四川遂宁市高中2015届高三英语下学期第二次诊断性考试试题

某某某某市高中2015届高三下学期第二次诊断性考历史试题文科综合共300分，包括思想政治、历史、地理三部分，考试时间共150分钟。

历史试卷分为第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。

满分100分。

注意事项：1．答题前，考生务必将自己的某某、班级、考号用0.5毫米的黑色墨水签字笔填写在答题卡上。

并检查条形码粘贴是否正确。

2．选择题使用2B铅笔填涂在答题卡对应题目标号的位置上，非选择题用0.5毫米黑色墨水签字笔书写在答题卡对应框内，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

3．考试结束后，将答题卡收回。

第Ⅰ卷（选择题，共48分）一、选择题（本题共12小题，每小题只有一个答案符合要求，每小题4分，共48分）1．美国学者卡拉贝尔在《被选中的》一书中追溯了美国精英大学百年来招生录取政策的变迁。

他写道：“（这些）招生方法，在今天看来，体现着典型的美国精神：机会平等（不因出身、财富等不同而被歧视）、贤能主义（meritocracy,众人皆因自身的才能和成就而获得地位和声望，实现向上的社会流动）。

”从中国人的视角来看，这种“美国精神”最接近先秦的A．墨家B．道家C．儒家D．法家2. 中国是纸币的故乡，产生于北宋时期（1023年）的交子是世界上最早的纸币，比欧洲早600多年。

然而，当1840年英国的坚船利炮轰开中国国门的时候，英格兰银行的纸币已经通行于世界，而中国却仍然用某某和铜钱作为货币。

造成这种现象的原因是什么？①政府曾滥发无信用纸币，造成纸币信用崩溃②海外贸易繁盛，某某相较纸币更具流通优势③海外贸易长期顺差，某某大量流入，原料易得④商品经济发展，资本主义萌芽出现A．①②B．②④C．①③D．③④3. 甲、乙、丙、丁四位同学打算各写一篇中国古代经济史方面的小论文，他们采用了不同的研究内容、过程。

其中，步骤最合理、论证最严谨的是甲 B．乙 C．丙 D．丁4．关于三元里抗英歼敌数目，在中方文献中有“十余人”，“百余人”，“二百余人”，“七百四十八人”等诸多说法，其中以“二百余人”一说最为流行。

