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2011~2015年全国课标卷试题高二下部分汇编

2011~2015年全国课标卷试题高二下部分汇编
2011~2015年全国课标卷试题高二下部分汇编

2011~2015年全国课标卷试题汇编

不等式与线性规划、排列组合与二项式定理、复数、导数、常见逻辑用语、离散型随机变量及其分布列一.选择题

1.(2011?新课标)复数的共轭复数是()

A.B.C.﹣i D.i

2.(2011?新课标)的展开式中各项系数的和为2,则该展开式中常数

项为()

A.﹣40 B.﹣20 C.20 D.40 3.(2012?新课标)将2名教师,4名学生分成2个小组,分别安排到甲、乙两地参加社会实践活动,每个小组由1名教师和2名学生组成,不同的安排方案共有()种

A.12 B.10 C.9 D.8

4.(2012?新课标)下面是关于复数z=的四个命题:其中的真命题为(),

P1:|z|=2 P2:z2=2i P3:z的共轭复数为1+i P4:z的虚部为﹣1 A.P2、P3B.P1、P2C.P2、P4D.P3、P4 5.(2013?新课标Ⅰ)若复数z满足(3﹣4i)z=|4+3i|,则z的虚部为()

A.﹣4 B.C.4 D.

6.(2013?新课标Ⅰ)设m为正整数,(x+y)2m展开式的二项式系数的最大值为a,(x+y)2m+1展开式的二项式系数的最大值为b,若13a=7b,则m=()

A.5 B.6 C.7 D.8 7.(2013?新课标Ⅰ)已知函数f(x)=,若|f(x)|≥ax,则a的取值范围是()

A.(﹣∞,0] B.(﹣∞,1] C.[﹣2,1] D.[﹣2,0] 8.(2013?新课标Ⅱ)设复数z满足(1﹣i)z=2i,则z=()

A.﹣1+i B.﹣1﹣i C.1+i D.1﹣i 9.(2013?新课标Ⅱ)已知a>0,实数x,y满足:,若z=2x+y的最小值为

1,则a=()

A.2 B.1 C.D.

10.(2013?新课标Ⅱ)已知(1+ax)(1+x)5的展开式中x2的系数为5,则a=()

A.﹣4 B.﹣3 C.﹣2 D.﹣1 11.(2013?新课标Ⅱ)已知函数f(x)=x3+ax2+bx+c,下列结论中错误的是()

A.?xα∈R,f(xα)=0

B.函数y=f(x)的图象是中心对称图形

C.若xα是f(x)的极小值点,则f(x)在区间(﹣∞,xα)单调递减

D.若xα是f(x)的极值点,则f′(xα)=0

12.(2014?新课标I)=()

A.1+i B.1﹣i C.﹣1+i D.﹣1﹣i 13.(2014?新课标I)4位同学各自在周六、周日两天中任选一天参加公益活动,则周六、周日都有同学参加公益活动的概率为()

A.B.C.D.

14.(2014?新课标I)不等式组的解集记为D,有下列四个命题:

P1:?(x,y)∈D,x+2y≥﹣2 P2:?(x,y)∈D,x+2y≥2

P3:?(x,y)∈D,x+2y≤3 P4:?(x,y)∈D,x+2y≤﹣1

其中真命题是()

A.P2、P3B.P1、P4C.P1、P2D.P1、P3 15.(2014?新课标I)已知函数f(x)=ax3﹣3x2+1,若f(x)存在唯一的零点x0,且x0>0,则实数a的取值范围是()

A.(1,+∞)B.(2,+∞)C.(﹣∞,﹣1) D.(﹣∞,﹣2) 16.(2014?新课标II)设复数z1,z2在复平面内的对应点关于虚轴对称,z1=2+i,则z1z2=() A.﹣5 B.5 C.﹣4+i D.﹣4﹣i 17.(2014?新课标II)某地区空气质量监测资料表明,一天的空气质量为优良的概率是0.75,连续两天为优良的概率是0.6,已知某天的空气质量为优良,则随后一天的空气质量为优良的概率是()

A.0.8 B.0.75 C.0.6 D.0.45 18.(2014?新课标II)设曲线y=ax﹣ln(x+1)在点(0,0)处的切线方程为y=2x,则a=() A.0 B.1 C.2 D.3

19.(2014?新课标II)设x,y满足约束条件,则z=2x﹣y的最大值为()

A.10 B.8 C.3 D.2 20.(2015?新课标Ⅰ)设复数z满足=i,则|z|=()

A.1 B.C.D.2 21.(2015?新课标Ⅰ)设命题p:?n∈N,n2>2n,则¬p为()

A.?n∈N,n2>2n B.?n∈N,n2≤2n C.?n∈N,n2≤2n D.?n∈N,n2=2n 22.(2015?新课标Ⅰ)(x2+x+y)5的展开式中,x5y2的系数为()

