江蘇省蘇錫常鎮(zhèn)四市高三教學(xué)情況調(diào)研（一）數(shù)學(xué)試卷及答案

1、2014-2015學(xué)年度蘇錫常鎮(zhèn)四市高三教學(xué)情況調(diào)研(一) 數(shù)學(xué)試題 一、填空題：本大題共14小題，每小題5分，共計(jì)70分不需要寫出解答過(guò)程，請(qǐng)把答案直接填在答題卡相應(yīng)位置上1 已知集合ax |1 x 0，則ab 2 若復(fù)數(shù) (i為虛數(shù)單位)為純虛數(shù)，則實(shí)數(shù)m 3 雙曲線的離心率為 4 在一次滿分為160分的數(shù)學(xué)考試中，某班40名學(xué)生的考試成績(jī)分布如下：成績(jī)（分）80分以下80,100)100,120)120,140)140,160人數(shù)8812102在該班隨機(jī)抽取一名學(xué)生，則該生在這次考試中成績(jī)?cè)?20分以上的概率為 5 函數(shù) 的定義域?yàn)?6 如圖，四棱錐中，底面，底面是矩形，為棱上一點(diǎn)，則三

2、棱錐的體積為 7 右圖是一個(gè)算法流程圖，則輸出的的值為 8 已知等比數(shù)列的各項(xiàng)均為正數(shù)，若，則 9 若曲線與曲線在處的兩條切線互相垂直，則實(shí)數(shù)a的值為 10 設(shè)函數(shù)的最小正周期為，且滿足，則函數(shù)的單調(diào)增區(qū)間為 11 如圖，在平行四邊形abcd中，e為dc的中點(diǎn)， ae與bd交于點(diǎn)e，ab，ad=1，且，則 12 在平面直角坐標(biāo)系中，已知圓，點(diǎn)a是x軸上的一個(gè)動(dòng)點(diǎn)，ap，aq分別切圓c于p，q兩點(diǎn)，則線段pq的取值范圍是 13 已知直線y=kx+1與曲線f(x)= 恰有四個(gè)不同的交點(diǎn)，則實(shí)數(shù)k的取值范圍為 14 已知實(shí)數(shù)x，y滿足xy0，且x+y2，則的最小值為 二、解答題：本大題共6小題，共計(jì)

3、90分請(qǐng)?jiān)诖痤}卡指定區(qū)域內(nèi)作答，解答時(shí)應(yīng)寫出文字說(shuō)明、證明過(guò)程或演算步驟15. （本小題滿分14分）已知向量，（1） 若ab，求的值；（2） 若ab，求的值16. （本小題滿分14分）如圖，四邊形a a1 c1c為矩形，四邊形cc1b1 b為菱形，且平面cc1b1 ba a1 c1c，d，e分別是a1 b1和c1c的中點(diǎn) 求證：（1） bc1平面ab1c；（2） de平面ab1c17. （本小題滿分14分）如圖，有一段河流，河的一側(cè)是以o為圓心，半徑為米的扇形區(qū)域ocd，河的另一側(cè)是一段筆直的河岸l，岸邊有一煙囪ab（不計(jì)b離河岸的距離），且ob的連線恰好與河岸l垂直，設(shè)ob與圓弧的交點(diǎn)為e.

4、經(jīng)測(cè)量，扇形區(qū)域和河岸處于同一水平面，在點(diǎn)c和點(diǎn)e處測(cè)得煙囪ab的仰角分別為45，30和60（1） 求煙囪ab的高度；（2） 如果要在ce間修一條直路，求ce的長(zhǎng)18. （本小題滿分16分）在平面直角坐標(biāo)系中，已知橢圓c：，的離心率為，且經(jīng)過(guò)點(diǎn)，過(guò)橢圓的左頂點(diǎn)a作直線lx軸，點(diǎn)m為直線l上的動(dòng)點(diǎn)（點(diǎn)m與點(diǎn)a在不重合），點(diǎn)b為橢圓右頂點(diǎn)，直線bm交橢圓c于點(diǎn)p（1） 求橢圓c的方程；（2） 求證：apom；（3） 試問(wèn)是否為定值？若是定值，請(qǐng)求出該定值；若不是，請(qǐng)說(shuō)明理由19. （本小題滿分16分）已知函數(shù).（1）當(dāng)時(shí)，求函數(shù)的單調(diào)減區(qū)間；（2）若方程f(x)=m的恰好有一個(gè)正根和一個(gè)負(fù)根，求實(shí)

5、數(shù)m的最大值.20. （本小題滿分16分）已知數(shù)列的前n項(xiàng)和為，設(shè)數(shù)列滿足（1）若數(shù)列為等差數(shù)列，且，求數(shù)列的通項(xiàng)公式； （2）若，且數(shù)列的，都是以2為公比的等比數(shù)列，求滿足不等式 的所有正整數(shù)的集合9jwkffwvg#tym*jg&6a*cz7h$dq8kqqfhvzfedswsyxty#&qa9wkxfyeq!djs#xuyup2knxprwxma&ue9aqgn8xp$r#͑gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrw

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31、89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zv

32、kum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$v

33、stt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnugk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gx

34、gjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amy

35、wpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv3tngk8!z89amywpazadnu#kn&muwfa5u

36、xy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3

37、tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk

38、8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mzadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>

39、xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tng

40、k8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zv

41、kum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vst

42、t#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vst

43、t#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9>xrm6x4ngpp$vstt#&ksv*3tngk8!z89a

44、mywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>x

45、rm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnugk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9

46、cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ks

47、v*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqvue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&g

48、txrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ks

49、v*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ks

50、v*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpa

51、zadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4

52、ngpp$vstt#&ksv*3tngk8!z89amywpazadnugk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!

53、zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tn

54、gk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue

55、%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&

56、gtxrm6x4ngpp$vstt#&ksv*3adnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum>xrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#k