2019年七宝中学高一期末

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上海市七宝中学高一数学理期末试题含解析

上海市七宝中学高一数学理期末试题含解析一、选择题：本大题共10小题，每小题5分，共50分。

在每小题给出的四个选项中，只有是一个符合题目要求的1. 函数y=Asin（ωx+φ）（A＞0，ω＞0）的部分图象如图所示，则f（1）+f（2）+f（3）+…+f （11）的值等于（）A．2 B．2+C．2+2D．﹣2﹣2参考答案：C【考点】由y=Asin（ωx+φ）的部分图象确定其解析式．【分析】根据图象，求出函数的解析式，结合函数周期性的性质进行转化求解即可．【解答】解：由图象知A=2，T=4×2=8，即=8，则ω=，即f（x）=2sin（x+φ），由五点对应法得×2+φ=，即φ=0，则f（x）=2sin（x），则f（1）+f（2）+f（3）+…+f（8）=0，则f（1）+f（2）+f（3）+…+f（11）=f（1）+f（2）+f（3），∵f（1）=2sin=2×=，f（2）=2sin（×2）=2sin=2，f（3）=2sin（×3）=2×=，∴f（1）+f（2）+f（3）=2+2，即f（1）+f（2）+f（3）+…+f（11）=2+2，故选：C．2. 设函数，集合，设，则（）A． B． C． D．参考答案：D略3. 已知f(x)在R上是奇函数，且满足f(x+4)=f(x), 当x∈(0,2)时，f(x)=2x2,则f(7)等于（）A．-2 B．2 C．-98 D．98参考答案：A略4. 函数y=的定义域为（）A．（﹣B．C．D．参考答案：B【考点】函数的定义域及其求法．【分析】两个被开方数都需大于等于0；列出不等式组，求出定义域．【解答】解：要使函数有意义，需，解得，故选B．5. 已知是函数的一个零点.若，则 ( ) A．B．C．D．参考答案：B6. 已知a=0.23.5，b=0.24.1，c=e1.1，d=log0.23，则这四个数的大小关系是（）A．a＜b＜c＜d B．a＞b＞c＞d C．d＜b＜a＜c D．b＞a＞c＞d参考答案：C【考点】对数值大小的比较．【分析】利用指数函数、对数函数的单调性求解．【解答】解：∵y=0.2x是减函数，3.5＜4.1，a=0.23.5，b=0.24.1，∴1=0.20＞a＞b＞0，c=e1.1＞e0=1，d=log0.23＜log0.21=0，∴d＜b＜a＜c．故选：C．7. 三个数0.76，60.7，log0.76的大小关系为（）A．0.76＜log0.76＜60.7 B．0.76＜60.7＜log0.76C．log0.76＜60.7＜0.76 D．log0.76＜0.76＜60.7参考答案：D【考点】指数函数单调性的应用．【分析】由对数函数的图象和性质，可得到log0.76＜0，再指数函数的图象和性质，可得0.76＜1，60.7＞1从而得到结论．【解答】解：由对数函数y=log0.7x的图象和性质可知：log0.76＜0由指数函数y=0.7x，y=6x的图象和性质可知0.76＜1，60.7＞1∴log0.76＜0.76＜60.7故选D8. 若，，则 ( )A． B．0 C．1 D ．2参考答案：A略9. 的展开式中的系数是A．B．C．D．参考答案：D略10. 已知函数，若函数g（x）=f（x）﹣m有三个不同的零点，则实数m的取值范围为（）A．B．C．D．参考答案：C【考点】函数的零点与方程根的关系．【分析】原问题等价于函数y=f（x）与y=m的图象有三个不同的交点，作出函数的图象，数形结合可得答案．【解答】解：函数g（x）=f（x）﹣m有三个不同的零点，等价于函数y=f （x ）与y=m 的图象有三个不同的交点，作出函数f （x ）的图象如图：由二次函数的知识可知，当x=时，抛物线取最低点为，函数y=m 的图象为水平的直线，由图象可知当m∈（，0）时，两函数的图象有三个不同的交点，即原函数有三个不同的零点，故选C二、填空题:本大题共7小题,每小题4分,共28分11. 计算下列几个式子，结果为的序号是．①tan25°+tan35°tan25°tan35°，②，③2（sin35°cos25°+sin55°cos65°），④．参考答案：①②③【考点】两角和与差的正切函数．【分析】先令tan60°=tan （25°+35°）利用正切的两角和公式化简整理求得tan25°+tan35°=（1﹣tan25°tan35°），整理后求得tan25°+tan35°+tan25°tan35°=；②中利用正切的两角和公式求得原式等于tan60°，结果为；③中利用诱导公式把sin55°转化才cos35°，cos65°转化为sin25°，进而利用正弦的两角和公式整理求得结果为，④中利用正切的二倍角公式求得原式等于，推断出④不符合题意．【解答】解：∵tan60°=tan （25°+35°）==∴tan25°+tan35°=（1﹣tan25°tan35°） ∴tan25°+tan35°tan25°tan35°=，①符合═tan （45°+15°）=tan60°=，②符合2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=，③符合=tan=，④不符合故答案为：①②③12. 设函数f （x ）=mx 2﹣mx ﹣1．若对一切实数x ，f （x ）＜0恒成立，求实数m 的取值范围．参考答案：【考点】6E ：利用导数求闭区间上函数的最值．【分析】通过讨论m=0成立，m≠0时，结合二次函数的性质求出m 的范围即可．【解答】解：m=0时f （x ）=﹣1＜0成立，或 m≠0时，结合题意得：，解得：﹣4＜m≤0，因此实数m 的取值范围（﹣4，0]．13. 定义在R 上的函数f （x ）既是偶函数又是周期函数，若的最小正周期是π，且当x∈（0，）时，f （x ）=sinx ，则= ．参考答案：【分析】由题意利用函数的周期性偶函数，转化为f （），即可求出它的值．【解答】解：定义在R 上的函数f （x ）既是偶函数又是周期函数，若f （x ）的最小正周期是π，且当x∈（0，）时，f （x ）=sinx ，所以=f （﹣）=f （）=sin=．故答案为：．14. 函数的极大值为_________。

2018-2019学年上海市闵行区七宝中学高一下学期期末数学试题(解析版)

2018-2019学年上海市闵行区七宝中学高一下学期期末数学试题一、单选题1．已知{}n a 、{}n b 都是公差不为0的等差数列，且lim 2nn na b →∞=，12n n S a a a =++⋯+，则22lim nn nS nb →∞的值为（） A ．2B ．-1C ．1D ．不存在【答案】C【解析】首先根据lim 2n n n a b →∞=求出数列{}n a 、{}n b 公差之间的关系，再代入22lim nn nSnb →∞即可。

【详解】因为{}n a 和{}n b 都是公差不为零的等差数列，所以设()()11121?1n n b b n d a a n d =+-=+- 故()()11121limlim 21nn n n a n d a b b n d →∞→∞+-==+-，可得122d d =又因为()112112n n n d a a a na -+++=+和()21121n b b n d =+-代入则()()1112122122lim lim 21212n n n nn n d na S d nb nb n n d d →∞→∞⎛⎫-+ ⎪=⨯== ⎪+- ⎪ ⎪⎝⎭．故选：C ．【点睛】本题主要考查了极限的问题以及等差数列的通项属于基础题。

2．设{}n a 是公比为()01q q <<的无穷等比数列，若{}n a 的前四项之和等于第五项起以后所有项之和，则数列21{}n a -是（） A ．公比为12的等比数列B ．公比为2的等比数列C ．公比为2或2-的等比数列D的等比数列【答案】B【解析】根据题意可得42n S S =，带入等比数列前n 和即可解决。

【详解】根据题意，若{}n a 的前四项之和等于第五项起以后所有项之和，则42n S S =，又由{}n a 是公比为()01q q <<的无穷等比数列，则()4111211a q a q q-=--，变形可得412q =，则q =，数列{}21n a -为{}n a 的奇数项组成的数列，则数列{}21n a -为公比为2q =列；故选：B ．【点睛】本题主要考查了利用等比数列前n 项和计算公比，属于基础题。

【35套试卷合集】上海市七宝中学2019-2020学年数学高一上期末模拟试卷含答案

2019-2020学年高一上数学期末模拟试卷含答案一、选择题（每小题5分，12小题，共60分。

每小题均只有唯一正确答案） 1. 已知集合M ＝{x|x ＜3}，N ＝{x |122x>}，则M ∩N 等于（） A ． ∅B. {x|0＜x ＜3}C. {x|－1＜x ＜3}D. {x|1＜x ＜3}2.下列各组函数中，表示同一函数的是（） A ．01,y y x ==B．y y x ==C ．33,x y x y ==D ．2)(|,|x y x y ==3.有以下四个结论 ① lg10=1；②lg(lne)=0；③若10=lgx ，则x=10； ④ 若e=lnx ，则x=e 2，其中正确的是（） A. ①③ B.②④ C. ①② D. ③④ 4.函数x xx y +=的图象是（）5.设函数3y x =与212x y -⎛⎫= ⎪⎝⎭的图象的交点为00()x y ，，则0x 所在的区间是（）A ．(01)，B ．(12)，C ．(23)，D ．(34)，6.已知直线l 上两点,A B 的坐标分别为(3,5),(,2)a ,且直线l 与直线3450x y +-=垂直，则a 的值为（）A .34-B .34C .43-D .437.函数()1xf x =-e 的图象大致是（）A B C D8.函数1()ln 2f x x =+的零点所在的区间是（）A.42(,)e e --B.2(,1)e - C.2(1,)e D.24(,)e e9.下列函数中既是奇函数又是(1,)+∞上的增函数的是 A. ()22xxf x -=+ B.()22xx f x -=-C.()ln f x x x =+D.()ln ||f x x x =10.经过点(－3,2)，倾斜角为60°的直线方程是( )． A ．y ＋2＝3(x －3) B ．y －2＝33(x ＋3)C ．y －2＝3(x ＋3)D ．y ＋2＝33(x －3) 11.若直线x －y ＝2被圆(x －a)2＋y 2＝4所截得的弦长为22，则实数a 的值为( )． A ．－1或 3B ．1或3C ．－2或6D ．0或412.已知圆()()221:231C x y -+-=,圆()()222:349C x y -+-=,,M N 分别是圆12,C C 上的动点,P 为x 轴上的动点,则PM PN +的最小值为（） A．4B1C．6-D二、填空题（每小题5分，4小题，共20分。

精品解析：上海市七宝中学2019届高三上学期期末考试数学试题(解析版)

2019年上海市闵行区七宝中学高考数学一模试卷注意事项：1、答题前，考生务必先将自己的姓名、准考证号填写在答题卡上，认真核对条形码上的姓名、准考证号，并将条形码粘贴在答题卡上的指定位置上。

