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2007普通高等學(xué)校招生全國統(tǒng)一考試(陜西)試卷類型B理科數(shù)學(xué) (必修+選修II)注意事項(xiàng):1本試卷分第一部分和第二部分,第一部分為選擇題,第二部分為非選擇題2考生領(lǐng)到試卷后,須按規(guī)定在試卷上填寫姓名,準(zhǔn)考證號,并在答題卡上填涂對應(yīng)的試卷類型信息點(diǎn)3所有答案必須在答題卡上指定區(qū)域內(nèi)作答,考試結(jié)束后,將本試卷和答題卡一并交回第一部分(共60分)一、選擇題:在每小題給出的四個(gè)選項(xiàng)中,只有一項(xiàng)是符合題目要求的(本大題共12小題,每小題5分,共60分)1在復(fù)平面內(nèi),復(fù)數(shù)對應(yīng)的點(diǎn)位于( )A第一象限 B第二象限C第三象限D(zhuǎn)第四象限2已知全集,集合,則集合等于( )ABCD3拋物線的準(zhǔn)線方程是( )ABCD4已知,則的值為( )ABCD5各項(xiàng)均為正數(shù)的等比數(shù)列 的前項(xiàng)和為為,若,則等于( )A80B30C26D166一個(gè)正三棱錐的四個(gè)頂點(diǎn)都在半徑為1的球面上,其中底面的三個(gè)頂點(diǎn)在該球的一個(gè)大圓上,則該正三棱錐的體積是( )ABCD7已知雙曲線(,),以的右焦點(diǎn)為圓心且與的漸近線相切的圓的半徑是( )ABCD8若函數(shù)的反函數(shù)為,則函數(shù)與的圖象可能是( )12121212121212129給出如下三個(gè)命題:四個(gè)非零實(shí)數(shù)依次成等比數(shù)列的充要條件是;設(shè),且,若,則;若,則是偶函數(shù)其中不正確命題的序號是( )ABCD10已知平面平面,直線,直線,點(diǎn),點(diǎn),記點(diǎn)之間的距離為,點(diǎn)到直線的距離為,直線和的距離為,則( )ABCD11是定義在上的非負(fù)可導(dǎo)函數(shù),且滿足對任意正數(shù),若,則必有( )ABCD12設(shè)集合,在上定義運(yùn)算為:,其中為被4除的余數(shù),則滿足關(guān)系式的的個(gè)數(shù)為( )A4B3C2D1第二部分(共90分)二、填空題:把答案填在答題卡相應(yīng)題號后的橫線上(本大題共4小題,每小題4分,共16分)13 14已知實(shí)數(shù)滿足條件則的最大值為15如圖,平面內(nèi)有三個(gè)向量,其中與的夾角為,與的夾角為,且,若,則的值為AOBC16安排3名支教教師去6所學(xué)校任教,每校至多2人,則不同的分配方案共有 種(用數(shù)字作答)三、解答題:解答應(yīng)寫出文字說明,證明過程或演算步驟(本大題共6小題,共74分)17(本小題滿分12分)設(shè)函數(shù),其中向量,且的圖象經(jīng)過點(diǎn)()求實(shí)數(shù)的值;()求函數(shù)的最小值及此時(shí)值的集合18(本小題滿分12分)某項(xiàng)選拔共有四輪考核,每輪設(shè)有一問題,能正確回答問題者進(jìn)入下一輪考核,否則即被淘汰已知某選手能正確回答第一、二、三、四輪的問題的概率分別為且各輪問題能否正確回答互不影響()求該選手被淘汰的概率;()該選手在選擇中回答問題的個(gè)數(shù)記為,求隨機(jī)變量的分布列與數(shù)學(xué)期望(注:本小題結(jié)果可用分?jǐn)?shù)表示)19(本小題滿分12分)如圖,在底面為直角梯形的四棱錐中,平面()求證:平面;()求二面角的大小20(本小題滿分12分)設(shè)函數(shù),其中為實(shí)數(shù)(I)若的定義域?yàn)?,求的取值范圍;(II)當(dāng)?shù)亩x域?yàn)闀r(shí),求的單調(diào)減區(qū)間21(本小題滿分14分)已知橢圓的離心率為,短軸一個(gè)端點(diǎn)到右焦點(diǎn)的距離為()求橢圓的方程;()設(shè)直線與橢圓交于兩點(diǎn),坐標(biāo)原點(diǎn)到直線的距離為,求面積的最大值22(本小題滿分12分)已知各項(xiàng)全不為零的數(shù)列的前項(xiàng)和為,且,其中(I)求數(shù)列的通項(xiàng)公式;(II)對任意給定的正整數(shù),數(shù)列滿足(),求2007年普通高等學(xué)校招生全國統(tǒng)一考試(陜西卷)數(shù) 學(xué)(理工農(nóng)醫(yī)類)參考答案一、選擇題:在每小題給出的四個(gè)選項(xiàng)中,只有一項(xiàng)是符合題目要求的(本大題共12小題,每小題5分,共60分)123456789101112二、填空題:把答案填在答題卡相應(yīng)題號后的橫線上(本大題共4小題,每小題4分,共16分)13141516三、解答題:解答應(yīng)寫出文字說明,證明過程或演算步驟(本大題共6小題,共74分)17(本小題滿分12分)解:(),由已知,得()由()得,當(dāng)時(shí),的最小值為,由,得值的集合為18(本小題滿分12分)解法一:()記“該選手能正確回答第輪的問題”的事件為,則,該選手被淘汰的概率()的可能值為,的分布列為123解法二:()記“該選手能正確回答第輪的問題”的事件為,則,該選手被淘汰的概率()同解法一19(本小題滿分12分)解法一:()平面,平面又,即又平面()過作,垂足為,連接平面,是在平面上的射影,由三垂線定理知,AEDPCBF為二面角的平面角又,又,由得在中,二面角的大小為解法二:()如圖,建立坐標(biāo)系,則,AEDPCByzx,又,平面()設(shè)平面的法向量為,則,又,解得平面的法向量取為,二面角的大小為20(本小題滿分12分)解:()的定義域?yàn)?,恒成立,即?dāng)時(shí)的定義域?yàn)椋ǎ?,令,得由,得或,又,時(shí),由得;當(dāng)時(shí),;當(dāng)時(shí),由得,即當(dāng)時(shí),的單調(diào)減區(qū)間為;當(dāng)時(shí),的單調(diào)減區(qū)間為21(本小題滿分14分)解:()設(shè)橢圓的半焦距為,依題意,所求橢圓方程為()設(shè),(1)當(dāng)軸時(shí),(2)當(dāng)與軸不垂直時(shí),設(shè)直線的方程為由已知,得把代入橢圓方程,整理得,當(dāng)且僅當(dāng),即時(shí)等號成立當(dāng)時(shí),綜上所述當(dāng)最大時(shí),面積取最大值22(本小題滿分12分)解:()當(dāng),由及,得當(dāng)時(shí),由,得因?yàn)?,所以從而,故()因?yàn)椋运怨示磉x擇題答案:123456789101112內(nèi)部資料僅供參考9JWKffwvG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ!djs#XuyUP2kNXpRWXmA&UE9aQGn8xp$R#͑GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmUE9aQGn8xp$R#͑GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z8vG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ!djs#XuyUP2kNXpRWXmA&UE9aQGn8xp$R#͑GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxG89AmUE9aQGn8xp$R#͑GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z8vG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ!djs#XuyUP2kNXpRWXmA&UE9aQGn8xp$R#͑GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmUE9aQGn8xp$R#͑GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWw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