山西太原五中2020届高三上学期阶段性检测

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山西省太原市第五中学2020届高三上学期阶段性检测(10月)数学(文)含参考答案

高三数学（文）第1页,共4页高三数学（文）第2页,共4页密学校班级姓名学号密封线内不得答题太原五中2019-2020学年度第一学期阶段性检测高三数学（文）命题、校对人：XXX一、选择题(本大题共12小题，每小题5分，共60分，每小题有且只有一个正确选项)1.已知集合{}2,1,0,1,2A =--，2{|4}B x x =≥，则下图中阴影部分所表示的集合为（） A.{}2,1,0,1-- B.{}0 C.{}1,0- D.{}1,0,1-2. 函数f(x)= x- 1-2x 的值域为（）A ． (0, 12 )B ．(0, 12 ]C ． (- ∞ , 12 ]D ．(- ∞ , 12)3. 已知命题:p R m ∈∃，函数1)1()(2+--=x m x x f 在),0(+∞上为增函数，命题:q若b a <,则ba 11>，下列命题为真命题的是（） A. q p ⌝∧ B. q p ∧⌝ C. q p ∧ D. q p ⌝∧⌝4. 已知α是第四象限角，且tan α=- 43, 则αsin = （）A. - 53B. 53C. 54D. - 545. 设点o 在ABC ∆的外部，且253=--，则=∆OBC ABC S S : （）A. 2:1B. 3:1C. 3:2D. 4:36.已知点)8,(m 在幂函数nx m x f )1()(-=的图象上，设)33(f a =，)(ln πf b =， )22(f c =，则a 、b 、c 的大小关系为（） A.b c a << B ．c b a << C ．a c b << D ． c a b << 7.函数)2ln(sin )(+=x xx f 的部分图象可能是（）8.已知函数2)(x a x f -=（21≤≤x )与1)(+=x x g 图象上存在关于x 轴对称的点，则实数a 的取值范围是（）A. [ -54 ,+ ∞)B. [1,2]C. [- 54 ,1] D.[-1,1]9.已知函数)()(xx e e x x f --=，若)()(21x f x f <，则（） A. 21x x > B. 021=+x x C. 21x x < D. 2221x x <10.已知函数⎩⎨⎧>≤+=0,log 0,1)(2x x x x x f ，则1)]([+=x f f y 的零点个数为（）.A 4 B . 3C. 2 D. 111.已知函数)(x f 的导函数x x f sin 2)(+='，且1)0(-=f ,数列{}n a 是以4π为公差的等差数列，若)()()(432a f a f a f ++=π3，则22019a a = （） ABCD高三数学（文）第3页,共4页高三数学（文）第4页,共4页A . 2019B . 2018C . 2017D . 201612.已知定义在R 上的连续函数f(x)满足2)()(x x f x f =-+,且0<x 时，x x f <')(恒成立，则不等式21)1()(-≤--x x f x f 的解集为（）A . ]21,(-∞B . )21,21(-C . [21,+∞) D . )0,(-∞二、填空题(本大题共4小题，每小题5分，共20分，把答案填在题中的横线上) 13. 函数132)(23+-=x x x f 的极大值与极小值之和为（）14.设函数⎪⎩⎪⎨⎧<≥=0,0,)(22x ex x e x x f x x ,则使得)1()12(+≤-x f x f 成立的x 取值范围是( ) 15. 已知奇函数)(x f 满足)()2(x f x f -=+,且当)1,0(∈x 时，213)(+=xx f ，则 )54(log 3f = ( )16.已知函数⎩⎨⎧>≤+=0,ln 0,4)(2x x x x x x x f ，1)(-=kx x g ,x )2,2(-∈时，方程)()(x g x f =有三个实数根，则k 的取值范围是（）三、解答题(本大题4小题，共70分，解答应写出文字说明、证明过程或演算步骤) 17.（满分12分）已知函数)1(log )1(log )(x x x f a a --+=)10(≠>a a 且（1）判断)(x f 的奇偶性并证明；（2）当10<<a 时，求使0)(<x f 时x 的取值范围.18.（满分12分）已知函数)()(a x ax xx f ≠-=（1）若2-=a ，用函数单调性定义证明：)(x f 在（- ∞ ，-2）上为单调递增函数；（说明：用其它方法证明不给分）（2）若0>a 且)(x f 在（1，+ ∞）上为单调递减函数，求实数a 的取值范围. 19.（满分12分）定义在R 上的函数3)(23+++=cx bx ax x f 同时满足以下条件：① )(x f 在)1,0(上为减函数，),1(+∞上是增函数；②)(x f '是偶函数；③)(x f 在0=x 处的切线与直线2+=x y 垂直.)1(求函数)(x f y =的解析式；)2(设xmx x g -=ln )(,若对∀],[2e e x ∈,使)()(x f x g '<成立,求实数m 的取值范围.20.（满分12分）已知函数b ax ax x g ++-=12)(2)0(>a 在区间]3,2[上有最小值1和最大值4，设xx g x f )()(=.(1)求b a ,的值；(2)若∃x ∈]1,1[-使不等式02)2(≥⋅-xx k f 成立，求实数k 的取值范围.21. （满分12分）已知函数)1()(--=x a e x f x有两个零点.（1）求实数a 的取值范围；（2）设1x 、2x 是)(x f 的两个零点，证明：2121x x x x +<⋅. 说明：请在22、23题中任选一题做答，写清题号．如果多做，则按所做第一题记分．22.（满分10分）已知曲线C 的参数方程为⎩⎨⎧+==ϕϕsin 33cos 3y x （ϕ为参数），以原点为极点，x 轴非负半轴为极轴建立极座标系. (1) 求曲线C 的极坐标方程；(2) 已知倾斜角为0135过点)2,1(P 的直线l 与曲线C 交于N M ,两点，求PNPM 11+的值. 23.（满分10分）若关于x 的不等式01323≥--++t x x 的解集为R,记实数t 的最大值为a ;(1) 求实数a 的值；(2) 若正实数n m ,满足a n m =+54，求nm n m y 33421+++=的最小值. 参考答案一、DCAAB AADDA BC二、13. 1 ；14. [0,2] ；15. - 2 ; 16. ( 32,2 ) ⋃ (1, ln2 e )高三数学（文）第1页,共4页高三数学（文）第2页,共4页密学校班级姓名学号密封线内不得答题三、17. (1) f(x)为奇函数；(2) (0 , 1)18. (1) 略；(2) (0,1]19. (1) f(x)= 13x 3-x+3 ; (2) (2e-e 3,+ ∞)20. (1) a= 1, b= 0 ；(2) (- ∞,1] 21. (1) (e 2,+ ∞) ; (2) 略 22. (1) ρ = 6sin θ ; (2) 6723. (1) a=3 ; (2) 3。

山西省太原市第五中学2020届高三英语上学期12月阶段检测试题

太原五中2020学年度第一学期阶段性检测高三英语(考试时间：120分钟试卷满分：150分)注意事项：1.答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

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1. What is Linda?A. A writer.B.A student. C. A teacher.2. What is the man afraid of?A. Having an accident.B. Missing the interview.C. Saying something wrong.3. What does the woman want to do?A. To return a jacket.B. To change a jacket.C. To buy another jacket.4. Why does the man feel upset?A. A guy stole his clothes.B. He found his clothes ugly.C. Someone said he was ugly.5. What does the woman mean?A. She disbelieves her son.B. She feels very sorry for her son.C. She wants her son to use a new key.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

