【英语】江苏省清江中学2014-2015学年高二下学期周练

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【数学】江苏省清江中学2014-2015学年高二下学期期中考试(文)

【数学】江苏省清江中学2014-2015学年高二下学期期中考试(文)

江苏省清江中学2014-2015学年高二下学期期中考试(文)一、填空题:本大题共14小题,每小题5分,计70分.不需写出解答过程,请把答案写在答题纸的指定位置上.1.命题“4>∀x ,162>x ”的否定是 . 2.已知⎪⎭⎫⎝⎛<<=2053cos πx x ,则x 2sin 的值为_________. 3.“4πα=” 是“tan 1α=”的 条件. (填“充分不必要”、“必要不充分”、“充要”或“既不充分也不必要”)4.若函数()f x ,则()f x 的定义域是 .5.用反证法证明某命题时,对结论“自然数,,a b c 至少有1个偶数”的正确假设为 “ ”.6.在实数等比数列{}n a 中,10a >,若243546225a a a a a a ++=,则35a a += . 7.已知向量)3,(x x -=,)3,1(x --=,若b a //,则x =8.已知实数,x y 满足20,0,1,x y x y x -+≥⎧⎪+≥⎨⎪≤⎩则2z x y =+的最小值为 .9.一元二次不等式210ax bx +->的解集为1{|1}3x x <<,则a b += 10.函数22ln y x x =-的最小值是 11.已知函数1y x =的图象的对称中心为(0,0),函数111y x x =++的图象的对称中心为1(,0)2-,函数11112y x x x =++++的图象的对称中心为(1,0)-,……,由此推测,函数111112y x x x x n=+++++++的图象的对称中心为 . 12.已知正数x 、y 满足1x y +=,则1ax y+的最小值是9,则正数a 的值为 13.已知函数f (x )=⎩⎨⎧+--ax a a e x 2)21(2 00>≤x x 对任意x 1≠x 2,都有0)()(2121>--x x x f x f 成立,则实数a 的取值范围是14.已知等差数列{}n a 的首项a 1及公差d 都是实数,且满足23242029S S S ++=,则d 的取值范围是 .二、解答题:本大题共6小题,计90分.解答应写出必要的文字说明,证明过程或演算步骤,请把答案写在答题纸的指定区域内.15.已知A 、B 、C 为ABC ∆的内角,向量)sin ,(sin B A =,)cos ,(cos A B =,且C 2sin =⋅,(Ⅰ)求角C 的大小;(Ⅱ)若A sin ,C sin ,B sin 成等差数列,且18)(=-⋅AC AB CA ,求AB 的长.16.解关于x 的不等式:① 2121≥--x x ; ② (2mx-1)(x-2)<0(m 为实常数)17. 如图,在半径为cm 30的41圆形(O 为圆心)铝皮上截取一块矩形材料OABC ,其中点B 在圆弧上,点A 、C 在两半径上,现将此矩形铝皮OABC 卷成一个以AB 为母线的圆柱形罐子的侧面(不计剪裁和拼接损耗),设矩形的边长xcm AB =,圆柱的体积为3Vcm . (1)写出体积V 关于x 的函数关系式;(2)当x 为何值时,才能使做出的圆柱形罐子体积V 最大?并求出最大值。

江苏省清江中学2014-2015学年高二下学期期中考试数学(文)试题

江苏省清江中学2014-2015学年高二下学期期中考试数学(文)试题

江苏省清江中学2014—2015学年度第二学期期中考试高二数学试卷(文科)时间:120分钟 满分:160分一、填空题:本大题共14小题,每小题5分,计70分.不需写出解答过程,请把答案写在答题纸的指定位置上.1.命题“4>∀x ,162>x ”的否定是 ▲ . 2.已知⎪⎭⎫⎝⎛<<=2053cos πx x ,则x 2sin 的值为____▲_____. 3.“4πα=” 是“tan 1α=”的 ▲ 条件.(填“充分不必要”、“必要不充分”、“充要”或“既不充分也不必要”)4.若函数()f x =,则()f x 的定义域是 ▲ .5.用反证法证明某命题时,对结论“自然数,,a b c 至少有1个偶数”的正确假设为 “ ▲ ”.6.在实数等比数列{}n a 中,10a >,若243546225a a a a a a ++=,则35a a += ▲ . 7.已知向量)3,(x x -=,)3,1(x --=,若//,则x = ▲8.已知实数,x y 满足20,0,1,x y x y x -+≥⎧⎪+≥⎨⎪≤⎩则2z x y =+的最小值为 ▲ .9.一元二次不等式210ax bx +->的解集为1{|1}3x x <<,则a b += ▲ 10.函数22ln y x x =-的最小值是 ▲ 11.已知函数1y x =的图象的对称中心为(0,0),函数111y x x =++的图象的对称中心为1(,0)2-,函数11112y x x x =++++的图象的对称中心为(1,0)-,……,由此推测,函数111112y x x x x n=+++++++的图象的对称中心为 ▲ . 12.已知正数x 、y 满足1x y +=,则1ax y+的最小值是9,则正数a 的值为 ▲13.已知函数f (x )=⎩⎨⎧+--ax a a e x 2)21(2 00>≤x x 对任意x 1≠x 2,都有0)()(2121>--x x x f x f 成立,则实数a 的取值范围是 ▲14.已知等差数列{}n a 的首项a 1及公差d 都是实数,且满足23242029S S S ++=,则d 的取值范围是▲ .二、解答题:本大题共6小题,计90分.解答应写出必要的文字说明,证明过程或演算步骤,请把答案写在答题纸的指定区域内.15.已知A 、B 、C 为ABC ∆的内角,向量)sin ,(sin B A =,)cos ,(cos A B =,且C 2sin =⋅, (Ⅰ)求角C 的大小;(Ⅱ)若A sin ,C sin ,B sin 成等差数列,且18)(=-⋅,求AB 的长.16.解关于x 的不等式:① 2121≥--x x ; ② (2mx-1)(x-2)<0(m 为实常数)17. 如图,在半径为cm 30的41圆形(O 为圆心)铝皮上截取一块矩形材料OABC ,其中点B 在圆弧上,点A 、C 在两半径上,现将此矩形铝皮OABC 卷成一个以AB 为母线的圆柱形罐子的侧面(不计剪裁和拼接损耗),设矩形的边长xcm AB =,圆柱的体积为3Vcm . (1)写出体积V 关于x 的函数关系式;(2)当x 为何值时,才能使做出的圆柱形罐子体积V最大?并求出最大值。

