湖北省2019～2020学年秋季鄂东南省级示范高中教育教学改革联盟学校高三上学期期中考试理科数学试题及答案

2019年秋季鄂东南省级示范高中教育教学改革联盟学校期中联考高三数学（文科）试卷一、选择题：在每小题给出的四个选项中，只有一项是符合题目要求的． 1．已知复数z 满足121ii z-=+，则z =（ ）ABCD 【答案】C【解析】由已知得：121i i z -=+，i i z +-=121i 2321+-=，z =2104941=+ 【方法点评】此题考查复数的除法，以及复数的模，基础题2．若函数()f x =与()()ln 1g x x =+的定义域分别为M 和N ，则MN =（ ）A ．{}11x x -<<B ．{}11x x -<≤C ．{}11x x -<≤D ．{}11x x -≤≤【答案】A【解析】由已知得：M ()1-，∞=，N ()∞+=，1-，M N ={}11x x -<<【方法点评】此题考查函数的定义域和集合的交集，基础题3．已知0.213a ⎛⎫= ⎪⎝⎭，13log 0.2b =，b c a =，则a 、b 、c 的大小关系为（ ）A ．a b c <<B ．c a b <<C ．a c b <<D ．b c a <<【答案】B【解析】由已知得：0.213a ⎛⎫= ⎪⎝⎭()1,0∈,13log 0.2b =0<,b c a =1>,所以c a b <<【方法点评】此题考查指数与对数比较大小，需要熟练掌握指数对数图像与性质4．已知等差数列{}n a 的前3项和为30，后3项和为90，且前n 项和为200，则n =（ ） A ．9B ．10C ．11D ．12【答案】B【解析】由已知得：4039030n 1=+=+a a ，()10,200240===n n S n【方法点评】此题考查数列的公式，基础题5．函数()1ln 1xf x x-=+的大致图像为（ ）A ．B ．C ．D ．【答案】D【解析】由已知得：求定义域11≠-≠x x 或，取特殊值，当21=x 时，03ln )(<-=x f ，排除BC ；当2-=x 时，03ln )(>=x f ，排除A ；正确答案是D 【方法点评】此题考查函数图像的性质6．设数列{}n a 前n 项和为n S ，已知145a =，112,02121,12n n n n n a a a a a +⎧⎪⎪=⎨⎪-<⎪⎩≤≤≤，则2020S =（ ）A ．1009B ．50485 C ．1010D ．50545【答案】C【解析】由已知得： (5)4,52,51,53,5454321=====a a a a a 4=T ，2020S =10102505=⨯7．已知()0,πα∈，且3sin 5α=，则πtan 4α⎛⎫+= ⎪⎝⎭（ ）A ．17-B ．7C ．17-或7-D ．17或7 【答案】D【解析】由已知得：已知()0,πα∈，且3sin 5α=，43tan ±=α， πtan 4α⎛⎫+= ⎪⎝⎭17或7【方法点评】此题考查三角函数和差公式，基础题8．若非零向量a 、b 满足a b =且()2a b b +⊥，则a 与b 的夹角为（ ）A ．π6B ．π3C ．2π3D ．5π6【答案】C【解析】由已知得：()2a b b +⊥，()02=+b b a 3201cos 2πθθ==+⇒， 【方法点评】此题考查向量的运算，涉及向量的垂直，基础题9．古希腊数学家阿基米德的墓碑上刻着一个圆柱，圆柱内有一个内切球，这个球的直径恰好与圆柱的高相等，相传这个图形是阿基米德最引以为自豪的发现．现有一底面半径与高的比值为1:2的圆柱，则该圆柱的体积与其内切球的体积之比为（ ）A ．43B ．32C ．2D ．83【答案】B【解析】由已知得：设地面所在圆的半径为r,h=2r,342ππ==球圆柱，V V ,23：：球圆柱=V V 【方法点评】此题考查圆柱的内切球，涉及空间想象和思维能力，对空间思维能力有一定的要求。