山西省2020年上学期太原市第五中学高三数学文月阶段性试题答案

山西省2020年上学期太原市第五中学高三数学文9月阶段性试题答案出题，校对：阴瑞玲 2020.09一、选择题（本大题共10小题，共40.0分） 1. 已知sinα=23，则cos (−2α)=( )．A. 19B. −19C. √53D. −√53【答案】A 【解析】【分析】本题考查了诱导公式及二倍角公式的应用，考查了计算能力，属于基础题．由题意，直接利用诱导公式及二倍角公式求解即可．【解答】解：cos(−2α)=cos2α=1−2sin 2α=1−2×(23)2=19．故选A ．2. 已知tanθ=2，则sin (π2+θ)cosθ−sinθcos (3π2+θ)=( )A. −45B. −35C. 35D. 45【答案】B 【解析】【分析】本题考查诱导公式和同角关系式，属于基础题；利用sin 2θ+cos 2θ=1，将要求式除以sin 2θ+cos 2θ，然后分子分母同时除以cos 2θ即可求解；【解答】解：由题意，tanθ=2，则sin (π2+θ)cosθ−sinθcos (3π2+θ) =cos 2θ−sin 2θ=cos 2θ−sin 2θsin 2θ+cos 2θ=1−tan 2θ1+tan 2θ=−35．故选B ．3. 已知函数，若要得到一个奇函数的图象，则可以将函数f(x)的图象( )A. 向左平移π6个单位长度 B. 向右平移π6个单位长度 C. 向左平移π12个单位长度D. 向右平移π12个单位长度【答案】C 【解析】【分析】本题考查y =Asin(ωx +φ)的图象变换规律，是基础题．利用辅助角公式化简，结合y =Asin(ωx +φ)的图象变换规律及正弦函数、余弦函数的奇偶性得出结论．【解答】解：f(x)=√3cos(2x −π2)−cos2x =√3sin2x −cos2x =2sin(2x −π6)，将函数f(x)=2sin(2x −π6)的图象向左平移π12个单位，可得y =2sin[2(x +π12)−π6]=2sin2x 的图象，显然，y =2sin2x 为奇函数，故选C ．4. 如图，在△ABC 中，AD ⃗⃗⃗⃗⃗⃗ =3DB ⃗⃗⃗⃗⃗⃗ ，P 为CD 上一点，且AP ⃗⃗⃗⃗⃗ =m AC ⃗⃗⃗⃗⃗ +12AB ⃗⃗⃗⃗⃗ ，则m 的值为( )A. 12B. 13C. 14D. 15【答案】B【解析】解：∵AD ⃗⃗⃗⃗⃗⃗ =3DB ⃗⃗⃗⃗⃗⃗ ， ∴AB ⃗⃗⃗⃗⃗ =43AD ⃗⃗⃗⃗⃗⃗ ，又AP ⃗⃗⃗⃗⃗ =m AC ⃗⃗⃗⃗⃗ +12AB ⃗⃗⃗⃗⃗ ， ∴AP ⃗⃗⃗⃗⃗ =m AC ⃗⃗⃗⃗⃗ +23AD ⃗⃗⃗⃗⃗⃗ ，且C ，P ，D 三点共线， ∴m +23=1，解得m =13．故选：B ．根据AD ⃗⃗⃗⃗⃗⃗ =3DB ⃗⃗⃗⃗⃗⃗ 即可得出AB ⃗⃗⃗⃗⃗ =43AD ⃗⃗⃗⃗⃗⃗ ，从而得出AP ⃗⃗⃗⃗⃗ =m AC ⃗⃗⃗⃗⃗ +23AD ⃗⃗⃗⃗⃗⃗ ，然后根据C ，P ，D 三点共线即可求出m 的值．本题考查了向量数乘的几何意义，向量的数乘运算，三点A ，B ，C 共线，且OB ⃗⃗⃗⃗⃗⃗ =λOA ⃗⃗⃗⃗⃗ +μOC ⃗⃗⃗⃗⃗ 时，λ+μ=1，考查了计算能力，属于基础题．5. 已知非零向量m⃗⃗⃗ ，n ⃗ 满足|n ⃗ |=4|m ⃗⃗⃗ |，且m ⃗⃗⃗ ⊥(2m ⃗⃗⃗ +n ⃗ )，则m ⃗⃗⃗ ，n ⃗ 的夹角为( ) A. π6B. π3C. π2D. 2π3【答案】D 【解析】【分析】本题考查向量的夹角与向量的数量积，属于中档题；由|n ⃗ |=4|m ⃗⃗⃗ |，且m ⃗⃗⃗ ⊥(2m ⃗⃗⃗ +n ⃗ )，可得m ⃗⃗⃗ ·(2m ⃗⃗⃗ +n ⃗ )=0，进一步得cos 〈m ⃗⃗⃗ ，n ⃗ 〉=−2|m ⃗⃗⃗ ||n ⃗⃗ |=−12，又0≤〈m ⃗⃗⃗ ，n⃗ 〉≤π，即可求解；【解答】解：∵|n⃗ |=4|m ⃗⃗⃗ |，且m ⃗⃗⃗ ⊥(2m ⃗⃗⃗ +n ⃗ )， ∴m ⃗⃗⃗ ·(2m ⃗⃗⃗ +n ⃗ )=2m ⃗⃗⃗ 2+m ⃗⃗⃗ ·n ⃗ =2|m ⃗⃗⃗ |2+|m ⃗⃗⃗ ||n ⃗ |cos 〈m ⃗⃗⃗ ，n⃗ 〉=0，且|m⃗⃗⃗ |≠0，|n⃗|≠0，∴2|m⃗⃗⃗ |+|n⃗|cos〈m⃗⃗⃗ ，n⃗〉=0，∴cos〈m⃗⃗⃗ ，n⃗〉=−2|m⃗⃗⃗ ||n⃗⃗ |=−12，又0≤〈m⃗⃗⃗ ，n⃗〉≤π，∴〈m⃗⃗⃗ ，n⃗〉=2π3．故选D．6.设等差数列{a n}的前n项和为S n，若S3，S9，S6成等差数列，且a2=10，则S9的值为()A. 28B. 36C. 42D. 46【答案】B【解析】【分析】本题主要考查等差数列的性质、前n项和公式，考查考生的化归与转化能力、运算求解能力．先根据等差数列的性质和前n项和公式求出首项和公差的关系，再根据a2=10求出首项和公差，最后利用等差数列的前n项和公式求出结果．【解答】解：解法一：因为S3，S9，S6成等差数列，所以2S9=S3+S6，所以(S9−S3)+(S9−S6)=0，所以(a4+a5+⋯+a9)+(a7+a8+a9)=0，所以9a7=0，所以a7=0．设{a n}的公差为d，因为a2=10，所以d=a7−a27−2=0−105=−2，所以S9=9a1+9×82d=9(a2−d)+9×82d=36．解法二：因为S3，S9，S6成等差数列，所以2S9=S3+S6，设{a n}的公差为d，则2×(9a1+9×82d)=3a1+3×22d+6a1+6×52d，得a1=−6d．又a2=10，所以a1=12，d=−2，所以S9=9a1+9×82d=36．7.已知函数f(x)=cos2(x+π6)−2sin2(x+π6)+2.则关于它该函数性质的说法中，正确的是()A. 最小正周期为2πB. 将其图象向右平移π6个单位，所得图象关于y轴对称C. 对称中心为(π12+kπ2,0)(k∈Z)D. [0,π2]上单调递减【答案】B【解析】解：函数f(x)=cos2(x+π6)−2sin2(x+π6)+2=1+cos(2x+π3 )2−2×1−cos(2x+π3)2+2=32cos(2x+π3)+32，周期为：T=2π2=π，所以A不正确；将其图象向右平移π6个单位，所得函数y=f(x−π6)=32cos2x+32，则图象关于y轴对称，所以B正确；令2x+π3=π2+kπ，k∈Z，解得x=π12+kπ2(k∈Z)，对称中心为(π12+kπ2,32)(k∈Z)，所以C不正确；当x∈[0,π2]时，2x+π3∈[π3,4π3]，函数先减后增，所以D不正确；故选：B．化简函数的解析式，求出函数的周期怕啥A；利用函数的平移变换求解函数的解析式判断B；利用函数的对称中心判断C，函数的单调性判断D；本题考查三角函数的图象变换，三角函数的化简求值，函数的单调性对称轴以及函数的周期的求法，是中档题．8. 若(a +b +c)(b +c −a)=3bc ，且sinA =2sinBcosC ，那么△ABC 是( )A. 直角三角形B. 等边三角形C. 等腰三角形D. 等腰直角三角形【答案】B 【解析】【分析】本题主要考查正余弦定理在解三角形计算中的综合应用．先由余弦定理化简可求得cos A 的值，进而可求A 得值，再由sinA =2sinBcosC ，利用正弦定理和余弦定理化简可得b =c ，进而可求答案．【解答】解：∵(a +b +c)(b +c −a)=3bc ， ∴(b +c)2−a 2=3bc ，b 2−bc +c 2=a 2．根据余弦定理a 2=b 2+c 2−2bccosA ，得b 2−bc +c 2=a 2=b 2+c 2−2bccosA ，即bc =2bccosA ， ∴cosA =12，∴A =60∘．又sinA =2sinBcosC ，∴sinAsinB=2cosC ，即a b=2⋅a 2+b 2−c 22ab，化简可得b 2=c 2，即b =c ， ∴△ABC 是等边三角形．故选B ．9. 已知α为锐角，sin α=cos α−√24，则sin (α+5π12)=( ) A. 3√5−18B. √15−√38C. 3√5+18D. √15+√38【答案】C【解析】【分析】本题主要考查两角和的正弦公式，诱导公式，同角三角函数的关系式，属于基础题．由已知α为锐角，sinα=cosα−√24，即cos (α+π4)=14，故α+π4仍为锐角，再根据诱导公式和两角和的正弦公式计算即可．【解答】解：由已知α为锐角，sinα=cosα−√24所以cosα−sinα=√2cos(α+π4)=√24，即cos(α+π4)=14，故α+π4仍为锐角，sin(α+π4)=√154，sin (α+5π12)=sin (α+π4+π6)=√154×√32+14×12=3√5+18．故选C ．10. 将函数f(x)=cosx 的图象先向右平移56π个单位长度，再把所得函数图象上的每个点的横坐标都变为原来的1ω(ω>0)倍，纵坐标不变，得到函数g(x)的图象，若函数g(x)在(π2,3π2)上没有零点，则ω的取值范围是( )A. (0,29]B. (0,29]⋃[23,89]C. (0,29]⋃[89,1]D. (0,1]【答案】B 【解析】【分析】本题考查函数y =Acos(ωx +φ)的图象变换及零点问题，属于较难题．根据y =Acos(ωx +φ)的图象变换规律，求得g(x)的解析式，根据定义域求出ωx −5π6的范围，再利用余弦函数的图象和性质，求得ω的取值范围．【解答】解：函数f(x)=cosx 的图象先向右平移56π个单位长度，可得y =cos(x −5π6)的图象，再将图象上每个点的横坐标变为原来的1ω(ω>0)倍(纵坐标不变)，得到函数g(x)=cos(ωx−5π6)的图象，∴周期T=2πω，若函数g(x)在(π2,3π2)上没有零点，∴ωπ2−5π6<ωπ−5π6<3ωπ2−5π6，∴(3ωπ2−5π6)−(ωπ2−5π6)≤T2=πω，∴ω2≤1，解得0<ω≤1，又{−π2+kπ≤ωπ2−5π6π2+kπ≥3ωπ2−5π6，解得3ω2−43≤k≤ω2−13，当k=0时，解23≤ω≤89，当k=−1时，又0<ω≤1，可得0<ω≤29，∴ω∈(0,29]∪[23,89].故选B．二、填空题（本大题共5小题，共20.0分）11.已知向量a⃗=(2,2√3)，若(a⃗+3b⃗ )⊥a⃗，则b⃗ 在a⃗上的投影是_______________．【答案】−43【解析】【分析】本题考查向量的投影的求法，考查向理垂直的充要条件应用，是基础题．首先由(a⃗+3b⃗ )⊥a⃗，得到a⃗·b⃗ =−163，然后代入投影公式计算即可．【解答】解：∵|a⃗|=4，(a⃗+3b⃗ )⊥a⃗，∴(a⃗+3b⃗ )·a⃗=a⃗2+3a⃗·b⃗ =16+3a⃗·b⃗ =0，∴a⃗·b⃗ =−163，∴b⃗ 在a⃗上的投影是a⃗ ⋅b⃗|a⃗ |=−43．故答案为−43．12.已知函数的部分图象如图所示，则函数f(x)的解析式为_______．【答案】f(x)=2sin(πx+π6)(x∈R)【解析】【分析】本题考查函数y=Asin(ωx+φ)的图象与性质，属于基础题．根据三角函数的图象求出A，ω和φ的值即可得到结论．【解答】解：由图象可知A=2，T4=56−13=12，所以T=2，ω=2πT=π．将点(13,2)代入f(x)=2sin(πx+φ)，得sin(π3+φ)=1，又|φ|<π2，所以φ=π6，故所求解析式为f(x)=2sin(πx+π6)(x∈R)．故答案为f(x)=2sin(πx+π6)(x∈R)．13.已知数列{a n}的前n项和为S n，若2S n=3a n−2n(n∈N∗)，则数列{a n}的通项公式为______ ．【答案】a n=3n−1【解析】【分析】本题考查数列的通项公式的求法，考查递推关系，是中档题．令n=1，得a1=2，当n≥2时，2a n=3a n−3a n−1−2，由此推导出数列{a n+1}是首项为3，公比为3的等比数列，从而得到a n=3n−1．【解答】解：令n=1，得2a1=3a1−2，解得a1=2，当n≥2时，由2S n=3a n−2n(n∈N∗)，得2S n−1=3a n−1−2(n−1)，两式相减得2a n=3a n−3a n−1−2，即a n=3a n−1+2，整理得a n+1a n−1+1=3，∴数列{a n+1}是首项为a1+1=3，公比为3的等比数列，∴a n+1=3n，∴a n=3n−1．故答案为a n=3n−1．14.在△ABC中，AB=6，AC=3√2，∠A=135°，点D在BC边上，AD=BD，则AD的长为______．【答案】√10【解析】解：如图所示，由∠BAC =135°，AB =6，AC =3√2，在△ABC 中，由余弦定理得BC 2=AB 2+AC 2−2AB ⋅ACcos∠BAC =36+18−2×6×3√2×(−√22)=90； ∴BC =3√10；在△ABC 中，由正弦定理得AC sinB =BC sin∠BAC ，∴sinB =3√2×√223√10=√10，∴cosB =√1−sin 2B =√10；过点D 作AB 的垂线DE ，垂足为E ，由AD =BD 得：cos∠DAE =cosB ，Rt △ADE 中，AD =AE cos∠DAE =3310=√10．故答案为：√10．由余弦定理求得BC 的值，由正弦定理求得sin B ，再求出cos B ；过点D 作DE ⊥AB ，利用直角三角形求得AD 的值．本题主要考查了正弦、余弦定理在解三角形中的应用问题，是基础题．15. 在等腰梯形ABCD 中，已知AB//DC ，AB =2，BC =1，∠ABC =60°.点E 和F 分别在线段BC 和DC 上，且BE ⃗⃗⃗⃗⃗ =23BC ⃗⃗⃗⃗⃗ ，DF ⃗⃗⃗⃗⃗ =16DC ⃗⃗⃗⃗⃗ ，则AE ⃗⃗⃗⃗⃗ ·AF ⃗⃗⃗⃗⃗ 的值为________．【答案】2918【解析】【分析】本题主要考查了平面向量的运算，属于基础题．基底法可以先取BA ⃗⃗⃗⃗⃗ ，BC⃗⃗⃗⃗⃗ 为一组基底，化简AE ⃗⃗⃗⃗⃗ ，AF ⃗⃗⃗⃗⃗ ，再用平面向量的数量积计算公式求解即可；坐标法可以建系，表示E 、F 坐标，再依据平面向量的坐标运算，即可推出结论．【解答】解：法一：取BA ⃗⃗⃗⃗⃗ ，BC ⃗⃗⃗⃗⃗ 为一组基底，则AE ⃗⃗⃗⃗⃗ =BE ⃗⃗⃗⃗⃗ −BA ⃗⃗⃗⃗⃗ =23BC ⃗⃗⃗⃗⃗ −BA ⃗⃗⃗⃗⃗ ，AF ⃗⃗⃗⃗⃗ =AB ⃗⃗⃗⃗⃗ +BC ⃗⃗⃗⃗⃗ +CF ⃗⃗⃗⃗⃗ =−BA ⃗⃗⃗⃗⃗ +BC ⃗⃗⃗⃗⃗ +512BA ⃗⃗⃗⃗⃗ =−712BA ⃗⃗⃗⃗⃗ +BC ⃗⃗⃗⃗⃗ ，所以AE ⃗⃗⃗⃗⃗ ·AF ⃗⃗⃗⃗⃗ =(23BC ⃗⃗⃗⃗⃗ −BA ⃗⃗⃗⃗⃗ )·(−712BA ⃗⃗⃗⃗⃗ +BC ⃗⃗⃗⃗⃗ )=712|BA ⃗⃗⃗⃗⃗ |2−2518BA ⃗⃗⃗⃗⃗ ·BC ⃗⃗⃗⃗⃗ +23|BC ⃗⃗⃗⃗⃗ |2=712×4−2518×2×1×12+23=2918．法二：以AB 所在直线为x 轴，A 为原点建立如图所示的坐标系．由于AB =2，BC =1，∠ABC =60°，所以CD =1，等腰梯形ABCD 的高为√32，所以A (0,0)，B (2,0)，D (12,√32)，C (32,√32)，所以BC ⃗⃗⃗⃗⃗ =(−12,√32)，DC ⃗⃗⃗⃗⃗ =(1,0)，又因为BE ⃗⃗⃗⃗⃗ =23BC ⃗⃗⃗⃗⃗ ，DF ⃗⃗⃗⃗⃗ =16DC ⃗⃗⃗⃗⃗ ，所以E (53,√33)，F (23,√32)，因此AE ⃗⃗⃗⃗⃗ ·AF ⃗⃗⃗⃗⃗ =(53,√33)·(23,√32)=53×23+√33×√32=109+12=2918．三、解答题（本大题共4小题，共40.0分）16. 已知函数f(x)=cos 2x +√3sinxcosx −12(x ∈R)．(1)求f(x)的最小正周期；(2)讨论f(x)在区间[−π4,π4]上的单调性；【答案】解：(1)f(x)=12+12cos2x +√32sin2x −12=sin(2x +π6)， ∴T =π；(2)依题意，令−π2+2kπ≤2x +π6≤π2+2kπ,k ∈Z ，解得−π3+kπ≤x ≤π6+kπ,k ∈Z ，∴f(x)的单调递增区间为[−π3+kπ,π6+kπ],k∈Z；设A=[−π4,π4],B=[−π3+kπ,π6+kπ]，易知A∩B=[−π4,π6]，∴当x∈[−π4,π4]时，f(x)在区间[−π4,π6]上单调递增，区间(π6,π4]上单调递减．【解析】(1)化简可得f(x)=sin(2x+π6)，进而求得最小正周期；(2)先求得f(x)的单调递增区间为[−π3+kπ,π6+kπ],k∈Z，进而求得f(x)在区间[−π4,π4]上的单调性．本题考查三角函数的恒等变换，以及三角函数的图象及性质，考查运算化简能力，属于基础题．17.在△ABC中，内角A，B，C所对的边分别为a，b，c.已知bsinA=asin(B+ π 3).(1)求角B的大小；(2)设a=4，c=6，求b和sin(2A−B)的值．【答案】解：(1)在△ABC中，由正弦定理，可得，又由bsinA=asin(B+ π 3)，得，即，又因为B∈(0,π)，所以B+B+ π 3=π，可得B= π 3．(2)在△ABC中，由余弦定理及a=4，c=6，B= π 3，有，故b=2√7，由bsinA=asin(B+ π 3)，可得，因为a<c，故，因此，，所以=4√37×12−17×√32=3√314，所以sin(2A−B)=3√314．【解析】本题主要考查两角和差的三角函数公式，正弦定理，余弦定理，以及二倍角公式的应用，属于基础题．(1)由正弦定理得，又bsinA=asin(B+ π 3)，由此可解得B．(2)由余弦定理得b=2√7，由bsinA=asin(B+ π 3)，得，则，由此能求出sin(2A−B)．18.已知等差数列{a n}的前n项和S n，n∈N∗，a5=6，S6=27，数列{b n}的前n项和T n，T n=2b n−n(n∈N∗)．(1)证明：{b n+1}是等比数列，并求b n；(2)求数列{a n⋅b n}的前n项和．【答案】(1)证明：由T1=2b1−1得，b1=1，因为T n−T n−1=(2b n−n)−(2b n−1−(n−1))(n≥2)，所以b n=2b n−1+1，从而由b n+1=2(b n−1+1)得，b n+1b n−1+1=2(n≥2)，所以{b n+1}是以2为首项，2为公比的等比数列．故b n=2n−1．(2)解：根据题意，设等差数列{a n}的公差为d，首项为a1，则a1+4d=6，6a1+15d=27，解得a1=2，d=1，∴a n=n+1．所以a n⋅b n=(n+1)(2n−1)=(n+1)×2n−(n+1)，设A n=2×2+3×22+⋯+(n+1)×2n，则2A n=2×22+3×23+⋯+(n+1)×2n+1，所以−A n=22+22+23+⋯+2n−(n+1)×2n+1=2+2(1−2n)1−2−(n+1)×2n+1=−n⋅2n+1，所以A n=n⋅2n+1，由B n=2+3+⋯+n+1=(2+n+1)n2=n2+3n2．所以数列{a n⋅b n}的前n项和为A n−B n=n⋅2n+1−n2+3n2．【解析】本题考查等比数列的判定和证明，等比数列的通项公式和求和公式，等差数列的通项公式和求和公式，错位相减法求和，属于中档题．(1)通过递推关系T n=2b n−n(n∈N∗)，用“两式相减法”可得b n=2b n−1+1，从而可得b n+1=2(b n−1+1)，即可求解；(2)设等差数列{a n}的公差为d，由题意可建立方程组，解得a1=2，d=1，从而可得a n=n+1，运用错位相减法与分组转化法求解数列{a n⋅b n}的前n项和即可．−1,cos2A)，且m⃗⃗⃗ ‖n⃗，A 19.在△ABC中，角A，B，C的对边分别为a，b，c，且向量m⃗⃗⃗ =(√3,−2sinA)，n⃗=(2cos2A2为锐角．(Ⅰ)求角A的大小；(Ⅱ)若a=2，求△ABC的面积的最大值．−1,cos2A)，且m⃗⃗⃗ ‖n⃗，【答案】解：(Ⅰ)∵m⃗⃗⃗ =(√3，−2sinA)，n⃗=(2cos2A2−1)，∴√3cos2A=−2sinA(2cos2A2∴√3cos2A=−2sinAcosA，∴√3cos2A=−sin2A，∴tan2A=−√3∵A为锐角∴A=π；3(Ⅱ)∵a=2，∴4=b2+c2−2bccosπ3∴4=b2+c2−bc≥bc(当且仅当b=c时等号成立)∴b=c时，bc取得最大值4bcsinA∵△ABC的面积等于12∴△ABC的面积的最大值为√3．【解析】(Ⅰ)利用向量共线的条件，建立等式，结合A为锐角，即可求角A的大小；(Ⅱ)根据a=2，利用余弦定理及基本不等式，结合三角形面积公式，即可求△ABC的面积的最大值．本题考查向量共线的条件，考查余弦定理，考查基本不等式，考查三角形的面积公式，考查学生的计算能力，属于中档题．。