清江中学2014-2015学年高二下学期期中考试数学试题及答案(文)

清江中学2014-2015学年高二下学期期中考试数学试题及答案(文)

江苏省清江中学2014-2015学年高二下学期期中考试(文)一、填空题:本大题共14小题,每小题5分,计70分.不需写出解答过程,请把答案写在答题纸的指定位置上.1.命题“4>∀x ,162>x ”的否定是 . 2.已知⎪⎭⎫⎝⎛<<=2053cos πx x ,则x 2sin 的值为_________. 3.“4πα=” 是“tan 1α=”的 条件. (填“充分不必要”、“必要不充分”、“充要”或“既不充分也不必要”)4.若函数()f x ,则()f x 的定义域是 .5.用反证法证明某命题时,对结论“自然数,,a b c 至少有1个偶数”的正确假设为 “ ”.6.在实数等比数列{}n a 中,10a >,若243546225a a a a a a ++=,则35a a += . 7.已知向量)3,(x x -=,)3,1(x --=,若b a //,则x =8.已知实数,x y 满足20,0,1,x y x y x -+≥⎧⎪+≥⎨⎪≤⎩则2z x y =+的最小值为 .9.一元二次不等式210ax bx +->的解集为1{|1}3x x <<,则a b += 10.函数22ln y x x =-的最小值是 11.已知函数1y x =的图象的对称中心为(0,0),函数111y x x =++的图象的对称中心为1(,0)2-,函数11112y x x x =++++的图象的对称中心为(1,0)-,……,由此推测,函数111112y x x x x n=+++++++的图象的对称中心为 . 12.已知正数x 、y 满足1x y +=,则1ax y+的最小值是9,则正数a 的值为 13.已知函数f (x )=⎩⎨⎧+--ax a a e x 2)21(2 00>≤x x 对任意x 1≠x 2,都有0)()(2121>--x x x f x f 成立,则实数a 的取值范围是14.已知等差数列{}n a 的首项a 1及公差d 都是实数,且满足23242029S S S ++=,则d 的取值范围是 .二、解答题:本大题共6小题,计90分.解答应写出必要的文字说明,证明过程或演算步骤,请把答案写在答题纸的指定区域内.15.已知A 、B 、C 为ABC ∆的内角,向量)sin ,(sin B A =,)cos ,(cos A B =,且C 2sin =⋅,(Ⅰ)求角C 的大小;(Ⅱ)若A sin ,C sin ,B sin 成等差数列,且18)(=-⋅AC AB CA ,求AB 的长.16.解关于x 的不等式:① 2121≥--x x ; ② (2mx-1)(x-2)<0(m 为实常数)17. 如图,在半径为cm 30的41圆形(O 为圆心)铝皮上截取一块矩形材料OABC ,其中点B 在圆弧上,点A 、C 在两半径上,现将此矩形铝皮OABC 卷成一个以AB 为母线的圆柱形罐子的侧面(不计剪裁和拼接损耗),设矩形的边长xcm AB =,圆柱的体积为3Vcm . (1)写出体积V 关于x 的函数关系式;(2)当x 为何值时,才能使做出的圆柱形罐子体积V 最大?并求出最大值。

江苏省清江中学2014-2015学年高一上学期期末考试英语试题 Word版含答案

江苏省清江中学2014-2015学年高一上学期期末考试英语试题 Word版含答案

江苏省清江中学2014-2015学年高一上学期期末考试英语试题时间:120分钟满分120分第I卷选择题(共三部分,共计85分)第一部分:听力 (共两节,满分20分)第一节 (共5小题;每小题1分,满分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. When will the music class begin on Tuesday?A. At 8:00 a.m.B. At 9:00 a.m.C. At 9:00 p.m.2. What does the man like best?A. Hiking.B. Playing basketball.C. Reading.3. What is the woman doing?A. Driving.B. Running.C. Cycling.4. Where are the speakers?A. In a post office.B. In a police station.C. In a university.5. What are the speakers talking about?A. A book.B. Some clothes.C. A fashion designer. 第二节(共15小题;每小题1分,满分15分)听下面5段对话或独白。

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,各小题将给出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至8题。

6. What does the man invite the woman to do tomorrow?A. Go to a concert.B. Watch a sports match.C. Visit a painting show.7. What does the man like better?A. Painting.B. Music.C. Singing.8. Where will the woman go first?A. The school theatre.B. The school hall.C. The school playground.听第7段材料,回答第9至10 题。

江苏省清江中学2014-2015学年高二下学期期中考试数学(理)试题

江苏省清江中学2014-2015学年高二下学期期中考试数学(理)试题

江苏省清江中学2014—2015学年度第二学期期中考试高二数学试卷(理科)时间:120分钟 满分:160分一、填空题:本大题共14小题,每小题5分,计70分.不需写出解答过程,请把答案写在答题纸的指定位置上.1.计算:3828C C += ▲ .(用数字作答) 2.二项式(3x x2-)8的展开式中第7项的二项式系数为 ▲ (用数字作答) 3.在矩阵1021⎡⎤⎢⎥⎣⎦变换下,点A (2,1)将会转换成 ▲4.已知向量),5,2(),1,0,(2t t =-=,若⊥,则t= ▲ . 5.在极坐标系中,圆2sin ρθ=(02θπ<≤)的圆心的极坐标为 ▲ .6.已知矩阵M=⎥⎦⎤⎢⎣⎡2263,则M 的特征值为 ▲ .7.从1,2,3,4,5,6中选出3个不同的数组成3位数,并将这些三位数由小到大打排 列,则第100个数是 ▲8.将参数方程()2()t t t tx e et y e e --⎧=+⎪⎨=-⎪⎩为参数化为普通方程,结果为 ▲ 9.已知随机变量X 的概率分布如下表所示,且其数学期望E (X )=2,则随机变量X 的方差是 _ __▲____ .10.某小组有4名男生,3名女生.若从男,女生中各选2人,组成一个小合唱队,要求站成一排且2名女生不相邻,共有 ▲ 种不同的排法? 11.555555+除以8余数是 ▲12.一袋中装有5个白球,3个红球,现从袋中往外取球,每次取出一个,取出后记下球的颜色,然后放回,直到红球出现10次停止,设停止时,取球次数为随机变量X,则==)12(X P ▲ (只需列式,不需计算结果). 13.已知直线113:()24x tl t y t =+⎧⎨=-⎩为参数与直线2:245l x y -=相交于点B ,又点(1,2)A ,则AB = ▲14.已知数列{}n a 满足11a =,11()2n n n a a -+=(2)n ≥,212222n n n S a a a =⋅+⋅++⋅,类比课本中推导等比数列前n 项和公式的方法,可求得132n n n S a +-⋅= ▲二、解答题:本大题共6小题,计90分.解答应写出必要的文字说明,证明过程或演算步骤,请把答案写在答题纸的指定区域内. 15.已知直线l 的参数方程:⎩⎨⎧+==,21,t y t x (t 为参数)和曲线C 的极坐标方程:⎪⎭⎫ ⎝⎛+=4sin 22πθρ。