2015年四川省遂宁市高考数学二诊试卷（文科）一、选择题（每小题5分，共50分）1．（5分）（2015•遂宁模拟）已知集合A=[﹣1，1]，B={x|（x+3）（2x﹣1）≤0}，则A∩B=（）A．[﹣3，] B．[﹣1，] C．[﹣1，）D．（﹣3，）【考点】：交集及其运算．【专题】：集合．【分析】：求出B中不等式的解集确定出B，找出A与B的交集即可．【解析】：解：由B中不等式解得：﹣3≤x≤，即B=[﹣3，]，∵A=[﹣1，1]，∴A∩B=[﹣1，]，故选：B．【点评】：此题考查了交集及其运算，熟练掌握交集的定义是解本题的关键．2．（5分）（2015•遂宁模拟）在某校的一次英语听力测试中用以下茎叶图记录了甲、乙两组各5名学生的听力成绩（单位：分）已知甲组数据的众数为15，乙组数据的中位数为17，则x、y 的值分别为（）A．2，5 B．5，5 C．5，7 D．8，7【考点】：茎叶图．【专题】：概率与统计．【分析】：根据茎叶图与题意，求出x、y的值，即可．【解析】：解：根据茎叶图知，甲组数据是9，15，10+x，21，27；∵它的众数为l5，∴x=5；同理，根据茎叶图知乙组数据是9，13，10+y，18，27，∵它的中位数为17，∴y=7．故x、y的值分别为：5，7．【点评】：本题考查茎叶图的应用问题，解题时利用茎叶图提供的数据，求出x、y的值，即可解答问题，是基础题．3．（5分）（2015•遂宁模拟）已知复数z满足：zi=2+i（i是虚数单位），则z的虚部为（）A．2i B．﹣2i C． 2 D．﹣2【考点】：复数代数形式的乘除运算．【专题】：数系的扩充和复数．【分析】：把已知的等式变形，然后利用复数代数形式的乘除运算化简得答案．【解析】：解：由zi=2+i，得，∴z的虚部是﹣2．故选：D．【点评】：本题考查了复数代数形式的乘除运算，考查了复数的基本概念，是基础题．4．（5分）（2015•遂宁模拟）为了得到函数y=sin3x的图象，可以将函数y=sin3x+cos3x的图象（）A．向右平移个单位长B．向右平移个单位长C．向左平移个单位长D．向左平移个单位长【考点】：函数y=Asin（ωx+φ）的图象变换；两角和与差的正弦函数．【专题】：三角函数的图像与性质．【分析】：利用两角和与差的三角函数化简已知函数为一个角的一个三角函数的形式，然后利用平移原则判断选项即可．【解析】：解：函数y=sin3x+cos3x=sin（3x+），故只需将函数y=sin（3x+）的图象向右平移个单位，得到y=sin[3（x﹣）+]=sin3x的图象．故选：A．【点评】：本题考查两角和与差的三角函数以及三角函数的平移变换的应用，基本知识的考查．5．（5分）（2015•遂宁模拟）设a、b是实数，则“a＞b＞0”是“a2＞b2”的（）A．充分必要条件B．必要而不充分条件C．充分而不必要条件D．既不充分也不必要条件【考点】：必要条件、充分条件与充要条件的判断．【专题】：简易逻辑．【分析】：根据充分条件和必要条件的定义进行判断即可．【解析】：解：若a＞b＞0，则a2＞b2成立，若a=﹣2，b=1，满足a2＞b2，但a＞b＞0不成立，故“a＞b＞0”是“a2＞b2”的充分不必要条件，故选：C【点评】：本题主要考查充分条件和必要条件的判断，根据不等式的关系是解决本题的关键．6．（5分）（2015•遂宁模拟）已知向量，若，则实数λ=（）A． 1 B．﹣1 C． 2 D．﹣2【考点】：平面向量数量积的坐标表示、模、夹角．【专题】：平面向量及应用．【分析】：由于，可得．于是=0，解得λ即可．【解析】：解：∵，∴．∴=λ（λ+2）+1=0，解得λ=﹣1．故选：B．【点评】：本题考查了向量的平行四边形法则、向量垂直与数量积的关系，属于基础题．7．（5分）（2015•遂宁模拟）在区间[﹣2，3]上随机选取一个数M，不变执行如图所示的程序框图，且输入x的值为1，然后输出n的值为N，则M≤N﹣2的概率为（）A．B．C．D．【考点】：几何概型；程序框图．【专题】：计算题；概率与统计；算法和程序框图．【分析】：计算循环中不等式的值，当不等式的值大于0时，不满足判断框的条件，退出循环，输出结果N，再以长度为测度求概率即可．【解析】：解：循环前输入的x的值为1，第1次循环，x2﹣4x+3=0≤0，满足判断框条件，x=2，n=1，x2﹣4x+3=﹣1≤0，满足判断框条件，x=3，n=2，x2﹣4x+3=0≤0满足判断框条件，x=4，n=3，x2﹣4x+3=3＞0，不满足判断框条件，输出n：N=3．