2、选择题答案使用2B铅笔填涂，如蒞改动，用橡皮搽干净后，再选涂其它答案的标号；非选择题答案使用0.5毫米的黑色中性（签字）笔或碳素笔书写，字体工整、笔迹清楚。

3、做选考题时，考生按照题目要求作答，并用铅笔在答题卡上把所选题目对应的题号涂黑。

一、选择题（本大题共4小题）1.设集合P1={x|x2+ax+1＞0}，P2={x|x2+ax+2＞0}，其中a∈R，下列说法正确的是（）A. 对任意a，P1是P2的子集B. 对任意a，P1不是P2的子集C. 存在a，使得P1不是P2的子集D. 存在a，使得P2是P1的子集【答案】 A【解析】【分析】由不等式的性质得：由x2+ax+1＞0，则有x2+ax+2=x2+ax+1+1＞0+1＞0，由x2+ax+2＞0，不能推出x2+ax+1＞0，由集合间的关系得：P1P2，得解．【详解】解：由x2+ax+1＞0，则有x2+ax+2=x2+ax+1+1＞0+1＞0，由x2+ax+2＞0，则有x2+ax+1=x2+ax+2-1＞-1，不能推出x2+ax+1＞0，即P1P2，故选：A．【点睛】本题考查了集合间的关系，不等式的性质，属简单题．2.△ABC中，a2：b2=tan A：tan B，则△ABC一定是（）A. 等腰三角形B. 直角三角形C. 等腰直角三角形D. 等腰或直角三角形【答案】 D【解析】【分析】由已知a2：b2=tanA：tanB，利用正弦定理及同角基本关系对式子进行化简，然后结合二倍角公式在进行化简即可判断.【详解】解：∵a2：b2=tanA：tanB，由正弦定理可得，∵sin AsinB≠０∴∴sin AcosA=sin BcosB即sin2A=sin2B∴2A=2B或2A+2B=π∴A=B或A+B=，即三角形为等腰或直角三角形故选：D．【点睛】本题考查同角三角函数的基本关系，正弦定理的应用，式子变形是解题的关键和难点．3.抛物线y=2x2上有一动弦AB，中点为M，且弦AB的长度为3，则点M的纵坐标的最小值为（）A. B. C. D. 1【答案】 A【解析】【分析】由题意设，，直线的方程为，代入抛物线方程，写出韦达定理关系式及弦长与点的纵坐标关系式，通过基本不等式确定最小值.【详解】由题意设，，，直线的方程为，联立方程，整理得，，，点M的纵坐标，弦的长度为，即，整理得，即根据基本不等式，，当且仅当，时取等，即，，点的纵坐标的最小值为.故选 A.【点睛】本题考查直线与抛物线位置关系，考查基本不等式在圆锥曲线综合问题中的应用，解题时要认真审题，注意等价转化思想的合理运用.解决直线与圆锥曲线综合问题基本步骤为：（1）设，即设交点坐标和直线方程，注意考虑直线斜率是否存在;（2）联，即联立直线方程与圆锥曲线，消元;（3）判，即直线与圆锥曲线的位置关系可以通过判别式加以判断;（4）韦，即韦达定理，确定两根与系数的关系.（5）代，即根据已知条件，将所求问题转换到与两点坐标和直线方程相关的问题，进而求解问题.4.已知正数数列{a n}满足a n+1≥２a n+1，且a n＜2n+1对n∈N*恒成立，则a1的范围为（）A. [1，3]B. （1，3）C. （0，3]D. （0，4）【答案】 C【解析】【分析】由条件可得1+a n+1≥２（a n+1），设b n=1+a n，（a n＞0，b n＞1），运用累乘法，结合不等式恒成立，即可得到所求范围．【详解】解：正数数列{a n}满足a n+1≥２a n+1，可得1+a n+1≥２（a n+1），设b n=1+a n，（a n＞0，b n＞1）即有b2≥２b1，b3≥２b2，…，b n≥２b n-1，累乘可得b n≥b1?2n-1，可得1+a n≥（1+a1）?2n-1，又a n＜2n+1对n∈N*恒成立，可得1+2n+1＞1+a n≥（1+a1）?2n-1，即有1+2n+1＞（1+a1）?2n-1，。

上海市七宝中学2018-2019学年高一化学期末考试试题

上海市七宝中学2018-2019学年高一化学期末考试试题一、单选题1．黑火药是硫磺粉、硝石、木炭粉按一定比例混合而成。

古文献《本草经集注》记载了区分硝石（KNO 3）和朴消（Na 2SO 4）的方法：“以火烧之，紫青烟起，乃真硝石也”。

下列推断不正确．．．的是 A ．“紫青烟”主要是指钾元素的焰色反应 B ．“朴消”在灼烧时火焰没有颜色 C ．“硝石”在黑火药中起氧化剂的作用 D ．“朴消”不能替代“硝石”制黑火药2．下列装置应用于实验室制氯气并回收氯化锰的实验，已知氯化锰可溶于水，二氧化锰难溶于水，能达到实验目的的是：A ．用装置甲制取氯气B ．用装置乙吸收实验过程中制取的多余的氯气C ．用装置丙分离二氧化锰和氯化锰溶液D ．用装置丁除去氯气中的少量氯化氢3．由二氧化硅制高纯硅的流程如下，下列判断中错误的是( )A ．①②③均属于氧化还原反应B ．H 2和HCl 均可循环利用C ．SiO 2是一种坚硬难熔的固体D ．SiHCl 3摩尔质量为135.5 g4．下列离子方程式书写正确的是A ．铁与稀硫酸反应：+3+22Fe+6H =2Fe +3H ↑B ．稀盐酸除碳酸钙水垢：2-+322CO +2H =CO +H O ↑ C ．浓硝酸与铜反应：+-2+32Cu+4H +2NO =Cu +2NO +2H O ↑D ．氢氧化钡溶液与稀硫酸反应：2+-+2-442Ba +2OH +2H +SO =BaSO +2H O ↓5．下列仪器中常用作反应容器的是A ．圆底烧瓶B ．量筒C．容量瓶D．分液漏斗6．下列表示对应化学反应的离子方程式正确的是A．Ca(HCO3)2溶液与足量 NaOH 溶液反应：2HCO3-＋Ca2+＋2OH-＝CaCO3↓＋CO32-＋2H2OB．硫酸亚铁溶液中加入用硫酸酸化的过氧化氢溶液：Fe2++2H++H2O2＝Fe3++2H2OC．氢氧化钡溶液与硫酸铜溶液反应：Ba2+＋SO42－＝BaSO4↓D．AlCl3与过量的氨水反应：Al3+＋4NH3·H2O＝AlO2-＋4NH4+＋2H2O7．常温下，将pH=a的NaOH溶液与pH=b的醋酸溶液等体积混合后，两者恰好完全反应，则该温度下醋酸的电离平衡常数约为A．1014-a-2b B．10 a+b-14 C．10a-2b D．10a-2b+148．化学为人类的进步做出了巨大贡献。

