2018年上海闵行区高三一模试题(附解答)

2018年上海市闵行区高考数学一模试卷一.填空题（本大题共12题，1-6每题4分，7-12每题5分，共54分）1. 集合P ={x|0≤x <3, x ∈Z}，M ={x|x 2≤9}，则P ∩M =________． 【答案】 {0, 1, 2} 【考点】 交集及其运算 【解析】求出集合P ，M ，由此能求出P ∩M ． 【解答】∵ 集合P ={x|0≤x <3, x ∈Z}={0, 1, 2}， M ={x|x 2≤9}={x|−3≤x ≤3}， ∴ P ∩M ={0, 1, 2}．2. 计算lim n→∞C n2n 2+1=________．【答案】 12【考点】 极限及其运算 【解析】根据组合公式求得C n2=n(n−1)2，根据极限的运算，即可求得答案．【解答】limn→∞C n2n 2+1=limn→∞n(n−1)2(n 2+1)=12limn→∞1−1n1+1n 2=12，3. 方程|1+lgx3−lgx11|=0的根是________．【答案】 10【考点】函数的零点与方程根的关系 【解析】化简方程求出x 的值． 【解答】 ∵ |1+lgx 3−lgx11|=0，即1+lgx −3+lgx =0，∴ lgx =1， ∴ x =10．4. 已知(sinα−35)+(cosα−45)i 是纯虚数（i 是虚数单位），则sin(α+π4)=________．−√2 【考点】虚数单位i 及其性质 复数的运算 复数的模复数的基本概念 【解析】 由题意可得sinα、cosα的值，展开两角和的正弦求得sin(α+π4)． 【解答】∵ (sinα−35)+(cosα−45)i 是纯虚数， ∴ {sinα−35=0cosα−45≠0，得sinα=35且cosα≠45， ∴ α为第二象限角，则cosα=−45．∴ sin(α+π4)=sinαcos π4+cosαsin π4=35×√22−45×√22=−√210．5. 已知直线l 的一个法向量是n →=(√3,−1)，则l 的倾斜角的大小是________． 【答案】 π3【考点】 平面的法向量 【解析】设直线l 的倾斜角为θ，θ∈[0, π)．设直线的方向向量为u →=(x, y)，则u →∗n →=0，可得tanθ=yx ．【解答】设直线l 的倾斜角为θ，θ∈[0, π)．设直线的方向向量为u →=(x, y)，则u →∗n →=√3x −y =0， ∴ tanθ=yx =√3，解得θ=π3．6. 从4名男同学和6名女同学中选取3人参加某社团活动，选出的3人中男女同学都有的不同选法种数是________（用数字作答） 【答案】 96【考点】排列、组合及简单计数问题 【解析】根据题意，用间接法分析：首先计算在10名学生中任取3人的选法数目，再分析其中只有男生和只有女生的选法数目，分析即可得答案．根据题意，在4名男同学和6名女同学共10名学生中任取3人，有C103=120种，其中只有男生的选法有C43=4种，只有女生的选法有C63=20种则选出的3人中男女同学都有的不同选法有120−4−20=96种；7. 在(1+2x)5的展开式中，x2项系数为________（用数字作答）【答案】40【考点】二项式定理的应用【解析】利用二项展开式的通项公式写出第r+1项，令x的指数为2求出展开式中x2的系数【解答】设求的项为T r+1=C5r(2x)r，今r=2，∴T3=22C52x2=40x2．∴x2的系数是408. 如图，在直三棱柱ABC−A1B1C1中，∠ACB=90∘，AC=4，BC=3，AB=BB1，则异面直线A1B与B1C1所成角的大小是________（结果用反三角函数表示）【答案】arccos 3√2 10【考点】异面直线及其所成的角【解析】由BC // B1C1，得∠A1BC是异面直线A1B与B1C1所成角，由此利用余弦定理能求出异面直线A1B与B1C1所成角．【解答】∵在直三棱柱ABC−A1B1C1中，∠ACB=90∘，AC=4，BC=3，AB=BB1，BC // B1C1，∴∠A1BC是异面直线A1B与B1C1所成角，∵A1B=√AA12+AB2=√(9+16)+(9+16)=5√2，A1C=√AA12+AC2=√(9+16)+16=√41，∴cos∠A1BC=A1B2+BC2−A1C22×A1B×BC =2×5√2×3=3√210．∴∠A1BC=arccos3√210．9. 已知数列{a n}、{b n}满足b n=lna n，n∈N∗，其中{b n}是等差数列，且a3∗a1007= e4，则b1+b2+...+b1009=________．【答案】2018【考点】数列的求和【解析】数列{a n}、{b n}满足b n=lna n，n∈N∗，其中{b n}是等差数列，可得b n+1−b n=lna n+1−lna n=ln a n+1a n =常数t．a n+1a n=常数e t=q>0，因此数列{an}为等比数列．由a3∗a1007=e4，可得a1a1009=a2a1008=a3∗a1007=e4=…．再利用对数运算性质即可得出．【解答】数列{a n}、{b n}满足b n=lna n，n∈N∗，其中{b n}是等差数列，∴b n+1−b n=lna n+1−lna n=ln a n+1a n=常数t．∴a n+1a n=常数e t=q>0，因此数列{a n}为等比数列．且a3∗a1007=e4，∴a1a1009=a2a1008=a3∗a1007=e4=…．则b1+b2+...+b1009=ln(a1a2...a1009)=ln√(e4)1009=lne2018=2018．10. 如图，向量OA→与OB→的夹角为120∘，|OA→|=2，|OB→|=1，P是以O为圆心，|OB→|为半径的弧BC^上的动点，若OP→=λOA→+μOB→，则λμ的最大值是________．【答案】12【考点】平面向量的基本定理平面向量的坐标运算【解析】如图建立平面直角坐标系，设P(cosθ, sinθ)，OP→=(cosθ,sinθ)，OA→=(2,0)，OB→=(−12,√32).cosθ=2λ−12μ，sinθ=√32μ，λμ=2√3−16cos2θ+16=13sin(2θ+β)+1 6≤12，如图建立平面直角坐标系，设P(cosθ, sinθ)， OP →=(cosθ,sinθ)，OA →=(2,0)，OB →=(−12,√32)． ∵ OP →=λOA →+μOB →，∴ cosθ=2λ−12μ，sinθ=√32μ．∴ {λ=12cosθ2√3μ=√3 ， ∴ λμ=23−16cos2θ+16=13sin(2θ+β)+16≤12，11. 已知F 1、F 2分别是双曲线x 2a2−y 2b 2=1(a >0, b >0)的左右焦点，过F 1且倾斜角为30∘的直线交双曲线的右支于P ，若PF 2⊥F 1F 2，则该双曲线的渐近线方程是________． 【答案】 y =±√2x 【考点】 双曲线的特性 【解析】设|PF 1|=m ，|PF 2|=n ，|F 1F 2|=2c ，由双曲线的定义和直角三角形中的性质，可得m ，n 的关系，由a ，b ，c 的关系可得b ，再由双曲线的渐近线方程即可得到所求． 【解答】设|PF 1|=m ，|PF 2|=n ，|F 1F 2|=2c ， 在直角△PF 1F 2中，∠PF 1F 2=30∘， 可得m =2n ，则m −n =2a =n ，即a =12n ， 2c =√3n ，即c =√32n ， b =√c 2−a 2=√22n ， 可得双曲线的渐近线方程为y =±ba x ，即为y =±√2x ，12. 如图，在折线ABCD 中，AB =BC =CD =4，∠ABC =∠BCD =120∘，E 、F 分别是AB 、CD 的中点，若折线上满足条件PE →∗PF →=k 的点P 至少有4个，则实数k 的取值范围是________．【答案】 9【考点】平面向量数量积的性质及其运算律【解析】以BC的垂直平分线为y轴，以BC为x轴，建立如图所示的平面直角坐标系，分别表示各个点的坐标，设P(x, y)，根据向量的数量积可得当k+9>0时，点P的轨迹为以(0, √3)为圆心，以√k+9为半径的圆，结合图象，即可求出满足条件PE→∗PF→=k的点P至少有4个的k的取值范围．【解答】以BC的垂直平分线为y轴，以BC为x轴，建立如图所示的平面直角坐标系，∵AB=BC=CD=4，∠ABC=∠BCD=120∘，∴B(−2.0)，C(2, 0)，A(−4, 2√3)，D(4, 2√3)，∵E、F分别是AB、CD的中点，∴E(−3, √3)，F(3, √3)，设P(x, y)，−4≤x≤4，0≤y≤2√3，∵PE→∗PF→=k，∴(−3−x, √3−y)(3−x, √3−y)=x2+(y−√3)+9=k，即x2+(y−√3)=k+9，当k+9>0时，点P的轨迹为以(0, √3)为圆心，以√k+9为半径的圆，当圆与直线DC相切时，此时圆的半径r=3√3，此时点有2个，2当圆经过点C时，此时圆的半径为r=√22+3=√7，此时点P有4个，∵满足条件PE→∗PF→=k的点P至少有4个，结合图象可得，∴27≤k+9≤7，4≤k≤−2，解得−94, −2]，故实数k的取值范围为[−94二.选择题（本大题共4题，每题5分，共20分）若空间中三条不同的直线l1、l2、l3，满足l1⊥l2，l2 // l3，则下列结论一定正确的是（）A.l1⊥l3B.l1 // l3C.l1、l3既不平行也不垂直D.l1、l3相交且垂直【答案】A【考点】平面的基本性质及推论【解析】由l1⊥l2，l2 // l3，得到l1⊥l3．【解答】∴l1⊥l3，若a>b>0，c<d<0，则一定有（）A.ad>bcB.ad<bcC.ac>bdD.ac<bd【答案】D【考点】不等式的基本性质【解析】利用不等式的基本性质即可得出．【解答】∵c<d<0，∴−c>−d>0．又a>b>0，则一定有−ac>−bd，可得ac<bd．无穷等差数列{a n}的首项为a1，公差为d，前n项和为S n(n∈N∗)，则“a1+d>0”是“{S n}为递增数列”的（）条件．A.充分非必要B.必要非充分C.充要D.既非充分也非必要【答案】B【考点】必要条件、充分条件与充要条件的判断【解析】根据充分必要条件的定义判断即可【解答】等差数列{a n}的首项为a1，公差为d，前n项和为S n=na1+n(n−1)2d，则S n+1=(n+1)a1+n(n+1)d2，则S n+1−S n=(n+1)a1+n(n+1)d2−na1−n(n−1)2d=a1+nd，若{S n}为递增数列，a1+nd>0，∵S2−S1=a1+d>0，∴a1+nd>0不能推出a1+d>0但a1+d能推出a1+nd，故a1+d>0”是“{S n}为递增数列必要非充分，已知函数f(x)={log12(1−x)−1≤x≤n22−|x−1|−3n<x≤m(n<m)的值域是[−1, 1]，有下列结论：①当n＝0时，m∈(0, 2]；②当n=12时，m∈(12,2]；1④当n ∈[0,12)时，m ∈(n, 2]；其中结论正确的所有的序号是（ ） A.①② B.③④ C.②③ D.②④ 【答案】 C【考点】分段函数的应用 【解析】根据函数函数的单调性及分段函数的定义，画出函数图象，根据图象即可求得答案． 【解答】当x >1时，x −1>0，f(x)＝22−x+1−3＝23−x −3，单调递减， 当−1<x <1时，f(x)＝22+x−1−3＝21+x −3，单调递增，∴ f(x)＝22−|x−1|−3在(−1, 1)单调递增，在(1, +∞)单调递减， ∴ 当x ＝1时，取最大值为1，∴ 绘出22−|x−1|−3的图象，如图下方曲线：①当n ＝0时，f(x)={log 12(1−x)−1≤x ≤022−|x−1|−30<x ≤m，由函数图象可知：要使f(x)的值域是[−1, 1]， 则m ∈(1, 2]；故①错误；②当n =12时，f(x)=log 12(1−x)，f(x)在[−1, 12]单调递增，f(x)的最大值为1，最小值为−1， ∴ m ∈(12,2]；故②正确；③当n ∈[0,12)时，m ∈[1, 2]；故③正确，④错误， 三.解答题（本大题共5题，共14+14+14+16+18=76分）已知函数f(x)=32sinωx +√32cosωx （其中ω>0）．（1）若函数f(x)的最小正周期为3π，求ω的值，并求函数f(x)的单调递增区间；（2）若ω=2，0<α<π，且f(α)=32，求α的值． 【答案】函数f(x)=32sinωx +√32cosωx =√3sin(ωx +π6)，∵ 函数f(x)的最小正周期为3π，即T =3π=2πω∴ ω=23那么：f(x)=√3sin(23x +π6)，得：3kπ−π≤x≤π2+3kπ∴函数f(x)的单调递增区间为[−π+3kπ,π2+3kπbrack，k∈Z；函数f(x)=32sinωx+√32cosωx=√3sin(ωx+π6)，∵ω=2∴f(x)=√3sin(2x+π6)，f(α)=32，可得sin(2α+π6)=√32∵0<α<π，∴π6≤(2α+π6)≤13π62α+π6=π3或2π3解得：α=π4或α=π12．【考点】三角函数中的恒等变换应用正弦函数的图象【解析】（1）利用辅助角公式化简，根据函数f(x)的最小正周期为3π，即可求ω的值和单调递增区间；（2）将ω=2，可得f(x)解析式，0<α<π，由f(α)=32，利用三角函数公式即可求α的值．【解答】函数f(x)=32sinωx+√32cosωx=√3sin(ωx+π6)，∵函数f(x)的最小正周期为3π，即T=3π=2πω∴ω=23那么：f(x)=√3sin(23x+π6)，由2kπ−π2≤23x+π6≤2kπ+π2，k∈Z，得：3kπ−π≤x≤π2+3kπ∴函数f(x)的单调递增区间为[−π+3kπ,π2+3kπbrack，k∈Z；函数f(x)=32sinωx+√32cosωx=√3sin(ωx+π6)，∵ω=2πf(α)=32，可得sin(2α+π6)=√32∵0<α<π，∴π6≤(2α+π6)≤13π62α+π6=π3或2π3解得：α=π4或α=π12．如图，已知AB是圆锥SO的底面直径，O是底面圆心，SO=2√3，AB=4，P是母线SA的中点，C是底面圆周上一点，∠AOC=60∘．（1）求圆锥的侧面积；（2）求直线PC与底面所成的角的大小．【答案】∵AB是圆锥SO的底面直径，O是底面圆心，SO=2√3，AB=4，P是母线SA的中点，C是底面圆周上一点，∠AOC=60∘．∴r=AB2=2，l=√AO2+SO2=√4+12=4，∴圆锥的侧面积S=πrl=π×2×4=8π．过点P作PE⊥圆O，交AO于E，连结CE，则E是AO中点，∴PE=12PO=√3，CE=√22−12=√3，∵OE=1，OC=2，∴CE⊥AO，∴∠PCE是直线PC与底面所成角，∵PE=CE，PE⊥CE，∴∠PCE=π4，∴直线PC与底面所成的角为π4．【考点】旋转体（圆柱、圆锥、圆台）【解析】AB（2）过点P 作PE ⊥圆O ，交AO 于E ，连结CE ，则E 是AO 中点，∠PCE 是直线PC 与底面所成角，由此能求出直线PC 与底面所成的角．【解答】∵ AB 是圆锥SO 的底面直径，O 是底面圆心，SO =2√3，AB =4，P 是母线SA 的中点，C 是底面圆周上一点，∠AOC =60∘．∴ r =AB 2=2，l =√AO 2+SO 2=√4+12=4，∴ 圆锥的侧面积S =πrl =π×2×4=8π．过点P 作PE ⊥圆O ，交AO 于E ，连结CE ，则E 是AO 中点，∴ PE =12PO =√3，CE =√22−12=√3，∵ OE =1，OC =2，∴ CE ⊥AO ，∴ ∠PCE 是直线PC 与底面所成角，∵ PE =CE ，PE ⊥CE ，∴ ∠PCE =π4，∴ 直线PC 与底面所成的角为π4．某公司举办捐步公益活动，参与者通过捐赠每天的运动步数获得公司提供的牛奶，再将牛奶捐赠给留守儿童，此活动不但为公益事业作出了较大的贡献，公司还获得了相应的广告效益，据测算，首日参与活动人数为10000人，以后每天人数比前一天都增加15%，30天后捐步人数稳定在第30天的水平，假设此项活动的启动资金为30万元，每位捐步者每天可以使公司收益0.05元（以下人数精确到1人，收益精确到1元）． （1）求活动开始后第5天的捐步人数，及前5天公司的捐步总收益；（2）活动开始第几天以后公司的捐步总收益可以收回启动资金并有盈余？【答案】设第x 天的捐步人数为x ，则f(x)={10000(1+15%)x−1,1≤x ≤30f(30),x >30． ∴ 第5天的捐步人数为f(5)=10000⋅(1+15%)4=17490．由题意可知前5天的捐步人数成等比数列，其中首项为10000，公比为1.15，∴ 前5天的捐步总收益为10000(1−1.155)1−1.15×0.05=3371；设活动第x 天后公司捐步总收益可以回收并有盈余，①若1≤x ≤30，则10000(1−1.15x )1−1.15×0.05>300000，解得x >log 1.1591≈32.3（舍）．②若x >30，则[10000(1−1.1530)1−1.15+10000⋅1.1529⋅(x −30)]•0.05>300000，解得x >32.87．∴ 活动开始后第33天公司的捐步总收益可以收回启动资金并有盈余．【考点】等比数列的性质根据实际问题选择函数类型【解析】（1）根据等比数列的性质求出；（2）对活动天数x 进行讨论，列出不等式求出x 的范围即可．【解答】设第x 天的捐步人数为x ，则f(x)={10000(1+15%)x−1,1≤x ≤30f(30),x >30． ∴ 第5天的捐步人数为f(5)=10000⋅(1+15%)4=17490．由题意可知前5天的捐步人数成等比数列，其中首项为10000，公比为1.15，∴ 前5天的捐步总收益为10000(1−1.155)1−1.15×0.05=3371；设活动第x 天后公司捐步总收益可以回收并有盈余，①若1≤x ≤30，则10000(1−1.15x )1−1.15×0.05>300000，解得x >log 1.1591≈32.3（舍）．②若x >30，则[10000(1−1.1530)1−1.15+10000⋅1.1529⋅(x −30)]•0.05>300000，解得x >32.87．∴ 活动开始后第33天公司的捐步总收益可以收回启动资金并有盈余．已知椭圆x 210+y 29=1的右焦点是抛物线Γ：y 2=2px 的焦点，直线l 与Γ相交于不同的两点A(x 1, y 1)、B(x 2, y 2)．（1）求Γ的方程；（2）若直线l 经过点P(2, 0)，求△OAB 的面积的最小值（O 为坐标原点）；（3）已知点C(1, 2)，直线l 经过点Q(5, −2)，D 为线段AB 的中点，求证：|AB|=2|CD|．【答案】由椭圆x 210+y 29=1，得a 2=10，b 2=9，则c =1． ∴ 椭圆x 210+y 29=1的右焦点，即抛物线Γ：y 2=2px 的焦点为(1, 0)， 则p 2=1，p =2，∴ Γ的方程为y 2=4x ；设直线l:x =my +2，联立{x =my +2y 2=4x，得y 2−4my −8=0． 则y 1+y 2=4m ，y 1y 2=−8．∴ S △OAB =12×2×|y 1−y 2|=√(y 1+y 2)2−4y 1y 2=√16m 2+32=4√m 2+2≥4√2，即△OAB 的面积的最小值为4√2；证明：当AB 所在直线斜率存在时，设直线方程为y +2=k(x −5)，即y =kx −5k −2．联立{y =kx −5k −2y 2=4x，可得ky 2−4y −20k −8=0． y 1+y 2=4k，y 1y 2=−20k+8k ． x 1+x 2=y 1+y 2+10k+4k =10k 2+4k+4k 2． x 1x 2=(y 1+5k +2)(y 2+5k +2)k 2=y 1y 2+(5k +2)(y 1+y 2)+(5k +2)2k 2 =−20k+8k +(5k+2)∗4k+(5k+2)2k 2=(5k+2)2k 2．∵ C(1, 2)，∴ CA →=(x 1−1,y 1−2)，CB →=(x 2−1,y 2−2)，则CA →∗CB →=(x 1−1)(x 2−1)+(y 1−2)(y 2−2)=x 1x 2−(x 1+x 2)+1+y 1y 2−2(y 1+y 2)+4=(5k+2)2k 2−10k 2+4k+4k 2−20k+8k −8k +4=0， 当AB 所在直线斜率不存在时，直线方程为x =5，联立{x =5y 2=4x，可得A(5, −2√5)，B(5, 2√5)， CA →=(4,−2√5−2)，CB →=(4,2√5−2)，有CA →∗CB →=0，∴ CA ⊥CB ，又D 为线段AB 的中点，∴ |AB|=2|CD|．【考点】椭圆的定义【解析】（1）由题意方程求出右焦点坐标，即抛物线焦点坐标，进一步可得抛物线方程； （2）设出直线方程，与抛物线方程联立，化为关于y 的一元二次方程，利用根与系数的关系求得|y 1−y 2|，代入三角形面积公式，利用二次函数求最值；（3）分直线AB 的斜率存在与不存在，证明有CA →∗CB →=0，可得CA ⊥CB ，又D 为线段AB 的中点，则|AB|=2|CD|．【解答】由椭圆x 210+y 29=1，得a 2=10，b 2=9，则c =1． ∴ 椭圆x 210+y 29=1的右焦点，即抛物线Γ：y 2=2px 的焦点为(1, 0)，则p 2=1，p =2，∴ Γ的方程为y 2=4x ；设直线l:x =my +2，联立{x =my +2y 2=4x，得y 2−4my −8=0． 则y 1+y 2=4m ，y 1y 2=−8．∴ S △OAB =12×2×|y 1−y 2|=√(y 1+y 2)2−4y 1y 2=√16m 2+32=4√m 2+2≥4√2，即△OAB 的面积的最小值为4√2；证明：当AB 所在直线斜率存在时，设直线方程为y +2=k(x −5)，即y =kx −5k −2．联立{y =kx −5k −2y 2=4x，可得ky 2−4y −20k −8=0． y 1+y 2=4k ，y 1y 2=−20k+8k ． x 1+x 2=y 1+y 2+10k+4k =10k 2+4k+4k 2． x 1x 2=(y 1+5k +2)(y 2+5k +2)k 2=y 1y 2+(5k +2)(y 1+y 2)+(5k +2)2k 2=−20k+8k +(5k+2)∗4k+(5k+2)2k 2=(5k+2)2k 2．∵ C(1, 2)，∴ CA →=(x 1−1,y 1−2)，CB →=(x 2−1,y 2−2)，则CA →∗CB →=(x 1−1)(x 2−1)+(y 1−2)(y 2−2)=x 1x 2−(x 1+x 2)+1+y 1y 2−2(y 1+y 2)+4=(5k+2)2k 2−10k 2+4k+4k 2−20k+8k −8k +4=0， 当AB 所在直线斜率不存在时，直线方程为x =5，联立{x =5y 2=4x，可得A(5, −2√5)，B(5, 2√5)， CA →=(4,−2√5−2)，CB →=(4,2√5−2)，有CA →∗CB →=0，∴ CA ⊥CB ，又D 为线段AB 的中点，∴ |AB|=2|CD|．对于函数y =f(x)(x ∈D)，如果存在实数a 、b （a ≠0，且a =1，b =0不同时成立），使得f(x)=f(ax +b)对x ∈D 恒成立，则称函数f(x)为“(a, b)映像函数”． （1）判断函数f(x)=x 2−2是否是“(a, b)映像函数”，如果是，请求出相应的a 、b 的值，若不是，请说明理由；（2）已知函数y =f(x)是定义在[0, +∞)上的“(2, 1)映像函数”，且当x ∈[0, 1)时，f(x)=2x ，求函数y =f(x)(x ∈[3, 7)）的反函数；（3）在（2）的条件下，试构造一个数列{a n }，使得当x ∈[a n , a n+1)(n ∈N ∗)时，2x +1∈[a n+1, a n+2)，并求x ∈[a n , a n+1)(n ∈N ∗)时，函数y =f(x)的解析式，及y =f(x)(x ∈[0, +∞)）的值域．【答案】由f(x)=x 2−2，可得f(ax +b)=(ax +b)2−2=a 2x 2+2abx +b 2−2， 由f(x)=f(ax +b)，得x 2−2=a 2x 2+2abx +b 2−2，则{a 2=12ab =0b 2−2=−2，∵ a ≠0，且a =1，b =0不同时成立， ∴ a =−1，b =0．∴ 函数f(x)=x 2−2是“(−1, 0)映像函数”；∵ 函数y =f(x)是定义在[0, +∞)上的“(2, 1)映像函数”，∴ f(x)=f(2x +1)，则f(0)=f(1)=f(3)，f(1)=f(3)=f(7)，∴ f(0)=f(3)，f(1)=f(7)，而当x ∈[0, 1)时，f(x)=2x ，∴ x ∈[3, 7)时，设f(x)=2sx+t ，由{3s +t =07s +t =1，解得s =14，t =−34． ∴ x ∈[3, 7)时，f(x)=214(x−3)．令y =214(x−3)(3≤x <7)，得14(x −3)=log 2y ，∴ x =log 2y 4+3(1≤y <2)，∴ 函数y =f(x)(x ∈[3, 7)）的反函数为y =log 2x 4+3(1≤x <2)；由（2）可知，构造数列{a n }，满足a 1=0，a n+1=2a n +1，则a n+1+1=2(a n +1)，∴ 数列{a n +1}是以1为首项，以2为公比的等比数列，则a n +1=2n−1，即a n =2n−1−1．当x ∈[a n , a n+1)=[2n−1−1, 2n −1)．令{(2n−1−1)s +t =0(2n −1)s +t =1，解得s =21−n ，t =21−n −1． ∴ x ∈[a n , a n+1)(n ∈N ∗)时，函数y =f(x)的解析式为f(x)=221−n x+21−n −1． 当x ∈[0, +∞)时，函数f(x)的值域为[1, 2)．【考点】函数解析式的求解及常用方法【解析】（1）直接由题意列关于a ，b 的方程组，求解得答案；（2）由题意可得f(0)=f(3)，f(1)=f(7)，而当x ∈[0, 1)时，f(x)=2x ，则x ∈[3, 7)时，设f(x)=2sx+t ，可得{3s +t =07s +t =1，求得s ，t 的值，则函数解析式可求，把x用含有y 的代数式表示，把x ，y 互换可得y =f(x)(x ∈[3, 7)）的反函数； （3）由（2）可知，构造数列{a n }，满足a 1=0，a n+1=2a n +1，可得数列{a n +1}是以1为首项，以2为公比的等比数列，由此求得a n =2n−1−1．当x ∈[a n , a n+1)=[2n−1−1, 2n−1)，令{(2n−1−1)s +t =0(2n −1)s +t =1 ，解得s =21−n ，t =21−n −1，可得x ∈[a n , a n+1)(n ∈N ∗)时，函数y =f(x)的解析式为f(x)=221−n x+21−n −1，并求得x ∈[0, +∞)时，函数f(x)的值域为[1, 2)．【解答】 由f(x)=x 2−2，可得f(ax +b)=(ax +b)2−2=a 2x 2+2abx +b 2−2， 由f(x)=f(ax +b)，得x 2−2=a 2x 2+2abx +b 2−2，则{a 2=12ab =0b 2−2=−2，∵ a ≠0，且a =1，b =0不同时成立， ∴ a =−1，b =0．∴ 函数f(x)=x 2−2是“(−1, 0)映像函数”；∵ 函数y =f(x)是定义在[0, +∞)上的“(2, 1)映像函数”，∴ f(x)=f(2x +1)，则f(0)=f(1)=f(3)，f(1)=f(3)=f(7)， ∴ f(0)=f(3)，f(1)=f(7)，而当x ∈[0, 1)时，f(x)=2x ，∴ x ∈[3, 7)时，设f(x)=2sx+t ，由{3s +t =07s +t =1，解得s =14，t =−34． ∴ x ∈[3, 7)时，f(x)=214(x−3)．令y =214(x−3)(3≤x <7)，得14(x −3)=log 2y ，∴ x =log 2y 4+3(1≤y <2)，∴ 函数y =f(x)(x ∈[3, 7)）的反函数为y =log 2x 4+3(1≤x <2)； 由（2）可知，构造数列{a n }，满足a 1=0，a n+1=2a n +1，则a n+1+1=2(a n +1)，∴ 数列{a n +1}是以1为首项，以2为公比的等比数列，则a n +1=2n−1，即a n =2n−1−1．当x ∈[a n , a n+1)=[2n−1−1, 2n −1)．令{(2n−1−1)s +t =0(2n −1)s +t =1，解得s =21−n ，t =21−n −1． ∴ x ∈[a n , a n+1)(n ∈N ∗)时，函数y =f(x)的解析式为f(x)=221−n x+21−n −1．当x ∈[0, +∞)时，函数f(x)的值域为[1, 2)．。