2019-2020学年湖北省鄂东南省级示范高中教育教学改革联盟学校高三（上）期中数学试卷（理科）一、选择题（在每小题给出的四个选项中，只有一项是符合题目要求的．）1. 若i为虚数单位，则复数z＝2i3+3i2的共轭复数z在复平面内对应的点位于（）A.第一象限B.第二象限C.第三象限D.第四象限【答案】B【考点】复数的代数表示法及其几何意义【解析】利用复数代数形式的乘除运算化简，进一步求得z的坐标得答案．【解答】∵z＝2i3+3i2＝−2i−3，∴z=−3+2i，则z在复平面内对应的点的坐标为(−3, 2)，位于第二象限．2. 已知集合A={x|y=√3−x}，B＝{y|y1+2019x}，则A∩B＝（）A.[1, 3]B.(−∞, 3]C.[3, +∞)D.(1, 3]【答案】D【考点】交集及其运算【解析】可以求出集合A，B，然后进行交集的运算即可．【解答】∵A＝{x|3−x≥0}＝{x|x≤3}，B＝{y|y>1}，∴A∩B＝(1, 3]．3. 已知a＝log20191π，b=(1π)2019，c=20191π，则（）A.c<a<bB.a<c<bC.b<a<cD.a<b<c 【答案】D【考点】对数值大小的比较【解析】利用指数函数与对数函数的单调性即可得出．【解答】a＝log20191π<0，b=(1π)2019∈(0, 1)，c=20191π>1，∴a<b<c．4. 函数f(x)=(1−21+e x)sinx的图象的大致形状是（）A.B.C.D.【答案】A【考点】函数的图象与图象的变换【解析】判断函数的奇偶性，结合对称性以及极限思想进行判断即可．【解答】f(x)=1+e x−21+e x ⋅sinx=e x−1e x+1⋅sinx，则f(−x)=e −x−1e−x+1⋅sin(−x)=1−e x1+e x(−sinx)=e x−1e x+1⋅sinx＝f(x)，则函数f(x)是偶函数，图象关于y轴对称，排除C，D，当x>0，且x→0，f(x)>0，排除B，5. 已知等差数列{a n}的公差为d，前n项和为S n，则“d≤0”是“S8+S10<2S9”的（）A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件【答案】B【考点】充分条件、必要条件、充要条件【解析】由S8+S10<2S9，得d<0，即d≤0成立；反之，当d＝0时，S8+S10<2S9不成立．结合充分必要条件的判定得答案．【解答】由S 8+S 10<2S 9，得8a 1+8×7d 2+10a 1+10×9d 2<2(9a 1+9×8d 2)，整理得：d <0，则d ≤0成立；当d ＝0时，S 8+S 10＝2S 9，S 8+S 10<2S 9不成立． ∴ “d ≤0”是“S 8+S 10<2S 9”的必要不充分条件．6. 已知命题p ：实数a 满足不等式2a ≤1；命题q ：函数f(x)=13x 3+a2x 2+x 有极值点．若“p ∧q ”是真命题，则实数a 的取值范围为（ ） A.(−2, 0] B.[−2, 0] C.(−∞, −2) D.(−∞, −2]【答案】 C【考点】复合命题及其真假判断 【解析】由2a ≤1，可得a ≤0，由函数f(x)=13x 3+a2x 2+x 有极值点，可得a 2>4，若“p ∧q ”是真命题，则p 为真且q 为真，即可得结果． 【解答】当2a ≤1时，可得a ≤0；当函数f(x)=13x 3+a2x 2+x 有极值点时，f′(x)＝x 2+ax +1，△>0，可得a 2>4，即a >2，或a <−2，因为“p ∧q ”是真命题，所以p 为真且q 为真，所以a <−2，7. 已知向量a →=(cosθ,sinθ)，b →=(0,−1)，θ∈(0,π2)，则向量a →与向量b →的夹角为（ ） A.π−θB.θ−π2C.π2+θD.θ【答案】 C【考点】数量积表示两个向量的夹角 【解析】根据条件即可求出cos <a →,b →>=−sinθ=cos(π2+θ)，根据θ的范围可求出π2<π2+θ<π，并且0≤<a →,b →>≤π，这样即可得出a →与b →的夹角．【解答】∵ a →⋅b →=−sinθ,|a →|=|b →|=1，且θ∈(0,π2)，∴ cos <a →,b →>=a →⋅b→|a →||b →|=−sinθ=cos(π2+θ)，又0≤<a →,b →>≤π，π2<π2+θ<π， ∴ a →,b →的夹角为π2+θ．8. 中国传统折扇文化有着极其深厚的底蕴，一般情况下，折扇可看作是由从一个圆面中剪下的扇形制作而成，设扇形的面积为S1，圆面中剩余部分的面积为S2，当S1与S2的比值为√5−12≈0.618（黄金分割比）时，扇面看上去形状较为美观，那么此时扇形的圆心角的度数约为（）A.127.50∘B.137.50∘C.147.50∘D.150.50∘【答案】B【考点】扇形面积公式【解析】由题意知S1与S2所在扇形圆心角的比即为它们的面积比，设S1与S2所在扇形圆心角分别为α、β，列出方程组求出即可．【解答】由题意知，S1与S2所在扇形圆心角的比即为它们的面积比，设S1与S2所在扇形圆心角分别为α，β，则αβ=√5−12≈0.618，又α+β＝360∘，∴α+α0.618≈360∘，解得α≈137.50∘．9. 已知将函数f(x)=cos(2x+φ)(0<φ<π2)的图象向左平移φ个单位长度后，得到函数g(x)的图象，若g(x)的图象关于原点对称，则f(π3)=()A.−√32B.√32C.−12D.12【答案】A【考点】函数y=Asin（ωx+φ）的图象变换【解析】由题意利用函数y＝Asin(ωx+φ)的图象变换规律，三角函数的图象的对称性，求出函数的解析式，可得f(π3)的值．【解答】将函数f(x)=cos(2x+φ)(0<φ<π2)的图象向左平移φ个单位长度后，得到函数g(x)＝cos(2x+2φ+φ)的图象．若g(x)＝cos(2x+3φ)的图象关于原点对称，则3φ=π2，φ=π6，故f(x)＝cos(2x+π6)，∴f(π3)=cos(2π3+π6)=−√32，10. 如图为我国数学家赵爽（约3世纪初）在为《周牌算经》作注时验证勾股定理的示意图，现在提供6种不同的颜色给其中5个小区域涂色，规定每个区域只涂一种颜色，相邻区域颜色不同，则A，C区域涂同色的概率为（）A.2 7B.57C.913D.413【答案】D【考点】古典概型及其概率计算公式【解析】本题从颜色使用数量上来分类，又由条件知至少使用三种颜色，所以只剩三种情况了．然后选色，再按照规定每个区域只涂一种颜色，相邻区域颜色不同，使用分步计数原理逐一涂色，即可求出总的基本事件，再弄清A，C区域涂同色的占了多少个基本事件，利用古典概型及其概率计算公式求答案．【解答】根据题意，至少使用3种颜色．由使用颜色数量，下面我们分三种情况：①使用5种颜色：选色C65，涂上去A55，共有C65A55=720种；②使用4种颜色：选色C64，先涂D有4种，下面，一、若A、C同色，则B和E各涂剩余的两色，有3A22种，二、若A、C不同色，则B和E必同色，有A33种．∴共C64×4×3A22+C64×4×A33= 360+360＝720种；③使用3种颜色：选色C63，先涂D有3种选择，D用掉一种颜色，下面只有A、C同色，B、E同色，有A22种，共C63×3A22=120种，∴共计720+720+120＝1560种，其中A，C区域涂同色的有360+120＝480种，则A，C区域涂同色的概率为4801560=413．11. 执行如图示的程序框图，输出的S的值等于（）A.tan101tan1−101 B.tan102tan1−102C.tan101tan1+99 D.tan100tan1+99【答案】A【考点】程序框图【解析】模拟程序框图的执行过程得出程序运行后输出S ＝tan1tan2+tan2tan3+...tan100tan101的值；利用tan(2−1)=tan2−tan11+tan2tan1求出tan1tan2=tan2tan1−2，同理求得S 的值． 【解答】模拟程序框图的执行过程知，该程序执行后输出 S ＝tan1tan2+tan2tan3+...tan100tan101的值； tan(2−1)=tan2−tan11+tan2tan1， ∴ tan1tan2=tan2tan1−2， 同理tan2tan3=tan3tan1−tan2tan1−1， …；∴ S ＝(tan2tan1−2)+(tan3tan1−tan2tan1−1)+...+(tan101tan1−tan100tan1−1)＝(tan2tan1+tan3tan1−tan2tan1+⋯+tan101tan1−tan100tan1)+(−2−1− (1)=tan101tan1−101．12. 若不等式xlnx +x(1−k)+2k >0对任意的x ∈(2, +∞)都恒成立，则整数k 的最大值为（ ） A.3 B.4 C.5 D.6 【答案】 B【考点】函数恒成立问题 【解析】 问题转化为k <xlnx+x x−2对任意x >2恒成立，令ℎ(x)=xlnx+x x−2，根据函数的单调性求出k的最大值即可． 【解答】问题转化为k(x −2)<x +xlnx ， 当x ＝2时，不等式显然成立， 当x >2时，即有k <xlnx+x x−2对任意x >2恒成立，令ℎ(x)=xlnx+x x−2，则ℎ′(x)=x−4−2lnx (x−2)2，令g(x)＝x −2lnx −4(x >2)， 则g′(x)＝1−2x >0，故g(x)在(2, +∞)递增，∵ g(8)＝4−6ln2<0，g(9)＝5−4ln3>0， ∴ ∃x 0∈(8, 9)，使得ℎ′(x 0)＝0，故lnx 0=x 0−42，故x ∈(2, x 0)时，ℎ′(x 0)<0，x ∈(x 0, +∞)时，ℎ′(x)>0，故ℎ(x)在(2, x0)递减，在(x0, +∞)递增，故ℎ(x)min＝ℎ(x0)=x0(lnx0+1)x0−2=x0(1+x0−42)x0−2=x02∈(4, 92)，故k<ℎ(x0)，故整数k的最大值为4，二、填空题（把正确答案填在题中横线上．）曲线y＝xlnx−x在点(1, −1)处的切线方程为________．【答案】y＝−1【考点】利用导数研究曲线上某点切线方程【解析】f′(x)＝lnx+1−1＝lnx，可得f′(1)＝0，即为切线的斜率，利用点斜式即可得出切线的方程．【解答】f′(x)＝lnx+1−1＝lnx，∴f′(1)＝0，∴曲线y＝f(x)在点（1, f(1)）处的切线方程为y＝−1．故答案为：y＝−1．已知n=∫πsinxdx，则(√x+1)n(x−1)6的展开式中x4的系数为________．【答案】−5【考点】定积分二项式定理及相关概念微积分基本定理【解析】直接利用定积分求出被积函数的原函数求出n的值，进一步利用二项展开式的应用求出展开式中x4的系数，进一步求出结果．【解答】已知n=∫πsinxdx，所以n＝−cosx|0π=−cosπ−(−cos0)＝2，所以(√x+1)n(x−1)6=(√x+1)2(x−1)6=(x−2√x+1)(x−1)6所以(x−1)6的展开式为T r+1=C6r x6−r⋅(−1)r，当r＝3时，系数为−C63，当r＝2时系数为C62，所以展开式中x4的系数为C62−C63=15−20=−5．已知点A(3, −1)，点P(x, y)满足线性约束条件{x−y−1≤0x≥02x+y−5≤0，O为坐标原点，那OP→在OA→方向上的投影的取值范围为________．【答案】 [−√102, √102]【考点】 简单线性规划 【解析】 由已知可得OP →在OA →方向上的投影为√1010(3x −y)，再由线性规划求得3x −y 的范围，则答案可求． 【解答】∵ A(3, −1)，P(x, y)，∴ OP →在OA →方向上的投影为|OP →|cos <OP →,OA →>=OA →⋅OP →|OA →|=√1010(3x −y)．由约束条件{x −y −1≤0x ≥02x +y −5≤0 作出可行域如图，令z ＝3x −y ，平移直线y ＝3x 至A 时，z 有最小值为−5，平移直线y ＝3x 至B(2, 1)时，z 有最大值为5，∴ OP →在OA →方向上的投影的取值范围为[−√102, √102]．设A ，B 分别在x 轴正半轴和y 轴正半轴上运动，以AB 为边向外作正△ABC （△ABC 与△OAB 不重叠），且正△ABC 的边长为2√2，M 为AC 的中点，则OC →⋅OM →的最大值为________． 【答案】 5+2√7 【考点】平面向量数量积的性质及其运算 【解析】设∠OAB ＝θ，(0<θ<π2)，运用解直角三角形和余弦定理，以及向量的数量积的定义和性质，两角和的余弦公式，化简可得OC →⋅OM →=2cos 2θ+4+6√3sinθcosθ，再由二倍角的正弦公式和余弦公式，以及辅助角公式，结合正弦函数的最值，可得所求最大值． 【解答】设∠OAB ＝θ，(0<θ<π2)，则|OA|＝2√2cosθ，|OC|2＝|OA|2+|AC|2−2|OA|⋅|AC|⋅cos(θ+π3) ＝8cos 2θ+8−16cosθcos(θ+π3)，OC →⋅OM →=OC →⋅12(OA →+OC →)=12(OA →⋅OC →+OC →2)=12[|OA →|⋅|OC →|⋅cos∠COA +8cos 2θ+8−16cosθcos(θ+π3)] =12[|OA|2+|OC|2−|AC|22+8cos 2θ+8−16cosθcos(θ+π3)] =12[8cos 2θ+8cos 2θ−16cosθcos(θ+π3)2+8cos 2θ+8−16cosθcos(θ+π3)] ＝8cos 2θ+4−12cosθcos(θ+π3)＝8cos 2θ+4−12cosθ(12cosθ−√32sinθ)＝2cos 2θ+4+6√3sinθcosθ＝cos2θ+3√3sin2θ+5＝5+2√7sin(2θ+φ)，其中sinφ=2√7，cosφ=√32√7，当sin(2θ+φ)＝1时，5+2√7sin(2θ+φ)取得最大值5+2√7， 三、解答题（解答应写出文字说明，证明过程或演算步骤．）△ABC 的内角A ，B ，C 的对边分别为a ，b ，c ，已知sin(A +C)＝8sin 2B2． （1）求tanB ；（2）若a +c ＝6，△ABC 的面积为2，求△ABC 的周长l ． 【答案】由题sin(A +C)＝8sin 2B2． 知sinB =8sin 2B 2=2sin B 2cos B2， 可得tan B 2=14， 于是tanB =2×141−(14)2=815，由（1）知，sinB =817，cosB =1517， 由S =12acsinB =417ac =2得ac =172，由余弦定理得b 2＝a 2+c 2−2ac ⋅cosB ＝(a +c)2−32＝4， 故a +c +b ＝8，故△ABC 的周长为8． 【考点】二倍角的三角函数 余弦定理 【解析】（1）利用已知条件结合三角形的内角和以及二倍角公式转化求解即可．（2）通过三角形的面积以及余弦定理，转化求解a +c 的值，然后求解三角形的周长． 【解答】由题sin(A+C)＝8sin2B2．知sinB=8sin2B2=2sin B2cos B2，可得tan B2=14，于是tanB=2×141−(14)2=815，由（1）知，sinB=817，cosB=1517，由S=12acsinB=417ac=2得ac=172，由余弦定理得b2＝a2+c2−2ac⋅cosB＝(a+c)2−32＝4，故a+c+b＝8，故△ABC的周长为8．已知S n为等差数列{a n}的前n项和，a5＝9，S13＝169．（1）求数列{a n}的通项公式；（2）设b n=a n3n，求数列{b n}的前n项和T n．【答案】由S13=13(a1+a13)2=13a7=169，得a7＝13，2d＝a7−a5＝4，d＝2，故a n＝9+(n−5)⋅2＝2n−1．b n=2n−13n，T n=1⋅13+3⋅13+5⋅13+⋯+(2n−1)⋅13，1 3T n=1⋅132+3⋅133+5⋅134+⋯+(2n−3)⋅13n+(2n−1)13n+1，两式相减可得23T n=13+2(132+133+⋯+13n)−(2n−1)13n+1=13+219(1−13n−1)1−13−2n−13n+1=23−2n+23n+1，故T n=1−n+13．【考点】数列的求和【解析】（1）利用等差数列的前n项和求出数列的公差，求出第7项，利用等差数列任意两项的关系求解通项公式．（2）化简通项公式，利用错位相减法求解数列的和即可．