山西高一會(huì)考試題及答案

一、單項(xiàng)選擇題（每題2分，共10題）1.設(shè)集合\(A=\{1,2,3\}\)，\(B=\{2,3,4\}\)，則\(A\capB=\)（）A.\(\{1\}\)B.\(\{2,3\}\)C.\(\{1,2,3,4\}\)D.\(\varnothing\)答案：B2.函數(shù)\(y=\sqrt{x-1}\)的定義域是（）A.\((-\infty,1]\)B.\((1,+\infty)\)C.\([1,+\infty)\)D.\((-\infty,1)\)答案：C3.已知\(a=2^{\frac{1}{3}}\)，\(b=\log_{2}3\)，\(c=\log_{3}2\)，則（）A.\(a<b<c\)B.\(c<a<b\)C.\(a<c<b\)D.\(c<b<a\)答案：B4.若\(\sin\alpha=\frac{1}{3}\)，且\(\alpha\in(0,\frac{\pi}{2})\)，則\(\cos\alpha=\)（）A.\(\frac{2\sqrt{2}}{3}\)B.\(-\frac{2\sqrt{2}}{3}\)C.\(\frac{\sqrt{2}}{3}\)D.\(-\frac{\sqrt{2}}{3}\)答案：A5.向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow{b}=(2,-1)\)，則\(\overrightarrow{a}\cdot\overrightarrow{b}=\)（）A.\(0\)B.\(3\)C.\(4\)D.\(-4\)答案：A6.在等差數(shù)列\(zhòng)(\{a_{n}\}\)中，\(a_{1}=1\)，\(d=2\)，則\(a_{5}=\)（）A.\(9\)B.\(10\)C.\(11\)D.\(12\)答案：A7.過點(diǎn)\((1,2)\)且斜率為\(3\)的直線方程為（）A.\(y-2=3(x-1)\)B.\(y+2=3(x+1)\)C.\(y-1=3(x-2)\)D.\(y+1=3(x+2)\)答案：A8.若二次函數(shù)\(y=ax^{2}+bx+c(a\neq0)\)的圖象開口向上，對(duì)稱軸為\(x=1\)，則\(f(2)\)與\(f(3)\)的大小關(guān)系為（）A.\(f(2)>f(3)\)B.\(f(2)=f(3)\)C.\(f(2)<f(3)\)D.無法確定答案：C9.已知\(\triangleABC\)中，\(A=60^{\circ}\)，\(a=\sqrt{3}\)，\(b=1\)，則\(B=\)（）A.\(30^{\circ}\)B.\(45^{\circ}\)C.\(60^{\circ}\)D.\(90^{\circ}\)答案：A10.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.\(\frac{2\pi}{3}\)答案：A二、多項(xiàng)選擇題（每題2分，共10題）1.下列函數(shù)中，是奇函數(shù)的有（）A.\(y=x^{3}\)B.\(y=\sinx\)C.\(y=\log_{2}x\)D.\(y=e^{x}-e^{-x}\)答案：ABD2.已知向量\(\overrightarrow{a}=(x_{1},y_{1})\)，\(\overrightarrow{b}=(x_{2},y_{2})\)，則下列結(jié)論正確的是（）A.若\(\overrightarrow{a}\parallel\overrightarrow{b}\)，則\(x_{1}y_{2}-x_{2}y_{1}=0\)B.若\(\overrightarrow{a}\perp\overrightarrow{b}\)，則\(x_{1}x_{2}+y_{1}y_{2}=0\)C.\(\vert\overrightarrow{a}\vert=\sqrt{x_{1}^{2}+y_{1}^{2}}\)D.\(\overrightarrow{a}-\overrightarrow{b}=(x_{1}-x_{2},y_{1}-y_{2})\)答案：ABCD3.對(duì)于指數(shù)函數(shù)\(y=a^{x}(a>0,a\neq1)\)，下列說法正確的是（）A.當(dāng)\(a>1\)時(shí)，函數(shù)在\(R\)上單調(diào)遞增B.當(dāng)\(0<a<1\)時(shí)，函數(shù)在\(R\)上單調(diào)遞減C.函數(shù)圖象恒過點(diǎn)\((0,1)\)D.函數(shù)的值域是\((0,+\infty)\)答案：ABCD4.下列命題正確的是（）A.平行于同一條直線的兩個(gè)平面平行B.垂直于同一條直線的兩個(gè)平面平行C.若一個(gè)平面內(nèi)有無數(shù)條直線平行于另一個(gè)平面，則這兩個(gè)平面平行D.若一個(gè)平面內(nèi)有兩條相交直線平行于另一個(gè)平面，則這兩個(gè)平面平行答案：BD5.在\(\triangleABC\)中，\(a,b,c\)分別為角\(A,B,C\)所對(duì)的邊，下列等式成立的是（）A.\(a^{2}=b^{2}+c^{2}-2bc\cosA\)B.\(b^{2}=a^{2}+c^{2}-2ac\cosB\)C.\(c^{2}=a^{2}+b^{2}-2ab\cosC\)D.\(\cosA=\frac{b^{2}+c^{2}-a^{2}}{2bc}\)答案：ABCD6.已知函數(shù)\(y=f(x)\)的圖象關(guān)于\(y\)軸對(duì)稱的是（）A.\(y=x^{2}\)B.\(y=\cosx\)C.\(y=e^{x}\)D.\(y=\vertx\vert\)答案：ABD7.