图1图2图3闵行区2018学年第一学期质量调研考试生命科学试卷(高二、高三年级)考生注意：1．全卷共8页，满分100分，考试时间60分钟。

2．本考试分设试卷和答题纸。

3．答题前，务必在答题纸上用钢笔、圆珠笔或签字笔清楚填写学校、姓名及考生号，并填涂考生号。

4．作答必须涂或写在答题纸上，在试卷上作答一律不得分。

一．选择题（共40分，每小题2分。

每小题只有一个正确答案）1．基因编辑是指对基因组进行定点修饰的一项技术。

此技术可以改变生物多样性中的 A .遗传多样性 B .细胞多样性 C .物种多样性 D .生态系统多样性2．图1所示化合物的虚框①~④中，属于某一氨基酸R 基的是A .①B .②C .③D .④3．使用目镜测微尺在显微镜的高倍镜40×下测得蚕豆叶下表皮一个保卫细胞的长占16格，换用低倍镜10×后，该保卫细胞的长所占格数是 A .4B .8C .16D .324．原核细胞和真核细胞在结构上最主要的区别是 A .细胞大小不同B .有无细胞器C .有无DNAD .有无成形的细胞核5．图2中甲物质为ADP ，其转变为乙物质时需要提供 A .磷酸、酶、腺苷和能量 B .能量、腺苷和酶 C .磷酸、能量和酶D .磷酸、能量6．图3是人体内物质代谢的部分示意图，字母代表物质，数字代 表过程。

