山东省实验中学2014届高三下学期第一次模拟测试试题
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2014年山东省实验中学高考数学一模试卷(理科)学校:___________姓名:___________班级:___________考号:___________一、选择题(本大题共10小题,共50.0分)1.已知集合M={x|-1<x<1},N={x|log2x<1},则M∩N等于()A.{x|0<x<1}B.{x|-1<x<2}C.{x|-1<x<0}D.{x|-1<x<1}【答案】A【解析】解:由N中的不等式变形得:log2x<1=log22,即0<x<2,∴N={x|0<x<2},∵M={x|-1<x<1},∴M∩N={x|0<x<1}.故选:A.求出N中不等式的解集确定出N,找出M与N的交集即可.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.设f(n)=+(n∈Z),则f(2014)()A.2B.-2C.2iD.-2i【答案】C【解析】解:∵,,且f(n)=+(n∈Z),∴f(2014)=i2013+(-i)2015=(i2)1006•i+(-1)2015•(i2)1007•i=2i.故选:C.首先利用复数的除法运算化简,,然后代入f(2014),最后利用虚数单位i的性质求值.本题考查了复数代数形式的混合运算,考查了虚数单位i的运算性质,是基础的计算题.3.下列函数中既是奇函数,又在区间[-1,1]上单调递减的函数是()A.f(x)=|tan2x|B.f(x)=-|x+1|C.f(x)=(2-x-2x)D.f(x)=【答案】C【解析】解:A,f(x)=|tan2x|为偶函数,不满足第一个条件.B,f(x)=-|x+1|为非奇非偶函数,不满足第一个条件.C,若f(x)=(2-x-2x),则f(-x)=(2x-2-x)=-f(x)为奇函数,∵f(x)=[()x-2x],y=()x为减函数,y=2x,为增函数,y=-2x为减函数,∴根据函数单调性的性质可知,函数f(x)在R上单调递减,满足条件.D,若f(x)=,则由>得-2<x<2,f(-x)=为奇函数,∵f(x)==,∴由复合函数的单调性可知函数f(x)在定义域上为增函数,不满足条件,故选:C.分别根据函数的奇偶性和单调性的定义进行判断即可.本题主要考查函数奇偶性和单调性的判断和应用,要求熟练掌握常见函数的奇偶性和单调性的性质.4.下列有关命题的说法正确的是()A.命题“若x2=1,则x=1”的否命题为:“若x2=1,则x≠1”B.“m=1”是“直线x-my=0和直线x+my=0互相垂直”的充要条件C.命题“∃x∈R,使得x2+x+1<0”的否定是:“∀x∈R,均有x2+x+1<0”D.命题“已知x,y为一个三角形的两内角,若x=y,则sinx=siny”的逆命题为真命题【答案】D【解析】解:对于A,根据否命题的意义可得:命题“若x2=1,则x=1”的否命题为:“若x2≠1,则x≠1”,因此原命题不正确,违背否命题的形式;对于B,“m=1”是“直线x-my=0和直线x+my=0互相垂直”的充要条件不准确,因为“直线x-my=0和直线x+my=0互相垂直”的充要条件是m2=1,即m=±1.对于命题C:“∃x∈R,使得x2+x+1<0”的否定的写法应该是:“∀x∈R,均有x2+x+1≥0”,故原结论不正确对于D,根据正弦定理,∵x=y⇔sinx=siny”,所以逆命题为真命题是正确的.故答案选:D.对于A根据否命题的意义即可得出;对于B按照垂直的条件判断;对于C按照含有一个量词的命题的否定形式判断;对于D按照正弦定理和大角对大边原理判断.本题考查了四种命题之间的关系、命题的否定,属于基础题.5.已知正三棱锥V-ABC的主视图,俯视图如图所示,其中VA=4,AC=,则该三棱锥的左视图的面积为()A.9B.6C.3D.【答案】B【解析】解:正三棱锥V-ABC的侧面是等腰三角形,底面是正三角形,底面上的高是3,所以V到底面的距离:;该三棱锥的左视图的面积:故选B.由题意可知,几何体的侧面是等腰三角形,要该三棱锥的左视图的面积,必须求出VA 在左视图的射影的长度,即求V到底面的距离.本题考查三视图求面积,空间想象能力,是中档题.6.已知x、y的取值如下表从所得的散点图分析,y与x线性相关,且=0.95x+a,则a=()A.2.1B.2.2C.2.4D.2.6【答案】D【解析】解:点,在回归直线上,计算得,;代入得a=2.6;故选D.本题考查的知识点是线性回归直线的性质,由线性回归直线方程中系数的求法,我们可知,在回归直线上,满足回归直线的方程,我们根据已知表中数据计算出,,再将点的坐标代入回归直线方程,即可求出对应的a值.统计也是高考新增的考点,回归直线方程的求法,又是统计中的一个重要知识点,其系数公式及性质要求大家要熟练掌握并应用.7.定义行列式运算=a1a4-a2a3,将函数f(x)=的图象向右平移m(m >0)个单位,所得图象对应的函数为奇函数,则m的最小值为()A. B. C. D.【答案】C【解析】解:由定义行列式运算=a1a4-a2a3,得f(x)====.将函数f(x)的图象向右平移m(m>0)个单位,所得图象对应的函数解析式为:g(x)=f(x-m)=,∵函数g(x)为奇函数,∴,,即,,取k=-1时,正数m的最小值为.故选:C.由定义的行列式运算得到函数f(x),化简后利用函数图象的平移得到,再由该函数为奇函数得到,,由此求得最小正数m的值.本题考查了三角函数的图象和性质,考查了三角函数的图象平移问题,训练了三角函数为奇函数的条件,是中档题.8.已知函数f(x)=x+2x,g(x)=x+lnx,的零点分别为x1,x2,x3,则x1,x2,x3的大小关系是()A.x1<x2<x3B.x2<x1<x3C.x1<x3<x2D.x3<x2<x1【答案】A【解析】解:f(x)=x+2x的零点必定小于零,g(x)=x+lnx的零点必位于(0,1)内,函数的零点必定大于1.因此,这三个函数的零点依次增大,故x1<x2<x3.故选A.利用估算方法,将各函数的零点问题确定出大致区间进行零点的大小比较问题是解决本题的关键.必要时结合图象进行分析.本题考查函数零点的定义,函数零点就是相应方程的根,利用估算方法比较出各函数零点的大致位置,进而比较出各零点的大小.9.八个一样的小球按顺序排成一排,涂上红、白两种颜色,5个涂红色,三个涂白色,求恰好有个三个连续的小球涂红色的涂法共有()A.24种B.30种C.20种D.36种【答案】A【解析】解:先把3个涂红色的小球捆绑,作为一体,再把3个涂白色的小球排起来第一步:把捆绑的小球插入3个涂白色的小球中有4种选择第二步:把剩下的2个红色小球插入:2个红色小球分开有3种插法,在一起也有3种插法即:涂法有4×(3+3)=24种故选A.先把3个涂红色的小球捆绑,作为一体,再把3个涂白色的小球排起来,利用乘法原理可得结论.本题考查乘法原理,考查学生分析解决问题的能力,属于基础题.10.若A i(i=1,2,3,…,n)是△AOB所在平面内的点,且•=•,给出下列说法:(1)||=||=||=…=|(2)||的最小值一定是||(3)点A和点A i一定共线(4)向量及在向量方向上的投影必定相等其中正确的个数是()A.1个B.2个C.3个D.4个【答案】B【解析】解:根据两个向量的数量积的定义,为定值,而•=||•||cos<,>,故①不一定成立,②也不一定成立.根据两个向量的数量积的定义,结合条件,可得向量及在向量的方向上的投影必相等,故④正确.再结合④可得点A、A i在一条直线上,故③正确.故选:B.根据两个向量的数量积的定义,为定值,可得③、④正确,而①、②不一定成立,从而得到答案.本题主要考查两个向量的数量积的定义,一个向量在另一个向量上的投影的定义,属于中档题.二、填空题(本大题共5小题,共25.0分)11.阅读如图的程序框图,执行相应的程序,则输出k的结果是______【答案】4【解析】解:第一次运行,S=0,满足S<100,S=2°=1,k=1,第二次运行,S=1,满足S<100,S=1+21=3,k=2,第三次运行,S=3,满足S<100,S=3+23=11,k=3,第四次运行,S=11,满足S<100,S=11+211=1,k=4,此时S>100,不满足条件,输出k=4,故答案为:4根据程序框图进行运行,直到不满足条件时,即可得到结论.本题主要考查程序框图的识别和运行,根据运行条件进行判断即可.12.设函数f(x)=|x+3|-|x-a|(a≠-3)的图象关于点(1,0)中心对称,则a的值为______ .【答案】5【解析】解:f(x)=|x-m|-|x-n|的图象关于点(,0)对称,又∵函数f(x)=|x+3|-|x-a|=|x-(-3)|-|x-a|的图象关于点(1,0)中心对称,故1=,解得a=5,故答案为:5根据f(x)=|x-m|-|x-n|的图象关于点(,0)对称,结合已知条件,可得a的值.本题考查的知识点是绝对值函数的对称性,其中熟练掌握f(x)=|x-m|-|x-n|的图象关于点(,0)对称,是解答的关键.13.在(a>0)的展开式中含常数项的系数是60,则sinxdx的值为______ .【答案】1-cos2【解析】解:展开式的通项a r C6r,令6-3r=0得r=2.∴常数项为15a2=60,a=2,∴sinxdx=sinxdx=(-cosx)=1-cos2.故答案为:1-cos2.利用二项展开式的通项公式求出通项,令x的指数为0,求出展开式的常数项,列出方程求出a,代入定积分求出值.本题考查利用二项展开式的通项公式解决二项展开式的特定项问题、求定积分值.14.已知点P(x,y)满足条件(k为常数),若z=x+3y的最大值为8,则k= ______ .【答案】-6【解析】解:画出可行域将z=x+3y变形为y=,画出直线平移至点A时,纵截距最大,z最大,联立方程得,代入,∴k=-6.故答案为-6画出可行域,将目标函数变形,画出相应的直线,将其平移,数学结合当直线移至点A时,纵截距最大,z最大.本题考查画不等式组的可行域;利用可行域求出目标函数的最值.15.双曲线-=1的左右焦点为F1,F2,P是双曲线左支上一点,满足||=||,直线PF2与圆x2+y2=a2相切,则双曲线的离心率e为______ .【答案】【解析】解:设PF2与圆相切于点M,∵||=||,∴△PF1F2为等腰三角形,∴|F2M|=|PF2|,又在直角△F2MO中,|F2M|2=|F2O|2-a2=c2-a2,∴|F2M|=b=|PF2|①又|PF2|=|PF1|+2a=2c+2a②,c2=a2+b2③由①②③解得e==.故答案为:.先设PF2与圆相切于点M,利用||=||,及直线PF1与圆x2+y2=a2相切,可得几何量之间的关系,从而可求双曲线的离心率的值.本题考查直线与圆相切,考查双曲线的定义,考查双曲线的几何性质,属于中档题.三、解答题(本大题共6小题,共75.0分)16.已知函数f(x)=-2sin2+sin(ωx+)-cos(ωx+)(ω>0,x∈R),且函数f(x)的最小正周期为π.(Ⅰ)求函数f(x)的解析式;(Ⅱ)在△ABC中,角A,B,C所对的边分别为a,b,c,若f(B)=1,•=,且a+c=4,试求b2的值.【答案】解:(Ⅰ)f(x)=sinωx+cosωx-1=2sin(ωx+)-1,∵T=π,∴ω=2,则f(x)=2sin(2x+)-1;(Ⅱ)f(B)=2sin(2B+)-1=1,即sin(2B+)=1,∴2B+=2kπ+(k∈Z),解得:B=kπ+(k∈Z),∵B为△ABC的内角,∴B=,∵•=cacos B=,∴ac=3,∵a+c=4,∴a2+c2=(a+c)2-2ac=16-6=10,∴由余弦定理得:b2=a2+c2-2accos B=10-3.