在区间[﹣2，3]上随机选取一个数M，长度为5，M≤1，长度为3，所以所求概率为，故选：C【点评】：本题考查循环结构的应用，注意循环的结果的计算，考查计算能力，考查概率的计算，确定N的值是关键．8．（5分）（2015•遂宁模拟）如图所示是一个几何体的三视图，则该几何体的表面积为（）A．4+2B．2+C．2+2D．4+【考点】：由三视图求面积、体积．【专题】：空间位置关系与距离．【分析】：由已知的三视图可得：该几何体是一个以俯视图为底面的三棱锥，画出几何体的直观图，求出各个面的面积，可得答案．【解析】：解：由已知的三视图可得：该几何体是一个以俯视图为底面的三棱锥，该几何体的直观图如下图所示：由三视图可得：CD=AD=1，SD=BD=2，SD⊥底面ABC，故S△ABC=S△ASC=2，由勾股定理可得：SA=SC=AB=AC=，SB=2，故△SAB和△SBC均是以2为底，以为高的等腰三角形，故S△SAB=S△SBC=，故该几何体的表面积为4+2，故选：A【点评】：本题考查的知识点是由三视图求体积和表面积，解决本题的关键是得到该几何体的形状．9．（5分）（2015•遂宁模拟）过抛物线y2=2px的焦点F作直线交抛物线于M，N两点，弦MN 的垂直平分线交x轴于点H，若|MN|=40，则|HF|=（）A．14 B．16 C．18 D．20【考点】：抛物线的简单性质．【专题】：计算题；圆锥曲线的定义、性质与方程．【分析】：先求MN的垂直平分线，求出MN的垂直平分线交x轴于H的坐标，进而求得|HF|=|MN|，即可得出结论．【解析】：解：设M（x1，y1），N（x2，y2），弦MN的中点为M′（x0，y0），则∴MN的垂直平分线为y﹣y0=﹣（x﹣x0）令y=0，则x H=x0+p∴|HF|=x0+∵|MN|=x1+x2+p=2x0+p∴|HF|=|MN|=20，故选：D．【点评】：本题以抛物线方程为载体，考查抛物线的性质，考查学生的计算能力，比较基础．10．（5分）（2015•遂宁模拟）函数f（x）的定义域为D，若函数f（x）满足：（1）f（x）在D上为单调函数；（2）存在区间[a，b]⊆D，使得f（x）在[a，b]上的值域为[，]，则称函数f（x）为“取半函数”．若f（x）=log c（c x+t）（c＞0，且c≠1）为“取半函数”，则t的取值范围是（）A．（﹣，）B．（0，）C．（0，）D．（，1）【考点】：对数函数的图像与性质．【专题】：函数的性质及应用．【分析】：根据复合函数的单调性，先判断函数f（x）的单调性，然后根据条件建立方程组，转化为一元二次方程根的存在问题即可得到结论．【解析】：解：若c＞1，则函数y=c x+t为增函数，y=log c x，为增函数，∴函数f（x）=log c（c x+t）为增函数，若0＜c＜1，则函数y=c x+t为减函数，y=log c x，为减函数，∴函数f（x）=log c（c x+t）为增函数，综上：函数f（x）=log c（c x+t）为增函数，若函数f（x）=log c（c x+t）（c＞0，c≠1）是函数f（x）为“取半函数”．，所以a，b是方程log c（c x+t）=，两个不等实根，即a，b是方程c x+t=c两个不等实根，化简得出：c x+t=0，可以转化为：m2﹣m+t=0有2个不等正数根．所以求解得出：0故选：B．【点评】：本题主要考查与指数函数和对数函数有关的信息题，判断函数的单调性是解决本题的关键，综合性较强，有一定的难度．二、填空题：（本大题共5小题，每小题5分，共25分，将答案填答题卷指定横线上）11．（5分）（2015•遂宁模拟）圆心在原点且与直线y=2﹣x相切的圆的方程为x2+y2=2．【考点】：圆的切线方程．【专题】：计算题；直线与圆．【分析】：可求圆的圆心到直线的距离，就是半径，写出圆的方程．【解析】：解：圆心到直线的距离：r==，所求圆的方程为x2+y2=2．故答案为：x2+y2=2．【点评】：本题考查圆的标准方程，直线与圆的位置关系，是基础题．12．（5分）（2015•遂宁模拟）已知偶函数f（x）在[0，+∞）单调递减，且f（﹣2）=0，若f （x﹣2）＞0，则x的取值范围是（0，4）．【考点】：奇偶性与单调性的综合．【专题】：函数的性质及应用．【分析】：根据函数奇偶性和单调性之间的关系将不等式等价转化为f（|x﹣2|）＞f（2），即可得到结论．