下列叙述正确的是 A .①表示转氨基作用 B .②也存在于脂肪代谢中C .葡萄糖转变为物质X 的过程发生于线粒体中D .物质Y 是丙酮酸图4图5图67．将紫色洋葱鳞叶外表皮细胞置于30%蔗糖溶液中数分钟后，用清水 引流，重复多次，此过程中图4细胞发生的变化是 A .①区扩大，②区紫色变浅 B .①区缩小，②区紫色加深 C .①区扩大，②区紫色不变 D .①区缩小，②区紫色变浅 8．在受涝时，植物根部会进行短时的无氧呼吸。

大部分植物细胞无氧呼吸时产生A .乙醇和CO 2B .乳酸和CO 2C .CO 2和H 2OD .乙醇和H 2O9．为研究细菌F 的生理活动，兴趣小组设计实施了如表1的实验，此实验的结论是A .淀粉遇碘显蓝色B .细菌F 能分泌淀粉酶C .细菌F 能利用碘液D .此淀粉固体培养基无杂菌污染10.图5为细胞周期模式图，下列叙述错误．．的是11．基因型为AaBb 的马铃薯要得到基因型为aabb 的后代，可采用的生殖方式是A .分裂生殖B .出芽生殖C .营养繁殖D .有性生殖12．肝脏细胞将甘油三酯运送到血液的脂蛋白形式是 A .高密度脂蛋白（HDL ） B .低密度脂蛋白（LDL ） C .极低密度脂蛋白（VLDL ） D .乳糜微粒（CM ）13．某地区甲虫的抗药性如图6所示，据图判断A .农药引起了原始甲虫的变异B .原始甲虫发生了定向变异C .抗药强的甲虫发生了进化D .农药对甲虫的抗药性状进行了选择 14．以下技术与应用匹配不正确．．．的是 A .核移植技术——培养鲤鲫核质杂交鱼 B .干细胞技术——提供用于移植的细胞或器官 C .细胞融合技术——培育单倍体植物D .酶的固定化技术——固定α淀粉酶连续水解废水中的淀粉A .与DNA 复制有关的酶合成于Y 期B .选择2期细胞诊断染色体遗传病C .3期细胞完成染色单体分离D .4期末消失的细胞结构有核仁、核膜图8 图9图10图1115．图7为反射弧模式图，下列叙述错误．．的是16．图8表示不同浓度生长素溶液对某植物芽生长 的影响，可正确解释植物呈宝塔状株形的顶芽和 侧芽的生长素浓度组合是17．下列关于“性状分离比模拟实验”的叙述正确的是 ①取2个相同小桶，在每桶内放入2种颜色的相同小球各10个②摇匀后从两桶内各随机抓取1个小球，记录后分别放回原桶，如此重复50次 ③统计每种小球组合和每种组合对应性状的合计数、占总数的百分率 ④统计小组的结果比全班的结果更接近孟德尔试验的分离比 A .①②③B .①②④C .①③④D .②③④18．若图9所示果蝇的一个原始生殖细胞产生了一个基因型为aX B 配子，则同时产生的另外三个子细胞的基因型是 A .aX B 、AY 、AY B .AX B 、aY 、aY C .AX B 、aY 、AYD .AY 、aX B 、aX B19．图10曲线表示某健康成年人饮1升清水后的尿生成速率，分析0.5(h)~1.5(h)时段内其血浆渗透压随时间的变化是20．图11为胰岛素降低血糖浓度的部分作用机理模式图，下列分析错误．．的是A .①为感受器，④为神经中枢B .③处兴奋时膜电位为内正外负C .⑥内通过化学物质传递信息D .增加⑤处细胞外Na +浓度，⑤处兴奋时膜内外电位差的峰值下降A .顶芽m ，侧芽nB .顶芽n ，侧芽gC .顶芽i ，侧芽gD .顶芽i ，侧芽mA .先升后降B .先降后升C .持续上升D .持续下降A .胰岛素起信号分子的作用，促进葡萄糖进入细胞从而降低血糖B .胰岛素能促进细胞合成蛋白质、脂肪和糖原C .若药物抑制细胞内ATP 的合成，会促进葡萄糖进入细胞的速率D .若体内出现胰岛素受体的抗体，会发生2型糖尿病图7二、综合分析题（共60分）（一）生命的基础（12分）图12为真核细胞结构及细胞内物质转运的示意图，其中①~⑥表示结构。

闵行区2017 学年第一学期高三年级质量调研考试英语试卷2017.12.27考生注意：1.考试时间120 分钟，试卷满分140 分.2.本考试设试卷和答题纸两部分，试卷共12 页。

所有答题必须涂(选择题)或写(非选择题)在答题纸上，做在试卷上一律不得分.3.答题前，务必在答题纸上填写考生号和姓名.Ⅰ. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversation and the questions will be spoken only once. After you hear a conversation and the question about it, read die four possible answers on your paper, and decide which one is the best answer to the question you have heard.1.A. At a gas station B. At a gas stationC. In a park.D. In an emergency room.2.A. Clean the backyard. B. Washing something.C. Sit in the backyard.D. Do some shopping.3.A. He finds his present job boring. B. He is too foolish to do the present job.C. lie has got a beer position.D. He doesn’t get on well with the others4.A. She has a tight schedule. B. She has lost interest in sports.C. The training is too hard.D. She is only interested ill routine work.5.A. Rules restricting smoking. B. Ways to quit smoking.C. Smokers’ health problems.D. Dangers of smoking6.A. He's going to visit a photo studio. B. He's just had his picture taken.C. He's on the way to the theater.D. He's just returned from a job interview.7.A. He had to reject their request. B. He felt sorry for the other students.C. He agreed to consider their requestD. He regretted that he had said “Yes".8.A. She is trying to find a good-looking chair.B.She thinks it is a well-designed chair.C.She thinks the chair is actually comfortable.D.She's never sat in that chair before.9.A. She used to be in poor health. B. She was popular among boysC. She was somewhat overweightD. She didn’t do well at high school10.A. Review the details of all her lessons B. Compare notes with his classmatesC. Talk with her about his learning problems.D. Focus on the main points of her lecturesSection BDirections: In Section B, you will hear two passages and a longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages and conversation will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one is the best answer to the question you have heard.Questions 11 to 13 are based on the following passage.11.A. The excitement of nerve activities in the brain.B.The difference between complex music and simple music.C.The effects of music on the results of math tests.D.The classical music and reasoning ability.12.A. Because it stimulates your nerve activity.B.Because it keeps you calmC.Because it strengthens your memory.D.Because it interferes your reasoning ability.13.A. Rock music might help improve your math test scoresB.The effects of music on tests do not last long.C.Listen to music just before you take a testD.The more you listen to music, the better your reasoning ability will beQuestions 14 to 16 are based on the following passage.14.A. It is the most unlucky day in a year. B. It is the busiest shopping day now.C. It is the day after ThanksgivingD. It is the day before Christmas.15.A. Check out the latest price reduction online.B.Look round for items in the physical stores.C.Order the products from the online stores.D.Wait in queue outside the stores overnight.16.A. 100 million dollars. B. 670 million dollars. C. 20 billion dollars. D. 25 billion dollars.Questions 17 to 20 are based on the following conversation.17.A Their attitudes about work B. Different forms of work.C. Importance of work for oneself.D. Balanced life and work.18.A. The most hopeful. B. The most challenging.C. The most creative.D. The most enjoyable.19.A. His negative attitude towards work.B.His unwillingness to do something for others.C.His selfishness in doing things.D.His misunderstanding about publishing work20.A. The work is worth doing if it is challenging and competitive.B.The work should be very creative leading to a wonder.C.One should like his work and stick to it as long as he takes it.D One should find satisfaction in his work if it is necessary.Ⅱ. Grammar and VocabularySection ADirections: After reading the passage below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blankHonesty, my mum always used to tell me, is the best policy. But when it comes to medicine, Ihad assumed it was important to always be honest with my patients. After all, the doctor-patient relationship is based on trust, and therefore honesty is essential, or so I thought.I had just started working in geriatrics(老年病科). Mr. McMahon 21 in when his bodywas found very swollen （浮肿的）. I took a medical history 22 his daughter who had accompanied him in the ambulance. She'd been his main career for years. I stood 23 (look) at him as she gave a detailed history. "Has he lost any weight recently?" I asked, "Well, it's funny you should mention that, but yes." She said slowly. There was silence for a few moments. "Why? What are you worried about?" she asked. She was obviously very involved in his care and it was only fair that I told 24 the truth. "Well, we need to prove it's not cancer." I said and talked briefly about some of the tests I was going to order.Half an hour later, a nurse called me: "Mr. McMahon's daughter broke down－she said you told her he had cancer." My heart sank. By the time I arrived at the ward, my consultant was already there, explaining that we still had to run lots of tests and that it was by no means confirmed 25 he had cancer. I stood silently at the end of the bed. My consultant was obviously angry with me and as we left Mr. McMahon, she turned to me. "Why on earth did you do that?" she asked in disbelief. I looked at her and bit my lip. "She asked me what I was worried about and I told her." I said, hanging my head. "And give her more 26 (worry) about?" replied my consultant. "You don't say the word 'cancer' until it's confirmed. 27 you suspect it, think very carefully before you tell people."As it turned out, it wasn't cancer. But I did learn that when someone is stressed and worried about their loved one they're sometimes selective in 29 they hear －and as a doctor it's important to be mindful of this. In being truthful, I'd made the situation 30 (bad).Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.How many times have parents had to ague with their young son or daughter about gettingtheir face out of their phone and focusing on the world around them? It's completely normal for parents of growing children to be concerned about their child's safely, but is their 31 to social media really harming them.Social media was created to connect people with others online and has recently been added to smartphones, making it fat more accessible than it 32 was. This new way to easily be able to use social media has encouraged children and teens to begin to use sites such as Facebook, Twitter and Instagram frequently. Maturing teens and children are usually very timid when it comes to 33 with their families, which they sometimes view as "annoying”. So, what do these kids use as a solution or a(n)“ 34 " The answer is simple social media.However, when they use social media for a large amount of time, parents lend to show concern for their child and blame social media for 35 their attention.The word, "social", was entered into the term, social media, for a reason. Parents of growing teens don't seem to understand that. When they see their child using Twitter or Instagram they think that they using it to get away from real world 36 . The truth, however, is that they are using it to conned with their close friends, make new friends, and receive information about what is currently happening in the modem worldChildren and teens are 37 accused for using social media only for entertainment purposes and for huge amounts of time. Sure, everyone who uses social media enjoys contacting their friends and viewing entertaining things, but how come children receive all of the 38 for abusing it? Parents should really think about how social media can help children and teens learn and grow in the real world rather than it just being another 39.Social media as a whole has both positive and negative aspects, but after all of the 40 from pre-teens, teens, and parents is put together, it shows that media is actually helping the newer generations in their lives.Ⅲ. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Your boss tells you that you did a bad job. Your coworker criticizes you in front of yourwhole team. Ouch! It's not easy to take criticism, no matter who it comes from. But, it is easy to_41_ the blow when you offer criticism to someone in English. Merely by altering your wording and your attitude, you can help someone grow instead of making them feel 42.Phrases like "You’re wrong! ” and “Your presentation was terrible!" have no place in effective 43. In fact, it's best to leave the word "you" out, if at all possible. 44 attacks make people feel defective, and then they won't really listen to anything you have to say.Before starting with the criticism, warm the person up with 45 .If you are discussing their work, find several things you truly like about what they have done. For example, "I enjoyed your presentation today. You presented a lot of good and helpful information in it, and I can tell you put a lot of effort into it. I appreciate your hard work." This will lower their 46 and make them feel appreciated.However, a short 47 compliments followed by "but" such as “It was a helpful talk, but you really need to improve your presentation skills" won't do much to help the process. After you’ve shared your compliments, allow them time to be 48 . As a matter of fact, 49 following your compliment with a “,but” will destroy all you've tried to accomplish by making your 50 seem false and insincere.Remember that the goal of constructive criticism isn’t to make the person feel terrible: it's to help them grow. Instead of directly 51 the person, try to get the message through to them in the form of light-hearted advice. Phrases like. "Next time you might want to…” or “I find it helpful to " can 52 the blame while still leaving an impact: "Next time you might want to give a little more attention to the audience. I find it helpful to look people in the eyes while I am speaking"People can't change overnight, especially if they don’t get detailed 53. As you might have known, 54 saying “you need to work on your presentation skills “won’t help a soul! Be detailed in your advice! Show moderation when you criticize anyone and keep in your mind that over-criticism can easily 55 people. Remember, you want them to keep trying and improving. Don't leave them feeling defeated'41. A. suffer B. accept C. soft D. ignore42. A defeated B encouraged C. motivated D. disturbed43. A. discussion B. argument C. explanation D. criticism44. A. Immediate B. Personal C. Accurate D. Continuous45. A. interactions B. impressions C. personalities D. compliments46. A. defense B spirit C. moral D. position47. A. decisive B. serious C. vague D. concrete48. A. corrected B. challenged C. debated D. absorbed49. A. carefully B. reluctantly C. immediately D. occasionally50. A. praise B. attitude C. assistance D. achievement51. A. helping B. accusing C. praising D. dismissing52. A. make up B. focus on C. lead to D. take away53. A. command B. comment C. instruction D. information54. A. sincerely B. simply C. politely D. unwillingly55. A. overload B promote C. inspire D simulateSection BDirections: Read the following passages. Each passage is followed by several questions or Unfinished statements. For each of them there are four choices marked A. B. C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)Korean Americans at GBS High SchoolGlenbrook South (GBS) High School is in a suburb of Chicago, Illinois, in the United States. It is an award-winning school with a highly competent teaching staff. It has over 400 Asian Pacific. American students-over 17 percent of die students in the school. Of these, the majority are Korean American. This is very unusual in a state where Korean Americans are less than 1 percent of the population. The interactions of the Korean American students at UBS were the subject of an article in Asian Week magazine.Different Korean American students react differently to being in a high school were most students are white. Professor Pyong Gap Min, an expert on Korean life in America, believes that Korean Americans in this situation can sometimes feel inhibited or ashamed of their Korean identity. Asian Week interviewed a number of GBS students, and each had a different attitude. Alice 18 years oldI used to spend time only with Korean American friends Although I felt secure with thosefriends, I found myself motivated to form closer relationship with non-Koreans, too. I felt I was missing out on new experiences and challenges.Paul 16 years oldI have some Korean American friends, but I spend most of my time with white friends. I’m often the only Asian American in the group, but I don’t mind. What I like about the white culture is that I can be more radical. I can be as loud and funny as I want t o be. I don’t see as much of that among the Asian students.John 17 years oldIn junior high school, most of my friends were white. After coming to GBS, my sense of my Korean American identity was restored, and I decided to have mainly Korean American friends. I feel that my Korean American friends and I mainly understand each other better. For example, we understand about severe parental pressures to succeed at school; I felt my white friends couldn’t really understand.Without belittle( 轻视）t he importance of what these students had to say, it’s important to remember that their opinions at this phase of their lives ate bound to change as they grow into adulthood. But these honest opinions can help us better understand issues of culture relations, and their honesty might help Americans from different cultural groups to get along better in the future.56.The passage mainly discusses .A.how Korean American students interact among themselves and with othersB.why Illinois is a very special stateC.how an Illinois high school welcomes Korean American studentsD.different opinions of the friends of Korean American students57.Which statement best summarizes Alice's attitude?A.She feels that her white friends don’t really understand herB.She likes her Korean American friends but wants to have non-Korean friends too.C.She feels she is missing out on experiences with her Korean American fiends.D.She doesn’t feel secure in her relationships with non-Koreans.58.The underlined word “radical” most probably means" "A. timidB. expressiveC. considerateD. sensitive(B)The documentary Blood Lions shows South Africa's cruel "canned' lion hunting industry. In canned hunts, lions are raised by humans and kept in enclosed spaces on private hunting areas. Hunters can get trophy （战利品）easily in exchange for fees of up to $50, 000. There are about 8,000 ranch lions in South Africa. So the country’s hunt operators can make a fortune.Ian Michler was a lead character in the film. He talked about Blood Lions last July when it was shown in Durban, South Africa. The film has since been viewed in 185 countries. More than 50 screenings have been held at film festivals and in meetings of special interest groups. This year, Blood Lions will be shown at every major tourism conference in Europe and Africa.Outside the film, Michler and the team are running a global campaign. They are aiming at ending canned hunts and other cold-blooded activities involving lions and other animals.Australia became the first country, in February 2015, to forbid imports of lion trophies. It was followed by France in November, That month, Blood Lions was shown in the European Parliament. As a result, the government of Finland, Italy, and Spain decided to hold their own screenings. There are a number of other countries likely to do the same.At the same time, at the end of last year, the world's leading group of African lion researchers offered an important suggestion They advised that any analysis of the present state of wild lions in South Africa should not include its thousands of ranch lions. Wild lions in South Africa now number some 3, 000. There are around 20,000 wild lions in Africa."The great majority of lion populations in Africa have been reduced,” says Hans Bauer, lion researcher at Oxford University Wildlife Conservation Research Unit. 'It's important to stress that South Africa's ranch lions are horror that has nothing to do with lion protection. These lions should never be taken into account in any serious analysis of the state of lions in Africa."59.What do we learn about the documentary Blood Lions?A. It has an international influence.B. It has attracted many tourists.C. It tell the story of a lion fighter.D. It has brought the producer lots of money60.Michler and his team's campaign .A. was first started in AustraliaB. has won little support in EuropeC. has achieved noticeable effectsD. aims to save endangered animals61.What can we infer about Hans Bauer?A .He suggests analyzing lions properly.B.He has seen an increase of African wild lionsC.He maybe a strong supporter of trophy hunting.D.He hopes that there will be more ranch lions in Africa.62.What is the main purpose of the passage?A.To explain the main idea of a new film.B.To report an animal protection campaignC.To encourage fanners lo raise ranch lions.D.To advertise South Africa's hunting industry.(C)One of the main challenges facing many countries is how to maintain their identity in the face of globalization and the growing multi-language trend. "One of the main reasons for economic failure in many African countries is the fact that, with a few important exceptions, mother-tongue education is not practiced in any of the independent African states." said Nellie Alexander, Director of the Project for the Study of Alternative education in South Africa at the University of Cape Town.In response to the spread of English and the increased multi-language trends arising from immigration, many countries have introduced language laws in the laws in the last decade. In some, the use of languages other than the national language is banned in public spaces such as advertising posters. One of the first such legal provisions was the 1994 "Toubon Law" in France, but the idea has been copied in many countries since then. Such efforts to govern language use are often dismissed as futile by language experts, who are well aware of the difficultly in controlling fashions in speech and know from research that language switching among bilinguals is a natural process.It is especially difficult for native speakers of English to understand the desire to maintain the “purity” of a language by law. Since the time of Shakespeare, English has continually absorbed foreign words into its own language. English is one of the most mixed and rapidly changing languages in the world, but there has not been a barrier to acquiring prestige and power. Another reason for the failure of many native English speakers to understand the role of state regulation is that it has never been the Anglo-Saxon way of doing things. English has never had a state-controlled authority for the language, similar, for example, to the Academic Francaise inFrance.The need to protect national languages is, for most western Europeans, a recent phenomenon—especially the need to ensure that English does not unnecessary take over too many fields. Public communication, education and new modes of communication promoted by technology, may be key fields lo defend63.Neville Alexander believes that?A.mother-tongue education is not practiced in all African countriesB.globalization has resulted in the economic failure of AfricaC.globalization has led to the rise of multi-language trendsck of mother-tongue education can lead to economic failure64.The underlined word “futile” (in paragraph 2) most probably means “”.A. workableB. practicalC. uselessD. unnecessary65.Why do many English-speaking countries not support the language protection efforts described in the passage?A.They think language protection laws are ineffective.B.They want their language to spread to other countries.C.They have a long history of taking words from other languages.D.It reduces a language's ability to acquire international importance66.What can we infer from the last paragraph?A.English has taken over fields like public communication and educationB.Many sheets of national culture are threatened by the spread of English.C.Most language experts believe it is important to promote a national language.D.Europeans have long realized the need to protect their national languages.Section CDirections: Read the following passage carefully. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once .Note that there are two more sentences than you need.A. But the brain is also very plastic.B.Most importantly, geniuses all seem to have a mission beyond their individual identityC.She is establishing habits of thought she can call upon in order to understand or solve future problems.D.Practicing ambitiously would be a driving force of women approaching the success.E.This contact would give the girl a vision of her future self.F.Instead, it's deliberate practice.The latest research suggests that the key factor separating geniuses from the merely accomplished is not IQ, a generally bad predictor' of success. 68 Top performers spend more hours practising their craft. If you wanted to picture how a typical genius might develop, you'd take a girl who possessed a slightly above average language ability. It wouldn’t have to be a big talent, just enough so that she might gain some sense of distinction. Then you would want her to meet, say, a novelist, who coincidentally some similar qualities. Maybe the writer was from the same town, had the same family background, or shared the same birthday.68 It would give her some idea of a fascinating circle she might someday join. It would also help if one of her parents died when she was 12, giving her a strong sense of insecurity and fuelling a desperate need for success, Armed with this ambition, she would read novels and life stories of writers without end. This would give her a primary knowle dge of her field. She’d able to see new writing in deeper ways and quickly understand its inner workings.Then she would practise writing. Her practice would be slow, painstaking and error focused. By practising in this way, site delays the automatizing process. Her mind wants to turn conscious, newly learned skills into unconscious, automatically performed skills. By practising slowly, by breaking skills down into tiny parts and repealing, she forces the brain to internalize a better pattern of performance. Then she would find an adviser who would provide a constant stream of feedback, viewing her performance from the outside, correcting the smallest errors, pushing her to take on tougher challenges. By now she is redoing problems-how do I get characters into a room-dozens and dozens of times. 69The primary quality our young writer possesses is not some mysterious genius. It's the ability to develop a purposeful, laborious and boring practice routine. The latest research takes some of the magic out of great achievement. But it underlines a fact that is often neglected. Public discussion is affected by genetics and what we're "hardwired" to do. And it's true that genes play arole in our capabilities. 70 We construct ourselves through behavior.Ⅳ. Summary WritingDirections: Read the following passage. Summarize the main idea and the main points of the passage in no more than 60 words. Use your own words as far as possible.California condors are North American’s largest birds, will wing-length of up to 3 meters. In the 1980s, electrical lines and lead poisoning nearly drove them to dying out. Now, electric shock training and medical treatment are helping to rescue these big birds.In the late 1980s, the last few condors were taken from the wild, and there are now more than 150 flying over California and nearby Arizona, Utah and Baja in Mexico. Electrical lines have been killing them off. “As they go in to rest for the night, they just don’t see the power lines,” says Bruce Rideout of San Diego Zoo. Their wings can bridge the gap between lines, resulting in electrocution(电死) if they touch two lines at once. So scientists have come up with a shocking idea. Tall poles, placed in large training areas, teach the birds to stay clear of electrical lines by giving them a painful but undeadly electric shock. Before the training was introduced, 66% of set-freed condors died of electrocution. This has now dropped to 18%.Lead poisonous has proved more difficult to deal with. When condors eat dead bodies of other animals containing lead, they absorb large quantities of lead. This affects their nervous systems and ability to produce baby birds, and can lead to kidney failures and death. So condors with high levels of lead are sent to Los Angeles Zoo, where they are treated with calcium EDTA, a chemical that removes lead from the blood over several days. This work is starting to pay off. The annual death rate for adult condors has dropped from 38% in 2000 to 5.4% in 2011.Rideout’s team thinks that the California condors’ average survival time in the wild is now just under eight years. “Although these measures are not effective forever, they are vital f or now,” he says. “They are truly good birds that are worth every effort we put into recovering them.”V.TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72.这个专家所推荐的方法被证明是十分有效的。