A.10 B.20 C.30 D.60 23.(2015?新课标Ⅰ)设函数f(x)=e x(2x﹣1)﹣ax+a,其中a<1,若存在唯一的整数x0使得f(x0)<0,则a的取值范围是()

A.[) B.[) C.[) D.[) 24.(2015?新课标II)若a为实数,且(2+ai)(a﹣2i)=﹣4i,则a=()

A.-1 B.0 C.1 D.2 25.(2015?新课标II)设函数f′(x)是奇函数f(x)(x∈R)的导函数,f(﹣1)=0,当x>0时,xf′(x)﹣f(x)<0,则使得f(x)>0成立的x的取值范围是()

A.(﹣∞,﹣1)∪(0,1) B.(﹣1,0)∪(1,+∞)

C.(﹣∞,﹣1)∪(﹣1,0) D.(0,1)∪(1,+∞)

二.填空题

26.(2011?新课标)若变量x,y满足约束条件则z=x+2y的最小值为.27.(2012?新课标)设x,y满足约束条件:;则z=x﹣2y的取值范围为.

28.(2012?新课标)某个部件由三个元件按右图方式连

接而成,元件1或元件2正常工作,且元件3正常工

作,则部件正常工作,设三个电子元件的使用寿命(单

位:小时)均服从正态分布N(1000,502),且各个元

件能否正常相互独立,那么该部件的使用寿命超过1000小时的概率为.29.(2014?新课标I)(x﹣y)(x+y)8的展开式中x2y7的系数为.(用数字填写答案) 30.(2014?新课标II)(x+a)10的展开式中,x7的系数为15,则a=.

31.(2015?新课标Ⅰ)若x,y满足约束条件.则的最大值为.32.(2015?新课标II)若x,y满足约束条件,则z=x+y的最大值为.

33.(2015?新课标II)(a+x)(1+x)4的展开式中x的奇数次幂项的系数之和为32,则a=.三.解答题

34.(2011?新课标)某种产品的质量以其质量指标值衡量,质量指标值越大表明质量越好,且质量指标值大于或等于102的产品为优质品,现用两种新配方(分别称为A配方和B配方)

做试验,各生产了100件这种产品,并测量了每件产品的质量指标值,得到下面试验结果:

(Ⅱ)已知用B配方生成的一件产品的利润y(单位:元)与其质量指标值t的关系式为

y=。从用B配方生产的产品中任取一件,其利润记为X(单位:元),求X

的分布列及数学期望.(以试验结果中质量指标值落入各组的频率作为一件产品的质量指标值落入相应组的概率)

35.(2011?新课标)已知函数f(x)=+,曲线y=f(x)在点(1,f(1))处的切线方程为x+2y﹣

3=0.(Ⅰ)求a、b的值;(Ⅱ)如果当x>0,且x≠1时,f(x)>+,求k的取值范围.

36.(2012?新课标)已知函数f(x)满足f(x)=f′(1)e x﹣1﹣f(0)x+x2;

(1)求f(x)的解析式及单调区间;(2)若,求(a+1)b的最大值.

37.(2013?新课标Ⅰ)一批产品需要进行质量检验,检验方案是:先从这批产品中任取4件作检验,这4件产品中优质品的件数记为n.如果n=3,再从这批产品中任取4件作检验,若都为优质品,则这批产品通过检验;如果n=4,再从这批产品中任取1件作检验,若为优质品,则这批产品通过检验;其他情况下,这批产品都不能通过检验.假设这批产品的优质品

率为50%,即取出的产品是优质品的概率都为,且各件产品是否为优质品相互独立.

(Ⅰ)求这批产品通过检验的概率;

(Ⅱ)已知每件产品检验费用为100元,凡抽取的每件产品都需要检验,对这批产品作质量检验所需的费用记为X(单位:元),求X的分布列及数学期望.

38.(2013?新课标Ⅰ)已知函数f(x)=x2+ax+b,g(x)=e x(cx+d)若曲线y=f(x)和曲线y=g(x)都过点P(0,2),且在点P处有相同的切线y=4x+2.

(Ⅰ)求a,b,c,d的值;(Ⅱ)若x≥﹣2时,f(x)≤kg(x),求k的取值范围.39.(2013?新课标Ⅱ)经销商经销某种农产品,在一个销售季度内,每售出1t该产品获利润

500元,未售出的产品,每1t亏

损300元.根据历史资料,得到

销售季度内市场需求量的频率分

布直方图,如图所示.经销商为

下一个销售季度购进了130t该农

产品.以x(单位:t,100≤x≤150)

表示下一个销售季度内的市场需

求量,T(单位:元)表示下一个销

售季度内经销该农产品的利润.