【解析】(Ⅰ)f(x)解析式利用二倍角的余弦函数公式,以及两角和与差的余弦函数公式化简,整理后化为一个角的正弦函数,根据周期公式求出ω的值,即可确定出函数f(x)的解析式;(Ⅱ)由第一问确定出的f(x)解析式,由f(B)=1,求出B的度数,再利用平面向量的数量积运算法则化简•=,求出ac的值,进而确定出a2+c2的值,利用余弦定理即可求出b2的值.此题考查了余弦定理,平面向量的数量积运算,以及三角函数的周期性及其运算,熟练掌握余弦定理是解本题的关键.17.在盒子里有大小相同,仅颜色不同的乒乓球共10个,其中红球5个,白球3个,蓝球2个.现从中任取出一球确定颜色后放回盒子里,再取下一个球.重复以上操作,最多取3次,过程中如果取出蓝色球则不再取球.求:(1)最多取两次就结束的概率;(2)整个过程中恰好取到2个白球的概率;(3)取球次数的分布列和数学期望.【答案】解:(1)由题意知,任取一球,取到红球的概率为=任取一球,取到白球的概率为=任取一球,取到蓝球的概率为=∵如果取出蓝色球则不再取球,∴最多取两次就结束的概率为++=(2)设A={整个过程中恰好取到2个白球},B i={第i次取到白球}H i={第i次取到红球}L i={第i次取到蓝球}则P(A)=P(B1B2)+P(H1B2B2)+P(B1H2B3)=×++=(3)设取球次数为X,则X的可能取值为1,2,3P(X=1)==P(X=2)=+=P(X=3)==随机变量X的分布列如下从而E(X)=1×+2×+3×=【解析】(1)先分别求出任取一球,取到每种颜色的球的概率,因为取出蓝色球则不再取球,所以最多取两次就结束有两种情况,第一种,第一次取球,取到蓝球,第二种情况,第一次取球,取到红球或白球,第二次取球,取到蓝球,把两种情况的概率求出,再相加即可.(2)由(1)知任取一球,取到白球的概率为,取到蓝球的概率为,取到红球的概率为,而恰好取到2个白球包括三个互斥事件,即(白,白,非白),(白,红,白),(红,白,白),分别计算它们的概率,最后相加即可(3)设取球次数为X,则X的可能取值为1,2,3,X=1即第一次就抓到蓝球,X=2即第一次不是蓝球,第二次是蓝球,X=3即第一次不是蓝球,第二次不是蓝球;分别计算它们的概率,列出分布列,由期望公式计算X的期望本题考察了古典概型概率的求法,互斥事件有一个发生的概率和相互独立事件同时发生的概率计算,以及离散型随机变量的分布列及其期望的求法18.如图,已知正三棱柱ABC-A1B1C1各棱长都为a,P为线段A1B上的动点.(Ⅰ)试确定A1P:PB的值,使得PC⊥AB;(Ⅱ)若A1P:PB=2:3,求二面角P-AC-B的大小.【答案】解:【法一】(Ⅰ)当PC⊥AB时,作P在AB上的射影D,连接CD,则AB⊥平面PCD,∴AB⊥CD,∴D是AB的中点,又PD∥AA1,∴P也是A1B的中点,即A1P:PB=1.反之当A1P:PB=1时,取AB的中点D',连接CD'、PD'.∵△ABC为正三角形,∴CD'⊥AB.由于P为A1B的中点时,PD'∥A1A∵A1A⊥平面ABC,∴PD'⊥平面ABC,∴PC⊥AB.…6′(Ⅱ)当A1P:PB=2:3时,作P在AB上的射影D,则PD⊥底面ABC.作D在AC上的射影E,连接PE,则PE⊥AC,∴∠DEP为二面角P-AC-B的平面角.又∵PD∥AA1,∴,∴.∴°,又∵,∴,∴∠,∴P-AC-B的大小为∠PED=60°.…12【法二】以A为原点,AB为x轴,过A点与AB垂直的直线为y 轴,AA1为z轴,建立空间直角坐标系A-xyz,如图所示,设P(x,0,z),则B(a,0,0)、A1(0,0,a)、,,.(Ⅰ)由得,,,,,即,∴,即P为A1B的中点,也即A1P:PB=1时,PC⊥AB.…4′(Ⅱ)当A1P:PB=2:3时,P点的坐标是,,.取,,.则,,,,,,,,,.∴是平面PAC的一个法向量.又平面ABC的一个法向量为,,.∴<,>,∴二面角P-AC-B的大小是60°.…(12分)【解析】【法一】(Ⅰ)利用三角形的中位线,可确定A1P:PB的值,使得PC⊥AB;(Ⅱ)先作出二面角P-AC-B的平面角,再进行计算;【法二】建立空间直角坐标系,(Ⅰ)由,可确定A1P:PB的值,使得PC⊥AB;(Ⅱ)确定平面的法向量,利用向量的夹角公式,即可求得结论.本题考查线线垂直,考查面面角,考查利用向量知识解决立体几何问题,确定平面的法向量是关键.19.已知点(1,)是函数f(x)=a x(a>0且a≠1)的图象上一点,等比数列{a n}的前n项和为f(n)-c,数列{b n}(b n>0)的首项为c,且前n项和S n满足S n-S n-1=+(n≥2).(1)求数列{a n}和{b n}的通项公式;(2)若数列{}前n项和为T n,问T n>的最小正整数n是多少?【答案】解:(1)∵点(1,)是函数f(x)=a x(a>0且a≠1)的图象上一点,∴f(1)=a=,∴f(x)=()x.,,,又数列{a n}是等比数列,∴,解得c=1,又公比,∴=-2()n,n∈N*.∵S n-S n-1=()()=,n≥2,又>,>,∴,数列{}构成一个首相为1公差为1的等差数列,=1+(n-1)=n,∴.当n≥2时,,∴,.(2)∵==,∴T n===.∵T n=>,∴n>,满足>的最小正整数为72.【解析】(1)由已知条件得f(x)=()x.所以,,,由数列{a n}是等比数列,得到c=1,,由此能求出数列{a n}的通项公式;S n-S n-1=()()=,得到数列{}构成一个首相为1公差为1的等差数列,由此能求出{b n}的通项公式.(2)==,由此利用裂项求和法能求出满足>的最小正整数.本题考查数列的通项公式的求法,考查满足不等式的最小正整数的求法,解题时要认真审题,注意裂项求和法的合理运用.20.已知椭圆C:+=1(a>b>0),F(,0)为其右焦点,过F垂直于x轴的直线与椭圆相交所得的弦长为2.(Ⅰ)求椭圆C的方程;(Ⅱ)设直线l:y=kx+m(|k|≤)与椭圆C相交于A、B两点,以线段OA,OB为邻边作平行四边形OAPB,其中顶点P在椭圆C上,O为坐标原点,求|OP|的取值范围.【答案】解:(Ⅰ)∵F(,0)为椭圆的右焦点,过F垂直于x轴的直线与椭圆相交所得的弦长为2.∴c=,=1,∵a2=b2+c2∴a2=4,b2=2.故椭圆C的方程为;(Ⅱ)当k=0时,P(0,2m)在椭圆C上,解得m=±,∴|OP|=;当k≠0时,直线方程代入椭圆方程,消y化简整理得:(1+2k2)x2+4kmx+2m2-4=0,△=16k2m2-4(1+2k2)(2m2-4)=8(4k2-m2-2>0①设A,B,P点的坐标分别为(x1,y1)、(x2,y2)、(x0,y0),则x0=x1+x2=-,y0=y1+y2=k(x1+x2)+2m=.由于点P在椭圆C上,∴.从而,化简得2m2=1+2k2,经检验满足①式,又|OP|==,∵0<|k|≤,∴1<1+2k2≤2,∴1≤<2,∴<|OP|≤,综上,所求|OP|的取值范围是[,].【解析】(Ⅰ)先由已知F(,0)为椭圆的右焦点,过F垂直于x轴的直线与椭圆相交所得的弦长为2,可得c=,=1,结合a2=b2+c2,解之即得a,b,从而写出椭圆C的方程;(Ⅱ)先对k分类讨论:当k=0时,P(0,2m)在椭圆C上,解得m=±,所以|OP|=;当k≠0时,将直线的方程代入椭圆的方程,消去y得到关于x的一元二次方程,再结合根系数的关系利用弦长公式即可求得|OP|的取值范围,从而解决问题.本题主要考查了直线与圆锥曲线的综合问题、椭圆的标准方程问题.当研究椭圆和直线的关系的问题时,常可利用联立方程,进而利用韦达定理来解决.21.已知函数f(x)=ln(x+1)+ax2-x,a∈R.(Ⅰ)当a=时,求函数y=f(x)的极值;(Ⅱ)是否存在实数b∈(1,2),使得当x∈(-1,b]时,函数f(x)的最大值为f(b)?若存在,求实数a的取值范围,若不存在,请说明理由.【答案】解:(Ⅰ)当时,f(x)=,则′,化简得′,(x>-1)∴函数在(-1,0),(1,+∞)上单调递增,在(0,1)上单调递减,且f(0)=0,f(1)=,∴函数y=f(x)在x=1处取到极小值为ln2-,在x=0处取到极大值为0.(Ⅱ)由题意f′(x)=,(1)当a≤0时,函数f(x)在(-1,0)上单调递增,在(0,+∞)上单调递减,此时,不存在实数b∈(1,2)使得当x∈(-1,b]时,函数f(x)的最大值为f(b);(2)当a>0时,令f′(x)=0,有x=0或x=,①当a=时,函数f(x)在(-1,+∞)上单调递增,显然符合题意;②当>0即<<时,函数f(x)在(-1,0)和(,+∞)上单调递增,在(0,)上单调递减,此时由题,只需f(1)>0,解得a>1-ln2,又1-ln2<,∴此时实数a的取值范围是<<③当<0即>时,函数f(x)在(-1,)和(0,+∞)上单调递增,在(,0)上单调递减,要存在实数b∈(1,2),使得当x∈(-1,b]时,函数f(x)的最大值为f(b),则f()<f(1),代入化简得>(*)令>,因′>0恒成立,故恒有>>,∴>时,(*)式恒成立.综上,实数a的取值范围是(1-ln2,+∞).【解析】(Ⅰ)将代入到f(x)的表达式中并求导,计算其单调区间从而确定其极值.(Ⅱ)f′(x)=,注意到分子中x前的系数为2a,则分成a≤0和a>0两种情况讨论.其中,当a>0时,′,(x>-1)再分成>0和<0两种情况分别讨论计算.本题主要运用了分类讨论的方法,由条件逐层分析,逐步确定分类条件,一步一步讨论,直至将问题解决,在用分类讨论的方法解决问题时,要记住做到“不重不漏”.。
2014年高考(35)山东实验中学第一次诊断性测试高考模拟2014-10-15 2113山东省实验中学2014届高三第一次诊断性测试语文试题第Ⅰ卷(选择题共36分)一、(15分,每小题3分)1.下列词语中加点的字,每对读音都不相同的一项是A.参省/参差累及/累卵行头/行当蹈藉/慰藉B.隽永/隽秀菲薄/芳菲煞尾/煞白歆羡/钦慕C.椽子/姻缘踮脚/惦记草茎/颈项负荷/感荷D.尽快/尽管搵泪/温驯修葺/鹿茸舟楫/作揖2.下列词语没有错别字的一组是A.笨胚戳子不更事屈打成召B.张皇简朴怅寥廓前合后偃C.圭臬诀绝打牙祭神智慌乱D.桥礅暧昧拴马桩回光反照3.填入各句横线处的词语,最恰当的一项是①这成就还没有,就全靠有书籍记载流传下来。
②所以马克思是当代最遭。
和最受诬蔑的人。
③临近的密密挤拚的人群,在讲,在听,在微笑,在皱眉,在____,在保留……A.湮没忌恨给予B.淹没忌恨给以C.湮没记恨给予D.淹没记恨给以4.下列各句中,加点的成语使用不恰当的一项是A.她要一个子儿一个子儿的捍卫自己那可怜的钱包,讨价还价,睚眦必报B.当时上海的报章都不敢载这件事……只在《文艺新闻》上有一点隐约其辞的文章。
C.你这人真不懂眉眼高低,人家正发愁呢,你还开玩笑。
D.国际社会上,一些国家只要是美国不为已甚,就希望同美国继续友好往来。
5.下列句子中,没有语病的一项是A.这是这个城里唯一的一所大学,,这所大学一直对孩子们充满了神秘感。
B.本刊将制定全新的规划,继续保持稿件的编辑水平,促进文学刊物的高品质。
C.北京是一座悠久的城市,岁月的雕饰在北京的各个角落留下了珍贵的符号,请救救北京的符号!D.许多游客反映,有些景点的票价太贵,如“三孔”泰山,票价都在60元至100元之间。
二、(9分,每小题3分)阅读下面文字,完成6-8题。
什么是艺术真实性呢?有各种各样的界说,但基本意思是认为艺术真实性是作品正确地反映了生活的本质和规律。
不但文学艺术要反映生活的本质和规律,一切科学都要反映客观世界的本质和规律。