上海市闵行区2018学年度第一学期高三数学（一模）期末质量监控试卷一、选择题（本大题共4小题，共12.0分）1.若a，b为实数，则“”是“”的A. 充要条件B. 充分非必要条件C. 必要非充分条件D. 既非充分必要条件【答案】B【解析】【分析】根据充分条件和必要条件的概念，即可判断出结果.【详解】解不等式得或；所以由“”能推出“或”，反之不成立，所以“”是“”的充分不必要条件.故选B【点睛】本题主要考查充分条件与必要条件的概念，熟记概念即可，属于基础题型.2.已知a，b为两条不同的直线，，为两个不同的平面，，，则下面结论不可能成立的是A. ，且B.C. ，且D. b与，都相交【答案】D【解析】【分析】由点线面的位置关系，结合题中条件，即可分析出结果.【详解】因为a，b为两条不同的直线，，为两个不同的平面，，，所以有以下三种情况：(1)若，则；(2)若，则；(3)若且，则且；因此不可能b与，都相交.故选D【点睛】本题主要考查空间中线面位置关系，由线线平行，分类讨论线面关系即可，属于基础题型.3.已知函数，与其反函数有交点，则下列结论正确的是A. B.C. D.a与b的大小关系不确定【答案】B【解析】【分析】由函数与其反函数有交点，可得函数与直线有交点，进而可得出结果.【详解】因为函数，与其反函数有交点，所以函数与直线有交点，即方程有实根，整理得，所以，又，所以.故选B【点睛】本题主要考查反函数的概念，原函数与反函数有交点，必然与直线有交点，由此即可求解，属于基础题型.4.在平面直角坐标系中，已知向量，O是坐标原点，M是曲线上的动点，则的取值范围A. B. C. D.【答案】A【解析】【分析】先设，由M是曲线上的动点，得到，再由向量数量积运算的坐标表示，即可求出结果.【详解】设，则，因为M是曲线上的动点，所以，又，所以；因为，所以的取值范围是.故选A【点睛】本题主要考查向量数量积的坐标运算，熟记公式即可，属于常考题型.二、填空题（本大题共12小题，共36.0分）5.已知全集，集合，则______．【答案】【解析】【分析】解不等式得到集合，进而可求出结果.【详解】解不等式得或，所以集合或，因为，所以.故答案为【点睛】本题主要考查补集的运算，熟记概念即可，属于基础题型.6.______．【答案】【解析】【分析】在原式的基础上，分子分母同除以，进而可求出结果.【详解】因为.故答案为【点睛】本题主要考查型极限，只需分子分母同除以即可得出结果，属于基础题型.7.若复数z满足是虚数单位，则______．【答案】【解析】【分析】由先得到，再由复数的除法运算即可得出结果.【详解】因为，所以.故答案为【点睛】本题主要考查复数的运算，熟记除法运算法则即可，属于基础题型.8.方程的解为______．【答案】【解析】【分析】方程可化为，求解即可.【详解】由得即，解得.故答案为【点睛】本题主要考查矩阵，由矩阵的运算转化为含指数的方程，即可求解，属于基础题型. 9.等比数列中，，，则______．【答案】256【解析】【分析】先设等比数列的公比为，根据题中条件求出，进而可求出结果.【详解】设等比数列的公比为，因为，，所以，因此，所以.故答案为256【点睛】本题主要考查等比数列的性质，熟记等比数列性质即可，属于基础题型.10.的展开式中项的系数为___．（用数字表示）【答案】【解析】试题分析：由得：项的系数为．考点：二项展开式定理求特定项11.已知两条直线：，：，则与的距离为______．【答案】【解析】【分析】将：化为，再由平行线间的距离公式即可求出结果.【详解】因为：可化为，所以与的距离为.故答案为【点睛】本题主要考查两条平行线间的距离公式，熟记公式即可，属于基础题型.12.已知函数，的值域为，则的取值范围是______．【答案】【解析】【分析】由作出其图像，由值域为，即可求出结果.【详解】因为，作出其图像如下：因为函数，的值域为，所以由图像可得，；所以.故答案为【点睛】本题主要考查函数的性质，根据函数的值域求参数范围，通常需要作出函数图像，由数形结合的思想来处理，属于常考题型.13.如图，在过正方体的任意两个顶点的所有直线中，与直线异面的直线的条数为______．【答案】12【解析】【分析】由异面直线的概念，一一列举出与异面的直线即可.【详解】由题中正方体可得与异面的直线有：，，，,，；,,，，，，共12条.故答案为12【点睛】本题主要考查异面直线，熟记概念即可，属于基础题型.14.在中，角A，B，C的对边分别为a，b，c，面积为S，且，则______．【答案】0【解析】【分析】由三角形面积公式和余弦定理可将化为，进而可求出结果.【详解】因为，余弦定理，又，所以有，即，所以，因此或，所以或，因为C三角形内角，所以，故.故答案为0【点睛】本题主要考查解三角形，熟记余弦定理和三角形面积公式即可求出结果，属于常考题型.15.已知向量，，且，若向量满足，则的最大值为______．【答案】【解析】【分析】先由题中条件求出，再由即可求出结果.【详解】因为，，且所以，所以，因此.故的最大值为【点睛】本题主要考查向量的模的最值问题，根据向量模的几何意义，即可求解，属于常考题型.16.若无穷数列满足：，当，时．其中表示，，，中的最大项，有以下结论：若数列是常数列，则若数列是公差的等差数列，则；若数列是公比为q的等比数列，则则其中正确的结论是______写出所有正确结论的序号【答案】【解析】【分析】根据题中条件,逐项判断即可.【详解】若数列是常数列，则有，所以，又，所以，故，又，所以，即.故正确；若数列是公差的等差数列，若，则数列是递增数列，则，则，，不能满足数列为公差的等差数列；若，则数列是递减数列，则，所以满足题意；故正确；若数列是公比为q的等比数列，若q>1，由可知数列是递增数列，所以，所以，即q=2满足题意；若0<q<1，由可知数列是递减数列，所以，所以，故，因为0<q<1，所以显然不成立，故0<q<1不满足题意；若q<0，则数列是摆动数列，不能满足题意；综上q>1，故正确.故答案为【点睛】本题主要考查数列的应用，灵活运用数列的性质是解题的关键，难度较大.三、解答题（本大题共5小题，共60.0分）17.如图，正三棱柱的各棱长均为2，D为棱BC的中点．求该三棱柱的表面积；求异面直线AB与所成角的大小．【答案】（1）；（2）.【解析】【分析】根据棱柱的表面积公式直接求解即可；先取AC中点E，连结DE，，根据题意可得是异面直线AB与所成角，解三角形即可. 【详解】解：正三棱柱的各棱长均为2，该三棱柱的表面积：．取AC中点E，连结DE，，为棱BC的中点，，，是异面直线AB与所成角或所成角的补角，，，，异面直线AB与所成角的大小为．【点睛】本题主要考查几何体的表面积公式以及异面直线所成的角，在几何体中作出异面直线所成的角即可，属于基础题型.18.已知抛物线C：．若C上一点到其焦点的距离为3，求C的方程；若，斜率为2的直线l交C于两点，交x轴的正半轴于点M，O为坐标原点，求点M的坐标．【答案】（1）；（2）.【解析】【分析】根据抛物线的定义，由C上一点到其焦点的距离为3，可求出，进而可求出抛物线方程；由先求出抛物线方程，再设直线l：，代入抛物线方程，设，，结合韦达定理和判别式，根据求出的值即可.【详解】解：由抛物线的定义得：，解得：，所以抛物线C的方程为：；时，抛物线C：，设直线l：，并代入抛物线C：得：，，解得设，，则，，，解得或当时，不在x轴正半轴上，舍去；当时，故点M的坐标为【点睛】本题主要考查抛物线的方程与简单性质，通常需要联立直线与抛物线方程，结合韦达定理和题中条件求解，属于常考题型.19.在股票市场上，投资者常根据股价每股的价格走势图来操作，股民老张在研究某只股票时，发现其在平面直角坐标系内的走势图有如下特点：每日股价元与时间天的关系在ABC段可近似地用函数的图象从最高点A到最低点C的一段来描述如图，并且从C 点到今天的D点在底部横盘整理，今天也出现了明显的底部结束信号．老张预测这只股票未来一段时间的走势图会如图中虚线DEF段所示，且DEF段与ABC段关于直线l：对称，点B，D的坐标分别是．请你帮老张确定a，，的值，并写出ABC段的函数解析式；如果老张预测准确，且今天买入该只股票，那么买入多少天后股价至少是买入价的两倍？【答案】（1）,,,，；（2）16.【解析】【分析】由B，D的坐标确定的值，和C的坐标，进而确定周期，求出，再由C的坐标，求出，即可得出函数解析式；(2)由(1)线求出DEF的解析式，令，求出即可.【详解】解：因为B，D的坐标分别是，且DEF段与ABC段关于直线l：对称，所以，所以，，，，由可得，，．由题意得DEF的解析式为：，由，得，故买入天后股价至少是买入价的两倍．【点睛】本题主要考查三角函数的应用，熟记三角函数的图像和性质即可，属于常考题型.20.对于函数，若函数是增函数，则称函数具有性质A．若，求的解析式，并判断是否具有性质A；判断命题“减函数不具有性质A”是否真命题，并说明理由；若函数具有性质A，求实数k的取值范围，并讨论此时函数在区间上零点的个数．【答案】（1），具有性质A；（2）假命题；（3）详见解析.【解析】【分析】由，结合即可得出解析式，和单调性，进而可得出结果；判断命题“减函数不具有性质A”，为假命题，举出反例即可，如；若函数具有性质A，可知在为增函数，进而可求出实数k的取值范围；再令，则在区间上零点的个数，即是的根的个数，结合k 的取值范围，即可求出结果.【详解】解：，，在R上递增，可知具有性质A；命题“减函数不具有性质A”，为假命题，比如：，在R上递增，具有性质A；若函数具有性质A，可得在递增，可得，解得；由，可得，即，可得，时显然成立；时，，由在递减，且值域为，时，或1，有三解，3个零点；当时，，即，可得，1个零点；当时，，t有一解，x两解，即两个零点；当，且时，无解，即x无解，无零点．【点睛】本题主要考查函数的解析式与函数的单调性，以及函数零点问题，按照题中条件结合函数的性质分析即可，属于常考题型.21.对于数列，若存在正数p，使得对任意都成立，则称数列为“拟等比数列”．已知，且，若数列和满足：，且，．若，求的取值范围；求证：数列是“拟等比数列”；已知等差数列的首项为，公差为d，前n项和为，若，，，且是“拟等比数列”，求p的取值范围请用，d表示．【答案】（1）详见解析；（2）.【解析】【分析】由即可求出结果；根据题中“拟等比数列”的定义，由，结合条件推出存在正数，使得有成立即可；由题中条件，，，先求出的范围；再根据是“拟等比数列”，分类讨论和，即可得出结果.【详解】解：，，且，，，．由题意得，当且时，，对任意，都有，即存在，使得有，数列数列是“拟等比数列”；，，，，，，由得，从而解得，又是“拟等比数列”，故存在，使得成立，当时，，，由得，由图象可知在时递减，故，当时，，，由得，由图象可知在时递减，故，由得p的取值范围是．【点睛】本题主要考查数列的应用，根据题中的新定义，结合条件，分类讨论即可求出结果，过程较繁琐，难度较大.。