【解答】由S13=13(a1+a13)2=13a7=169，得a7＝13，2d＝a7−a5＝4，d＝2，故a n ＝9+(n −5)⋅2＝2n −1． b n =2n−13n ，T n =1⋅13+3⋅132+5⋅133+⋯+(2n −1)⋅13n ，13T n =1⋅132+3⋅133+5⋅134+⋯+(2n −3)⋅13n+(2n −1)13n+1，两式相减可得23T n =13+2(132+133+⋯+13n )−(2n −1)13n+1 =13+219(1−13n−1)1−13−2n−13n+1=23−2n+23n+1，故T n =1−n+13n．已知a →=(2cos 2x −1,−1)，b →=(1,sin(2x +π6))，设f(x)=a →⋅b →，且x ∈(0, π)． （1）求f(x)的单调递减区间；（2）若函数y ＝3f(x)+k 恰有2个零点，求k 的取值范围． 【答案】由题a →=(2cos 2x −1,−1)，b →=(1,sin(2x +π6))，f(x)=a →⋅b →=2cos 2x −1−sin(2x +π6)=cos2x −√32sin2x −12cos2x =12cos2x −√32sin2x =−sin(2x −π6)，由2x −π6∈(2kπ−π2,2kπ+π2) 得x ∈(kπ−π6,kπ+π3)，k ∈Z ， ∵ x ∈(0, π)∴ x ∈(0,π3)和(56π,π)，∴ f(x)的单调递减区间为(0,π3)和(56π,π)．原函数y ＝3f(x)+k 恰有两个零点⇔sin(2x −π6)=k 3⇔y =sin(2x −π6)，x ∈(0, π)与y =k3有两个不同交点，作出y =sin(2x −π6)，x ∈(0, π)的图象如图， 由图知，−1<k3<−12或−12<k3<1， 故k 的取值范围为(−3,−32)∪(−32,3)．【考点】平面向量数量积的性质及其运算 正弦函数的单调性 【解析】（1）利用向量的数量积以及两角和与差的三角函数化简函数的解析式，利用正弦函数的单调性求解求f(x)的单调递减区间；（2）函数y ＝3f(x)+k 恰有2个零点，⇔sin(2x −π6)=k3⇔y =sin(2x −π6)，利用函数的图象，转化求解k 的取值范围． 【解答】由题a →=(2cos 2x −1,−1)，b →=(1,sin(2x +π6))，f(x)=a →⋅b →=2cos 2x −1−sin(2x +π6)=cos2x −√32sin2x −12cos2x =12cos2x −√32sin2x =−sin(2x −π6)，由2x −π6∈(2kπ−π2,2kπ+π2) 得x ∈(kπ−π6,kπ+π3)，k ∈Z ， ∵ x ∈(0, π)∴ x ∈(0,π3)和(56π,π)， ∴ f(x)的单调递减区间为(0,π3)和(56π,π)．原函数y ＝3f(x)+k 恰有两个零点⇔sin(2x −π6)=k 3⇔y =sin(2x −π6)，x ∈(0, π)与y =k3有两个不同交点，作出y =sin(2x −π6)，x ∈(0, π)的图象如图， 由图知，−1<k3<−12或−12<k3<1， 故k 的取值范围为(−3,−32)∪(−32,3)．世界军人运动会，简称“军运会”，是国际军事体育理事会主办的全球军人最高规格的大型综合性运动会，每四年举办一届，会期7至10天，比赛设27个大项，参赛规模约100多个国家8000余人，规模仅次于奥运会，是和平时期各国军队展示实力形象、增进友好交流、扩大国际影响的重要平台，被誉为“军人奥运会”．根据各方达成的共识，军运会于2019年10月18日至27日在武汉举行，赛期10天，共设置射击、游泳、田径、篮球等27个大项、329个小项．其中，空军五项、军事五项、海军五项、定向越野和跳伞5个项目为军事特色项目，其他项目为奥运项目．现对某国在射击比赛预赛中的得分数据进行分析，得到如图的频率分布直方图：（1）估计某国射击比赛预赛成绩得分的平均值x（同一组中的数据用该组区间的中点值代表）；（2）根据大量的射击成绩测试数据，可以认为射击成绩X近似地服从正态分布N(μ, σ2)，经计算第（1）问中样本标准差s的近似值为50，用样本平均数x作为μ的近似值，用样本标准差s作为σ的估计值，求射击成绩得分X恰在350到400的概率；[参考数据：若随机变量ξ服从正态分布N(μ, σ2)，则：P(μ−σ<ξ≤μ+σ)≈0.6827，P(μ−2σ<ξ≤μ+2σ)≈0.9545，P(μ−3σ<ξ≤μ+3σ)≈0.9973•]（3）某汽车销售公司在军运会期间推广一款新能源汽车，现面向意向客户推出“玩游戏，送大奖”，活动，客户可根据抛掷骰子的结果，操控微型遥控车在方格图上行进，若遥控车最终停在“胜利大本营”，则可获得购车优惠券．已知骰子出现任意点数的概率都是1，方格图上标有第0格，第1格，第2格，……第50格．遥控车开始在第0格，客6户每抛掷一次骰子，遥控车向前移动一次，若抛掷出正面向上的点数是1，2，3，4，5点，遥控车向前移动一格（从k到k+1），若抛掷出正面向上的点数是6点，遥控车向前移动两格（从k到k+2），直到遥控车移动到第49格（胜利大本营）或第50格（失败大本营）时，游戏结束．设遥控车移动到第n格的概率为P n，试证明{P n−P n−1}(1≤n≤49)是等比数列，并求P50，以及根据P50的值解释这种游戏方案对意向客户是否具有吸引力．【答案】X=0.002×50×205+0.004×50×255+0.009×50×305+0.004×50×355+0.001×50×405=300．因为X ∼N(300, 502)，所以P(350<X ≤400)=12(0.9545−0.6827)=0.1359； 摇控车开始在第0格为必然事件，P 0＝1，第一次掷骰子，正面向上不出现6点， 摇控车移动到第1格，其概率为56，即P 1=56；摇控车移到第n 格(2≤n ≤49)格的情况是下列两种，而且也只有两种；①摇控车先到第n −2格，抛掷出正面向上的点数为6点，其概率为16P n−2； ②摇控车先到第n −1格，抛掷骰子正面向上不出现6点，其概率为56P n−1，故P n =16P n−2+56P n−1，P n −P n−1=−16(P n−1−P n−2)，故1≤n ≤49时，{P n −P n−1}是首项为P 1−P 0=−16，公比为−16的等比数列，故P n −P n−1=(−16)n ，P n ＝P 0+(P 1−P 0)+(P 2−P 1)+...+(P n −P n−1)=1+(−16)+(−16)2+⋯+(−16)n =1−(−16)n+11−(−16)=67[1−(−16)n+1]，P 50=16P 48=16⋅67⋅[1−(−16)49]=17[1+(16)49]<12，P 49=1−P 50>12，故这种游戏方案客户参与中奖的可能性较大，对意向客户有吸引力． 【考点】 数列的应用 【解析】（1）利用组中值代入求平均值；（2）写出正态分布N(μ, σ2)，代入即可；（3）根据题意确定，{P n −P n−1}是首项为P 1−P 0=−16，公比为−16的等比数列，写出通项公式，利用差分求出Pn ，再求P 50 【解答】X =0.002×50×205+0.004×50×255+0.009×50×305+0.004×50×355+0.001×50×405=300．因为X ∼N(300, 502)，所以P(350<X ≤400)=12(0.9545−0.6827)=0.1359； 摇控车开始在第0格为必然事件，P 0＝1，第一次掷骰子，正面向上不出现6点， 摇控车移动到第1格，其概率为56，即P 1=56；摇控车移到第n 格(2≤n ≤49)格的情况是下列两种，而且也只有两种；①摇控车先到第n −2格，抛掷出正面向上的点数为6点，其概率为16P n−2； ②摇控车先到第n −1格，抛掷骰子正面向上不出现6点，其概率为56P n−1，故P n =16P n−2+56P n−1，P n −P n−1=−16(P n−1−P n−2)，故1≤n ≤49时，{P n −P n−1}是首项为P 1−P 0=−16，公比为−16的等比数列，故P n −P n−1=(−16)n ，P n ＝P 0+(P 1−P 0)+(P 2−P 1)+...+(P n −P n−1)=1+(−16)+(−16)2+⋯+(−16)n=1−(−16)n+11−(−16)=67[1−(−16)n+1]，P 50=16P 48=16⋅67⋅[1−(−16)49]=17[1+(16)49]<12，P 49=1−P 50>12，故这种游戏方案客户参与中奖的可能性较大，对意向客户有吸引力．已知函数f(x)=1x 2+alnx(a ∈R)． （1）讨论f(x)的单调性；（2）若x 1，x 2(x 1<x 2)是f(x)的两个零点，求证：2aln(x 2−x 1+ea )+1<0． 【答案】f(x)的定义域为(0, +∞)，且f ′(x)=−2x−3+ax =ax 2−2x 3，①当a ≤0时，f ′(x)≤0，f(x)的单调递减区间为(0, +∞)； ②当a >0时，由f ′(x)>0得x >√2a ，故f(x)的单调递增区间为(√2a,+∞)，单调递减区间为(0,√2a)．证明：∵ f(x)有两个零点，∴ 由（1）知a >0且f(√2a)=a 2+a 2ln 2a<0，∴ a >2e ，要证原不等式成立，只需证明ln(x 2−x 1+ea )<−12a ，只需证明x 2−x 1<e −12a −ea，只需证明e a <x 1<√2a<x 2<e −12a ．一方面∵ a >2e ，∴ √2a <√1e=√e −1<√e −1a <1，∴ f(e −12a )=e 1a +alne −12a =e 1a −12>e 0−12=12>0，∴ f(√2a)f(e −12a )<0，且f(x)在(√2a,+∞)单调递增，故√2a<x 2<e −12a ；另一方面，令g(x)=lnx +1ex ，(x >0)， 则g ′(x)=1x −1ex 2=ex−1ex 2，当0<x <1e 时，g ′(x)<0；当x >1e 时，g ′(x)>0；故g(x)min =g(1e )=−1+1=0，故g(x)≥0即lnx ≥−1ex 时x ∈(0, +∞)恒成立， 令x =ea ，则ln ea >−ae 2，于是f(ea )=a 2e 2+aln ea >a 2e 2−a 2e 2=0， 而e 2a 2−(√2a )2=e 2−2a a 2<e 2−4e a 2<0，【考点】利用导数研究函数的单调性 利用导数研究函数的最值 【解析】（1）f(x)的定义域为(0, +∞)，求出导函数，通过①当a ≤0时，②当a >0时，判断导数的符号，判断函数的单调性即可．（2）利用f(x)有两个零，得到f(√2a )=a 2+a 2ln 2a<0，推出a >2e ，要证原不等式成立，只需证明ln(x 2−x 1+ea )<−12a ，利用分析法推出√2a<x 2<e −12a ；另一方面，令g(x)=lnx +1ex ，(x >0)，通过函数的导数，转化求解函数的最值，转化求解即可． 【解答】f(x)的定义域为(0, +∞)，且f ′(x)=−2x−3+ax =ax 2−2x 3，①当a ≤0时，f ′(x)≤0，f(x)的单调递减区间为(0, +∞)； ②当a >0时，由f ′(x)>0得x >√2a ，故f(x)的单调递增区间为(√2a,+∞)，单调递减区间为(0,√2a)．证明：∵ f(x)有两个零点，∴ 由（1）知a >0且f(√2a)=a 2+a 2ln 2a<0，∴ a >2e ，要证原不等式成立，只需证明ln(x 2−x 1+ea )<−12a ，只需证明x 2−x 1<e −12a −ea，只需证明e a <x 1<√2a<x 2<e −12a ．一方面∵ a >2e ，∴ √2a <√1e=√e −1<√e −1a <1，∴ f(e −12a )=e 1a +alne −12a =e 1a −12>e 0−12=12>0，∴ f(√2a)f(e −12a )<0，且f(x)在(√2a,+∞)单调递增，故√2a<x 2<e −12a ；另一方面，令g(x)=lnx +1ex ，(x >0)， 则g ′(x)=1x −1ex 2=ex−1ex 2，当0<x <1e 时，g ′(x)<0；当x >1e 时，g ′(x)>0；故g(x)min =g(1e )=−1+1=0，故g(x)≥0即lnx ≥−1ex 时x ∈(0, +∞)恒成立， 令x =ea ，则ln ea >−ae 2，于是f(ea )=a 2e 2+aln ea >a 2e 2−a 2e 2=0， 而e 2a 2−(√2a )2=e 2−2a a 2<e 2−4e a 2<0，（二）选考题：请考生在第22，23题中任选一题作答．如果多做，则按所做的第一题计分．作答时请写清题号．【选修4-4：坐标系与参数方程】在直角坐标系xOy 中，以坐标原点O 为极点，x 轴的正半轴为极轴建立极坐标系，曲线C 的极坐标方程为ρ2(1+8sin 2θ)＝9，直线l 的参数方程为{x =−1+4ty =1−t （t 为参数）．（1）求C 与l 的交点的直角坐标；（2）求C 上的点到直线l 的距离的最大值． 【答案】曲线C 的直角坐标方程为x 2+9y 2＝9，直线l 的普通方程为x +4y ＝3， 由{x 2+9y 2=9x +4y =3 得25y 2−24y ＝0，于是{x =3y =0 í或{x =−2125y =2425 ， 即C 与l 的交点直角坐标为(3, 0)和(−2125,2425)； 设曲线C 上一点P(3cosθ, sinθ)， 则P 到直线l 的距离d =√17≤√17=8√1717，故C 上的点到直线l 的距离的最大值为8√1717． 【考点】参数方程与普通方程的互化 圆的极坐标方程 【解析】（1）将曲线C 和直线l 的方程转化为直角坐标方程，然后联立解方程组可得其交点坐标； （2）曲线C 上一点P(3cosθ, sinθ)，则P 到直线l 的距离d =√17，然后求出d的最大值即可． 【解答】曲线C 的直角坐标方程为x 2+9y 2＝9，直线l 的普通方程为x +4y ＝3， 由{x 2+9y 2=9x +4y =3 得25y 2−24y ＝0，于是{x =3y =0 í或{x =−2125y =2425 ， 即C 与l 的交点直角坐标为(3, 0)和(−2125,2425)； 设曲线C 上一点P(3cosθ, sinθ)， 则P 到直线l 的距离d =17≤17=8√1717，故C 上的点到直线l 的距离的最大值为8√1717． 【选修4-5：不等式选讲】已知函数f(x)＝|x +1|+2|x −1|． （1）求不等式f(x)≥4的解集；（2）若函数y ＝f(x)图象的最低点坐标为(p, q)，正数a ，b 满足pa +qb ＝2，求4a +1b 的最小值． 【答案】因为f(x)＝|x +1|+2|x −1|，f(x)≥4， 所以当x ≥1时，由f(x)＝3x −1≥4，得x ≥53；当−1<x <1时，由f(x)＝−x +3≥4，得x ≤−1，舍去； 当x ≤−1时，由f(x)＝−3x +1≥4，得x ≤−1， 综上，原不等式的解集为(−∞,−1]∪[53,+∞)．由f(x)={3x −1(x ≥1)−x +3(−1<x <1)−3x +1(x ≤−1) ，得f(x)min ＝f(1)＝2，故函数y ＝f(x)图象的最低点为(1, 2)，于是a +2b ＝2，4a+1b=12(4a +1b )(a +2b)=12(6+a b+8b a)≥12(6+2√8)=3+2√2，当且仅当ab =8b a，即a ＝4−2√2，b =√2−1时取等号，故4a +1b 的最小值为3+2√2．【考点】绝对值不等式的解法与证明 基本不等式及其应用 【解析】（1）根据f(x)≥4，分x ≥1，−1<x <1和x ≤−1三种情况去绝对值，然后解不等式即可；（2）求出f(x)的最小值可得a +2b ＝2，然后根据4a +1b =12(4a +1b )(a +2b)=12(6+a b+8ba)，利用基本不等式求出4a +1b 的最小值． 【解答】因为f(x)＝|x +1|+2|x −1|，f(x)≥4， 所以当x ≥1时，由f(x)＝3x −1≥4，得x ≥53；当−1<x <1时，由f(x)＝−x +3≥4，得x ≤−1，舍去； 当x ≤−1时，由f(x)＝−3x +1≥4，得x ≤−1， 综上，原不等式的解集为(−∞,−1]∪[53,+∞)．由f(x)={3x −1(x ≥1)−x +3(−1<x <1)−3x +1(x ≤−1) ，得f(x)min ＝f(1)＝2，故函数y ＝f(x)图象的最低点为(1, 2)，于是a +2b ＝2， 4a+1b =12(4a +1b )(a +2b)=12(6+ab +8ba)≥12(6+2√8)=3+2√2， 当且仅当ab =8b a，即a ＝4−2√2，b =√2−1时取等号，故4a +1b的最小值为3+2√2．。