2019-2020学年七宝中学高一下期末英语考试

七宝中学2019年学年第二学期高一年级英语期末试卷I. Listening Comprehension (30 points)Part A Short ConversationsDirections: In Part A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. There is some mechanical problem with the man’s cell phone.B. The man should buy a battery right now.C. The man must have taken some cash with him.D. The man is accustomed to paying the bill with his cell phone.2. A. She can handle the work.B. The increasing work stops her from taking a rest.C. She will take a rest soon after the work is finished.D. She enjoys her work.3. A. The man will visit Russia in the near future.B. The man has a good command of Russian.C. Russia doesn’t hold immediate appeal to the man.D. The man will never consider taking a trip to Russia.4. A. Fashion designer. B. Vet. C. Model. D. Coach.5. A. New forms of money. B. Market potential for a new product.C. Governments, attitudes to e-commerce.D. Replacement of old coins.6. A. Because he wants to save money.B. Because he wants to stay away from crowds.C. Because he is too exhausted with his work.D. Because the ticket price is higher.7. A. Impatient. B. Regretful. C. Angry. D. Relieved.8. A. Wedding rings will last forever.B. Good wedding rings are always expensive.C. It is a serious matter to choose a wedding ring.D. The value of wedding rings determines the quality of marriage.9. A. In a department store. B. In a map shop.C. In a geography class.D. At a metro station.10. A. Jenny can’t have another make-up exam.B. Jenny doesn’t study hard.C. Jenny has wasted four opportunities.D. Jenny should pay a high price for her carelessness.Section BDirections: In Section B, you will hear two short passages and one longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages and the conversation will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. One year. B. Ten years. C. Eighteen years. D. Twenty years.12. A. It’s comfortable.B. It’s time-saving. C. It’s cheap. D. It is enjoyable.13. A. It’s safer. B. It’s healthier. C. It’s more convenient. D. It’s colorful.Questions 14 through 17 are based on the following passage.14. A. Because he could not catch a fish.B. Because his father was not patient with him.C. Because his father did not teach him fishing.D. Because he could not join the local fishing club as his father did.15. A. They like deep water. B. They are insensitive to water temperature.C. Their eyelids help to block the sunlight.D. They are cold-blooded animals.16. A. It is easy to think like a customer.B. His father’s fishing advice is inspiring.C. Salespeople should find older and richer clients.D. It is difficult to sell services to poor people.Questions 18 through 20 are based on the following conversation17. A. Because books are too heavy.B. Because a cell phone is portable.C. Because his books are not popular among travelers.D. Because users can rate the restaurants and food on the app.18. A. He accepts advice from taxi drivers.B. He does a lot of research into the difficult menus.C. The hotel staff recommends restaurants to him.D. He talks with local people and walk around to spot good restaurants.19. A. He checks out the place the chef comes from.B. He ignores fancy restaurants and only visits small restaurants.C. He tries high-priced wines.D. He decides the hygiene conditions by using the bathroom first.20. A. The importance of menus and services. B. Young people’s travelling budget.C. The choice of good food and restaurants.D. The advantages of a food app.II. Grammar and Vocabulary (15points + 30points)Section ADirections: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)The ability to play is not only critical to being happy, but it also helps us to maintain social relationships and become creative, innovative people. If that seems to be a big claim, consider 21______ the world would be like without play. It's not just an absence of games or sports. Life without play is a life without books, without movies, art, music, jokes, or dramatic stories. I sometimes compare play to oxygen--it's all around us, yet goes mostly unnoticed or unappreciated 22______ it is missing.At some point as we get older, however, we 23_______(make) to feel guilty about playing. We are told that itis unproductive, a waste of time. The 24________ (remain) play is, like league sports, mostly very organized, rigid, and competitive. We try 25_______ (become) productive, and if an activity doesn't teach us a skill, make us money, or get us on the boss's good side, then we feel we should not be doing it. Sometimes the sheer demands of daily living seem to rob us of the ability to play.The skeptics（怀疑者）among the audience 26 _______ _______ I talk say, "Well, of course you will be happy if you play all the time. But for those of us who aren't rich, or retired, or both, there's simply no time for play." Or they might say that if they truly gave in to the joy of free play, they would never get anything done.This is not the case. We don't need to play all the time to be fulfilled. The truth is that in most cases play is a catalyst. The beneficial effects of the true play, even when27 ________(get)only a little, can spread through our lives, actually making us 28________ (tense) and more productive..(B)A joint proposal made by three CPPCC members, Jin Wei, Zhou Ping and Tao Yinyan, takes aim at the controversial topic of school bullying.According to the proposal, most school bullying cases happen in primary and middle schools. Bullying usually has such a negative influence on young victims' well-being and studies 29________ some even develop personality disorders.It i s common to associate bullying with hitting or kicking someone, or taking others’ things without permission. In other cases, however, 30_______ _______ hurting others physically, bullying can be verbal – saying or writing things that are not nice. Another type of bullying is social – choosing not to include someone, embarrassing someone or telling other people not to be friends with them. Based on data, nearly half of junior high school students have encountered verbal bullying. More than one-thirds have suffered relational bullying, while some 20 percent said they 31________ (bully) physically.The proposal states that experiences from Japan and other countries can be used 32________ references for Shanghai. In 2013, Japan passed a bullying prevention law, which requires schools to take specific actions against bullying when it's discovered. Japan also opened a 24-hour hotline to help those being bullied.The UK and the US have also cracked down on bullying recently, with 12 states in the latter now 33________ (list) bullying as a crime.The three political advisers suggest that Shanghai's education authorities 34________ (establish) an anti-school-bullying education system with schools, families and students.Schools 35________ respond quickly to bullying and give victims an opportunity to report abuse and seek protection. Reporting and prevention systems should also be set up, according to the proposal.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.lifestyle for younger generations.The development and popularity of the internet has generated occupations that are especially ___36___ in space and time. With a lower barrier to entry, these businesses allow more people to make quick cash.Qiu Xiaoai works in the purchasing department of a state-owned company that produces bus carriages. Her everyday work includes buying machine parts from suppliers according to instructions from her ___37___.At night, Qiu likes watching TV in her bedroom, while selling makeup on WeChat. She posts advertisements via social media, chats with her potential customers and ___38___ the makeup she sells for delivery the next day."I work ___39___ like a machine during the day time, but I get excited while doing my own business. I feel energetic even if I need to do a sideline after work," the 25-year-old makeup seller said.About 8.2 percent of people have a sideline income, according to a(n) ___40___last year by Zhaopin, a Chinese online recruitment service provider. WeChat business, design and writing are the top three sideline job categories white-collar workers ___41___, accounting for 26.8, 16.7 and 10.8 percent of survey respondents who have sidelines, the report said.Seller on WeChat, which ___42___ products by posting advertisements on the WeChat Moments and sells them to users' friends, is the most popular avocation（副业）. It is easy to get started and flexible in time and location, as well as a good way to make quick cash, the report said.Second to WeChat business are design and writing, which have a good market ___43___ with no space and time limitations. Other popular avocations include private tutoring, insurance sales, photography and translation, it said.The report also lists some ___44___ side jobs, including mobile gaming, mobile applications programming, tea art performing and designated driving. The report said that as long as one has expertise in a technology or talent, it's ___45___ possible to develop that expertise into a second career.aging - they might signal heart disease risk.The study, from researchers in France, found that people with numerous, deep forehead wrinkles — more than is ___46___for their age — were more likely to die from heart disease, compared with those without forehead wrinkles.The study authors said that, if the findings are confirmed with additional research, looking at forehead wrinkles could be an easy, low-cost way to help identify people at high risk for heart disease.However, the study found only a(n) ___47___between forehead wrinkles and an increased risk of heart disease; and so the findings don't mean that wrinkles ___48___indicate heart disease.Moreover, the researchers noted that looking at forehead wrinkles wouldn’t take the place of ___49___people for classic risk factors, such as high blood pressure. But if a person has a lot of deep forehead wrinkles, it could raise a red flag.In the new study, the researchers analyzed data from more than 3,200 French adults aged 32, 42, 52 and 62 at the beginning. The participants ___50___an exam in which doctors assessed their forehead wrinkles and ___51___ the participants a score based on the number and depth of the wrinkles. A score of zero meant no wrinkles, while a score of 3 meant “numerous deep wrinkles.”The participants were followed for about 20 years. People with a wrinkle score of 1 were five times more likely to die from heart disease, and people with a wrinkle score of 2 or 3 were nearly 10 times more likely to die from heart disease, compared with people with a wrinkle score of 0.The findings ___52___even after the researchers took into account factors that could affect people's risk of death from heart disease, including their age, gender, education level and whether they had diabetes.The new findings “suggest that the ___53___of forehead wrinkles may provide some insight into future risk of early death, and could ___54___be considered more than skin-deep,” Fonarow told Live Science.Still, Fonarow said that future studies are needed to confirm the findings and to evaluate the link in broaderpopulations of adults.The study has not yet been published in a ___55___-reviewed journal.III. Reading Comprehension (15 points+40 points)Section ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Words to Turn a Conversation AroundIt’s not what you say, but it’s how you say it —isn’t it? According to a language expert, we may have this wrong. “We are pushed and pulled around by language far more than we 56. __________,” says Elizabeth Stoke, professor of social interaction at Loughborough University. Stoke and her colleagues have 57. __________ thousands of hours of recorded conversations, from customer services to mediation（调解）hotlines and police crisis 58. __________. They discovered that certain words or phrases have the power to change the course of a conversation.Some of these words are surprising , and 59. __________ what we’ve been taught to believe. For example, in a study of conversations between doctors and patients, evidence showed that doctors who 60. __________ options rather than recommended best solutions, got a better response, despite the suggestion from hospital guidelines to talk about the best interests of the patient. But, from conversation experts such as Stoke to FBI negotiators and communication coaches, we’re learning which words are likely to 61. __________ or persuade us.Stoke found that people who had already responded 62. __________ when asked if they would like to attend mediation seemed to change their minds when the mediator used the phrase, “Would you be willing to come for a meeting?” “As soon as the word ‘willing’ was used, people would say: ‘Oh, yes, definitely’ — they would actually 63. __________ the sentence to agree.” Stoke found it had the same effect in different settings: with business-to-business cold callers; with doctors trying to 64. __________ people to go to a weight-loss class. She also looked at phrases such as “Would you like to” and “Would you be interested in”. “Sometimes they 65. __________, but ‘willing’ was the one that got people to agree more rapidly and with more enthusiasm.”“ ‘Hello’ is a really important word that can change the 66. __________ of a conversation,” Stoke says. “It’s about how you respond to people who are what we call ‘first movers’ — people who say something really 67. ___________.” “It might be the work colleagues who are extremely an gry to your desk with a complaint or the neighbor who 68. __________ rude words about parking as you’re putting out the bins.” “What do you do with that person? Rather than respond in the same manner, saying something nice, such as a very bright ‘Hello!’ , socializes that other person a little bit.” Use it when you want to resist getting into a 69. __________. “You have to be careful not to sound too passive-aggressive,” Stoke says, “but just one friendly word in a bright tone can delete the 70. __________ of the conversation.”56. A. suggest B. realize C. imply D. emphasize57. A. analyzed B. addressed C. simplified D. discovered58. A. instructions B. revolutions C. associations D. negotiations59. A. get into B. turn away C. go against D. insist on60. A. pointed B. inspired C. motivated D. listed61. A. comfort B. defend C. support D. protect62. A. actively B. positively C. negatively D. passively63. A. finish B. reject C. refuse D. interrupt64. A. persuade B. stimulate C. force D. tempt65. A. interacted B. worked C. responded D. initiated66. A. approach B. course C. evolution D. pattern67. A. impractical B. unimaginative C. critical D. illogical68. A. keeps back B. answers for C. agrees on D. launches into69. A. conflict B. disaster C. strike D. damage70. A. challenge B. debate C. worry D. silenceSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)Have you ever had the experience of talking to someone and you think they are lying? Well, you are not alone. We’ve all had that feeling. But did you know that there are several things you can look for to see if you are being lied to?Sometimes you can tell if a person is lying by observing what they do with their body. When people are lying they tend not to move their arms, hands or legs very far from their body. They don’t want to take up very much space because they don’t want to be noticed. Sometimes a person who is lying will not look you in the eyes. Other times people who lie try to look at you in a strong way because they want to convince you they are telling the truth.Liars also use deflection. For example, if you ask a liar the question “Did you steal Fatima’s bag?”, they may answer with something like “Fatima is my friend. Why would I do that?” In this situation the person is telling the truth, but they are also not answering the question. They are trying to deflect your attention. Liars may also give too many details. They may try to over-explain things. They do this because they want to convince you of what they are saying.Often when a person is lying, they do not want to continue talking about their lie. If you think someone is lying, quickly change the subject. If the person is lying, they will appear more comfortable because they are not talking about their lie any longer. A little later, change the subject back to what you were talking about before. If the person seems uncomfortable again, they may be lying.It’s very hard for a liar to avoid filling silence created by you. He or she wants you to believe the lies being woven; silence gives no feedback on whether or not you’ve bought the story. If you’re a good listener, you’ll already be avoiding interruptions, which in itself is a great technique to let the story unfold.Just because a person is showing these behaviors, it does not mean they are lying. They might be shy or nervous. But, if you think someone is lying, you might want to use some of these techniques. Hopefully, you won’t need to very often.71.By saying “Liars also use deflection”, the writer means that liars may __________.A. tell great storiesB. change tone of voiceC. ask a question in replyD. avoid direct answers72.According to the passage, a person could be lying if he or she ____________.A. offers more information than necessaryB. appears to be shy or nervousC.changes the subject of the conversationD. speaks very fast and vaguely73.Which of the following can be learned from the passage?A. Liars always try to avoid direct eye contact when they tell lies.B. We can make people lie by changing the subject in a conversation.C. Liars are often expansive in hand and arm movements while talking.D. We make liars uncomfortable by giving no feedback in a conversation.74.The passage mainly talks about __________.A. who deceives usB. why people tell liesC. how to detect liesD. what to do with liars(B)On Sept. 15, TripAdvisor, one of the world’s largest travel review websites named the world’s top 25 museums in its Travelers’ Choice Awards, based on the reviews and opinions of travelers worldwide.Metropolitan Museum of Art, New York CityIt is the largest museum in the Western Hemisphere（半球）, with a collection of 2 million items from more than 5,000 years of world culture. The museum includes important collections from ancient Egypt and medieval （中世纪的）Europe as well as ancient Greece and Rome. Here, visitors can get lost in different centuries: They can see the Temple of Dendur from early Egypt, Dutch painter Vincent Van Gogh’s Wheatfield With Cypresses, and US pop artist Andy Warhol’s Souper Dress, all in one place.Musée d’Orsay, ParisLocated in the center of Paris on the banks of the River Seine, the Musée d’Orsay houses the world’s most amazing collections of impressionist and post-impressionist art. It offers the chance to view major works from the greats like Van Gogh and Claude Monet.Art Institute of Chicago, IllinoisIt was named the world’s best museum in 2014. The world-famous Windy City museum houses nearly 300,000 works, including one of the largest collections of modern art including pieces such as Spanish painter Pablo Picasso’s The Old Guitarist and French artist Henri Matisse’s Bathers by a River. A TripAdvisor reviewer commented, “Paintings from every era and works from every great artist make the museum worth a hundred visits.”Museo Nacional del Prado, MadridNowhere is able to present the entire history of Spanish art like the Museo Nacional del Prado. Here visitors can enjoy a detailed view of Spanish school of the Modern Age. In fact, “the study of almost any Spanish painter and his work is almost impossible without visiting the many galleries of the Museo Nacional del Prado”, TripAdvisor noted.The Italian school is another highlight of the museum’s collection, as it includes 15th century masterpieces such as The Annunciation by Fra Angelico. The museum also has a fine collection of 16th century Venetian paintings, 17th century French classicists, Baroque paintings and Roman sculpture.75.Which of the following is TRUE about the Metropolitan Museum of Art?A. It’s the largest art museum among the four.B. It’s so big that visitors may easily get lost in it.C. It has the largest collection of the four museums.D. Its collection includes works from ancient Egypt.76.________ is a must-visit place if you are interested in impressionism.A. the Metropolitan Museum of ArtB. the Musée d’OrsayC. Art Institute of ChicagoD. the Museo Nacional del Prado77.According to the article, both the Art Institute of Chicago and the Museo Nacional del Prado________.A. include a bigger collection of modern art than ancient artB. are perfect places to study the history of Spanish artC. contain a collection of art from different eras and countriesD. are home to a large number of works from the Italian school78. Who are most probably the intended readers of the passage?A. international studentsB. senior businessmenC. experienced tour guidesD. global sightseers(C)Getting kids to share their toys is a never-ending battle, and forcing them to do so never seems to help. New research suggests that allowing children to make a choice to sacrifice their own toys in order to share with someone else makes them share more in the future. The new findings are published in Psychological Science.These experiments were conducted by psychological scientists, Nadia Chernyak and Tamar Kushnir of Cornell University. They found that sharing things with others when they are given a difficult choice leads children to think of themselves as people who like to share. It also makes them more likely to act in a pro-social manner in the future.Previous research has explained why rewarding children for sharing can backfire. Children come to think of themselves as people who don't like to share since they had to be rewarded for doing so. Because they don't view themselves as "sharers" they are less likely to share in the future.Chernyak and Kushnir were interested in finding out whether freely chosen sacrifice might have the opposite effect on kids' willingness to share. To test this, the researchers introduced five-year-old children to Doggie, a sad puppet. Some of the children were given a difficult choice: Share a precious sticker with Doggie, or keep it for themselves. Other children were given an easy choice between sharing and putting the sticker away, while children in a third group were required by the researcher to share.Later on, all the children were introduced to Ellie, another sad puppet. They were given the option of how many stickers to share (up to three). The kids who earlier made the difficult choice to help Doggie shared more stickers with Ellie. The children who were initially faced with an easy choice or who were required to give their sticker to Doggie, on the other hand, shared fewer stickers with Ellie. Therefore, children did not benefit from simply giving something up, but rather from willingly choosing to give something up of value.“You might imagine that making difficult, costly choices is taxing for young children or even that once children share, they don’t feel the need to do so again,” Chernyak says. “But this wasn't the case: once children made a difficult decision to give up something for someone else, they were more generous, not less, later on.” Chernyak concludes.79._____ helps children to share more in the future.A. Rewarding children for sharing stickersB. Requiring children to share their favorite toysC. Allowing children to share what they don’t needD. Encouraging children to share precious things willingly80.The underlined word “backfire” means _____.A. serve as a pushB. have an opposite effectC. cause angerD. avoid taking things back81.Those who were required to share give fewer stickers to Ellie because _____.A. it’s not their own choiceB. they regret what they didC. Ellie is not as sad as DoggieD. they like to share with a real person82.We can conclude from the passage that _____.A. parents will never find a way to get children to share toysB. a gift should be given to make up for children’s sacrificeC. making difficult choices may influence sharing behaviorD. children pretend to be generous when they are being observed(D)It could be said that the age of adventure peaked with Sir Ernest Shackleton the moment his ship Endurance became hopelessly locked in ice on its way to Antarctica in January 1915. For ten months the 28 men aboard Shackleton’s ship waited and prayed fo r ice to break. When it finally did, Endurance sank, leaving the crew homeless and adrift on a sea of ice in one of the world’s most dangerous environments.In January 2000 a luxury ocean liner found itself similarly trapped in the cold waters off Antarctica. Argentine authorities sent off an icebreaker straight away from the nearest naval base, and in 24 hours, all 176 passengers and crew were free. Tour company’s spokesperson spun the potential disaster as a value-added reward in extreme travel. “The people on board are looking at this as sort of a great adventure,” she said.Ever since Jon Krakauer’s book Into Thin Air made Everest a household name, the sub-culture of adventure has blown up like a Himalayan avalanche（雪崩）into public consciousness. Magazines promise “extreme” content, television offers adventure programmes, and the growing collective fascination with adventure has produced a flow of published accounts about the world’s greatest expeditions. Combine that with today’s access to previously isolated places, and adventure’s newly found mass appeal makes good business sense. Today the only thing blocking a would-be adventurer’s passage to Antarctica is the cost --- which typically runs well over $ 10,000.Despite very different implications, adventure was just as popular in Shackleton’s time. He had little trouble filling the Endurance --5000 men are said to have responded to his recruitment（招募）notice: “Men wanted for risky journey. Small wages. Bitter co ld. Long months of complete darkness. Constant danger. Safe return doubtful.”After five months drifting on ice, the crew were forced to take to their lifeboats to Elephant Island. Reaching the wasteland, Shackleton went on with one lifeboat and five of his best men 1300 kilometres across the bone-chilly Scotia Sea to South Georgia island. Shivering with cold, dressed in rags, Shackleton marched into a whaling station and set about organising a rescue expedition to Elephant Island. Almost two years after becoming shipwrecked on ice, Shackleton picked up his crew. “Not a life lost, and we have been through hell,” he remark ed earnestly.83. We can learn from the first sentence of this passage that ______.A. the times of adventure ended with the ship Endurance trapped in iceB. the times of adventure began with the ship Endurance trapped in iceC. Shackleton’s adventure ma rked the highest point of pure explorationD. Shackleton’s adventure predicted that the golden age of exploration was approaching84. The word “spun” in the second paragraph can be replaced by______ .A. summed upB. made upC. brought aboutD. announced85. Since Jon Krakauer’s book was published _______.A. the costs of extreme travel have gone upB. media have been involved in adventureC. Everest has got its nameD. People have got fascinated by Himalayan avalanches86. The adventure in Shack leton’s time has different implications from today’s in that ___.A. Shackleton enrolled volunteers more easilyB. No one was missing during Shacldeton’s adventureC. Shackleton’s adventure lasted longer than any other adventure nowadaysD. Shackleton’s ad venture was entirely for the sake of adventureSection C。