闵行区2018学年第一学期高三年级质量调研考试语文试卷1、本考试设试着和答题纸两部分，试卷包括试题与答题要求，所有答题必须写在答题纸上，做在试着上一律不得分2、答题纸与试卷在试题编号上是一一对应的，答题时应注意，不能错位。

3、考试时150分钟。

试卷满分150分。

一、积累与运用（10分）1、按要求填空（5分）（1）分野中峰变，___________________。

（王维《终南山》）（2）郴江幸自绕郴山，___________________。

（秦观《_________・郴州旅舍》）（3）李白《登金陵凤凰台》一诗中，暗示皇帝被奸邪包围，自己报国无门，心情沉痛的句子是“___________________，___________________。

”2、按要求选择（5分）（1）下列选项中，名句运用不恰当的一项是（）。

（2分）A.生活中，老李是个很直率的人，和人交往向来是“知无不言，言无不尽”。

B.时代的洪流滚滚向前，改变了千年来“日出而作，日落而息”的生活方式。

C.对待传统文化，我们应如鲁迅先生所说的，做到“取其精华，去其糟粕”。

D.不少同学作文时往往是“下笔千言，离题万里”，搜肠刮肚也找不到材料。

（2）将下列编号的语句依次填入语段的空白处，语意连贯的一项是（）。

（3分）规则意识的淡漠或者缺失，不仅仅是关乎个人素质的问题，__________，没有成熟的规则意识，同样会影响人与人之间的交流成本，让合作变得艰难。

①增加了个体在社会运行中不可预料的风险②因为没有规则意识契约精神就不可能成为社会主流③往大处说是阻碍社会文明进步的硬伤④往小处说将直接影响每个人的生活⑤没有契约精神何谈文明A.④①⑤③②B.③②⑤④①C.④①③②⑤ D.③①④②⑤二、阅读（70分）（一）阅读下文，完成第3-7题（16分）海洋，孕育上海海派文化时平（1）上海文化以引领时尚著称，在国际上也是一门引人关注的显学，而对上海海洋文化的研究却属于新生事物。