【校级联考】湖北省鄂东南省级示范高中教育教学改革联盟2019届高三上学期期中考试英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读选择These are some of Nicest Small Towns in America everyone should visit before they're 50.Jacksonville, OregonOne of the original major cities of the Gold Rush, Jacksonville was founded in the early 1850s by pioneers hoping to become rich. The entire town, was designated as a U.S.National Landmark in the 1960s, so it's definitely worth visiting, especially if you're a history buff. Jacksonville is home to over 100 National Historical buildings sprinkled throughout the community in the heart of Oregon's wine country and surrounded by gorgeous greenery, so there really is something for everyone.Traverse City, MichiganLocated on the shores of Lake Michigan, Traverse City is the best outdoor and water activities destination. In the warmer months, you'll find everyone hiking and biking the numerous trails and participating in the most popular recreational water sports kayaking, fishing, windsurfing, and paddleboarding. There's also golfing and bird watching for those who are looking for a more leisurely vacation. July is an especially busy month in Traverse City, as it's when hundreds of thousands of visitors come in for the National Cherry Festival. And the many farm-to-table dining options, breweries, wineries, and distilleries make it a destination worth visiting even in the winter.Sedona, ArizonaBesides its famous gorgeous red rock geography which is truly a jaw-dropping natural wonder, Sedona is known for its eclectic art scene, near-perfect weather, and of course, fantastic food and wine. Sedona truly has it all, whether you're looking for a girl's spa weekend, an outdoor family excursion-based trip, or a romantic getaway. There's really no bad time to visit because events like art festivals, concerts, and cusine tastings happen year-round thanks to the warm weather.Beaufort, South CarolinaIf you've ever watched the legendary movie Forrest Gump, you've already seen parts ofone of the best small towns in America: Beaufort, South Carolina. As the second-oldest city in South Carolina, Beaufort is known for its antebellum mansions and historic downtown district. Since Beaufort is located right on Port Royal Island, there are a ton of popular water sports like fishing and boating, in addition to wonderful, fresh seafood. The city is also known as one of America's best art towns thanks to its dozens of museums, film festivals, and art galleries. Bay Street is Beaufort's main road that borders the harbor where you'll find plenty of good restaurants and local shops.Port Townsena, WashingtonIt is one of Washington's greatest Victorian seaside towns and just one of three historic Victorian seaports in the entire United States. Situated on the northeastern tip of the Olympic Peninsula, you'll find a nature lover's paradise with the sea on one side and the Fort Worden Historical State Park on the other. In addition to the local shops, brightly colored mansions, and historic buildings that line the ocean side streets, Port Townsend puts on award-winning theater productions and hosts a variety of concerts, cultural events, and festivals all year round.1．If you are interested in history of America, which towns are your better choice ________. A．Beaufort, South Carolina and Sedona, ArizonaB．Jacksonville, Oregon and Traverse City, MichiganC．Sedona, Arizona and Port Townsend, WashingtonD．Jacksonville, Oregon and Beaufort, South Carolina2．According to the passage, in how many towns you can enjoy many tasty foods?A．5 B．4C．3 D．23．What is common to Traverse City, Sedona and Port Townsend?A．There are many outdoor water sports you can enjoy.B．You can probably have fun there whenever you go to these places.C．It's easy for you to taste good wine there.D．The weather is always warm in those towns.二、七选五The Art of Slow ReadingIf you are reading this article in print, chances are that you will only get through half of what I have written. And if you are reading this online, you may not even finish a fifth. 4．Theysuggest that many of us no longer have the concentration to read articles through to their conclusion.So are we getting stupider? Actually, our online habits are damaging the mental power we need to process and understand textual information. Round-the-clock news makes us read from one article to the next without necessarily engaging fully with any of the content. Our reading is frequently interrupted by the noise of the latest email and we are now absorbing short bursts of words on Twitter and Facebook more regularly than longer texts. 5．But we are gradually forgetting how to sit back, think carefully, and relate all the facts to each other.6．A desperate bunch of academics want us to take our time while reading, and re-reading. They ask us to switch off our computers every so often and rediscover both the joy of personal engagement with printed texts, and the ability to process them fully. What's to be done then? Most slow readers realize that total rejection of the web is extremely unrealistic. They feel that getaway from technology for a while is the answer. 7．Personally, I'm not sure whether I could ever go offline for long. Even while writing this article, I am switching constantly between sites, skimming too often, absorbing too little. Internet reading has become too rooted in my daily life for me to change. I read essays and articles not in hard copy but as PDFs. I suspect that many readers are in a similar position. 8．You can download a computer application called Freedom, which allows you to read in peace by cutting off your Internet connection. Or if you want to avoid being disturbed by the Internet, you could always download offline reader Instapaper for your iPhone. If you're still reading my article, that is slow reading.A．The Internet is probably part of the problem.B．Now some campaigns are advocating slow reading.C．These are the two findings from the recent research projects.D．But if you just occasionally want to read more slowly, help is at hand.E.Some of them have suggested turning their computers off for one day a week.F.Slow reading can help connect a reader to neighborhood and become popular.G.Because of the Internet, we have become very good at collecting information.三、完形填空It was the day before my daughter's birthday. I'd just collected her from preschool when she cautioned me to 9 the elderly person walking across the car park. l was struck by her 10 and had no idea how much she really 11 it.The following day--her birthday-we decided to buy cupcakes for her. After we 12the cupcakes, Norah was busy standing up in the trolley(手推车), 13 waving and happily declaring, "Hi, old person! It's my birthday today!" 14 I could stop her calling him an old person, the stone-faced man 15 to hen His expression softened as he replied, "Well, hello, little lady! And how old are you today? "They 16 for a few minutes, he wished her a happy birthday, and we went our 17 ways. A few minutes later, Norah asked me if she could take a 18 with the old man. I agreed. We found the man a couple of shelves over, and I approached him. When I told him Norah's 19 , his expression changed from 20 to shocked finally to delighted. He took a step back, steadied himself on his shopping trolley, and 21 his free hand on his chest. "A photo? With me?" he asked. "Yes, Sir, for my birthday!" Norah begged. And so he did. I 22 my iPhone, and they posed together. Norah placed her soft hand on top of his hand. He wordlessly stared at her with 23 eyes as she kept his hand in hers. I asked his name, and he told us to call him Dan. We were 24 other shoppers, but they didn't care. There was 25 happening in the supermarket that day, and we could all sense it.That afternoon I 26 the story and a photo of the two of them on the Facebook. Later that night, I received a private 27 from a local reader who recognized Mr. Dan. He told me Dan's wife had passed away six months earlier and he wanted to let me know that he was certain Dan's heart was touched by my little girl and Dan would never forget that 28 with my daughter.9．A．spot B．delay C．mind D．stop 10．A．selflessness B．carefulness C．loneliness D．thoughtfulness 11．A．meant B．ended C．proved D．showed 12．A．kept up B．picked up C．turned up D．put up 13．A．excitedly B．disappointedly C．calmly D．anxiously 14．A．After B．Before C．Since D．Until 15．A．turned B．referred C．appealed D．walked 16．A．hesitated B．chatted C．rested D．waited 17．A．regular B．single C．separate D．natural 18．A．picture B．walk C．rest D．break 19．A．dream B．command C．request D．suggestion 20．A．nervous B．upset C．confused D．impatient21．A．reached B．placed C．touched D．patted 22．A．pulled out B．put down C．turned off D．glanced at 23．A．glaring B．twinkling C．sharp D．big 24．A．blocking B．delaying C．preventing D．interrupting 25．A．discount B．magic C．incident D．embarrassment 26．A．posted B．wrote C．read D．printed 27．A．note B．gift C．message D．report 28．A．connection B．combination C．construction D．contribution四、用单词的适当形式完成短文阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

