高考复习5 高考3年联考数学精品题库 16页

第七章不等式第一节简单不等式及其解法一、选择题1.（2009安徽卷理）下列选项中，p是q的必要不充分条件的是A.p:＞b+d,q:＞b且c＞dB.p:a＞1,b>1q:的图像不过第二象限C.p:x=1,q:D.p:a＞1,q:在上为增函数答案A解析由＞b且c＞d＞b+d，而由＞b+d＞b且c＞d，可举反例。选A。2.（2009安徽卷文）“”是“且”的A.必要不充分条件B.充分不必要条件C.充分必要条件D.既不充分也不必要条件答案A解析易得时必有.若时，则可能有，选A。3.（2009四川卷文）已知，，，为实数，且＞.则“＞”是“－＞－”的A.充分而不必要条件B.必要而不充分条件C.充要条件D.既不充分也不必要条件答案B解析显然，充分性不成立.又，若－＞－和＞都成立，则同向不等式相加得＞即由“－＞－”“＞”4.（2009天津卷理）,若关于x的不等式＞的解集中的整数恰有3个，则A.B.C.D.答案C5.（2009四川卷理）已知为实数，且。则“”是“”的A.充分而不必要条件B.必要而不充分条件C．充要条件D.既不充分也不必要条件【考点定位】本小题考查不等式的性质、简单逻辑，基础题。（同文7）答案B解析推不出；但，故选择B。解析2：令，则；由可得，因为，则，所以。故“”是“”的必要而不充分条件。\n6.（2009重庆卷理）不等式对任意实数恒成立，则实数的取值范围为（）A．B．C．D．答案A解析因为对任意x恒成立，所以二、填空题7.（2009年上海卷理）若行列式中，元素4的代数余子式大于0，则x满足的条件是________________________.答案解析依题意，得：(-1)2×(9x-24)＞0，解得：三、解答题8.（2009江苏卷）(本小题满分16分)按照某学者的理论，假设一个人生产某产品单件成本为元，如果他卖出该产品的单价为元，则他的满意度为；如果他买进该产品的单价为元，则他的满意度为.如果一个人对两种交易(卖出或买进)的满意度分别为和，则他对这两种交易的综合满意度为.现假设甲生产A、B两种产品的单件成本分别为12元和5元，乙生产A、B两种产品的单件成本分别为3元和20元，设产品A、B的单价分别为元和元，甲买进A与卖出B的综合满意度为，乙卖出A与买进B的综合满意度为(1)求和关于、的表达式；当时，求证：=；(2)设，当、分别为多少时，甲、乙两人的综合满意度均最大？最大的综合满意度为多少？\n(3)记(2)中最大的综合满意度为，试问能否适当选取、的值，使得和同时成立，但等号不同时成立？试说明理由。解析本小题主要考查函数的概念、基本不等式等基础知识，考查数学建模能力、抽象概括能力以及数学阅读能力。满分16分。(1)当时，,,=（2）当时，由，故当即时，甲乙两人同时取到最大的综合满意度为。（3）（方法一）由（2）知：=由得：，令则，即：。同理，由得：\n另一方面，当且仅当，即=时，取等号。所以不能否适当选取、的值，使得和同时成立，但等号不同时成立。第一部分五年高考荟萃2009年高考题2005--2008年高考题一、选择题1.（2008天津）已知函数，则不等式的解集是(　　)A.　B.　　C.　　D.答案A2.（2008江西）若，则下列代数式中值最大的是（　　）A．　B．　C．　D．答案A3.（2008浙江）已知，b都是实数，那么“”是“>b”的（）A．充分而不必要条件B.必要而不充分条件C．充分必要条件D.既不充分也不必要条件答案D4.（2008海南）已知，则使得都成立的取值范围是（）A.（0，）B.（0，）\nC.（0，）D.（0，）答案B5、（2008山东）不等式的解集是（）A．B．C．D．解析本小题主要考查分式不等式的解法。易知排除B;由符合可排除C;由排除A,故选D。也可用分式不等式的解法,将2移到左边直接求解。答案D6、（2007广东）设，若，则下列不等式中正确的是（）A、B、C、D、解析利用赋值法：令排除A,B,C,选D答案D7、（2007湖南）．不等式的解集是（）A．B．C．D．答案D8．（2007福建）已知集合A＝，B＝，且，则实数的取值范围是（）A．B．a<1C．D．a>2答案C9．(2007安徽)若对任意R,不等式≥ax恒成立，则实数a的取值范围是（）(A)a＜-1(B)≤1(C)＜1D.a≥1答案B10．(2007浙江)“x＞1”是“x2＞x”的（）(A)充分而不必要条件(B)必要而不充分条件(C)充分必要条件　　(D)既不充分也不必要条件答案A11．（2007湖南）1．不等式的解集是（）A．B．C．D．答案D\n12．（2007广东）．已知集合M={x|1+x>0}，N={x|>0}，则M∩N=（）A．{x|-1≤x＜1B．{x|x>1}C．