2018年上海市闵行区高考数学一模试卷一.填空题（本大题共12题，1-6每题4分,7－12每题５分，共54分）1.（4分）集合P=｛x｜0≤x<3，ｘ∈Z}，M＝{x|x2≤9}，则Ｐ∩Ｍ=. 2．(4分）计算=.3．(4分)方程的根是．４.(4分）已知是纯虚数（i是虚数单位）,则= .（4分)已知直线ｌ的一个法向量是，则l的倾斜角的大小是.５．6．（4分)从4名男同学和6名女同学中选取3人参加某社团活动,选出的３人中男女同学都有的不同选法种数是（用数字作答）7．(５分）在（1+2x）5的展开式中,x2项系数为(用数字作答)8.（5分）如图，在直三棱柱ABC﹣A１B1C1中，∠ＡＣB＝90°,AC=4,BＣ=3，AB=BB1，则异面直线A1Ｂ与B1Ｃ1所成角的大小是（结果用反三角函数表示)9.（5分）已知数列｛aｎ}、{b n}满足b n=ｌna n，n∈N*,其中{b n}是等差数列,且，则b1+b２＋…+ｂ1009= ．1０.（5分)如图,向量与的夹角为１20°,,，P是以O为圆心，为半径的弧上的动点，若,则λμ的最大值是．11.（5分)已知F１、F２分别是双曲线(a＞0，b>０)的左右焦点，过F１且倾斜角为30°的直线交双曲线的右支于P,若PF２⊥F１Ｆ2，则该双曲线的渐近线方程是．12．(5分)如图，在折线ABCD中,AB=BＣ=CＤ=4，∠ABC=∠BCD＝12０°,E、F分别是ＡB、CD的中点，若折线上满足条件的点Ｐ至少有4个,则实数k 的取值范围是.二.选择题(本大题共4题,每题5分,共2０分)1３．（５分)若空间中三条不同的直线l1、l2、l3，满足l1⊥l2，l2∥l3,则下列结论一定正确的是( )A.ｌ1⊥l3ﻩB.l1∥l３C．l１、ｌ３既不平行也不垂直 D.l１、ｌ3相交且垂直14.（5分）若a>b＞0,c＜d＜0,则一定有()Ａ．ad＞ｂc B.ad<bｃﻩC.ac>bｄD．ａc＜bd１5.（５分）无穷等差数列{aｎ}的首项为ａ１，公差为d,前n项和为S n(ｎ∈N*），则“ａ1＋d>0”是“｛Ｓn}为递增数列”的( )条件.A.充分非必要Ｂ．必要非充分C.充要D．既非充分也非必要１6.（5分)已知函数（n＜m)的值域是[﹣１，１]，有下列结论:①当n=0时，m∈（0，2]；②当时，；③当时,m∈[1,2］;④当时，ｍ∈（ｎ,2］；其中结论正确的所有的序号是（)A.①②ﻩＢ．③④Ｃ．②③ D.②④三．解答题(本大题共５题，共１４+１4＋14＋1６+18=76分)17．(1４分）已知函数(其中ω＞０）.（１）若函数f(x)的最小正周期为３π，求ω的值,并求函数f(x）的单调递增区间;（2）若ω=2,０<α<π，且，求α的值．１8．（14分）如图,已知AＢ是圆锥SO的底面直径,O是底面圆心，,AＢ＝４,P是母线SA的中点,C是底面圆周上一点，∠AOC＝６０°.（1）求圆锥的侧面积；(２)求直线PＣ与底面所成的角的大小.1９．(14分）某公司举办捐步公益活动,参与者通过捐赠每天的运动步数获得公司提供的牛奶，再将牛奶捐赠给留守儿童,此活动不但为公益事业作出了较大的贡献，公司还获得了相应的广告效益,据测算,首日参与活动人数为１0０00人,以后每天人数比前一天都增加１５%,30天后捐步人数稳定在第３０天的水平，假设此项活动的启动资金为30万元,每位捐步者每天可以使公司收益０.０5元(以下人数精确到１人,收益精确到1元)．（1）求活动开始后第５天的捐步人数，及前5天公司的捐步总收益；(２)活动开始第几天以后公司的捐步总收益可以收回启动资金并有盈余？２０.（16分)已知椭圆的右焦点是抛物线Γ:y2＝２pｘ的焦点,直线l与Γ相交于不同的两点A(ｘ１,ｙ１）、B(ｘ2,ｙ2）．（1）求Γ的方程;(２)若直线ｌ经过点P(2，０),求△OAB的面积的最小值(O为坐标原点)；（3）已知点C(１，２),直线l经过点Q（5,﹣２）,Ｄ为线段ＡB的中点,求证:|ＡB|=２|ＣＤ|．21．（１８分)对于函数y=ｆ(x）（x∈D)，如果存在实数a、b（ａ≠0，且ａ=1，b=0不同时成立)，使得f(x)=ｆ（ax+b)对x∈D恒成立，则称函数ｆ（x）为“(a,ｂ)映像函数”.（１)判断函数f(x)=x２﹣２是否是“(a,b）映像函数”，如果是，请求出相应的a、b 的值，若不是，请说明理由;(2）已知函数y＝f（x)是定义在[0，＋∞）上的“(2,1)映像函数”,且当ｘ∈［0，1）时，f（x）=2x，求函数y=f（x)（ｘ∈[３,7))的反函数；｝,使得当ｘ∈[a n,aｎ＋１）（n∈N*）时,2（3）在（2）的条件下,试构造一个数列{aｎｘ+1∈[ａn,ａn+2），并求x∈［a n,a n+１)(n∈N*)时，函数y=f(ｘ）的解析式，及y+1＝f（ｘ）(x∈［0，＋∞））的值域.ﻬ２０18年上海市闵行区高考数学一模试卷参考答案与试题解析一.填空题（本大题共12题，１-6每题4分,７－12每题5分，共５4分）1．（4分）集合Ｐ={x｜0≤ｘ<３,x∈Z}，M=｛x｜x２≤9｝，则Ｐ∩M＝{0，1，2} .【解答】解:∵集合P={x|０≤x＜3,x∈Z}={0,1，2｝,M=｛x|x2≤９}={x|﹣3≤x≤3}，∴Ｐ∩Ｍ={0,1，2｝．故答案为:｛0,1，2}．2.(4分)计算=．【解答】解：＝=＝，故答案为:.3.(4分)方程的根是10 .【解答】解：∵,即１+lgx﹣3+lgｘ＝０，∴lgx＝１，∴ｘ=10．故答案为：10.4.（４分)已知是纯虚数(ｉ是虚数单位），则=．【解答】解:∵是纯虚数,∴,得ｓｉn且cｏs,∴α为第二象限角,则ｃos.∴=ｓｉnαｃos+cosαｓｉn=.故答案为:﹣．5．(4分）已知直线ｌ的一个法向量是，则l的倾斜角的大小是．【解答】解:设直线ｌ的倾斜角为θ，θ∈[0，π）.设直线的方向向量为＝(ｘ,y）,则＝x﹣y=0,∴ｔanθ==，解得θ=.故答案为：.6．（４分)从4名男同学和６名女同学中选取3人参加某社团活动，选出的3人中男女同学都有的不同选法种数是96 （用数字作答)【解答】解：根据题意，在4名男同学和６名女同学共１0名学生中任取3人，有Ｃ10３=1２0种,其中只有男生的选法有C４3＝4种，只有女生的选法有C６3=20种则选出的３人中男女同学都有的不同选法有１２0﹣4﹣２０=96种;故答案为：96.7.(5分)在（1+2ｘ）5的展开式中，ｘ2项系数为４0(用数字作答）【解答】解:设求的项为T r+１=C5r（2x）r,今ｒ＝2，∴T3=22Ｃ52x2=40x2.∴x２的系数是4０8．（5分）如图,在直三棱柱AＢC﹣A1B1C1中,∠ACＢ=9０°，AC=4，ＢC＝３,AＢ＝ＢＢ１，则异面直线A１B与B1Ｃ１所成角的大小是ａrccoｓ(结果用反三角函数表示）【解答】解：∵在直三棱柱ABC﹣A1Ｂ1C1中,∠AＣB＝９０°,ＡC=4，BC=3,AB=BB1, BC∥B1Ｃ1，∴∠ＡBC是异面直线A1Ｂ与B1Ｃ1所成角，１∵A1B＝==5,A1C＝＝=,∴cｏs∠A1BC===．∴∠A1BC=arccos.∴异面直线A1B与Ｂ1C１所成角的大小是arｃcoｓ.故答案为:arｃcｏs．9.(5分)已知数列｛aｎ}、｛ｂn｝满足b n=ｌｎa n,ｎ∈N＊，其中{b n｝是等差数列,且，则b1＋b2＋…+b1009=2018．【解答】解:数列｛a n}、{ｂn}满足ｂn=lnａn，n∈N*,其中{b n}是等差数列,∴b n＋１﹣ｂｎ=lnaｎ＋１﹣lna n=ln=常数t．∴＝常数e t=q＞0,}为等比数列.因此数列{aｎ且，∴a1a10０9=a2ａ100８==…．则b1+b2＋…+ｂ1０09=ln（a1a2…a10０9)=＝lnｅ201８=２018．故答案为:2018．10．（5分)如图,向量与的夹角为120°,，,P是以O为圆心,为半径的弧上的动点，若，则λμ的最大值是.【解答】解:如图建立平面直角坐标系，设Ｐ(cosθ，ｓinθ),，，.∵，∴,ｓiｎθ=．∴,∴λμ=﹣+=+，故答案为:1１.（5分)已知F1、F2分别是双曲线（a>0，b>0)的左右焦点,过Ｆ1且倾斜角为30°的直线交双曲线的右支于P，若PＦ2⊥F1F2,则该双曲线的渐近线方程是ｙ＝±x .｜＝ｍ，｜PF2|=n，|F1Ｆ２｜＝2ｃ，【解答】解：设|PＦ１在直角△ＰF1F2中，∠PF1Ｆ２＝30°，可得m=2n，则ｍ﹣n=2ａ＝n，即a=n，2c＝n,即c＝ｎ，b==ｎ，可得双曲线的渐近线方程为y=±x，即为y＝±x，故答案为:y=±x.１2.(5分)如图，在折线AＢCD中,ＡB=ＢC=CD＝４，∠ABＣ=∠BCD=120°，E、F 分别是ＡＢ、CD的中点,若折线上满足条件的点P至少有４个,则实数k 的取值范围是(﹣，﹣2) ．【解答】解:以BC的垂直平分线为y轴,以ＢC为x轴，建立如图所示的平面直角坐标系,∵AB=BC=CD=４，∠ABＣ=∠ＢＣD=1２0°,∴B(﹣2.0）,C(2,0),A(﹣4,２）,Ｄ（4，２),∵Ｅ、Ｆ分别是AB、CＤ的中点,∴E（﹣3，）,F(３,）,设P(x,y）,﹣4≤x≤4,0≤y≤2，∵，∴（﹣３﹣x,﹣ｙ）(3﹣x，﹣ｙ)=x２+(ｙ﹣）+9＝k，即x2+（y﹣）﹣9=ｋ+９,当ｋ＋９＞０时，点P的轨迹为以(0，)为圆心，以为半径的圆,当圆与直线DＣ相切时，此时圆的半径r＝，此时点有2个，当圆经过点C时，此时圆的半径为r=＝，此时点P有4个，∵满足条件的点Ｐ至少有4个，结合图象可得，∴<ｋ＋9＜７,解得﹣＜k<﹣2，故实数k的取值范围为（﹣,﹣２),故答案为：(﹣,﹣2）二．选择题(本大题共4题，每题5分,共2０分）1３．（5分)若空间中三条不同的直线l1、ｌ２、l3,满足l１⊥l2,l２∥ｌ3,则下列结论一定正确的是(）A．ｌ1⊥ｌ3ﻩB．ｌ1∥l3C.l１、l3既不平行也不垂直ﻩＤ．l1、ｌ3相交且垂直【解答】解:∵空间中三条不同的直线l、l2、l3，满足l1⊥ｌ2，l2∥l3，１∴l1⊥l3,故选:A.14.（5分)若a＞b＞0，c＜d<0，则一定有()A.ad＞bcﻩＢ.ad<bcﻩC．ac>bｄD．ａc<bd【解答】解:∵c<d＜0，∴﹣ｃ＞﹣ｄ＞０．又a＞b>0，则一定有﹣aｃ＞﹣bd,可得ac＜ｂd．故选:D.1５．（5分）无穷等差数列{ａｎ}的首项为a1，公差为ｄ，前n项和为Ｓn(n∈N*）,则“a1+d＞0”是“{Ｓn}为递增数列”的()条件.A.充分非必要ﻩB.必要非充分C．充要 D.既非充分也非必要【解答】解：等差数列{ａn}的首项为ａ１，公差为ｄ,前ｎ项和为Sｎ=na１+d，则Ｓn+1=(n+1)a１+,则S n+１﹣S n=(n＋1)a１+﹣na1﹣d=a1+nd，若{Sｎ｝为递增数列，ａ１+nd>0,∵Ｓ2﹣S１=a1+ｄ＞0，∴a1+ｎd>0不能推出a1+d＞0但a１+ｄ能推出a1+nd，故a1＋ｄ>０”是“{Sｎ｝为递增数列必要非充分，故选：B16.(5分）已知函数（ｎ＜m)的值域是［﹣１，1],有下列结论：①当ｎ=0时,m∈（0，２］；②当时,；③当时,m∈［1，2];④当时，m∈（n，2]；其中结论正确的所有的序号是( ）A.①②Ｂ．③④C．②③D．②④【解答】解：当x>1时，x﹣1＞０,f（x）=2２﹣x+1﹣３=2３﹣x﹣3,单调递减，当﹣1<x<1时，f(x)=２2+x﹣1﹣3=２1+x﹣3，单调递增,∴f(ｘ)=22﹣｜x﹣1｜﹣3在（﹣１,１）单调递增,在(1，+∞)单调递减,∴当ｘ=1时,取最大值为1,∴绘出ｆ（x）的图象，如图：①当n=０时,f（ｘ)=,由函数图象可知：要使ｆ(ｘ）的值域是[﹣１,１]，则ｍ∈(1,2]；故①错误;②当时，f(ｘ)＝,f（x)在[﹣１,］单调递增,f（x)的最大值为1,最小值为﹣1，∴;故②正确;③当时，ｍ∈[1,2]；故③正确，④错误，故选Ｃ.三.解答题(本大题共5题，共14+１4＋14+1６＋１8=76分)17.(1４分）已知函数(其中ω>0）.(1）若函数f（ｘ)的最小正周期为３π，求ω的值，并求函数f(ｘ）的单调递增区间；（2）若ω＝2，0＜α<π,且，求α的值.【解答】解：（1)函数=sｉn（ωx）,∵函数f（x)的最小正周期为3π，即T=3π=∴ω＝那么:，由，ｋ∈Ｚ，得：∴函数f(x）的单调递增区间为，k∈Z；（2）函数=sｉn（ωｘ),∵ω=2∴f（x）＝sin（2ｘ）,,可得sin（２α）＝∵0<α＜π,∴≤（2α）≤2α＝或解得：α＝或α＝.１8.（14分）如图,已知ＡB是圆锥SO的底面直径,O是底面圆心,,AＢ＝4,Ｐ是母线SA的中点，Ｃ是底面圆周上一点，∠AOＣ=60°．(１）求圆锥的侧面积;（2）求直线PＣ与底面所成的角的大小.【解答】解:（１)∵AＢ是圆锥ＳO的底面直径，Ｏ是底面圆心，,ＡB=4, P是母线SＡ的中点，C是底面圆周上一点，∠AＯC=６0°．∴r=＝2，l==＝4,∴圆锥的侧面积S=πrl＝π×２×4=8π.（2）过点Ｐ作PE⊥圆O,交AＯ于Ｅ，连结ＣE,则E是AO中点,∴PE=ＰＯ=,CE==,∴∠PCE是直线PC与底面所成角,∵PE=CＥ,ＰＥ⊥CE,∴,∴直线PＣ与底面所成的角为．１9．(14分)某公司举办捐步公益活动，参与者通过捐赠每天的运动步数获得公司提供的牛奶，再将牛奶捐赠给留守儿童，此活动不但为公益事业作出了较大的贡献，公司还获得了相应的广告效益，据测算，首日参与活动人数为10000人，以后每天人数比前一天都增加15%，30天后捐步人数稳定在第30天的水平,假设此项活动的启动资金为3０万元,每位捐步者每天可以使公司收益0.05元（以下人数精确到1人，收益精确到1元).（1)求活动开始后第５天的捐步人数，及前５天公司的捐步总收益；(2）活动开始第几天以后公司的捐步总收益可以收回启动资金并有盈余？【解答】解:（1）设第x天的捐步人数为x，则ｆ（x）=．∴第5天的捐步人数为f（5）=1０000•（1+１５%）4=１７4９0.由题意可知前5天的捐步人数成等比数列,其中首项为10000，公比为1.15,∴前5天的捐步总收益为×０.05=3371；(2)设活动第ｘ天后公司捐步总收益可以回收并有盈余,①若1≤x≤30，则×０.05＞30００00,91≈３２.３(舍）.解得ｘ＞log1.１5②若ｘ>30，则[+10000•1.1529•(x﹣３0）］•0．05>30000０，解得x＞３２.87．∴活动开始后第33天公司的捐步总收益可以收回启动资金并有盈余. 20．(16分）已知椭圆的右焦点是抛物线Γ:y2＝２px的焦点，直线ｌ与Γ相交于不同的两点A（x1,ｙ１）、B（x2,y2)．(1）求Γ的方程;（2)若直线l经过点P(2，0),求△OAB的面积的最小值（O为坐标原点）;(3）已知点C(1,2）,直线l经过点Ｑ(5，﹣2），D为线段ＡＢ的中点，求证：|AB|=2|C Ｄ|．【解答】(１）解:由椭圆,得a2=10，b2=9,则c＝1．∴椭圆的右焦点，即抛物线Γ:ｙ2=2px的焦点为（1,0）,则，p＝2，∴Γ的方程为y2=4ｘ;（2)解:设直线l：ｘ=my+2,联立，得ｙ2﹣4my﹣8=0．则y１+y２=4m,y1ｙ2＝﹣8.∴==，即△ＯAＢ的面积的最小值为;(3）证明:当AB所在直线斜率存在时,设直线方程为y+2=k(x﹣5）,即ｙ=kx﹣５k ﹣2．联立,可得ky2﹣４y﹣20k﹣8=0．,．＝．＝==．∵C(1,2）,∴，,则=(x1﹣1)(x2﹣１)+(y1﹣2）（y2﹣２）=x1ｘ２﹣（ｘ1+x２）+1＋y１y２﹣2(ｙ1+y２）＋4=，当AＢ所在直线斜率不存在时，直线方程为x=5,联立，可得A（5，﹣）,B（5，2)，，，有,∴ＣA⊥CB，又D为线段AB的中点,∴|ＡB|=2|CD｜.２1.（18分）对于函数y=ｆ(ｘ）(ｘ∈D），如果存在实数ａ、b(ａ≠0,且a=1，ｂ=0不同时成立),使得ｆ（x）=f(ax+ｂ）对x∈D恒成立,则称函数ｆ（x)为“（a,b)映像函数”．（１)判断函数f（x)=x2﹣2是否是“(a，b)映像函数”,如果是,请求出相应的a、b的值,若不是,请说明理由；（２）已知函数y=f(x）是定义在[0，+∞)上的“（2,1)映像函数”,且当x∈[0,1）时，f(x）=2x,求函数y＝f（x）（x∈[3,7））的反函数;(3）在（2)的条件下,试构造一个数列{ａn},使得当ｘ∈[a n，a n+1）(n∈N*）时，２x+1∈[a n+1，a n+２)，并求ｘ∈［ａn,a n+１）(n∈Ｎ*)时，函数ｙ=f(x）的解析式,及ｙ=f（x)(x∈［０，+∞))的值域．【解答】解：（1)由f（x）=x2﹣２，可得f(ax＋b)=（ax+ｂ)2﹣2=a2x2＋２abｘ+b2﹣2,由f(x）=ｆ（ａx＋b)，得x2﹣2＝a2x2+２abｘ＋ｂ2﹣2，则，∵a≠0,且a=1,b=０不同时成立,∴a=﹣1,b=0．∴函数f(ｘ)=x２﹣2是“（﹣1，0）映像函数”；（２）∵函数y=f（x)是定义在[0,＋∞）上的“(2,1)映像函数”，∴f（x)=f(2x+1）,则f(0)=f(1)=f（３)，ｆ(1)=f(3）=f(7）,∴f（0）＝ｆ(3),f（1)=f（７），而当x∈[０,1)时，f(x）=2x，∴x∈［3，7)时,设ｆ（x)=2sx+ｔ,由,解得s=,t=﹣．∴ｘ∈[３,7）时，f(x）=．令y=(３≤x<7),得，∴x=(1≤y<2),∴函数y=ｆ（x)（x∈[3，７）)的反函数为ｙ=（１≤x＜2）;(3)由（2)可知，构造数列{ａn},满足ａ1=0,a n+1=2ａｎ＋1,＋1＝2(ａn+1）,则ａn+1∴数列{ａn＋1｝是以1为首项,以2为公比的等比数列，则,即.当x∈［a n,ａｎ＋1)=［2ｎ﹣1﹣1，2n﹣１).令,解得s=21﹣n,t=２1﹣n﹣1.∴x∈[a n，a n＋１)(n∈N*）时,函数ｙ=f(x)的解析式为f(x)=．当x∈［0，+∞)时，函数f(x）的值域为［1，２)．。