0204-七宝中学高一下期末(2019.6)

七宝中学高一下期末数学试卷2019.6一、填空题 1．计算：21lim33n n n →∞-=+ ．2．已知数列{}n a 是等差数列，如果15a =，22a =，那么3a = ．3．已知数列{}n a 是正实数组成的等比数列，如果41a =，816a =，则q = ． 4．已知等差数列{}n a 前10项和为20，则14710a a a a +++= ． 5．等比数列{}n a 中，121a a +=，5616a a +=，则910a a += ．6．如果无穷递缩等比数列{}n a 所有奇数项的和等于所有项和的5倍，则公比q = ． 7．已知等比数列{}n a 为单调递增数列，设其前n 项和为n S ，若22a =，37S =，则5a 的值为．8．若数列{}n a 满足112,(0)2121,(1)2n n n n n a a a a a +⎧⎪⎪=⎨⎪-<⎪⎩≤≤≤，若159a =，则2019a = ．9．在A BC △中，,,A B C ∠∠∠的对边分别为,,a b c ．若2222019a b c +=，则cot cot cot CA B=+ ．10．已知数列{}n a 的通项公式为1sin 22020n n a a ⎛⎫=+- ⎪⎝⎭，若满足1232019a a a a +++⋅⋅⋅+=4038，则a = ．11．若等差数列{}n a 、{}n b 的公差都为(0)d d ≠，若满足对于任意*n ∈N ，都有n n b a kd -=，其中k 为常数，*k ∈N ，则称它们互为“同宗”数列．已知等差数列{}n a 中，首项为11a =，2d =．数列{}n b 为数列{}n a 的“同宗”数列，若112233111123lim 90n n n a b a b a b a b →∞⎛⎫+++⋅⋅⋅+=⎪⎝⎭，则k = ．12．现有正整数构成的数阵如下：第一行：1 第二行：1 2 第三行：1 1 2 3 第四行：1 1 2 1 1 2 3 4第五行：1 1 2 1 1 2 3 1 1 2 1 1 2 3 4 5………………第k 行：先抄写第1行，接着按原顺序抄写第2行、第3行、⋅⋅⋅直至按原顺序抄写第1k -行，最后添上数k （如第四行，先抄写第一行的数1，接着抄写第二行的数1，2，接着抄写第三行的数1，1，2，3，最后添上4），将按照上述方式写下的第n 个数记作n a （如11a =，21a =，32a =，⋅⋅⋅，143a =，⋅⋅⋅），则1232019a a a a +++⋅⋅⋅+= ．二、选择题13．已知数列{}n a 是等差数列且,,,k l m p 是正整数，则“k l m p +=+”是“k l m p a a a a +=+”的（）A ．充分非必要条件B ．必要非充分条件C ．充要条件D ．既非充分又非必要条件 14．数列{}n a 和{}n b 分别是等差数列和各项均为正数的等比数列，若55a b =，则（） A ．3746a a b b +>+ B ．3746a a b b ++≥ C ．3746a a b b +<+ D ．3746a a b b ++≤ 15．对任意的锐角,αβ，下列不等关系中正确的是（）A ．cos()sin sin αβαβ+<+B ．sin()cos cos αβαβ+>+C ．cos()cos cos αβαβ+<+D ．sin()sin sin αβαβ+>+16．已知1234,,,a a a a 是等比数列，且1234123lg()a a a a a a a +++=++，若11a >，则（） A ．1324,a a a a << B ．1324,a a a a >< C ．1324,a a a a <> D ．1324,a a a a >>三、解答题17．已知函数()sin()(0,||)2f x A x πωϕωϕ=+><的部分图像如右图．（1）求,,A ωϕ；（2）7[,]26x ππ∈时，求()f x 的值域和单调递减区间．18．已知正项数列{}n a 的首项11a =，前n 项和n S 满足22n n n a a S +=．（1）求数列{}n a 的通项公式；（2）若数列{}n b 是公比为5的等比数列，且11b a -，22b a -，33b a -也是等比数列，若数列n n a b λ⎧⎫+⎨⎬⎩⎭单调递增，求实数λ的取值范围．19．已知等比数列{}n a 的公比1q >，且23414a a a ++=，31a +是2a ，4a 的等差中项．数列{}n b 满足16b =-，数列1{()}n n n b b a +-的前n 项和为2n ．（1）求q 的值；（2）求数列{}n b 的通项公式．20．由函数()y f x =确定数列{}n a ，()n a f n =．若函数1()y f x -=能确定数列{}n b ，1()n b f n -=，则称数列{}n b 是数列{}n a 的“反数列”．（1）若函数()f x ={}n a 的反数列为{}n b ，求数列{}n b 的通项公式；（2）对（1）中的{}n b21log (82)2a a a ⋅⋅⋅+-对任意的正整数n 恒成立，求实数a 的取值范围；（3）设*1(1)1(1)3(21),22n n c n λλλ+---=⋅+⋅-∈N ，若数列{}n c 的反数列为{}n d ，{}n c 与{}n d 的公共项组成的数列为{}n t （公共项k p q t c d ==，*,,k p q ∈N ），求数列{}n t 的前n 项和n S ．21．已知数列{}n a 满足：11a =，2114n n a a m +=+，其中*n ∈N ，m ∈R ．（1）若12,,a m a 成等差数列，求m 的值；（2）若0m =，求数列{}n a 的通项n a ；（3）若对任意正整数n ，都有2n a <，求m 的最大值．参考答案一、填空题 1．23 2．1- 3．2 4．8 5．256 6．45- 7．16 8．299．1009 10．2 11．3 12．3988【第9题解析】cos cos cot sin sin cos sin sin cos cos sin cos sin cos cot cot sin sin()sin sin sin sin C CC A B C C C A B A B B A A B C A B A B A B ===++++ 222222222222sin sin cos 201921009sin 22a b c ab A B C a b c c c ab C c c c +-⋅+--=====．【第10题解析】∵sin sin()0x x +-=， ∴120192201820202(12019,)n n a a a a a a a n n *-+=+==+=∈N ≤≤，∴123201920194038a a a a a +++⋅⋅⋅+==，从而2a =．【第11题解析】改编自2019宝山一模12由题意，111111()(21)(212)221212n n n n a b a a kd n n k k n n k ⎛⎫===- ⎪+--+--+⎝⎭．①1k =时，11223311111111111213352121n n a b a b a b a b n n ⎛⎫+++⋅⋅⋅+=-+-++- ⎪-+⎝⎭111221n ⎛⎫=- ⎪+⎝⎭，11223311111lim 2nn n a b a b a b a b →∞⎛⎫+++⋅⋅⋅+= ⎪⎝⎭，不符； ②2k =时，1122331111111114132123n n a b a b a b a b n n ⎛⎫+++⋅⋅⋅+=+-- ⎪++⎝⎭，11223311111lim 3n n n a b a b a b a b →∞⎛⎫+++⋅⋅⋅+= ⎪⎝⎭，不符； ③3k =时，1122331111111111123613521232590n n a b a b a b a b n n n ⎛⎫+++⋅⋅⋅+=++---=⎪+++⎝⎭，符合．【第12题解析】由题意，第n 行共有12-n 个数，前n 行共有21122221n n -++++=-个数，解212019n -≥得11n ≥，说明2019a 在第11行，前10行共有1023个，第11行的前511个数为前9行所有数字的复制；之后的255个数为前8行所有数字的复制；之后的127个数为前7行所有数字的复制；之后的63个数为前6行所有数字的复制；之后的31个数为前5行所有数字的复制，至此共有2010个数．之后的9个数为前4行的前9个数1，1，2，1，1，2，3，1，1．记前n 行的所有数的和为n T ，则11T =，12(2)n n T T n n -=+≥， 12[(1)]n n T kn b T k n b -++=+-+，化简得12(2)n n T T kn b k -=++-，∴1k =且20b k -=，∴122[(1)2]n n T n T n -++=+-+，即{2}n T n ++是首项为4，公比为2的等比数列，从而122n n T n +=--，∴12320195678910133988a a a a T T T T T T +++⋅⋅⋅+=++++++=．【说明】前n 行共有1个n ，2个1n -，22个2n -，…，2n k -个k ，，…，12n -个1， ∴211(1)22212n n n T n n --=⨯+-⨯++⨯+⨯，后续可采用错位相减法求解n T ，过程略．二、选择题13．A 14．D 15．C 16．B【第16题解析】取12a =，设公比为x ，借助计算器的solve 功能，解方程232102(1)log (222)x x x x x +++=++，可得0.927x ≈-，选B ．三、解答题17．（1）2ω=，2A =，3πϕ=-；（2）[-，11[,]212ππ． 18．（1）n a n =；（2）1158n n b -=-⋅，118()5n nn a n b λλ-+⎛⎫=-+⋅ ⎪⎝⎭，由题意，1max 113044n n n n a a n b b λλλλ++++⎛⎫->⇒>-+⇒>- ⎪⎝⎭． 19．（1）2q =；（2）12n n a -=，记1()n n n n b b a c +-=，则212n c c c n +++=，易得21n c n =-，于是11212n n n n b b +---=，应用累加法及错位相减法，可求出2212nn n b -+=-． 20．改编自2014年长宁一模理23（1）21()(0)9x f x x -=≥，则2()9n n b n *=∈N ．（2）不等式化为：23331log (82)1222a a a n n n +++>-++，设333122n T n n n =+++++，因为13302122n n T T n n +-=->++，所以{}n T 单调递增，则min 13()2n T T ==．因此213log (82)22a a a -<，即2log (82)3a a a -<．①01a <<时，22382082a a a a a ⎧->⎨->⎩，解得01a <<； ②1a >时，22382082a a a a a ⎧->⎨-<⎩，解得24a <<；综上，a 的取值范围是(0,1)(2,4)．（3）当λ为奇数时，21n c n =-，1(1)2n d n =+．由121(1)2p q -=+，得43q p =-，即{}{}n n c d ，因此21n t n =-，所以2n S n =．当λ为偶数时，3n n c =，3log n d n =．由33log p q =，得33p q =，即{}{}n n c d ，因此3n n t =，所以3(31)2n n S =-．21．改编自2019年杨浦二模21 （1）214a m =+，由122m a a =+，得1214m m =++，所以54m =；（2）2114n n a a +=，显然，0n a >恒成立所以，221221log log 22log 4n n n a a a +==-+，即2122log 2(2log )n n a a +-+=-+，所以，112122log 2(2log )22n n n n a a --+-+=-+=-⨯，整理得，1222n n a --=；（3）22111(2)(1)144n n n n n a a a a m a m m +-=-+=-+--≥故1122111()()()(1)(1)n n n n n a a a a a a a a a n m ---=-+-++-++--≥，当1m >时，令1(1)(1)2a n m +--≥，即1211a n m -+-≥，则1(1)(1)2n a a n m +--≥≥，与已知矛盾；所以，1m ≤．（另解：当1m >时，注意到n →+∞时，(1)(1)m n --→+∞因此，存在充分大的n ，使得1(1)(1)2m n +-->，即2n a >，与已知矛盾）若1m =，则21124n n a a +=+，下用数学归纳法证明02n a <<．1n =时，显然成立，假设02k a <<，则22111121244k k a a +=+<⨯+=，而10k a +>显然成立．故对所有正整数n ，都有2n a <．所以，m 的最大值为1．。

