七宝中学高三上期中(含答案解析版)

2019-2020学年上海市七宝实验中学高三英语上学期期中考试试卷及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AWhen it comes to the greatest inventions of the world, China’s name is sure to be mentioned several times. There are hundreds of things which were invented by the Chinese.AlcoholShocked? I was because when they said alcohol I thought about either the US or the UK. China had never crossed my mind. In China, alcohol was made by two legendary persons named Yi Di and Du Kang who belonged to the Xia Dynasty. This period was about 2000 BC - 1600 BC. Research says that in ancient China, beer with 4% alcoholic content was widely consumed by people.TeaChina is the proud inventor of tea which was first drunk by Shen Nong, a Chinese emperor around 2737 BC. Tea production was rapidly developed, making tea a popular drink during the Tang and Song Dynasties.The Mechanical ClockHave you ever wondered what on earth we would be doing without any idea of time? A clock really is an invention without which things were incomplete. The credit of making the first mechanical clock goes to ancient China. The first mechanical clock was invented by Yi Xing in the Tang Dynasty. This was during 618 and 907.Silk FabricSilk, the favorite fabric of many girls out there, is also a Chinese invention. Although we all know that silk is made by silkworms, it was Chinese people who first invented a way to harvest the silk and then use it to make clothes. The oldest silk which has been found so far is in Henan Province and dates back to 3630 BC.1.We can learn from Paragraph 2 that ________.A.people in the US like alcoholB.beer was popular in the Xia DynastyC.Yi Di and Du Kang invented alcohol by accidentD.the author didn’t know alcohol is a Chinese invention2.The author asks the question in Paragraph 4 to show ________.A.ancient Chinese inventors were wiserB.many things in our lives are incompleteC.ancient Chinese people never wasted timeD.the invention of the mechanical clock is important3.Which of the following invention has a longer history?A.Tea.B.Alcohol.C.Silk fabric.D.The mechanical clock.BA city inSouth Korea, which has the world’s largest number of people using smartphones, has placed flashing lights and laser beams at a road crossing to warn “smartphone zombies” to look up and drivers to slow down, in the hope of preventing accidents.The designers of the system were motivated by growing worry that more pedestrians glued to their phones will become victims in a country that already has some of the highest road death and injury rates among developed countries. State-run Korea Institute of Civil Engineering and Building Technology (KICT) believes its system of flashing lights at zebra crossings can warn both pedestrians and drivers.In addition to red, yellow and blue LED lights on the pavement, “smombies” - smartphone zombies - will be warned by laser beam projected from power poles and a warning sent to the phones by an app that they are about to step into traffic.“Increasing number of smombie accidents have occurred in pedestrian crossings, so these zombie lights are essential to prevent these pedestrian accidents,” said KICT senior researcher Kim Jong-hoon. Drivers are warned by the flashing lights, which have shown to be effective 83.4 percent of the time in the institute’s tests involving about 1,000 vehicles.In 2017, more than 1,600 pedestrians were killed in auto related accidents, which is about 40 percent of total traffic deaths, according to data from the Traffic Accident Analysis System. For now, the smombie warning system is placed only in Ilsan, a suburban city about30 kmnorthwest of the capital,Seoul, but is expected to go nationwide, according to the institute.Kim Dan-hee, a 23-year-old resident of Ilsan, welcomed the system, saying she was often too absorbed in her phone to remember to look at traffic. “This flashing light makes me feel safe as it makes me look around again, and I hope that we can have more of these in town,” she said.4. What do the underlined words “smartphone zombies” in paragraph 1 refer to?A. Drivers driving after drunk.B. Pedestrians buried in their phones.C. Passengers crazy about phones.D. Policemen in charge of traffic.5. What do we know about the warning system?A. It has reduced death rate by 83.4%.B. It has been spread nationwide.C. It gives a warning to the smartphones.D. It is being tried out in many places.6. What was the residents’ attitude to the traffic system?A. Negative.B. Unconcerned.C. Disapproving.D. Favorable.7. What is the best title for the text?A.South KoreaWarns Smartphone Zombies of TrafficB. Flashing Lights Are Used to Prevent AccidentsC. Smartphone Zombies Are Causing Traffic AccidentsD.South KoreaUses a New Traffic SystemCI had very good parents. My mother came toAmericafromScotlandby herself when she was 11, and she didn’t have much education. My dad was kind of a street kid, and he eventually went into the insurance business, selling nickel policies door to door.One day, my dad asked his boss, “What's the toughest market to sell?” and the insurance guy replied “Well, black people. They don’t buy insurance.” My dad thought, but they have kids; they have families. Why wouldn’t they buy insurance? So he said, “Give meHarlem.”When my dad died in 1994, I talked about him onThe Tonight Show. I told the story of how he worked in Harlem and how he always taught us to be open-minded and not to say or think things of racism (种族主义). Then one day, I got a letter from a woman who was about 75 years old.She wrote that when she was a little girl, a man used to come to her house to collect policies. She said this man was the only white person who had ever come to dinner at their house. The man was very kind to her, she said, and his name was Angelo—was this my father?The letter made me cry. I called her up and said yes, that was in fact my dad, and she told me how kind he had been to her family. Her whole attitude toward white people was based on that one nice man she met in her childhood, who always treated her with kindness and respect and always gave her a piece of candy. From this experience, I learned a valuable life lesson: never judge people and be open-minded and kind to others.8. What did my father do after knowing what was the toughest market to sell?A. He asked his boss to give him some insurance.B. He went toScotlandto improve his education.C. He specially went to white families with kids.D. He choseHarlemto face the toughest challenge.9. What can we learn from the third paragraph?A. It was rare that a businessman had dinner in his customer's house.B. Angelo was the only white person to sell insurance inHarlem.C. The little girl admired Angelo very much.D. Racism was a serious problem inAmericaat that time.10. Which of the following can best describe the author’s father?A. Stubborn and generous.B. Patient and intelligent.C. Determined and open-minded.D. Confident and romantic.11. What can be the best title of the passage?A. Memories from a TV Show.B. A Letter from an Old Lady.C. Life Lessons from My Father.D. My Father's Experience inHarlem.DJennifer Mauer has needed more willpower than the typical college student to pursue her goal of earning a nursing degree. That willpower bore fruit when Jennifer graduated from University of Wisconsin-Eau Claire and became the first in her large family to earn a bachelor's(学士) degree.Jennifer grew up on a farm in a family of 10 children. Her dad worked at a job away from the farm, and her mother ran the farm with the kids. After high school, Jennifer attended a local technical college, working to pay her tuition(学费), because there was no extra money set aside for a college education. After graduation, she worked to help her sisters and brothers pay for their schooling.Jennifer now is married and has three children of her own. She decided to go back to college to advance her career and to be able to better support her family