2019-2020学年湖北省鄂东南省级示范高中联考高三（上）期中英语试卷一、阅读理解（本大题共15小题，共30.0分）A4 Fun Runs Even Non-Runners Will EnjoyEven people who swear they hate running will manage to enjoy these races that somehow make the sport fun．Hot Chocolate 5KWhat better motivation on a cold morning run than the promise of a steaming cup of cocoa and lots of chocolate treats？At the Hot Chocolate 5K series that's exactly what awaits you at the finish line．There are prizes given to the top three male and female finishers，but casual participation is encouraged．The events are scheduled in the cooler months in major cities around the country．Color RunKnown as "The Happiest 5K on the Planet，" runners wear white and are painted from head to toe in different colors at each kilometer，crossing the finish line in a variety of colors．The fun run is untimed，taking the pressure off runners to keep a specific pace or worry about placing．Instead，the stress is on fun．Disney Running SeriesWhy not combine a trip to the happiest place on earth with a little exercise？Run Disney offers a number of half-marathon and marathon weekend packages，many of which also feature the more accessible 5K distance．On Disneyland's Super Heroes Half Marathon Weekend，Friday features a Spiderman-themed 5K，while the Disney World Marathon Weekend runs a family-friendly 5K through Epcot．Running with the BalloonsThis cross-country style 3.1-mile race in Reddington，New Jersey runs over grass，and concrete to create a new challenge．But，the highlight is the launch of more than 100 hot air balloons during the Reddington Festival of Ballooning，the largest summertime hot air balloon and music festival in North America．The motivation？The top male finisher and the top female finisher will each win a free ride in a hot air balloon!1.What is special about Color Run？______A. It brings you lots of fun．B. It combines running with music．C. There are no winners．D. There are colorful activities．2.Which run is suitable for family running at weekend？______A. Hot Chocolate 5K．B. Color Run．C. Disney Running Series．D. Running with the Balloons．3.What award will you get if you win Running with the Balloons？______A. A hot air balloon．B. A cup of hot chocolate．C. A free ticket to the festival．D. An exciting ride．BShoes can tell you a lot about a person．Winston was a firm believer in this．Although he had grown up hearing that eyes were "the windows to the soul，" he was always quite confused by this expression．That day，Winston was seated in his regular spot，a bench in the train station，watching the usuals pass by．But he noticed something different．Two bare feet walked past．Strange．He wondered what kind of a man couldn't afford to buy himself shoes．A dangerous man，perhaps．Certainly not the kind of man Winston wanted to be anywhere near．He shrank to one side of the bench，turning his eyes downward．The man，however，took the space made free by Winston's shrinking．"Sorry，it has been a rough day，" the shoeless person offered apologetically，placing a plastic bag down．"I had to sell my shoes．It's my little girl's birthday．All she wanted this year was a birthday cake with her name spelled out nice on the top．So that's what I went and got her．" He seemed to be speaking to no one in particular．He gestured to the bag．It was a small cake with the name "Amelia"．"It sure is pretty，ain't it？" the man said，noticing Winston's interest．"I just had to get it for her．But I had to sell my shoes for it …it was worth it，of course．"There was a crack in his voice like he was about to cry and Winston did something he rarely ever did；he looked up and met the stranger's eyes．They were kind eyes，sad，sweet and beautiful eyes，sharply contrasting his bare and dirty feet．While staring at the man，a sense of shame washed over Winston．Slowly，Winston reached down and slid off his white sneakers，exposing his socked feet to the cold of the station．He picked up the shoes and handed them to the stranger beside him．4.What did Winston use to believe？______A. Eyes are the windows to the soul．B. Clothes often show personality．C. A man can not be judged by his look．D. Seeing is believing．5.Why did Winston shrink to one side of the bench？______A. To avoid contact with the man．B. To make some space for the man．C. To sit more comfortably．D. To show his hate for the man．6.Which of the following best describes the stranger？______A. Kind and humorous．B. Poor but selfless．C. Poor but optimistic．D. Kind and ambitious．7.What made Winston ashamed？______A. The awkward staring．B. The man's bare and dirty feet．C. His comfortable but boring life．D. His wrong judgement of the man．CPicture this：You're searching the Internet and come across a website with interesting articles．Some are news stories．Others only look like news stories．They're actually advertisements，or ads．How do you，the reader，tell the difference between a news story and an ad？In the past，it was easier．We got most of our information from newspapers．Big news stories appeared on the front page，and ads were boxed off and clearly labeled．But on the Internet，the two are often presented together．It can be hard to tell which is which．So a research group conducted a study in which students were shown the home page of a popular digital magazine and found out what was a news story and what was an ad．Most were great at identifying certain types of ads．"It has a discount code， a big company logo，and the words limited time offer．" one student said．So where did kids get stuck？Some ads seem identical to real news stories．They have headlines and contain information．But they may also include the words sponsored content．Sponsored means "paid for，" and content refers to the information in the story．"Sponsored content" is a way of saying that something is an ad．Just because something is sponsored doesn't necessarily mean it's false．It means someone paid money for it to appear．Companies pay so that readers will see their stories，buy their products，and like what the company stands for．As a reader，you have a right to know who's behind the information you're consuming．The Internet is a vast sea of information．To use it well，you not only have to know how to swim but also how to avoid the sharks．Learning to tell the difference between an ad and a news story is an important step to becoming Internet-smart．8.What does the underlined phrase "boxed off" in paragraph 2 probably mean？______A. SeparatedB. Hidden．C. Marked．D. Ignored．9.Which of the following ads are easy for students to identify？______A. Ads with headlines．B. Ads with certain labels．C. Ads similar to real new stories．D. Ads containing some real information．10.What do we know about "sponsored content"？______A. It is always false．B. It is a real news story．C. It is an ad in disguise．D. Readers have to pay for it．11.What is the best title of the passage？______A. Be Internet smart．B. Sponsored contents．C. Ads on the Internet．D. False news stories．DWhen Omar Yaghi was growing up in Jordan，his neighborhood received water for only about 5 hours once every 2 weeks．If Yaghi wasn't up at dawn to turn on the taps to store water，his family，their cow，and their garden had to go without．At a meeting last week，Yaghi，now a chemist at the University of California，reported that he and his colleagues have created a solar-powered device that could provide water for millions in water-stressed regions．At its heart is a porous crystalline（多孔晶体）material，known as a metal-organic framework （MOF），which acts like a sponge：It sucks water vapor out of air，and then releases it as liquid water．Yaghi and his colleagues first developed a zirconium（锆）-based MOF in 2014 that could harvest and release water．But at ﹩160 per kilogram，zirconium is too expensive for massive use．So，last year，his team came up with an alternative called MOF-303，based on aluminum，which costs just ﹩3 per kilogram，but the harvest was only about 0.2 liters per kilogram of MOF per day．In July 2019，Yaghi reported that his team has designed a new and far more productive water harvester．Supported by a solar panel to power a fan and heater，which speed the cycles，the new device produces up to 1.3 liters of water per kilogram of MOF per day from desert air．Yaghi expects further improvements to increase that number to 8 to 10 liters per day．And his company this fall plans to release a microwave-size device able to provide up to 8 liters per day this fall．The company promises an enlarged version next year that will produce 22，500 liters per day，enough to supply a small village．However，it needs to be shown that Yaghi's MOFs can be produced cheaply on a large scale．Each potential commercial MOF needs to prove itself in stability，efficiency，and life span．But if MOFs can pass those tests，they could offer a solution to some of the world's most pressing problems．12.Why is Omar Yaghi's childhood mentioned at the beginning？______A. To show how serious water problem is．B. To arouse reader's interest．C. To introduce the chemist．D. To lead in the topic．13.What is the problem of MOF-303？______A. It costs too much．B. It is low in efficiency．C. It is hard to operate．D. It can't last long．14.According to Yaghi，how much water will a large water harvester produce per day？______A. 1.3 liters．B. 22，500 liters．C. 10 liters．D. 8 liters．15.What can be concluded from the last paragraph？______A. Yaghi's MOFs are in great demand now．B. Yaghi's MOFs have already entered the market．C. Yaghi's MOFs may help solve water shortage．D. Mass production of Yaghi's MOFs is impossible．二、阅读七选五（本大题共5小题，共10.0分）Ways to Achieve Your GoalsPeople often set goals．Perhaps you want to save money，lose weight or learn a new skill．But then you get busy．(1) So，how can we find time to work on these larger life goals？(2) If a goal is too general，it may be hard to pursue let alone achieve it．Let's say your goal is to get in better physical shape．That's a fine idea-but psychologists might say as a goal，it is too general．Instead，you could sign up for a regular exercise class．Experts say writing down your goal is another important step．It gets the goal out of your brain and into the real world．Some psychologists suggest that writing a goal on paper is better than typing it on a device or saying it into your phone．Your brain receives information differently when it comes from handwriting．(3)(4) If someone else knows about your goals，you are held accountable for any progress or lack of progress．Your friend might ask，"So，how many pages of your novel have you written？" If you keep saying "none，" you might feel badly．Now you feel a pressure to do it-the pressure of your friend's opinion of you．You should also break down big goals into small ones．(5) Some can be quite big．And for those bigger goals，experts suggest breaking them down into smaller ones．A．Not all goals are created equal．B．As you identify your goals，be specific．C．When setting a goal，make it achievable．D．Telling someone your goal is also helpful．E．If you write down your goal，you can post it somewhere as a reminder．F．Writing things down seems to say to the brain，"I am important! Remember me!" G．Before you know it，weeks，then months have gone by，and you are no closer to your goal．16. A. A B. B C. C D. D E.E F.F G. G17. A. A B. B C. C D. D E.E F.F G. G18. A. A B. B C. C D. D E.E F.F G. G19. A. A B. B C. C D. D E.E F.F G. G20. A. A B. B C. C D. D E.E F.F G. G三、完形填空（本大题共20小题，共30.0分）Layton's family owned some rental cabins（小屋）on Shields Mountain．Layton was 20 minutes from home when he got a call from his mother．She(21) "The mountain's on fire．" Layton(22)the gas immediately．Finding the police (23)all traffic on the main road，he turned around and headed for a back road．Halfway up the steep(24)path，his car(25) He called McGee，who drove in his pickup（皮卡货车）．They(26)first to Layton's rental cabins．"I wanted to make sure our guests were(27) They were．" says Layton．At that point，he had a(28)：try to save his cabins or rescue people renting other cabins nearby．"On the mountain，you don't have many(29)．They're mostly tourists who don't know their way around．" he says．Over the next hours，the two friends crossed the smoky(30)，knocking on doors and leading (31)people to safety．Layton would(32)into the driver's seat of a tourist's car and drive the family down the mountain on roads nearly(33)．"