2018-2019学年上海市闵行区七宝中学高一年级上学期期末物理试卷

2018-2019学年上海市闵行区七宝中学高一年级上学期期末物理试卷一、单选题1. 已知7世纪意大利科学家伽利略在研究运动和力的关系时,提出了著名的斜面实验,其中应用的物理思想方法属于( )A. 等效替代B. 实验归纳C. 理想实验D. 控制变量【答案】C【解答】实验条件现实中无法达到2. 下列说法正确的是( )A. 矢量的大小是标量B. 位移的大小是路程C. 平均速度的大小是平均速率D. 瞬时速度的大小是瞬时速率【答案】D【解答】矢量的大小非负，标量有正有负。

平均速度的大小是位移和时间的比值，平均速率的大小是路程和时间的比值故选：D。

3. 下列哪组是国际单位中的基本单位( )A. 米，牛顿，千克B. 千克，米/秒2，秒C. 米/秒2，千克，牛顿D. 米，千克，秒【答案】D【解答】只能靠记忆，记不住就不会，没办法。

4. 关于摩擦力，以下说法中正确的是（）A. 运动物体可能受到静摩擦力作用，但静止物体不可能受到滑动摩擦力作用B. 摩擦力的存在依赖于正压力，其大小与正压力成正比C. 摩擦力的方向一定与物体的运动方向相反D. 摩擦力的方向有可能与速度方向不在一直线上【答案】D【解答】摩擦力和运动方向无关5. 如图所示是物体在某段运动过程中的v －t 图象，在t1和t2时刻的瞬时速度分别为v1和v2，则时间由t1到t2的过程中（）A. 加速度不断增大B. 加速度不断减小C. 平均速度2v v v 21+= D. 平均速度v ＞2v v 21+ 【答案】B【解答】加速度和倾斜率有关6. 关于惯性，以下说法中正确的是( )A. 水平拉动静止木块比水平拉着木块匀速运动所需的力大，所以静止物体惯性较大B. 同一木块速度大时不易停下，所以速度较大的物体惯性也比较大C. 木块在粗糙桌面上运动时较容易停下，所以物体受到的摩擦力越大惯性就越小D. 物体惯性的大小与是否受外力作用或外力大小均无关【答案】D【解答】惯性只和质量有关，所以D选项是正确的7. 如图所示,物体静止在一固定在水平地面上的斜面上,下列说法正确的是( )A. 物体对斜面的压力和斜面对物体的支持力是一对平衡力B. 物体对斜面的摩擦力和物体重力沿斜面的分力是一对作用力和反作用力C. 物体所受重力和斜面对物体的作用力是一对平衡力D. 物体所受重力可以分解为沿斜面的力和对斜面的压力【答案】C【解答】二力平衡8. 将甲乙两小球先后以同样的速度在距地面不同高度处竖直向上抛出,抛出时间相隔2s,它们运动的v-t图象分别如右图中直线甲、乙所示。

【全国百强校】上海市七宝中学2019-2020学年高一下物理期末模拟试卷含解析〖加17套期末中考模拟卷〗

【全国百强校】上海市七宝中学2019-2020学年高一下物理期末模拟试卷一、选择题（本题共12小题，每小题5分，共60分，在每小题给出的四个选项中，有的小题只有一个选项正确，有的小题有多个选项正确.全部选对的得5分，选不全的得3分，有选错的或不答的得0分）1、如图所示，a、b两点位于以负点电荷为球心的球面上，c点在球面外，则（）A．a点场强与b点场强相同B．a点场强的大小比c点大C．b点场强的大小比c点小D．条件不足，无法判断a、b、c场强大小关系2、如图所示，光滑水平面上，质量为m的小球在拉力F作用下做匀速圆周运动。

若小球运动到P点时，拉力F发生变化，下列关于小球运动情况的说法中正确的是（）A．若拉力突然消失，小球将沿轨迹Pa做离心运动B．若拉力突然变小，小球将沿轨迹Pa做离心运动C．若拉力突然变大，小球将沿轨迹Pb做离心运动D．若拉力突然变小，小球将沿轨迹Pc做向心运动3、如图所示，小球从高处下落到竖直放置的轻弹簧上，在将弹簧压缩到最短的整个过程中，忽略空气阻力，下列叙述中正确的是A．刚接触弹簧时，小球的速度最大B．小球的动能一直增大C．只有重力和弹簧弹力对小球做功，小球动能和势能之和是守恒的D．小球、弹簧和地球作为—个系统，重力势能、弹性势能和动能之和保持不变4、质量为m的物体从倾角为固定的光滑斜面顶端山静止开始下滑，斜面高为h，则物体下滑过程中重力做功的平均功率及物体滑至斜面底端时重力的瞬时功率分别为A．B．C．D．5、一根弹簧的弹力F-伸长量（位移）x图象如图所示，当弹簧的伸长量块由3.0cm变到6.0cm的过程中A．弹力所做的功是0.45J，弹性势能减少了0.45JB．弹力所做的功是0.6J，弹性势能减少了0.6JC．弹力所做的功是-0.45J，弹性势能增加了0.45JD．弹力所做的功是-45J，弹性势能增加了45J6、如图所示，一个质量为m的小球，用长为L的轻绳悬挂于O点，小球在水平力F作用下，从平衡位置P很缓慢地移动到Q点，则力F所做的功为（）A．FLsinθB．mgLcosθC．FL (1- cosθ)D．mgL (1- cosθ)7、一气球由地面匀速上升，当气球下的吊梯上站着的人沿梯子上爬时，下列说法正确的是（）A．气球可能匀速上升B．气球可能相对地面静止C．气球可能下降D．气球运动速度不发生变化8、2019年1月3日，嫦娥四号成功着陆在月球背面南极-艾特肯盆地冯·卡门撞击坑的预选着陆区．它是嫦娥探月工程计划中嫦娥系列的第四颗人造探月卫星，主要任务是更深层次、更加全面的科学探测月球地貌、资源等方面的信息，完善月球档案资料．已知月球的半径为R，月球表面的重力加速度为g，引力常量为G，嫦娥四号离月球中心的距离为r，绕月周期为T．根据以上信息可求出（）A ．月球的平均密度为3233r GT Rπ B ．嫦娥四号绕月运行的速度为2r gRC ．月球的平均密度23GTπD ．嫦娥四号绕月运行的速度为2rTπ 9、如图所示，质量m=0.2kg 的物块在斜面顶端由静止开始沿倾角为30°的粗糙斜面匀加速下滑，加速度a=2m/s 2，下滑的距离为4m ．下列判断正确的是（取g=10m/s 2）A ．物块的重力势能减少8JB ．物块的动能增加4JC ．物块的机械能减少2.4JD ．物块的合外力做功为1.6J10、如图所示，在一次救灾工作中，一架沿水平直线飞行的直升机A ，用悬索(重力可忽略不计)救起了伤员B 。

【优选】上海市七宝中学2019年高三上学期期末考试数学试题(精品解析)