while doing something she loves: nursing. She chose the UW-Eau Claire program at Ministry Saint Joseph's Hospital in Marshfield because she was able to pursue her four-year degree close to home. She could drive to class and be home in the evening to help with her kids. Jennifer received great support from her family as she worked to earn her degree: Her husband worked two jobs to cover the bills, and her 68-year-old mother helped take care of the children at times.Through it all, she remained in good academic standing and graduated with honors. Jennifer sacrificed(牺牲)a lot to achieve her goal, giving up many nights with her kids and missing important events to study. “Some nights my heart was breaking to have to pick between my kids and studying for exams or papers,” she says. However, her children have learned animportant lesson, witnessing their mother earn her degree. Jennifer is a first-generation graduate and an inspiration to her family—and that's pretty powerful.12. What did Jennifer do after high school?A. She helped her dad with his work.B. She ran the family farm on her own.C. She taught her sisters and brothers.D. She supported herself through college.13. Why did she choose the program at Ministry Saint Joseph's Hospital?A. To learn from the best nurses.B. To take care of her kids easily at night.C. To save money for her parents.D. To find a well-paid job there.14. What did Jennifer sacrifice to achieve her goal?A. Her health.B. Her chance of promotion.C Her reputation. D. Her time with family.15. What can we learn from Jennifer's story?A. Hard work pays off.B. Love breaks down barriers.C. Time is money.D. Education is the key to success.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2021年上海市七宝中学高三生物上学期期中考试试题及答案解析一、选择题：本题共15小题，每小题2分，共30分。

每小题只有一个选项符合题目要求。

1. 下列有关内环境稳态的叙述，正确的是（）A. 内环境稳态是指内环境的成分和理化性质恒定不变B. 通过神经、内分泌和免疫三大系统的协调就可维持内环境稳态C. 内环境稳态是机体进行正常生命活动的必要条件D. 内环境稳态遭到破坏必将引起渗透压的下降2. 九价宫颈癌(HPV)疫苗可预防HPV引起的宫颈癌，中国内地首针预防宫颈癌的九价HPV疫苗于2018年5月30日在海南博鳌超级医院接种，该疫苗将分三次接种。

下列相关叙述错误的是A.从免疫学的角度分析，九价HPV疫苗为抗原B.初次接种九价HPV疫苗，会刺激一种B细胞分泌多种抗体C.当机体再次感染HPV时，记忆B细胞的细胞周期会明显缩短D.该疫苗分三次接种的目的是让机体产生更多的抗体和记忆B细胞3. 下列有关细胞核的叙述中，错误的是（）A. 细胞核是细新陈代谢的主要场所B. 细胞核是细胞遗传的控制中心C. 细胞核是遗传物质储存和复制场所D. 细胞核是细胞代谢的控制中心4. 观察洋葱表皮细胞质壁分离和复原、观察黑藻叶片细胞细胞质流动、花生子叶细胞内脂肪的鉴定实验中，共同点是（）A.实验过程中都有颜色变化B.都需要设计对照实验C.都需要使用光学显微镜观察D.温度对实验都无影响5. 种植过农作物的土地，闲置数年后逐渐被灌木丛覆盖。

该过程中不会发生A.群落的物种组成逐渐发生改变，空间结构越来越复杂B.光照、土壤湿度和盐碱度等影响着群落中生物的分布C.生物与环境间共同进化，环境对多种种群的容纳量增大D.生态系统的能量传递效率及生物多样性的价值逐渐增大6. 人体对病原菌具有一定的防御功能，下列叙述错误的是（）A. 唾液中的溶菌酶可杀死一些病原菌B. 口腔黏膜对病原菌有一定的屏障作用C. 淋巴因子在特异性免疫中发挥作用D. 免疫系统由免疫细胞和免疫活性物质组成7. 下列各对生物性状中，属于相对性状的是A．狗的短毛和狗的卷毛B．人的右利手和人的左利手C．豌豆的红花和豌豆的高茎D．羊的黑毛和兔的白毛8. 下图为存在捕食关系的两个种群数量变化曲线，下列有关叙述正确的是（）A.甲为被捕食者，在图中D点时甲种群增长速率最大B.稳定状态时，乙种群数量将保持稳定不再变化C.在图中C点时，甲种群的年龄结构属于衰退型D.如果乙种群大量繁殖，则会使甲种群灭绝9. 水分子中氢原子以共用电子对与氧原子结合。

2020-2021年七宝中学高三期中考数学试卷一、填空题1.已知全集U R =，集合{}12A x x =->，则U C A =_________.2.若函数2()(4)4,(5)f x x x =-+≥，则1(5)f-=_________.3. ()214732limn n n→∞++++-=_________.4.已知数列{}n a 为等差数列，且191,25a a ==-，则5a =_________.5.设函数2()41f x x mx =-+在(],2-∞上是减函数，则实数的取值范围是_________.6.已知222a b +=，则a b +的取值范围是_________.7.若函数()2sin sin 2f x x x =-在区间[]0,a 上的零点个数为3个，则实数a 的取值范围是_________.8.已知两变量x 、y 之间的关系为lg()lg lg y x y x -=-，则以x 为自变量的函数y 的最小值是_________.9.已知函数()xf x a b =-（0a >且1,a b R ≠∈），()1g x x =+若对任意实数x 均有()()0f x g x ⋅≤，则14a b+的最小值为_________. 10.设函数()sin()(0,0)6f x A x A πωω=->>，[]0,2x π∈若()f x 恰有4个零点，则下述结论中：①0()()f x f x ≥恒成立，则0x 的值有且仅有2个；②存在0ω>，使得()f x 在80,19π⎡⎤⎢⎥⎣⎦上单调递增；③方程1()2f x A =一定有4个实数根，其中真命题的序号为_________.11.函数11()22f x x =-≤≤的图像绕着原点旋转弧度θ(0)θπ≤≤，若得到的图像仍是函数图像，则θ可取值的集合为_________.12.对任意闭区间I ，用I M 表示函数sin y x =在I 上的最大值，若有且仅有一个正数a 使得[][]0,,2a a a M kM =成立，则实数k 的取值范围是_________.二、选择题13.下列各组不等式中，解集完全相同的是（ ）A.2611x x x x +<++与26x x <+B.2(2)(1)0x x x x-+<与(2)(1)0x x -+< C.(2)(1)01x x x +->-与20x +> D.2232111x x x x x x -+>-+-+与321x x ->+ 14.若数列{}n a 的前n 项和为n S ，则“{}n a 是递增数列”是“{}n S 为递增数列”的（ ）A.充分非必要条件B.必要非充分条件C.充要条件D. 既不充分也不必要条件15.已知集合,M P 都是非空集合，若命题“M 中的元素都是P 中的元素”是假命题,则下列说法必定为真命题的是（ ）A.M P =∅B.M 中至多有一个元素不属于PC.P 中有不属于M 的元素D. M 中有不属于P 的元素16.单调递增的数列{}n a 中共有N 项，且对任意,,(1),i j k i j k N ≤<<≤i j a a +，j k a a +和k i a a +中至少有一个是{}n a 中的项，则N 的最大值为（ ）A.9B.8C.7D.6 三、解答题17.如图，已知长方体1111ABCD A B C D -中，AB ，BC =1AA =.（1）求异面直线1AB 与1BC 所成角的大小； （2）求点C 到平面1ABD 的距离.18.已知在ABC ∆中，角,,A B C 的对边分别为,,a b c ,且(cos 2cos )(2)cos c B A a b C -=-.（1）求ab的值； （2）若3cos ,24C c ==，求ABC ∆的面积.19. 某供应商为华为公司提供芯片，由以往的经验表明，不考虑其他因素，该芯片次品率p 与日产量x （万枚）间的关系为：1,04,62,4,3x xp x ⎧<≤⎪⎪-=⎨⎪>⎪⎩，已知每生产1枚合格芯片供应商可盈利30元，每出现1件次品亏损15元.（1）将日盈利额y （万元）表示为日常量x （万枚）的函数；（2）为使日盈利额最大，日产量应为多少万枚？（注：次品率=100%⨯次品数产品总数）.20.已知双曲线2222:1x y C a b-=过点M ，且右焦点为(2,0)F .（1）求双曲线C 的方程；（2）过点F 的直线l 与双曲线C 的右支交于,A B 两点，交y 轴于点P ，若PA mAF =，PB nBF =，求证：m n +为定值.（3）在（2）的条件下，若点Q 是点P 关于原点O 的对称点，求证：三角形QAB 的面积2310QAB S ∆>；21.若实数列{}n a 满足条件212,1,2,n n n a a a n +++≥=，则称{}n a 是一个“凸数列”.（1）判断数列2n a n n =-+和3()2n n b =是否为“凸数列”?（2）若{}n a 是一个“凸数列”，证明：对正整数,,k m n ，当1k m n ≤<<时， 有n m m ka a a a n m m k--≥--； （3）若{}n a 是一个“凸数列”证明：对1i n ≤≤，有111(1)i n iia a a nn++≤-+.2020-2021年七宝中学高三期中考数学试卷一、填空题1.已知全集U R =，集合{}12A x x =->，则U C A =_________. 【解析】{}()()12,13,A x x =->=-∞-+∞，所以[]1,3U C A =-.2.若函数2()(4)4,(5)f x x x =-+≥，则1(5)f -=_________.【解析】令2()(4)45(5)f x x x =-+=≥，解得5x =，所以1(5)5f-=.3. ()214732limn n n→∞++++-=_________.【解析】()214732lim n n n →∞++++-=2(132)32lim 2n x n n →∞+-=. 4.已知数列{}n a 为等差数列，且191,25a a ==-，则5a =_________. 【解析】由等差数列的性质，得()5191122a a a =+=-.5.设函数2()41f x x mx =-+在(],2-∞上是减函数，则实数的取值范围是_________.【解析】由题意得22m ≥，所以1m ≥.6.已知222a b +=，则a b +的取值范围是_________.【解析】令2,2a θb θ==，则[]222sin 2,24a b ⎛⎫+==+∈- ⎪⎝⎭πθθθ.7.若函数()2sin sin 2f x x x =-在区间[]0,a 上的零点个数为3个，则实数a 的取值范围是_________. 【解析】令()2sin sin 20f x x x =-=，得2sin 2sin cos 0x x x -=，即sin (1cos )0x x -=， 故当[)0,x ∈+∞时，零点分别为0,,2,3,πππ，所以23πa π≤<.8.已知两变量x 、y 之间的关系为lg()lg lg y x y x -=-，则以x 为自变量的函数y 的最小值是_________.【解析】由lg()lg lg y x y x -=-得00y x x y y x x ⎧⎪->⎪>⎨⎪⎪-=⎩，所以2(1)x y x -=，显然1x ≠，所以201x y x =>-，故1x >， 所以22[(1)1]1124111x x y x x x x -+===-++≥---，当且仅当2x =时取等号， 故以x 为自变量的函数y 的最小值是4.9.已知函数()xf x a b =-（0a >且1,a b R ≠∈），()1g x x =+若对任意实数x 均有()()0f x g x ⋅≤，则14a b+的最小值为_________.【解析】作出(),()f x g x 的图像，如图所示，则()x f x a b =-过点(1,0)-，所以10a b --=，即1ab =，因为0a >，所以0b >，所以1444b a b b+=+≥，当且仅当1,22a b ==时取等号，故14a b+的最小值为4. 10.设函数()sin()(0,0)6f x A x A πωω=->>，[]0,2x π∈，若()f x 恰有4个零点，则下述结论中：①0()()f x f x ≥恒成立，则0x 的值有且仅有2个；②存在0ω>，使得()f x 在80,19π⎡⎤⎢⎥⎣⎦上单调递增；③方程1()2f x A =一定有4个实数根，其中真命题的序号为_______. 【解析】因为()f x 恰有4个零点，所以160,1,2,36k ππωx k πx k ω⎛⎫+ ⎪⎝⎭-=⇒=⇒=，所以1134662πx πωω⎛⎫⎛⎫++ ⎪ ⎪⎝⎭⎝⎭≤<，即19251212ω≤<，①()0f x A =即0262ππωx k π-=+，由上述知0,1k =， 故0x 的值有且仅有2个，正确；②当0x =时，66ππωx -=-，当819πx =时，81962πππω⋅-≤，解得1912ω≤，又19251212ω≤<，故存在1912ω=，使得()f x 在80,19π⎡⎤⎢⎥⎣⎦上单调递增，正确； ③11()sin 262πf x A ωx ⎛⎫=⇒-= ⎪⎝⎭，而2[3,4)6ππωππ-∈，所以6πωx -可取51317,,,6666ππππ，共4个解，正确， 综上，真命题的序号是①②③.11.函数11()22f x x =-≤≤的图像绕着原点旋转弧度θ(0)θπ≤≤，若得到的图像仍是函数图像，则θ可取值的集合为_________.【解析】20,,33πππ⎡⎤⎡⎤⎢⎥⎢⎥⎣⎦⎣⎦12.对任意闭区间I ，用I M 表示函数sin y x =在I 上的最大值，若有且仅有一个正数a 使得[][]0,,2a a a M kM =成立，则实数k 的取值范围是_________.【解析】①当0,4πa ⎡⎤∈⎢⎥⎣⎦时，[0,][,2]20,,sin ,sin 22a a a πa M a M a ⎡⎤∈==⎢⎥⎣⎦， 由[][]0,,2a a a M kM =，得sin sin 2a k a =，所以12cos k a=；②当,42ππa ⎡⎤∈⎢⎥⎣⎦时，[0,][,2]2,,sin ,12a a a πa πM a M ⎡⎤∈==⎢⎥⎣⎦，由[][]0,,2a a a M kM =，得sin k a =；③当,2πa π⎡⎤∈⎢⎥⎣⎦时，[0,][,2]2[,2],1,sin a a a a ππM M a ∈==，由[][]0,,2a a a M kM =，得1sin k a =，所以1sin k a=； ④当5,4πa π⎡⎤∈⎢⎥⎣⎦时，[0,][,2]52[2,],1,sin 22a a a a ππM M a ∈==， 由[][]0,,2a a a M kM =，得1sin 2k a =，所以1sin 2k a=， ⑤当5,+4πa ⎡⎤∈∞⎢⎥⎣⎦时，[0,][,2]52[,3],1,12a a a a ππM M ∈==由[][]0,,2a a a M kM =，得1k =，所以1,0,2cos 4sin ,,421,,sin 215,,sin 2451,,4πa a ππa a πk a πaπa πaπa ⎧⎡⎤∈⎪⎢⎥⎣⎦⎪⎪⎡⎤∈⎪⎢⎥⎣⎦⎪⎪⎪⎡⎤=∈⎨⎢⎥⎣⎦⎪⎪⎡⎤∈⎪⎢⎥⎣⎦⎪⎪⎡⎤⎪∈+∞⎢⎥⎪⎣⎦⎩，作出图像，得实数k 的取值范围是1,12⎛⎫⎪⎝⎭. 【变式1】2020-2021年上海市普陀区0.5模12题.对任意闭区间I ，用I M 表示函数sin y x =在上的最大值，若正数a 满足[][]0,,22a a a M M =⋅，则a的值为_________.