{x|-1＜x＜1}D．{x|x≥-1}答案C13．（2006安徽）不等式的解集是（）A．B．C．D．答案D解：由得：，即，故选D14．（2006山东）设f(x)=则不等式f(x)>2的解集为(A)（1，2）（3，+∞）(B)（，+∞）(C)（1，2）（，+∞）(D)（1，2）答案C15、（2006江西）若a>0，b>0，则不等式－b<D.x<或x>答案D解析故选D16．(2006上海)如果，那么，下列不等式中正确的是（）A.B.C.D.答案A解析如果，那么，∴，选A.答案A17．（2006上海春）若，则下列不等式成立的是()A..B..C..D..答案C解析应用间接排除法．取a=1,b=0，排除A.取a=0,b=-1，排除B;取c=0，排除D．故应该选C．显然，对不等式a>b的两边同时乘以，立得成立\n18．（2006年陕西）已知不等式对任意正实数恒成立，则正实数的最小值为（）（Ａ）8　　　　（Ｂ）6　　　　C.4　　　　D.2答案D19．（2005福建）不等式的解集是（）A．B．C．D．答案A20.（2005辽宁）在R上定义运算若不等式对任意实数成立，则（）A．B．C．D．答案C21.（2005山东），下列不等式一定成立的是（）A.B.C.D.答案A二、填空题22、（2008上海）不等式的解集是　　　　　．答案（0，2）23.（2008山东）若不等式｜3x-b｜＜4的解集中的整数有且仅有1，2，3，则b的取值范围.答案（5，7）.24.（2008江西）不等式的解集为．答案25．（2007北京）已知集合，．若，则实数的取值范围是（2，3）．\n26．（2006江苏）不等式的解集为　　【思路点拨】本题考查对数函数单调性和不等式的解法答案解析，0〈，.解得27.（2006浙江）不等式的解集是　　　　　　　　。.答案x<－1或x>2解析Û（x＋1）（x－2）>0Ûx<－1或x>2.28.（2006上海）不等式的解集是.答案．解析应用结论：．不等式等价于(1-2x)(x+1)>0，也就是，所以，从而应填．三、解答题29.（2007北京）记关于的不等式的解集为，不等式的解集为．（I）若，求；（II）若，求正数的取值范围．解：（I）由，得．（II）．由，得，又，所以，即的取值范围是．30．（2007湖北）已知m，n为正整数.（Ⅰ）用数学归纳法证明：当x>-1时，(1+x)m≥1+mx；\n（Ⅱ）对于n≥6，已知，求证，m=1,1,2…，n；（Ⅲ）求出满足等式3n+4m+…+(n+2)m=(n+3)n的所有正整数n.解：（Ⅰ）证：当x=0或m=1时，原不等式中等号显然成立，下用数学归纳法证明：当x>-1，且x≠0时，m≥2,(1+x)m>1+mx.(i)当m=2时，左边＝1+2x+x2,右边＝1+2x，因为x≠0,所以x2>0，即左边>右边，不等式①成立；（ii）假设当m=k(k≥2)时，不等式①成立，即（1+x）k>1+kx,则当m=k+1时，因为x>-1,所以1+x>0.又因为x≠0,k≥2,所以kx2>0.于是在不等式（1+x）k>1+kx两边同乘以1+x得（1+x）k·(1+x)>(1+kx)(1+x)=1+(k+1)x+kx2>1+(k+1)x,所以（1+x）k+1>1+(k+1)x,即当m＝k+1时，不等式①也成立.综上所述，所证不等式成立.(Ⅱ)证：当而由（Ⅰ），（Ⅲ）解：假设存在正整数成立，即有（）+＝1.　　②又由（Ⅱ）可得（）++与②式矛盾，故当n≥6时，不存在满足该等式的正整数n.故只需要讨论n=1,2,3,4,5的情形；当n=1时，3≠4，等式不成立；当n=2时，32+42＝52，等式成立；当n=3时，33+43+53＝63，等式成立；当n=4时，34+44+54+64为偶数，而74为奇数，故34+44+54+64≠74,等式不成立；当n=5时，同n=4的情形可分析出，等式不成立.综上，所求的n只有n=2,3.第二部分三年联考题汇编2009年联考题\n一、选择题1、（山东省乐陵一中2009届高三考前练习）已知为非零实数，且，则下列命题成立的是（）A.B.C.D.答案C2.若，则(安徽省示范高中皖北协作区2009届高三第一次联考试题)下列不等式中正确的是（）ABCD答案D3．（福建省福州市普通高中09年高三质量检查）已知，则不等式的解集是（）A．（—2，0）B．C．D．答案C4．（安徽省合肥市2009届高三上学期第一次教学质量检测）不等式的解集为A．B．C．D．答案C5.(北京市朝阳区2009年4月高三一模理)蔬菜价格随着季节的变化而有所变化.根据对农贸市场蔬菜价格的调查得知，购买2千克甲种蔬菜与1千克乙种蔬菜所需费用之和大于8元，而购买4千克甲种蔬菜与5千克乙种蔬菜所需费用之和小于22元.