2019年上海市闵行区七宝中学高考数学一模试卷一、选择题（本大题共4小题）1.设集合P1={x|x2+ax+1＞0}，P2={x|x2+ax+2＞0}，其中a∈R，下列说法正确的是（）A. 对任意a，P1是P2的子集B. 对任意a，P1不是P2的子集C. 存在a，使得P1不是P2的子集D. 存在a，使得P2是P1的子集【答案】A【解析】【分析】由不等式的性质得：由x2+ax+1＞0，则有x2+ax+2=x2+ax+1+1＞0+1＞0，由x2+ax+2＞0，不能推出x2+ax+1＞0，由集合间的关系得：P1P2，得解．【详解】解：由x2+ax+1＞0，则有x2+ax+2=x2+ax+1+1＞0+1＞0，由x2+ax+2＞0，则有x2+ax+1=x2+ax+2-1＞-1，不能推出x2+ax+1＞0，即P1P2，故选：A．【点睛】本题考查了集合间的关系，不等式的性质，属简单题．2.△ABC中，a2：b2=tan A：tan B，则△ABC一定是（）A. 等腰三角形B. 直角三角形C. 等腰直角三角形D. 等腰或直角三角形【答案】D【解析】【分析】由已知a2：b2=tan A：tan B，利用正弦定理及同角基本关系对式子进行化简，然后结合二倍角公式在进行化简即可判断.【详解】解：∵a2：b2=tan A：tan B，由正弦定理可得，∵sin A sin B≠0∴∴sin A cosA=sin B cosB即sin2A=sin2B∴2A=2B或2A+2B=π∴A=B或A+B=，即三角形为等腰或直角三角形故选：D．【点睛】本题考查同角三角函数的基本关系，正弦定理的应用，式子变形是解题的关键和难点．3.抛物线y=2x2上有一动弦AB，中点为M，且弦AB的长度为3，则点M的纵坐标的最小值为（）A. B. C. D. 1【答案】A【解析】【分析】由题意设，，直线的方程为，代入抛物线方程，写出韦达定理关系式及弦长与点的纵坐标关系式，通过基本不等式确定最小值.【详解】由题意设，，，直线的方程为，联立方程，整理得，，，点M的纵坐标，弦的长度为，即，整理得，即根据基本不等式，，当且仅当，时取等，即，，点的纵坐标的最小值为.故选A.【点睛】本题考查直线与抛物线位置关系，考查基本不等式在圆锥曲线综合问题中的应用，解题时要认真审题，注意等价转化思想的合理运用.解决直线与圆锥曲线综合问题基本步骤为：（1）设，即设交点坐标和直线方程，注意考虑直线斜率是否存在;（2）联，即联立直线方程与圆锥曲线，消元;（3）判，即直线与圆锥曲线的位置关系可以通过判别式加以判断;（4）韦，即韦达定理，确定两根与系数的关系.（5）代，即根据已知条件，将所求问题转换到与两点坐标和直线方程相关的问题，进而求解问题.4.已知正数数列{a n}满足a n+1≥2a n+1，且a n＜2n+1对n∈N*恒成立，则a1的范围为（）A. [1，3]B. （1，3）C. （0，3]D. （0，4）【答案】C【解析】【分析】由条件可得1+a n+1≥2（a n+1），设b n=1+a n，（a n＞0，b n＞1），运用累乘法，结合不等式恒成立，即可得到所求范围．【详解】解：正数数列{a n}满足a n+1≥2a n+1，可得1+a n+1≥2（a n+1），设b n=1+a n，（a n＞0，b n＞1）即有b2≥2b1，b3≥2b2，…，b n≥2b n-1，累乘可得b n≥b1•2n-1，可得1+a n≥（1+a1）•2n-1，又a n＜2n+1对n∈N*恒成立，可得1+2n+1＞1+a n≥（1+a1）•2n-1，即有1+2n+1＞（1+a1）•2n-1，可得a1＜3+恒成立，由3+＞3，可得0＜a1≤3．故选：C．【点睛】本题考查数列的递推式，注意累乘法的运用，考查等比数列的通项公式，考查不等式的性质和恒成立思想，属于中档题．二、填空题（本大题共12小题）5.设A={x||x|≤2018，x∈R}，B={x|y=，x∈R}，则A∩B=______．【答案】【解析】【分析】可解出集合A，B，然后进行交集的运算即可．【详解】解：A={x|-2018≤x≤2018}，B={2019}；∴A∩B=∅．故答案为：∅．【点睛】考查描述法、列举法的定义，绝对值不等式的解法，以及交集的运算6.已知定义域在[-1，1]上的函数y=f（x）的值域为[-2，0]，则函数y=f（cos）的值域是______．【答案】[-2，0]【解析】【分析】可以看出-1，从而对应的函数值，这便得出了该函数的值域．【详解】解：∵cos∈[-1，1]；∴；即y∈[-2，0]；∴该函数的值域为[-2，0]．故答案为：[-2，0]．【点睛】考查函数定义域、值域的概念，本题可换元求值域：令cos=t，-1≤t≤1，从而得出f（t）∈[-2，0]．7.若行列式的展开式的绝对值小于6的解集为（-1，2），则实数a等于______．【答案】4【解析】【分析】推导出|ax-2|＜6的解集为（-1，2），从而-4＜ax＜8解集为（-1，2），由此能求出a的值．【详解】解：∵行列式的展开式的绝对值小于6的解集为（-1，2），∴|ax-2|＜6的解集为（-1，2），∴-6＜ax-2＜6，即-4＜ax＜8解集为（-1，2），解得a=4．故答案为：4．【点睛】本题考查实数值的求法，考查行列式展开法则、不等式的性质等基础知识，考查运算求解能力，是基础题．8.在（0，2π）内使sin3x＞cos3x成立的x的取值范围是______．【答案】（，）【解析】【分析】设f（x）=sin3x-cos3x，x∈（0，2π），化f（x）=（sin x-cos x）（1+sin2x），判断sin x-cos x ＞0时f（x）＞0，由此求出不等式成立的x的取值范围．【详解】解：由题意，设f（x）=sin3x-cos3x，x∈（0，2π），∴f（x）=（sin x-cos x）（sin2x+sin x cosx+cos2x）=（sin x-cos x）（1+sin2x），又1+sin2x＞0恒成立，∴sin x-cos x＞0，即sin x＞cos x，即＜x＜时，f（x）＞0，∴（0，2π）内使sin3x＞cos3x成立的x的取值范围是（，）．故答案为：（，）．【点睛】本题考查了三角函数的图象与性质的应用问题，也考查了转化应用问题，是中档题．9.在等差数列{a n}中，S7=8，则a4=______．【答案】【解析】【分析】由等差数列的性质及前n项和列式求解．【详解】解：在等差数列{a n}中，由S7=，得．故答案为：．【点睛】本题考查等差数列的前n项和，考查等差数列的性质，是基础题．10.已知f（x+1）=2x-2，那么f-1（2）的值是______．【答案】3【解析】【分析】令t=x+1，将已知等式中的x一律换为t，求出f（t）即得到f（x），然后令f（x）=2x-1-2=2，求出相应的x，即为f-1（2）的值．【详解】解：令t=x+1则x=t-1所以f（t）=2t-1-2所以f（x）=2x-1-2令f（x）=2x-1-2=2，解得x=3∴f-1（2）=3故答案为：3．【点睛】已知f（ax+b）的解析式，求f（x）的解析式，一般用换元的方法或配凑的方法，换元时，注意新变量的范围，同时考查了反函数求值，属于基础题．11.甲、乙、丙、丁四位同学站成一排照相留念，已知甲、乙相邻，则甲、丙相邻的概率为______．【答案】【解析】【分析】4人排成一排，其中甲、乙相邻的情况有12种，其中甲丙相邻的只有4种，由此能求出甲乙相邻，则甲丙相邻的概率．【详解】解：甲、乙相邻的方法有=12种情况，如果满足甲、丙相邻，则有4种情况，所以所求的概率为P=故答案为：．【点睛】本题考查概率的求法，是基础题，解题时要认真审题，注意等可能事件概率计算公式的合理运用．12.若P（x，y）是双曲线上的动点，则|x-y|最小值是______．【答案】2【解析】【分析】利用双曲线方程，通过三角代换转化求解x，y，然后求解|x-y|的最小值．【详解】解：P（x，y）是双曲线上的动点，设：x=，y=2tanθ，所以|x-y|=|-2tanθ|=，表达式的几何意义是单位圆上的点与（0，）斜率的2倍，可得：2∈[2，2+2]，故答案为：2【点睛】本题考查双曲线的简单性质的应用，考查转化思想以及计算能力．13.设点P到平面α的距离为，点Q在平面α上，使得直线PQ与平面α所成角不小于30°且不大于60°，则这样的PQ所构成的区域体积为______．【答案】【解析】【分析】由题意画出图形，分别求出两个圆锥的半径，代入圆锥体积公式作差即可．【详解】解：如图，过P作PO⊥α，则PO=，当∠PQO=60°时，OQ=1，当∠PQO=30°时，OQ=3．∴PQ所构成的区域体积为V=．故答案为：．【点睛】本题考查圆锥体积的求法，考查空间想象能力与思维能力，是中档题．14.已知AB为单位圆上弦长为的弦，P为单位圆上的点，若f（λ）=的最小值为m（其中λ∈R），当点P在单位圆上运动时，则m的最大值为______．【答案】【解析】【分析】设λ，根据向量减法的运算法则，转化为点到直线的距离，利用直线和圆相交时的垂径定理结合勾股定理进行求解即可．【详解】解：设λ，则f（λ）===，又C点在直线AB上，要求f（λ）最小值，等价为求出的最小值，显然当CP⊥AB时，CP最小，可得f（λ）的最小值m为点P到AB的距离，∵|AB|=，∴|BC|=，则|OC|=则|CP|=|OP|+|OC|=1+=，即m的最大值为，故答案为：．【点睛】本题考查向量共线定理的运用，以及圆的垂径定理和勾股定理的运用，利用向量的基本运算结合数形结合是解决本题的关键．综合性较强，有一定的难度．15.已知函数f（a，x）=sin x+cos x随着a，x在定义域内变化时，该函数的最大值为______【答案】【解析】【分析】运用辅助角公式和正弦函数的值域可得f（a，x）≤，再由柯西不等式，计算可得所求最大值．【详解】解：函数f（a，x）=sin x+cos x=sin（x+θ）（θ为辅助角），即有f（a，x）≤（sin（x+θ）=1取得等号），由柯西不等式可得（）2≤（1+1）（a+1-a）=2，当且仅当a=时，取得等号，即有≤，即f（a，x）的最大值为．故答案为：．【点睛】本题考查函数的最值求法，注意运用辅助角公式和正弦函数的值域，以及柯西不等式，考查运算能力，属于中档题．16.已知定义在上的函数f（x）=，设a，b，c为三个互不相同的实数，满足f（a）=f（b）=f（c），则abc的取值范围为______．【答案】（81，144）【解析】【分析】先判断函数的性质以及图象的特点，设a＜b＜c，由图象得ab是个定值，利用数形结合的思想去解决即可．【详解】解：作出f（x）的图象如图：当x＞9时，由f（x）=4-=0，得x=16，若a，b，c互不相等，不妨设a＜b＜c，因为f（a）=f（b）=f（c），所以由图象可知0＜a＜3＜b＜9，9＜c＜16，由f（a）=f（b），得1-log3a=log3b-1，即log3a+log3b=2，即log3（ab）=2，则ab=9，所以abc=9c，因为9＜c＜16，所以81＜9c＜144，即81＜abc＜144，所以abc的取值范围是（81，144）．故答案为：（81，144）．【点睛】本题主要考查函数与方程的应用，利用数形结合得到ab是个常数是解决本题的关键．综合考查学生的推理能力．三、解答题（本大题共5小题）17.在长方体ABCD-A1B1C1D1中（如图），AD=AA1=1，AB=2，点E是棱AB的中点．（1）求异面直线AD1与EC所成角的大小；（2）《九章算术》中，将四个面都是直角三角形的四面体称为鳖臑，试问四面体D1CDE是否为鳖臑？并说明理由．【答案】(1) (2)见解析【解析】【分析】（1）取CD中点F，连接AF，则AF∥EC，即∠D1AF为异面直线AD1与EC所成角，解三角形可得△AD1F为等边三角形，从而得到异面直线AD1与EC所成角的大小；（2）证明DE⊥CE，进一步得到D1E⊥CE，可知四面体D1CDE是鳖臑．【详解】解：（1）取CD中点F，连接AF，则AF∥EC，∴∠D1AF为异面直线AD1与EC所成角．在长方体ABCD-A1B1C1D1中，由AD=AA1=1，AB=2，得∴△AD1F为等边三角形，则．∴异面直线AD1与EC所成角的大小为；（2）连接DE，∵E为AB的中点，∴DE=EC=，又CD=2，∴DE2+CE2=DC2，得DE⊥CE．∵D1D⊥底面DEC，则D1D⊥CE，∴CE⊥平面D1DE，得D1E⊥CE．∴四面体D1CDE的四个面都是直角三角形，故四面体D1CDE是鳖臑．【点睛】本题考查异面直线所成角的求法，考查空间中直线与直线，直线与平面位置关系的判定，考查空间想象能力与思维能力，是中档题．18.设S，T是R的两个非空子集，如果函数y=f（x）满足：①T={f（x）|x∈S}；②对任意x1，x2，当x1＜x2时，恒有f（x1）＜f（x2），那么称函数y=f（x）为集合S到集合T的“保序同构函数”．（1）试判断下列函数f（x）=，f（x）=tan（πx-）是否是集合A={x|0＜x＜1}到集合R的保序同构函数；请说明理由．（2）若f（x）=是集合[0，s]到集合[0，t]是保序同构函数，求s和t的最大值．【答案】（1）见解析；（2）s的最大值为1，t的最大值为【解析】【分析】（1）根据集合A={x|0＜x＜1}到集合R的保序同构函数的定义，判断函数是否是单调递增函数即可；（2）利用导数研究函数f（x）=在x≥0上的单调区间，结合保序同构函数的定义进行求解即可．【详解】解：（1）由②知，函数为增函数即可．若f（x）=，当0＜x＜1时，-1＜-x＜0，函数y=为增函数，同时y=为增函数，即f（x）=增函数，满足条件．若f（x）=tan（πx-），当0＜x＜1时，0＜πx＜π，-＜πx-＜，此时函数f（x）为增函数，满足条件．即两个函数都是集合A={x|0＜x＜1}到集合R的保序同构函数．（2）函数f（x）为f′（x）==，当x＞0时，由f′（x）＞0得1-x2＞0得x2＜1，得0＜x＜1，由f′（x）＜0得1-x2＜0得x2＞1，即x＞1，即函数f（x）在[0，1]上是增函数，在[1，+∞）上是减函数，则s的最大值为1，t的最大值为f（1）=．【点睛】本题主要考查函数与方程的应用，结合新定义保序同构函数转化为判断函数的单调性是解决本题的关键．19.如图，已知一个长方形展览大厅长为20m，宽为16m，展厅入口位于其长边的中间位置，为其正中央有一个圆心为C的圆盘形展台，现欲在展厅一角B点处安装一个监控摄像头对展台与入口进行监控（如图中阴影所示），要求B与圆C在同一水平面上．（1）若圆盘半径为2m，求监控摄像头最小水平摄像视角的正切值；（2）若监控摄像头最大水平摄像视角为60°，求圆盘半径的最大值．（注：水平摄像视角指镜头中心点与水平观察物体边缘的视线的夹角）【答案】(1) 1+ (2) 5-4【解析】【分析】（1）分别求出∠ABC和∠CBE的正切值，利用两角和的正切公式计算；（2）利用两角差的正切公式计算tan∠CBE，再根据正切的定义列方程求出圆的半径．【详解】解：（1）过C作入口所在边的高AC，垂足为A，由题意可知AC=8，AB=10，BC==2，∴tan∠ABC=，过B作圆C的切线BE，切点为E，则CE⊥BE，CE=2，且∠ABE为监控摄像头最小水平摄像视角．∵BE==12，∴tan∠CBE=，∴tan∠ABE=tan（∠ABC+∠CBE）=1+．∴当圆盘半径为2时，监控摄像头最小水平摄像视角的正切值为1+．（2）过B作直线BD，使得∠ABD=60°，过C作CM⊥BD，垂足为M，则∠CBD=60°-∠ABC，∴tan∠CBD=tan（60°-∠ABC）=．设圆盘的最大半径为r，则tan∠CBD=．解得r=5-4．∴圆盘的最大半径为5-4．【点睛】本题考查了函数模型的应用，直线与圆的位置关系，属于中档题．20.已知椭圆C：（a＞b＞0）的左右焦点分别为F1，F2，过F1任作一条与坐标轴都不垂直的直线，与C交于A，B两点，且△ABF2的周长为8．当直线AB的斜率为时，AF2与x轴垂直．（1）求椭圆C的方程（2）若A是该椭圆上位于第一象限的一点，过A作圆x2+y2=b2的切线，切点为P，求|AF1|-|AP|的值；（3）设P（0，m）（m≠±b）为定点，直线l过点P与x轴交于点Q，且与椭圆交于C，D两点，设，，，求λ+μ的值．【答案】（1）=1（2）2（3）【解析】【分析】（1）根据题意4a=8，再根据勾股定理求出c=1，即可求出椭圆方程，（2）由题意，根据直线和圆相切，以及勾股定理可得AF1|=2+x0，|PA|=x0，即可求出|AF1|-|AP|的值（3）根据向量的运算可得λ+μ=2+m（+），再题意直线l的方程为x=y（x+m），代入，由此利用韦达定理结合已知条件，即可求出．【详解】解：（1）∵△ABF2的周长为8，∴4a=8，即a=2，∵tan∠AF1F2=，设|AF2|=3m，则|F1F2|=2c=4m，∴|AF1|=5m，∵|AF1|+|AF2|=2a=4，∴3m+5m=4，∴m=，∴2c=2，∴c=1，∴b2=a2-c2=3，∴椭圆C的方程=1，（2）设A（x0，y0），则=1，（|x0|＜2）∴|AF1|2=（x0+1）2+y02=（x0+4）2，∴|AF1|=2+x0，连接OP，OP，由相切条件知：|PA|2=|OP|2-|OP|2=x02+y02-3=x02+3-x02-3=x02，∴|PA|=x0，∴|AF1|-|AP|=2+x0-x0=2．（3）设C（x1，y1），D（x2，y2），显然可知直线l的斜率存在且不为0，设直线l的方程为x=k（y-m），令y=0，可得x=-km，则Q（-km，0），由，得（x1+km，y1）=λ（x1，y1-m），则y1=λ（y1-m），即λ==1+，，可得（x2+km，y2）=μ（x2，y2-m），即μ=1+将x=k（y-m），代入椭圆=1中（4+3k2）y2-6mk2y+3k2m2-12=0，由韦达定理得y1+y2=，y1y2=，∴λ+μ=2+m（+）=2+m•=2+==．【点睛】本题考查椭圆的求法，考查直线和椭圆的位置关系，韦达定理，考查两数和为定值的证明，解题时要认真审题，注意函数与方程思想的合理运用．21.设正项数列{a n}的前n项和为S n，首项为1，q为非零正常数，已知对任意整数n，m，当n＞m时，S n-S m=q m•S n-m恒成立．（1）求数列{a n}的通项公式；（2）证明数列是递增数列；（3）是否存在正常数c使得{lg（c-S n）}为等差数列？若存在，求出常数c的值；若不存在，说明理由．【答案】（1) a n=q n-1 (2)见证明 (2)见解析【解析】【分析】（1）由已知条件，可令m=n-1，代入结合数列的递推式，即可得到所求通项公式；（2）讨论公比q是否为1，求得S n，以及，由单调性的定义即可得证；（3）假设存在正常数c使得{lg（c-S n）}为等差数列，结合对数的运算性质和等差数列的通项公式，即可得到所求结论．【详解】解：（1）因为对任意正整数n，m，当n＞m时，S n-S m=q m•S n-m总成立，所以n≥2时，令m=n-1，得到S n-S n-1=q n-1•S1，即a n=a1q n-1=q n-1，当n=1时，也成立，所以a n=q n-1，（2）证明：当q=1时，S n=n，=随着n的增大而增大；当q＞0，q≠1时，S n=，，由＜0，可得数列{}是递增数列；（3）假设存在正常数c使得{lg（c-S n）}为等差数列．当q=1时，S n=n，q≠1时，S n=，{lg（c-S n）}为等差数列，可得q≠1，lg（c-+）=lg=n lg q-lg（1-q）为等差数列，即有c=（0＜q＜1），【点睛】本题考查数列的通项和求和的关系，考查等比数列的通项公式和求和公式，以及数列的单调性的判断，考查运算能力，属于中档题．。