山东省实验中学2011级高三第一次模拟考试数学试题(理科) (2014.3)第I 卷(选择题 50分)一、选择题:本大题共10小题,每小题5分,共50分.在每小题列出的四个选项中,选出符合题目要求的一项.1.已知集合{}{}211,log 1,M x x N x x M N =-<<=<⋂则等于 A.{}01x x << B.{}1x x -<<2 C.{}x x -1<<0 D.{}11x x -<<2.设()()()1111201411n n i i f n n Z f i i -++-⎛⎫⎛⎫=+∈= ⎪ ⎪-+⎝⎭⎝⎭,则 A.2 B.2- C.2i D.2i -3.下列函数中既是奇函数,又在区间[]1,1-上单调递减的函数是A.()tan 2f x x =B.()1f x x =-+C.()()1222x x f x -=-D.()22x f x x-=+ 4.下列有关命题的说法正确的是A.命题“若211x x ==,则”的否命题为:“若211x x =≠,则”;B.“1m =”是“直线00x my x my -=+=和直线互相垂直”的充要条件C.命题“x R ∃∈,使得210x x ++<”的否定是:“x R ∀∈,均有210x x ++<”;D.命题“已知x,y 为一个三角形的两内角,若x=y ,则sin sin x y =”的逆命题为真命题.5.已知正三棱锥V-ABC 的主视图、俯视图如下图所示,其中4,VA AC ==,则该三棱锥的左视图的面积为A.9B.6C.6.已知x 、y 的取值如下表所示:若y 与x 线性相关,且0.95,y x a a ∧=+=则A.2.2B.2.9C.2.8D.2.67.定义行列式运算()1234sin 2142 3.cos2a a x a a x a a a a f x =-=将函数的图象向右平移()0m m >个单位,所得图象对应的函数为奇函数,则m 的最小值为 A.12π B. 6π C. 3π D. 23π8.已知函数()()()2,l n ,1x f x x g x x x x x =+=+--的零点分别为123123,,,,x x x x x x ,则的大小关系是A.123x x x <<B. 213x x x <<C. 132x x x <<D. 321x x x << 9.八个一样的小球按顺序排成一排,涂上红、白两种颜色,5个涂红色,三个涂白色,恰好有三个连续的小球涂红色,则涂法共有A.24种B.30种C.20种D.36种10.若()1,2,3,,i A i n AOB =⋅⋅⋅∆是所在的平面内的点,且i OA OB OA OB ⋅=⋅.给出下列说法: ①12n OA OA OA OA ==⋅⋅⋅==; ②1OA 的最小值一定是OB ;③点A 、i A 在一条直线上;④向量i OA OA OB 及在向量的方向上的投影必相等.其中正确的个数是A.1个B.2个C.3个D.4个二、填空题:本大题共5小题,每小题5分,共25分.11.阅读右面的程序框图,执行相应的程序,则输出k 的结果是_______12.设函数()3f x x x a =+--的图象关于点(1,0)中心对称,则a 的值为_______13.在()60a a x ⎫>⎪⎭的展开式中含常数项的系数是60,则0sin axdx ⎰的值为_______14.已知点(),p x y 满足条件0,,20x y x x y k ≥⎧⎪≤⎨⎪++≤⎩(k 为常数),若3z x y =+的最大值为8,则k=_________.15.双曲线22221x y a b-=的左右焦点为12,F F ,P 是双曲线左支上一点,满足2221122PF F F PF x y a =+=,直线与圆相切,则双曲线的离心率e 为________.三、解答题:本大题共6小题,共75分.解答应写出文字说明,演算步骤或证明过程.16.(本小题满分12分)已知函数()()22sinsin cos 0,263x f x x x x R ωππωωω⎛⎫⎛⎫=-++-+>∈ ⎪ ⎪⎝⎭⎝⎭,且函数()f x 的最小正周期为π。
【组卷说明】本卷以各地名市级模拟考试和各校的联合考试为主题、以山东省新课标卷为模板、以“高考考试大纲”为指导进行组卷,是高考复习必备的重组试卷.根据2013年全国新课标试题进行组合,试题总体难度适中,新题题目较多,个别试题需要耐心思考。
本套试题有如下的鲜明特点:1.注重基础知识的考查:选择题的1-6题,重在基础知识的把握;填空中的13、15,强调基础运算能力,也是高考中必要的得分点.2.注重新颖试题的筛选和组合:如选择题的12,试题设计新颖,但是难度不大;再如填空题14题,体现在知识的交汇点出题的原则,有一定的难度,可以锻炼学生的解题能力.3.大题难度和新课标高考基本一致,其中21和22体现拔高功能,锻炼学习解题能力:第17题——考查了三角化简以及三角函数的性质,同时将图象平移联系在一起,考查公式应用能力以及运算能力;第18题——立体几何问题,考查学生空间想象能力和计算分析能力第19题——概率和期望,以体育赛事的射击为背景,考查学生转化分析能力和阅读能力;;第20题——数列题型,考查了数列的通项以及数列的求和;第21题——函数与导数,着重考查导数基础知识、函数与方程思想以及分类讨论思想;第22题——以椭圆为背景考查轨迹问题和直线与曲线相交问题,考查逻辑思维能力,以及运算能力.第Ⅰ卷(共60分)一、选择题:本大题共12个小题,每小题5分,共60分.在每小题给出的四个选项中,只有一项是符合题目要求的.1.【2014)(A) 第一象限 (B)第二象限 (C)第三象限 (D)第四象限2.【山东烟台莱阳一中高三第三次模拟】设全集,{|(3)0},{|1},U R A x x x B x x ==+<=<- 则下图中 阴影部分表示的集合为( )A.{|31}x x -<<-B.}{|30x x x -<<C.{|0}x x >D.{|1}x x <-3.【山东省烟台市2013年3月高三检测】已知()f x 是定义在R 上的奇函数,当0x ≥时()3x f x m =+(m 为常数),则3(log 5)f -的值为( )A.4B.-4C.6D.-64.【山东省淄博市2013届高三模拟测试】设,m n 是两条不同直线,,αβ是两个不同的平面,下列命题正确的是( ) A .//,//m n αβ且//αβ,则//m n B .,m n αβ⊥⊥且αβ⊥,则m n ⊥C .,,m n m n αβ⊥⊂⊥,则αβ⊥D .,,//,//m n m n ααββ⊂⊂,则//αβ5.【山东省诸城市2013届高三检测】已知()sin()2f x x π=+,()cos()2g x x π=-,则()f x 的图象( )A .与()g x 的图象相同B .与()g x 的图象关于y 轴对称C .向左平移2π个单位,得到()g x 的图象D .向右平移2π个单位,得到()g x 的图象6.【2013年山东高考题理】在平面直角坐标系xOy 中,M 为不等式组220210380x y x y x y --≥⎧⎪+-≥⎨⎪+-≤⎩所表示的区域上一动点,则直线OM 斜率的最小值为( )A.2B.C.31-D.21-101.303--=--7.【山东省德州市2013年高三联考】设,,,,a b R ∈则“1a ≥且1b ≥”是“2a 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8.【2014()A. B. C. D.9.【山东省济宁市2013届高三测试】若圆C 与直线0x y -=及40x y --=都相切,圆心在直线0x y +=上,则圆C 的方程为( )A.()()22112x y ++-= B.()()22112x y -+-= C.()()22112x y -++=D.()()22112x y +++=10.【河北省高阳中学2014届高三上学期第一次月考】从6名学生中选3名分别担任数学、物理、化学科代表,若甲、乙2人至少有一人入选,则不同的方法有( )A .40种B .60种C .96种D .120种11.【2013年山东高考题】抛物线1C :221x p y =(p >0)的焦点与双曲线2C :1322=-y x 的右焦点的连线交1C 于第一象限的点M 。
山东省实验中学2011级第三次诊断性测试理综试题(2014.3)本试卷分第I卷(选择题)和第II卷(非选择题)两部分。
满分300分,考试时间150分钟。
可能用到的相对原子质量:O 16 Na 23 S 32 Ba 137第I卷(选择题 107分)二、选择题(本题包括7小题,每小题给出的四个选项中,有的只有一个选项正确,有的有多个选项正确,全部选对的得6分,选对但不全的得3分,有选错的得0分)14.在推导匀变速运动位移公式时,把整个运动过程划分成很多小段,每一小段近似看作匀速直线运动,然后把各小段的位移相加,物理学中把这种研究方法叫做“微元法”.下列几个实例中应用到这一思想方法的是A.在不需要考虑物体本身的大小和形状时,用点来代替物体,即质点B.在“探究弹性势能的表达式”的活动中为计算弹簧弹力所做功,把拉伸弹簧的过程分为很多小段,拉力在每小段可以认为是恒力,用各小段做功的代数和代表弹力在整个过程所做的功C.一个物体受到几个力共同作用产生的效果与某一个力产生的效果相同,这个力叫做那几个力的合力D.在探究加速度与力和质量之间关系时,先保持质量不变探究加速度与力的关系,再保持力不变探究加速度与质量的关系15.2012年伦敦奥运会上中国选手周璐璐在女子75公斤级比赛中以333公斤的总成绩获得冠军,并打破世界纪录。
如图为她挺举时举起187公斤的图片,两臂成120°,周璐璐沿手臂撑的力F及她对地面的压力N的大小分别是(g取10m/s2)A.F=4080N,N=1870N B.F=2620N,N=1870NC.F=1870N,N=4080N D.F=1870N,N=2620N16.我国“蛟龙号”深潜器经过多次试验,终于在2012年6月24日以7020m 深度创下世界最新纪录(国外最深不超过6500m),预示着可以征服全球99.8%的海底世界,假设在某次实验时,深潜器内的显示屏上显示出了从水面开始下潜到最后返回水面10min 内全过程的深度曲线(a)和速度图像(b),如图示则有A .(a)图中致代表本次最大深度,应为6.0mB .潜水器下潜过程的加速度大于返回过程的加速度C .潜水员感到超重现象应发生在3-4min 和6-8min 的时间段内D .潜水器在4-6min 时间段内匀速下潜。