【解析】①当0,4πa ⎡⎤∈⎢⎥⎣⎦时，[0,][,2]20,,sin ,sin 22a a a πa M a M a ⎡⎤∈==⎢⎥⎣⎦， 由[][]0,,2a a a M M =，得sin 2a a =，所以cos 4a =，无解； ②当,42ππa ⎡⎤∈⎢⎥⎣⎦时，[0,][,2]2,,sin ,12a a a πa πM a M ⎡⎤∈==⎢⎥⎣⎦，由[][]0,,2a a a M M =，得sin a =③当,2πa π⎡⎤∈⎢⎥⎣⎦时，[][0,][,2]2,2,1,sin a a a a ππM M a ∈==，由[][]0,,2a a a M M =，得1a =，所以sin 2a =，34πa =； ④当5,4πa π⎡⎤∈⎢⎥⎣⎦时，[0,][,2]522,,1,sin 22a a a a ππM M a ⎡⎤∈==⎢⎥⎣⎦，由[][]0,,2a a a M M =，得12a =，所以sin 2a =98πa =；⑤当5,+4πa ⎡⎤∈∞⎢⎥⎣⎦时，[0,][,2]52,3,1,12a a a a ππM M ⎡⎤∈==⎢⎥⎣⎦由[][]0,,2a a a M M =，得无解，综上，34πa =或98πa =.【变式2】2019-2020年上海市七宝中学高三下三模第11题.用I M 表示函数sin y x =在闭区间I 上的最大值，若正数a 满足[0,][,2]2a a a M M ≥，则a 的最大值为 .【解析】①当0,4πa ⎡⎤∈⎢⎥⎣⎦时，[0,][,2]20,,sin ,sin 22a a a πa M a M a ⎡⎤∈==⎢⎥⎣⎦，由[0,][,2]2a a a M M ≥，得sin 2sin 2a a ≥，所以1cos 4a ≤，无解； ②当,42ππa ⎡⎤∈⎢⎥⎣⎦时，[0,][,2]2,,sin ,12a a a πa πM a M ⎡⎤∈==⎢⎥⎣⎦，由[0,][,2]2a a a M M ≥，得sin 2a ≥，无解；③当,2πa π⎡⎤∈⎢⎥⎣⎦时，[][0,][,2]2,2,1,sin a a a a ππM M a ∈==，由[0,][,2]2a a a M M ≥，得12sin a ≥，所以1sin 2a ≤，5,6πa π⎡⎤∈⎢⎥⎣⎦； ④当5,4πa π⎡⎤∈⎢⎥⎣⎦时，[0,][,2]522,,1,sin 22a a a a ππM M a ⎡⎤∈==⎢⎥⎣⎦， 由[0,][,2]2a a a M M ≥，得12sin 2a ≥，所以1sin 22a ≤，13,12πa π⎡⎤∈⎢⎥⎣⎦；⑤当5,+4πa ⎡⎤∈∞⎢⎥⎣⎦时，[0,][,2]52,3,1,12a a a a ππM M ⎡⎤∈==⎢⎥⎣⎦由[0,][,2]2a a a M M ≥，得无解，综上，513,612ππa ⎡⎤∈⎢⎥⎣⎦，故a 的最大值为1312π. 二、选择题13.下列各组不等式中，解集完全相同的是（ D ）A.2611x x x x +<++与26x x <+B.2(2)(1)0x x x x-+<与(2)(1)0x x -+< C.(2)(1)01x x x +->-与20x +> D.2232111x x x x x x -+>-+-+与321x x ->+ 14.若数列{}n a 的前n 项和为n S ，则“{}n a 是递增数列”是“{}n S 为递增数列”的（ D ）A.充分非必要条件B.必要非充分条件C.充要条件D.既不充分也不必要条件15.已知集合,M P 都是非空集合，若命题“M 中的元素都是P 中的元素”是假命题,则下列说法必定为真命题的是（ D ）A.M P =∅B.M 中至多有一个元素不属于PC.P 中有不属于M 的元素D.M 中有不属于P 的元素16.单调递增的数列{}n a 中共有N 项，且对任意,,(1),i j k i j k N ≤<<≤i j a a +，j k a a +和k i a a +中至少有一个是{}n a 中的项，则N 的最大值为（ ）A.9B.8C.7D.6【解析】本题为2016年清华大学自招与领军计划试题.法一：假设0a b c d <<<<是{}n a 中大于0的最大的4项，对于,,b c d 来说， 因为,b d d c d d +>+>，所以b d +和c d +都不是{}n a 中的项， 又由题意得,b c b d ++和c d +中至少有一个是{}n a 中的项， 所以b c +是{}n a 中的项，且b c c +>，所以b c d +=，对于,,a c d 来说，因为,a d d c d d +>+>，所以a d +和c d +都不是{}n a中的项，又由题意得,b c b d ++和c d +中至少有一个是{}n a 中的项， 所以a c +是{}n a 中的项，且a c c +>，所以a c d +=， 所以a d =，矛盾，所以{}n a 中大于0的最多有3项，同理，{}n a 中小于0的最多有3项，加上0，故N 的最大值为7， 此时存在数列{}:3,2,1,0,1,2,3n a ---满足题意，故选C.法二：假设存在三项1,,m N N a a a -为正，则1,N N m N a a a a -++都不是{}n a 中的项， 所以1m N a a -+是{}n a 中的项，且11m N N a a a --+>， 所以1m N N a a a -=-，所以数列{}n a 中最多有3个正项，同理数列{}n a 中最多有3个负项，加上0，故N 的最大值为7， 此时存在数列{}:3,2,1,0,1,2,3n a ---满足题意，故选C.三、解答题17.如图，已知长方体1111ABCD A B C D -中，AB，BC =1AA =.（1）求异面直线1AB 与1BC 所成角的大小； （2）求点C 到平面1ABD 的距离.【解析】（1）连接111,AD B D ，则11AD BC ∥， 所以11B AD ∠即为所求角，或其补角，1AB ==，13AD ==，11B D ==在11B AD ∆中，由余弦定理得22211111111cos 22AB AD B D B AD AB AD +-∠==，所以114πB AD ∠=，即异面直线1AB 与1BC 所成角的大小为4π； （2）1111322ABD S AB AD ∆=⨯==，11222ABC S AB BC ∆=⨯==，1DD =， 设点C 到平面1ABD 的距离为h ，由等体积法，得11C ABD D ABC V V --=，即111133ABD ABC S S h DD ∆∆⨯=⨯，所以h =所以点C 到平面1ABD 18.已知在ABC ∆中，角,,A B C 的对边分别为,,a b c ,且(cos 2cos )(2)cos c B A a b C -=-.B 1D 1A 1D C 1CBA（1）求ab的值； （2）若3cos ,24C c ==，求ABC ∆的面积. 【解析】（1）由已知及正弦定理得sin (cos 2cos )(2sin sin )cos C B A A B C -=-，得sin()2sin()B C A C +=+，因为A B C π++=，所以sin 2sin A B =，由正弦定理得2ab=； （2）因为3cos ,2,24aC c b===，由余弦定理得222324a b c ab +-=，即222(2)4344b b b +-=，解得b =，所以2a b ==sin C ==所以11sin 22ABC S ab C ∆==⨯=.20. 某供应商为华为公司提供芯片，由以往的经验表明，不考虑其他因素，该芯片次品率p 与日产量x （万枚）间的关系为：1,04,62,4,3x xp x ⎧<≤⎪⎪-=⎨⎪>⎪⎩，已知每生产1枚合格芯片供应商可盈利30元，每出现1件次品亏损15元.（3）将日盈利额y （万元）表示为日常量x （万枚）的函数；（4）为使日盈利额最大，日产量应为多少万枚？（注：次品率=100%⨯次品数产品总数）.【解析】（1）当4x >时，23p =，所以123015033y x x =⋅⋅-⋅⋅=， 当04x <≤时，16p x=-， 所以21115(921301566)6x x y x x x x x -⎛⎫=-⋅⋅-⋅⋅= ⎪---⎝⎭， 所以()21592,04(6)0,4x x x y x x ⎧-⎪<≤=⎨-⎪>⎩；（2）当04x <≤时，22)15(96x x y x-=-，令[)62,6t x =-∈，则()215962(6)1815(152)t t y t tt⎡⎤---⎣⎦==--，所以15(1545y ≤-=万元， 当且仅当182t t=，即3,3t x ==时取等号，所以为使日盈利额最大，日产量应为3万枚.20.已知双曲线2222:1x y C a b-=过点M ，且右焦点为(2,0)F .（1）求双曲线C 的方程；（2）过点F 的直线l 与双曲线C 的右支交于,A B 两点，交y 轴于点P ，若PA mAF =，PB nBF =，求证：m n +为定值.（3）在（2）的条件下，若点Q 是点P 关于原点O 的对称点，求证：三角形QAB 的面积2310QAB S ∆>； 【解析】（1）由题意得22921,2c a b-==，又222c a b =+，解得223,1a b ==， 所以双曲线C 的方程为2213x y -=； （2）法一：设()()1122,,,,(0,)A x y B x y P t ，由PA mAF =得11211m x mt y m ⎧=⎪⎪+⎨⎪=⎪+⎩，又点A 在双曲线上，所以2221131m t m m ⎛⎫⎪+⎛⎫⎝⎭-= ⎪+⎝⎭，整理得226330m m t ---=， 同理，由PB nBF =，得226330n n t ---=，因为,A B 两点不重合，所以m n ≠，所以,m n 是方程226330x x t ---=的两根，所以6m n +=，为定值；法二：设()()1122,,,A x y B x y ，由题意得直线l 的斜率存在，所以设直线:(2)l y k x =-，所以(0,2)P k -，由2213(2)x y y k x ⎧-=⎪⎨⎪=-⎩，得2222(31)121230k x k x k --++=，所以2212122212123,3131k k x x x x k k ++==--，由PA mAF =，PB nBF =得1122(2),(2)x m x x n x =-=-，所以1212211212(2)(2)22(2)(2)x x x x x x m n x x x x -+-+=+=---- 22121222212122()2242(123)6642()4(31)241231x x x x k x x x x k k k +--+-====-++--++-， 所以6m n +=，为定值；（3）在（2）法二的基础上，得(0,2)Q k ，1212122QAB QPB QPA S S S PQ x x k x x ∆∆∆=-=⨯-=-， 所以()()222221212124()44QABS k x x k x x x x ∆⎡⎤=-=+-⎣⎦()22242222222212123144(4812)(31)444313131k k k k k k k k k k ⎡⎤⎛⎫+-+-=⎢-⎥= ⎪--⎢⎥⎝⎭-⎣⎦()()222222221212(1)4483131k k k kkk++==--，因为直线l 与双曲线C 的右支交于,A B 两点，所以22121222121230,03131k k x x x x k k ++==--＞＞， 所以2310t k =-＞， 所以()()2222222111(1)48(1)(4)334848931QABt t k k t t S t t k ∆++⎛⎫+ ⎪+++⎝⎭===-22224854484519215139998t t t t t t ++⎛⎫⎛⎫==++=+- ⎪ ⎪⎝⎭⎝⎭， 因为0t ＞，所以10t＞，所以()222192151925163398983QABS t ∆⎛⎫⎛⎫=+--=⎪ ⎪⎝⎭⎝⎭＞， 所以232.31310QAB S ∆>≈>，证毕. 21.若实数列{}n a 满足条件212,1,2,n n n a a a n +++≥=，则称{}n a 是一个“凸数列”.（1）判断数列2n a n n =-+和3()2nn b =是否为“凸数列”?（2）若{}n a 是一个“凸数列”，证明：对正整数,,k m n ，当1k m n ≤<<时，有n m m ka a a a n m m k--≥--；（3）若{}n a 是一个“凸数列”证明：对1i n ≤≤，有111(1)i n iia a a n n++≤-+. 【解析】（1）因为222212(2)(2)2(1)2(1)n n n a a a n n n n n n +++-=-+-+++++-+20=-＜，所以数列2n a n n =-+不为“凸数列”，因为+21233339221322224nn n nn n n b b b ++⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫+-=+-=+- ⎪ ⎪⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭13042n⎛⎫=≥ ⎪⎝⎭，所以数列3()2n n b =为“凸数列”；（2）由题意得112(2,3,)k k k a a a k -++≥=，所以11k k k k a a a a +--≥-，而()()()()11211()n m n n n n m m m m a a a a a a a a n m a a ---++-=-++++-≥--，所以1mm m n a a a a n m+-≥--，又()()()()11211()k m k m m m m k m m a a a a a a a a m k a a ---+--=-++++-≤--，所以1m km m a a a a m k --≤--，故n m m k a a a a n m m k--≥--，证毕；（3）①当1i =时，111(1)i n ii a a a nn ++≤-+即21111(1)n a a a n n+≤-+， 由（2）得()1221(1)n a a n a a +-≥--，所以211(1)n na n a a +≤-+，故21111(1)n a a a n n+≤-+，成立； ②当i n =时，111(1)i n i ia a a nn++≤-+即11n n a a ++≤，显然成立， ③当1i n ＜＜时，由（2）得1111n i i a a a a n i i+++--≥-，所以1111()()n i i ia ia n i a n i a +++-≥---，所以111()i n na ia n i a ++≤+-，故111(1)i n i ia a a n n++≤-+成立， 综上所述，对1i n ≤≤，有111(1)i n i ia a a n n++≤-+.。

2019-2020学年上海市七宝实验中学高三英语上学期期中试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AThe history ofpop art begins with abstract art. Pop art emerged from the foundation of abstract art in the 1950s, first gaining recognition in Great Britain, then establishing itself in the United States in the 1960s.In the 1930s and 1940s, abstract art was greatly popular, but people began to hate this art form. Most abstract art produced in this era could be found in art galleries or the homes of the elite(名流), not in the homes of everyday people. Pop art sprung onto the scene as the people's art.Some art critics say pop art is a rebellion against abstract art; others say it is an extension of abstract art. You can see elements of abstract art in many pop art prints, especially those that consist of a collage（拼贴画）of images. However, some pop art pieces have nothing to do with abstract art, looking more like a photo of a popular consumer item, which impressed people deeply.Richard Hamilton and Eduardo Paolozzi were two of the first contemporary pop art pioneers recognised in Great Britain. They were a part of the Independent Group, an organised group of British artists who wanted to challenge ruling modernist approaches to culture. They recognised the value of modern advertising and comic book images. They used these popular images in art as a social commentary, often building irony and humour into their artworks, thus creating a new form of art. These pieces were mass-produced and sold at affordable prices.When pop art took off in the United States, it expanded to include a celebration of kitsch and the common images found in movies and television. Andy Wharhol is perhaps the most famous American pop art artist, known for his prints of the actress Marilyn Monroe, the singer Elvis Presley and of Campbell's soup cans. Andy Wharhol was inspired by images from advertisements and common consumer items. He also made a series of paintings which showed images of car accidents.1. Why did people dislike abstract art?A. People found it hard to understand.B. Ordinary people couldn't afford it.C. People disliked enjoying it in galleries.D. It wasn't based on everyday life.2. What impression do pop art works leave on people?A. They are a rebellion against abstract art.B. They have many elements of abstract art.C. They are created so real.D. They are products of advertisers.3. The Independent Group was set up to ________.A. introduce a new art form to the worldB. develop modern advertising furtherC. create new comic book imagesD. make British culture better knownBA Virginia teen is doing his part to make sure frontline health care workers are getting the meals they need to help them take care of themselves and others.Arul Nigam, 17, of Tyson's Corner, Va. , has had to make several adjustments since his school year ended abruptly in mid-March due to the coronavirus pandemic(新冠疫情).