2020届山西省太原市第五中学高三上学期阶段性检测(10月) 英语(PDF版)

密学校班级姓名学号密封线内不得答题太原五中2019—2020学年度第一学期阶段性检测高三英语(2019.10.9)第一部分阅读理解（共两节，满分60分）第一节（共15小题；每小题3分，满分45分）(A)Many of us know about Russia ’s Lake Baikal from our textbooks, or by listening to Chinese singer Li Jian’s hit song, Lake Baikal. But over the past decade, the world’s deepest freshwater lake has been in the spotlight for an extreme sport.Each March since 2005, about 150 people from around the world sign up for the Baikal Ice Marathon . They come to explore the lake’s breathtaking beauty and challenge themselves in unpredictable conditions.The 26-mile (41. 84-kilometers) journey starts on the lake’s eastern shore. In March, the ice is a meter thick and iron-hard. Runners cross this frozen surface, finishing on the western side of the lake.Known as the “blue eye of Siberia ”, Lake Baikal has exceptionally clear waters. This means its ice is almost perfectly transparent. “Seen from above, a runner on the ice looks as if he or she is jogging through space,” The New York Times noted.Th e landscape might be beautiful, but it’s also harsh. Strong winds blast (侵袭) across the lake and frostbite (冻伤) can occur within half an hour. Runners say the cold climate is what draws them. They want to test their limits.“When you are in such an environment, you don’t have cars around you, you don’t have the noise around. I think these extreme races allow you to be alone with nature,” Alicja Barahona, a 64-year-old runner from the US, told ABC News.The location offers some strange and unique characteristics for this marathon. The finish line is visible from the start. But the endless white offers no progress markers. The race also ends with little fanfare (喧闹). Tourists crowding the ice are mostly addicted to snapping series (自拍) and just ignore the runners.For some runners, the absence of spectators makes the ra ce more challenging, because it’s lonely. They must fight with themselves. “You are alone on Bai kal. It is your race. You are alone with yourself. All you need to do is to defeat yourself,” Veronique Messina, a French runner, told the Telegraph.1. What can we know about the Baikal Ice Marathon from the text?A. It takes runners from the northern end to the southern end of the lake.B. It involves extreme weather and beautiful scenery.C. It attracts more and more participants each year.D. It is about 26 kilometers in length.2. How does the Baikal Ice Marathon differ from other marathons? A. Only men are allowed to run in this race.B. The runners can see the finish line from the start.C. The runners are often distracted by tourists.D. There are many progress markers on the ice.3. What is the most difficult part of the race for Messina? A. Loneliness. B. The long distance. C. The cold climate. D. Noisy surroundings.(B)In 1972, a social worker named Sanjit Bunker Roy founded Barefoot College in Tilonia, Rajasthan. Today the college trains women from villages for six months to build and maintain solar panels and other instruments. Barefoot College also offers education to the younger generation both during the day and at its solar bridge schools that meet by lamplight at night.The philosophy of Barefoot College is largely inspired by the principles of Gandhi, starting with equality beyond caste (种姓), gender or religion. As a matter of fact, women are prioritized (优先考虑) as an underserved population that is essential to bringing villages together. Another central principle of the college is self-reliance, teaching students to support and think for themselves.After the college’s female students have completed their half-year of training, they return to their villages where they wait for solar panel parts to arrive from the college. Once they have all the pieces they need, they construct the panels and begin collecting solar energy. For each village, the college also provides solar lamps. Villagers can, in addition, order parts for other solar-powered devices, such as water heaters and cooking stoves. Once assembled, they and the lamps are powered by the solar panels.The effect on the villages is huge. Before the solar panels and lamps arrived, villagers had only candles to light their homes. This prevented adults from doing serious work at night, and it made studying difficult for children as well. As for physicians, they had difficulty treating patients and performing operations at night because they had to rely on flashlights.Now there is power for not only the electrical appliances that the college provides but also devices like televisions, radios and computers. For the first time, the villagers can even connect to the world through the Internet.密封线内不得答题4. What does this text explain about the college? A. How it accomplishes its goals. B. How its global efforts are funded. C. How its founder hires employees. D. How it works with the government.5. Which idea is communicated by the college to women? A. They should be more involved in politics. B. They don’t have to depend on others .C. They aren’t educating their daughters enough .D. They focus too much on their communities.6. Which role do the women play after they return to their villages? A. They’re merchants . B. They’re composers . C. They’re technicians . D. They’re journalists .7. In the past, what was hard to provide in villages after dark? A. Dry shelter B. Clean water C. Medical care D. Food supplies(C)Imagine you are opening your own company and want to hire a manager. You have two candidates and they are both capable and experienced, so who would you rather hire: Julia Watson or Shobha Bhattacharva? Chances are that you would prefer Watson, right? But why? “Easy names are evaluated as more familiar, less risky and less dangerous, ” Eryn Newman, a scientist at Victoria University of Wellington, New Zealand, told Scientific American. As a result, people with easier names are often assumed to be more trustworthy. This is what Newman and her teammates have found in their recent study.In the experiment, they picked 18 different foreign names, including difficult-to-pronounce ones like Yevgeni Dherzhinsky and easy names like Bodo Wallmeyer. They then attached each name with a statement such as “turtles are deaf” and “giraffes are the only mammals that cannot jump” and asked volunteers whether they thought the claims were true.The results showed that claims connected to easier names were more often ranked as believable than those attributed to difficult names, regardless of what the truth really was. In fact, previous studies have already found that our judgments about products can be affected by their names. For example, we tend to think of a food additive (添加剂) with an easier name as safer and a stock with an easier name as more lucrative (利润丰厚的)，according to Medical Daily.But researchers pointed out that this effect can change depending on where someone comes from. For example, a native British ma n may find “Yevgeni Dherzhinsky” hard to pronounce while Russian people could say it without effort. Newman hopes that this finding can make us better see our biases (偏见). It’s not just unfair to people that we make judgments based on gut feelings (直觉) rather than facts, and it can sometimes have serious consequences.For example, we may choose to believe certain eyewitnesses in court simply because their names sound more trustworthy even if they are actually lying. Or, we may let go of qualified job candidates due to their “difficult” names.Now, if you could make that decision again, would you still prefer Julia Watson to Shobha Bhattacharva?8. What did Newman and her teammates discover in their experiment? A. Volunteers with easier names were more likely to choose true claims.B. A difficult name doesn’t influence the way the volunteers viewed the claims.C. V olunteers trusted claims paired with easy names more often.D. V olunteers trusted claims connected with difficult names.9. The underlined w ords “this effect” in Paragraph 5 refer to the effect ______. A. names have on peoples judgmentsB. gut feelings have on people from different placesC. of decisions made based on factsD. of people ’s biases against certain types of people 10. What can we conclude from the last paragraph?A. We should think twice before we make a decision.B. The harder your name is to pronounce, the more likely it is you will get a job.C. Judging people based on their names may cause serious problems.D. Russian s have less bias against people’s names than the British. 11. What is probably the best title for the text? A. Names Affect ProductsB. Employers Prefer Shobha BhattacharvaC. Difficult Names are TrustworthyD. Easy Names Win Out(D)Many of us have had this experience: we lie down in a bed other than our own, perhaps at a friend’s house or in a hotel room, and find it difficult or impossible to fall asleep. Is it because the bed is uncomfortable? Maybe, but perhaps there can be other reasons.According to a new study published in Current Biology, a significant reason is what the scientists call “first night effect”. They believe that one side of the brain acts as a “night watch” to warn us about potential dangers. It forces us to stay awake on the first night in a new environment. For the study, 35 young volunteers were asked to sleep in a sleep lab for several days. Meanwhile, researchers watched their brain activities.密学校班级姓名学号密封线内不得答题According to the researchers, on their first night, the left brains were more active than the right brains and people had a hard time sleeping. However, left-brain activity decreased as days went by, falling even to the point of complete calm. In this process, the participants got an increasingly better sleep experience.The findings suggest that the different rhythms (5%) of the sides of the brain affect our sleep. When the two sides work differently, the balance between them is broken. Thus, the brain can’t relax and is sensitive to anything strange in the surroundings, just as it is in daytime.“At some level, the brain is continuing to analyze things, even though you are not aware of the ana lysis, ” US professor Jerome Siegel told Smithsonian Magazine. “If something unusual happens --- if a door opens or you hear a key in a lock--- you can be alert, even though the intensity of the stimulus (刺激) is quite low.”More surprisingly, this phenomenon is similar to the way some animals sleep. Whales, dolphins, and many birds can sleep with half of their brain while the other half stays awake, with its corresponding eye staying open.The researchers think that it is the result of evolution, and works to protect us in potentially dangerous environments.If you have ever had what you think is “first night effect”, researchers suggest that you bring your own pillow or sleep in a room similar to your bedroom next time you sleep away from home.12. What did the new study published in Current Biology find?A. A comfortable bed could help people sleep well in a new environment.B. Most people could sleep well in a new environment after the first night.C. Brain activities affected people ’s sleep in a new environment.D. The right brain determined how well people slept in a new environment. 13. What was found out about the volunteers?A. Their left brains were more active on the first night.B. Their right brains became more active as days went by.C. Their right brains kept them awake the whole night.D. They slept better in the sleep lab than at home.14. What do the researchers think makes the brain sensitive to new things? A. The bad sleep experiences people have had. B. The tiredness that people suffer from in daytime. C. The imbalance between the two sides of the brain. D. The strangeness of the things that people come across 15. What do the researchers think of “first night effect” ? A. It has evolved as a way to protect us.B. It’s a characteristic that animals don’t have.C. It’s completely different from the way animals sleep.D. It helps people to get used to new environments quickly.第二节（共5小题；每小题3分，满分15分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

