巴市一中高三上學期期中考試數(shù)學（理）試題

學必求其心得，業(yè)必貴于專精學必求其心得，業(yè)必貴于專精學必求其心得，業(yè)必貴于專精說明:1.本試卷分第I卷和第II卷兩部分，共150分.2。將第I卷選擇題答案代號用2B鉛筆填在答題卡上。第I卷（選擇題共60分）一、選擇題（5分×12=60分）在每小題給出的四個選項只有一項正確1.函數(shù)SKIPIF1<0的零點所在區(qū)間為（）SKIPIF1<0B。SKIPIF1〈0C.SKIPIF1〈0D.SKIPIF1<02。在等比數(shù)列SKIPIF1〈0中,SKIPIF1〈0，則SKIPIF1<0=（)A.SKIPIF1〈0B.SKIPIF1<0C。SKIPIF1〈0D。SKIPIF1〈03.已知SKIPIF1〈0，SKIPIF1〈0,則SKIPIF1<0的值為（)A.SKIPIF1<0B.SKIPIF1<0C。SKIPIF1〈0D.SKIPIF1<04.已知實數(shù)SKIPIF1<0滿足SKIPIF1〈0,且SKIPIF1<0，則下列選項中不恒成立的是（）A。SKIPIF1<0B.SKIPIF1〈0C.SKIPIF1<0D。SKIPIF1〈05。點SKIPIF1<0位于第（)象限A。一B。二C。三D。四6。定義SKIPIF1〈0，已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0,則SKIPIF1〈0（）A。SKIPIF1<0B.SKIPIF1〈0C。SKIPIF1<0D.不能確定7.已知SKIPIF1<0，則SKIPIF1〈0的最小值是（)A.2B.SKIPIF1〈0C.4D.SKIPIF1〈08。設SKIPIF1<0,若SKIPIF1〈0，則SKIPIF1〈0（）A。SKIPIF1<0B。SKIPIF1〈0C。SKIPIF1<0D。SKIPIF1〈09.已知遞減的等差數(shù)列SKIPIF1<0滿足SKIPIF1<0，則數(shù)列SKIPIF1〈0的前SKIPIF1〈0項和SKIPIF1<0取最大值時,SKIPIF1<0=（）A.3B。4C。4或5D。10。已知SKIPIF1<0與SKIPIF1<0的夾角為SKIPIF1〈0，SKIPIF1〈0，則SKIPIF1<0與SKIPIF1〈0的夾角為（）A。SKIPIF1<0B。SKIPIF1〈0C。SKIPIF1〈0D.SKIPIF1<011.已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的導函數(shù)，函數(shù)SKIPIF1〈0的圖像如圖所示，且SKIPIF1〈0，則不等式SKIPIF1〈0的解集為（)A.SKIPIF1〈0B.SKIPIF1<0C.SKIPIF1<0D。SKIPIF1〈012。已知定義在R上的函數(shù)SKIPIF1〈0既是奇函數(shù)，又是周期為3的周期函數(shù)，當SKIPIF1<0時,SKIPIF1〈0，則函數(shù)SKIPIF1〈0在區(qū)間SKIPIF1〈0上的零點個數(shù)是(）A.3B。5C。7D。第II卷(非選擇題共90分）二、填空題（5分×4=20分）將最后結(jié)果直接填在橫線上.13。SKIPIF1〈014。若實數(shù)SKIPIF1〈0滿足SKIPIF1<0，則SKIPIF1<0的最小值是15。在數(shù)列SKIPIF1<0中，已知SKIPIF1〈0，則SKIPIF1<016.關于函數(shù)SKIPIF1<0,有下列命題:①其圖象關于SKIPIF1〈0軸對稱；②當SKIPIF1〈0時，SKIPIF1<0是增函數(shù)；當SKIPIF1<0時，SKIPIF1〈0是減函數(shù)；③SKIPIF1<0的最小值是SKIPIF1〈0；④SKIPIF1〈0在區(qū)間SKIPIF1〈0上是增函數(shù)；⑤SKIPIF1〈0無最大值,也無最小值．其中所有正確結(jié)論的序號是．三、解答題（10分+12分+12分+12分+12分+12分=70分）17。我市用2160萬元購得一塊空地,計劃在該塊地上建造一棟至少10層、每層2000平方米的樓房，經(jīng)計算，如果將樓房建為SKIPIF1<0層，則每平方米的平均建筑費用為SKIPIF1<0（單位：元)，為了使樓房每平方米的平均綜合費用最少,該樓房應建為多少層？SKIPIF1<018。已知函數(shù)SKIPIF1〈0(1）求函數(shù)SKIPIF1〈0的最小正周期及單調(diào)增區(qū)間；（2）如果SKIPIF1<0，且SKIPIF1〈0,求SKIPIF1<0的值.

DCBA19.如圖,在△ABC中，已知SKIPIF1〈0,D為BC邊上一點：DCBA（1)若AD=2,SKIPIF1<0,求DC的長；（2)若AB=AD，試求△ADC的周長的最大值.20。已知數(shù)列SKIPIF1<0的前SKIPIF1<0項和為SKIPIF1〈0，且SKIPIF1<0（1)求SKIPIF1<0的通項公式；（2）數(shù)列SKIPIF1<0滿足SKIPIF1<0，求數(shù)列SKIPIF1<0前SKIPIF1〈0項和SKIPIF1〈0;（3）若SKIPIF1<0對一切正整數(shù)SKIPIF1<0恒成立，求實數(shù)SKIPIF1〈0的取值范圍。21.我校數(shù)學興趣小組在某次活動中研究了函數(shù)SKIPIF1<0上的點SKIPIF1<0與原點O的連線所在的直線的斜率SKIPIF1<0的值的變化規(guī)律.記直線OP的斜率SKIPIF1<0。（1)同學甲發(fā)現(xiàn)：點P從左向右運動時，SKIPIF1<0不斷增大。試問：他的判斷是否正確？若正確，請說明理由；若不正確,請給出你的正確判斷.（2）同學乙發(fā)現(xiàn)：總存在正實數(shù)SKIPIF1<0，使SKIPIF1〈0。試問：他的判斷是否正確?若正確，請求出實數(shù)SKIPIF1〈0的取值范圍，若不正確,請給出你的正確判斷.（提示：SKIPIF1<0）（3）同學丙發(fā)現(xiàn)：當SKIPIF1〈0時，函數(shù)SKIPIF1<0的圖象總在函數(shù)SKIPIF1<0的圖象的下方。試問：他的判斷是否正確?若正確，請說明理由;若不正確，請