上海市七宝中学2018-2019学年高一下学期期末考试数学试卷含解析

11. 中，，则A的取值范围为______．
【答案】
【解析】
【分析】
由正弦定理将sin2A≤sin2B＋sin2C－sinBsinC变为，然后用余弦定理推论可求，进而根据余弦函数的图像性质可求得角A的取值范围。
【详解】因为sin2A≤sin2B＋sin2C－sinBsinC，所以，即。
所以，
【详解】设，则
∴ 为偶函数，其图象关于轴对称，
又依题意只有一个零点，故此零点只能是，
所以，
∴ ，
∴ ，
∴ ，∴ ，
故答案为：
【点睛】本题主要考查了函数奇偶性以及零点与方程的关系，方程的根就是对应函数的零点，本题属于基础题。
13.等差数列前项和为，已知，，则 _____．
【答案】4028
当a不是零点时，a+kπ（k∈z）也都不是零点，区间[a+kπ，a+（k+1）π]上恰有两个零点，故在[a，a+10π]上有20个零点．
综上，y=g（x）在[a，a+10π]上零点个数的所有可能值为21或20．
考点：函数y=Asin（ωx+φ）的图象变换；函数奇偶性的判断；根的存在性及根的个数判断
点评：本题考查函数y=Asin（ωx+φ）的图象变换、函数的奇偶性、根的存在性及根的个数的判断，考查数形结合思想，结合图象分析是解决（2）问的关键
【解析】
【分析】
首先根据、即可求出和，从而求出。
【详解】，①
，②
① ②得，
，
即，
∴ ，
即，
∴ ，
故答案为：4028．
【点睛】本题主要考查了解方程，以及等差数列的性质和前项和。其中等差数列的性质:若则比较常考，需理解掌握。