2020届山西太原五中高三阶段性检测语文试卷 (1)

山西太原五中2020届高三阶段性检测语文试题★祝你考试顺利★注意事项：1、考试范围：高考考查范围。

2、答题前，请先将自己的姓名、准考证号用0.5毫米黑色签字笔填写在试题卷和答题卡上的相应位置，并将准考证号条形码粘贴在答题卡上的指定位置。

用2B铅笔将答题卡上试卷类型A后的方框涂黑。

3、选择题的作答：每个小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

写在试题卷、草稿纸和答题卡上的非选择题答题区域的答案一律无效。

4、主观题的作答：用0.5毫米黑色签字笔直接答在答题卡上对应的答题区域内。

写在试题卷、草稿纸和答题卡上的非主观题答题区域的答案一律无效。

5、选考题的作答：先把所选题目的题号在答题卡上指定的位置用2B铅笔涂黑。

答案用0.5毫米黑色签字笔写在答题卡上对应的答题区域内，写在试题卷、草稿纸和答题卡上的非选修题答题区域的答案一律无效。

6、保持卡面清洁，不折叠，不破损。

7、本科目考试结束后，请将本试题卷、答题卡、草稿纸一并依序排列上交。

一、现代文阅读（36分）（一）论述类文本阅读（本题共3小题，9分）阅读下面的文字，完成1～3题。

作为巫书的《山海经》，其内容是由古代巫师若干世纪的承传附益积累，再由不同时期巫师群中的不同作者（可能还有才士文人参与其事）将它们笔之于书而成就起来的。

古代的巫师，实际上就是古代的知识分子，一切文化知识都要通过巫师的手进行传播。

因而在这部书里，除神话传说外，还涉及地理、历史、宗教、民俗、历象、动物、植物、矿物、医药、人类学、民族学、地质学、海洋学等等，这真可以说是一部奇书，一部古代人们生活日用的百科全书，虽然只有三万一千多字。

为什么以神话为主的一部巫书竟会包括那么多学科？因为这正是原始时代原始先民通过神话思维刻印下来的痕迹。

所有探讨认识的一切，都蒙上神话或宗教的色彩。

有些探讨认识，仍是比较正确的，那就成了科学的萌芽，给我们提供了很高的认识价值和研究价值。

原始社会母权制时期的神话，有《大荒西经》所记的女娲之肠化为十神的神话。

山西省太原市第五中学2020届高三上学期阶段性检测(10月)数学(文)含答案

太原五中2019—2020学年度第一学期阶段性检测高三数学(文)一、选择题(本大题共12小题，每小题5分，共60分，每小题有且只有一个正确选项)1. 若集合{}0)1(A <-=x x x , {}2B x y y ==,则 ( )B A A =..B B A ⊆ R B A C =⋃. A B D ⊆..2 若复数iiz +-=11，则z = （） 1A. .B 1- .C i .D 1- .3设非空集合P 、Q 满足P Q P =⋂，则（） .A Q x ∈∀ ,P x ∈ .B Q x ∉∀, P x ∉.C ,0Q x ∉∃ P x ∈0 .D ,0P x ∈∃ Q x ∉0.4 已知31)21(=a ， 3log 2=b ， 7log 4=c ，则实数a ,b ,c 的大小关系为（）c b a A <<.c a b B <<. b a c C <<. b c a D <<..5 已知ABC ∆中，E 是BC 上一点，2=，若μλ+=，则=+μλ（）1.A2.B 3.C 4.D.6如图是函数)sin()(ϕω+=x A x f (R x A ∈<<>>,20,0,0πϕω)在区间]65,6[ππ-上的图象，为了得到)(sin R x x y ∈=的图象，只要将函数)(x f 的图象上所有的点( ).A 向左平移3π个单位长度，再把所得各点的横坐标缩短到原来的21倍，纵坐标不变； .B 向右平移3π个单位长度，再把所得各点的横坐标伸长到原来的2倍，纵坐标不变；.C 向左平移6π个单位长度，再把所得各点的横坐标缩短到原来的21倍，纵坐标不变；.D 向右平移6π个单位长度，再把所得各点的横坐标伸长到原来的2倍，纵坐标不变.x.7 函数8ln )(2x x x f -= 图象大致为( )8.在圆O 中，若弦6=AB ，10=AC ，则=⋅（） .A 16- 2-.B 32.C 16.D.9已知圆O 的半径为1，PA 、PB 为该圆的两条切线，A 、B 为两切点，则PB PA ⋅的最小值为( ) 24.+-A .B 23-+ 224.+-C .D 223-+.10在ABC ∆中，若3AB CB AB CA =⋅+⋅）（，则B A tan 1tan +的最小值（） .A 5 52.B 6.C 26.D .11若),4(ππα∈，且)4sin(42cos 3απα-=，则=α2sin （）.A 97 97-.B 91.-C 91.D.12 已知O 是平面上一定点，AB C ，，是平面上不共线的三个点，动点P 满足s i n s i n A B A C O P O A A B B A C C λ⎛⎫ ⎪=++ ⎪⎝⎭，(0)λ∈+∞，，则动点P 的轨迹一定通过ABC △的（） A . 外心 B . 内心 C . 重心 D . 垂心填空题(本大题共4小题，每小题5分，共20分，把答案填在题中的横线上.13已知两个单位向量a与b 的夹角为600，则向量b a -在向量a 方向上的投影为（）C.14.若点M 是ABC ∆所在平面内一点，且满足03=--AB AM ，则A B M ∆与ABC ∆的面积之比值为（）=-+002010sin 210cos 4110tan 3.15）（=（） .16 将函数x x x f cos sin 3)(-=的图象沿着x 轴向右平移a 个单位(0>a ）后的图象关于y 轴对称，则a 的最小值为（）三、解答题(本大题4小题，共70分，解答应写出文字说明、证明过程或演算步骤) 17.（满分12分）已知函数a x x x x f -+=)cos (sin sin 2)(的图象经过点），（12π，R a ∈. （1）求a 的值，并求函数)(x f 的单调递增区间；（2）若]2,0[π∈x ，不等式m x f ≥)(恒成立，求实数m 的取值范围.18.（满分12分）在ABC ∆中，角A 、B 、C 的对边分别为c b a ,,, 且满足ABa b c cos cos 2=-.（1）求角A 的大小；（2）若52=a ,求ABC ∆面积的最大值.19.（满分12分）设函数R a a ax x x x f ∈+-+=,2ln )(22（1）当0=a 时，曲线)(x f y =与直线m x y +=3相切，求实数m 的值；（2）若函数)(x f 在[1,3]上存在单调递增区间，求实数a 的取值范围.20. 如图，D 是直角ABC ∆斜边BC 上一点，AD AB =，记CAD ∠=α，ABC ∠= β.（1）证明：1cos 2sin 2=+βα；（2）若DC AC 3=，求βα2+的值.21.（满分12分）已知函数xe xf =)(,a x xg +=ln )(。