I know that mountain so well，" Layton said，"I could drive andknow(34)where I am just by time traveled．" McGee followed in his pickup，and when one family was safe，they returned in search of other(35)persons．They helped one elderly woman(36)barefoot and found a man nearly(37)in a burning cabin．Fourteen people died in the town．But the fire didn't (38)a single life on Shields Mountain．Though his home and business were(39)，Layton said "I wasn't worried about the(40)damage when I saw people trapped on the mountain．I knew I was gonna help them．"21. A. said B. replied C. shouted D. screamed22. A. hit B. filled C. fueled D. started23. A. reducing B. blocking C. directing D. controlling24. A. folding B. rising C. winding D. changing25. A. worked out B. came up C. broke out D. gave up26. A. headed B. walked C. ran D. escaped27. A. gone B. lost C. involved D. stuck28. A. challenge B. choice C. puzzle D. difficulty29. A. locals B. tourists C. policemen D. firefighters30. A. road B. mountain C. cabin D. car31. A. depressed B. injured C. panicked D. burned32. A. come B. sit C. go D. jump33. A. unbearable B. unbelievable C. invisible D. inconvenient34. A. absolutely B. truly C. immediately D. exactly35. A. tired B. terrified C. trapped D. upset36. A. avoid B. drive C. flee D. run37. A. dead B. unconscious C. dizzy D. desperate38. A. claim B. kill C. threaten D. risk39. A. abolished B. established C. hurt D. destroyed40. A. equipment B. property C. material D. income四、语法填空（本大题共1小题，共15.0分）41.In the US，high school students take the SAT exam to try for a spot at their dreamuniversity．In China，that all-or-nothing exam is the gaokao，the national college entrance examination students have to carefully cross (1) （reach）the next stage of their lives．A Little Reunion，a hit TV drama focusing on gaokao，came to (2) end on July 27th．(3)（adapt）from best-selling writer Lu Yingong's novel，the drama follows stories of three Beijing middle-class families (4) （optimism）couple with a poorly-performing son anda genius nephew； a divorced coule who later reunites for their daughter；and a pair ofofficials struggling to reconnect with their son after a six-year (5) （absent）from his life．The drama can (6) （easy）set off floods of memories related (7) the exam．"The series brings me back to 2014，the year (8) I took gaokao，" reads one popular comment on Weibo．Such comments (9) （be）common since it was released．The drama scores 8.3 on Douban，(10) （make）it the highest scorer among all series released through satellite channels in 2019 thus far．五、短文改错（本大题共1小题，共10.0分）42.假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文．文中共有 10 处语言错误，每句中最多有两处．每处错误仅涉及一个单词的增加、删除或修改．增加：在缺词处加一个漏字符号（^），并在其下面写出该加的词．删除：把多余的词用斜线（）划掉．修改：在错的词下面画一横线，并在该词下面写出修改后的词．注意：1．每处错误及其修改均仅限一词；2．只允许修改 10 处，多者（从第 11 处起）不计分．The water pen is wide used in the process of study， but we often have trouble using it because of its limiting ink and other disadvantages．To deal with these problem， consequently， I have worked heart and soul to create my own magic waterpen．The most shining function of the newly designed pen is it will contain special ink pow der which makes it to have endless ink． Furthermore， the pen is made of extremely st rong materials， that can protect the pen from damage when it might fall down onto the ground． Good still， so smoothly does it write that it can contribute to make your hand writing better．Such is a magic water pen． Are you interested in it？ Hoping it will be of great use f or users．六、书面表达（本大题共1小题，共25.0分）43.假设你是李华，你的美国朋友 Mike 想跟你讨论中国书法的有关知识，但原定的见面时间因故需要推迟，请给 Mike 写一封电子邮件，说明情况．内容如下：1．表示歉意并说明原因；2．重约见面时间；3．建议先参观中国书法展．注意：1．词数 100 左右；2．可适当增加细节，以使行文连贯．Dear Mike，________Yours，Li Hua答案和解析1.【答案】【小题1】C 【小题2】C 【小题3】D【解析】1．C．细节理解题．根据文章第三段The fun run is untimed， taking the pressure off runners to keep a specific pace or worry about placing．乐趣跑是不定时的，减轻跑步者的压力，以保持一个特定的速度或担心放置．可知颜色运行的特殊之处是没有赢家；故选C．2．C．细节理解题．根据文章第四段On Disneyland's Super Heroes Half Marathon Weekend， Friday features a Spiderman-them ed 5K， while the Disney World Marathon Weekend runs a family-friendly 5K through Epcot在迪斯尼乐园的超级英雄半程马拉松周末，周五的主题是蜘蛛侠主题的5K，而迪斯尼世界马拉松周末则有一个家庭友好型的5K穿越爱泼科特．可知迪斯尼跑步系列适合于周末的家庭运行；故选C．3．D细节理解题．根据文章最后一段The motivation？ The top male finisher and the top female finisher will each win a free ride in a hot air balloon!动机？顶部的男性修整器和上凹的修整器将每一个都能在热气球中获得免费的游乐设施！可知如果你赢了气球，你会得到令人兴奋的游乐设施奖励；故选 D 本文属于说明文阅读，作者通过这篇文章主要向我们描述了甚至那些发誓不喜欢跑步的人都会设法享受这些比赛，这些比赛在某种程度上让运动变得有趣．考察学生的细节理解和推理判断能力，做细节理解题时一定要找到文章中的原句，和题干进行比较，再做出正确的选择．在做推理判断题不要以个人的主观想象代替文章的事实，要根据文章事实进行合乎逻辑的推理判断．4.【答案】【小题1】B 【小题2】A 【小题3】B 【小题4】D【解析】1．B．细节理解题．根据diyiduanShoes can tell you a lot about a person． Winston was a firm believer in this．鞋子可以告诉你很多关于一个人的信息．温斯顿坚信这一点．可知，温斯顿曾经相信衣服经常表现出个性．故选B．2．A．细节理解题．根据第三段He shrank to one side of the bench， turning his eyes downward． The man， however， to ok the space made free by Winston's shrinking．他缩到板凳的一侧，向下看．然而，那人抢走了温斯顿缩小的空间．可知，温斯顿移动到板凳的一侧是为了避免与男人接触．故选A．3．B．细节理解题．根据第四段he shoeless person offered apologetically，placing a plastic bag down．"I had to sell my shoes．It's my little girl's birthday．All she wanted this year was a birthday cake with her name spelled out nice on the top．So that's what I went and got her．这个赤脚的人道歉地说道，放下一个塑料袋．"我必须卖掉鞋子．这是我小女孩的生日．今年她想要的只是一个生日蛋糕，上面写着漂亮的名字．这就是我去得到她的原因．"可知，陌生人是可怜但无私的．故选B．4．D．细节理解题．根据最后一段There was a crack in his voice like he was about to cry and Winston did something he rarely ever did；he looked up and met the stranger's eyes．They were kind eyes，sad，sweet and beautiful eyes，sharply contrasting his bare and dirty feet．他的声音就像他快要哭了一样破裂，温斯顿做了他从未做过的事情；他抬起头，见了陌生人的眼睛．他们那双仁慈的眼睛，悲伤，甜美而美丽的眼睛，与他那双肮脏的双脚形成鲜明的对比．可知，他对那个人的错误判断让他感到羞愧．故选D．本文是一篇社会文化类阅读，主要讲述了温斯顿遇到了一个赤脚的男人，男人为了给女儿买蛋糕把鞋子卖掉了．阅读理解考察学生的细节理解和推理判断能力，做细节理解题时一定要找到文章中的原句，和题干进行比较，再做出正确的选择．在做推理判断题不要以个人的主观想象代替文章的事实，要根据文章事实进行合乎逻辑的推理判断．8.【答案】【小题1】A 【小题2】B 【小题3】C 【小题4】A【解析】1-4 ABCA1．A．细节理解题．根据第二段"Big news stories appeared on the front page， and ads were boxed off and clearly labeled重大新闻报道出现在头版，广告被框起来，并清楚地标示出来‘．可知"boxed off"意为"分离"．故选A．2．B．细节理解题．根据第三段" Most were great at identifying certain types of ads． "It has a discount code， a big compa ny logo， and the words limited time offer大多数人都擅长识别特定类型的广告．它有一个折扣代码，一个大公司的标志，还有"限时优惠"的字样‘．可知有特定标签的广告容易被学生识别．故选B．3．C．推理判断题．根据第四段"They have headlines and contain information． But they may also include the words sponso red content． Sponsored means "paid for，" and content refers to the information in the story． "Sponsored content" is a way of saying t hat something is an ad．他们有标题和包含信息．但它们也可能包含单词sponsored content．赞助是指"付费"，内容是指故事中的信息．"赞助内容"是表示某物是广告的一种方式．‘．可知"sponsored content"是一个伪装的广告．故选C．4．A．推理判断题．根据最后一段" As a reader， you have a right to know who's behind the information you're consuming．The Internet is a vast sea of information． To use it well， you not only have to know how to swim but also how to avoid the sharks． Learning to tell the difference between an ad and a news story is an important step to becoming Internet-smart．作为读者，你有权利知道你所消费的信息背后的人是谁．互联网是一个巨大的信息海洋．为了更好地利用它，你不仅要知道如何游泳，还要知道如何躲避鲨鱼．学会区分广告和新闻报道是成为互联网智能的重要一步．‘．可知"Be Internet smart互联网是聪明的"是本文最好的题目．故选A．本文是一篇科教类阅读，文章主要介绍了互联网是聪明的．此题主要考查学生的细节理解和推理判断能力．做细节理解题时一定要找到文章中的原句，和题干进行比较，再做出正确选择．在做推理判断题时不要以个人的主观想象代替文章的事实，要根据文章事实进行合乎逻辑的推理判断．12.【答案】【小题1】D 【小题2】B 【小题3】B 【小题4】C【解析】1．D．细节理解题．根据文章第一段When Omar Yaghi was growing up in Jordan， his neighborhood received water for only about 5 hours once every 2 weeks．当奥马尔?亚吉（Omar Yaghi）在约旦长大时，他所在的社区每两周只接受一次大约5小时的水供应．可知第一段提到奥马尔?亚吉（Omar Yaghi）的童年是为了引出这一话题；故选D．2．B．细节理解题．根据文章第二段So， last year， his team came up with an alternative called MOF-303， based on aluminum ， which costs just ﹩3 per kilogram， but the harvest was only about 0.2 liters per kilogram of MOF per day．因此，去年，他的团队提出了一种名为MOF-303的替代品，其成本仅为每公斤3美元，但收获量仅为每天0.2升/千克．可知MOF-303的问题是它的效率很低；故选B．3．B．细节理解题．根据文章第三段The company promises an enlarged version next year that will produce 22，500 liters per day， enough to supply a small village．该公司承诺明年将扩大版本，每天生产22，500升水，足以供应一个小村庄．可知根据雅吉的说法，一台大型取水机每天能生产22，500升水；故选B．4．C．细节理解题．根据文章最后一段 But if MOFs can pass those tests， they could offer a solution to some of the world's mostpressing problems．和寿命．可知从最后一段可以得出Yaghi的MOF可能有助于解决缺水问题；故选 C本文属于说明文阅读，作者通过这篇文章主要向我们描述了Yaghi的MOF可能有助于解决缺水问题，考察学生的细节理解和推理判断能力，做细节理解题时一定要找到文章中的原句，和题干进行比较，再做出正确的选择．在做推理判断题不要以个人的主观想象代替文章的事实，要根据文章事实进行合乎逻辑的推理判断．16.【答案】【小题1】G 【小题2】B 【小题3】F 【小题4】D 【小题5】A【解析】1-5 GBFDA1．G．细节理解题．根据前文" Perhaps you want to save money，lose weight or learn a new skill．But then you get busy也许你想省钱、减肥或学习一项新技能．但是你会变得很忙"．可知此处应填"不知不觉中，几周、几个月过去了，你仍然没有接近你的目标"．故选G．2．B．细节理解题．根据下文"If a goal is too general，it may be hard to pursue let alone achieve it如果一个目标太笼统，就很难去追求，更别说实现了"．可知此处应填"当你确定你的目标时，要具体"．故选B．3．F．细节理解题．根据前文"Your brain receives information differently when it comes from handwriting当信息来自手写时，你的大脑会以不同的方式接收信息"．可知此处应填"把事情写下来似乎是对大脑说："我很重要!还记得我!""．故选F．4．D．推理判断题．根据下文"If someone else knows about your goals，you are held accountable for any progress or lack of progress如果别人知道你的目标，你要对任何进展或缺乏进展负责"．可知此处应填"告诉别人你的目标也是有帮助的"．故选D．5．A．推理判断题．根据前文"You should also break down big goals into small ones你也应该把大目标分解成小目标"．可知此处应填"不是所有的目标都是平等的"．故选A．本文是一篇选句填空，文章主要介绍了实现目标的方法．此题主要考查学生的细节理解和推理判断能力．做细节理解题时一定要找到文章中的原句，和题干进行比较，再做出正确选择．在做推理判断题时不要以个人的主观想象代替文章的事实，要根据文章事实进行合乎逻辑的推理判断．21.【答案】【小题1】D 【小题2】A 【小题3】B 【小题4】C 【小题5】D 【小题6】A 【小题7】A 【小题8】B 【小题9】A 【小题10】B 【小题11】C 【小题12】D 【小题13】C 【小题14】D 【小题15】C 【小题16】C 【小题17】B 【小题18】A 【小题19】D 【小题20】B【解析】1-5 DABCD 6-10 AABAB 11-15 CDCDC 16-20 CBADB（1）D．考查动词动词辨析及句意理解．A．said说；B．replied回答；C．shouted 喊叫；D．screamed尖叫．根据句意根据内容山上着火了，可见是尖叫着说出的．所以选D．（2）A．考查动词辨析及句意理解．A．hit打击；B．filled填满；C．fueled 加油；D．started开始．根据句意莱顿立刻打油门．所以选A．（3）B．考查动词辨析及句意理解．A．reducing 减少；B．blocking 拥堵；C．directing 指导；D．controlling控制．根据句意发现经常堵满了所有的主要道路．所以选B．（4）C．考查动词辨析及句意理解．A．folding 折叠；B．rising升高；C．winding 蜿蜒；D．changing改变．根据句意上山的路应该是蜿蜒的路．所以选C．（5）D．考查短语辨析及句意理解．A．worked out计算出；B．came up上来；C．broke out 爆发；D．gave up放弃．根据句意车上不去了．所以选D．（6）A．考查动词辨析及句意理解．A．headed向前；B．walked 走；C．ran 跑；．escaped 逃脱．根据句意先去莱顿的出租屋．所以选A．（7）A．考查动词辨析及句意理解．A．gone离开；B．lost 迷路；C．involved涉及到；D．stuck粘着．根据句意我想确定我们的客人都走了．所以选A．（8）B．考查名词辨析及句意理解．A．challenge 挑战；B．choice 选择；C．puzzle 迷惑；D．difficulty困难．根据句意试着去救他的小屋或者去救附近租其他小屋的人．这应该是一种选择，所以选B．（9）A．考查名词辨析及句意理解．A．locals当地人；B．tourists旅游的人；C．policemen 警察；D．firefighters消防员．根据句意山上的人大部分都是游客，所以是没有当地人．所以选A．（10）B．考查名词辨析及句意理解．A．road 道路；B．mountain 山；C．cabin 小屋；D．car车．根据句意那两个朋友穿过冒着烟雾的山．所以选B．（11）C．考查动词辨析及句意理解．A．depressed 沮丧的；B．injured受伤的；C．panicked 惊慌失措的；D．burned烧伤的．根据句意带领惊慌的人们去到安全的地方．所以选C．（12）D．考查动词辨析及句意理解．A．come来；B．sit坐下；C．go去；D．jump 跳跃．根据句意Layton跳进卡车的司机座位上开着车下山．所以选D．（13）C．考查形容词辨析及句意理解．A．unbearable无法忍受的；B．unbelievable 难以置信的；C．invisible 看不见的；D．inconvenient不方便的．根据句意在几乎看不见的路上开车送一家人下山．所以选C．（14）D．考查副词辨析及句意理解．A．absolutely完全地；B．truly真实地；C．immediately马上；D．exactly确切地．根据句意"我对那座山非常了解，"莱顿说，"我可以开车去了解准确地说，我只是时间旅行．．所以选D．（15）C．考查形容词辨析及句意理解．A．tired疲倦的；B．terrified 害怕的；C．trapped 被困的；D．upset不安的．根据句意他们返回寻找被困人员．所以选C．（16）C．考查动词辨析及句意理解．A．avoid避免；B．drive 驾驶；C．flee 逃跑；D．run跑．根据句意他们帮助一位老妇人赤脚逃离，发现一名男子在燃烧的小屋中几乎失去知觉，14人在镇上死亡．．所以选C．（17）B．考查形容词辨析及句意理解．A．dead死的；B．unconscious 失去知觉的；C．dizzy 眩晕的；D．desperate绝望的．根据句意他们帮助一位老妇人赤脚逃离，发现一名男子在燃烧的小屋中几乎失去知觉，14人在镇上死亡．．所以选B．（18）A．考查动词辨析及句意理解．A．claim 索取；B．kill 杀掉；C．threaten恐吓；D．risk冒险．根据句意但大火并没有夺去希尔兹山上的一条命．所以选A．（19）D．考查动词辨析及句意理解．A．abolished 抛光，打磨；B．established 已确立的；C．hurt 伤害；D．destroyed破坏．根据句意尽管他的家和生意都被毁了．所以选D．（20）B．考查名词辨析及句意理解．A．equipment 设备；B．property 财产；C．material 材料；D．income收入．根据句意当我看到有人被困在山上时，我并不担心财产损失．我知道我会帮助他们的．"．所以选B．本文写了我们所住小屋的山上起火了，在大火中去救小屋里的人或者附近租其他小屋的人的故事．做完型填空首先要通读全文，了解大意．一篇完形填空的文章有许多空格，所以，必须先通读一至两遍，才能大概了解文章的内容．千万不要看一句，做一句．其次要逐句分析，前后一致．选择答案时，要考虑整个句子的内容，包括搭配、时态、语法等．答案全部填完后，再通读一遍文章，检查是否通顺流畅了，用词得当，意思正确．41.【答案】【小题1】to reach【小题2】an【小题3】Adapted【小题4】optimistic【小题5】absence【小题6】easily【小题7】to【小题8】when【小题9】have been【小题10】making【解析】1．to reach．考查不定式．此处用不定式作状语表示目的．2．an．考查冠词．come to an end是固定搭配，意为"落下帷幕，结束"．3．Adapted．考查非谓语动词．通过分析可知这里要用非谓语动词作状语，这时adapt 与the drama之间是被动关系，因此要用过去分词形式．4．optimistic．此处用形容词作定语修饰couple．5．absence．考查名词．句意：一对在儿子离开六年后，官员们努力与他重新建立联系，根据前面的 a six-year可知这里要用名词．6．easily．考查副词．此处用副词修饰can set off．7．to．考查介词．be related to是固定搭配，意为"与…有关"，此处作定语修饰floods of memories．8．when．考查定语从句引导词．这里是一个定语从句，先行词是the year，且从句缺少状语，因此要用when来引导．9．have been．考查时态．句意：这样的评论自发布以来就屡见不鲜，根据后面的since it was released可知这里要用现在完成时．10．making．考查非谓语动词．通过分析可知这里要用非谓语动词作状语表示一种自然而然的结果．本文通过一部一部以高考为主题的热播电视剧《小团圆》说明，在中国，高考就是高考，全国高考的学生必须小心翼翼地跨过这一关，才能进入人生的下一个阶段．。