上海市闵行区七宝中学高一英语下学期期末考试试题

上海市闵⾏区七宝中学⾼⼀英语下学期期末考试试题上海市七宝中学2013学年⾼⼀第⼆学期英语期末试卷I. Listening Comprehension （17%）Section A (10%)1. A. At 9:25. B. At 9:30 C. At 9:40 D. At 9:452. A In a garage. B. At the airport. C. In the clinic. D. At a restaurant.3. A. The service is slow. B. The food is poor.C. The prices are high.D. The restaurant is new.4. A. Pick up her son from school. B. Meet the man in his office.C. Work on a report.D. Prepare dinner for her son.5. A. She failed to contact Mr. Wright.B. She is about to call M r. Wright’s secretary.C. She will see Mr. Wright at lunch time.D. She discussed the sports program with Mr. Wright.6. A. He was late for the exam. B. He usually went to class late.C. He was sick for a long time.D. He did not finish the test paper.7. A. He finds the presentation hard to follow.B. He considers the presentation very dull.C. He thinks Professor White has chosen an interesting topic.D. He speaks highly of the presentation.8. A. Its price. B. Its service. C. Its location.D. Its facilities.9. A. She lost a lot of weight in two years.B. She stopped exercising two years ago.C. She had a unique way of staying healthy.D. She never stuck to doing anything she did.10. A. Intelligence determines admission to college.B. Highly motivated students usually do well in college.C. Successful college students usually are intelligent.D. A successful college motivates its students.Section B (3%)Questions 11 through 13 are based on the following passage.11. A. He earns a high salary. B. He does not go out much.C. He runs a computer company.D. He lives with his parents.12. A. Learning to drive a car. B. Releasing new computer games.C. Spending money like an adult.D. Finding a highly-paid job13. A. His firm might go bankrupt some day.B. Computer games might not always sell so well.C. One has to be young to write computer programs.D. He wants to stop working when he is a millionaire.Section C (4%)Complete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and VocabularyA: Fill in each of the blanks with a proper word or a proper form of the given word. 10%HAVE you ever seen buses on the street for donating blood? Medical workers on board collect blood from volunteers. The blood is then stored up and given to __18__ has lost a large amount of it due to accidents or diseases.Blood is one of the most crucial substances__19__ (support) our lives. But for now, the only way we ___20___ get more of it is__21__ donation. And donated blood has its own problems.First of all, certain blood types are extremely rare. Type O negative blood (O-), for example, only exists in 7 percent of people, according to The Sunday Times. There are fewer donors and therefore there isn’t enough of this type of blood for everybody who needs it.In addition, donated blood comes from various people, which means that it has to be screened carefully for diseases such as hepatitis (肝炎) and HIV to make sure that it’s safe for transfusion.This is why scientists all over the world have been trying to make blood in labs. And now, someone finally succeeded – Marc Turner at the Scottish National Blood Transfusion Service__22__ (produce) blood fit for transfusion, reported Forbes. Unlike many other scientists, who have tried to make blood substitutes by blending different ingredients together, Turner chose__ 23__ (grow) blood directly from human stem cells. He developed a special technique to create a chemical environment similar to__24__ in our bone marrow (⾻髓). This environment encourages stem cells to mature into red blood cells. According to Turner, his version of artificial blood is unlikely to contain disease viruses or produce side effects. And the best part is that what he managed to produce was type O- blood. Not only is it a rare blood type, it’s also a universal type, __25__ means it can be transfused into any patient.The new blood__26__ (schedule) for human tests in 2016. However, Turner stressed that the new study should not be taken as a signal for people to stop donating blood because it could be another 20 years __27__ the artificial blood can be manufacturedon a large scale.Section B: Choose one word for each blank. 9%请考⽣按题号从41题继续填涂答题卡，切记！Ignore Everyone, Be yourselfPeople love to give advice. They love to share their opinions about how you should live your life .But really, what do they know about you and how you should live your life?Nothing.Here’s the thing ----how many times have you ever taken someone’s advice and ignored the small__41__ inside your head screaming at you to do the __42__? And how many times have youkicked yourself after because you knew what you needed to do, but you just didn’t listen to yourself.By listening to the__43__ of others too much, we are putting ourselves at risk. We risk valuing ourselves on the opinions of others, and this can only lead to __44__, because you can’t please all the people all the time.If you look back in history at the most iconic innovators of our time they did not listen to others. Because __45__ people understand that the most important person to__46__ is yourself. Once you realize this you let go of being held hostage by other people’s opinions and you free yourself to be you.The other reason why it’s dangerous to consistently act upon the opinions of others is it creates a values conflict.Personal values are the things that__47__ most to you in life. Let’s assume, “innovation “is one of your values. If you were to follow someone else’s advice and do something __48__, you would experience a “value conflict”because this is not “who you are ”and it’s __49__ that you would start to feel uneasy, frustrated and unhappy.So, should you never listen to anyone else’s advice?Of course not.It can be very useful to gain a second opinion from others ----They may have a fresh take on something that you have been too close to .The point is , don’t make other people’s advice for the sake of it. Make sure you make your own decisions. Perhaps you take a small part of what someone is saying and ignore the rest! The most important thing is that you make your own decisions or you will end up living someone else’s life.III. Reading Comprehension 39%Section A: Cloze 15%COMPUTERS and robots are becoming smarter every day, affording hopes of technological advances for human beings.__50__, the growth of artificial intelligence could also cause chaos (混乱), a __51__ that has been explored frequently in recent science fiction. Now a new film, Transcendence, which hit global theaters on April 18, is shaking people’s __52__ in technology once more.In Transcendence, Dr Will Caster (played by Johnny Depp) is an artificial intelligence researcher. He has spent his whole life trying to design a computer with human__53__. “Its analytical power will be greater than the __54__ intellig ence of every person in the history of the world,” he says in a lecture. His experiments have made him famous, but anti-technology activists want to do whatever it __55__ to stop him.After Caster is shot by anti-technology activists, his wife Evelyn attempts to save his __56__ by uploading his mind into a computer. A few years in, the computer with his consciousness (意识) transcends (超越) human __57__. As his powers threaten to overwhelm (征服) the world, people begin to __58__whether he should be regarded as mankind’s savior -– or its downfall.“The theories associated with the film say that when a strong artificial intelligence wakes up, it will quickly become more__59__ than [any] human being,” screenwriter Jack Paglen told New York Post, referring to a concept known as “technological singularity (奇点)”.Technological singularity, most notably predicted by Google’s __60__ Ray Kurzweil, will be the moment around the year 2045, when artificial intelligence becomes smarter than the human mind. Such a singularity could lead to numerous solutions to human problems, __61__ cures for diseases and even the end of __62__. But what we see in the film goes beyond just healing, as the people whom the virtual version of Caster heals develop special powers – for example, one is suddenly able to jump from the ground right onto the roof of a building.Will computer technology, which is __63__every day, continue to improve our lives? Or will it become a force that can’t be controlled and will __64__destroy the human race?50. A. Moreover B. However C. Therefore D. Otherwise51. A. program B. belief C. fear D. field52. A. faith B. viewpoint C. suspect D. craze53. A. emotions B. spirit C. experience D. behaviors54. A. artificial B. individual C. extreme D. collective55. A. pays B. takes C. likes D. creates56. A. intelligence B. wish C. fame D. life57. A. wisdom B. knowledge C. control D. progress58. A. doubt B. state C. debate D. estimate59. A. threatening B. intelligent C. inferior D. accessible60. A. futurist. B. technician C. designer D. advertiser61. A. rather than B. apart from C. other than D. such as62. A. depression B. aging C. dieting D. boredom63. A. changing B. emerging C. advancing D. increasing64. A. violently B. regrettably C. actually D. eventuallySection B: Reading 24%(A)When my old dog developed major health problems, I knew that watching him fail would be painful, but I wasn’t prepared for the powerful lessons he’d offer in the last year of his life.Chance was 14 when the problems started. First, he developed a cancer that left him whistling for breath. Then came cataracts (⽩内障) in both eyes, arthritis (关节炎) in his legs, and a series of ministrokes (⼩中风) that threw off his balance. Any one of these misfortunes would have left me begging for relief, but Chance became calmer as the disabilities piled up. When leg pain left him frozen on the floor, unable to rise for a quick pat as I came home, he didn’t complain. He just lay there patiently, hammering tail, each movement of his tail spelling out the value of waiting for the things you want. When his cataracts made steering impossible after dark, he’d stand calmly until I could guide him inside, proving how easy it is to find happiness if you let go of your pride and insecurities and learn to lean on those who love you. When ministrokes had him walk unsteadily like a drunk, he taught the value of persistence. For days after each attack, he’d fall as he moved about. Yet again and again he’d try to walk, each day moving a few more steps until finally he was able to get outside and back by himself.There were lessons in so much of what he did, but the key one surely was the importance of obtaining all the joy possible from each experience whether it’s a day lazing under a warm sun or a few minutes appreciating a favorite meal.For most of our life together, Chance was always rushing ahead, searching out new adventures, then circling back to let me know what lay around the next bend. As an old dog, he did the same thing, using his attitude, instead of his once-fast legs, to show the way.65. Chance suffered very much from all the diseases he had except for ______.A. having problem with breathB. walking around awkwardlyC. having trouble drinkingD. losing his eyesight in darkness66. ______ is the most important lesson the author learned from Chance.A. Living in the present and enjoying what we haveB. Learning to depend on those who we love and trustC. That we should expect good things to happen patientlyD. That we should persevere in what we believe is worth trying67. It is implied in the passage that ______.A. people might suffer from different diseases when they grow oldB. people could face aging with courage and dignityC. pets would become calmer for lack of energy in their last daysD. pets and masters should stick together helping each other in difficulty68. Which of the following words best describes the author’s feelings to Chance?A. CaringB. GratefulC. InsecureD. Painful(B)“Opinion” is a word that is used carelessly today. It is used to refer to matters of taste, belief, and judgment. This casual use would probably cause little confusion if people didn’t attach too much importance to opinion. Unfortunately, most to attach great importance to it. “I have as much right to my opinion as you to yours,”and “Everyone’s entitled to his opinion,” are common expressions. In fact, anyone who would challenge another’s opinion is likely to be branded intolerant.Is that label accurate? Is it intolerant t o challenge another’s opi nion? It depends on what definition of opinion you have in mind. For example, you may ask a friend “What do you think of the new Ford cars?” A nd he may reply, “In my opinion, they’re ugly.” In this case, it would not only be intolerant to challenge his statement, but foolish. For it’s obvious that by opinion he means his personal preference, a matter of taste. And as the old saying goes, “It’s pointless to arg ue about matt ers of taste.”But consider this very different use of the term, a newspaper reports that the Supreme Court has delivered its opinion in a controversial case. Obviously the justices did not shale their personal preferences, their mere likes and dislikes, they stated their considered judgment, painstakingly arrived at after thorough inquiry and deliberation.Most of what is referred to as opinion falls somewhere between these two extremes. It is not an expression of taste. Nor is it careful judgment. Yet it may contain elements of both. It is a view or belief more or less casually arrived at, with or without examining the evidence.Is everyone entitled to his opinion? Of course, this is not only permitted, but guaranteed. We are free to act on our opinions only so long as, in doing so, we do not harm others.69. According to the author, who of the following would be labeled as intolerant?A. Someone who turns a deaf ear to oth ers’ opinions.B. Someone wh o can’t put up wi th oth ers’ tas tes.C. Someone who values only their own opinions.D. Someone whose opinion harms other people.（B）70. The new Ford cars are used here as an example to show that ________.A. it is foolish to criticize a famous brandB. one should not alw ays agree to others’ opinio nsC. personal tastes are not something to be challengedD. it is unwise to express on e’s likes and dislikes in public（C）71. Considered judgment is different from personal preference because ________.A. it is stated by judges in the courtB. it reflects public like and dislikesC. it is a result of a lot of controversyD. it is based on careful thought （D）72. As indicated in the passage, being free to act on one’s opinion ________.A. means that one can ignore other people’s critic ismB. means that one can impose his preferences on othersC. do esn’t mean that one has the right to do things at willD. doesn’t mean that one has the right to charge others without evidence（C） (C )Section C: Q & ADirections: Read the passage carefully. Then answer the questions or complete the statements according to the instruction given .Many artists late in the last century were in search of a means to express their individuality(个性). Modern dance was one of the ways some of these people sought to free their creative spirit. At the beginning there was no exact technique or no foundation from which to build. In later years, trial, error and genius founded the techniques and the principles of the movement. Eventually, innovators even learned from ballet, but first they had to abandon all that was academic so that the new could be discovered. The beginnings of modern dance were happening before Isadora Duncan, but she was the first person to bring the new dance to general audiences and saw it accepted.Her search for a natural movement form sent her to nature. She believed movement should be as natural as the swaying(摇摆) of the tree and the rolling waves of the sea and should be in harmony with the movements of the Earth. Her great contributions are in three areas.First, she began the expansion of the kinds of movements that could be used in dance. Before Duncan danced, ballet was the only type of dance performed in concert. In the ballet the feet and legs were emphasized, with virtuosity(精湛技巧) shown by complicated positions and movements. Duncan performed dance by using all her body in the freest possible way. Her dance came from her heart and soul. She was one of the pioneers who broke tradition so others might be able to develop the art. Her second contribution lies in dance costumes. She gave up corsets(紧⾝⾐), ballet shoes and still costumes. These were replaced with long loose dresses, bare feet, and unbound hair. She believed in the natural body being allowed to move freely, and her dress displayed this idea.Her third contribution ____________. In her performance she used the symphonies of great masters, including Beethoven and Wagner, which was not the usual custom. She was as exciting and eccentric(古怪的) in her personal life as in her dance. What would be the best title of the passage? (Please answer within 8 words)__________________________________________________________________________ Please fill in the blank in the fifth paragraph with proper words or phrases to complete the sentence. (Please answer within 8 words)__________________________________________________________________________According to the passage, what does the following paragraph most probably discuss? (Please answer within 8 words)__________________________________________________________________________ Translate the underlined sentence into Chinese.____________________________________________________________________________________________________________________________________________________IV. Translation 15% (2+2+3+4+4)1. ⼤难不死的⼈更懂得⽣命之精彩。