【解析】：解：∵偶函数f（x）在[0，+∞）单调递减，f（﹣2）=0，∴f（﹣2）=f（2）=0，∴不等式f（x﹣，2）＞0等价为f（x﹣2）＞f（2），即f（|x﹣2|）＞f（2），∴|x﹣2|＜2，解得0＜x＜4，故答案为：（0，4）【点评】：本题主要考查函数奇偶性和单调性之间的关系的应用，将不等式等价转化为f（|x ﹣2|）＞f（2）是解决本题的关键．13．（5分）（2015•遂宁模拟）已知双曲线=1（a＞0，b＞0）的离心率为2，焦点到渐近线的距离为，则此双曲线的焦距等于4．【考点】：双曲线的简单性质．【专题】：计算题；圆锥曲线的定义、性质与方程．【分析】：运用离心率公式和渐近线方程，结合点到直线的距离公式可得b，再由a，b，c的关系即可得到c，进而得到焦距．【解析】：解：双曲线=1（a＞0，b＞0）的离心率为2，则e==2，即c=2a，设焦点为（c，0），渐近线方程为y=x，则d===b=，又b2=c2﹣a2=3，解得a=1，c=2．则有焦距为4．故答案为：4．【点评】：本题考查双曲线的方程和性质，主要考查离心率和渐近线方程的运用，属于基础题．14．（5分）（2015•遂宁模拟）如图，为测量坡高MN，选择A和另一个山坡的坡顶C为测量观测点．从A点测得M点的仰角∠MAN=60°，C点的仰角∠CAB=45°以及∠MAC=75°；从C 点测得∠MCA=60°．已知坡高BC=50米，则坡高MN=75米．【考点】：解三角形的实际应用．【专题】：应用题；解三角形．【分析】：由题意，可先求出AC的值，从而由正弦定理可求AM的值，在RT△MNA中，AM=50m，∠MAN=60°，从而可求得MN的值．【解析】：解：在RT△ABC中，∠CAB=45°，BC=150m，所以AC=50m．在△AMC中，∠MAC=75°，∠MCA=60°，从而∠AMC=45°，由正弦定理得，，因此AM=50m．在RT△MNA中，AM=50m，∠MAN=60°，由得MN=50×=75m．故答案为：75．【点评】：本题主要考查正弦定理的应用，考查解三角形的实际应用，属于中档题．15．（5分）（2015•遂宁模拟）若函数y=f（x）满足f（a+x）+f（a﹣x）=2b（其中a，b不同时为0），则称函数y=f（x）为“准奇函数”，称点（a，b）为函数f（x）的“中心点”．现有如下命题：①函数f（x）=sinx+1是准奇函数；②函数f（x）=x3是准奇函数；③若准奇函数y=f（x）在R上的“中心点”为（a，f（a）），则函数F（x）=f（x+a）﹣f（a）为R上的奇函数；④已知函数f（x）=x3﹣3x2+6x﹣2是准奇函数，则它的“中心点”为（1，2）；其中正确的命题是①③④．（写出所有正确命题的序号）【考点】：抽象函数及其应用．【专题】：新定义；函数的性质及应用．【分析】：由诱导公式，计算f（﹣x）+f（x），即可判断①；由f（﹣x）+f（x）=0，则a=b=0，不满足条件，即可判断②；运用准奇函数的定义和奇函数的定义，即可判断③；运用准奇函数的定义，化简整理，由恒等式知识求出中心，即可判断④．【解析】：解：对于①，函数f（x）=sinx+1有f（﹣x）+f（x）=sin（﹣x）+1+sinx+1=﹣sinx+sinx+2=2，则y=f（x）为“准奇函数”，且（0，1）为f（x）的“中心点”，则①正确；对于②，函数f（x）=x3，由f（﹣x）+f（x）=0，则a=b=0，不满足条件，则②不正确；对于③，若准奇函数y=f（x）在R上的“中心点”为（a，f（a）），即有f（a+x）+f（a﹣x）=2f （a），F（﹣x）+F（x）=f（a﹣x）﹣f（a）+f（x+a）﹣f（a）=2f（a）﹣2f（a）=0，则函数F（x）=f （x+a）﹣f（a）为R上的奇函数，则③正确；对于④，已知函数f（x）=x3﹣3x2+6x﹣2是准奇函数，则f（a+x）+f（a﹣x）=（a+x）3﹣3（a+x）2+6（a+x）﹣2+（a﹣x）3﹣3（a﹣x）2+6（a﹣x）﹣2=（6a﹣6）x2+（2a3﹣6a2+12a﹣4）=2b，即有6a﹣6=0且2a3﹣6a2+12a﹣4=2b，解得a=1，b=2，．则它的“中心点”为（1，2），则④正确．故答案为：①③④．【点评】：本题考查新定义的理解和运用，考查函数的性质和运用，主要考查函数的对称性，运用定义和掌握定义是迅速解题的关键．三、解答题（本大题共6个小题，共75分）解答应写出文字说明，证明过程或推演步骤．答在答题卷指定位置．16．