“We didn'thave any classes for like over a month and then after that there were a lot of technical difficulties. So I started to have a lot more free time,” he tells Yahoo Life. “It was really saddening, but it was also something that really surprised me, that our health care workers are facing something like that,” Nigam says. “So I wanted to see what I could do to help them because obviously, they're sacrificing so much and giving so much for all of us. ”In late March, the teen started fundraising efforts with the help of friends and family to help these health care workers receive much-needed meals. He also began doing research about what hospitals had the most amount of coronavirus cases, so he could prioritize those places first. He was also arranging for the orders to be fulfilled at local family-owned restaurants impacted by shutdown orders. So far, Nigam has delivered over 1,000 meals to 22 hospitals in 13 states, including New York, Massachusetts and Maryland.Nigam's efforts have not only helped health care workers, but restaurants as well. With quarantine restrictionstaking a toll onthe food industry, places like Best Coast Burrito in Oakland, Calif. , have lost business over the last few weeks. Best Coast's owner,Alvin Shen, tells Yahoo Life that being able to partner with Arul and others in efforts to feed those on the frontline has been a big help.4. What would Nigam probably do according to his words?A. Study at home by himself.B. Spend the more free time playing.C. Donate some money to health care workers.D. Do something helpful for health care workers.5. What is Nigam's priority when delivering food?A. The urgency of meals.B. The severity of the virus.C. The number of doctors.D. The position of hospitals.6. What does the phrase “taking a toll on” in the last paragraph mean?A. Turning a blind eye to.B. Keeping an eye on.C Causing lots of damage to.D. Answering completely for.7. Where can you probably read this text?A. Science fiction.B. Fashion magazine.C. Life magazine.D. Entertainment newspaper.CI once had my Chinese MBA students brainstorming on “two-hour business plans.” I separated them into six groups and gave them an example: a restaurant chain. The more original their ideas, the better, I said. Finally, five of the six groups presented plans for restaurant chains. The sixth proposed a catering service. Though I admitted the time limit had been difficult, I expressed my disappointment.My students were middle managers, financial analysts and financiers from state-owned enterprises and global companies. They were without talent or opinions, but they had been shaped by an educational system that rarely stressed or rewarded critical thinking or inventiveness. The scene I just described came in different forms during my two years teaching at the school. Papers were often copied from the Web and the Harvard Business Review. Case study debates were written up and just memorized. Students frequently said that copying is a superior business strategy, better than inventing and creating.InChina, every product you can imagine has been made and sold. But so few well-developed marketing and management minds have been raised that it will be a long time before most people in the world can name a Chinese brand.With this problem in mind, partnerships with institutions like Yale and MIT have been established. And then there's the “thousand talent scheme.” this new government program is intended to improve technological modernization by attracting top foreign-trained scientists to the mainland with big money. But there are worries aboutChina's research environment. It's hardly known for producing independent thinking and openness, andeven big salary offers may not be attractive enough to overcome this.At last, forChina, becoming a major world creator is not just about setting up partnership with top western universities. Nor is it about gathering a group of well-educated people and telling them to think creatively. It's about establishing a rich learning environment for young minds. It's not that simple.8. Why does the writer feel disappointed at his students?A. Because there is one group presenting a catering service.B. Because the six groups did not cooperate well in the brainstorm.C. Because all the students copied a case for the difficult topic.D. Because the students' ideas were lacking in creativeness.9. Which of the following scenes is NOT considered as lack of creation?A. Papers were often downloaded from the Internet.B. Students often said that copying is a preferable business strategy.C. Students combine knowledge and critical thoughts to solve a problem.D. Case study debates were written up as well as recited.10. We can infer form the passage that ________.A. China can make and sell any product all over the world from its own creation.B. high pay may not solve the problem ofChina's research environment.C. cooperation with institutions has been set up to make a Chinese brand.D. the new government program is aimed at encouraging imagination.11. Which is the best title for the passage?A Look for a new way of learning B. Reward creative thinkingC. How to become a creatorD. Establish a technical environmentDA dog spentthe lastfour years of his life waitingat a crossroad in the Thai city ofKhon Kaenas if waiting for someone. People originally thought the dog had been abandoned, but then realized that he looked healthy, so people asked around about him. It turned out that the dog had indeed been spending most of his time around that crossroad, but a woman had been coming round regularly to bring him food and water.One day, while photographing the dog everyone called Leo, a reporter met the woman who had been taking care of him. She had come to drop off some food. After learning the story about the dog and the woman, the reporter decided to share the story on social media. The post soonwent viraland the photos of Leo got sharedhundreds of times. And the photos reached the eyes of Leo’s former old owner.Nang Noi Sittisarn, a 64-year-old woman fromThailand’sRoiEtProvince, almost had a heart attack when her daughter showed her a photo of the beloved dog named BonBon she had lost during a car trip. When she learned that he had been waiting for her in the same spot for the last four years，her heart melted(融化).Auntie Noi told her daughter to drive her to where the dog was waiting. When she got there and called his name. BonBon，the poor dog started wiggling(扭动)his tailand came to her，but when she tried to take him home with her, he was unwilling to follow. She didn’ t want to force the dog to come with her so she agreed to leave him with his new master. However, she and her daughter will come to visit him regularly.12.Why did the dog look healthy after separation from his former owner?A. He walked around the crossroad constantly.B. He was kept at a woman’s home all the time.C. A local reporter brought him food and water.D. A woman looked after him on a regular basis.13. What does the underlined phrase “went viral” in paragraph 2 probably mean?A. Changed surprisingly.B. Spread quickly.C. Appeared gradually.D. Fell directly.14. How did Nang Noi Sittisam feel about the dog's waiting for her?A. Shocked.B. Regretful.C. Touched.D. Proud.15. What can we mainly learn from the story about the dog?A. Unbelievable success is worth waiting for.B. We should adjust ourselves to environments.C. We need to learn to be faithful and thankful.D. No one knows the result until the last minute第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