下列關(guān)于數(shù)列的說法正確的是（）A.數(shù)列\(zhòng)(1,-1,1,-1,\cdots\)是等比數(shù)列B.數(shù)列\(zhòng)(1,2,3,4,\cdots\)是等差數(shù)列C.數(shù)列的通項(xiàng)公式是唯一的D.數(shù)列可以看作是一個(gè)定義域?yàn)檎麛?shù)集\(N^{}\)（或它的有限子集\(\{1,2,\cdots,n\}\)）的函數(shù)答案：ABD8.若直線\(l_{1}:y=k_{1}x+b_{1}\)，\(l_{2}:y=k_{2}x+b_{2}\)平行，則（）A.\(k_{1}=k_{2}\)B.\(b_{1}=b_{2}\)C.\(k_{1}k_{2}=-1\)D.\(k_{1}=k_{2}\)且\(b_{1}\neqb_{2}\)答案：AD9.下列函數(shù)在\((0,+\infty)\)上單調(diào)遞增的是（）A.\(y=x^{2}\)B.\(y=\lnx\)C.\(y=\frac{1}{x}\)D.\(y=e^{x}\)答案：ABD10.已知圓\(C:x^{2}+y^{2}=r^{2}(r>0)\)，則下列說法正確的是（）A.圓心\(C(0,0)\)B.半徑為\(r\)C.圓關(guān)于\(x\)軸對(duì)稱D.圓關(guān)于\(y\)軸對(duì)稱答案：ABCD三、判斷題（每題2分，共10題）1.空集是任何集合的子集。（）答案：正確2.若\(a>b\)，則\(ac^{2}>bc^{2}\)。（）答案：錯(cuò)誤3.函數(shù)\(y=\tanx\)的周期是\(\pi\)。（）答案：正確4.兩個(gè)向量相等當(dāng)且僅當(dāng)它們的模相等。（）答案：錯(cuò)誤5.若直線\(l\)的斜率不存在，則直線\(l\)垂直于\(x\)軸。（）答案：正確6.等比數(shù)列\(zhòng)(\{a_{n}\}\)中，若\(a_{1}=1\)，\(q=-1\)，則\(a_{n}=(-1)^{n-1}\)。（）答案：正確7.二次函數(shù)\(y=ax^{2}+bx+c(a\neq0)\)，當(dāng)\(a<0\)時(shí)，函數(shù)圖象開口向下。（）答案：正確8.在\(\triangleABC\)中，\(A+B+C=\pi\)。（）答案：正確9.函數(shù)\(y=f(x)\)與\(y=f(-x)\)的圖象關(guān)于\(y\)軸對(duì)稱。（）答案：正確10.若\(a,b\inR\)，則\(\verta+b\vert\leqslant\verta\vert+\vertb\vert\)。（）答案：正確四、簡(jiǎn)答題（每題5分，共4題）1.求函數(shù)\(y=\frac{1}{x-1}\)在\(x=3\)處的導(dǎo)數(shù)。答案：先求\(y=(x-1)^{-1}\)，根據(jù)求導(dǎo)公式\((X^{n})^\prime=nX^{n-1}\)，\(y^\prime=-(x-1)^{-2}\)，當(dāng)\(x=3\)時(shí)，\(y^\prime=-\frac{1}{4}\)。2.已知向量\(\overrightarrow{a}=(2,3)\)，\(\overrightarrow{b}=(-1,2)\)，求\(\overrightarrow{a}+2\overrightarrow{b}\)。答案：\(\overrightarrow{b}=(-1,2)\)，\(2\overrightarrow{b}=(-2,4)\)，\(\overrightarrow{a}+2\overrightarrow{b}=(2,3)+(-2,4)=(0,7)\)。3.求直線\(y=2x+1\)與\(y=-x+4\)的交點(diǎn)坐標(biāo)。答案：聯(lián)立方程\(\begin{cases}y=2x+1\\y=-x+4\end{cases}\)，將\(y=2x+1\)代入\(y=-x+4\)得\(2x+1=-x+4\)，\(3x=3\)，\(x=1\)，把\(x=1\)代入\(y=2x+1\)得\(y=3\)，交點(diǎn)坐標(biāo)為\((1,3)\)。4.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)中，\(a_{1}=2\)，\(d=3\)，求\(a_{5}\)。答案：根據(jù)等差數(shù)列通項(xiàng)公式\(a_{n}=a_{1}+(n-1)d\)，\(n=5\)時(shí)，\(a_{5}=2+(5-1)\times3=2+12=14\)。五、討論題（每題5分，共4題）1.討論函數(shù)\(y=x^{3}-3x\)的單調(diào)性。答案：對(duì)\(y=x^{3}-3x\)求導(dǎo)得\(y^\prime=3x^{2}-3=3(x+1)(x-1)\)。當(dāng)\(x<-1\)或\(x>1\)時(shí)，\(y^\prime>0\)，函數(shù)單調(diào)遞增；當(dāng)\(-1<x<1\)時(shí)，\(y^\prime<0\)，函數(shù)單調(diào)遞減。2.討論向量\(\overrightarrow{a}=(1,2)\)與\(\overrightarrow{b}=(2,4)\)的關(guān)系。答案：因?yàn)閈(\overrightarrow{b}=2\overrightarrow{a}\)，所以\(\overrightarrow{a}\)與\(\overrightarrow{b}\)是平行向量，且\(\overrightarrow{b}\)的模是\(\overrightarrow{a}\)模的\(2\)倍。3.討論在\(\triangleABC\)中，角\(A,B,C\)滿足\(A