各省高三期末考試試卷及答案

一、單項(xiàng)選擇題（每題2分，共10題）1.設(shè)集合\(A=\{1,2,3\}\)，\(B=\{x|x^2-4x+3=0\}\)，則\(A\capB=(\)\)A.\(\{1\}\)B.\(\{2\}\)C.\(\{3\}\)D.\(\{1,3\}\)2.已知\(i\)為虛數(shù)單位，復(fù)數(shù)\(z=\frac{1+2i}{1-i}\)，則\(|z|=(\)\)A.\(\frac{\sqrt{10}}{2}\)B.\(\sqrt{10}\)C.\(\frac{5}{2}\)D.\(5\)3.函數(shù)\(f(x)=\log_2(x^2-3x+2)\)的定義域?yàn)閈((\)\)A.\((1,2)\)B.\((-\infty,1)\cup(2,+\infty)\)C.\([1,2]\)D.\((-\infty,1]\cup[2,+\infty)\)4.等差數(shù)列\(zhòng)(\{a_n\}\)中，\(a_3=5\)，\(a_5=9\)，則\(a_7=(\)\)A.\(11\)B.\(13\)C.\(15\)D.\(17\)5.已知向量\(\overrightarrow{a}=(1,m)\)，\(\overrightarrow=(3,-2)\)，且\((\overrightarrow{a}+\overrightarrow)\perp\overrightarrow\)，則\(m=(\)\)A.\(-8\)B.\(-6\)C.\(6\)D.\(8\)6.已知\(\sin\alpha=\frac{3}{5}\)，\(\alpha\in(\frac{\pi}{2},\pi)\)，則\(\cos\alpha=(\)\)A.\(\frac{4}{5}\)B.\(-\frac{4}{5}\)C.\(\frac{3}{5}\)D.\(-\frac{3}{5}\)7.雙曲線(xiàn)\(\frac{x^2}{4}-\frac{y^2}{5}=1\)的漸近線(xiàn)方程為\((\)\)A.\(y=\pm\frac{\sqrt{5}}{2}x\)B.\(y=\pm\frac{2\sqrt{5}}{5}x\)C.\(y=\pm\frac{5}{4}x\)D.\(y=\pm\frac{4}{5}x\)8.執(zhí)行如圖所示的程序框圖，若輸入\(n=3\)，則輸出\(S=(\)\)（此處省略程序框圖）A.\(\frac{1}{3}\)B.\(\frac{1}{2}\)C.\(\frac{2}{3}\)D.\(\frac{3}{4}\)9.已知\(a=\log_32\)，\(b=\ln2\)，\(c=5^{-\frac{1}{2}}\)，則\(a\)，\(b\)，\(c\)的大小關(guān)系為\((\)\)A.\(c<a<b\)B.\(a<b<c\)C.\(b<a<c\)D.\(c<b<a\)10.已知函數(shù)\(f(x)=\sin(\omegax+\varphi)(\omega>0,|\varphi|<\frac{\pi}{2})\)的最小正周期為\(\pi\)，其圖象向左平移\(\frac{\pi}{6}\)個(gè)單位后得到函數(shù)\(g(x)=\cos\omegax\)的圖象，則\(\varphi=(\)\)A.\(\frac{\pi}{6}\)B.\(\frac{\pi}{3}\)C.\(-\frac{\pi}{6}\)D.\(-\frac{\pi}{3}\)答案：1.D2.A3.B4.B5.D6.B7.A8.C9.A10.C二、多項(xiàng)選擇題（每題2分，共10題）1.下列函數(shù)中，在區(qū)間\((0,+\infty)\)上單調(diào)遞增的有\(zhòng)((\)\)A.\(y=2^x\)B.\(y=\log_2x\)C.\(y=x^2\)D.\(y=\frac{1}{x}\)2.已知\(a\)，\(b\)，\(c\)為實(shí)數(shù)，則下列命題正確的是\((\)\)A.若\(a>b\)，則\(ac^2>bc^2\)B.若\(ac^2>bc^2\)，則\(a>b\)C.若\(a<b<0\)，則\(\frac{1}{a}>\frac{1}\)D.若\(a<b<0\)，則\(a^2>ab>b^2\)3.一個(gè)正方體的展開(kāi)圖如圖所示，\(A\)，\(B\)，\(C\)，\(D\)為原正方體的頂點(diǎn)，則在原來(lái)的正方體中\(zhòng)((\)\)（此處省略展開(kāi)圖）A.\(AB\parallelCD\)B.\(AB\)與\(CD\)相交C.\(AB\perpCD\)D.\(AB\)與\(CD\)所成的角為\(60^{\circ}\)4.已知函數(shù)\(f(x)=\sin(2x+\frac{\pi}{3})\)，則下列說(shuō)法正確的是\((\)\)A.\(f(x)\)的最小正周期為\(\pi\)B.\(f(x)\)的圖象關(guān)于點(diǎn)\((\frac{\pi}{3},0)\)對(duì)稱(chēng)C.\(f(x)\)的圖象關(guān)于直線(xiàn)\(x=\frac{\pi}{6}\)對(duì)稱(chēng)D.\(f(x)\)在\([0,\frac{\pi}{6}]\)上單調(diào)遞增5.下列關(guān)于圓錐曲線(xiàn)的說(shuō)法正確的是\((\)\)A.橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的離心率\(e=\frac{c}{a}\)（\(c\)為半焦距），且\(0<e<1\)B.雙曲線(xiàn)\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a>0,b>0)\)的漸近線(xiàn)方程為\(y=\pm\frac{a}x\)C.拋物線(xiàn)\(y^2=2px(p>0)\)的焦點(diǎn)坐標(biāo)為\((\frac{p}{2},0)\)D.