江苏省清江中学2014-2015学年高二数学 午练练习(34)苏教版

江苏省清江中学2014-2015学年高二数学 午练练习(34)苏教版

午练练习(34)1.⎩⎨⎧≤->-063012x x 的解集为A,全集U=R, 则=A C R _____. 2 .cos43°cos77°+sin43°cos167°的值为 .3. 已知8)(35-++=bx ax x x f 且10)2(=-f ,那么=)2(f _____________ 4.已知函数()f x 是定义在[,0)(0,]e e -⋃上的奇函数,当[,0)x e ∈-时,()ln()f x ax x =+-,则当(0,]x e ∈时,()f x = .5.在平面直角坐标系中, 不等式组⎩⎪⎨⎪⎧x +y ≥0x -y +4≥0x ≤a (a 为常数)表示的平面区域面积是9,那么实数a 的值为 .6、若()π,0∈A ,且137cos sin =+A A ,则=-+A A A A cos 7sin 15cos 4sin 5___ .7.在公差不为零的等差数列{}n a 中,有23711220a a a -+=,数列{}n b 是等比数列,且77b a =,则68b b = .8.将函数y=f(x)sinx 的图象向右平移4π个单位,再作关于x 轴的对称曲线,得到函数y=1-2sin2x 的图象,则f(x)是 .9.定义在[-1,1]上的奇函数f(x),已知当x ∈[-l ,0]时,1()()42x x a f x a R =-∈.(1)写出f(x)在[0,1]上的解析式;(2)求f(x)在[0,1]上的最大值;(3)若f(x)是[0,1]上的增函数,求实数a 的取值范围.(34)参考答案 1.()+∞⎥⎦⎤ ⎝⎛∞-,221, 2 .12- 3. 26- 4. ln ax x - 5. 1 6、438 7. 16 8. 2cosx9.(1)设[]0,1x ∈,则[]1,0x -∈-,1()42()42x x x x a f x a f x ---=-=-⋅=-∴()24x x f x a =⋅-,[]0,1x ∈(2)()24x x f x a =⋅-,[]0,1x ∈,令[]2,1,2x t t =∈,222()()24a a g t at t t =-=--+ max 2max max a 1,a 2,()(1)1;2a 12,()();2242,()(2)24;a 2g t g a a a g t g a g t g a ≤≤==-<<==≥≥==-≤当即当即2<a<4时,当即a 4时,综上:当时,f(x)最大值为a-1,当2<a<4时,f(x)最大值为2a-4(3)因为函数f(x)在[0,1]上是增函数,所以'()ln 22ln 442ln 2(22)0,x x x x f x a a =⋅-⋅=-⋅≥∴220x a -⋅≥恒成立,22x a ≥⋅,[]21,2x ∈,则4a ≥]211[4211]211[2n n -=--。

