高考幾何體題庫及答案

一、單項(xiàng)選擇題(每題2分,共10題)1.一個(gè)正方體的棱長(zhǎng)為2,則其外接球的表面積為（）A.8πB.12πC.16πD.20π2.已知圓錐的底面半徑為1,母線長(zhǎng)為3,則該圓錐的體積為()A.2πB.\(\frac{2\sqrt{2}π}{3}\)C.\(\frac{4\sqrt{2}π}{3}\)D.\(\frac{2\sqrt{3}π}{3}\)3.若直線\(l\)過點(diǎn)\((1,2)\)且與直線\(2x-y-1=0\)平行,則直線\(l\)的方程為()A.\(2x-y=0\)B.\(2x-y-3=0\)C.\(x+2y-5=0\)D.\(x-2y+3=0\)4.已知向量\(\vec{a}=(1,2)\),\(\vec=(2,-2)\),則\(\vec{a}\cdot\vec\)的值為()A.-2B.0C.2D.45.函數(shù)\(y=\sin(2x+\frac{π}{3})\)的最小正周期為()A.\(\frac{π}{2}\)B.πC.2πD.4π6.設(shè)集合\(A=\{x|x^2-2x-3\lt0\}\),\(B=\{x|x\gt1\}\),則\(A\capB=\)()A.\((1,3)\)B.\((1,+∞)\)C.\((-1,3)\)D.\((-1,+∞)\)7.若\(\log_2a+\log_2b=3\),則\(a+b\)的最小值為()A.2\(\sqrt{2}\)B.4C.4\(\sqrt{2}\)D.88.雙曲線\(\frac{x^2}{4}-\frac{y^2}{12}=1\)的漸近線方程為()A.\(y=±\frac{1}{2}x\)B.\(y=±\frac{\sqrt{3}}{2}x\)C.\(y=±\sqrt{3}x\)D.\(y=±2x\)9.已知函數(shù)\(f(x)\)滿足\(f(x+1)=f(x-1)\),且\(f(x)\)是偶函數(shù),當(dāng)\(x\in[0,1]\)時(shí),\(f(x)=x^2\),則\(f(\frac{9}{2})\)的值為()A.\(\frac{1}{4}\)B.\(\frac{1}{2}\)C.1D.\(\frac{9}{4}\)10.從5名學(xué)生中選2名參加數(shù)學(xué)競(jìng)賽,共有()種不同的選法。A.5B.10C.15D.20答案:1.B2.B3.A4.B5.B6.A7.D8.C9.A10.B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.\(y=\frac{1}{x}\)D.\(y=2^x\)2.已知直線\(l_1:ax+y+1=0\),\(l_2:x+ay+1=0\),則下列說法正確的是()A.當(dāng)\(a=1\)時(shí),\(l_1\)與\(l_2\)平行B.當(dāng)\(a=-1\)時(shí),\(l_1\)與\(l_2\)垂直C.當(dāng)\(a=0\)時(shí),\(l_1\)與\(l_2\)相交D.\(l_1\)與\(l_2\)一定不重合3.設(shè)\(a\gt0\),\(b\gt0\),則下列不等式恒成立的是()A.\(a+b\geq2\sqrt{ab}\)B.\(\frac{a}+\frac{a}\geq2\)C.\(a^2+b^2\geq2ab\)D.\((a+b)^2\leq2(a^2+b^2)\)4.已知函數(shù)\(y=f(x)\)的圖象關(guān)于點(diǎn)\((1,0)\)對(duì)稱,且當(dāng)\(x\gt1\)時(shí),\(f(x)=x^2-2x\),則當(dāng)\(x\lt1\)時(shí),\(f(x)\)的解析式可能為()A.\(f(x)=-x^2+2x\)B.\(f(x)=-x^2-2x\)C.\(f(x)=x^2+2x\)D.\(f(x)=x^2-2x\)5.已知圓\(C:x^2+y^2-2x-4y+1=0\),則下列說法正確的是()A.圓心坐標(biāo)為\((1,2)\)B.半徑為2C.圓\(C\)與\(x\)軸相切D.圓\(C\)與\(y\)軸相切6.設(shè)等比數(shù)列\(zhòng)(\{a_n\}\)的公比為\(q\),其前\(n\)項(xiàng)和為\(S_n\),則下列說法正確的是()A.若\(q=1\),則\(S_n=na_1\)B.若\(q=-1\),且\(n\)為偶數(shù),則\(S_n=0\)C.若\(q\neq1\),則\(S_n=\frac{a_1(1-q^n)}{1-q}\)D.\(S_n\)一定不為07.已知函數(shù)\(y=\cosx\),則下列說法正確的是（）A.函數(shù)\(y=\cosx\)的圖象關(guān)于\(y\)軸對(duì)稱B.