山东省实验中学高三下学期一模考试(4月)英语试卷(后附答案)第Ⅰ卷第一部分听力(共两节,满分30分)第一节(共5小题;每小题1.5分,满分7.5分)听下面5段对话.每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置.听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题.每段对话仅读一遍. 1.What does the woman’s father want her to do? ________A.Teach art. B.Go to art school. C.Study law.2.Where does the man work? ________A.In a hotel. B.In a travel agency. C.At an airport.3.Where is the man going? ________A.To 5th Avenue. B.To 6th Avenue. C.To 8th Avenue.4.What are the speakers mainly talking about? ________A.A visit plan. B.A dinosaur exhibition. C.Their favorite animal.5.Where does the conversation take place? ________A.At a company. B.At a gym. C.At home.第二节(共15小题;每小题1.5分,满分22.5分)听下面5段对话或对白,每段对话或独白后有几个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置,听每段对话或独白前,你将有时间阅读各个小题.每小题5秒钟;听完后,各小题给出5秒钟的作答时间.每段对话或独白读两遍.听第6段材料,回答第6、7题.6.What are the speakers doing? ________A.Watching overseas news.B.Looking at a job advertisement.C.Planning a holiday in a foreign country.7.What does the man mean? ________A.He has no interest in the position.B.He isn’t in need of a holiday now.C.He would like to get a new place.听第7段材料,回答第8、9题.8.What do we know about the man? ________A.He is new in town.B.He will call a taxi for the woman.C.He doesn’t know how to get to the restaurant.9.How will the woman go? ________A.By bus. B.By taxi. C.On foot.听第8段材料,回答第10至12题.10.How did the woman feel when waiting for Tom? ________A.Scared. B.Nervous. C.Excited.1l.What kind of man does the woman like? ________A.One who is interested in sports.B.One who is good-looking.C.One who likes going to the pub.12.Why is the woman dissatisfied with Tom? ________A.He wears glasses. B.He isn’t tall enough. C.They don’t have the same interest. 13.What do the man’s children prefer to do? ________A.Travel by car. B.Play on the beach. C.Stay with the nurse. 14.Where is the man’s family likely to go? ________A.To the south coast. B.To the north coast. C.To the east coast.15.How will the man’s family house themselves during the holiday? ________A.By living in tents. B.By staying at a hotel. C.By borrowing a house. 16.What will the woman discuss with her sister? ________A.Whether to leave the children behind.B.Whether to go to the man’s party on the beach.C.Whether to join the man’s family for the holiday.听第10段材料,回答第17至20题.17.What do Dave and Miranda do on Tuesday afternoons? ________A.They show people how to make kites.B.They teach people to fly kites.C.They give away free kites.18.Why are Dressed to Kill and Togged Up so popular? ________A.The sales assistants are young.B.They offer the lop designer clothes.C.They sell clothes of high quality at low prices.19.When can people buy things at the Flea Market? ________A.On Sunday mornings. B.On Saturday mornings. C.On Tuesday mornings. 20.What should people pay attention to when shopping at the Flea Market? ________A.The price of the things. B.The owner of the things. C.The quality of the things.第二部分阅读理解(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,并在答题卡上将该项涂黑.AEver wondered how your brain works? Join six leading brain scientists to explore what we know about “the most difficult kilo of matter in the universe”.The day will be chaired by psychologist and presenter of BBC Radio 4’s All in the Mind. Claudia Hammond. Speakers:Andrew Jackson-Welcome Trust senior research fellow at the institute of Neuroscience, Newcastle University Peggy St. Jacques-lecturer in psychology and memory research at the University of SussexPlus-4 more leading experts on the brain to be announcedArtists:Morten Kringelbach, Mary Morrell, Andrew Jackson. Peggy St Jacques, Cathy Price, George Mather, Claudia HammondOverview:The brain has long been a source of fascination. Today, this event will introduce you to the evolution of the brain. We’ll study techniques for controlling the brain as well as the latest technologies that allow you to control the outside world using your mind alone.Topics covered will include:●Evolution of the brain●How memory makes US human●Emotion●Sleep and the brainBooking information:●The event will be held in the Brunei Auditorium. And doors to the Auditorium will open at 9:15a. m.●We require the name of each person attending-please ensure this is provided at the time of booking.●The ticket price includes a buffet lunch, as well as morning and afternoon refreshments.●The schedule for the day will be confirmed closer to the event, and will be emailed to all ticket holders.●A minimum of 100 early bird discounted tickets are available priced at£l29(saving£20 on the full ticket price of £149).21.Which of the following is an expert in memory? ________A.Claudia Hammond.B.Peggy St. Jacques.C.Andrew Jackson.D.William Lawrence.22.When you book your tickets, you are required to ________.A.offer your emailB.take your packed lunchC.pay£100 in advanceD.arrive at 9:15 a.m.23.The passage is mainly to ________.A.teach knowledgeB.give adviceC.entertain the readersD.offer informationBIvanka Trump, daughter of US President Donald Trump, has been given her own West Wing office, confirming her position as a key member of her father’s White House team.When she moved to Washington earlier this year, Ivanka said she would not be playing a formal role in the administration.However, it was confirmed that the first daughter now has a West Wing office next to senior adviser Dina Powell, who serves on the National Security Council.Ivanka will get access to classified information and be