2014-2015年江苏省淮安市清江中学高二(下)期中数学试卷(文科)和答案

2014-2015学年江苏省淮安市清江中学高二(下)期中数学试卷(文科)一、填空题:本大题共14小题,每小题5分,计70分.不需写出解答过程,请把答案写在答题纸的指定位置上.1.(5分)命题“∀x>4,x2>16”的否定是.2.(5分)已知cos x=(0<x<),则sin2x的值为.3.(5分)“α=”是“tanα=1”的条件.(填“充分不必要”、“必要不充分”、“充要”或“既不充分也不必要”)4.(5分)若函数,则f(x)的定义域是.5.(5分)用反证法证明时,对结论“自然数a,b,c至少有1个为偶数”的正确假设为.6.(5分)在等比数列{a n}中,若a1>0,a2a4+2a3a5+a4a6=25,则a3+a5=.7.(5分)已知向量,,若,则x=.8.(5分)已知实数x,y满足,则z=2x+y的最小值是.9.(5分)一元二次不等式ax2+bx﹣1>0的解集为{x|<x<1},则a+b=.10.(5分)函数y=2x2﹣lnx的最小值是.11.(5分)已知函数的图象的对称中心为(0,0),函数的图象的对称中心为,函数的图象的对称中心为(﹣1,0),…,由此推测,函数的图象的对称中心为.12.(5分)已知正实数x,y满足x+y=1,若的最小值为9,则正数a=.13.(5分)已知函数f(x)=对任意x1≠x2,都有>0成立,则实数a的取值范围是..14.(5分)已知等差数列{a n}的首项a1及公差d都是实数,且满足,则d的取值范围是.二、解答题:本大题共6小题,计90分.解答应写出必要的文字说明,证明过程或演算步骤,请把答案写在答题纸的指定区域内.15.(14分)已知向量=(sin A,sin B),=(cos B,cos A),=sin2C,其中A、B、C为△ABC的内角.(Ⅰ)求角C的大小;(Ⅱ)若sin A,sin C,sin B成等差数列,且,求AB的长.16.(14分)解关于x的不等式:①;②(2mx﹣1)(x﹣2)<0(m 为实常数)17.(14分)如图,在半径为3m的圆形(O为圆心)铝皮上截取一块矩形材料OABC,其中点B在圆弧上,点A、C在两半径上,现将此矩形铝皮OABC 卷成一个以AB为母线的圆柱形罐子的侧面(不计剪裁和拼接损耗),设矩形的边长AB=xm,圆柱的体积为Vm3.(1)写出体积V关于x的函数关系式,并指出定义域;(2)当x为何值时,才能使做出的圆柱形罐子体积V最大?最大体积是多少?18.(16分)已知函数f(x)=x+(x>0)的最小最小值为,设点P是函数图象上的任意一点,过点P分别作直线y=x和y轴的垂线,垂足分别为M、N.(1)求a的值;(2)问:PM•PN是否为定值?若是,则求出该定值,若不是,请说明理由;(3)设O为坐标原点,求四边形OMPN面积的最小值.19.(16分)已知函数.(1)若函数f(x)的图象在点(2,f(2))处的切线方程为9x﹣y+b=0,求实数a,b的值;(2)若a≤0,求f(x)的单调减区间;(3)对一切实数a∈(0,1),求f(x)的极小值的最大值.20.(16分)已知等差数列{a n} 中,a3=7,a1+a2+a3=12,令b n=a n•a n+1,数列{}的前n项和为T n.(1)求数列{a n}的通项公式;(2)求证:T n<;(3)是否存在正整数m,n,且1<m<n,使得T1,T m,T n成等比数列?若存在,求出m,n的值,若不存在,请说明理由.2014-2015学年江苏省淮安市清江中学高二(下)期中数学试卷(文科)参考答案与试题解析一、填空题:本大题共14小题,每小题5分,计70分.不需写出解答过程,请把答案写在答题纸的指定位置上.1.(5分)命题“∀x >4,x 2>16”的否定是 ∃x >4,x 2≤16 .【解答】解:因为全称命题的否定是特称命题,所以,命题“∀x >4,x 2>16”的否定是:∃x >4,x 2≤16. 故答案为:∃x >4,x 2≤16;2.(5分)已知cos x =(0<x <),则sin2x 的值为 .【解答】解:∵cos x =,x ∈(0,),∴sin x =,∴sin2x =2sin x cos x =,故答案为:.3.(5分)“α=”是“tan α=1”的 充分不必要 条件.(填“充分不必要”、“必要不充分”、“充要”或“既 不充分也不必要”) 【解答】解:时,tan α=1;tan α=1时,,所以不一定得到;∴是tan α=1的充分不必要条件.故答案为:充分不必要. 4.(5分)若函数,则f (x )的定义域是 [﹣1,0)∪(0,1] .【解答】解:∵函数,则有 .解得﹣1≤x ≤1且x ≠0,故函数的定义域为[﹣1,0)∪(0,1],故答案为[﹣1,0)∪(0,1].5.(5分)用反证法证明时,对结论“自然数a,b,c至少有1个为偶数”的正确假设为a,b,c都是奇数.【解答】解:用反证法法证明数学命题时,应先假设要证的命题的反面成立,即要证的命题的否定成立,而命题:“自然数a,b,c中至少有一个是偶数”的否定为:“a,b,c都是奇数”,故答案为:a,b,c都是奇数.6.(5分)在等比数列{a n}中,若a1>0,a2a4+2a3a5+a4a6=25,则a3+a5=5.【解答】解:∵{a n}是等比数列,且a1>0,a2a4+2a3a5+a4a6=25,∴a32+2a3a5+a52=25,即(a3+a5)2=25.再由a3=a1•q2>0,a5=a1•q4>0,q为公比,可得a3+a5=5,故答案为:5.7.(5分)已知向量,,若,则x=3或﹣1.【解答】解:向量,,若,可得﹣(3﹣x)=x(3﹣x),解得x=3或﹣1.故答案为:3或﹣1.8.(5分)已知实数x,y满足,则z=2x+y的最小值是﹣1.【解答】解:画出可行域,得在直线x﹣y+2=0与直线x+y=0的交点A(﹣1,1)处,目标函数z=2x+y的最小值为﹣1.故答案为﹣1.9.(5分)一元二次不等式ax2+bx﹣1>0的解集为{x|<x<1},则a+b=1.【解答】解:由题意知,、1是方程ax2+bx﹣1=0的两根,且a<0,所以,解得,所以a+b=(﹣3)+4=1,故答案为:1.10.(5分)函数y=2x2﹣lnx的最小值是+ln2.【解答】解:函数y=2x2﹣lnx的定义域为(0,+∞),y′=4x﹣=,∴函数y=2x2﹣lnx在(0,)上单调递减,在(,+∞)上单调递增,∴当x=时,函数y=2x2﹣lnx有最小值,最小值为=+ln2.故答案为:+ln2.11.