上海2020-2021学年七宝中学高三上学期期中仿真密卷数学学科参考答案一. 填空题1. (,3][1,0)-∞--2. 79-3. 24. 3log 1x +（1(0,)3x ∈） 5. 312n n a n n =⎧=⎨≥⎩6. 507. 10108.9. 110. 1}-11. (3--- 12.1288二. 选择题13. B 14. C 15. C 16. B 三.解答题17．如图，长方体ABCD –A 1B 1C 1D 1的底面ABCD 是正方形，点E 在棱AA 1上，BE ⊥EC 1.（1）证明：BE ⊥平面EB 1C 1；（2）若AE =A 1E ，求二面角B –EC –C 1的正弦值.【答案】（1）证明见解析；（2【解析】【分析】（1）利用长方体的性质，可以知道11B C ⊥侧面11A B BA ，利用线面垂直的性质可以证明出11B C EB ⊥，这样可以利用线面垂直的判定定理，证明出BE ⊥平面11EB C ；（2）以点B 坐标原点，以1,,BC BA BB 分别为,,x y z 轴，建立空间直角坐标系，设正方形ABCD 的边长为a ，1B B b =，求出相应点的坐标，利用1BE EC ⊥，可以求出,a b 之间的关系，分别求出平面EBC 、平面1ECC 的法向量，利用空间向量的数量积公式求出二面角1B EC C --的余弦值的绝对值，最后利用同角的三角函数关系，求出二面角1B EC C --的正弦值. 【详解】证明（1）因为1111ABCD A B C D -是长方体，所以11B C ⊥侧面11A B BA ，而BE ⊂平面11A B BA ，所以11BE B C ⊥又1BE EC ⊥，1111B C EC C ⋂=，111,B C EC ⊂平面11EB C ，因此BE ⊥平面11EB C ； （2）以点B 坐标原点，以1,,BC BA BB 分别为,,x y z 轴，建立如下图所示的空间直角坐标系，1(0,0,0),(,0,0),(,0,),(0,,)2bB C a C a b E a ，因为1BE EC ⊥，所以2210(0,,)(,,)002224b b b BE EC a a a a b a ⋅=⇒⋅-=⇒-+=⇒=，所以(0,,)E a a ，1(,,),(0,0,2),(0,,)EC a a a CC a BE a a =--==，设111(,,)m x y z =是平面BEC 的法向量，所以111110,0,(0,1,1)0.0.ay az m BE m ax ay az m EC +=⎧⎧⋅=⇒⇒=-⎨⎨--=⋅=⎩⎩，设222(,,)n x y z =是平面1ECC 的法向量，所以2122220,0,(1,1,0)0.0.az n CC n ax ay az n EC =⎧⎧⋅=⇒⇒=⎨⎨--=⋅=⎩⎩， 二面角1B EC C --的余弦值的绝对值为122m n m n⋅==⨯⋅，所以二面角1B EC C --=【点睛】本题考查了利用线面垂直的性质定理证明线线垂直，考查了利用空间向量求二角角的余弦值，以及同角的三角函数关系，考查了数学运算能力.18．在ABC ∆在在在在A在B ，C 所对的边分别为a ，b ，c.已知sin cos 6b A a B π⎛⎫=-⎪⎝⎭. ，1）求角B 的大小；，2）设a =2，c =3，求b 和()sin 2A B -的值.【答案】(Ⅰ)3πⅠ(Ⅰ)b =【解析】分析：ⅠⅠⅠ由题意结合正弦定理边化角结合同角三角函数基本关系可得tanB=，则B =π3Ⅰ ⅠⅡ）在△ABC 中，由余弦定理可得b Ⅰ结合二倍角公式和两角差的正弦公式可得()214sin A B -=详解：ⅠⅠ）在△ABC 中，由正弦定理a bsinA sinB=，可得bsinA asinB =Ⅰ 又由π6bsinA acos B ⎛⎫=-⎪⎝⎭，得π6asinB acos B ⎛⎫=- ⎪⎝⎭Ⅰ即π6sinB cos B ⎛⎫=- ⎪⎝⎭，可得tanB =又因为()0πB ∈，，可得B =π3Ⅰ ⅠⅡ）在△ABC 中，由余弦定理及a =2Ⅰc =3ⅠB =π3Ⅰ 有22227b a c accosB =+-=，故b由π6bsinA acos B ⎛⎫=-⎪⎝⎭，可得sinA =a <c，故cosA =Ⅰ因此22sin A sinAcosA ==Ⅰ212217cos A cos A =-=．所以，()222sin A B sin AcosB cos AsinB -=-=1127-= 点睛：在处理三角形中的边角关系时，一般全部化为角的关系，或全部化为边的关系．题中若出现边的一次式一般采用到正弦定理，出现边的二次式一般采用到余弦定理．应用正、余弦定理时，注意公式变式的应用．解决三角形问题时，注意角的限制范围．19．华为董事会决定投资开发新款软件，估计能获得10万元到1000万元的投资收益，讨论了一个对课题组的奖励方案:奖金y (单位:万元)随投资收益x (单位:万元)的增加而增加，且奖金不超过9万元，同时奖金不超过投资收益的20%. （1）请分析函数11005x y =-是否符合华为要求的奖励函数模型，并说明原因； （2）若华为公司采用模型函数110100100510100100010x x y x a x x ⎧-≤≤⎪⎪=⎨-⎪<≤⎪+⎩作为奖励函数模型，试确定正整数a 的取值集合.【答案】（1）不符合，原因见解析（2）a 的取值集合为{}910911912，， 【解析】【分析】（1）根据题意，总结奖励模型需要满足的条件①()f x 在定义域[10,1000]上是增函数；②()9f x ≤恒成立；③()5xf x ≤恒成立；判断单调性及最值，即可求解； （2）由题意，依此判断分段函数的单调性，最大值和()5xf x ≤，即可求解参数范围，由a 为正整数，即可确定取值集合. 【详解】（1）设奖励函数模型为()y f x =，按公司对函数模型的基本要求，函数()y f x =满足:当[10,1000]x ∈时，①()f x 在定义域[10,1000]上是增函数；②()9f x ≤恒成立；③()5x f x ≤恒成立.对于函数模型11005x y =-.当[10,1000]x ∈时，11005x y =-是增函数，max1000149()(1000)910055f x f ==-=>所以()9f x ≤不恒成立.故该函数模型不符合公司要求.（2）对于函数模型110100100510100100010x x y x a x x ⎧-≤≤⎪⎪=⎨-⎪<≤⎪+⎩，当10100x ≤≤时，()f x 在定义域[10,100]上是增函数，且()9f x ≤恒成立；当1001000x <≤时，10100()101010x a a f x x x ---==+++，只有1000410005110a a --<⎧⎪-⎨≤⎪⎩时，()f x 在定义域[10,1000]上是增函数；要使()9f x ≤在[10,1000]x ∈恒成立，(1000)9f ≤，即100041000[100,912]5110(1000)9a aa f --<⎧⎪-⎪≤⇒∈⎨⎪≤⎪⎩；要使()5x f x ≤恒成立对[10,1000]x ∈恒成立，即11010010055101001000105x xx x a x x x ⎧-<≤≤⎪⎪⎨-⎪<<≤⎪+⎩，即24050x x a -+≥恒成立，所以910a ≥； 综上所述，910a ≥，所以满足条件的正整数a 的取值集合为{}910911912，，【点睛】本题结合实际问题，考查了（1）函数的单调性，最值和恒成立问题；（2）由函数的单调性最值和不等式确定参数的取值范围；考查计算能力，考查数学建模思想，属于中等题型.20．已知椭圆2222:1x y C a b +=(0)a b >>经过点(2,1)A，离心率为2，过点(3,0)B 的直线l 与椭圆C 交于不同的两点M N 、， （1）求椭圆C 的方程； （2）求BM BN ⋅的取值范围；（3）设直线AM 和AN 的斜率分别为AM k 和AN k ，求证:AM AN k k +为定值.【答案】（1）22163x y+= （2）(2,3] （3）证明见解析 【解析】【分析】（1）根据离心率和(2,1)A 代入椭圆方程可求得a 和c ，进而求得b ，方程可得；（2）由题意显然直线l 方程为()3y k x =-，联立直线与椭圆的方程22(3)163y k x x y =-⎧⎪⎨+=⎪⎩消去y 得()222212121860k xk x k +-+-=.因为直线l 与椭圆C 交于不同的两点M ，N ，∴>0∆，可得11k -<<，再用坐标表示出BM BN ⋅，即可求取值范围. （3）由（2）用坐标表示出AM AN k k +化简即可.【详解】（1）由题意得22222411a b a b c c a⎧+=⎪⎪⎪=+⎨⎪⎪=⎪⎩，解得a =b =∴椭圆C 的方程为22163x y +=.（2）由题意显然直线l 的斜率存在，设直线l 的方程为()3y k x =-，由22(3)163y k x x y =-⎧⎪⎨+=⎪⎩得()222212121860k x k x k +-+-=.∵直线l 与椭圆C 交于不同的两点M ，N ， ∴()()()42221444121862410k kkk ∆=-+-=->，解得11k -<<.设M ，N 的坐标分别为()11,x y ，()22,x y ，则21221212k x x k+=+，212218612k x x k -=+， 又()113y k x =-，()223y k x =-，()()121233BM BN x x y y =--+⋅()()21212139k x x x x =+-++⎡⎤⎣⎦ ()2223333122212k k k +==+++， ∵11k -<<，∴()233232212k <+≤+， ∴BM BN ⋅的范围为(]2,3. （3）由（2）得121211=22AMAN y y k k x x --++--()()()()()()122112312312=22kx k x kx k x x x ---+-----()()()12121212251124=24kx x k x x k x x x x -++++-++()()()()()2222222186511212412=18624412k k k k k k k k k --+⋅+++--++2244=22k k -+- 2=-所以AM AN k k +为定值，=2AM AN k k +- 【点睛】本题考查主要考查椭圆的标准方程求解，运用韦达定理解决直线与椭圆相交问题，椭圆定点问题，考查逻辑推理能力和计算求解能力，综合性较强，有一定难度.21．已知定义在R 上的函数()f x 和数列{}n a 满足下列条件:121,a a a a =≠，当n *∈N 且2n ≥时，1()n n a f a -=且11()()()n n n n f a f a k a a ---=-，其中a k 、均为非零常数.（1）数列{}n a 是等差数列，求k 的值；（2）令1()n n n b a a n N *+=-∈，若11b =，求数列{}n b 的通项公式；（3）证明:{}n a 数列是等比数列的充要条件是()(1)f x kx k =≠. 【答案】（1）1（2）n b ()1210n ka a -=-≠（3）证明见解析【解析】 【分析】（1）由题意知1()n n a f a -=，11()()()n n n n f a f a k a a ---=-()2n ≥，得()()112n n n n a a k a n a --=-≥-，再由等差数列，即可求解k 值；（2）由1210b a a =-≠，可得()()()23221210b a a f a f a k a a =-=-=-≠，因此()()()1111n n n n n n n n b a a f a f a k a a kb +---=-=-=-=，由此可知，数列{}n b 是一个公比为k 的等比数列.（3）先进行充分性证明：若()(1)f x kx k =≠则{}n a 数列是等比数列；再进行必要性证明：若{}n a 数列是等比数列，则()(1)f x kx k =≠.【详解】（1）由已知()1n n a f a -=，()()()()112,3,4,n n n n f a f a k a a n ---=-=⋅⋅⋅， 得()()()()1112,3,4,n n n n n n a a f a f a k a a n +---=-=-=⋅⋅⋅， 由数列{}n a 是等差数列，得()112,3,4,n n n n a a a n a +-=-=-⋅⋅⋅， 所以，()11n n n n a a k a a ---=-，()2,3,4,n =⋅⋅⋅，得1k =.（2）由1210b a a =-≠，可得()()()23221210b a a f a f a k a a =-=-=-≠，且当2n >时，()()()111n n n n n n n b a a f a f a k a a +--=-=-=-()1210n k a a -==-≠，所以，当2n ≥时，()()()1111111n n n n n n n n n n n n n n f a f a k a a b a a k b a a a a a a --+-------====---，因此，数列{}n b 是一个公比为k 的等比数列. 故通项公式为()1210n n b ka a -=-≠（3）{}n a 是等比数列的充要条件是()()1f x kx k =≠，充分性证明:若()()1f x kx k =≠，则由已知10a a =≠，()()12,3,4,n n a f a n -==⋅⋅⋅ 得()12,3,4,n n n a ka -==⋅⋅⋅，所以，{}n a 是等比数列. 必要性证明:若{}n a 是等比数列，由（2）知，()()1*21n n b ka a n N-=-∈，()()()12121211n n n b b b a a a a a a --++⋅⋅⋅+=-+-+⋅⋅⋅+-()12n a a n =-≥，()1121n n a a b b b -=+++⋅⋅⋅+.当1k =时，()()()12112n a a a a n n =+--≥.上式对1n =也成立， 所以，数列{}n a 的通项公式为:()()()()*1n a a f a an n N =+--∈.所以，当1k =时，数列{}n a 是以a 为首项，()f a a -为公差的等差数列. 所以，1k ≠.当1k ≠时，()()1121121n n k a a a a n k--=+-≥-. 上式对1n =也成立，所以，()11()1n n k a a f a a k --=+--1()(())11n f a a f a a k a k k---=+---. 所以，()0()1f a aa f a ka k-+=⇒=-.Ⅰ，等式()(1)f x kx k =≠对于任意实数a 均成立.所以()(1)f x kx k =≠.【点睛】本题考查等差数列的定义，利用等比数列定义证明，求解等比数列通项公式及证明，考查分类讨论思想，考查计算能力，属于难题.。

