高一下冊(cè)期末試題及答案

一、單項(xiàng)選擇題(每題2分,共10題)1.下列函數(shù)中,在\((0,+∞)\)上單調(diào)遞增的是（）A.\(y=\frac{1}{x}\)B.\(y=x^2-x\)C.\(y=2^x\)D.\(y=\log_{0.5}x\)2.已知向量\(\overrightarrow{a}=(1,2)\),\(\overrightarrow=(-1,m)\),若\(\overrightarrow{a}\parallel\overrightarrow\),則\(m\)的值為()A.2B.-2C.\(\frac{1}{2}\)D.\(-\frac{1}{2}\)3.直線\(x+\sqrt{3}y-5=0\)的傾斜角為()A.\(60^{\circ}\)B.\(120^{\circ}\)C.\(30^{\circ}\)D.\(150^{\circ}\)4.已知\(\sin\alpha=\frac{3}{5}\),\(\alpha\)在第二象限,則\(\cos\alpha\)的值為()A.\(\frac{4}{5}\)B.\(-\frac{4}{5}\)C.\(\frac{3}{4}\)D.\(-\frac{3}{4}\)5.若\(a\gtb\gt0\),則下列不等式成立的是()A.\(a^2\ltb^2\)B.\(\frac{1}{a}\gt\frac{1}\)C.\(a^3\gtb^3\)D.\(\log_{0.5}a\gt\log_{0.5}b\)6.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)中,\(a_{3}=5\),\(a_{5}=9\),則\(a_{7}\)的值為()A.11B.12C.13D.147.函數(shù)\(y=\sin(2x+\frac{\pi}{3})\)的最小正周期是()A.\(\pi\)B.\(2\pi\)C.\(\frac{\pi}{2}\)D.\(\frac{\pi}{4}\)8.圓\((x-1)^2+(y+2)^2=9\)的圓心坐標(biāo)和半徑分別是()A.\((1,-2)\),3B.\((-1,2)\),3C.\((1,-2)\),9D.\((-1,2)\),99.若\(x\),\(y\)滿足約束條件\(\begin{cases}x+y\geq1\\x-y\leq1\\y\leq1\end{cases}\),則\(z=3x-y\)的最大值為（）A.1B.3C.5D.710.已知\(\alpha\),\(\beta\)是兩個(gè)不同平面,\(m\),\(n\)是兩條不同直線,下列命題正確的是()A.若\(m\parallel\alpha\),\(n\parallel\alpha\),則\(m\paralleln\)B.若\(m\subset\alpha\),\(n\subset\beta\),\(\alpha\parallel\beta\),則\(m\paralleln\)C.若\(m\perp\alpha\),\(n\perp\beta\),\(\alpha\perp\beta\),則\(m\perpn\)D.若\(\alpha\cap\beta=m\),\(n\parallelm\),則\(n\parallel\alpha\)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.\(y=x^2+1\)B.\(y=\cosx\)C.\(y=\ln(x+\sqrt{x^2+1})\)D.\(y=2^{|x|}\)2.已知等比數(shù)列\(zhòng)(\{a_{n}\}\),公比\(q\)滿足\(|q|\gt1\),則下列說法正確的是()A.數(shù)列\(zhòng)(\{a_{n}\}\)是遞增數(shù)列B.數(shù)列\(zhòng)(\{a_{n}\}\)是遞減數(shù)列C.數(shù)列\(zhòng)(\{a_{n}\}\)的奇數(shù)項(xiàng)同號(hào)D.數(shù)列\(zhòng)(\{a_{n}\}\)的偶數(shù)項(xiàng)同號(hào)3.以下關(guān)于直線方程的說法正確的是()A.直線\(y=kx+b\)的斜率為\(k\)B.直線\(Ax+By+C=0\)(\(A\),\(B\)不同時(shí)為\(0\))的斜率為\(-\frac{A}{B}\)C.過點(diǎn)\((x_0,y_0)\)且斜率為\(k\)的直線方程為\(y-y_0=k(x-x_0)\)D.過兩點(diǎn)\((x_1,y_1)\),\((x_2,y_2)\)(\(x_1\neqx_2\))的直線方程為\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)4.下列三角函數(shù)值為正的是(）A.\(\sin225^{\circ}\)B.\(\cos(-30^{\circ})\)C.\(\tan135^{\circ}\)D.\(\sin(-\frac{\pi}{3})\)5.已知向量\(\overrightarrow{a}=(x_1,y_1)\),\(\overrightarrow=(x_2,y_2)\),則下列向量運(yùn)算正確的是()A.\(\overrightarrow{a}+\overrightarrow=(x_1+x_2,y_1+y_2)\)B.\(\overrightarrow{a}-\overrightarrow=(x_1-x_2,y_1-y_2)\)C.\(\lambda\overrightarrow{a}=(\lambdax_1,\lambday_1)\)(\(\lambda\)為實(shí)數(shù))D.\(\overrightarrow{a}\cdot\overrightarrow=x_1x_2+y_1y_2\)6.若\(a\),\(b\),\(c\)滿足\(c\ltb\lta\)且\(ac\lt0\),則下列不等式一定成立的是（）A.\(ab\gtac\)B.\(c(b-a)\gt0\)C.\(cb^2\ltab^2\)D.\(ac(a-c)\lt0\)7.關(guān)于圓的方程,以下說法正確的是()A.