(5分)已知函数的图象的对称中心为(0,0),函数的图象的对称中心为,函数的图象的对称中心为(﹣1,0),…,由此推测,函数的图象的对称中心为.【解答】解:题中所涉及的函数的对称中心的横坐标依次为0,,﹣1,…,即0,,,…,由此推测,函数的图象的对称中心为故答案为:12.(5分)已知正实数x,y满足x+y=1,若的最小值为9,则正数a=4.【解答】解:∵a>0,∴=()(x+y)=1+a+≥a+1+2=(+1)2,当且仅当取等号,则有,解得a=4.故答案为:4.13.(5分)已知函数f(x)=对任意x1≠x2,都有>0成立,则实数a的取值范围是.[).【解答】解:由题意知函数f(x)在R上单调递增;∴f(x)的两段函数在各自区间上单调递增;∴1﹣2a>0,即;又e0﹣2≤(1﹣2a)•0+2a;∴﹣1≤2a;∴;∴实数a的取值范围是[).故答案为:[).14.(5分)已知等差数列{a n}的首项a1及公差d都是实数,且满足,则d的取值范围是.【解答】解:∵,由等差数列的前n项公式得(2a1+d)(2a1+3d)+(a1+d)2=﹣2,展开并化简整理得5a12+10a1d+4d2+2=0,将此式看作关于a1的一元二次方程,d 为系数.∵a1、d为实数,∴△=100d2﹣4×5×(4d2+2 )≥0.化简整理得d2﹣2≥0,∴d∈(﹣∞,﹣]∪[,+∞)故答案为:(﹣∞,﹣]∪[,+∞)二、解答题:本大题共6小题,计90分.解答应写出必要的文字说明,证明过程或演算步骤,请把答案写在答题纸的指定区域内.15.(14分)已知向量=(sin A,sin B),=(cos B,cos A),=sin2C,其中A、B、C为△ABC的内角.(Ⅰ)求角C的大小;(Ⅱ)若sin A,sin C,sin B成等差数列,且,求AB的长.【解答】解:(Ⅰ)(2分)对于△ABC中A+B=π﹣C,0<C<π∴sin(A+B)=sin C,∴(4分)又∵,∴(7分)(Ⅱ)由sin A,sin C,sin B成等差数列,得2sin C=sin A+sin B,由正弦定理得2c=a+b(9分)∵,∴,即ab cos C=18,ab=16(12分)由余弦弦定理c2=a2+b2﹣2ab cos C=(a+b)2﹣3ab,∴c2=4c2﹣3×36,,c=6(14分)16.(14分)解关于x的不等式:①;②(2mx﹣1)(x﹣2)<0(m 为实常数)【解答】解:①原不等式可化为,即,所以有,解得:,可得不等式的解集为{x|≤x<}.②对于不等式(2mx﹣1)(x﹣2)<0,当m=0时,原不等式即为﹣(x﹣2)<0解得:x>2.当m≠0时,原不等式可化为,当m<0时,得,解得它的解集为{x|}.当m>0时,原不等式可化为,当0<m<时,>2,所以不等式的解集为{x|};当m=时,=2,所以原不等式无解;当m>时,可得<2,所以不等式的解集为{x|}.综上所得:原不等式的解集为:当m<0时,解集为;当m=0时,解集为(2,+∞);当0<m<时,解集为;当m=时,解集为φ;当m>时,解集为.17.(14分)如图,在半径为3m的圆形(O为圆心)铝皮上截取一块矩形材料OABC,其中点B在圆弧上,点A、C在两半径上,现将此矩形铝皮OABC 卷成一个以AB为母线的圆柱形罐子的侧面(不计剪裁和拼接损耗),设矩形的边长AB=xm,圆柱的体积为Vm3.(1)写出体积V关于x的函数关系式,并指出定义域;(2)当x为何值时,才能使做出的圆柱形罐子体积V最大?最大体积是多少?【解答】解:(1)连接OB,在Rt△OAB中,∵AB=x,∴OA=,设圆柱底面半径为r,则=2πr,即4π2r2=9﹣x2,∴V=πr2•x=,其中0<x<3.…(6分)(2)由V′==0及0<x<3,得x=,…(8分)列表如下:…(10分)所以当x=时,V有极大值,也是最大值为.…(14分)答:当x为m时,做出的圆柱形罐子体积最大,最大体积是m3.…(16分)18.(16分)已知函数f(x)=x+(x>0)的最小最小值为,设点P是函数图象上的任意一点,过点P分别作直线y=x和y轴的垂线,垂足分别为M、N.(1)求a的值;(2)问:PM•PN是否为定值?若是,则求出该定值,若不是,请说明理由;(3)设O为坐标原点,求四边形OMPN面积的最小值.【解答】解:(1)∵x>0,若a≤0,则f(x)递增,没有最小值,∴a>0,∴,∴x=时,;∴.(2)设,则,PN=x0,则PM•PN=1;(3)设,则直线PM:,由得,M;S OMPN=S△OPN+S△OPM==≥.(当且仅当,即x0=1时取等号);故四边形OMPN面积的最小值.19.(16分)已知函数.(1)若函数f(x)的图象在点(2,f(2))处的切线方程为9x﹣y+b=0,求实数a,b的值;(2)若a≤0,求f(x)的单调减区间;(3)对一切实数a∈(0,1),求f(x)的极小值的最大值.【解答】解:(1)f′(x)=ax2﹣(a+1)x+1(a∈R),…(1分)由f′(2)=9,得a=5.,…(2分)∴∴f(2)=3,∴(2,3)在直线9x﹣y+b=0上,∴b=﹣15.…(4分)(2)①若a=0,,∴f(x)的单调减区间为(1,+∞).…(6分)②若a<0,则,令f′(x)<0,得.∴,或x>1.…(9分)∴f(x)的单调减区间为,(1,+∞).…(10分)(3),0<a<1,列表:,,…(12分)∴f(x)的极小值为=.…(14分)当时,函数f(x)的极小值f()取得最大值为.…(16分)20.(16分)已知等差数列{a n} 中,a3=7,a1+a2+a3=12,令b n=a n•a n+1,数列{}的前n项和为T n.(1)求数列{a n}的通项公式;(2)求证:T n<;(3)是否存在正整数m,n,且1<m<n,使得T1,T m,T n成等比数列?若存在,求出m,n的值,若不存在,请说明理由.(1)设数列{a n}的公差为d,由解得.∴【解答】解:a n=1+(n﹣1)×3=3n﹣2.(2)∵a n=3n﹣2,a n+1=3n+1,∴b n=a n•a n+1=(3n﹣2)(3n+1),∴.∴.(3)由(2)知,,∴,,∵T1,T m,T n成等比数列,∴,即.当m=2时,,n=16,符合题意;当m=3时,,n无正整数解;当m=4时,,n无正整数解;当m=5时,,n无正整数解;当m=6时,,n无正整数解;当m≥7时,m2﹣6m﹣1=(m﹣3)2﹣10>0,则,而,所以,此时不存在正整数m,n,且1<m<n,使得T1,T m,T n成等比数列.综上,存在正整数m=2,n=16,且1<m<n,使得T1,T m,T n成等比数列.。