2019年秋季鄂东南省级示范高中教育教学改革联盟学校期中联考高三数学（文科）试卷一、选择题：在每小题给出的四个选项中，只有一项是符合题目要求的．1．已知复数z 满足121ii z -=+，则z =（ ）ABCD2．若函数()f x =与()()ln 1g x x =+的定义域分别为M 和N ，则M N =（） A ．{}11x x -<< B ．{}11x x -<≤C ．{}11x x -<≤D ．{}11x x -≤≤3．已知0.213a ⎛⎫= ⎪⎝⎭，13log 0.2b =，b c a =，则a 、b 、c 的大小关系为（ ）A ．a b c <<B ．c a b <<C ．a c b <<D ．b c a <<4．已知等差数列{}n a 的前3项和为30，后3项和为90，且前n 项和为200，则n =（） A ．9 B ．10C ．11D ．125．函数()1ln 1xf x x -=+的大致图像为（ ）A ．B ．C ．D ．6．设数列{}n a 前n 项和为n S ，已知145a =，112,02121,12n n n n n a a a a a +⎧⎪⎪=⎨⎪-<⎪⎩≤≤≤，则2020S =（） A ．1009 B ．50485C ．1010D ．505457．已知()0,πα∈，且3sin 5α=，则πtan 4α⎛⎫+= ⎪⎝⎭（ ） A ．17-B ．7C ．17-或7- D ．17或7 8．若非零向量a 、b 满足a b =且()2a b b +⊥，则a 与b 的夹角为（ ）A ．π6 B ．π3 C ．2π3D ．5π6 9．古希腊数学家阿基米德的墓碑上刻着一个圆柱，圆柱内有一个内切球，这个球的直径恰好与圆柱的高相等，相传这个图形是阿基米德最引以为自豪的发现．现有一底面半径与高的比值为1:2的圆柱，则该圆柱的体积与其内切球的体积之比为（ ）A ．43B ．32C ．2D ．8310．已知O 、A 、B 为平面内三点，满足5OA OB ==，点C 在直线AB 上，且min 3OC =，则()tOA OB t +∈R 的最小值为（ ）A ．245 B ．4 C ．165 D ．12511．已知ABC △的内角A 、B 、C 的对边分别为a 、b 、c ，且c o s b c B B a +=，3b =，点D 是ABC △的重心，AD =ABC △的外接圆半径为（ ）AB ．3C D12．已知函数212y x =的图象在点2001,2x x ⎛⎫ ⎪⎝⎭处的切线为直线l ，若直线l 与函数ln y x =，()0,1x ∈的图象相切，则0x 必满足条件（ ）A ．001x <<B ．01x <<C 0x <D 02x < 二、填空题：13．曲线()20x y x e --=在点()0,2-处的切线方程为________．14．若函数()2ln f x mx x x =+-在定义域内有递减区间，则实数m 的取值范围是________．15．已知函数()()sin 2f x x ϕ=+，其中ϕ为实数，若()π3f x f ⎛⎫ ⎪⎝⎭≤对x ∀∈R 恒成立，且()π2f f π⎛⎫< ⎪⎝⎭，则()f x 的单调递增区间是________． 16．若m 、n 表示直线，α、β、γ表示不同平面，下列四个命题：①m αβ=，n α⊂，m n ⊥，则αβ⊥；②m α⊥，n β⊥，m n ⊥，则αβ⊥；③m αγ=，n βγ=，m n ∥，则αβ∥；④m αβ=，n 与α、β所成的角相等，则m n ⊥．其中真命题的有________．（请填入编号）三、解答题：解答应写出文字说明、证明过程或演算步骤，每个试题考生都必须作答．17．设命题p ：不等式2515x x a a ++->-对x ∀∈R 恒成立；命题q ：方程2680ax x a -+-=有两不同正根．当命题p 和命题q 不都为假命题时，求实数a 的取值范围．18．已知正项等差数列{}n a 满足259a a +=，3420a a ⋅=，等比数列{}n b 的前n 项和n S 满足2n n S c =-，其中c 是常数．（1）求c 以及数列{}n a 、{}n b 的通项公式；（2）设n n n c a b =，求数列{}n c 的前n 项和n T ．19．在三角形ABC 中，a 、b 、c 分别为角A 、B 、C 的对边，且)3sin sin 2BB B +=． （1）求角B 的大小；（2）若b =ABC △面积的最大值．20．如图，已知四棱锥P ABCD -的底面为菱形，且π3ABC ∠=，E 是DP 中点． （1）证明：PB ∥平面ACE ；（2）若AP PB =2AB PC ==，求三棱锥C PAE -的体积．21．为庆祝建国70周年，某高中准备设计一副宣传画，要求画面面积为24840cm ，画面高与宽的比为()1a a <，画的上下部分各留出5cm 的空白，左右部分各留出8cm 的空白．（1）当25a =时，该宣传画的高和宽分别为多少？ （2）如何确定画面的高与宽，使得宣传画所用纸张面积最小，并求出此时a 的值．22．已知函数()sin f x ax x =-，π0,2x ⎡⎤∈⎢⎥⎣⎦，其中a 为常数． （1）若函数()f x 在π0,2⎡⎤⎢⎥⎣⎦上是单调函数，求a 的取值范围； （2）当1a ≤时，证明：()316f x x ≤．2019年秋季鄂东南省级示范高中教育教学改革联盟学校期中联考高三数学（文科）参考答案13．x ＋y ＋2＝0 14．1,8⎛⎫-∞ ⎪⎝⎭ 15．2,36k k ππ⎡⎤-+π-+π⎢⎥⎣⎦（k ∈Z ） 16．②三、解答题：解答应写出文字说明、证明过程或演算步骤．17．∵|x ＋5|＋|x-1|≥6，∴a 2-5a-6＜0，解得-1＜a ＜6；∵方程ax 2-6x ＋a-8＝0有两不同正根，∴a ≠0，利用判别式和韦达定理可得：()1212364806080a a x x a a x x a ⎧-->⎪⎪⎪+=>⎨⎪⎪-⋅=>⎪⎩解得8＜a ＜9， ∵p ∨q 为真，∴a ∈（-1,6）∪（8,9）．18．（1）∵数列{a n }为正项等差数列，∴公差d ＞0，∵a 2＋a 5＝a 3＋a 4＝9，又a 3·a 4＝20，∴a 3＝4，a 4＝5，即可得a n ＝n ＋1；∵S n ＝2n -c …①当n ＝1时，b 1＝2-c ，当n ≥2时，S n-1＝2n-1-c …②①-②即可得b n ＝2n-1，n ≥2，又∵{b n }为等比数列，∴b 1＝20＝1＝2-c ，即可得c ＝1，∴b n ＝2n-1，n ∈N *；（2）由题意得c n ＝（n ＋1）2n-1，T n ＝2·20＋3·21＋…＋（n ＋1）·2n-12T n ＝2·21＋…＋n ·2n-1＋（n ＋1）·2n-T n ＝2＋21＋22＋…＋2n-1-（n ＋1）·2nT n ＝n ·2n19．（123cos sin 2B B B +=12cos 212B B -=， ∴sin 216B π⎛⎫-= ⎪⎝，即可得262B ππ-=，∴3B π=； （2）∵b 3B π=，由余弦定理得2231cos 22a c B ac +-==， 即可得a 2＋c ＝3＋ac ≥2ac ，∴ac ≤3，∴11sin 322ABC S ac B =≤⋅=△ 20．（1）连接BD 交AC于F ，连接EF∵四边形ABCD 为菱形，∴F 为AC 中点，那么EF ∥PB又∵EF ⊂平面ACE ，PB ⊄平面ACE∴PB ∥平面ACE ；（2）由勾股定理易知AP ⊥BP 且△ABC 为正三角形，∵E 为DP中点，∴12C PAE P ACD V V --=， 取AB 中点M ，连接PM 、CM ，由几何性质可知PM ＝1，CM =又∵PC ＝2，∴PC 2＝PM 2＋MC 2，即PM ⊥MC ，∵PM ⊥AB ，∴PM ⊥平面ABCD ，∴111232P ACD V -=⋅⋅⋅，∴12C PAE P ACD V V --==． 21．（1）设画面的高为2x cm ，则宽5x cm ，由题意得10x 2＝4840，解得x ＝22， ∴该画的高为：44＋10＝54 cm ，宽为：110＋16＝126 cm ；（2）设画面的高为x cm ，则宽为4840cm x ，根据题意得 ()48401016S x x ⎛⎫=++ ⎪⎝⎭4840050001650006760x x =++≥+= 当且仅当484016x x =即x ＝55时等号成立，此时宽为484088x =， ∴555888a ==． 22．（1）求导得f'（x ）＝a-cosx ，0,2x π⎡⎤∈⎢⎥⎣⎦， ①当f （x ）在0,2π⎡⎤⎢⎥⎣⎦上为单调递减函数时，即f'（x ）＝a-cosx ≤0恒成立， 又∵cosx ∈[0,1]，∴a ≤（cosx ）min ＝0；②当f （x ）在0,2π⎡⎤⎢⎥⎣⎦上为单调递增函数时，即f'（x ）＝a-cosx ≥0恒成立， 又∵cosx ∈[0,1]，∴a ≥（cosx ）max ＝1；综上所述：当a ≤0时，f （x ）在0,2π⎡⎤⎢⎥⎣⎦上为单调递减函数； 当a ≥1时，f （x ）在0,2π⎡⎤⎢⎥⎣⎦上为单调递增函数； （2）要证()316f x x ≤，只需证31sin 06ax x x --≤恒成立， 令()31sin 6g x ax x x =--，0,2x π⎡⎤∈⎢⎥⎣⎦，则()21cos 2g x a x x '=--， 令()21cos 2h x a x x =--，0,2x π⎡⎤∈⎢⎥⎣⎦，则h'（x ）＝sinx-x ， 易证当0,2x π⎡⎤∈⎢⎥⎣⎦时，sinx ≤x ， ∴h'（x ）＜0，即h （x ）在0,2π⎡⎤⎢⎥⎣⎦上递减， ∴h （x ）≤h （0）＝a-1≤0，即g'（x ）≤0，∴g （x ）在0,2π⎡⎤⎢⎥⎣⎦上递减，∴g （x ）≤g （0）＝0即31sin 06ax x x --≤，命题得证． （方法不唯一，酌情给分）。