過(guò)拋物線(xiàn)\(y^2=2px(p>0)\)焦點(diǎn)的弦長(zhǎng)為\(x_1+x_2+p\)（\(x_1\)，\(x_2\)為弦端點(diǎn)的橫坐標(biāo)）6.已知向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(-3,4)\)，則下列說(shuō)法正確的是\((\)\)A.\(\overrightarrow{a}\cdot\overrightarrow=5\)B.\(|\overrightarrow{a}+\overrightarrow|=2\sqrt{5}\)C.向量\(\overrightarrow{a}\)在向量\(\overrightarrow\)方向上的投影為\(\frac{\sqrt{5}}{5}\)D.與向量\(\overrightarrow{a}\)同向的單位向量為\((\frac{\sqrt{5}}{5},\frac{2\sqrt{5}}{5})\)7.已知\(a\)，\(b\)，\(c\)滿(mǎn)足\(a+b+c=0\)，\(a^2+b^2+c^2=4\)，則\(ab+bc+ca\)的值為\((\)\)A.\(-2\)B.\(-\frac{1}{2}\)C.\(\frac{1}{2}\)D.\(2\)8.已知函數(shù)\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x\geq0\)時(shí)，\(f(x)=x(1+x)\)，則下列說(shuō)法正確的是\((\)\)A.\(f(-1)=-2\)B.當(dāng)\(x<0\)時(shí)，\(f(x)=x(1-x)\)C.\(f(x)\)的圖象關(guān)于原點(diǎn)對(duì)稱(chēng)D.函數(shù)\(f(x)\)的值域?yàn)閈(R\)9.已知\(x\)，\(y\)滿(mǎn)足約束條件\(\begin{cases}x+y\geq1\\x-y\leq1\\y\leq1\end{cases}\)，則\(z=3x-y\)的取值范圍是\((\)\)A.\([-1,2]\)B.\([-1,4]\)C.\([2,4]\)D.\([-1,+\infty)\)10.已知函數(shù)\(f(x)=\frac{1}{3}x^3-x^2+ax-1\)有兩個(gè)極值點(diǎn)\(x_1\)，\(x_2\)，則下列說(shuō)法正確的是\((\)\)A.\(a<1\)B.若\(x_1<x_2\)，則\(f(x_1)\)是極大值，\(f(x_2)\)是極小值C.\(f(x_1)+f(x_2)<-\frac{4}{3}\)D.\(f(x_1)-f(x_2)=\frac{4}{3}\sqrt{1-a^3}\)答案：1.ABC2.BCD3.D4.ABD5.ABCD6.ABD7.A8.ACD9.B10.ABC三、判斷題（每題2分，共10題）1.空集是任何集合的子集。（）2.若\(a>b\)，則\(a^2>b^2\)。（）3.函數(shù)\(y=\sinx\)的最小正周期是\(2\pi\)。（）4.直線(xiàn)\(Ax+By+C=0\)（\(A\)，\(B\)不同時(shí)為\(0\)）的斜率為\(-\frac{A}{B}\)。（）5.若向量\(\overrightarrow{a}\)與向量\(\overrightarrow\)平行，則\(\overrightarrow{a}\)與\(\overrightarrow\)的方向相同或相反。（）6.橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)的長(zhǎng)軸長(zhǎng)為\(2a\)。（）7.若函數(shù)\(y=f(x)\)在區(qū)間\((a,b)\)內(nèi)有零點(diǎn)，則\(f(a)\cdotf(b)<0\)。（）8.數(shù)列\(zhòng)(\{a_n\}\)滿(mǎn)足\(a_{n+1}=2a_n\)，則\(\{a_n\}\)是等比數(shù)列。（）9.函數(shù)\(y=\log_2x\)與\(y=2^x\)的圖象關(guān)于直線(xiàn)\(y=x\)對(duì)稱(chēng)。（）10.已知\(x\)，\(y\)為正實(shí)數(shù)，若\(x+y=1\)，則\(\frac{1}{x}+\frac{1}{y}\)的最小值為\(4\)。（）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)\(f(x)=x^2-2x+3\)在區(qū)間\([0,3]\)上的最值。答案：對(duì)\(f(x)=x^2-2x+3\)配方得\(f(x)=(x-1)^2+2\)。對(duì)稱(chēng)軸為\(x=1\)，在區(qū)間\([0,3]\)內(nèi)。\(f(1)=2\)為最小值，\(f(3)=6\)為最大值。2.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n\)，\(a_3=5\)，\(S_5=25\)，求\(a_n\)。答案：設(shè)等差數(shù)列\(zhòng)(\{a_n\}\)公差為\(d\)，由\(a_3=5\)得\(a_1+2d=5\)，\(S_5=5a_1+\frac{5\times4}{2}d=25\)即\(a_1+2d=5\)，聯(lián)立解得\(a_1=1\)，\(d=2\)，所以\(a_n=1+2(n-1)=2n-1\)。3.求過(guò)點(diǎn)\((1,2)\)且與直線(xiàn)\(2x-y+1=0\)平行的直線(xiàn)方程。答案：直線(xiàn)\(2x-y+1=0\)斜率為\(2\)，所求直線(xiàn)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\(y-2=2(x-1)\)，即\(2x-y=0\)。4.已知\(\sin\alpha=\frac{3}{5}\)，\(\alpha\in(\frac{\pi}{2},\pi)\)，求\(\tan\alpha\)的值。答案：因?yàn)閈(\sin\alpha=\frac{