七宝中学高三上期中英语试卷I. Listening Comprehension （30%）Section ADirections：In Section A，you will hear ten short conversations between two speakers. At the end of each conversation，a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it，read the four possible answers on your paper，and decide which one is the best answer to the question you have heard. 1．（1.5分）A．A basketball player．B．A laundry worker．C．A window washer．D．A rock climber．2．（1.5分）A．To a stationery shop．B．To a gymnasium．C．To a paint store．D．To a news stand．3．（1.5分）A．15 minutes．B．45 minutes．C．An hour．D．An hour and a quarter．4．（1.5分）A．＄6．B．＄16．C．＄30．D．＄60．5．（1.5分）A．Looking for a timetable．B．Buying some furniture．C．Reserving a table．D．Window shopping．6．（1.5分）A．Egyptian．B．Greek．C．German．D．American．7．（1.5分）系统找不到该试题8．（1.5分）A．Dangerous．B．Brave．C．Rude．D．Modest．9．（1.5分）A．A job．B．An article．C．A book．D．An author．10．（1.5分）A．More sleep can get the man back onto the right track．B．Tiredness is a typical symptom of lack of exercise．C．The man should spend more time outdoors．D．People tend to work longer hours with artificial lighting．Section BDirections：In Section B，you will hear two short passages and one longer conversation，and you will be asked to questions on each of the passages. The passages will be read twice，but the questions will be spoken only once. When you hear a question，read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.11．（4.5分）（1）A．One case．B．Two cases．C．Three cases．D．Four cases．（2）A．They fled the scene in a white car．B．They ran off into a lane．C．They ran along the Seventh Ave．D．They left by the front entrance．（3）A． A safe．B．Cash．C．A bike．D．A metal pole．12．（6分）（1）A．50 million．B．57 million．C．120 million．D．128 million（2）A．For financial aid．B．For accurate policy making．C．For economic growth．D．For knowing the level of education．（3）A．Some people are unwilling to be recorded．B．Most developing countries lack civil registration systems．C．All the developing countries have no registration system．D．The civil registration is accused by the public．（4）A．Helping the developing countries．B．Establishing a partnership with the WHO．C．Improving people's health．D．Keeping correct records of births and deaths．13．（4.5分）（1）A．In a student dormitory．B．In a homestay family．B．In a quiet hotel room．D．In a lonely house．（2）A．High expense．B．Noisy environment．C．Safety concern．D．Difficult transportation．（3）A．He will be supported by a fund．B．His family can support him．C．He has saved some money．D．He can do part﹣time jobs．II. Grammar and vocabulary （20%）Section ADirections：Read the following two passages. Fill in the blanks to make the passage coherent. For the blanks with a given word，fill in each blank with the proper from of the given word. For the other blanks，fill in each blank with one proper word. Make sure that your answers are grammatically correct.14．（10分）Best News Ever：Researchers Confirm Chocolate Is Good for Your Brain Sure，chocolate is a delicious treat，and it's a staple of some of our favorite desserts．But it's not exactly a health food，so it should be enjoyed in moderation﹣right？Well，it turns out that（1）（eat）chocolate might actually have a pretty significant health benefit．According to recent research（2）（conduct）by five scientists in Italy，compounds found in chocolate，called flavanols （黄烷醇），can help boost cognitive （认知的）performance．Yes，chocolate's good for your brain．The scientists，studying at the Universities of Rome and L'Aquila，（3）（record）research from 10 different studies．The studies assessed people's performance on cognitivetests before and after eating cocoa or chocolate．The results were telling：in 9 out of the 10 studies，there was a noticeable improvement （4）the subjects had eaten the chocolate．The scientists found improvements in "general cognition，attention，processing speed，and working memory．" Sounds pretty good to us!And that's not all．In subjects，especially women，who performed the tests while sleep﹣deprived，the flavanols helped "counteract" the negative effects of the sleep deprivation．And there's even more good news．（5）（take）daily over periods ranging from five days to three months，chocolate can produce noticeable long﹣term improvements in cognition．Older adults，（6）memories were already declining，saw an especially significant improvement．All chocolate has flavanols，since they occur naturally in cocoa．However，dark chocolate lovers，are happier，（7）it has more flavanols than any other type of chocolate．In fact，the scientists （8）have claimed that，after doing this research，they've started eating dark chocolate every day! Here are some other health benefits of eating dark chocolate．Now，we're not saying that you （9）start eating chocolate for breakfast，lunch，and dinner﹣it's still high in sugar and low in nutrients．But next time you find yourself yawning after a sleepless night，snack on some chocolate and let the flavanols work their magic．Go ahead，（10）take advantage of chocolate's newfound brainpower with these delicious recipes．Section B Directions：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.15．（10分）A．Delivered；B．alert；C．documented；D．arising；AB．Temporary；AC．Recommendation；AD．Accommodate；BC．Demand；BD．Increase；CD．Contributing；ABC．practicesThe throngs of tourists flooding Russian cities for the World Cup are expected to provide a（n）（1）boost to the country's economy．However，the influx has proved difficult for some host cities to fully （2）visitors．In the city of Samara，where England will play Sweden on Saturday in a quarterfinal match，water pressure is decreasing due to a（n）（3）in customers．In response，the city utility company has offered an unusual solution to mitigate （缓解）the low pressure．The proposal by the city's water system authorities was （4）in a simple statement．"Save water，take showers in pairs，" the company said，accompanying its（5）with a smiley face．The Moscow Times reported the water authorities have increased output in recent days to compensate for the visitors，but the utility company is still trying to（6）residents about the strains placed on the water service．Rather than trying to change the habits of visitors，the water service has asked locals to alter their daily（7）．"Thousands of the city's visitors，who also consume water，are （8）to the increase，" the utility company，Samarskiye Kommunalniye Systemy，wrote in a press release on Wednesday．Recommended SlideshowsThe city has also experienced a heat wave that has increased the （9）for water during the tournament．The Associated Press reported said that medical staff distributed water to fans traveling to last month's game between Russia and Uruguay via public transit．Utility issues also arose when Russia hosted the 2014 Winter Olympics in Sochi．The host nation seemed unable to provide the infrastructure needed to host athletes，fans，reporters and others who attended the tournament．Journalists who visited the city to report on the games （10）discolored and brown water coming out of faucets（龙头）．Reading Comprehension （45%）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.16．（15分）How Facebook Programmed Our RelativesThree years ago，on his birthday， a law professor watched his e﹣mail inbox as usual．But it was filled with Facebook notifications（通告）（1）that friends had posted messages on his wall．The messages made him sad．The blocked inbox was （2），but what really upset him was having disclosed his birth date to Facebook in the first place．It's not necessary for social networking to comply with （遵守）privacy laws，as some people （3）believe．He hadn't paid much attention when he signed up﹣as with most electronic contracts，there was no room for negotiation about terms．He（4）Facebook's instructions，entered the data and clicked a button．A few days later，the law professor decided to change the birth date on his Facebookprofile to（5）the same situation next year．But when the fake date rolled around，his inbox again was flooded with Facebook notifications．Two of the messages were from close relatives，one of whom he had spoken with on the phone on his actual birthday!How could she not realize that the date was （6）？Our hypothesis （假设）：she'd been programmed!That law professor was one of us，and it confirmed his（7）that most people respond （8）to Facebook's prompts （提示）to provide information or contact a friend without really thinking much about it．That's because digital networked technologies are engineering humans to behave like simple stimulus﹣response machines．Social media plays a tremendous role in modern life．Facebook，LinkedIn and Twitter have become the primary ways of keeping in touch with friends，family，classmates and colleagues．To date，（9），researchers have not fully explored the degree to which these platforms are literally programming human responses．