湖北省鄂东南省级示范高中教育教学改革联盟2019-2020学年高三上学期期中考试物理试题注意事项：1．答题前填写好自己的姓名、班级、考号等信息；2．请将答案正确填写在答题卡上。

第I卷（选择题）一、单选题1．在物理现象的发现和物理理论的建立过程中物理学家总结出许多科学方法。

如理想实验、演绎推理、科学假说、类比等。

类比法是通过两个或两类研究对象进行比较，找出它们之间相同点和相似点，并以此为根据把其中某一个或某一类对象的有关知识和结论，推移到另一个或另一类对象上，从而推论出它们也可能有相同或相似的结论的一种逻辑推理和研究方法。

以下观点的提出或理论的建立没有．．应用类比的思想的是（）A．法拉第通过多次实验最终发现“磁生电—电磁感应”现象B．伽利略提出“力不是维持物体运动的原因”的观点C．牛顿推理得到太阳与行星间的引力与太阳和行星的质量的乘积成正比，与它们之间的距离的平方成反比D．安培为解释磁现象提出了“物质微粒内部存在着一种环形电流—分子电流”的观点2．如图所示，A物体的质量是B物体的k倍。

A物体放在光滑的水平桌面上通过轻绳与B物体相连，两物体释放后运动的加速度为a1，轻绳的拉力为T1；若将两物体互换位置，释放后运动的加速度为为a2，轻绳的拉力为T2。

不计滑轮摩擦和空气阻力，则（）A．a1∶a2=1∶k B．a1∶a2=1∶1C．T1∶T2=1∶k D．T1∶T2=1∶1 3．质量为m、电量为q的带电粒子垂直磁感线射入磁感应强度为B的匀强磁场中，在洛仑兹力作用下做半径为R的匀速圆周运动，关于带电粒的圆周运动，下列说法中正确的是（）A ．圆周运动的角速度与半径R 成正比B ．圆周运动的周期与半径R 成反比C ．圆周运动的加速度与半径R 成反比D ．圆周运动的线速度与半径R 成正比4．如图所示，K 是光电管M 中逸出功为W 的碱金属，G 是灵敏电流计，S 是双刀双掷开关；若入射光的频率为ν，电子电量为-e ，则以下判断中正确的是（ ）A ．当Wh ν≥时，灵敏电流计G 中一定有电流通过 B ．若W h ν>，当KA h WU eν->时，灵敏电流计G示数为零 C ．若W hν>，当S 接a 和b 且滑线变阻器的滑动端P 向右滑动时，灵敏电流计G 中的电流会增大 D ．若W hν>，当S 接c 和d 且滑线变阻器的滑动端P 向右滑动时，灵敏电流计G 中的电流一定会增大5．2019年9月24日，中国科学院李春来领导的“嫦娥四号”研究团队，精确定位了“嫦娥四号”的着陆位置，并对“嫦娥四号”的落月过程进行了重建。

2019-2020学年湖北省鄂东南省级示范高中教育教学改革联盟学校高三（上）期中物理试卷一、单选题（本大题共6小题，共24.0分）1.在静电场理论的研究和建立的过程中，许多物理学家作出了重要贡献．下列说法中错误的是()A. 自然界中的电荷只有两种，富兰克林将其分别命名为正电荷和负电荷B. 密立根通过油滴实验首先比较准确地测出了元电荷的电荷量C. 库仑通过扭秤实验得出了任意两个电荷间的库仑力F=k Q1Q2的规律r2D. 法拉第认为电荷间有相互作用力是通过电荷激发的电场而产生的2.如图所示，质量为M的物体A放在光滑平台上，通过轻绳跨过光滑的固定滑轮与质量为m的物体B相连，释放物体B，二者共同加速运动，物体A运动过程中不会与滑轮相碰，已知重力加速度为g，以下说法正确的是()A. 两物体的加速度相同B. 轻绳上的拉力T<mgC. 轻绳上的拉力T>MgD. 物体Ａ的加速度大小为mgM3.下列说法中正确的是()A. 匀速圆周运动是一种速度保持不变的运动B. 物体做匀速圆周运动时所受的合外力是恒力C. 作匀速圆周运动的物体的受的合外力为零D. 匀速圆周运动的合力方向始终指向圆心4.如图所示，图甲为光电效应的实验电路图，图乙为光电子最大初动能与光电管入射光频率关系图象，下列说法正确的是()A. 光电管加正向电压时，电压越大光电流越大B. 光电管加反向电压时不可能有光电流|C. 由图可知，普朗克常量数值上等于|ab|D. 由图可知，普朗克常量数值上等于|ba5.甲、乙两物体质量之比m1:m2=3:1，速度之比v1:v2=1:3，在相同的阻力作用下逐渐停下，则它们的位移之比x1:x2是()A. 1∶1B. 1∶3C. 3∶1D. 4∶16.在如图所示的电路中，已知电源的电动势E为6.0V，内电阻r为1.0Ω.闭合开关S后，电路中的电流I为2.0A，则外电路的电阻R的阻值为()A. 2.0ΩB. 3.0ΩC. 4.0ΩD. 6.0Ω二、多选题（本大题共6小题，共26.0分）7.(多选)如图所示，一块长度为a、宽度为b、厚度为d的金属导体，当加有与侧面垂直、磁感应强度大小为B的匀强磁场，且通以图示方向的电流I时，用电压表测得导体上、下表面M、N 间电压为U.已知自由电子的电荷量为e，下列说法中正确的是()A. M面比N面电势高B. 导体单位体积内自由电子数越多，电压表的示数越大C. 导体中自由电子定向移动的速度为v=UBdD. 导体单位体积内的自由电子数为BIeUb8.(多选题)根据开普勒关于行星运动的规律和圆周运动知识知：太阳对行星的引力F∝mr2，行星对太阳的引力F′∝Mr2，其中M、m、r分别为太阳、行星质量和太阳与行星间的距离．下列说法正确的是()A. 由F∝mr2和F′∝Mr2知F：F′=m：MB. F和F′大小相等，是作用力与反作用力C. F和F″大小相等，是同一个力D. 太阳对行星的引力提供行星绕太阳做圆周运动的向心力9.如图，∠M是锐角三角形PMN最大的内角，电荷量为q(q>0)的点电荷固定在P点。

湖北鄂东南联盟2020届高三上学期期中考试语文试题及答案（逐题解析）人教版高三总复习秋季鄂东南省级示范高中教育教学改革联盟学校期中联考高三语文试卷一、现代文阅读（一）论述类文本阅读阅读下面的文字，完成下列小题。

松竹梅与中国文化风骨①松、竹、梅是中国人所喜爱的自然事物，也是中国人所推崇的一种人格精神的象征。

这种人格的象征物，既是中国文化精神的体现，也是中国文化的一种独特的表达方式。

②中国自古以来便有将自然人化的传统，这个传统，既可能源于古人与自然和谐相处的经验，又与中国古代哲学和文学的影响有关。

中国古代哲学讲天人合一，物我同一，所以自然事物就容易被人格化。

中国古代文学重托物言志，以物喻人，所以用自然事物作文化和人格的象征，也就成了一种修辞手法。

这种人格化的自然事物，在植物界，松、竹、梅被称为“岁寒三友”，已是尽人皆知的常识。

③传说苏轼被贬到黄州，有个地方官去拜访他，问他一个人在这儿是否感到寂寞，苏轼指指门外说，我这儿有“风泉两部乐，松竹三益友”，何寂寞之有。

又传说爱梅成痴的林逋终生不娶，以梅为妻，以鹤为子，所谓“梅妻鹤子”，都是典型的例证。

④中国人喜爱松、竹、梅，固然离不开观赏其外在形象，但更多地却是欣赏其内在品格。

这种品格虽然古人对之有不同的提炼和概括，但如松的枝干如铁、岁寒后凋，竹的中空外直、宁折不弯，梅的凌霜傲雪、玉洁冰清等等，却是自魏晋以降中国人所推崇、所提倡的一种风骨。

这种源于先秦儒者“浩然之气”的风骨，在中国古代曾用来评品人物、鉴赏书画，后来又用于论文，成了一个重要的文学理论范畴，对推动历代诗文革新，起了重要的作用。

⑤由松、竹、梅这些自然事物所体现的风骨，在中国文化传统中之所以显得如此重要，首先是出于中国人遵循天道的积极进取的人生态度，所谓“天行健，君子以自强不息”是也。

故古人主张养“浩然之气”，培植一种强旺的内在精神，以应对人生的各种艰难困苦，成就人生的各种事业，这是中国文化讲风骨的精神源头。