江苏省清江中学2014-2015学年高二数学午间练习(119) Word版含答案

午练练习(119)1.如图,在正四棱锥P ABCD -中,点M 为棱AB 的中点,点N 为棱PC 上的点.(1)若PN NC =,求证://MN 平面PAD ; (2)试写出(1)的逆命题,并判断其真假. 若为真,请证明;若为假,请举反例.2.在平面直角坐标系xOy 中,设点( ) (0)A a b ab ≠,,点B 为直线l :y bx =与抛物线C :21x y ab=异于原点的另一交点.(1)若a =1,b =2,求点B 的坐标;(2)若点A 在椭圆2214x y +=上,求证:点B 落在双曲线22441x y -=上; (3)若点B 始终落在曲线22()y c x d =-(其中c d 、为常数,且0c ≠)上,问动点A 的轨迹落在哪种二次曲线上?并说明理由.参考答案(119)1.【证明】(1)延长CM ,DA 交于点Q ,连结PQ ,因为点N 为线段PC 上的点,且PN NC =,所以点N 为线段PC 的中点,又点M 为线段AB 的中点, D N (第1题) P A B CM Q所以//MN PQ ,(3分) 又MN ⊄平面PAD , PQ ⊂平面PAD , 所以//MN 平面PAD .(6分)(2)(1)的逆命题为:若//MN 平面PAD , 则PN NC =(真命题),(8分) 下证之: 因为//MN 平面PAD , MN ⊂平面PQC , 平面PAD 平面PQC PQ =, 所以//MN PQ ,(12分) 在PQC ∆中,点M 为线段AB 的中点,点N 为线段PC 上的点, 所以,点N 为线段PC 的中点.(14分)2.解:(1)由y bx =与则21x y ab =联立方程组得()1 b B a a,, 又a =1,b =2,则()1 2B ,;(3分) (2)将( ) (0)A a b ab ≠,代入椭圆2214x y +=得2214a b +=, 将()1 b B a a ,代入()()22222211444441b b x y a a a --=-=⨯=,即证;(7分) (3)将()1 b B a a ,代入22()y c x d =-(其中c d 、为常数,0c ≠)得()()212b c d a a =-,()0c ≠,① 若0d =,则22b ca =,()0c ≠,所以点A 的轨迹落在抛物线上;(9分)若0d ≠,则()222121124a d b c d d -+=()0c ≠, ②若12cd =,则点A 的轨迹落在圆上;(11分) ③若0cd >,且12cd ≠,则点A 的轨迹落在椭圆上;(13分) ④若0cd <,则点A 的轨迹落在双曲线上.(15分)。

江苏省清江中学2014-2015学年高二下学期期中考试化学试卷 Word版含答案.pdf

江苏省清江中学2014—2015学年高二第二学期期中考试 化学试题 可能用到的相对原子质量:H:1 C:12 N:14 O:16 Na:23 S:32 Cl:35.5 Ca:40 Ba:137 单项选择题:本题包括12小题,每小题4分,共计48分。

每小题只有一个选项符合题意。

1.下列与化学反应能量变化相关的叙述正确的是( )A.生成物总能量一定低于反应物总能量 B.放热反应的反应速率总是大于吸热反应的反应速率 C.应用盖斯定律,可计算某些难以直接测量的反应焓变 D.同温同压下,H2(g)+Cl2(g)2HCl(g)在光照和点燃条件下的△H不同下列生产或实验事实引出的相应结论不正确的是( ) 选项事实结论A其他条件相同,Na2S2O3溶液和H2SO4溶液反应,升高溶液的温度,析出硫沉淀所需时间缩短当其他条件不变时,升高反应温度,化学反应速率加快B工业制硫酸中,在SO3的吸收阶段,吸收塔里要装填瓷环增大气液接触面积,使SO3的吸收速率增大C在容积可变的密闭容器中发生反应:2NH3(g)?N2H4(l)+H2(g),把容积的体积缩小一半正反应速率加快,逆反应速率减慢DA、B两支试管中分别加入等体积5%的H2O2溶液,在B试管中加入2~3滴FeCl3溶液,B试管中产生气泡快当其他条件不变时,催化剂可以改变化学反应速率甲醇质子交换膜燃料电池中将甲醇蒸气转化为氢气的两种反应原理是 ①CH3OH(g)+H2O(g)CO2(g)+3H2(g)△H=+49.0kJ/mol ②CH3OH(g)+O2(g)CO2(g)+2H2(g)△H=192.9kJ/mol 根据上述反应,下列说法正确的是( ) A.反应①中的能量变化如图所示 B.CH3OH转变成H2的过程一定要吸收能量 C.1mol CH3OH充分燃烧放出的热量为192.9kJ D.可推知2H2(g)+O2(g)2H2O(g)△H=483.8 kJ/mol4.用于净化汽车尾气的反应:2NO(g)+2CO(g)?2CO2(g)+N2(g),已知该反应570K时平衡常数为1×1059,但反应速率极慢.下列说法正确的是( ) A.装有尾气净化装置的汽车排出的气体中不再含有NO或CO B.提高尾气净化效率的常用方法是升高温度 C.增大压强,上述平衡右移,故可通过增压的方法提高尾气净化效率 D.提高尾气净化效率的最佳途径是使用高效催化剂氢氧燃料电池所耗原料为H2和O2,电极为多孔镍,电解质溶液为30%的KOH溶液。

江苏省清江中学2014-2015学年高二数学午间练习(102) Word版含答案

C 午练练习(102)1.计算12sin 22.5-的结果等于 .2.设323log ,log log a b c π===a 、b 、c 由大到小排列为____________. 3.已知向量a =(2,-1),b =(-1,m ),c =(-1,2)若(a +b )∥c ,则m = . 4.设n S 为等比数列{}n a 的前n 项和,2580a a +=,则52S S = . 5.直线3y kx =+与圆()()22324x y -+-=相交于M,N两点,若MN ≥k 的取值范围是 .6.若复数 z 满足z (1+i) =1-i (I 是虚数单位),则其共轭复数z =__________________ .7.从某小学随机抽取100名同学,将他们的身高(单位:厘米)数据绘制成频率分布直方图(如图)。

由图中数据可知a = 。

若要从身高在[ 120 , 130),[130 ,140) , [140 , 150]三组内的学生中,用分层抽样的方法选取18人参加一项活动,则从身高在[140 ,150]内的学生中选取的人数应为 。

8.函数())1,0(13log ≠>-+=a a x y a 的图象恒过定点A,若点A 在直线01=++ny mx 上,其中0>mn ,则nm 21+的最小值为 . 9.已知函数)(x f y =的导函数)(x f y '=的图像如下,则一下说法正确的是 . A .函数)(x f 有1个极大值点,1个极小值点 B .函数)(x f 有2个极大值点,2个极小值点 C .函数)(x f 有3个极大值点,1个极小值点 D .函数)(x f 有1个极大值点,3个极小值点10.设非空集合|||S x m x l =≤≤满足:当x S ∈时,有2x S ∈。