（12分）（2015•遂宁模拟）已知函数f（x）=sinAsinx+cos2x（x∈R），且满足cos（A+）=﹣，A∈（，）（1）求sinA的值；（2求f（x）的最大值．【考点】：三角函数中的恒等变换应用；正弦函数的图象．【专题】：函数的性质及应用；三角函数的求值．【分析】：（1）直接利用三角函数关系式的变换求出函数的值．（2）首先利用函数关系式的恒等变换，把函数关系式变形成二次函数的形式，进一步利用内函数的值域求出函数的最值．【解析】：解：（1）∵A∈（，），∴，∴cos（A+）=﹣，，故sinA=sin[（A+）﹣]=；（2）f（x）=2sinx+cos2x=2sinx+1﹣2sin2x=，x∈R．则：sinx∈[﹣1，1]，当sinx=时，函数f（x）的最大值为．【点评】：本题考查的知识要点：利用三角函数的关系式求函数的值，三角函数关系式的恒等变换，复合函数的最值问题．属于基础题型．17．（12分）（2015•遂宁模拟）某学校有男老师45名，女老师15名，按照分层抽样的方法组建了一个4人的学科攻关小组．（1）求某老师被抽到的概率及学科攻关小组中男、女老师的人数；（2）经过一个月的学习、讨论，这个学科攻关小组决定选出2名老师做某项实验，方法是先从小组里选出1名老师做实验，该老师做完后，再从小组内剩下的老师中选1名做实验，求选出的2名老师中恰有1名女老师的概率．【考点】：列举法计算基本事件数及事件发生的概率；分层抽样方法．【专题】：概率与统计．【分析】：（1）按照分层抽样的按比例抽取的方法，男女老师抽取的比例是45：15，4人中的男女抽取比例也是45：15，从而解决；（2）先算出选出的2名老师的基本事件数，有（a1，a2），（a1，a3），（a2，a3），（a1，b），（a2，b），（a3，b），共6种；再算出恰有1名女老师事件事件数，两者比值即为所求概率．【解析】：解：（1）由题意知，该校共有老师60名，故某老师被抽到的概率为=．设该学科攻关小组中男老师的人数为x，则，解得x=3，所以该学科攻关小组中男、女老师的人数分别为3，1．（2）由（1）知，该3名男老师和1名女老师分别记为a1，a2，a3，b，则选取2名老师的基本事件有：（a1，a2），（a1，a3），（a2，a3），（a1，b），（a2，b），（a3，b），共6种，其中恰有1名女老师的基本事件有3种，所以选出的2名老师中恰有1名女老师的概率为P==．【点评】：本题主要考查分层抽样方法、概率的求法，是一道简单的综合性的题目，解答的关键是正确理解抽样方法及样本估计的方法，属基础题．18．（12分）（2015•遂宁模拟）如图，ABCD为梯形，PD⊥平面ABCD，AB∥CD，∠BAD=∠ADC=90°，DC=2AB=2a，DA=a，PD=a，E为BC中点（Ⅰ）求证：平面PBC⊥平面PDE；（Ⅱ）线段PC上是否存在一点F，使PA∥平面BDF？若有，请找出具体位置，并进行证明；若无，请分析说明理由．【考点】：平面与平面垂直的判定；直线与平面平行的判定．【专题】：空间位置关系与距离．【分析】：（Ⅰ）连结BD，由已知得BC⊥DE，BC⊥PD，从而BC⊥平面PDE，由此能证明平面PBC⊥平面PDE．（Ⅱ）连结AC，BD交于O点，AB∥CD，从而△AOB∽△COD，AB=DC，进而△CPA中，AO=AC，由PF=，得OF∥PA，由此得到当点F位于PC三分之一分点（靠近P点）时，PA∥平面BDF．【解析】：（本小题满分12分）（Ⅰ）证明：连结BD，∠BAD=∠ADC=90°，AB=a，DA=，所以BD=DC=2a，E为BC中点，所以BC⊥DE，…（3分）又因为PD⊥平面ABCD，所以BC⊥PD，因为DE∩PD=D，…（4分），所以BC⊥平面PDE，…（5分）因为BC⊂平面PBC，所以平面PBC⊥平面PDE．…（6分）（Ⅱ）解：当点F位于PC三分之一分点（靠近P点）时，PA∥平面BDF，…（7分）连结AC，BD交于O点，AB∥CD，所以△AOB∽△COD，AB=DC，所以△CPA中，AO=AC，…（10分）而PF=，所以OF∥PA，…（11分）而OF⊂平面BDF，PA⊄平面BDF，所以PA∥平面BDF．…（12分）【点评】：本题考查面面垂直的证明，考查线面平行时点的位置的确定与证明，考查学生的空间想象能力、逻辑推理能力和运算求解能力，是中档题．19．（12分）（2015•遂宁模拟）已知数列{a n}为等差数列，其中a1=1，a7=13（1）求数列{a n}的通项公式；（2）若数列{b n}满足b n=，T n为数列{b n}的前n项和，当不等式λT n＜n+8（n∈N*）恒成立时，求实数λ的取值范围．