.\(|\overrightarrow{AB}|=2\sqrt{2}\)C.與\(\overrightarrow{AB}\)同向的單位向量為\((\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})\)D.與\(\overrightarrow{AB}\)垂直的單位向量為\((\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})\)10.下列曲線中，離心率為\(\frac{\sqrt{2}}{2}\)的有（）A.\(\frac{x^{2}}{2}+y^{2}=1\)B.\(\frac{x^{2}}{4}+\frac{y^{2}}{2}=1\)C.\(\frac{x^{2}}{4}-\frac{y^{2}}{2}=1\)D.\(\frac{x^{2}}{2}-\frac{y^{2}}{4}=1\)答案1.ABD2.C3.ABCD4.BD5.ABCD6.AC7.ABCD8.BCD9.ABC10.AB三、判斷題（每題2分，共10題）1.若\(a\gtb\)，則\(a^{2}\gtb^{2}\)。（）2.函數(shù)\(y=\tanx\)的定義域是\(\{x|x\neqk\pi+\frac{\pi}{2},k\inZ\}\)。（）3.空間中垂直于同一條直線的兩條直線一定平行。（）4.若\(a\)，\(b\)，\(c\)成等差數(shù)列，則\(2b=a+c\)。（）5.函數(shù)\(y=2^{x}\)與\(y=\log_{2}x\)的圖象關(guān)于直線\(y=x\)對(duì)稱。（）6.雙曲線\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)的漸近線方程是\(y=\pm\frac{a}x\)。（）7.若向量\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}=\overrightarrow{0}\)或\(\overrightarrow=\overrightarrow{0}\)。（）8.函數(shù)\(y=\sin^{2}x\)的最小正周期是\(\pi\)。（）9.若\(x\gt0\)，\(y\gt0\)，且\(x+y=1\)，則\(xy\)的最大值是\(\frac{1}{4}\)。（）10.拋物線\(x^{2}=2py(p\gt0)\)的準(zhǔn)線方程是\(y=-\frac{p}{2}\)。（）答案1.×2.√3.×4.√5.√6.√7.×8.√9.√10.√四、簡(jiǎn)答題（每題5分，共4題）1.求函數(shù)\(y=3\sin(2x+\frac{\pi}{6})\)的最大值、最小值以及取得最值時(shí)\(x\)的取值集合。答案：最大值為\(3\)，此時(shí)\(2x+\frac{\pi}{6}=2k\pi+\frac{\pi}{2}(k\inZ)\)，解得\(x=k\pi+\frac{\pi}{6}(k\inZ)\)。最小值為\(-3\)，此時(shí)\(2x+\frac{\pi}{6}=2k\pi-\frac{\pi}{2}(k\inZ)\)，解得\(x=k\pi-\frac{\pi}{3}(k\inZ)\)。2.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)中，\(a_{3}=5\)，\(a_{7}=13\)，求\(a_{1}\)和\(d\)。答案：由等差數(shù)列通項(xiàng)公式\(a_{n}=a_{1}+(n-1)d\)，可得\(\begin{cases}a_{1}+2d=5\\a_{1}+6d=13\end{cases}\)，兩式相減得\(4d=8\)，即\(d=2\)，將\(d=2\)代入\(a_{1}+2d=5\)，得\(a_{1}=1\)。3.求過點(diǎn)\((1,2)\)且與直線\(2x-y+1=0\)平行的直線方程。答案：直線\(2x-y+1=0\)斜率為\(2\)，所求直線與之平行，斜率也為\(2\)。由點(diǎn)斜式\(y-y_{0}=k(x-x_{0})\)（\((x_{0},y_{0})=(1,2)\)，\(k=2\)），可得\(y-2=2(x-1)\)，整理得\(2x-y=0\)。4.計(jì)算\(\int_{0}^{1}(x^{2}+1)dx\)。答案：根據(jù)定積分運(yùn)算法則\(\int_{0}^{1}(x^{2}+1)dx=\int_{0}^{1}x^{2}dx+\int_{0}^{1}1dx\)。\(\int_{0}^{1}x^{2}dx=\frac{1}{3}x^{3}\big|_{0}^{1}=\frac{1}{3}\)，\(\int_{0}^{1}1dx=x\big|_{0}^{1}=1\)，所以結(jié)果為\(\frac{1}{3}+1=\frac{4}{3}\)。五