Social media platforms encode a range of social （10）：Facebook notifies us when it is time to wish our friends a happy birthday；LinkedIn prompts us to congratulate contacts on their work anniversaries．As a result，social interactions are often（11）to the click of a button．Facebook may increase the number of people to whom we wish a happy birthday with a few clicks of a button；it's not as if we remember the birth dates of that high school classmate or distant cousin．But if it becomes （12）behavior，is it even meaningful？As for people who aren't on Facebook or don't post their birth dates publicly，the（13）they exercise over their data comes at a cost：they don't receive scores of well﹣wishes from far﹣flung contacts．（14），it's still nice to be thought of，even if just once a year．Digital platforms are （15）what it means to be human，and we can't rely on the platforms to police or research themselves．In the meantime，when your birthday rolls around，enjoy the warm feelings from friends sending their regards﹣but remember that they don't know when your birthday really is any more than you do theirs．（1）A．requiring B．recognizing C．indicating D．summarizing （2）A．annoying B．embarrassing C．frustrating D．exciting（3）A．hardly B．passionately C．mistakenly D．slowly（4）A．lacked B．suspended C．obeyed D．offered（5）A．accept B．avoid C．analyze D．arrange（6）A．significant B．definite C．correct D．fake（7）A．doubt B．appointment C．statement D．plan（8）A．cautiously B．positively C．automatically D．aggressively （9）A．thus B．however C．moreover D．otherwise（10）A．reforms B．problems C．issues D．behaviors（11）A．adapted B．reduced C．committed D．admitted（12）A．suspected B．accepted C．programmed D．horrified（13）A．control B．judgements C．influence D．skills（14）A．In return B．In addition C．For example D．After all（15）A．enriching B．examining C．shaping D．retaining Section B Directions：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.17．（8分）Measles （麻疹），which once killed 450 children each year and disabled even more，was nearly wiped out in the United States 14 years ago by the universal use of the MMR vaccine （疫苗）．But the disease is making a comeback，caused by a growing anti﹣vaccine movement and misinformation that is spreading quickly．Already this year，115 measles cases have been reported in the USA，compared with 189 for all of last year．The numbers might sound small，but they are the leading edge of a dangerous trend．When vaccination rates are very high，as they still are in the nation as a whole，everyone is protected．This is called "herd immunity"，which protects the people who get hurt easily，including those who can't be vaccinated for medical reasons，babies too young to get vaccinated and people on whom the vaccine doesn't work．But herd immunity works only when nearly the whole herd joins in．When some refuse vaccination and seek a free ride，immunity breaks down and everyone is in even bigger danger．That's exactly what is happening in small neighborhoods around the country from Orange County，California，where 22 measles cases were reported this month，to Brooklyn，N．Y．，where a 17﹣year﹣old caused an outbreak last year．The resistance to vaccine has continued for decades，and it is driven by a real but very small risk．Those who refuse to take that risk selfishly make others suffer．Making things worse are state laws that make it too easy to opt out （决定不参加）of what are supposed to be required vaccines for all children entering kindergarten．Seventeen states allow parents to get an exemption（豁免），sometimes just by signing a paper saying they personally object to a vaccine．Now，several states are moving to tighten laws by adding new regulations for opting out．But no one does enough to limit exemptions．Parents ought to be able to opt out only for limited medical or religious reasons．Butpersonal opinions？Not good enough．Everyone enjoys the life﹣saving benefits vaccines provide，but they'll exist only as long as everyone shares in the risks．（1）The first two paragraphs suggest that．A．a small number of measles cases can start a dangerous trendB．the outbreak of measles attracts the public attentionC．anti﹣vaccine movement has its medical reasonsD．information about measles spreads quickly（2）Herd immunity works well when．A．exemptions are allowedB．several vaccines are used togetherC．the whole neighborhood is involved inD．new regulations are added to the state laws（3）What is the main reason for the comeback of measles？A．The overuse of vaccine．B．The lack of medical care．C．The features of measles itself．D．The vaccine opt﹣outs of some people．（4）What is the purpose of the passage？A．To introduce the idea of exemption．B．To discuss methods to cure measles．C．To stress the importance of vaccination．D．To appeal for equal rights in medical treatment．18．（6分）Suppose you're in a rush，feeling tired，not paying attention to your screen，and you send an email that could get you in trouble．Realisation will probably set in seconds after you've clicked "send"．You freeze in horrors and burn with shame．What to do？Here are four common email accidents，and how to recover．Clicking "send" too soonDon't waste your time trying to find out if the receivers has read it yet．Write another email as swiftly as you can and send it with a brief explaining that this is the correct version and the previous version should be ignored．Writing the wrong timeThe sooner you notice，the better．Respond quickly and briefly，apologizing for yourmistake．Keep the tone measured：don't handle it too lightly，as people can be offended，especially if your error suggests a misunderstanding of their culture（i．e．incorrect ordering of Chinese names）．Clicking "reply all" unintentionallyYou accidentally reveal（透露）to entire company what menu choices you would prefer at the staff Christmas dinner，or what holiday you'd like to take．In this instance，the best solution is to send a quick，light﹣hearted apology to explain your awkwardness．But it can quickly rise to something worse，when everyone starts hitting "reply all" to join in a long and unpleasant conversation．In this instance，step away from your keyboard to allow everyone to calm down．Sending an offensive message to its subjectThe most awkward email mistake is usually committed in anger．You write an unkind message about someone，intending to send it to a friend，but accidentally send it to the person you're discussing．In that case，ask to speak in person as soon as possible and say sorry．Explain your frustrations calmly and sensibly﹣see it as an opportunity to clear up any difficulties you may have with this person．（1）If you have written the wrong name in an email，it is best to．A．apologise in a serious mannerB．tell the receiver to ignore the errorC．learn to write the name correctlyD．send a short notice to everyone（2）What should you do when an unpleasant conversation is started by your "reply all" email？A．Try offering other choices．B．Avoid further involvement．C．Meet other staff members．D．Make a light﹣hearted apology．（3）What is the passage mainly about？A．Defining email errors．B．Reducing email mistakes．C．Handling email accidents．D．Improving email writing．19．（8分）Discoveries in science and technology are thought by "untaught minds" to come in blinding flashes or as the result of dramatic accidents．Sir Alexander Fleming did not，aslegend would have it，look at the mold （霉）on a piece of cheese and get the idea for penicillin there and then．He experimented with antibacterial substances for nine years before he made his discovery．Inventions and innovations almost always come out of tough trial and error．Innovation is like soccer；even the best players miss the goal and have their shots blocked much more frequently than they score．The point is that the players who score most are the ones who take most shots at the goal﹣and so it goes with innovation in any field of activity．The prime difference between innovation and others is one of approach．Everybody gets ideas，but innovators work consciously on theirs，and they follow them through until they prove practicable or otherwise．