given security clearance.Ivanka has been a very visible presence during Trump’s first two months in the White House, participating in meetings with Shinzo Abe, the Japanese prime minister, Justin Trudeau, the Canadian prime minister, and Angela Merkel, the German chancellor.Her regular presence has raised eyebrows because she has no official position.Jamie Gorelick, a lawyer and ethics adviser for Ivanka, detailed her new privileges and said she would follow the ethics rules that apply to government employees.24.Where is this passage likely to be read? ________A.Magazine. B.Journal. C.Newspaper. D.Document.25.How long has Ivanka been working in the White House? ________A.Since the beginning this year. B.Since two months ago.C.Since Trump came to power. D.Since she was appointed.26.Who works together with Ivanka in the White House? ________A.Dina Powell. B.Shinzo Abe. C.Justin Trudeau. D.Angela Merkel. 27.Which of the following can replace the underlined words “raised eyebrows”? ________A.drawn attention. B.caused surprise. C.brought anger. D.made argument.CAfter one of his close Family friends known for her generosity died of cancer in 2013,26-year-old Luke Cameron decided to do at least one good deed a day, for 365 days, and he has not missed yet.The Gloucester resident performed his first good deed on January l, 2014 Jvith the simple act of greeting a waitress at a cafe he visited. The next day he bought food and drinks for some homeless people and followed it up by donating coins to a woman, who did not have enough to feed a parking meter.Though most of his kind gestures have been welcomed, Luke says there nave been a few awkward situations. When he was attempting to give away a£20 bill to an elderly lady whose granddaughter was doubtful of his intentions and the time he bought a sausage roll(腊肠卷)for a homeless man, he happened to be a vegetarian.The majority of Luke’s good deeds, which have been recorded in an online diary, have been about helping people with small things. He helped to take out the garbage for an elderly neighbor or helped a disabled lady pick out a dress for a party. However, the young man has also spent close to£4,000 of his own money, buying groceries or gifts for the children in need.To try to encourage others to perform good deeds, Luke has created a deck of cards called “Cards for Kindness”. Each suggests a simple act of kindness-things like giving a stranger a hug or making peace with an enemy. The best pall is that all the money he collects from distributing the cards is donated to the British Heart Foundation, a charity that helps the homeless.Luke’s generosity has not gone unnoticed. To reward the young man, Dominos recently awarded him a year’s supply of free pizza. Not surprisingly, the big-hearted youngster has decided to use the gift to hold special pizza days for charity.28.What inspired Luke to determine to do good deeds? ________A.The death of a generous friend. B.The simple act of a waitress.C.The suffering of homeless people. D.The experience at a parking lot.29.What happened when Luke tried to help the elderly lady? ________A.His kind deed was appreciated. B.She turned out to he a vegetarian.C.She bought a sausage roll tor a homeless man. D.He was misunderstood by her granddaughter. 30.What can we learn about Luke’s good deeds? ________A.He was employed by a British charity. B.He only helped people with small things.C.He encouraged good deeds through cards. D.He raised£4,000 for the children in need. 31.What can be inferred from the last paragraph? ________A.Dominos offered gifts to the charity. B.Luke was not surprised at the Pizza.C.Luke was awarded by the government. D.Luke would donate the pizza to others.DRecently, I had lunch with a young Chinese student who studies at a college in New York. He is very bright and aspiring and I enjoyed our conversation. Still I felt frustrated and useless afterwards because I was not able to provide him with any good news. Graduating at the end of this year, he asked me how he could find a job in this country and fulfill his career dreams.In recent years, students who found a job here after graduation have had to go through a cruel lottery system to obtain their HIB working visa. And the success rates have been declining year after year because of the ever growing number of applicants. Last year, there were 233.000 applicants, and only 30 percent of them were lucky, less than half of the rate in 2013.And it can only become President Donald Trump’s immigration policies in this country aretightening up and this trend will continue for at least the next few years. In this case, foreign students studying social sciences, a field in which starting salaries are rarely above the required amount, car, kiss their visa hopes goodbye.Compared to the older generation of Chinese students, today’s young people no longer consider the US as the only option. Many start to think China offers better opportunities in