高中月考卷題庫(kù)及答案

一、單項(xiàng)選擇題(每題2分,共10題)1.已知集合\(A=\{x|x^2-3x+2=0\}\),\(B=\{x|0<x<6,x\inN\}\),則\(A\capB=(\)\)A.\(\{1,2\}\)B.\(\{2,3\}\)C.\(\{1,2,3\}\)D.\(\{2,4,5\}\)2.函數(shù)\(y=\sqrt{x-1}+\frac{1}{x-2}\)的定義域?yàn)閈((\)\)A.\([1,2)\cup(2,+\infty)\)B.\((1,+\infty)\)C.\([1,2)\)D.\([1,+\infty)\)3.已知\(a=\log_20.3\),\(b=2^{0.1}\),\(c=0.2^{1.3}\),則\(a,b,c\)的大小關(guān)系是\((\)\)A.\(a<b<c\)B.\(c<a<b\)C.\(a<c<b\)D.\(b<c<a\)4.已知向量\(\overrightarrow{a}=(1,2)\),\(\overrightarrow=(3,1)\),則\(\overrightarrow{a}+\overrightarrow\)的坐標(biāo)為\((\)\)A.\((4,3)\)B.\((3,4)\)C.\((2,3)\)D.\((3,2)\)5.若\(\sin\alpha=\frac{3}{5}\),且\(\alpha\)為第二象限角,則\(\cos\alpha=(\)\)A.\(-\frac{4}{5}\)B.\(\frac{4}{5}\)C.\(-\frac{3}{5}\)D.\(\frac{3}{5}\)6.圓\((x-2)^2+y^2=4\)的圓心坐標(biāo)和半徑分別為\((\)\)A.\((0,2)\),\(2\)B.\((2,0)\),\(2\)C.\((-2,0)\),\(4\)D.\((2,0)\),\(4\)7.已知直線\(l_1:2x+y-3=0\),\(l_2:x-y+6=0\),則\(l_1\)與\(l_2\)的交點(diǎn)坐標(biāo)為\((\)\)A.\((-1,4)\)B.\((1,2)\)C.\((-2,5)\)D.\((2,-1)\)8.等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_2=3\),\(a_5=9\),則公差\(d=(\)\)A.\(1\)B.\(2\)C.\(3\)D.\(4\)9.函數(shù)\(y=\sin2x\)的最小正周期為\((\)\)A.\(\pi\)B.\(2\pi\)C.\(\frac{\pi}{2}\)D.\(\frac{\pi}{4}\)10.從\(1\),\(2\),\(3\),\(4\),\(5\)中任取\(2\)個(gè)不同的數(shù),事件\(A\)為"取到的\(2\)個(gè)數(shù)之和為偶數(shù)",事件\(B\)為"取到的\(2\)個(gè)數(shù)均為偶數(shù)",則\(P(B|A)=(\)\)A.\(\frac{1}{8}\)B.\(\frac{1}{4}\)C.\(\frac{2}{5}\)D.\(\frac{1}{2}\)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\(zhòng)((\)\)A.\(y=x^2\)B.\(y=\cosx\)C.\(y=\sinx\)D.\(y=|x|\)2.下列命題中,正確的有\(zhòng)((\)\)A.若\(a>b\),\(c>d\),則\(a-c>b-d\)B.若\(a>b\),\(c>d\),則\(ac>bd\)C.若\(a>b\),則\(a^2>b^2\)D.若\(a>b\),\(c>0\),則\(ac>bc\)3.已知向量\(\overrightarrow{a}=(1,1)\),\(\overrightarrow=(-1,1)\),則下列向量與\(2\overrightarrow{a}-\overrightarrow\)平行的有\(zhòng)((\)\)A.\((1,0)\)B.\((0,1)\)C.\((-1,1)\)D.\((1,-1)\)4.下列函數(shù)中,在\((0,+\infty)\)上單調(diào)遞增的有\(zhòng)((\)\)A.\(y=x^3\)B.\(y=\lnx\)C.\(y=2^x\)D.\(y=\cosx\)5.已知\(\triangleABC\)中,角\(A,B,C\)所對(duì)的邊分別為\(a,b,c\),則下列結(jié)論正確的有\(zhòng)((\)\)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.\(\cosA=\frac{b^2+c^2-a^2}{2bc}\)6.已知圓\(C:x^2+y^2-2x-4y+1=0\),則下列說(shuō)法正確的有\(zhòng)((\)\)A.