高三年级质量调研考试数学试卷 第1页共11页闵行区2018学年第一学期高三年级质量调研考试数 学 试 卷（满分150分，时间120分钟）考生注意：1．答卷前，考生务必在答题纸上将学校、班级、考生号、姓名等填写清楚．2．请按照题号在答题纸各题答题区域内作答，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．本试卷共有21道试题．一、填空题（本大题共有12题，满分54分）考生应在答题纸上相应编号的空格内直接填写结果，第1～6题每个空格填对得4分，第7～12题每个空格填对得5分，否则一律得零分． 1. 已知全集U =R ，集合2{30}A x x x =-≥，则U A ð= ．2. 2221lim 331n n n n →∞-=++ ． 3. 若复数z 满足(12)43i z i +=+（i 是虚数单位），则z = ． 4. 方程110322x=-的解为 ．5. 等比数列}{n a 中，121=+a a ，5616a a +=，则910a a += ．6. ()512x -的展开式中3x 项的系数为 ．（用数字作答）7. 已知两条直线12:4230:2+10l x y l x y +-=+=和，则12l l 与的距离为 ． 8. 已知函数[]()|1|(1),,f x x x x a b =-+∈的值域为[]0 8，，则a b +的取值范围是 ． 9. 如图，在过正方体1111ABCD A B C D -的任意两个顶点的所有直线中，与直线1AC 异面的直线的条数为 ． 10. 在ABC △中，角 A B C 、、的对边分别为 a b c 、、，面积为S ，且224()S a b c =+-，则cos C = ．高三年级质量调研考试数学试卷 第2页共11页11. 已知向量()()cos ,sin ,cos ,sin a b ααββ==，且3παβ-=，若向量c 满足1c a b --=，则c 的最大值为 .12. 若无穷数列{}n a 满足：10a ≥，当*,2n n ∈≥N 时，{}1121max ,,,n n n a a a a a ---=（其中{}121max ,,,n a a a -表示121,,,n a a a -中的最大项），有以下结论：①若数列{}n a 是常数列，则()*0n a n =∈N ； ②若数列{}n a 是公差0d ≠的等差数列，则0d <； ③若数列{}n a 是公比为q 的等比数列，则1q >；④若存在正整数T ，对任意*n ∈N ，都有n T n a a +=，则1a 是数列{}n a 的最大项.则其中的正确结论是 .（写出所有正确结论的序号）二、选择题（本大题共有4题，满分20分）每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分． 13. 若,a b 为实数，则“1a <-”是“11a>-”的 ( )(A) 充要条件 (B) 充分非必要条件(C) 必要非充分条件 (D) 既非充分也非必要条件 14. 已知a 、b 为两条不同的直线，α、β为两个不同的平面， a αβ=， //a b ，则下列结论不可能．．．成立的是 ( ) (A) //b b βα，且Ü (B) //b b αβ，且Ü (C) // //b b αβ，且 (D) b 与 αβ、都相交15.已知函数(),0,0y x a a b =≥>>与其反函数有交点，则下列结论正确的是 ( )(A) a b = (B) a b < (C) a b > (D)a b 与的大小关系不确定 16. 在平面直角坐标系中，已知向量(1,2)a =，O 是坐标原点，M 是曲线22x y +=上的动点，则a OM ⋅的取值范围为 ( ) (A) []2,2-(B) ⎡⎣(C) ⎡⎢⎣⎦(D)⎡⎢⎣高三年级质量调研考试数学试卷 第3页共11页三、解答题（本大题满分76分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤．17. （本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分． 如图，正三棱柱111ABC A B C -的各棱长均为2，D 为棱BC 的中点． （1）求该三棱柱的表面积；（2）求异面直线AB 与1C D 所成角的大小．18. （本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分．已知抛物线Γ：22(0)y px p =≠.（1）若Γ上一点(1,)M t 到其焦点的距离为3，求Γ的方程；（2）若2p =，斜率为2的直线l 交Γ于两点A B 、，交x 轴的正半轴于点M ，O 为坐标原点，0OA OB ⋅=，求点M 的坐标.高三年级质量调研考试数学试卷 第4页共11页19. （本题满分14分）本题共有2个小题，第1小题满分8分，第2小题满分6分． 在股票市场上，投资者常根据股价（每股的价格）走势图来操作．股民老张在研究某只股票时，发现其在平面直角坐标系内的走势图有如下特点：每日股价()y 元与时间()x 天的关系在ABC 段可近似地用函数()()sin 200,0,0y a x a ωϕωϕπ=++>><<的图像从最高点A 到最低点C 的一段来描述（如右图），并且从C 点到今天的D 点在底部横盘整理，今天也出现了明显的底部结束信号．老张预测这只股票未来一段时间的走势图会如图中虚线DEF 段所示，且DEF 段与ABC 段关于直线:34l x =对称，点B D 、的坐标分别是()()12,2044,12、． （1）请你帮老张确定,,a ωϕ的值，并写出ABC 段的函数解析式；（2）如果老张预测准确，且今天买入该只股票，那么买入多少天后股价至少是买入价的两倍？高三年级质量调研考试数学试卷 第5页共11页20. (本题满分16分)本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分6分．对于函数()y f x =，若函数()(1)()F x f x f x =+-是增函数，则称函数()y f x =具有性质A .(1)若2()2xf x x =+，求()F x 的解析式，并判断()f x 是否具有性质A ； (2)判断命题“减函数不具有性质A ”是否真命题，并说明理由；(3)若函数23()(0)f x kx x x =+≥具有性质A ，求实数k 的取值范围，并讨论此时函数()(sin )sin g x f x x =-在区间[]0,π上零点的个数.高三年级质量调研考试数学试卷 第6页共11页21. (本题满分18分)本题共有3个小题，第1①小题满分4分，第1②小题满分6分，第2小题满分8分．对于数列{}n a ，若存在正数p ，使得1n n a pa +≤对任意*n ∈N 都成立，则称数列{}n a 为“拟等比数列”．（1）已知0 0a b >>，，且a b >，若数列{}n a 和{}n b满足：11 2a ba b +==，且*11 )2n nn n a b a b n +++==∈N ，． ①若11a =，求1b 的取值范围；②求证：数列*{}()n n a b n -∈N 是“拟等比数列”．（2）已知等差数列{}n c 的首项为1c ，公差为d ，前n 项和为n S ，若10c >，403540360,0S S ><，且{}n c 是“拟等比数列”，求p 的取值范围（请用1,c d 表示）．高三年级质量调研考试数学试卷 第7页共11页闵行区2018学年第一学期高三年级质量调研考试数学试卷参考答案与评分标准一. 填空题 1．()0,3； 2．23； 3．2i -； 4．2log 5x =； 5．256； 6．80-； 7．2；8．[]2 4，；9．12； 10．0； 11．1+12．①②③④. 二. 选择题 13．B ； 14．D ； 15．B ； 16．A ． 三. 解答题17．[解] （1）22=32+22S ⨯ ………6分 （2）取AC 的中点E ，联结1DE C E 、，则//ED AB ，所以1C DE ∠（或其补角）是异面直线AB 与1C D 所成的角．…8分 在1C DE △中，11C D C E =1DE =，所以2221111cos 210C D DE C E C DE C D DE +-∠===⋅⋅．………12分 所以AB 与1C D所成的角的大小为． …………14分 18．[解] （1）由条件知1342pp +=⇒=, ………………4分 所以Γ的方程为28y x =. ………………………6分 （2）设点M A B 、、的坐标分别为(),0(0)m m >、()11,A x y ，()22,B x y ， 则直线l 的方程为2()y x m =-； ………………………8分{222()2404y x m y y m y x=-⇒--==， ………………………10分 2221212124,16y y y y m x x m ⇒=-== ………………………12分21212404OA OB x x y y m m m ⋅=+=-+=⇒=，高三年级质量调研考试数学试卷 第8页共11页所以M 点的坐标为()4,0. ………………………14分19．[解] （1）因为C D 、两点关于直线l 对称，所以点C 的坐标为()24,12，……2分又点B 恰在平衡位置，C 为最低点，得2448248124ππω==⇒=⇒=T T …4分 将()12,20B 代入解析式可得：sin 120cos 024πϕϕ⎛⎫⋅+=⇒= ⎪⎝⎭，∴2πϕ=， …………………………6分再结合C 点是最低点，可得8a =. ∴ABC 段的解析式为[]8sin +20,0,24242y x x ππ⎛⎫=+∈⎪⎝⎭……………………8分 （2）由对称性得，DEF 段的解析式为：()()[]8sin 68+208cos 68+20,44,6824224y x x x πππ⎡⎤⎡⎤=-+=-∈⎢⎥⎢⎥⎣⎦⎣⎦，…10分若股价至少是买入价的两倍，则()8cos 68+202424x π⎡⎤-≥⎢⎥⎣⎦ ………………………………12分()1cos 68242x π⎡⎤⇒-≥⎢⎥⎣⎦解得6068x ≤≤所以买入16天后，股价至少是买入价的两倍. …………………………14分 20．[解] (1)212()(1)()(1)22221x x x F x f x f x x x x +=+-=++--=++ ……2分而()221xF x x =++在(),-∞+∞上是增函数，所以()f x 是否具有性质A . ………………………………4分 (2)假命题. ………………………………6分如函数()0)f x x =≥是减函数， ………………………………8分高三年级质量调研考试数学试卷 第9页共11页()F x ==函数()F x 在[0 )+∞，上单调递增，∴()0)f x x =≥具有性质P ．∴命题是假命题. ………………………………10分 (3) 23232()(1)(1)3(23)1(0)F x k x x kx x x k x k x =+++--=++++≥， 因为函数23()(0)f x kx x x =+≥具有性质A ， 所以233062k k +-≤⇒≥- ． ………………………………12分 23()(sin )sin sin sin sin g x f x x k x x x =-=+-，由()0g x =得23sin sin sin 0sin 0k x x x x +-=⇒=或2sin sin 1k x x =-+0x ⇒=或x π=或1sin sin k x x ⎛⎫=-- ⎪⎝⎭()0,x π∈． …………………14分设sin x t =，则(]1,0,1k t t t ⎛⎫=--∈ ⎪⎝⎭由函数(]1,0,1k t t t ⎛⎫=--∈ ⎪⎝⎭的图像可知当3,02k ⎡⎫∈-⎪⎢⎣⎭时，11t t =>，1sin x t =无解；当0k =时，11t =，sin 1x =⇒2x π=；当()0,k ∈+∞时，()10,1t t =∈，1sin x t =在()0,π上有两个解；综上所述：当3,02k ⎡⎫∈-⎪⎢⎣⎭时，()g x 在区间[]0,π上零点的个数为2； 当0k =时，()g x 在区间[]0,π上零点的个数为3；当()0,k ∈+∞时，()g x 在区间[]0,π上零点的个数为4．………………16分 21．[解] （1）①∵0 0a b >>，，且a b >，112a ba +==，∴11b <，高三年级质量调研考试数学试卷 第10页共11页∴1(0 1)b ∈，， ……………………………………4分②依题意得：112a ba b +=>= 所以，当* 2n n ∈≥N ，时，1102n n n n a b a b --+-=>，……………6分 所以对任意*n ∈N ，都有111()222n n n n n n n n a b a b a b a b ++++-=<=-， ………………8分 即存在12p =，使得11()n n n n a b p a b ++-<-，∴数列*{}(N )n n a b n -∈是“拟等比数列”．……………………………………10分（2）()201840351403640364035004036002c S c c S ⋅>⎧>⎧⎪⇒⎨⎨+⋅<<⎩⎪⎩…………………12分 201820181201820192019100201700020180c c c d c c c c d >>+>⎧⎧⎧⇒⇒⇒⎨⎨⎨+<<+<⎩⎩⎩ 由10c >可知0d <，从而解得120182017c d-<<-， …………………14分 又{}n c 是“拟等比数列”，故存在0p >，使得1n n c pc +≤1︒当2018n ≤时，0n c >，()()+11111111111n n c c n d dp c c c n d c n dn d +⋅≥==+=++-⋅+-⋅⎛⎫-- ⎪⎝⎭由1120182017201812019c cd d-<<-⇒<-<， 由图像可知1111c n d +⎛⎫-- ⎪⎝⎭在2018n ≤时递减，故211201620171,20172018c d p c c ⎛⎫≥=+∈ ⎪⎝⎭； ………………………16分高三年级质量调研考试数学试卷 第11页共11页2︒当2019n ≥时，0n c <，()()+11111111111n n c c n d d p c c c n d c n d n d +⋅≤==+=++-⋅+-⋅⎛⎫-- ⎪⎝⎭ 由1120182017201812019c c d d-<<-⇒<-<， 由图像可知1111c n d +⎛⎫-- ⎪⎝⎭在2019n ≥时递减，故1p ≤； 由12︒︒可得，此时p 的取值范围是111d c ⎡⎤+⎢⎥⎣⎦， ………………………18分。

