溫州高二數(shù)學(xué)題庫(kù)及答案

單項(xiàng)選擇題(10題,每題2分)1.橢圓\(\frac{x^2}{25}+\frac{y^2}{9}=1\)的長(zhǎng)軸長(zhǎng)為(）A.5B.6C.10D.122.函數(shù)\(f(x)=x^3-3x\)的單調(diào)遞增區(qū)間是()A.\((-\infty,-1)\)B.\((1,+\infty)\)C.\((-1,1)\)D.\((-\infty,-1)\cup(1,+\infty)\)3.等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=2\),公比\(q=3\),則\(a_4=\)()A.18B.24C.54D.814.雙曲線(xiàn)\(\frac{x^2}{4}-\frac{y^2}{5}=1\)的離心率為()A.\(\frac{3}{2}\)B.\(\frac{\sqrt{5}}{2}\)C.2D.35.若\(f(x)=\lnx\),則\(f^\prime(e)=\)()A.\(e\)B.\(\frac{1}{e}\)C.1D.06.拋物線(xiàn)\(y^2=8x\)的焦點(diǎn)坐標(biāo)為()A.\((2,0)\)B.\((-2,0)\)C.\((0,2)\)D.\((0,-2)\)7.數(shù)列\(zhòng)(\{a_n\}\)滿(mǎn)足\(a_{n+1}=a_n+2\),\(a_1=1\),則\(a_5=\)()A.7B.8C.9D.108.函數(shù)\(f(x)=x^2-2x\)的極值點(diǎn)為()A.\(x=0\)B.\(x=1\)C.\(x=2\)D.不存在9.已知橢圓短軸長(zhǎng)為4,焦距為2,則長(zhǎng)軸長(zhǎng)為()A.6B.\(2\sqrt{5}\)C.\(2\sqrt{3}\)D.510.若\(f(x)=xe^x\),則\(f^\prime(x)=\)()A.\(e^x\)B.\(xe^x\)C.\((x+1)e^x\)D.\((x-1)e^x\)多項(xiàng)選擇題(10題,每題2分)1.下列函數(shù)中,在\((0,+\infty)\)上單調(diào)遞增的有（）A.\(y=x^2\)B.\(y=\lnx\)C.\(y=e^x\)D.\(y=\frac{1}{x}\)2.關(guān)于雙曲線(xiàn)\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)(\(a>0,b>0\)),正確的是()A.焦點(diǎn)在\(x\)軸上B.漸近線(xiàn)方程為\(y=\pm\frac{a}x\)C.離心率\(e>1\)D.\(c^2=a^2-b^2\)3.數(shù)列\(zhòng)(\{a_n\}\)為等差數(shù)列的條件有()A.\(a_{n+1}-a_n=d\)(常數(shù))B.\(2a_{n+1}=a_n+a_{n+2}\)C.\(a_n=kn+b\)(\(k,b\)為常數(shù))D.\(a_n=2^n\)4.函數(shù)\(f(x)\)在\(x=x_0\)處可導(dǎo)的必要條件有(）A.\(f(x)\)在\(x_0\)處連續(xù)B.\(f(x)\)在\(x_0\)處有定義C.\(f(x)\)在\(x_0\)處極限存在D.\(f(x)\)在\(x_0\)處可微5.拋物線(xiàn)\(x^2=-2py\)(\(p>0\))的性質(zhì)包括()A.開(kāi)口向下B.焦點(diǎn)\((0,-\frac{p}{2})\)C.準(zhǔn)線(xiàn)\(y=\frac{p}{2}\)D.對(duì)稱(chēng)軸為\(y\)軸6.下列求導(dǎo)正確的有()A.\((\sinx)^\prime=\cosx\)B.\((\cosx)^\prime=\sinx\)C.\((e^x)^\prime=e^x\)D.\((\lnx)^\prime=\frac{1}{x}\)7.等比數(shù)列\(zhòng)(\{a_n\}\)中,若\(a_3=4\),\(a_6=32\),則()A.公比\(q=2\)B.\(a_1=1\)C.\(a_4=8\)D.\(S_3=7\)8.