圓心坐標(biāo)為\((1,2)\)B.圓心坐標(biāo)為\((-1,-2)\)C.半徑為\(2\)D.半徑為\(4\)7.已知直線\(l:y=kx+b\),則下列說(shuō)法正確的有\(zhòng)((\)\)A.當(dāng)\(k>0\)時(shí),直線\(l\)單調(diào)遞增B.當(dāng)\(k<0\)時(shí),直線\(l\)單調(diào)遞減C.直線\(l\)恒過(guò)定點(diǎn)\((0,b)\)D.直線\(l\)與\(x\)軸交點(diǎn)坐標(biāo)為\((-\frac{k},0)\)8.已知數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=n^2\),則下列說(shuō)法正確的有\(zhòng)((\)\)A.\(a_1=1\)B.\(a_n=2n-1\)C.\(a_n=n^2\)D.數(shù)列\(zhòng)(\{a_n\}\)是等差數(shù)列9.已知函數(shù)\(y=\sinx\),則下列說(shuō)法正確的有\(zhòng)((\)\)A.函數(shù)\(y=\sinx\)的最大值為\(1\)B.函數(shù)\(y=\sinx\)的最小值為\(-1\)C.函數(shù)\(y=\sinx\)的周期為\(2\pi\)D.函數(shù)\(y=\sinx\)是奇函數(shù)10.從裝有\(zhòng)(2\)個(gè)紅球和\(2\)個(gè)黑球的口袋內(nèi)任取\(2\)個(gè)球,則下列事件中是互斥事件的有\(zhòng)((\)\)A.至少有一個(gè)黑球與都是黑球B.至少有一個(gè)黑球與至少有一個(gè)紅球C.恰有一個(gè)黑球與恰有兩個(gè)黑球D.至少有一個(gè)黑球與都是紅球三、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\(\frac{1}{a}<\frac{1}\)。（)3.函數(shù)\(y=\sqrt{x^2}\)與\(y=x\)是同一個(gè)函數(shù)。()4.向量的模一定是非負(fù)實(shí)數(shù)。()5.若\(\sin\alpha=0\),則\(\alpha=0\)。（)6.圓的標(biāo)準(zhǔn)方程可以確定圓的圓心和半徑。()7.直線的斜率不存在時(shí),直線垂直于\(x\)軸。（)8.等差數(shù)列的通項(xiàng)公式是唯一的。()9.函數(shù)\(y=\cosx\)是奇函數(shù)。()10.互斥事件一定是對(duì)立事件。(）四、簡(jiǎn)答題(每題5分,共4題)1.已知\(f(x)=x^2-2x+3\),求\(f(0)\),\(f(1)\),\(f(2)\)的值。答案：\(f(0)=3\),\(f(1)=2\),\(f(2)=3\)。2.求過(guò)點(diǎn)\((1,2)\)且斜率為\(3\)的直線方程。答案:由點(diǎn)斜式得\(y-2=3(x-1)\),即\(3x-y-1=0\)。3.在\(\triangleABC\)中,\(A=60^{\circ}\),\(a=\sqrt{3}\),\(b=1\),求角\(B\)。答案:由正弦定理\(\frac{a}{\sinA}=\frac{\sinB}\),得\(\sinB=\frac{1}{2}\),又\(b<a\),所以\(B=30^{\circ}\)。4.已知等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=2\),\(a_4=16\),求公比\(q\)和通項(xiàng)公式\(a_n\)。答案：\(q^3=\frac{a_4}{a_1}=8\),得\(q=2\),\(a_n=2\times2^{n-1}=2^n\)。五、討論題(每題5分,共4題)1.討論函數(shù)\(y=x^2-4x+3\)的單調(diào)性。答案:對(duì)稱軸為\(x=2\),在\((-\infty,2)\)上單調(diào)遞減,在\((2,+\infty)\)上單調(diào)遞增。2.討論直線\(y=kx+1\)與圓\(x^2+y^2=4\)的位置關(guān)系。答案:圓心到直線距離\(d=\frac{1}{\sqrt{k^2+1}}\)。當(dāng)\(d<2\)即\(k>\frac{\sqrt{3}}{3}\)或\(k<-\frac{\sqrt{3}}{3}\)時(shí)相交;\(d=2\)即\(k=\pm\frac{\sqrt{3}}{3}\)時(shí)相切;\(d>2\)即\(-\frac{\sqrt{3}}{3}<k<\frac{\sqrt{3}}{3}\)時(shí)相離。3.討論在等差數(shù)列\(zhòng)(\{a_n\}\)中,若\(a_n=2n-1\),求其前\(n\)項(xiàng)和\(S_n\)的表達(dá)式。答案：\(S_n=\fr