the longer term.This is not to say that Chinese students in the US are not interested in job opportunities here any more. A few years of work experience in the US can give them leverage when they finally land back in their home country .But if the job opportunities are largely reduced by the tightening of immigration policy, I expect there will be a decline. And if that happens, it is the American economy that will suffer from the loss of those educated, hard-working and talented immigrants.32.The author felt frustrated because ________.A.he was not interested in the talk B.he didn’t fulfill his career dreamsC.he couldn’t provide helpful advice D.he thought the student was useless33.Which of the following statement is NOT true according to the passage? ________A.The lottery system for HIB working visa is too tough.B.Chinese students have no choice but to return to China.C.President Trump is tightening up the immigration policies.D.More and more students are applying for the working visa.34.What does the word “leverage” in paragraph 5 probably mean? ________A.advantage. B.language. C.ability. D.education.35.What is the author’s attitude to the tightening of immigration policy? ________A.doubtful. B.supportive. C.indifferent. D.worried.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.选项中有两项为多余选项.The essential role that mobile devices play in our lives means that we are storing more and more personal data on them. (36)Back it up.Many people lose their phones, have them stolen or damaged every year. (37)You can do this by ‘syncing’ your phone to your laptop. desktop or an external hard drive.(38)Using Wi-Fi in a public place such as a hotel, cafe or bar can expose your data to a network which is not secure. Never use public Wi-Fi connections for confidential transactions like banking and shopping.Check the Wi-Fi network.(39)However, criminals have become skilled at setting up fake Wi-Fi networks which allow them to steal your details. For your own peace of mind, ask somebody who works at the place where you are using the Wi-Fi to confirm that you’re connecting to their network.Check app privacy settings.In your settings menu, check carefully what level of access to your data that these apps have. (40)While this might be useful at times, it may give potential criminals too much detailed information about your whereabouts. Check carefully which apps have access to your location information. If it’s not needed for that app, turn it off.A.Set a password for Wi-Fi.B.Avoid public Wi-Fi for transactions.C.When are way’s to make sure of the data.D.When you’re cut aria about it can be easy to connect to Wi-Fi.E.Some apps allow you to share your location information publicly.F.How can we be certain that this information is as secure as possible?G.So it’s a good idea to make sure the data on your phone is backed up somewhere.第三部分英语知识运用(共两节,满分45分)第一节完形填空(共20小题;每题1.5分,满分30分)阅读下面短文,从短文后各题所给的四个选项(A.B.C和D)中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑.My daughter (now 18)was born with a hemangioma tumor(血管瘤)by her eye. At first it was small and hardly (41).After five months, it became the (42)of a coin. (43)I took her out, people could not (44)their comments to themselves. “Who hit her?” “Is that a bug bite?” I never could think of a(n)(45)response for these people. I was (46)to be kind and understanding, and assumed that other people had also been taught these (47)8.One day I was at the (48)8,with my 3-year-old son, my daughter, and at this time pregnant with my third child. A woman (49)me, I thought here we go (50).She said that God must not have wanted my daughter to (51)him, as he left her with a (52).She went on to say that (53)with these kisses were always surrounded by angels. I was astonished. What a (54).more loving approach to someone with a problem!My daughter will (55)this year from High School. She is beautiful. Her early years were spent in and out of (56).Finally the tumor was removed, because it (57)her vision. It is not noticeable (58)in the bright sun. She spent this year as the dance scholar for our school. She danced for 4 years on our dance-drill team. She had (59)many scholarships. Her life is wonderful. The woman in the mall made me a better parent. Perhaps, this (60)will help make someone else a better parent, too. 41.A.noticeable B.bearable C.recognized D.accepted 42.A.colour B.weight C.size D.width43.A.One day B.Every time C.Later D.Recently 44.A.make B.help C.tell D.hold45.A.exact B.appropriate C.rude D.practical46.A.learned B.brought C.considered D.taught 47.A.qualities B.principles C.questions D.opinions 48.A.party B.office C.mail D.meeting 49.A.approached B.saw C.appreciated D.called50.A.now B.later C.again D.quickly 51.A.understand B.leave C.hate D.remember 52.A.scar B.kiss C.mark D.sign53.A.mothers B.gods C.faces D.babies 54.A.stranger B.cleverer C.kinder D.happier 55.A.develop B.succeed C.graduate D.improve 56.A.hospitals B.schools C.illness D.sight 