2020山西省太原五中高三上学期阶段性检测(9月)数学(文)试卷

太原五中2019-2020学年度第一学期阶段性检测高三数学（文）命题、校对人：吕兆鹏（2019.9）一、选择题(本大题共12小题，每小题5分，共60分，每小题有且只有一个正确选项) 1.已知集合{}2,1,0,1,2A =--，2{|4}B x x =≥，则下图中阴影部分所表示的集合为（） A.{}2,1,0,1-- B.{}0 C.{}1,0- D.{}1,0,1-2. 函数f(x)= x- 1-2x 的值域为（）A ． (0, 12 )B ．(0, 12 ]C ． (- ∞ , 12 ]D ．(- ∞ , 12)3. 已知命题:p R m ∈∃，函数1)1()(2+--=x m x x f 在),0(+∞上为增函数，命题:q若b a <,则ba 11>，下列命题为真命题的是（） A. q p ⌝∧ B. q p ∧⌝ C. q p ∧ D. q p ⌝∧⌝4. 已知α是第四象限角，且tan α=- 43, 则αsin = （）A. - 53B. 53C. 54D. - 545. 设点o 在ABC ∆的外部，且253=--，则=∆OBC ABC S S : （）A. 2:1B. 3:1C. 3:2D. 4:36.已知点)8,(m 在幂函数nx m x f )1()(-=的图象上，设)33(f a =，)(ln πf b =， )22(f c =，则a 、b 、c 的大小关系为（） A.b c a << B ．c b a << C ．a c b << D ． c a b << 7.函数)2ln(sin )(+=x xx f 的部分图象可能是（）8.已知函数2)(x a x f -=（21≤≤x )与1)(+=x x g 图象上存在关于x 轴对称的点，则实数a 的取值范围是（）A. [ -54 ,+ ∞)B. [1,2]C. [- 54 ,1] D.[-1,1]9.已知函数)()(xx e e x x f --=，若)()(21x f x f <，则（） A. 21x x > B. 021=+x x C. 21x x < D. 2221x x <10.已知函数⎩⎨⎧>≤+=0,log 0,1)(2x x x x x f ，则1)]([+=x f f y 的零点个数为（）.A 4 B . 3 C . 2 D . 111.已知函数)(x f 的导函数x x f sin 2)(+='，且1)0(-=f ,数列{}n a 是以4π为公差的等差数列，若)()()(432a f a f a f ++=π3，则22019a a = （）ABCD高三数学（文）第3页,共4页高三数学（文）第4页,共4页A . 2019B . 2018C . 2017D . 201612.已知定义在R 上的连续函数f(x)满足2)()(x x f x f =-+,且0<x 时，x x f <')(恒成立，则不等式21)1()(-≤--x x f x f 的解集为（）A . ]21,(-∞B . )21,21(-C . [21,+∞) D . )0,(-∞二、填空题(本大题共4小题，每小题5分，共20分，把答案填在题中的横线上) 13. 函数132)(23+-=x x x f 的极大值与极小值之和为（）14.设函数⎪⎩⎪⎨⎧<≥=0,0,)(22x ex x e x x f x x ,则使得)1()12(+≤-x f x f 成立的x 取值范围是( ) 15. 已知奇函数)(x f 满足)()2(x f x f -=+,且当)1,0(∈x 时，213)(+=xx f ，则 )54(log 3f = ( )16.已知函数⎩⎨⎧>≤+=0,ln 0,4)(2x x x x x x x f ，1)(-=kx x g ,x )2,2(-∈时，方程)()(x g x f =有三个实数根，则k 的取值范围是（）三、解答题(本大题4小题，共70分，解答应写出文字说明、证明过程或演算步骤) 17.（满分12分）已知函数)1(log )1(log )(x x x f a a --+=)10(≠>a a 且（1）判断)(x f 的奇偶性并证明；（2）当10<<a 时，求使0)(<x f 时x 的取值范围.18.（满分12分）已知函数)()(a x ax xx f ≠-=（1）若2-=a ，用函数单调性定义证明：)(x f 在（- ∞ ，-2）上为单调递增函数；（说明：用其它方法证明不给分）（2）若0>a 且)(x f 在（1，+ ∞）上为单调递减函数，求实数a 的取值范围. 19.（满分12分）定义在R 上的函数3)(23+++=cx bx ax x f 同时满足以下条件：① )(x f 在)1,0(上为减函数，),1(+∞上是增函数；②)(x f '是偶函数；③)(x f 在0=x 处的切线与直线2+=x y 垂直.)1(求函数)(x f y =的解析式；)2(设xmx x g -=ln )(,若对∀],[2e e x ∈,使)()(x f x g '<成立,求实数m 的取值范围.20.（满分12分）已知函数b ax ax x g ++-=12)(2)0(>a 在区间]3,2[上有最小值1和最大值4，设xx g x f )()(=.(1)求b a ,的值；(2)若∃x ∈]1,1[-使不等式02)2(≥⋅-xx k f 成立，求实数k 的取值范围.21. （满分12分）已知函数)1()(--=x a e x f x有两个零点.（1）求实数a 的取值范围；（2）设1x 、2x 是)(x f 的两个零点，证明：2121x x x x +<⋅. 说明：请在22、23题中任选一题做答，写清题号．如果多做，则按所做第一题记分．22.（满分10分）已知曲线C 的参数方程为⎩⎨⎧+==ϕϕsin 33cos 3y x （ϕ为参数），以原点为极点，x 轴非负半轴为极轴建立极座标系. (1) 求曲线C 的极坐标方程；(2) 已知倾斜角为0135过点)2,1(P 的直线l 与曲线C 交于N M ,两点，求PNPM 11+的值. 23.（满分10分）若关于x 的不等式01323≥--++t x x 的解集为R,记实数t 的最大值为a ;(1) 求实数a 的值；(2) 若正实数n m ,满足a n m =+54，求nm n m y 33421+++=的最小值.。

山西省太原五中2020届高三上学期阶段性检测(9月)数学(理)试卷答案

太原五中2019—2020学年度第一学期阶段性检测高三数学(理)高三数学答案（理）一、选择题题号123 4 5 6 7 8 9 10 11 12 答案 B B B A D A B C A A D A 题号13 14 15 16答案9 (-∞, -5)1217.(1)证明：f(x+y)=f(x)+f(y) (x，y∈R)，①令x=y=0，代入①式，得f(0+0)=f(0)+f(0)，即 f(0)=0．令y=-x，代入①式，得 f(x-x)=f(x)+f(-x)，又f(0)=0，则有0=f(x)+f(-x)．即f(-x)=-f(x)对任意x∈R成立，所以f(x)是奇函数．(2)解：＞0，即f(3)＞f(0)，又在R上是单调函数，所以在R上是增函数又由(1)f(x)是奇函数．f(k·3)＜-f(3-9-2)=f(-3+9+2)，∴ k·3＜-3+9+2，3-(1+k)·3+2＞0对任意x∈R成立．令t=3＞0，问题等价于t-(1+k)t+2＞0对任意t＞0恒成立．()23log3f=()x f()x fx x x x xx x x2x xx2R 恒成立．18.（Ⅰ）f(x)的单调递减区间是(－∞，ln2)，单调递增区间是(ln2，＋∞),极小值为f(ln2)＝eln2－2ln2＋2a ＝2(1－ln2＋a)；19. 解析：由题意得f ′(x )＝2x ＋ax －(2＋a )＝2x 2－(2＋a )x ＋a x ＝(2x －a )(x －1)x，x ∈(0，＋∞)．(1))①当a ≤0时，函数f (x )在(0,1)上单调递减，在(1，＋∞)上单调递增． ②当a >0时，令f ′(x )＝0得x ＝1或x ＝a2，当a2＝1，即a ＝2时，在(0，＋∞)上恒有f ′(x )≥0，故函数f (x )在(0，＋∞)上单调递增．当a 2<1，即0<a <2时，函数f (x )在(0,a2)，(1，＋∞)上单调递增，在⎝⎛⎭⎫a 2，1上单调递减；当a2>1，即a >2时，函数f (x )在(0,1)，⎝⎛⎭⎫12a ，＋∞上单调递增，在⎝⎛⎭⎫1， a 2上单调递减； (2) ()()g x f x =即22115ln 233x x x x x -=--，化简得23ln 202x x x --=令23()ln 22F x x x x =-- ()2'1321(31)(1)32x x x x F x x x x x--+-=--==所以()F x 在（0,1）上为减函数，在（1，+∞）上为增函数，极小值为1(1)2F =-且113()ln 40432F =->，(2)2ln 20F =-> 故()F x 有两个零点从而函数()()g x f x 与的图象有两个交点. 20.21.解：（Ⅰ）∵，∴. ……………………………1分∵切线与直线平行，∴，∴. ……………………………………………2分（Ⅱ）易得()，∴ ().由题意，知函数存在单调递减区间,等价于在上有解，∵，则故可设.…………………………………4分而，所以，要使在上有解，则只须，即，故所求实数的取值范围是. ……………………………………………5分（Ⅲ）由（Ⅱ）知，，令，得.∵()是函数的两个极值点，∴()是方程的两个根，∴，. …………………………………………………7分∴…………………………………………8分令，∵，∴，且.∵，∴，∴化简整理，得,解得或.而，∴. ……………………………………………………10分又，∴函数在单调递减，∴. …………………………………………………11分故的最小值为. ………………………………………12分。

2019年10月山西省太原五中2020届高三年级阶段性质量检测英语答案

On the other hand, as a well-known school, the main school is more professional and experienced in holding such activities asart exhibition. Its professional security guards and advanced facilities can better protect those famous paintings from being damaged or stolen.
In my opinion, it is more advisable to hold the art exhibition in the main school than in the new one. My reasons are as follows.
On one hand, it is more convenient for people to get to the main one, which is located in the center of the city. Besides, it can provide visitors with a more comfortable environment for appreciating art.
绝密★启用前
山西省太原市第五中学
2020届高三年级上学期10月阶段性质量检测
英语试题答案
2019年10月9日
第一部分阅读理解（共两节，满分60分）
第一节（共15小题；每小题3分，满分45分）
1-3BBA
4-7ABCC
8-11CACD
12-15CACA
第二节（共5小题；每小题3分，满分15分）