给出如下三个命题工:①若1m =,则|1|S =;②若12m =-,则114l ≤≤;③若12l =,则0m ≤≤。

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江苏省清江中学高二英语周练7一、单项选择1. Saddam Hussein was ___________ death by the Iraqi government; they declared that Saddam had killed many people when he was in power.A. condemned toB. starved toC. demanded toD. beaten to2. At the invitation of Zhang Yimou, a famous director in China, Zhou Runfa ________ in the film Curse of the Golden Flower.A. helpedB. ledC. foughtD. starred3. Mary ________into the deserted building by herself on so dark a night.A. dares not goB. dares not to goC. dare not to goD. doesn’t dare to go4. The ________increase in the robbery rate made a number of residents ________ at night.A. disturbing; terrifiedB. disturbing; terrifyingC. disturbed; terrifiedD. disturbed; terrifying5. Some experts thought that the standards of education __________ these years in China.A. has declinedB. had declinedC. has raisedD. had raised6. After graduation from Nanjing Normal University, most of our classmates have long ______ to have a get-together in the near future.A. managedB. connectedC. joinedD. desired7. At the request of the director, he was ________for the part of a disabled youth in the film.A. askedB. castC. thrownD. acted8. At the sight of her daughter kissing an ugly boy in the street, Mother _______with anger.A. excitedB. trembledC. disappointedD. terrified9. The idea of a holiday to Tibet by train is certainly ________to some young men in China.A. meaningB. hopingC. appealingD. thinking10. The meeting was ____________ when the chairman fell ill.A. cut downB. cut outC. cut offD. cut short11. There is no denying the fact that as one grows older, one’s memory __________.A. refusesB. declinesC. decreasesD. falls12. The computer system ___suddenly while he was searching for information on the Internet.A. broke downB. broke outC. broke upD. broke in13. Immediately, the two fall in love with each other. However, Zhu Yintai’s parents demand she___ another man.A. be married withB. marriesC. marryD. marry to14. It was ______ back home after the evening party was over.A. not until midnight did he goB. not until midnight that he wentC. until midnight that he didn’t goD. until midnight when he went15. Kevin kicked the ball so hard that up ______, higher and higher, until it was a small dot in the sky.A. fly did itB. flew itC. did it flyD. it flew16. — I followed your advice on how to appreciate Great Expectations, but I still can’t find aneffective way to get clear its plot. Why?— Well, ______.A. all is well that ends wellB. no pains, no gainsC. no sweet without sweatD. one man’s meat is another man’s poison17.--We've cross-checked the data collected from the Internet.--Good. Anyway,_______.A. you can't be careful enoughB. you are careful enoughC. you can't be so carelessD. you are never careless enough18. --Some people believe that English is one of the most important subjects for us students.--It _______ . But things seem to be changing in recent years.A. used toB. used to beC. used to doD. was used to be19. --My goodness, you crossed the double yellow line!--I tried not to, but _______ . The car in front changed lane suddenly.A. in timeB. in caseC. in needD. in vain20. Liu opened her mouth as if _ something to Calaf, but gave up seeing his passionate eyes locked on Turandot.A. to sayB. wanted to sayC. sayingD. to be saying21.In his plays, Shakespeare _______ his characters live through their language.A. will makeB. had madeC. was makingD. makes22. --I don't know _______ that makes her music different from that of others.--The true emotions, I think.A. how is itB. how it isC. what is itD. what it is23. The new School Safety Guidelines states that under no circumstances _______ leave the campus alone.A. a student is toB. is a student toC. a student be toD. be a student to24.Toward the end of class, the teacher dealt in detail with the question _______ on at the beginning.A. discussedB. touchedC. referredD. cast25. One of the complaints about the Hollywood movies is that they sometimes are _______ to show off the special effects _______ to develop the movie's theme and plot.A. rather; thanB. further; thanC. less; thanD. more; than26. “______ to Michelle and having two beautiful girls in my house never allow me to look downupon women,” said Obama.A. MarryingB. Having marriedC. Being marriedD. Married27. With proper measures, the economy in China is beginning to ______ again.A. break upB. hold onC. pick upD. take on28. Toyota Motor President Akio Toyoda on Monday apologized to Chinese consumers, who______ the world’s biggest auto market, over the company’s massive global recall.A. make upB. bring upC. put downD. set down29. Never shall I forget that poem and the inspiration _____ provided for my first novel.A. whichB. thatC. itD. what30. Thanks to Mr. Smith, the father and the son eventually ________ after ten years' cold relationship between them.A. took upB. made upC. broke upD. turned up31. His mother had thought it would be good for his character to ______ from home.A. run awayB. take awayC. keep awayD. get away32. He was so kind that he was always ready to _______ money and clothes to those in the flooded areas.A. let outB. give awayC. bring inD. make up33. I wish you’d do _________ talking and some more work. Thus things will b ecome better.A. a bit lessB. any lessC. much moreD. a little more34. The book _______ his sister as a birthday gift, is lost during the mail.A. intended forB. intending forC. intended toD. intending to35. In that school, English is compulsory for all students, but French and Russian are _______.A. specialB. regionalC. optionalD. original36. Do you think their table tennis team will win the first place at the coming Asian Games?---- _______. Ours is much stronger than theirs.A. Of courseB. It dependsC. Don’t mention itD. By no means37. Hardly _____ into the country ______ it began to rain.A. we had got; whenB. we got; thanC. had we got; whenD. did we got; than38. --------Do you think it is going to rain over the weekend? -----__________.A. I don’t believeB. I don’t believe itC. I believe not soD. I believe not39. Are you chairman? --- No, and I _________.A. don’t want toB. don’t wantC. don’t want to beD. don’t want be40. _________ the city, he looked forward to the visit anxiously.A. Having not been toB. Having never been toC. Not having gone toD. Never having been to二、完形填空My father and I disagreed about curfew (晚间在家的时间). He’d say I was to be in by 9:30 on weekdays, and 11:00 on weekends, no exceptions without my first asking. I told him it made me 36 like a junior-high kid. He explained that while a curfew 37 sound like a restriction, it’s really about people looking out for one another.The very next Friday after that pretty heated 38 , my dad and I had tickets to see our town’s professional football game. On that day he was 39 to a nearby city to meet with some major clients and 40 me that his getting home and our leaving for the game would be tight.To make sure we could 41 off the moment he walked in, I got everything prepared. When a half hour had passed from the time he said he’d be home, I understood that he was a little 42 . But then, nearly a whole hour passed. I was getting 43 . We were going to miss the kick-off! And why hadn’t he44 me and let me know he was going to be really late? As I anxiously 45 the floor, another half hour passed. That’s when I got really angry. How inconsiderate of my father! Now we were going to 46 the whole game! When yet another half hour passed, my anger turned to 47 . What if something terrible had happened