57.A.blocked B.stopped C.injured D.deepened 58.A.despite B.except C.although D.because59.A.given B.proved C.left D.received 60.A.lesson B.story C.adventure D.tumor第Ⅱ卷第三部分英语知识运用(共两节,满分45分)第二节(共10小题;每小题1.5分,满分15分)阅读下面材料,在空白处填入适当的内容(1个单词)或括号内单词的正确形式.BEIJING·China will establish a new special economic zone in the (61)(heavy)polluted province of Hebei to promote integration(一体化)with (62)neighboring cities of Beijing and Tianjin, the government has announced.The Xiongan New Area will be (63)the same national significance as the Shenzhen Special Economic Zone, (64)helped kick-start China’s economic reforms in 1980,the official Xinhua news agency said, citing a circular released by the Chinese Cabinet.The new special economic zone is (65)(locate)around 100km south-west of Beijing, close to the Hebei provincial capital of Shijiazhuang and will house some of Beijing’s relocated “non-capital functions”. It is currently 100 square kilometers in area (66)will eventually be expanded to 2,000 square kilometers.Beijing, home to 22 million people, (67)(try)to control population growth and relocate industries and other non-capital functions to Hebei in the (68)(come)years as part of its efforts to prevent pollution and crowdedness.The removal of non-capital functions from Beijing is part of a greater strategy to integrate the development of Beijing, Tianjin and Hebei for a better economic structure, (69)(clean)environment and improved public (70)(serve).第四部分写作(共两节,满分35分)第一节短文改错(共10小题,每小题1分,满分10分)假定英语课上老师要求同桌之间交换修改作文,请你修改你同桌写的以下短文.短文中共有10处错误,每句中最多有两处.错误涉及一个单词的增加、删除或修改.增加:在缺词处加一个漏字符号(∧),并在此符号下面写出该加的词.删除:把多余的词用斜线(\)划掉.修改:在错的词下划一横线,并在该词下面写出修改后的词.注意:1.每处错误及其修改均仅限一词;2.只允许修改10处,多者(从第11处起)不计分.Dear Stella,Thank you very much for your congratulation! I do be satisfied with myself in English learning. Not only can I find easy to understand English, but I can also speak English fluent. What’s more, I can read and write English well.I am happy to say my efforts have been paid off.When if comes for your Chinese learning, I really have some suggestions, that, I think, will be helpful to you. Firstly, find more chances to listen more and speak more, or you will find it easier to learn Chinese. Secondly, learning as many Chinese characters as you can so that you can do more reading and writing. Thirdly, no pains, no gains. As long as you devote myself to learning you were sure to make great progress.Best wishes!Li Hua 第二节书面表达(25分)假如你韩梅梅,是一名中学生,你的美国网友Sara喜欢排球,而且是郎平的粉丝.她发E-mail给你想了解中国学生对中国女排和教练郎平的印象,请你给她回一封E-mail, 包括以下内容:1.中国中学生也喜欢女排和郎平教练;2.简要介绍中国女排和女排精神.要求:1.词数100左右;2.可以适当增加细节,以使文章通顺.山东省实验中学高三下学期一模考试(4月)英语试卷答案1~5.CBAAB 6~10.BACBB 11~15.ACBAC 16~20.CACAC21~25.BADCC 26~30.ABADC 31~35.DCBAD 36~40.FGBDE41~45.ACBDB 46~50.DACAC 51~55.BBDCC 56~60.AABDB 61.heavily62.the63.of64.which65.located66.but67.is trying /tries68.coming69.cleaner70.service(s)短文改错Dear Stella,Thank you very much for your congratulation! I do be satisfied with myself in English learning. Not only can Icongratulationsfind ∧easy to understand English, but I can also speak English fluent. What's more, I can read and write English it fluentlywell. I am happy to say my efforts have been(去掉)paid off.When if comes for your Chinese learning, I really have some suggestions, that, I think, will be helpful to you.To whichFirstly, find more chances to listen more and speak more, or you will find it easier to learn Chinese. Secondly, learningAnd learn as many Chinese characters as you can so that you can do more reading and writing. Thirdly, no pains, no gains. As long as you devote myself to learning you were sure to make great progress.Yourself areBest wishes!Li Hua 书面表达Dear Sara,I am much delighted to learn that you like the sport of playing volleyball and you are a fan of Lang Ping, head coach of the Chinese Women’s Volleyball Team. Just like you, we are big fans of her and she is our idol.The team first won the world championship in the early 1980s, since when it has made one miracle after another. Consequently, the Chinese people are greatly inspired by the players. As a former player and present coach, Lang Ping has won the love and respect from the people of all ages. The spirits of the team, going all out and winning honor for the country, have encouraged several Chinese generations.We are proud of Lang Ping and often model ourselves on the team.Han Meimei。
山东省实验中学2014届高三第一次模拟考试英语试题(2014.3)第I卷(选择题 105分)第一部分英语知识运用(共两节,满分55分)第一节单项填空(共l0小题;每小题l.5分,满分10分)从A B C D四个选项中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑1.—What about __________ lecture yesterday?—Well,__________ most boring one indeed.A./;theB. the;aC. the; theD./;a2.The haze or smog was so serious that the winter running _________.Some students complained as they ranA. could have cancelledB. should have cancelledC. must have been cancelledD. ought to have been cancelled3. It will be about 100 days __________the College Enhance Examination comes.A. whenB. asC. beforeD. since【答案】C【解析】试题分析:考查连词。