2020届山西省太原市第五中学高三上学期阶段性检测(10月) 英语

太原五中2019—2020学年度第一学期阶段性检测高三英语(2019.10.9)第一部分阅读理解（共两节，满分60分）第一节（共15小题；每小题3分，满分45分）(A)Many of us know about Russia’s Lake Baikal from our textbooks, or by list ening to Chinese singer Li Jian’s hit song, Lake Baikal. But over the past decade, the world’s deepest freshwater lake has been in the spotlight for an extreme sport.Each March since 2005, about 150 people from around the world sign up for the Baikal Ice Marathon. They come to explore the lake’s breathtaking beauty and challenge themselves in unpredictable conditions.The 26-mile (41. 84-kilometers) journey starts on the lake’s eastern shore. In March, the ice is a meter thick and iron-hard. Runners cross this frozen surface, finishing on the western side of the lake.Known as the “blue eye of Siberia”, Lake Baikal has exceptionally clear waters. This means its ice is almost perfectly transparent. “Seen from above, a runner on the ice looks as if he or she is jogging through space,” The New York Times noted.The landscape might be beauti ful, but it’s also harsh. Strong winds blast (侵袭) across the lake and frostbite (冻伤) can occur within half an hour. Runners say the cold climate is what draws them. They want to test their limits.“When you are in such an environment, you don’t have cars around you, you don’t have the noise around. I think these extreme races allow you to be alone with nature,” Alicja Barahona, a 64-year-old runner from the US, told ABC News.The location offers some strange and unique characteristics for this marathon. The finish line is visible from the start. But the endless white offers no progress markers. The race also ends with little fanfare (喧闹). Tourists crowding the ice are mostly addicted to snapping series (自拍) and just ignore the runners.For some runners, the absence of spectators makes the ra ce more challenging, because it’s lonely. They must fight with themselves. “You are alone on Bai kal. It is your race. You are alone with yourself. All you need to do is to defeat yourself,” Veronique Messina, a French runner, told the Telegraph.1. What can we know about the Baikal Ice Marathon from the text?A. It takes runners from the northern end to the southern end of the lake.B. It involves extreme weather and beautiful scenery.C. It attracts more and more participants each year.D. It is about 26 kilometers in length.2. How does the Baikal Ice Marathon differ from other marathons?A. Only men are allowed to run in this race.B. The runners can see the finish line from the start.C. The runners are often distracted by tourists.D. There are many progress markers on the ice.3. What is the most difficult part of the race for Messina?A. Loneliness.B. The long distance.C. The cold climate.D. Noisy surroundings.(B)In 1972, a social worker named Sanjit Bunker Roy founded Barefoot College in Tilonia, Rajasthan. Today the college trains women from villages for six months to build and maintain solar panels and other instruments. Barefoot College also offers education to the younger generation both during the day and at its solar bridge schools that meet by lamplight at night.The philosophy of Barefoot College is largely inspired by the principles of Gandhi, starting with equality beyond caste (种姓), gender or religion. As a matter of fact, women are prioritized (优先考虑) as an underserved population that is essential to bringing villages together. Another central principle of the college is self-reliance, teaching students to support and think for themselves.After the college’s female students have completed their half-year of training, they return to their villages where they wait for solar panel parts to arrive from the college. Once they have all the pieces they need, they construct the panels and begin collecting solar energy. For each village, the college also provides solar lamps. Villagers can, in addition, order parts for other solar-powered devices, such as water heaters and cooking stoves. Once assembled, they and the lamps are powered by the solar panels.The effect on the villages is huge. Before the solar panels and lamps arrived, villagers had only candles to light their homes. This prevented adults from doing serious work at night, and it made studying difficult for children as well. As for physicians, they had difficulty treating patients and performing operations at night because they had to rely on flashlights.Now there is power for not only the electrical appliances that the college provides but also devices like televisions, radios and computers. For the first time, the villagers can even connect to the world through the Internet.4. What does this text explain about the college?A. How it accomplishes its goals.B. How its global efforts are funded.C. How its founder hires employees.D. How it works with the government.5. Which idea is communicated by the college to women?A. They should be more involved in politics.B. They don’t have to depend on others.C. They aren’t educating their daughters enough.D. They focus too much on their communities.6. Which role do the women play after they return to their villages?A. They’re merchants.B. They’re composers.C. They’re technicians.D. They’re journalists.7. In the past, what was hard to provide in villages after dark?A. Dry shelterB. Clean waterC. Medical careD. Food supplies(C)Imagine you are opening your own company and want to hire a manager. You have two candidates and they are both capable and experienced, so who would you rather hire: Julia Watson or Shobha Bhattacharva?Chances are that you would prefer Watson, right? But why?“Easy names are evaluated as more familiar, less risky and less dangerous, ”Eryn Newman, a scientist at Victoria University of Wellington, New Zealand, told Scientific American. As a result, people with easier names are often assumed to be more trustworthy. This is what Newman and her teammates have found in their recent study.In the experiment, they picked 18 different foreign names, including difficult-to-pronounce ones like Yevgeni Dherzhinsky and easy names like Bodo Wallmeyer. They then attached each name with a statement such as “turtles are deaf” and “giraffes are the only mammals that cannot jump”and asked volunteers whether they thought the claims were true.The results showed that claims connected to easier names were more often ranked as believable than those attributed to difficult names, regardless of what the truth really was. In fact, previous studies have already found that our judgments about products can be affected by their names. For example, we tend to think of a food additive (添加剂) with an easier name as safer and a stock with an easier name as more lucrative (利润丰厚的)，according to Medical Daily.But researchers pointed out that this effect can change depending on where someone comes from. For example, a native British ma n may find “Yevgeni Dherzhinsky” hard to pronounce while Russian people could say it without effort. Newman hopes that this finding can make us better see our biases (偏见). It’s not just unfair to people that we make judgments based on gut feelings (直觉) rather than facts, and it can sometimes have serious consequences.For example, we may choose to believe certain eyewitnesses in court simply because their names sound more trustworthy even if they are actually lying. Or, we may let go of qualified job candidates due to their “difficult” names.Now, if you could make that decision again, would you still prefer Julia Watson to Shobha Bhattacharva?8. What did Newman and her teammates discover in their experiment?A. Volunteers with easier names were more likely to choose true claims.B. A difficult name doesn’t influence the way the volunteers viewed the claims.C. V olunteers trusted claims paired with easy names more often.D. V olunteers trusted claims connected with difficult names.9. The underlined w ords “this effect” in Paragraph 5 refer to the effect ______.A. names have on peoples judgmentsB. gut feelings have on people from different placesC. of decisions made based on factsD. of people’s biases against certain types of people10. What can we conclude from the last paragraph?A. We should think twice before we make a decision.B. The harder your name is to pronounce, the more likely it is you will get a job.C. Judging people based on their names may cause serious problems.D. Russian s have less bias against people’s names than the British.11. What is probably the best title for the text?A. Names Affect ProductsB. Employers Prefer Shobha BhattacharvaC. Difficult Names are TrustworthyD. Easy Names Win Out(D)Many of us have had this experience: we lie down in a bed other than our own, perhaps at a friend’s house or in a hotel room, and find it difficult or impossible to fall asleep. Is it because the bed is uncomfortable? Maybe, but perhaps there can be other reasons.According to a new study published in Current Biology, a significant reason is what the scientists call “first night effect”. They believe that one side of the brain acts as a “night watch” to warn us about potential dangers. It forces us to stay awake on the first night in a new environment. For the study, 35 young volunteers were asked to sleep in a sleep lab for several days. Meanwhile, researchers watched their brain activities.According to the researchers, on their first night, the left brains were more active than the right brains and people had a hard time sleeping. However, left-brain activity decreased as days went by, falling even to the point of complete calm. In this process, the participants got an increasingly better sleep experience.The findings suggest that the different rhythms (5%) of the sides of the brain affect our sleep. When the two sides work differently, the balance between them is broken. Thus, the brain can’t relax and is sensitive to anything strange in the surroundings, just as it is in daytime.“At some level, the brain is continuing to analyze things, even though you are not aware of the analysis, ” US professor Jerome Siegel told Smithsonian Magazine. “If something unusual happens --- if a door opens or you hear a key in a lock--- you can be alert, even though the intensity of the stimulus (刺激) is quite low.”More surprisingly, this phenomenon is similar to the way some animals sleep. Whales, dolphins, and many birds can sleep with half of their brain while the other half stays awake, with its corresponding eye staying open.The researchers think that it is the result of evolution, and works to protect us in potentially dangerous environments.If you have ever had what you think is “first night effect”, researchers suggest that you bring your own pillow or sleep in a room similar to your bedroom next time you sleep away from home.12. What did the new study published in Current Biology find?A. A comfortable bed could help people sleep well in a new environment.B. Most people could sleep well in a new environment after the first night.C. Brain activities affected people’s sleep in a new environment.D. The right brain determined how well people slept in a new environment.13. What was found out about the volunteers?A. Their left brains were more active on the first night.B. Their right brains became more active as days went by.C. Their right brains kept them awake the whole night.D. They slept better in the sleep lab than at home.14. What do the researchers think makes the brain sensitive to new things?A. The bad sleep experiences people have had.B. The tiredness that people suffer from in daytime.C. The imbalance between the two sides of the brain.D. The strangeness of the things that people come across15. What do the researchers think of “first night effect” ?A. It has evolved as a way to protect us.B. It’s a characteristic that animals don’t have.C. It’s completely different from the way animals sleep.D. It helps people to get used to new environments quickly.第二节（共5小题；每小题3分，满分15分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

山西省太原市第五中学2020届高三上学期阶段性检测(10月)数学(理) 含答案

太原五中2019—2020学年度第一学期阶段性检测高三数学（理）一、选择题：本题共12题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要 1. 2.设R ∈x ，则1>x 是1<x 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3.已知函数()()⎩⎨⎧>+-≤-=.1,1log ,1,222x x x x f x 且()3-=a f ，则()a f -6＝（）A.12 B. 0 C. 32 D. 32- 4.函数x x y ln 212-=的单调递减区间为（） A. ()1,1- B. ()0,1 C. ()1,+∞ D.()0,+∞5.若,,22ππαβ⎡⎤∈-⎢⎥⎣⎦，且sin sin 0ααββ->，则下列结论正确的是（） A. αβ> B. 0αβ+> C. αβ< D. 22αβ>）A. 等腰三角形B. 等边三角形C. 直角三角形D. 等腰直角三角形7.已知函数()()⎪⎭⎫ ⎝⎛<>+=2,0sin πϕωϕωx x f 的最小正周期是π，若将其图象向右平移3π个单位后得到的图象关于原点对称，则函数()x f 的图象（）C.关于点⎪⎭⎫ ⎝⎛0,12π对称D.关于点⎪⎭⎫ ⎝⎛0,125π对称 8.在直角△ABC 中，CD 是斜边AB 上的高，则下列等式不成立的是（）A ⋅=B ⋅=C⋅= D()()⋅⨯⋅=10.若存在正数x 使()12<-a x x 成立，则a 的取值范围是（）A ．(－∞，＋∞)B ．(－2，＋∞)C ．(0，＋∞)D ．(－1，＋∞)11.已知函数()83cos 22-++-=m m x m x x f 有唯一零点，则实数m 的值为（） A.2 B. 4- C.4-或2 D.012.已知()()R ∈+-=a ax x x f 1223在(0，＋∞) 内有且只有一个零点，则()x f 在[]1,1-上的值域为（）A. []4,0-B. []4,1-C. []1,3-D. 3,122⎡⎤-⎢⎥⎣⎦二、填空题：本题共4小题，每小题5分，共20分13.已知α为锐角，且7sin 2cos2αα=，则cos α=_________.14.设当θ=x 时，函数()x x x f cos 2sin -=取得最大值，则θcos =_________.15.如图，已知四边形ABCD 是边长为4的正方形，动点P 在以AB为直径的圆弧APB 上，则PC →·PD →的取值范围是________．16.已知函数()12+--=-x e e x f x x ,若对于R ∈∀x ，不等式()()222>++ax f a x f 恒成立，则实数a 的取值范围为________.三、解答题：共70分。

2020山西省太原五中高三上学期阶段性检测(9月)数学(理)试卷

太原五中2019—2020学年度第一学期阶段性检测高三数学(理)出题人：张福兰校对人：王琪时间：2019.9一、选择题：本题共12题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1. 已知集合{|lg 0},{|21}xA x xB x =≤=≤则A B =（） A.(,1)-∞ B.(,1]-∞ C.(1,)+∞ D.[1,)+∞ 2.下列函数在其定义域上既是奇函数又是增函数的是（）A.()2xf x = B.()||f x x x = C.1()f x x=-D.()lg ||f x x = 3.函数)y x =-的定义域为（）A.（0,1）B.[0,1)C.(0,1]D.[0,1] 4.已知命题p ：存在正数M,N,满足lg()lg lg M N M N +=+；命题q ：对满足11a a >≠且的任意实数a ,2log 2log 2a a +≥.则下列命题为真命题的是（） A. ()p q ∧⌝ B. p q ∧ C. p q ⌝∧ D. p q ⌝∨5.已知13241,log 3,log 72a b c ⎛⎫=== ⎪⎝⎭，则a ，b ，c 的大小关系为（）A ．a ＜b ＜cB ．b ＜a ＜cC ．c ＜a ＜bD ．a ＜c ＜b6.由曲线32,x y x y ==围成的封闭图形面积为（）A.121B.41C.31D.127 7.若函数()log (2)(0,1)a f x ax a a =->≠在区间()1,3内单调递增，则a 的取值范围是（）A ．2[,1)3B ．2(0,]3C ．3(1,)2D ．3[,)2+∞8.已知函数()4f x x =+，x x x g 2)(2-=，(),()()()(),()()f x f xg x F x g x f x g x ≥⎧⎪=⎨<⎪⎩，则)(x F 的最值是（）A ．最大值为8，最小值为3；B ．最小值为-1，无最大值；C ．最小值为3，无最大值；D ．最小值为8，无最大值．xA ．①④②③ B．①④③② C．④①②③ D．③④②①10.“a ≤－1”是“函数f (x )＝ln x ＋ax ＋1x在[1，＋∞)上为单调函数”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11.函数()f x 在(0,)+∞上单调递增，且(2)f x +关于2x =-对称，若(2)1f -=，则(2)1f x -≤的x 的取值范围是（）A ．[2,2]-B ．(][),22,-∞-⋃+∞ C ．(][),04,-∞⋃+∞D ．[0,4] 12.已知'()f x 是函数()f x 的导函数，且对任意的实数x 都有()()()e 23x f x x f x '=++，()01f =，则不等式()5x f x e <的解集为（）A ．()4,1-B ．(1,4)-C ．(,4)(1,)-∞-+∞UD ．(,1)(4,)-∞-+∞二、填空题：本题共4小题，每小题5分，共20分13.已知函数211log (2),1()2,1x x x f x x -+-<⎧=⎨≥⎩，则2(2)(12)f f log -+=14.命题“(1,2)x ∃∈，使得不等式240x mx ++≥”是假命题，则m 的取值范围为__________高三数学(理) 第3页(共4页) 高三数学(理) 第4页(共4页)15.已知函数2|log |,02()sin(),2104x x f x x x π<<⎧⎪=⎨≤≤⎪⎩，若存在实数1234,,,x x x x ，满足1234x x x x <<<，且1234()()()()f x f x f x f x ===，则3412+x x x x 的值是 . 16.已知函数13,(1,0]1()3,(0,1]x x f x x x ⎧-∈-⎪+=⎨⎪∈⎩，且函数()()g x f x mx m =--在(1,1]-内有且仅有两个不同的零点，则实数m 的取值范围是________.三、解答题：共70分。