【考点】：数列的求和；等差数列的性质．【专题】：等差数列与等比数列．【分析】：（1）由题意和等差数列的通项公式求出公差，代入等差数列的通项公式化简求出a n；（2）由（1）化简b n=，利用裂项相消法求出T n，代入不等式λT n＜n+8分离出λ，利用基本不等式求出式子的最小值，再由对于n∈N*恒成立求出实数λ的取值范围．【解析】：解：（1）设等差数列{a n}的公差为d，∵a1=1，a7=13，∴a1+6d=13，解得d=2，所以a n=a1+（n﹣1）d=2n﹣1…（5分）（2）由（1）得，b n==（），∴T n=[（1﹣）+（）+…+（）]=（1﹣）=…（8分）要使不等式λT n＜n+8（n∈N*）恒成立，只需不等式=+17恒成立即可…（10分）∵，当且仅当时，即n=2取等号，∴λ＜25…（12分）【点评】：本题考查等差数列的通项公式，裂项相消法求数列的和，以及利用基本不等式求最值，属于中档题．20．（13分）（2015•遂宁模拟）已知定点A（﹣2，0），F（1，0），定直线l：x=4，动点P与点F的距离是它到直线l的距离的．设点P的轨迹为C，过点F的直线交C于D、E两点，直线AD、AE与直线l分别相交于M、N两点．（1）求C的方程；（2）试判断以线段MN为直径的圆是否过点F，并说明理由．【考点】：直线与圆锥曲线的综合问题；轨迹方程．【专题】：圆锥曲线中的最值与范围问题．【分析】：（1）设P（x，y）为E上任意一点，依题意有=，化简即可得出；（2）设DE的方程为x=ty+1，与椭圆方程联立化为（3t2+4）y2+6ty﹣9=0，设D（x1，y1），E（x2，y2），由A（﹣2，0），可得直线AD的方程为y=，点M，同理可得N．利用根与系数的关系只要证明=0即可．【解析】：解：（1）设P（x，y）为E上任意一点，依题意有=，化为．（2）设DE的方程为x=ty+1，联立，化为（3t2+4）y2+6ty﹣9=0，设D（x1，y1），E（x2，y2），则，t1t2=．由A（﹣2，0），可得直线AD的方程为y=，点M，同理可得N．∴======9﹣9=0．∴以线段MN为直径的圆恒过定点F．【点评】：本题考查了椭圆的标准方程及其性质、直线与椭圆相交问题转化为方程联立可得根与系数的关系、斜率计算公式、向量垂直与数量积的关系、圆的性质、两点之间的距离公式，考查了推理能力与计算能力，属于难题．21．（14分）（2015•遂宁模拟）已知函数f（x）=（x+1）ln（x+1），g（x）=kxe x（k为常数，e=2.71828…是自然对数的底数），g′（x）为g（x）的导函数，且g′（0）=1，（1）求k的值；（2）对任意x＞0，证明：f（x）＜g（x）；（3）若对所有的x≥0，都有f（x）≥ax成立，求实数a的取值范围．【考点】：导数的运算；利用导数求闭区间上函数的最值．【专题】：导数的综合应用．【分析】：（1）先求导，再代入值计算即可；（2）构造函数G（x），根据函数的单调性，即可证明；（3）构造函数令h（x）=（x+1）ln（x+1）﹣ax，求导，再分类讨论，即可求出a的取值范围．【解析】：解：（1）g'（x）=k（x+1）e x所以g'（0）=k=1…（3分）（2）证明：令G（x）=e x﹣x﹣1，G′（x）=e x﹣1，当x∈（0，+∞），G′（x）＞0，所以当x∈（0，+∞）时G（x）单调递增，从而有G（x）＞G（0）=0，x＞0；所以e x＞x+1＞0⇒x＞ln（x+1）＞0，∴xe x＞（x+1）ln（x+1），所以当x∈（0，+∞），f（x）＜g（x）；…（8分）（3）令h（x）=（x+1）ln（x+1）﹣ax，则h′（x）=1﹣a+ln（x+1），令h′（x）=0，解得x=e a﹣1﹣1，（i）当a≤1时，所以x=e a﹣1﹣1＜0，从而对所有x＞0，h′（x）＞0；h（x）在[0，+∞）上是增函数．故有x＞0，h（x）＞h（0）=0即当a≤1时，对于所有x≥0，都有f（x）≥ax．（ii）当a＞1时，对于0＜x＜e a﹣1﹣1，h′（x）＜0，所以h（x）在（0，e a﹣1﹣1）上是减函数，所以对于0＜x＜e a﹣1﹣1有h（x）＜h（0）=0，即f（x）＜ax，所以，当a＞1，不是所有的x≥0都有f（x）≥ax成立，综上，a的取值范围是（﹣∞，1]…（14分）【点评】：本题考查了导数和函数的单调性的关系以及参数的取值范围，属于中档题．。