上海市闵行区2018届高考一模英语试题第I卷 (共 107 分)I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. At a grocery. B. At a laundry. C. At a restaurant. D. At a post office.2. A. Generous. B. Considerate. C. Diligent.D. Impersonal.3. A. Travelling plan. B. Personal interest.C. Overseas study.D. Job opportunity.4. A. Having a break. B. Continuing themeeting.C. Moving on to the next item.D. Waiting a little longer.5. A. Take exercises. B. See a doctor. C. Havea test. D. Give a speech.6. A. It is a routine offer. B. It is quite healthy.C. It is new on the menu.D. It is a good bargain.7. A. She is driving fast to the airport. B. She may be late for the football game.C. She is worried about missing her flight.D. She is currently caught in a traffic jam.8. A. The man can stay in her brother’s apartment.B. Her brother can help the man find a cheaper hotel.C. Her brother can find an apartment for the man.D. The man should have booked a less expensive hotel.9. A. He was looking forward to seeing the giraffes.B. He enjoyed watching the animal performance.C. He got home too late to see the TV special.D. He fell asleep in the middle of the TV program.10. A. The man should consider his privacy first.B. The man will choose a low-rent apartment.C. The man is not certain if he can find a quieter place.D. The man is unlikely to move out of the dormitory. Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. The storm. B. The flood. C. The wind. D. The rain.12. A. Cold and dry. B. Cloudy and rainy.C. Warm and sunny.D. Windy and cool.13. A. On Friday morning. B. On Friday night.C. On Saturday morning.D. On Saturday night.Questions 14 through 16 are based on the following passage.14. A.It’ll allow them to receive free medical treatment.B.It’ll protect them from possible financial crise s.C.It’ll enable them to enjoy the best medical care.D.It’ll prevent the doctors from overcharging them .15.A.They may not be able to receive timely medical trea tment.B.They can only visit doctors who speak their native languages.C.They have to go through very complicated applicati on procedures.D.They can’t immediately get back the money paid fo r their medical cost.16. A. How to obtain student health insurance before going abroad.B. How to save money when you are buying overseas insurance.C. The importance of obtaining insurance when studying abroad.D. The advantages of student insurance over international travel insurance.Section CDirections: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet. Blanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.Complete the form. Write no more than THREE WORDS for each answer.II. Grammar and VocabularySection ADirections: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks,use one word that best fits each blank.(A)One of the most important skills in reading is the knowledge of words. Since Vocabulary Building and Word Study, another book in this series, (25) ______ (devote) to vocabulary development, we are not going to deal with this skill directly, but you should be aware of the basic fact (26) ______ the number of words you know determines the difficulty and complexity of the material you can read and understand. (27) ______ you have an extremely limited reading vocabulary, you will be able to read only very simple material. For example, children just beginning to read in first grade must use books that only have a few dozen words in them. As they progress through school their reading vocabulary keepsincreasing (28) ______ they are adults. Adults typically have reading vocabularies of over 50,000 words.Failure (29) ______(develop) an extensive reading vocabulary will definitely hold you back in your efforts to improve comprehension. Most people learn new words by encountering them in reading or conversation, (30) ______ the meaning is usually clear from the context. A few words are learned by looking them up in the dictionary.If you feel that vocabulary is a problem for you, you may wish to do something systematic about it. There are many good books (31) ______ to help develop vocabulary, including the one in this series. (32) ______(begin) with any of them will help your vocabulary.(B)Conversation is an important part of life to everyone. However some people are afraid of starting a casual conversation with a stranger (33) ______ ______ a fear of not having anything interesting to say.Fear of rejection is also a reason for keeping silent. Small talk in a conversation can serve as a way of warming up and getting to know each other. Most people, (34) ______ ______ ______ successful they are at work, will find the process of making small talk uncomfortable, even pointless. However, you (35) ______ (have) a pretty small world if you refuse to let others in. Starting off with (36) ______ usual comment or question will make others comfortable, and even just greeting them with a simple “hello” will often be enough.Once you have made the first move, there is no turning back. You need to keep things going before you can gracefully say goodbye. Think about what you would like to share with a new friend and that is (37) ______ you can ask the other person about. Work, family, hobbies or interests are some general points of discussion. (38) ______ (keep) the ball rolling, you can show that you are really interested in what they are saying. Once you find common points of interest, things will definitely take off from there.Small talk (39) ______ turn out to be a pleasantexperience. The conversation should be brief and casual without turning into a long and boring discussion. Do not let yourself control the conversation. Let (40) ______ talk too. Stop worrying about how big of a fool you may appear to be. You may even find out later on that you have the “talent” of getting people to open up to you by engaging them in small talk.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.Job seekers should know the rules of labor market before they try to find a proper job. Most career organizations 41 three stages for graduates to follow the process of securing a suitable career:recognizing abilities, matching these to available jobs and presenting them well to possible employers.Job seekers have to make a careful assessment of their abilities. One area of assessment should be of their 42 qualifications, which include special skills within their subject area. Graduates should also consider their own values and attitudes. An honest assessment of personal interests and abilities such as creative skills, or skills acquired from work experience, should also be given careful 43 .The second stage is to study the opportunities which are available for employment. To do this, graduates can study job and 44 information in newspapers, or they can pay a visit to a careers office, write to friends or relatives who may already be 45 in a particular profession. After studying all the various 46 , they should be in a position to make informed comparisons between various careers.Good personal 47 is essential in the search for a good career. Job application forms should be filled in carefully and correctly, without grammar of spelling errors. They should also prepare properly byfinding out all they can about the possible employer. When 48information is asked for, job seekers should describe their abilities and work experience in more depth, as well as 49 their own abilities with the employer’s needs, explain why the y are interested in a career with the 50 company and try to show that they already know something about the company and its activities. Interviewees should try to give positive answers and not be afraid of asking questions about anything they are unsure about.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.People read for different purposes. Sometimes people read for information while on other occasions, for understanding. Therefore, we can know that the word “reading” has two51 senses.The first sense is the one in which we read newspapers, magazines, and so on. We can get access to the content of those materials 52 . Such materials may increase our 53of information, but they cannot improve our understanding. And clearly we don’t have any difficulty in gaining the new information, for our understanding is 54 to them before we start. Otherwise, we would have felt the shock of puzzlement.The second sense is the one in which we read something that at first we do not completely 55 . Here the thing to be read is at the first sight better or higher than the reader. The writer is communicating something that can increase the reader’s understanding. Such 56 between unequals –people who know and people who don’t know – must be made possible. Otherwise one person could never learn from another. Here “learning” means understanding more, not 57 more information.What are the 58 in this kind of reading? First, there is inequality in understanding. The writer mustbe “ 59 ”to the reader in understanding. Besides, his book must convey something he possesses while his potential readers 60 . Second, the reader must be able to 61 this inequality in some degree. And he should always try to reach the same level of understanding with the writer. If the 62 is approached, success of communication is achieved.Besides gaining information and understanding, there’s another goal of reading:63 . It is the least 64 and requires the least amount of effort. Everyone who knows how to read can read for entertainment if he wants to. 65 , any book that can be read for understanding or information can probably be read for entertainment as well.51. A. meaningful B. broad C. separateD. informative52. A. easily B. wholly C. brieflyD. highly53. A. analysis B. comprehension C. appreciation D. store54. A. equal B. contrary C. inferiorD. devoted55. A. agree B. understand C. approve D. enjoy56. A. contact B. relationship C. methodD. communication57. A. selecting B. ignoring C. rememberingD. creating58. A. conditions B. procedures C. approachesD. purposes59. A. humble B. superior C. kind D. generous60. A. know B. acquire C. lack D. deny61. A. recognize B. follow C. neglect D. overcome62. A. principle B. equality C. informationD. content63. A. knowledge B. ability C. entertainment D. culture64. A. enjoyable B. reasonable C. flexibleD. demanding65. A. In fact B. On the contrary C. In addition D. On the other handSection BDirections: Read the following passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)Dennis Sinar, 51, a doctor from New York, is quick to explain why he took a year-long break from his job. “I was pretty burned out after practicing medicine for 26 years. I needed a recharge.” So he took a “gap year”, from July 2011 to June 2018, to explore things like ancient buildings, antique restoration, archaeology and traditional Eastern medicine, in locations including Alaska, Nepal and Romania.“Taking a break from work is an excellent way for adults to go into a new career or refresh an old one,”said Holly Bull, president of Princeton, N, J. “In recent years, mid-career breaks have been gaining more interest,” she said. A report on adult gap years published this year by a market research company also described the potential American market for gap yearsas a “sleeping giant.”“A gap year is a challenge for the older individual to step out of a comfort zone and take a risk. I enjoyed that side most.” said Dr. Sinar, who kept a daily blog about his experience. His time studying Eastern medicine “assured the reasons I went into health care,”said Dr. Sinar, who returned to practice medicine at his old job, although he works fewer days. “I use those experiences to provide my patients with more care,” he added. “And I listen better than I did before.”George Garritan, chairman of the Department of Leadership and Human Capital Management at New York University, certainly agrees with Dr. Sinar. He said a gap-year experience could be worthwhile for employees and companies. For employees, investing in themselves and improving skill sets is a move that will benefit throughout their career. He added that returning employees feel refreshed and have given more thought to their career. For companies, offering unpaid leaves makes good sense for attracting and keeping talented employees.66. Dr. Sinar took a gap year because he ________.A. had lost his old jobB. wanted to refresh after 26 years’ workC. had a desire for travellingD. became interested in historical research67. The phrase “sleeping giant” (in 2nd paragraph) indicates that ________.A. it’s too early for people to accept the conception of gap yearB. the effect of gap year policy remains to be seenC. it’s difficult to foresee the gap year marketD. more American people will accept the gap year policy68. What’s George Garritan’s at titude toward the “gap year”?A. Positive.B. DoubtfulC. Uninterested.D. Uncertain.69. What’s the passage mainly about?A. How an adult plans a mid-career gap year.B. Why a gap year is worthwhile for adults.C. Whether a gap year is popular with adults.D. Why a gap year is challenging for individuals.(B)Submitting Assignment OnlineIn order to upload an assignment to the system properly, you must save the assignment using one of the following applications: Microsoft Word, Corel WordPerfect, or Microsoft Excel.After you complete an assignment, it is important to save your work. This ensures that assignment being uploaded to the system is the most updated version. Your word processing program may attempt to save the assignment to a folder on your computer. We recommend creating a new folder, named after your course, in a location that is easy to remember, such as “My Documents.”File Name RequirementsSelect a file name for the assignment that is easy to remember. The file name must NOT contain spaces. Any spaces used in the file name will prevent the file from uploading to the system. File names using the extensions .rtf, .html, .zip, .jpg, or .exe are NOT allowed.Assignment Upload ProcedureWhen the file is ready to upload, follow these steps:1. Sign in the system.2. Enter your address information and click the CONTINUE button. You will be routed to the “Directions” screen.3. Review the directions and click the CONTINUE button. You will be routed to the “Special Assignment Upload” screen.4. Click the SEARCH button. The “Choose File” window pops up.5. Find the location on your computer where you saved your assignment, and select the file.After you have selected the file, click the UPLOAD button to upload your assignment to the system. Assignment Submission DatesAssignments must be submitted by midnight on the specified due date. Submit your assignment on time so that it reaches the system on or before the due date. No late assignments will be accepted or marked. Assignments delivered after the due date will not be assessed and will be failed. Please manage your timecarefully as family and work demands will not be accepted as excuses for late or non-submissions. Tutors and administrators do not have the authority to grant extensions.70. Which of the following file names is acceptable for submitting assignment?A. research paper.docB. research paper.pdfC. researchpaper.docD. researchpaper.rtf71. Students are advised to save an assignment to a specific folder in order to ________.A. sign in the systemB. remember where the document isC. choose the appropriate applicationD. remember the document name quickly72. The phrase “pops up” in the passage probably means “________”.A. appearsB. eliminatesC. scansD. browses73. If you summit your assignment after the due time, you ________.A. can have a second chanceB. should ask a tutor for helpC. may apply for an extensionD. will get a fail for the work(C)Even in a weak job market, the old college try is n’t the answer for everyone. A briefing paper from the Brookings Institution warns that “we may have overdone the message” on college, senior fellow Isabel Sawhill said.“We’ve been telling students and their families for years that college is the only way to succeed in the economy and of course there’s a lot of truth to that,” Ms. Sawhill said. “On average it does pay off… But if you load up on a whole lot of student debt and then you don’t graduate, that is a very bad situation.”One comment that people often repeat among the years of slow job growth has been the value of education for landing a job and advancing in a career. April’s national unemployment rate stood at 7.5%, according to the Labor Department. The unemployment rate forhigh-school gradua tes over 25 years old who hadn’t attended college was 7.4%, compared with 3.9% for those with a bachelor’s degree or more education. The difference is even bigger among those aged 16-24. The jobless rate for those with only a high school diploma in that age group is about 20%. At the same time, recent research by Canadian economists cautions that a college degree is no guarantee of promising employment.Ms. Sawhill pointed out that among the aspects that affect the value of a college education is the field of one’s major: Students in engineering or other sciences end up earning more than ones who major in the arts or education. The cost of tuition and the availability of financial aid are other considerations, with public institutions generally a better financial bargain than private ones.She suggested two ways for improving the situation: increasing vocational-technical training programs and taking a page from Europe’s focus on early education rather than post-secondary learning. “The European countries put a little more attention to getting people prepared in the primary grades,” she said. “Then theyhave a higher bar for whoever goes to college—but once you get into college, you’re more likely to be highly subsidized (资助).”She also is a supporter of technical training—to teach students how to be plumbers, welders and computer programmers—because “employers are desperate” for workers with these skills.74. According to the passage, people usually think that ________.A. the cost of technical schooling is a problemB. one will not succeed without a college degreeC. technical skills are most important for landing a jobD. there is an increased competition in getting intoa college75. The underlined part “taking a page from”probably means “ ________ ”A. revisingB. promotingC. definingD. adopting76. What can we infer from the passage?A. Public institutions charge more for education.B. European universities are stricter with students.C. Students with certain skills are in great demand.D. Canadian students prefer to major in engineering.77. Ms. Sawhill may probably agree that ________.A. too much stress has been put on the value of college degreesB. technical training is more important than college educationC. a college degree will ensure promising employmentD. it’s easier for art students to find favorite jobsSection CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Skeptics are a strange lot. Some of them refuse to admit the serious threat of human activities to the environment, and they are tired of people who disagree with them. Those people, say skeptics, spread nothing but bad news about the environment. The “eco-guilt”brought on by the discouraging news about our planetgives rise to the popularity of skeptics as people search for more comforting worldviews.Perhaps that explains why a new book by Bjorn Lomborg received so much publicity. That book, The Skeptical Environmentalist, declares that it measures the “real state of the world” as fine. Of course , another explanation is the deep pockets of some big businesses with special interests. Indeed, Mr. Lomborg's views are similar to those of some industry- funded organizations, which start huge activities through the media to confuse the public about issues like global warming.So it was strange to see Mr. Lomborg's book go largely unchallenged in the media though his beliefs were contrary to most scientific opinions. One national newspaper in Canada ran a number of articles and reviews full of words of praise, even with the conclusion that “After Lomborg, the environmental movement will begin to die down.”Such one-sided views should have immediately been challenged. But only a different review appeared in Nature, a respected science magazine with specificreadership. The review remarked that Mr. Lomborg's “preference for unexamined materials is incredible(不可信的)”．A critical (批判的)eye is valuable, and the media should present information in such a way that could allow people to make informed decisions. Unfortunately, that is often inaccessible as blocked by the desire to be shocking or to defend some special interests. People might become half-blind before a world partially exhibited by the media. That's a shame, because matters concerning the health of the planet are far too important to be treated lightly.78. Skeptics are searching for more comfortingworldviews to argue that the environment isn’t threatened by _________________.79. What’s the result of Mr. Lomborg’s views?80. The author mentioned “articles and reviews fullof words of praise” to illustrate that Mr.Lomborg’s views ____________________.81. According to the last paragraph, only if________________ can people make right decisions.第II 卷 (共 43 分)I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 请你方便的时候打电话给我。

闵行区2017-2018学年第一学期期末考质量监测高三年级历史学科试卷2018.1考生注意：1．考试时间60分钟，试卷满分100分。

2．本考试设试卷和答题纸两部分，试卷包括试题与答题要求；所有答题必须写在答题纸上；做在试卷上一律不得分。

3．答题前，务必在答题纸上填写准考证号和姓名。

4．答题纸与试卷在试题编号上是一一对应的，答题时应特别注意，不能错位。

一、选择题（共40分，每小题2分。

每小题只有一个正确答案）1．回顾人类从早期游徙不定到定居生活的转变过程，最具决定性意义的一步是A．谷物种植B．房屋建造C．陶器制作D．牲畜饲养2．“构成中国的内聚性的又一重要因素是，存在着一种可追溯到数千年前、最古老的商朝的书面语。

”句中“商朝的书面语”具体指A．甲骨文B．大篆C．小篆D．隶书3．“周幽王烽火戏诸侯”、“孔子周游列国”，以下与“诸侯”、“列国”相关的制度是A．禅让制B．世袭制C．分封制D．郡县制4．孔子思想中主张以爱人之心调解和谐社会人际关系的是①“仁者爱人”②贵贱有“序”③“己所不欲，勿施于人”④“有教无类”A．①②B．①③C．①④D．②④5．秦始皇建立的封建专制主义中央集权制度的基本特征是A．确立皇权至高无上B．最高统治者称皇帝C．地方实行郡县制D．中央三公九卿等官职6．通经致用，普及儒家教化并获得巨大成功的第一人是A．孔子B．孟子C．秦始皇D．汉武帝7．图示法是历史学习的一种好方法。

下面那幅图直观反应了三国鼎立的形势A B C D8．“它排除了丞相个人专断，相权过大威胁皇权而出现的政治危机，而且增强了决策施政的程序性和合理性，提高了行政效率。

”材料中的“它”是指A．西汉郡国并行制度B．唐朝三省六部制度C．元朝的行省制度D．明朝的内阁制度9．下图为《元朝疆域图》，其中宣政院管辖的地区是A．①B．②C．③D．④10．“利玛窦是天主教在中国传教的开拓者之一，同时也是18世纪以来第一位阅读中国文学并对中国典籍进行钻研的西方学者，被尊称为‘泰西儒士’”。