山西省太原市第五中学2020届高三数学上学期11月阶段性考试试题理【含答案】

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山西省太原市第五中学2020届高三上学期阶段性检测(10月月考)英语试卷含答案

太原五中2019—2020学年度第一学期阶段性检测高三英语出题人、校题人：史海玲荆晋慧张旭军王轶芳郝媛(2019.10.9)第一部分阅读理解（共两节，满分60分）第一节（共15小题；每小题3分，满分45分）(A)Many of us know about Russia’s Lake Baikal from our textbooks, or by listening to Chinese singer Li Jian’s hit song, Lake Baikal. But over the past decade, the world’s deepest freshwater lake has been in the spotlight for an extreme sport.Each March since 2005, about 150 people from around the world sign up for the Baikal Ice Marathon. They come to explore the lake’s breathtaking beauty and challenge themselves in unpredictable conditions.The 26-mile (41. 84-kilometers) journey starts on the lake’s eastern shore. In March, the ice is a meter thick and iron-hard. Runners cross this frozen surface, finishing on the western side of the lake.Known as the “blue eye of Siberia”, Lake Baikal has exceptionally clear waters. This means its ice is almost perfectly transparent. “Seen from above, a runner on the ice looks as if he or she is jogging through space,” The New York Times noted.Th e landscape might be beautiful, but it’s also harsh. Strong winds blast (侵袭) across the lake and frostbite (冻伤) can occur within half an hour. Runners say the cold climate is what draws them. They want to test their limits.“When you are in such an environment, you don’t have cars around you, you don’t have the noise around. I think these extreme races allow you to be alone with nature,”Alicja Barahona, a 64-year-old runner from the US, told ABC News.The location offers some strange and unique characteristics for this marathon. The finish line is visible from the start. But the endless white offers no progress markers. The race also ends with little fanfare (喧闹). Tourists crowding the ice are mostly addicted to snapping series (自拍) and just ignore the runners.For some runners, the absence of spectators makes the ra ce more challenging, because it’s lonely. They must fight with themselves. “You are alone on Bai kal. It is your race. You are alone with yourself. All you need to do is to defeat yourself,” Veronique Messina, a French runner, told the Telegraph.1. What can we know about the Baikal Ice Marathon from the text?A. It takes runners from the northern end to the southern end of the lake.B. It involves extreme weather and beautiful scenery.C. It attracts more and more participants each year.D. It is about 26 kilometers in length.2. How does the Baikal Ice Marathon differ from other marathons?A. Only men are allowed to run in this race.B. The runners can see the finish line from the start.C. The runners are often distracted by tourists.D. There are many progress markers on the ice.3. What is the most difficult part of the race for Messina?A. Loneliness.B. The long distance.C. The cold climate.D. Noisy surroundings.(B)In 1972, a social worker named Sanjit Bunker Roy founded Barefoot College in Tilonia, Rajasthan. Today the college trains women from villages for six months to build and maintain solar panels and other instruments. Barefoot College also offers education to the younger generation both during the day and at its solar bridge schools that meet by lamplight at night.The philosophy of Barefoot College is largely inspired by the principles of Gandhi, starting with equality beyond caste (种姓), gender or religion. As a matter of fact, women are prioritized (优先考虑) as an underserved population that is essential to bringing villages together. Another central principle of the college is self-reliance, teaching students to support and think for themselves.After the college’s female students have completed their half-year of training, they return to their villages where they wait for solar panel parts to arrive from the college. Once they have all the pieces they need, they construct the panels and begin collecting solar energy. For each village, the college also provides solar lamps. Villagers can, in addition, order parts for other solar-powered devices, such as water heaters and cooking stoves. Once assembled, they and the lamps are powered by the solar panels.The effect on the villages is huge. Before the solar panels and lamps arrived, villagers had only candles to light their homes. This prevented adults from doing serious work at night, and it made studying difficult for children as well. As for physicians, they had difficulty treating patients and performing operations at night because they had to rely on flashlights.Now there is power for not only the electrical appliances that the college provides but also devices like televisions, radios and computers. For the first time, the villagers can even connect to the world through the Internet.4. What does this text explain about the college?A. How it accomplishes its goals.B. How its global efforts are funded.C. How its founder hires employees.D. How it works with the government.5. Which idea is communicated by the college to women?A. They should be more involved in politics.B. They don’t have to depend on others.C. They aren’t educating their daughters enough.D. They focus too much on their communities.6. Which role do the women play after they return to their villages?A. They’re merchants.B. They’re composers.C. They’re technicians.D. They’re journalists.7. In the past, what was hard to provide in villages after dark?A. Dry shelterB. Clean waterC. Medical careD. Food supplies(C)高三英语第3页(共22页)高三英语第4页(共22页)Imagine you are opening your own company and want to hire a manager. You have two candidates and they are both capable and experienced, so who would you rather hire: Julia Watson or Shobha Bhattacharva? Chances are that you would prefer Watson, right? But why?“Easy names are evaluated as more familiar, less risky and less dangerous, ” Eryn Newman, a scientist at Victoria University of Wellington, New Zealand, told Scientific American. As a result, people with easier names are often assumed to be more trustworthy. This is what Newman and her teammates have found in their recent study.In the experiment, they picked 18 different foreign names, including difficult-to-pronounce ones like Yevgeni Dherzhinsky and easy names like Bodo Wallmeyer. They then attached each name with a statement such as “turtles are deaf” and “giraffes are the only mammals that cannot jump”and asked volunteers whether they thought the claims were true.The results showed that claims connected to easier names were more often ranked as believable than those attributed to difficult names, regardless of what the truth really was. In fact, previous studies have already found that our judgments about products can be affected by their names. For example, we tend to think of a food additive (添加剂) with an easier name as safer and a stock with an easier name as more lucrative (利润丰厚的)，according to Medical Daily.But researchers pointed out that this effect can change depending on where someone comes from. For example, a native British ma n may find “Yevgeni Dherzhinsky” hard to pronounce while Russian people could say it without effort. Newman hopes that this finding can make us better see our biases (偏见). It’s not just unfair to people that we make judgments based on gut feelings (直觉) rather than facts, and it can sometimes have serious consequences.For example, we may choose to believe certain eyewitnesses in court simply because their names sound more trustworthy even if they are actually lying. Or, we may let go of qualified job candidates due to their “difficult” names.Now, if you could make that decision again, would you still prefer Julia Watson to Shobha Bhattacharva?8. What did Newman and her teammates discover in their experiment?A. V olunteers with easier names were more likely to choose true claims.B. A difficult name doesn’t influence the way the volunteers viewed the claims.C. V olunteers trusted claims paired with easy names more often.D. Volunteers trusted claims connected with difficult names.9. The underlined w ords “this effect” in Paragraph 5 refer to the effect ______.A. names have on peoples judgmentsB. gut feelings have on people from different placesC. of decisions made based on factsD. of people’s biases against certain types of people10. What can we conclude from the last paragraph?A. We should think twice before we make a decision.B. The harder your name is to pronounce, the more likely it is you will get a job.C. Judging people based on their names may cause serious problems.D. Russian s have less bias against people’s names than the British.11. What is probably the best title for the text?A. Names Affect ProductsB. Employers Prefer Shobha BhattacharvaC. Difficult Names are TrustworthyD. Easy Names Win Out(D)Many of us have had this experience: we lie down in a bed other than our own, perhaps at a friend’s house or in a hotel room, and find it difficult or impossible to fall asleep. Is it because the bed is uncomfortable? Maybe, but perhaps there can be other reasons.According to a new study published in Current Biology, a significant reason is what the scientists call “first night effect”. They believe that one side of the brain acts as a “night watch”to warn us about potential dangers. It forces us to stay awake on the first night in a new environment. For the study, 35 young volunteers were asked to sleep in a sleep lab for several days. Meanwhile, researchers watched their brain activities.According to the researchers, on their first night, the left brains were more active than the right brains and people had a hard time sleeping. However, left-brain activity decreased as days went by, falling even to the point of complete calm. In this process, the participants got an increasingly better sleep experience.The findings suggest that the different rhythms (5%) of the sides of the brain affect our sleep. When the two sides work differently, the balance between them is broken. Thus, the brain can’t relax and is sensitive to anything strange in the surroundings, just as it is in daytime.“At some level, the brain is continuing to analyze things, even though you are not aware of the ana lysis, ”US professor Jerome Siegel told Smithsonian Magazine. “If something unusual happens --- if a door opens or you hear a key in a lock--- you can be alert, even though the intensity of the stimulus (刺激) is quite low.”More surprisingly, this phenomenon is similar to the way some animals sleep. Whales, dolphins, and many birds can sleep with half of their brain while the other half stays awake, with its corresponding eye staying open.The researchers think that it is the result of evolution, and works to protect us in potentially dangerous environments.If you have ever had what you think is “first night effect”, researchers suggest that you bring your own pillow or sleep in a room similar to your bedroom next time you sleep away from home.12. What did the new study published in Current Biology find?A. A comfortable bed could help people sleep well in a new environment.B. Most people could sleep well in a new environment after the first night.C. Brain activities affected people’s sleep in a new environment.D. The right brain determined how well people slept in a new environment.13. What was found out about the volunteers?A. Their left brains were more active on the first night.B. Their right brains became more active as days went by.C. Their right brains kept them awake the whole night.D. They slept better in the sleep lab than at home.14. What do the researchers think makes the brain sensitive to new things?A. The bad sleep experiences people have had.B. The tiredness that people suffer from in daytime.C. The imbalance between the two sides of the brain.D. The strangeness of the things that people come across高三英语第7页(共22页)高三英语第8页(共22页)15. What do the researchers think of “first night effect” ?A. It has evolved as a way to protect us.B. It’s a characteristic that animals don’t have.C. It’s completely different from the way animals sleep.D. It helps people to get used to new environments quickly.第二节（共5小题；每小题3分，满分15分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

山西省太原市第五中学2020届高三上学期11月阶段性考试语文答案

太原五中2019—2020学年度第一学期阶段性检测高三语文参考答案（2019.11）1.A（B强加因果。

C或然变必然，缺少了“据有的学者说”“如所说无误”。

D以偏概全，少了修饰语“某些”。

）2.B（“比喻论证”错。

）3.D（“原始社会”错，文章第5段末句“它却打破了神话只能和原始社会同终始、不能进入阶级社会的旧说。

”）4.D（D项，“年轻人不愿意留在农村”“向往城市生活”表述不当，考生需要明确一个概念，就是“新生代流动人口”不仅包括农村里的年轻人，也包括城市中的年轻人。

）5.B（B项，“隐约地表达了对流动人口减少而导致城市劳动力不足的担忧”于文无据。

）6.（6分）①产业转移。

劳动密集型产业和资源密集型产业向中西部地区转移，以前传统型的劳动者也伴随产业转移而回到离家更近的城区就业，从而使流动人口减少。

②劳动力结构的优化。

随着产业结构的不断优化、产品结构的逐步多元化，传统的生产经营已经很难满足市场需求，只会从事简单劳动的劳动者也逐渐失去了优势。

③国家一系列政策的实施。

党的十八大之后，中央实行了一系列的政策，如“有序推进农业转移人口市民化”“确保农村贫困人口全部脱贫”，让农民愿意留在农村，建设自己的家乡。

④新生代流动人口愿意把户口迁入流入地。

新生代流动人口表现出对城市社会较好的适应性与较高的融入意愿，他们喜欢现在居住的城市。

（每点2分，答出3点即可）7.B（对主题理解错误。

）8.（6分）①热爱文学，直率真诚：七十高龄仍热衷于鼓励文学青年的文学梦，主动承担零售杂志的任务。

②做事执着，不屈不挠：对方不接电话他会一直拨打，对文学的热爱一生不变。

③公私分明，正直认真：别人看不上的四十元零五角钱，他认真报账，不占公家一分钱便宜。

④古道热肠，见义勇为：看到小偷偷的即使是块石头，他也绝不姑息，奋力追回。

（答出1点给2分，答出3点即可给6分。

）9.（6分）①讲述故事：小说故事是由“我”叙述出来的，真实可信。

②推进情节：“我”是事件的参与者，由于“我”的轻视和处理方式，情节得以发展变化。

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山西太原五中2020届高三上学期阶段性检测山西太原五中2020届高三上学期阶段性检测一、现代文阅读（36分）（一）论述类文本阅读（本题共3小题，9分）阅读下面文字，完成1～3题。