圓\(x^2+y^2=r^2\)的圓心是\((0,0)\),半徑是\(r\)B.圓\((x-a)^2+(y-b)^2=r^2\)的圓心是\((a,b)\),半徑是\(r\)C.圓\(x^2+y^2+Dx+Ey+F=0\)(\(D^2+E^2-4F\gt0\))的圓心是\((-\frac{D}{2},-\frac{E}{2})\),半徑是\(\frac{\sqrt{D^2+E^2-4F}}{2}\)D.已知圓上三點(diǎn)\(A(x_1,y_1)\),\(B(x_2,y_2)\),\(C(x_3,y_3)\),可通過聯(lián)立方程求出圓的方程8.已知\(\alpha\)是三角形內(nèi)角,且\(\sin\alpha+\cos\alpha=\frac{1}{5}\),則下列結(jié)論正確的是()A.\(\sin\alpha=\frac{4}{5}\),\(\cos\alpha=-\frac{3}{5}\)B.\(\sin\alpha=-\frac{3}{5}\),\(\cos\alpha=\frac{4}{5}\)C.\(\tan\alpha=-\frac{4}{3}\)D.\(\alpha\)是鈍角9.已知直線\(l_1\):\(A_1x+B_1y+C_1=0\),\(l_2\):\(A_2x+B_2y+C_2=0\),則下列說法正確的是()A.若\(l_1\parallell_2\),則\(\frac{A_1}{A_2}=\frac{B_1}{B_2}\neq\frac{C_1}{C_2}\)(\(A_2\),\(B_2\),\(C_2\)均不為\(0\))B.若\(l_1\perpl_2\),則\(A_1A_2+B_1B_2=0\)C.兩直線\(l_1\)與\(l_2\)的交點(diǎn)坐標(biāo)可通過聯(lián)立方程組\(\begin{cases}A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0\end{cases}\)求解D.直線\(l_1\)與\(l_2\)的距離\(d=\frac{|C_1-C_2|}{\sqrt{A_1^2+B_1^2}}\)10.已知\(x\gt0\),\(y\gt0\),且\(x+y=1\),則()A.\(xy\)有最大值\(\frac{1}{4}\)B.\(\frac{1}{x}+\frac{1}{y}\)有最小值\(4\)C.\(x^2+y^2\)有最小值\(\frac{1}{2}\)D.\(\sqrt{x}+\sqrt{y}\)有最大值\(\sqrt{2}\)三、判斷題(每題2分,共10題)1.函數(shù)\(y=\sqrt{x-1}\)的定義域是\([1,+∞)\)。()2.若\(a\),\(b\)為實(shí)數(shù),且\(a\gtb\),則\(a^2\gtb^2\)。（)3.向量\(\overrightarrow{a}=(1,0)\)與向量\(\overrightarrow=(0,1)\)垂直。()4.等差數(shù)列\(zhòng)(\{a_{n}\}\)的前\(n\)項(xiàng)和\(S_{n}=\frac{n(a_{1}+a_{n})}{2}\)。()5.函數(shù)\(y=\sinx\)的圖象關(guān)于原點(diǎn)對(duì)稱。()6.直線\(x=1\)的斜率不存在。()7.圓\(x^2+y^2-2x+4y=0\)的圓心坐標(biāo)是\((1,-2)\)。()8.若\(\alpha\),\(\beta\)是兩個(gè)不同平面,直線\(m\subset\alpha\),直線\(n\subset\beta\),則\(m\),\(n\)異面。（)9.不等式\(x^2-3x+2\gt0\)的解集是\((1,2)\)。()10.已知\(a\),\(b\),\(c\)成等比數(shù)列,則\(b^2=ac\)。（）四、簡(jiǎn)答題(每題5分,共4題)1.求函數(shù)\(y=\log_2(x^2-3x+2)\)的定義域。答案:要使函數(shù)有意義,則\(x^2-3x+2\gt0\),即\((x-1)(x-2)\gt0\),解得\(x\lt1\)或\(x\gt2\),所以定義域?yàn)閈((-∞,1)\cup(2,+∞)\)。2.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)中,\(a_{1}=1\),\(d=2\),求\(a_{5}\)及前\(5\)項(xiàng)和\(S_{5}\)。答案:根據(jù)等差數(shù)列通項(xiàng)公式\(a_{n}=a_{1}+(n-1)d\),可得\(a_{5}=1+(5-1)\times2=9\)。再由前\(n\)項(xiàng)和公式\(S_{n}=na_{1}+\frac{n(n-1)}{2}d\),得\(S_{5}=5\times1+\frac{5\times4}{2}\times2=25\)。3.已知向量\(\overrightarrow{a}=(2,-1)\),\(\overrightarrow=(-3,4)\),求\(\overrightarrow{a}+\overrightarrow\)與\(\overrightarrow{a}\cdot\overrightarrow\)的值。答案:\(\overrightarrow{a}+\overrightarrow=(2-3,-1+4)=(-1,3)\)；\(\overrightarrow{a}\cdot\overrightarrow=2\times(-3)+(-1)\times4=-6-4=-10\)。4.求直線\(2x-y+1=0\)與直線\(x+2y-5=0\)的交點(diǎn)坐標(biāo)。答案:聯(lián)立方程組\(\begin{cases}2x-y+1=0\\x+2y-5=0\end{cases}\),由第一個(gè)方程得\(y=2x+1\),代入第二個(gè)方程得\(x+2(2x+1)-5=0\),解得\(x=1\),則\(y=2\times1+1=3\),交點(diǎn)坐標(biāo)為\((1,3)\)。五、討論題(每題5分,共4題)1.討論在等比數(shù)列中,