(精修版)2015年高考全国卷II(新课标)英语试题及答案解析2015年普通高等学校招生全国统一考试英语（课标卷II）第Ⅰ卷第一部分阅读理解（共两节，满分40分）第一节（共15小题：每小题2分，满分30分）阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项。

AMy color television has given me nothing but a headache. I was able to buy it a little over a year ago because I had my relatives give me money for my birthday instead of a lot of clothes that wouldn’t fit. I let a salesclerk fool me into buying a discontinued model. I realized this a day later, when I saw newspaper advertisements for the set at seven-five dollars less than I had paid. The set worked so beautifully when I first got it home that I would keep it on until stations signed off for the night.Fortunately, I didn’t get any channels showing all-night movies or I would never have gotten to bed.Then I started developing a problem with the set that involved static(静电) noise. For some reason, when certain shows switched into a commercial, a loud noise would sound for a few seconds. Gradully, this noise began to appear during a show, and to get rid of it, I had to change to another channel and then change it back. Sometimes this technique would not work, and I had to pick up the set and shake it to remove the sound. I actually began to build up my arm muscles(肌肉) shaking my set.When neither of these methods removed the static noise ,I would sit helplessly and wait for the noise to go away.At last I ended up hitting the set with my fist,and it stopped working altogether.My trip to the repair shop cost me $62, and the set is working well now,but I keep expecting more trouble.1. Why did the author say he was fooled into buying the TV set?A.He got an older model than he had expected.B.He couldn’t return it when it was broken.C.He could have bought it at a lower price.D.He failed to find any movie shows on it.2. Which of the following can best replace the phrase”signed off”in Paragraph 1?A.ended all their programsB.provided fewer channelsC.changed to commercialsD.showed all-night movies3. How did the author finally get his TV set working again?A. By shaking and hitting it.B. By turning it on and off.C. By switching channels.D. By having it repaired.4. How does the anthor sound when telling the story?A. CuriousB. AnxiousC. CautiousD. HumorousBYour house may have an effect on your figure. Experts say the way you design your home could play a role in whether you pack on the pounds or keep them off. You can make your environment work for you instead of against you. Here are some ways to turn your home into part of diet plan.Open the curtains and turn up the lights. Dark environments are more likely to encourage overeating , for people are often less self-conscious（难为情）when they’re in poorly lit places-and so more likely to eat lots of food . If your home d oesn’t have enough window light, get more lamps and flood the place with brightness.Mind the colors. Research suggests warm colors fuel our appetites. In one study , people who ate meals in a blue room consumed 33 percent less than those in a yellow or red room . Warm colors like yellow make food appear more appetizing , while cold colors make us feel less hungry . So when it’s time to repaint, go blue.Don’t forget the clock-or the radio. People who eat slowly tend to consume about 70 fewer calories（卡路里）per meal than those who rush through their meals. Begin keeping track of the time, and try to make dinner last at least 30 minutes. And while you’re at it, actually sit down to eat. If you need some help slowing down, turn on relaxing music. It makes you less likely to rush through a meal.Downsize the dishs. Big serving bowls and plates can easily make us fat. We eat about 22 percent more when using a 12-inch plate instead of a 10-inch plate. When we choose a large spoon over a smaller one ,total intake（摄入）jumps by 14 percent. And we’ll pour about 30 percent more liquid into a short, wide glass than a tall, skinny glass.5. The text is especially helpful for those who care about_______.A. their home comfortsB. their body shapeC. house buyingD. healthy diets6. A home environment in blue can help people_________.A.digest food betterB.reduce food intakeC.burn more caloriesD.regain their appetites7. What are people advised to do at mealtimes?A. Eat quickly.B. Play fast music.C. Use smaller spoons.D. Turn down the lights.8. What can be a suitable title for the test?A.Is Your Hourse Making You Fat?B.Ways of Serving DinnerC.Effects of Self-ConsciousnessD. Is Your Home Environment Relaxing?CMore student than ever cefore are taking a gap-year (间隔年)before going toCrescent and the Costume Museum.Stonehenge is one of the world’s most famous prehistoric monuments dating back over 5,000 years.Tour B-Oxford & Stratford including entrance fees to the University St Mary’s Church Tower and Anne Hathaway's house-￡32 until 12 March and -￡36 thereafter.Oxford: Includes a guided of England’s oldest university city and colleges. Look over the “city of dreaming spires(尖顶)”form St Mary’s Church Tower. Stratford: Includes a guided tour exploring much of the Shakespeare wonder. Tour C—Windsor Castle & Hampton Court including entrance fees to Hampton Court Palace-£34 until 11 March and -£37 thereafter.Includes a guided tour of Windsor and Hampton Court, Henry Vill’s favourite palace. Free time to visit Windsor Castle（entrace fees not included）. With 500 years of history, Hampton Court was once the home of four Kings and one Queen. Now this former royal palace is open to the public as a major tourist attraction. Visit the palace and its various historic gardens, which include the famous maze(迷宫)where it is easy to get lost!Tour D-Cambridge including entrance fees to the Tower of Saint Mary the Great-£33 until 18 March and £37 thereafter.Includes a guided tour of Cambridge, the famous university town, and the gardens of the 18th century.13. Which tour will you choose if you want to see Engl and’s olde stuniversity city? A.Tour A B.Tour B C.Tour CD.Tour D14. Which of the following tours charges the lowest fee on 17 March?A. Windsor Castle & Hampton Court.B.Oxford & StratfordC. Bath &Stonehenge.D. Cambridge.15. Why is Hampton Court a major tourist attraction?A.It used to be the home of royal families.B.It used to be a well-known mazeC.It is the oldest palace in BritainD.It is a world-famous castle.第二节（共5小题：每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