本题考查it will … before …句型,表示“还有……就……”。
句意:还有大约100天就要高考了。
故C正确。
考点:考查连词4.Word came that Chinese sports delegation has won 9 medals in the 2014 Winter Olympics in Sochi,Russia, __________the 12th of the medal list.A. rankingB. rankedC. to rankD. having ranked5. Last night on my way home I saw an old lady driving a BMW car at __________I thought was a dangerous speed.A. thatB. whichC. whatD. how6.—Mum, shall I watch the TV program Happy Camp today?—__________.You have so much homework to do!A. Forget itB. Not at allC. Go aheadD. That’s rig ht【答案】A【解析】试题分析:考查交际用语。
理综试题(2014.3)本试卷分第I卷(选择题)和第II卷(非选择题)两部分。
满分300分,考试时间150分钟。
可能用到的相对原子质量:O 16 Na 23 S 32 Ba 137第I卷(选择题 107分)一、选择题(本题共13小题,每小题5分。
在每个小题给出的四个选项中,只有一项是符合题目要求的。
)1.下列有关生物学实验的叙述正确的是A.观察细胞中的脂肪、染色体、叶绿体、线粒体等物质或结构都需要染色B.观察洋葱根尖细胞有丝分裂实验过程为取材→解离→漂洗→染色→制片→观察C.探究温度对酶活性的影响时最好选用过氧化氢酶作实验材料D.用洋葱鳞片叶做“色素提取和分离的实验”应用丙酮等有机溶剂做提取液2.下列有关物质的合成和运输途径,可能存在于造血干细胞中的是A.吸收葡萄糖:细胞膜→细胞质基质→线粒体B.合成血红蛋白:核糖体→内质网→高尔基体→细胞膜C.转录mRNA:细胞核→细胞质基质→核糖体D.合成DNA聚合酶:细胞核→细胞质基质→线粒体3.甲磺酸乙酯(EMS)能使鸟嘌呤变成7-乙基鸟瞟呤,后者不与胞嘧啶配对而与胸腺嘧啶配对。
为获得更多的水稻变异类型,育种专家常用适宜浓度的EMS溶液浸泡种子后再进行大田种植。
下列叙述正确的是A.EMS的处理可使种了基因重组的频率提高B.EMS的处理可使DNA分子的热稳定性提高C.获得的变异植株其细胞核DNA的嘌呤含量高于嘧啶D.EMS的处理可使种子的基因型发生改变4.下列关于生物进化的叙述正确的是A.自然选择的实质是保留种群的有利基因,不决定新基因的产生B.地理隔离不会导致种群基因库间的差异,不一定导致生殖隔离C.自然选择过程中,直接受选择的是基因型,进而导致基因频率的改变D.基因突变的方向、自然选择的方向和生物进化的方向总是一致5.植物越冬休眠和夏天生长受多种激素的调节,如下图所示,有关叙述正确的是A.越冬休眠时,植物体内的赤霉素和脱落酸的含量都会增加B.秋末①→③→⑤过程能增加叶肉细胞内的胡萝卜素含量,提高光合作用速率C.夏季①→③→④过程能增加植物体内细胞分裂素含量,促进植物生长D.各种植物激素通过直接参与细胞内的代谢过程实现对生命活动的调节6.B淋巴细胞在免疫系统中会发生两次选择:在骨髓中分化时经历第一次选择,凡是不能识别自身抗原的B淋巴细胞会凋亡,保留下来的B淋巴细胞一般不会对自身抗原产生免疫应答;在外周免疫系统中,B淋巴细胞识别特异性外来抗原后发生第二次选择.凡是能表达高亲和力抗原识别受体的保留下来,其余的几天后死亡。
英语动词时态与语态试题答案及解析1. Across the Yangtze River _____ more than one bridge, the Nanjing Changjiang Bridge being the first one.A.lay B.lie C.lies D.laid【答案】C【解析】考查时态和倒装句:句意:不止一座桥横跨长江,南京长江大桥是第一个。
动词用位于“lie”,因为是客观事实,所以是一般现在时,排除AD,这句话是地点状语Across the Yangtze River提前,用完全倒装,主语是more than one bridge,谓语是单数,选C。
【考点】考查时态和倒装句2.(2014届山东省实验中学高三第一次模拟考试(三诊))Camacho,the former Chinese football coach,__________ in China between 2011 and 2013 A.have worked B.worked C.had worked D.works【答案】B【解析】考查时态。
根据句中时间状语between 2011 and 2013,本题用一般过去时,陈述过去的事实。
句意:卡马乔,前中国足球教练,于2011年到2013年在中国工作。
故B正确。
3. (2013·辽宁,22)He was unhappy when he sold his guitar.After all, he ________ it for a very long time.A.has had B.had hadC.has D.had【答案】B【解析】考查时态的用法。
句意:他卖吉他时很不高兴,毕竟,他拥有这把吉他很久了。
由句意可知,“拥有”这一动作,发生在“卖吉他”这一动作之前,“卖吉他”用了一般过去时,“拥有”这一动作是发生在“过去的过去”,故用过去完成时。
山东省实验中学2014届高三下学期第一次模拟测试数学文
试题
(2014.3)
第I 卷(选择题 50分)
一、选择题:本大题共10小题,每小题5分,共50分.在每小题列出的四个选项中,选出符合题目要求的一项.
1.已知i 为虚数单位,复数212,21i z a i z z z =+=-=,且,则实数a 的值为
A.2
B.2-
C.2或2-
D.20±或
2.已知全集{}{}
()2=12,680,U U R A x x B x x x C A B =->=-+<⋂,且则等于 A.[)14-,
B.(]23,
C.()23,
D.()14-, 3.cos sin cos sin 12121212ππππ⎛
⎫⎛⎫-+ ⎪⎪⎝⎭⎝⎭
的值为
A.2-
B.12-
C.12
D.2
4.若一个几何体的三视图如右图所示,则它的体积为 A.12 B.32 C.1 D.13
5.已知x 、y 的取值如下表所示:若y 与x 线性相关,且
0.95y x a ∧
=+,则a 的值为
A.2.2
B.2.9
C.2.8
D.2.6
6.下列结论错误..
的是 A.命题“若2
3404x x x --==,则”的逆否命题为“若24,340x x x ≠--≠则” B.“4x =”是“2340x x --=”的充分条件
C.命题“若200m x x m >+-=,则方程有实根”的逆命题为真命题
D.命题“若2200=0m n m n +==,则且”的否命题是“若220.m n +≠则0m ≠或0n ≠”
7.设,z x y x y =+,其中实数满足200,0x y x y y k +≥⎧⎪-≤⎨⎪≤≤⎩
,若z 的最大值为12,则z 的最小值为
A.3-
B.6-
C.3
D.6
8.已知ABC ∆的三边长为a 、b 、c ,满足直线2201ax by c x y ++=+=与圆相离,则ABC ∆是
A.锐角三角形
B.直角三角形
C.钝角三角形
D.以上情况都有可 9.抛物线212y x =-的准线与双曲线22
193
x y -=的两条渐近线所围成的三角形的面积等于
A.
B. C.2
10.已知函数()()()()
()21010x x f x f x x a f x x -⎧-≤⎪==+⎨->⎪⎩,若方程有且只有两个不相等的实数根,则实数a 的取值范围为
A.(],0-∞
B.[)0,1
C.(),1-∞
D.[)0,+∞
二、填空题:本大题共5小题,每小题5分,共25分.
11.已知向量()
,,2,2,a b a b a b a ==-⊥满足,则向量a b 与的夹角为_______.
12.如果执行右边的框图,输入N=5,则输出的数等于
_________.
13.若ABC ∆三边长a,b,c 满足等式
()()a b c a b c ab +-++=,则角C 的大小为_______.
14.已知数列{}12132143211121231234n a ⋅⋅⋅为:,,,,,,,,,,,依它
的前10项的规律,则50a =___.
15.若函数()y f x =是奇函数,则()y f x =的图像关于y
轴对称;②若函数()f x 对任意()()()
121f x x R f x f x -∈+=+满足,则4是函数()f x 的一个周期;③若log 3log 30,0m n m n <<<<<1则;④若()[)1x a f x e -=+∞在
,上是增函数,
则1a ≤.其中正确命题的序号是________.
三、解答题:本大题共6小题,共75分.解答应写出文字说明,演算步骤或证明过程.
16.(本小题满分12分)
已知函数()()cos sin 244f x x x x πππ⎛
⎫⎛⎫=++-+ ⎪ ⎪⎝⎭⎝
⎭. (I )求函数()f x 的最小正周期和单调递增区间;
(II )若将()f x 的图象向右平移12
π个单位,得到函数()g x 的图象,求函数()g x 在区间0,2π⎡⎤⎢⎥⎣⎦
上的最大值和最小值.
17.(本小题满分12分)
对山东省实验中学高三年级学生参加社区服务次数进行统计,随机抽取M 名学生作样本,得到这M 名学生参加社区服务的次数,根据此数据作出了频数与频率的统计表和频率分布直方图如图:
(I )求出表中M ,p 及图中a 的值;
(II )在所取样本中,从参加社区服务的次数不少于20次的学生中任选2人,求两人来自同一小组的概率.
18.(本小题满分12分)
如图,点C 是以AB 为直径的圆上一点,直角梯形BCDE 所在平面与圆O 所在的平面垂直,且DE//BC ,1,2, 3.2
DC BC DE BC AC CD ⊥====
(I )证明:EO//平面ACD ;
(II )证明:平面ACD ⊥平面BCDE ;
(III )求三棱锥E-ABD 的体积.
19.(本小题满分12分)
已知等差数列{}250,,n a d a a >的公差且是方程{}2
12270n x x b -+=的两根,数列的前n 项和为()
*11,3,23.n n n T b b T n N +==+∈且满足
(I )求数列{}n a ,{}n b 的通项公式;
(II )设数列{}n c 满足,n n n
a c
b =
,求数列{}n c 的前n 项和.n M
20.(本小题满分13分) 已知椭圆()22
22:10x y C a b a b
+=>>
构成等腰直角三角形.
(I )求椭圆C 的标准方程.
(II )过点()2,0P l C A B
-作直线与椭圆交于、两点,求1AF B ∆的面积的最大值.
21.(本小题满分14分)
已知函数()()211ln 2
f x x ax a x =-+-. (I )函数()()()
22f x f 在点,处的切线与30x y ++=平行,求a 的值; (II )讨论函数()f x 的单调性;
(III )对于任意()()()12121221,0,,,x x x x f x f x x x ∈+∞>->-有,求实数a 的范围.。