中国绘画发展到了相对成熟的北宋以后，除了民间画家、宫廷画家等创作群体外，还出现了诗人、士大夫等各类文化人参与创作的现象。

他们以自身文化人的气质，崇尚和追求唐代诗人兼画家王维作品中所蕴含的“诗中有画，画中有诗”的艺术境界。

在绘画创作中，他们以诗人的思考方式，把表现对象提升到诗的艺术境界，创作了很多为后人惯称的“文人画”。

诗人的思考方式，实际上就是中国文人画家基于中国传统画论中东晋大画家顾恺之所言的“迁想妙得”，及后来唐代画家张璪所言的“外师造化，中得心源”的绘画理论，将表现的对象在心中“迁想”成诗的艺术形象的思维过程。

中国文人画家的这种诗人的思考方式，是大文化学养背景下成就的结果。

诗人和音乐家一样，在感情世界里是最敏感的人群，他们所创作的文人画相较西方画家以科学家的思考方式所表现的科学的艺术形象而言，更接近感情的本质，也更显得纯洁与透明。

中国的文人画家在具体创作中，以顾恺之提出的“传神”的艺术理念为要求，以追求作品的出神入化为最终目的。

如宋代画家梁楷所画的《布袋和尚图》和《泼墨仙人图》，以两种粗细不同的艺术手段，表现诙谐而玩世不恭的人物形象。

另外，中国文人画家又以诗人的拟人化手段将表现的对象人格化。

如明代画家徐渭在《墨葡萄图》中所表现的“笔底明珠无卖处，闲抛闲掷野藤中”。

基于大文化学养背景的文人画家创作的文人画，在具体的画面处理中，比单纯追求形象与色彩变化的西方绘画艺术显得更有广度和深度。

他们不仅追求表现对象的“实”处，还以太极中“阴阳”的理念追求其相对“虚”的空间；进而提出了“计白当黑”的画论，将表现的形象延伸到一个更大的审美空间，达到了“此时无声胜有声”的诗意境界。

如八大山人的《鱼鸭图卷》、齐白石的《雏鸡》等作品。

中国的文人画家以大文化学养背景铸就了“心旷神怡、超然物外”的冲淡平和的心态，所以在作品中容易叙述心灵的情怀。

如宋代米友仁的《潇湘奇观图》表现的“山色空蒙雨亦奇”的境界，元代画家吴镇的《渔父图卷》表现的“斜风细雨不须归”的超然境界。

中国的文人画家在诗、文、书法等各方面的学养上往往都有很高的造诣。

中国文人画，那种集诗、书、画于一体的绘画形式，在世界绘画史上是绝无仅有的。

文人画不但是中国古代文明在绘画中的综合体现，而且是世界绘画史皇冠上的明珠。

这些传世优秀的文人画作品，足以与晋唐的书法及唐诗宋词，共同构成中国文化史上三大具有代表性的板块。

（摘编自了庐《文人画是用诗人的思考方式去绘画，源于“迁想妙得”》）1．下列关于原文内容的理解与分析，不正确的一项是（3分）A．王维作品中蕴含的“诗中有画，画中有诗”的艺术境界是北宋以后参与绘画创作的各类文化人崇尚的。

B．诗人的思考方式，是指中国文人画家基于中国传统画论，将表现的对象“迁想”成诗的艺术形象的思维过程。

C．诗人创作的文人画相较于西方画家以科学家的思考方式所表现的科学的艺术形象，显得更纯洁。

D．中国文人画在世界绘画史上的地位，足以使其成为中国文化史上三大具有代表性的板块之一。

2．下列对原文论证的相关分析，不正确的一项是（3分）A．对于文人画，文章先交代产生的背景，接着逐层分析，最后指出文人画的成就及其地位。

B．文章第三段从两个方面分析文人画家具体创作过程中的表现以及其主要特点，并以实例来论证。

C．文章在论述中把文人画和西方绘画艺术作比较，指出文人画家主要追求表现对象相对“虚”的空间。

D．文章用文人创作的作品来论证分析，文人画家因其大文化学养背景铸就出来的独特的艺术境界。

3．下列关于原文内容的理解和分析，不正确的一项是（3分）A．宋代梁楷的《泼墨仙人图》，运用粗放的艺术手段“传形”，借助细腻的艺术手段“传神”，追求出神入化的效果。

B．明代徐渭在《墨葡萄图》中所表现的“笔底明珠无卖处，闲抛闲掷野藤中”，人格化了表现对象。

C．齐白石的《雏鸡》践行“计白当黑”的画论，延伸了审美空间，达到了“此时无声胜有声”的诗意境界。

D．宋代米友仁因为铸就了冲淡平和的心态，所以在《潇湘奇观图》中叙述了“山色空蒙雨亦奇”的情怀。

（二）实用类文本阅读（本题共3小题，12分）阅读下面的文字，完成4～6题。

材料一：“双元制”是一种国家立法支持、校企合作共建的办学制度。

所谓“双元”，是指职业培训要求参加培训的人员必须经过两个场所的培训。

“一元”是指职业学校，其主要职能是传授与职业有关的专业知识；“另一元”是指企业或公共事业单位等校外实训场所，其主要职能是让学生在企业里接受职业技能方面的专业培训。

“双元制”职业教育不同于一般的大学教育。

大学教育重视理论学习，是学科体系，而“双元制”职业教育以岗位要求为培训目标，更加重视学生的实践能力。

这种侧重实践的教育形式非常受欢迎，很多年轻人选择“双元制”教育培训，而不是去上大学。

“双元制”教学体制使得学生和企业有了更多的交流机会，大大提高了学生培训后就业的能力，有利于为劳动市场输送大量合格的劳动力。

（摘编自网络，有删改）材料二：职业教育主要关注点分布（摘自环球网《大数据透视两会教育热点─2019年全国两会教育热点问题分析报告》）材料三：最近，湖北潜江一所职业教育学院设立了“小龙虾专业”，该专业的学生还没毕业就被“销售一空”，薪酬也着实可观。

细品“小龙虾学院”这道“菜”，不难咂摸出这样的“味道”：接地气、把握市场脉搏的职业教育其实有很广阔的前景。

一直以来，就业市场存在结构矛盾：一边是大学生面临就业难，一边是企业面临招工难、用工荒。

劳动力需求与供给之间“错位”。

这恰恰说明经济社会发展需要大批技术、技能型人才，只有大力发展职业教育，培养大量高素质劳动者和应用型人才，才能从根本上解决这一问题。

近年来，对“工匠精神”的呼唤成为社会共识。

能力是最好的学历，本事是最大的优势。

职业教育的大发展，也需要在劳动观、价值观上进行一场深刻的革命。

消除偏见和误解的坚冰，让广大青年凭一技之长实现人生价值，让各行各业的劳动者都拥有尊严与荣光，创新、创业、创造的无穷活力必然会竞相迸发。

（摘编自《“小龙虾学院”折射职业教育“大前景”》，有删改）材料四：3月15日，2019年全国两会落下帷幕。

今年的政府工作报告提出“改革完善高职院校考试招生办法，鼓励更多人报考”“支持企业和社会力量兴办职业教育”等，这些重要举措迅速抬升了职业教育舆情热度，使之成为今年两会期间教育主题。

两会前，国务院印发《国家职业教育改革实施方案》引发热议。

《方案》指出，从2019年开始，在职业院校、应用型本科高校启动“学历证书+若干职业技能等级证书”制度试点工作。

经过5～10年时间，职业教育基本完成由政府举办为主向政府统筹管理、社会多元办学的格局转变，由参照普通教育办学模式向企业社会参与、专业特色鲜明的类型教育转变，大幅度提升新时代职业教育现代化水平，为促进经济社会发展和提高国家竞争力提供优质人才资源支撑。

《方案》要求，要加强党对职业教育工作的全面领导，做好职业教育改革组织实施和相关保障工作。

提高技术技能人才待遇水平，健全经费投入机制，加强职业教育办学质量督导评价。

（摘编自新华社《国家职业教育改革实施方案》，有删改）4.下列对材料相关内容的理解，不正确的一项是（3分）A.与一般的大学教育重视理论学习相比，以岗位要求为培训目标的“双元制”教育模式更加重视学生的实践能力。

B.职业教育学院设立“小龙虾专业”的事情说明，在经济社会中能够培养应用型人才、把握市场脉搏的专业前景广阔。

C.两会前，国务院印发《国家职业教育改革实施方案》引发热议，使职业教育成为今年两会期间教育主题。

D.今后，我国将大幅提升新时代职业教育现代化水平，职业教育将为促进经济社会发展和提高国家竞争力做出贡献。

5.下列对材料相关内容的概括和分析，正确的一项是（3分）A.“双元制”教学体制下的学生和企业有更多交流机会，具有更强的就业能力，较其他大学生更受企业欢迎。

B.从材料二看，职业教育招生制度舆论关注度最高，说明国家对职业教育越来越重视，职业教育前景广阔。

C.随着人们劳动观、价值观的转变，我国将会有越来越多的年轻人选择职业教育培训，而不是去上大学，市场将越来越重能力而轻学历。

D.大力发展职业教育，培养大量高素质劳动者和应用型人才，是解决我国就业市场结构性矛盾的根本途径。

6.根据上述材料，谈谈我国为进一步办好新时代职业教育，可采取哪些具体措施。

（6分）（三）文学类文本阅读（本题共3小题，15分）阅读下面的文字，完成7～9题。

断桥蒋寒接连两场暴雨，上百年的古桥，被山洪毁了。

洪水将山寨与外界天各一方，孩子们上学，大人们赶集，只能靠树杆、木梯、竹竿慢慢爬过去了。

村民们找到郭支书，请他拿主意。

郭支书住在山寨对岸的郭家坨，郭家坨地势高，再大的洪水也奈何不了它。

郭支书听了村民的反映，吧嗒着旱烟，思忖着，不急。

乡亲们急啊，挤了他家满满一屋子，支书娘子忙着为大家沏茶添水。

山寨丙成代表大伙说：“就那样断着，不是个事啊！大人进进出出好办，娃娃们上学呢？你不是常说，一切为了下一代嘛！”郭支书伸出两指捻了捻火星闪动的旱烟，吧嗒着，不吭声。

有人小声说：“我们知道，你肯定还在生大伙的气。

入夏以来，见你没少往古桥下跑，东瞅瞅，西敲敲，大伙说你是盼着古桥垮了，好向上面申请救济款，以便从中捞……”声音小得没人听得见。

屋外的大狼狗汪汪地叫了，天空还是阴沉沉的。

天气预报说了，近期还将有持续暴雨，省、市、县层层拉响了防汛警报。

村委会也早作了安排，这会儿，马主任正带着工作队现场走访……丙成说：“郭书记，你大人大量，快替大家拿个主意吧。

上面要不拨款，我们各家凑也行。

”郭支书翻大伙一眼，说：“钱，我来想办法，力，大家得出。

”“要得要得！”大伙就兴高采烈地散了。

有人见，第二天一早，郭支书拎着包朝镇上去了。

几天后回村，他就给望眼欲穿的乡亲们一个天大的喜讯：修桥款弄到了，钢筋水泥什么的都联系好了，接着就送来，天晴就动工……时不我待，趁着阳光天气，两台吊车就轰轰隆隆开进断桥现场，洪水也下降了许多，山寨老少能动的都出来了，大伙说说笑笑，干得热火朝天……郭支书和马主任在现场指挥。

马主任抹了抹烟嘴，递给郭支书，白烟就从郭支书的鼻孔里冒出来，一脸欣慰。

马主任感慨道：“老伙计啊，真是难为你了，镇上县上一毛不拔，得亏你家老大开明啊，从自己公司支持50万。

”郭支书笑：“我们养育下一代图啥，不就是为我们修桥修路修康庄大道嘛。

”马主任向他竖起了大拇指。

半个月之后，一座崭新的现代大桥就牢牢地架在了天河上，连接着山寨与外面的世界。

可是随后，村里传出了关于郭支书的风言风语，说是郭支书这回准是贪了不少上面的修桥款，有人甚至闹着要找郭支书讨工钱。