2015年普通高等学校招生全国统一考试（全国卷2）英语本试卷分第I卷（选择题）和第II卷（非选择题）两部分。

考试结束后, 将本试卷和答题卡一并交回。

第I卷第一部分阅读理解(共两节, 满分40分)第一节(共15小题; 每小题2分, 满分30分)阅读下面短文, 从每题所给的四个选项(A、B、C和D)中, 选出最佳选项, 并在答题卡上将该项涂黑。

AMy color television has given me nothing but a headache. I was able to buy it a little over a year ago because I had my relatives give me money for my birthday instead of a lot of clothes that wouldn’t fit. I let a salesclerk fool me into buying a discontinued model. I realized this a day late, when I saw newspaper advertisements for the set at seventy-five dollars less than I had paid. The set worked so beautifully when I first got it home that I would keep it on until stations signed off for the night. Fortunately, I didn’t got any channels showing all-night movies or I would never have gotten to bed.Then I started developing a problem with the set that involved static(静电)noise. For some reason, when certain shows switched into a commercial, a loud noise would sound for a few seconds. Gradually, this noise began to appear during a show, and to get rid of it, I had to change to another channel and then change it back. Sometimes this technique would not work, and I had to pick up the set and shake it to remove the sound. I actually began to build up my arm muscles(肌肉) shaking my set.When neither of these methods removed the static noise, I would sit helplessly and wait for the noise to go away. At last I ended up hitting the set with my fist, and it stopped working altogether. My trip to the repair shop cost me $62, and the set is working well now, but I keep expecting more trouble.( )1. Why did the author say he was fooled into buying the TV set?A. He got an older model than he had expected.C. He could have bought it at a lower price. B. He couldn’t return it when it was broken.D. He failed to find any movie shows on it.( )2. Which of the following can best replace the phrase “signed off” in Paragraph 1?A. ended all their programs C. changed to commercialsB. provided fewer channels D. showed all-night movies( )3. How did the author finally get his TV set working again?A. By shaking and hitting it.C. By switching channels. B. By turning it on and off.D. By having it repaired.( )4. How does the author sound when telling the story?A. Curious.B. Anxious.C. Cautious.D. Humorous.BYour house may have an effect on your figure. Experts say the way you design your home could play a role in whether you pack on the pounds or keep them off. You can make your environment work for you instead of against you. Here are some ways to turn your home into part of diet plan.Open the curtains and turn up the lights. Dark environments are more likely to encourage overeating, for people are often less self-conscious(难为情)when they’re in poorly lit places---and so more likely to eat lots of food. If your home doesn’t have enough window light, get more lamps and flood the place with brightness.Mind the colors. Research suggests warm colors fuel our appetites. In one study, people who ate meals in a blue room consumed 33 percent less than those in a yellow or red room. Warm colors like yellow make f ood appear more appetizing, while cold colors make us feel less hungry. So when it’s time to repaint, go blue.Don’t forget the clock-or the radio. People who eat slowly tend to consume about 70 fewer calories(卡路里) per meal than those who rush through their meals. Begin keeping track of the time, and try to make dinner last at least 30 minutes. And while you’re at it, actually sit down to eat. If you need some help slowing down, turn on relaxing music. It makes you less likely to rush through a meal.Downsize the dishes. Big serving bowls and plates can easily make us fat. We eat about 22 percent more when using a 12-inch plate instead of a 10-inch plate. When we choose a large spoon over a smaller one, total intake(摄入)jumps by 14 percent. And we’ll pour about 30 percent more liquid into a short, wide glass than a tall, skinny glass.( )5. The text is especially helpful for those who care about __________.A. their home comforts C. house buyingB. their body shape D. healthy diets( )6. A home environment in blue can help people __________.A. digest food better C. burn more caloriesB. reduce food intake D. regain their appetites( )7. What are people advised to do at mealtimes?A. Eat quickly.C. Use smaller spoons. B. Play fast music.D. Turn down the lights.( )8. What can be a suitable title for the test?A. Is Your House Making You Fat?B. Ways of Serving DinnerC. Effects of Self-ConsciousnessD. Is Your Home Environment Relaxing?CMore student than ever before are taking a gap-year(间隔年) before going to university. It used to be called the “year off” between school and university. The gap-year phenomenon originated(起源) with the months left over to Oxbridge applicants between entrance exams in November and the start of the next academic year.This year, 25,310 students who have accepted places in higher education institutions have put off their entry until next year, according to statistics on university entrance provided by University and College Admissions Service(UCAS).That is a record 14.7% increase in the number of students taking a gap year. Tony Higgins from UCAS sa id that the statistics are good news for everyone in higher education. “Studen ts who take a well-planned year out are more likely to be satisfied with, and complete, their chosen course. Students who take a gap year are often more mature and responsible,” he said.But not everyone is happy. Owain James, the president of the National Union of Students(NUS), argued that the increase is evidence of student had ship---young people are being forced into earning money before finishing their education. “New students are now aware that they are likely to leave university up to £15,000 in debt. It is not surprising that more and more students are taking a gap year to earn money to support their study for the degree. NUS statistics show that over 40% of students are forced to work during term time and the figure increases to 90% during vacatio n periods,”he said.( )9. What do we learn about the gap year from the text?A. It is flexible in length. C. It is increasingly popular.B. It is a time for relaxation. D. It is required by universities.( )10. According to Tony Higgins,students taking a gap year __________.A. are better prepared for college studiesB. know a lot more about their future jobsC. are more likely to leave university in debtD. have a better chance to enter top universities( )11. How does Owain James feel about the gap-year phenomenon?A. He’s puzzled.B. He’s worried.C. He’s surprised.D. He’s annoyed. ( )12. What would most students do on their vacation according to NUS statistics?A. Attend additional courses.C. Earn money for their education.B. Make plans for the new term.D. Prepare for their graduate studies. DChoose Your One-Day ToursTour A---Bath & Stonehenge including entrance fees to the ancient Roman bathrooms andStonehenge---£37 until 26 March and £39 thereafter.Visit the city with over 2,000 years of history and Bath Abbey, the Royal Crescent and the Costume Museum. Stonehenge is one of the world’s most famous prehistoric monuments dating back over 5,000 years.Tour B----Oxford & Stratford including entrance fees to the University St Mar y’s Church Tower and Anne Hathaway’s house---£32 until 12 March and £36 thereafter.Oxford: Includes a guided of England’s oldest university city and colleges. Look over the “city of dreaming spires(尖顶)”form St Mary’s Church Tower. Stratford: Includes a guided tour exploring much of the Shakespeare wonder.Tour C---Windsor Castle & Hampton Court including entrance fees to Hampton Court Palace---£34 until March and £37 thereafter.Includes a guided tour of Windsor and Hampton Court, Henry Mill’s favourite p alace. Free time to visit Windsor Castle (entrance fees not included). With 500 years of history, Hampton Court was once the home of four Kings and one Queen. Now this former royal palace is open to the public as a major tourist attraction. Visit the palace and its various historic gardens, which include the famous maze(迷宫) where it is easy to get lost!Tour D---Cambridge including entrance fees to the Tower of Saint Mary the Great---£33 until 18 March and £37 thereafter.Includes a guided tour of Cambridge,the famous university town,and the gardens of the 18th century. ( )13. Which tour will you choose if you want to see England’s oldest university city?A. Tour A.B. Tour B.C. Tour C.D. Tour D. ( )14. Which of the following tours charges the lowest fee on 17 March?A. Windsor Castle & Hampton Court.C. Bath &Stonehenge. B. Oxford & Stratford.D. Cambridge.( )15. Why is Hampton Court a major tourist attraction?A. It used to be the home of royal families.C. It is the oldest palace in Britain. B. It used to be a well-known maze.D. It is a world-famous castle.第二节(共5小题; 每小题2分, 满分10 分)根据短文内容, 从短文后的选项中选出能填入空白处的最佳选项。