(Ⅰ)将T表示为x的函数;(Ⅱ)根据直方图估计利润T不少于57000元的概率;

(Ⅲ)在直方图的需求量分组中,以各组的区间中点值代表该组的各个值,并以需求量落入该区间的频率作为需求量取该区间中点值的概率(例如:若x∈[100,110))则取x=105,且x=105的概率等于需求量落入[100,110)的频率,求T的数学期望.

40.(2013?新课标Ⅱ)已知函数f(x)=e x﹣ln(x+m)

(Ⅰ)设x=0是f(x)的极值点,求m,并讨论f(x)的单调性;(Ⅱ)当m≤2时,证明f(x)>0.

41.(2014?新课标I)从某企业生产的某种产品中抽取500件,测量这些产品的一项质量指标值,由测量结果得如下频率分布直方图:

(Ⅰ)求这500件产品质量指标值的样本平均数和样本方差s2(同一组中数据用该组区间的中点值作代表);

(Ⅱ)由直方图可以认为,这种产品的质量指标值Z服从正态分布N(μ,σ2),其中μ近似为样本平均数,σ2近似为样本方差s2.

(i)利用该正态分布,求P(187.8<Z<212.2);

(ii)某用户从该企业购买了100件这种产品,记X表示这100件产品中质量指标值位于区间(187.8,212.2)的产品件数,利用(i)的结果,求EX.

附:≈12.2.若Z﹣N(μ,σ2)则P(μ﹣σ<Z<μ+σ)=0.6826,P(μ﹣2σ<Z<μ+2σ)=0.9544.

42.(2014?新课标I)设函数f(x)=ae x ln x+,曲线y=f(x)在点(1,f(1))处得切线方程为y=e(x ﹣1)+2.(Ⅰ)求a、b;(Ⅱ)证明:f(x)>1.

43.(2014?新课标II)已知函数f(x)=e x﹣e﹣x﹣2x.

(Ⅰ)讨论f(x)的单调性;

(Ⅱ)设g(x)=f(2x)﹣4bf(x),当x>0时,g(x)>0,求b的最大值;

(Ⅲ)已知1.4142<<1.4143,估计ln2的近似值(精确到0.001).

44.(2015?新课标I)已知函数f(x)=x3+ax+,g(x)=﹣ln x

(i)当a为何值时,x轴为曲线y=f(x)的切线;

(ii)用min {m,n }表示m,n中的最小值,设函数h(x)=min { f(x),g(x)}(x>0),讨论h(x)零点的个数.

45.(2015?新课标II)设函数f(x)=e mx+x2﹣mx.

(1)证明:f(x)在(﹣∞,0)单调递减,在(0,+∞)单调递增;

(2)若对于任意x1,x2∈[﹣1,1],都有|f(x1)﹣f(x2)|≤e﹣1,求m的取值范围.

高考数学试题分类汇编集合理

2013年全国高考理科数学试题分类汇编1:集合 一、选择题 1 .(2013年普通高等学校招生统一考试重庆数学(理)试题(含答案))已知全集 {}1,2,3,4U =,集合{}=12A ,,{}=23B ,,则 ()=U A B ( ) A.{}134, , B.{}34, C. {}3 D. {}4 【答案】D 2 .(2013年普通高等学校招生统一考试辽宁数学(理)试题(WORD 版))已知集合 {}{}4|0log 1,|2A x x B x x A B =<<=≤=,则 A.()01, B.(]02, C.()1,2 D.(]12, 【答案】D 3 .(2013年普通高等学校招生统一考试天津数学(理)试题(含答案))已知集合A = {x ∈R | |x |≤2}, A = {x ∈R | x ≤1}, 则A B ?= (A) (,2]-∞ (B) [1,2] (C) [2,2] (D) [-2,1] 【答案】D 4 .(2013年普通高等学校招生统一考试福建数学(理)试题(纯WORD 版))设S,T,是R 的两个非空子集,如果存在一个从S 到T 的函数()y f x =满足:(){()|};()i T f x x S ii =∈ 对任意12,,x x S ∈当12x x <时,恒有12()()f x f x <,那么称这两个集合“保序同构”.以下集合对不是“保序同构”的是( ) A.* ,A N B N == B.{|13},{|8010}A x x B x x x =-≤≤==-<≤或 C.{|01},A x x B R =<<= D.,A Z B Q == 【答案】D 5 .(2013 年高考上海卷(理))设常数a R ∈,集合 {|(1)()0},{|1}A x x x a B x x a =--≥=≥-,若A B R ?=,则a 的取值范围为( ) (A) (,2)-∞ (B) (,2]-∞ (C) (2,)+∞ (D) [2,)+∞ 【答案】B. 6 .(2013年普通高等学校招生统一考试山东数学(理)试题(含答案))已知集合 A ={0,1,2},则集合 B ={},x y x A y A -∈∈中元素的个数是 (A) 1 (B) 3 (C)5 (D)9 【答案】C

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