函數(shù)\(y=\cosx\)在\([0,π]\)上單調(diào)遞減C.函數(shù)\(y=\cosx\)的最小正周期為\(2π\(zhòng))D.函數(shù)\(y=\cosx\)的值域?yàn)閈([-1,1]\)8.已知\(A(1,0)\),\(B(0,1)\),則線段\(AB\)的垂直平分線方程為()A.\(x+y-1=0\)B.\(x-y+1=0\)C.\(y=x\)D.\(y=-x\)9.已知函數(shù)\(f(x)=x^3-3x\),則下列說法正確的是()A.函數(shù)\(f(x)\)在\(x=-1\)處取得極大值2B.函數(shù)\(f(x)\)在\(x=1\)處取得極小值-2C.函數(shù)\(f(x)\)的單調(diào)遞增區(qū)間為\((-∞,-1)\)和\((1,+∞)\)D.函數(shù)\(f(x)\)的單調(diào)遞減區(qū)間為\((-1,1)\)10.從1,2,3,4,5中任取3個(gè)不同的數(shù),則這3個(gè)數(shù)能構(gòu)成一個(gè)三角形三邊的概率為()A.\(\frac{3}{10}\)B.\(\frac{1}{5}\)C.\(\frac{1}{10}\)D.\(\frac{2}{5}\)答案:1.ABC2.ABD3.ABCD4.A5.AB6.ABC7.ACD8.A9.ABCD10.A三、判斷題(每題2分,共10題)1.空集是任何集合的子集。()2.若\(a\gtb\),則\(ac^2\gtbc^2\)。（)3.函數(shù)\(y=\tanx\)的定義域?yàn)閈(R\)。()4.若向量\(\vec{a}\cdot\vec=0\),則\(\vec{a}=\vec{0}\)或\(\vec=\vec{0}\)。（)5.直線\(x=1\)的傾斜角為\(90°\)。()6.若\(a\),\(b\),\(c\)成等差數(shù)列,則\(2b=a+c\)。（)7.函數(shù)\(y=\sqrt{x}\)在\([0,+∞)\)上單調(diào)遞增。()8.橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a\gtb\gt0)\)的離心率\(e\in(0,1)\)。()9.若函數(shù)\(f(x)\)滿足\(f(x+2)=-f(x)\),則函數(shù)\(f(x)\)的周期為4。(）10.若\(x\gt0\),則\(x+\frac{1}{x}\geq2\)。（）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.求過點(diǎn)\((1,1)\)且與直線\(x+2y-1=0\)垂直的直線方程。答案:已知直線斜率為\(-\frac{1}{2}\),所求直線斜率為2,由點(diǎn)斜式可得\(y-1=2(x-1)\),即\(2x-y-1=0\)。2.已知等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_3=5\),\(a_5=9\),求\(a_7\)。答案：根據(jù)等差數(shù)列性質(zhì)\(a_3+a_7=2a_5\),所以\(a_7=2a_5-a_3=2×9-5=13\)。3.求函數(shù)\(y=2\sin(2x-\frac{π}{6})+1\)的最大值及取得最大值時(shí)\(x\)的值。答案:當(dāng)\(\sin(2x-\frac{π}{6})=1\)時(shí),\(y\)取最大值3,此時(shí)\(2x-\frac{π}{6}=\frac{π}{2}+2kπ\(zhòng)),解得\(x=\frac{π}{3}+kπ(k\inZ)\)。4.已知圓\(C\)的方程為\(x^2+y^2-4x-6y+12=0\),求圓心坐標(biāo)和半徑。答案：將方程化為標(biāo)準(zhǔn)式\((x-2)^2+(y-3)^2=1\),圓心坐標(biāo)為\((2,3)\),半徑為1。五、討論題(每題5分,共4題)1.討論函數(shù)\(y=x^3-3x^2\)的單調(diào)性。答案:求導(dǎo)得\(y^\prime=3x^2-6x=3x(x-2)\)。令\(y^\prime\gt0\),得\(x\lt0\)或\(x\gt2\),函數(shù)遞增;令\(y^\prime\lt0\),得\(0\ltx\lt2\),函數(shù)遞減。2.如何判斷兩條直線的位置關(guān)系?答案:通過比較斜率判斷平行或相交,斜率相等且截距不同則平行,斜率不同則相交;斜率乘積為-1則垂直;還可聯(lián)立方程看解的情況判斷。3.討論在等比數(shù)列中,公比\(q\)對(duì)數(shù)列性質(zhì)的影響。答案：