橢圓\(\frac{x^2}{m}+\frac{y^2}{n}=1\)(\(m>n>0\))的焦點(diǎn)坐標(biāo)可能為()A.\((\pm\sqrt{m-n},0)\)B.\((0,\pm\sqrt{m-n})\)C.\((\pm\sqrt{n-m},0)\)D.不存在9.函數(shù)\(f(x)=x^3-3x^2\)的極值情況為()A.\(x=0\)處有極大值B.\(x=2\)處有極小值C.無(wú)極值D.\(x=1\)處有極值10.下列數(shù)列中,極限存在的有()A.\(a_n=\frac{1}{n}\)B.\(a_n=(-1)^n\)C.\(a_n=\frac{n+1}{n}\)D.\(a_n=2^n\)判斷題(10題,每題2分)1.等差數(shù)列的前\(n\)項(xiàng)和公式一定是二次函數(shù)。()2.函數(shù)在某點(diǎn)可導(dǎo),則在該點(diǎn)一定連續(xù)。()3.雙曲線(xiàn)的離心率越大,開(kāi)口越窄。()4.拋物線(xiàn)的標(biāo)準(zhǔn)方程中,\(p\)表示焦點(diǎn)到準(zhǔn)線(xiàn)的距離。()5.若\(f^\prime(x_0)=0\),則\(x_0\)一定是極值點(diǎn)。(）6.等比數(shù)列中,若\(q>1\),則數(shù)列單調(diào)遞增。（)7.橢圓的短軸長(zhǎng)等于\(2b\)(\(b\)為短半軸長(zhǎng))。()8.\((x^n)^\prime=nx^{n-1}\)對(duì)任意實(shí)數(shù)\(n\)成立。()9.數(shù)列\(zhòng)(\{a_n\}\)收斂,則其一定有界。（)10.函數(shù)\(f(x)=|x|\)在\(x=0\)處不可導(dǎo)。(）簡(jiǎn)答題(4題,每題5分)1.已知等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=3\),\(d=2\),求\(a_8\)和\(S_5\)。答案:\(a_8=3+7×2=17\)；\(S_5=5×3+\frac{5×4}{2}×2=35\)。2.求函數(shù)\(f(x)=x^2-4x+3\)的極值。答案:\(f^\prime(x)=2x-4\),令\(f^\prime(x)=0\)得\(x=2\),\(f(2)=-1\),故極小值為\(-1\),無(wú)極大值。3.寫(xiě)出雙曲線(xiàn)\(\frac{y^2}{9}-\frac{x^2}{16}=1\)的焦點(diǎn)坐標(biāo)、漸近線(xiàn)方程。答案:焦點(diǎn)\((0,\pm5)\),漸近線(xiàn)\(y=\pm\frac{3}{4}x\)。4.已知\(f(x)=e^x\cosx\),求\(f^\prime(x)\)。答案:\(f^\prime(x)=e^x\cosx-e^x\sinx=e^x(\cosx-\sinx)\)。討論題(4題,每題5分)1.舉例說(shuō)明等差數(shù)列與等比數(shù)列的區(qū)別。答案:等差數(shù)列差為常數(shù)(如\(1,3,5\),差\(2\));等比數(shù)列比為常數(shù)(如\(2,4,8\),比\(2\)),通項(xiàng)、和公式也不同。2.分析函數(shù)可導(dǎo)與連續(xù)的關(guān)系。答案:可導(dǎo)必連續(xù),連續(xù)不一定可導(dǎo)(如\(y=|x|\)在\(x=0\)連續(xù)不可導(dǎo)),可導(dǎo)是更強(qiáng)條件。3.說(shuō)明橢圓、雙曲線(xiàn)、拋物線(xiàn)的定義差異。答案:橢圓是到兩焦點(diǎn)距離和為定值;雙曲線(xiàn)是距離差絕對(duì)值為定值;拋物線(xiàn)是到焦點(diǎn)與準(zhǔn)線(xiàn)距離相等,定義決定曲線(xiàn)形狀差異。4.討論導(dǎo)數(shù)在求函數(shù)極值中的作用。答案:先求導(dǎo)找臨界點(diǎn),再判斷單調(diào)性或二階導(dǎo)符號(hào),確定極值,導(dǎo)數(shù)是工具,簡(jiǎn)化極值判斷過(guò)程。答案單項(xiàng)選擇題1.C2.D3.C4.A5.B6.A7.C8.B9.B