设购买2千克甲种蔬菜所需费用为元，购买3千克乙种蔬菜所需费用为元，则（）A．B．C．D．大小不确定答案A6．(北京市西城区2009年4月高三一模抽样测试理)设R，且，，则()\nA.B.C.D.答案D7.(北京市丰台区2009年3月高三统一检测理)已知，都是定义在上的函数，且满足以下条件：①=·（）；②；③。若，则使成立的x的取值范围是A.（，）∪（，+∞）B.（，）C.（－∞，）∪（，+∞）D.（，+∞）答案B8、（2009福州三中理）已知互不相等的正数a、b、c满足，则下列不等在中可能成立的是（）A．a>b>cB．b>a>cC．b>c>aD．c>a>b答案B9、（2009龙岩一中理）若不等式的解集为非空集合，则实数的取值范围是（）A．B．C．D．答案C10、（2009龙岩一中文）已知a,b∈R，且a>b，则下列不等式中恒成立的是（）A．a2>b2B．()a<()bC．lg(a－b)>0D．>1答案B11、（2009泉州市）答案D12、（2009广州一模）已知p：关于x的不等式x2+2ax－a>0的解集是R，q：－1ac是b>c的A.充分不必要条件B.必要不充分条件C.充要条件D.即不充分也不必要条件答案D4、(2008江苏省启东中学高三综合测试四)不等式≥1的解集为()A．B．C．D．答案C5、(2008江西省五校2008届高三开学联考)设,则对任意正整数,都成立的是A．B．C．D．答案C.故应选C\n6、(陕西长安二中2008届高三第一学期第二次月考)设，那么()A.B.C。D.答案C7、(四川省乐山市2008届第一次调研考试)已知满足，则下列选项中不一定能成立的是（　　）　A．；　　　　B.；　　　C.；　　　　　D.；答案C8、(四川省乐山市2008届第一次调研考试)不等式的解集为（　　）　A.；　　　B.；　　　　C.；　　　　　D.答案D9、(北京市十一学校2008届高三数学练习题)已知函数为上的连续函数且存在反函数，若函数满足下表：231235那么，不等式的解集是（）A.B.C.D.答案A10、(甘肃省河西五市2008年高三第一次联考)已知则不等式的解集为（）ABCD答案D\n11、(贵州省贵阳六中、遵义四中2008年高三联考)如果a>b，给出下列不等式：（1）<(2)a3>b3(3)a2+1>b2+1(4)2>2其中成立的是（）A.(2)(3)B.(1)(3)C.(3)(4)D.(2)(4)答案D12、(贵州省贵阳六中、遵义四中2008年高三联考)在R上定义运算若不等式对任意实数成立，则（）A．B．C．D．答案C13、(黑龙江省哈尔滨三中2008年高三上期末)不等式的解集为（）A．B．C．D．答案A内部资料仅供参考9JWKffwvG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z8vG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^G89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z8vG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRWXmA&UE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmUE9aQ@Gn8xp$R#͑Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$U*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$U*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz84!z89Amv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$U*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$U*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5ux^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu##KN&MuWFA5uxY7JnD6YWRrWwc^vR9CpbK!zn%Mz849Gx^Gjqv^$UE9wEwZ#Qc@UE%&qYp@Eh5pDx2zVkum&gTXRm6X4NG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