to my dad, like he had a heart attack or had been in an accident, or something? I began to really48 . I’d already called his cellphone about ten times, but no 49 .I was beside myself, assuming the worst had happened.Finally, the phone rang, and my dad said 50 , “Son, I’m so sorry about the game, but…there was a terrible accident…on the freeway coming home, and I 51 to help… and ended up going to the hospital. I 52 my cellphone in the car, so I couldn’t call until now.”I was so relieved to hear from my father and to 53 that he was safe that I actually cried. That was 54 I “got” the importance of a curfew: Checking in! It’ s about knowing that someone you love is 55 . It was one more proof of my father’s loving me as much as he does.36. A. go B. feel C. turn D. grow37. A. might B. must C. needed D. should38. A. speech B. match C. description D. exchange39. A. cycling B. driving C. flying D. walking40. A. allowed B. advised C. informed D. ordered41. A. pay B. hold C. cut D. move42. A. late B. lazy C. forgetful D. careless43. A. upset B. sorry C. rude D. puzzled44. A. warned B. signaled C. phoned D. showed45. A. hit B. paced C. cleared D. measured46. A. play B. watch C. miss D. start47. A. sadness B. surprise C. doubt D. fear48. A. envy B. worry C. regret D. cry49. A. excuse B. way C. time D. answer50. A. strangely B. casually C. breathlessly D. angrily51. A. stopped B. forgot C. failed D. refused52. A. left B. lost C. saw D. got53. A. wonder B. guess C. expect D. learn54. A. what B. when C. whether D. why55. A. confident B. great C. safe D. honest三、阅读理解AIt was the summer of 1965. DeLuca, then 17, visited Peter Buck, a family friend. Buck askedDeLuca about his plans for the future. “I’m going to college, but I need a way to pay for it,” DeLuca recalls, saying “Buck said, ‘You should open a sandwich shop.’”That afternoon, they agreed to be partners. And they set a goal: to open 32 stores in ten years. After doing some research, Buck wrote a check for $1000. DeLuca rented a storefront (店面) in Connecticut, and when they couldn’t cover their start-up costs, Buck kicked in another $1000.But business didn’t go smoothly as they expected. DeLuca says, “After six months, we were doing poorly, but we didn’t know how badly, because we didn’t have any financial controls.” All he and Buck knew was that their sales were lower than their costs.DeLuca was managing the store and going to the University of Bridgeport at the same time. Buck was working at his day job as a nuclear physicist in New York. They’d meet Monday evenings and brainstorm ideas for kee ping the business running. “We convinced ourselves to open a second store. We figured we could tell the public, ‘We are so successful, we are opening a second store.” And they did—in the spring of 1966. Still, it was a lot of learning by trial and error.But the partners’ learn-as-you-go approach turned out to be their greatest strength. Every Friday, DeLuca would drive around and hand-deliver the checks to pay their suppliers. “It probably took me two and a half hours and it wasn’t necessary, but as a result, the suppliers got to know me very well, and the personal relationships established really helped out,” DeLuca says.And having a goal was also important. “There are so many problems that can get you down. You just have to keep working toward yo ur goal,” DeLuca adds.DeLuca ended up founding Subway Sandwich, the multimillion-dollar restaurant chain.56. They decided to open a second store probably because they __________.A. had enough money to do it.B. had succeeded in their businessC. wished to meet the increasing demand of customersD. wanted to make people believe that they were successful57. What contribute most to their success according to the author?A. Learning by trial and error.B. Making friends with suppliers.C. Finding a good partner.D. Opening chain stores.B58. What is a major function of Lipitor?A. To help quit smoking.B. To control blood pressure.C. To improve unhealthy diet.D. To lower “bad” cholesterol.59. If it has been over 12 hours since you missed a dose, you should___________.A. change the amount of your next doseB. eat more when taking your next doseC. have a dose as soon as you rememberD. take the next dose at your regular time60. Which of the following is a common side effect of taking Lipitor?A. Face swelling.B. Upset stomach.C. Kidney failure.D. Muscle weaknessCA high school history teacher once told us, “If you make one close friend in school, you will be most fortunat e. A true friend is someone who stays with you for life.” Experience teaches that he was right. Good friendships are just not easily formed. Why?One reason is that it is easy to move around in our society. Mr. Darrell Sifford, a news reporter for the Washington Daily, has been studying and talking about friendships for a number of years. He reports what one woman thought about the effect of ease of movement on friendship: “I was nine, and we’d just moved from South Carolina to New Jersey, and I didn’t knowanybody. My mother had a way of getting to the root of things and she said to me, ‘Amelia, I know you’re feeling bad because you don’t have any friends. But you can fix that. Just walk across the street —I know there’s a girl about your age over there — and knock on the door and ask her to be your friend.’”“As a 9-year-old, I could do that. I knocked on the door and said, ‘Hi, my name is Amelia, and I’d like for us to be friends.’ And to my surprise, she said that she would like that too—and we became fr iends.”She added that going about it directly always worked when she was a child. But as she left childhood, she found that the simple direct approach was more and more difficult for her to follow. So, as an adult, Amelia longed to have friends but her hands were tied when it came to doing anything about it. The problem, according to her, is that society teaches us in a number of ways that direct action is not an acceptable way of doing things. We need to be less direct so that our feelings will not be hurt if our offer of friendship is refused.Mr. Sifford goes on to describe his own ideas on the subject:“To most of us, friendship is very important, but we need to have clear in our own minds the kinds of friendships we want. Are they to be very close or k ept at arm’s length? Do we want to share ourselves or do we want to walk on the surface?”“For some people, an ordinary friendship is enough —and that’s all right. But at some point we need to make sure that what we expect from the friendship is the same as what our friends expect from it. If one wants more from the friendship than the other, and if this is not talked about, one is likely eventually to feel that he’s not being given enough attention.“The sharing of close secrets, including our fears as we ll as our dark dreams, is the surest way to deepen friendships. But the process must be gone through slowly and continued only if there are signs of interest and our efforts are answered.”What are some of the problems in forming friendships? According to Mr. Sifford, the biggest problem is to expect too much too soon. Deep relationships take time. Another “big difficulty” is to think one “possesses” the other and that he should spend all his time only with you. Similarly, friendships require action from both sides. In short, you must give as much as you take. Finally there is a question of developing friendship. Unless you spend enough time together, talking on the phone, writing letters, doing things together, friendships will gradually fade away.。

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