What ordinary people see as fanciful abstractions，professional innovators see as solid possibilities．"Creative thinking may mean simply the realization that there's no particular goodness in doing things the way they have always been done．" Wrote Rudolph Flesch， a language authority．This accounts for our reaction to seemingly simple innovations like plastic garbage bags and suitcases on wheels that make life more convenient："How come nobody thought of that before？"The creative approach begins with the proposal that nothing be as it appears．Innovators will not accept that there is only one way to do anything．Faced with getting from A to B，the average person will automatically set out on the best﹣known and apparently simplest route．The innovator will search for alternate courses，which may prove easier in the long run and are sure to be more interesting and challenging even if they lead to dead ends．Highly creative individuals really do march to a different drummer．（1）What does the author probably mean by "untaught mind" in the first paragraph？A．An individual who often comes up with new ideas by accident．B．A person who has had no education．C．A citizen of a society that restricts personal creativity．D．A person ignorant of the hard work involved in experimentation．（2）According to the author，what differs innovators from non﹣innovators？A．The way they present their findings．B．The way they deal with problems．C．The intelligence they possess．D．The variety of ideas they have．（3）The phrase "march to a different drummer" （the last line of the passage）suggests that highly creative individuals are．A．unwilling to follow common ways of doing thingsB．diligent in pursuing their goalsC．concerned about the advance of societyD．devoted to the progress of science（4）The most suitable title for this passage might be．A．The Relation Between Creation and DiligenceB．To Be a Creative Expert in the Study of Human CreativityC．What Are So Special about Creative IndividualsD．Discoveries and InnovationSection C Directions：Completethefollowingpassagebyusingthesentencesgivenbelow．Eachsentencecanbeusedonly once．Notethattherearetwomoresentencesthanyouneed．20．（8分）A．So if they're not building by imitation or carrying out instructions，how is this knowledge getting passed around？B．Crafting tool is a kind of culture，which can be passed down from generation to generation by crows．C．However，the crows only got treats when they popped in a paper "coin" of a certain size．D．These birds，native to the islands of New Caledonia east of Australia，are known for their ability to craft tools．AB．Seeing this in action is important because it supports the idea that New Caledonian crows are capable of building﹣at least when it comes to crafting tools．AC．Jelbert and her team then gave the crows paper to let them cut into proper size．There's no denying crows are smart．They can remember where food has been hidden，recognize faces and craft tools．And，according to a new paper in Scientific Reports，some crows can even make those tools from memory．This skill may point to these clever corvids having a sort of culture of their own．Researchers，led by Sarah Jelbert at the University of Cambridge，worked specifically with New Caledonian crows．（1）But experts haven't been able to make sure where the crows pick up their skills．A bird in one area can construct the same tool as another bird miles away ﹣but there's no evidence bird one watched bird two build the gadget in order to copy it．And New Caledonian crows don't really have a language，either．（2）Jelbert and her team had a hunch（预感）that it was because the birds were building based on the memory of tools they'd seen．To test this，the group trained eight crows to place pieces of paper into a pseudo﹣vending machine （really just a wooden box）to get a treat．（3）Once they learned which sizes were rewarded，Jelbert and her team then gave the feathered participants large cards；the birds could fashion these into the coin sizes they'd picked up on earlier．Importantly，the crows didn't get any sort of template（模板）when they were working with the big cards．And the birds snipped them into pieces that were similar in size to the coins they'd learned would get them treats．Given the lack of a template to copy，it seems the crows were able to construct mental images of the coins and use it to replicate a tool．（4）These birds can see something and not just build it from memory，but potentially make improvements in their designs．"Most importantly，" the authors say in the study，"an improvement made by a crow during its lifetime could become part of the template learnt by subsequent generations，leading to an increase in tool complexity over time．" And this progression is a key component of cultural progression．Jelbert and her team recognize there's still work to be done to see if their hypothesis is solid，like testing how long the crows can remember their mental images of the tools．I．Summary（15%）21．（15分）Directions：Read the following passage．Summarize in no more than 60 words the main idea of the passage and how it is illustrated．Use your own words as far as possible．Are your children getting on your last nerve？Did a coworker's comment rub you the wrong way？There's no need to plug the steam coming out of your ears．In fact，science now gives you full permission to release those emotions；you might actually be happier for it．If that seems counterintuitive（违反直觉的），hear us out．A new study suggests that people tend to be happier if they can feel and express emotions as they want．That goes for unpleasant emotions like anger and hatred，too．An international team of researchers recruited 2，300 university students from the United States，Brazil，China，Germany，Ghana，Israel，Poland，and Singapore．They then asked the participants to tell them which emotions they desired and which ones they actually felt，and then compared those responses to how the participants rated their overall happiness or life satisfaction．The results showed an interesting trend．While participants wanted to experience more pleasant emotions，they reported higher life satisfaction if the emotions they experienced matched those they desired．More surprising still，11 percent of people wanted to feel lessof positive emotions，such as love and empathy，and 10 percent of people wanted to feel more negative emotions，such as hatred and anger．At first glance，these results might seem confusing．But there's a simple explanation，according to the study's authors．Happiness is "more than simply feeling pleasure and avoiding pain，" they write．It is also learning to release negative emotions when you feel them，instead of ignoring them or bottling them up．"If you feel emotions you want to feel，even if they're unpleasant，then you're better off，" lead researcher Dr Maya Tamir from The Hebrew University of Jerusalem told the BBC News website．Translation （15%）Directions：Translate the following sentences into English，using the words given in the brackets.22．（3分）他刚一坐下，服务员就给他上茶了．（Hardly…）23．（3分）把新的科学发现应用于工业生产要花几年的时间．（before）24．（3分）再尝试与这台电脑的客服联系，否则我们只能求助于同学和好友了．（contact）25．（6分）当听到两架飞机在机场侥幸避开碰撞（collision）的消息，我们禁不住佩服飞行员在紧急情况下表现出的勇敢和果断．（escape）III. Guided Writing （25%）26．（25分）Directions：Write an English composition in no less than 150 words according to the instructions given below in Chinese．微信朋友圈WeChat moments拉黑pull sb．into blacklist七宝中学高三（上）期中英语试卷参考答案与试题解析I. Listening Comprehension （30%）Section ADirections：In Section A，you will hear ten short conversations between two speakers. At the end of each conversation，a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it，read the four possible answers on your paper，and decide which one is the best answer to the question you have heard. 1．（1.5分）A．A basketball player．B．A laundry worker．C．A window washer．D．A rock climber．【分析】略【解答】C【点评】略2．（1.5分）A．To a stationery shop．B．To a gymnasium．C．To a paint store．D．To a news stand．【分析】略【解答】A【点评】略3．（1.5分）A．15 minutes．B．45 minutes．C．An hour．D．An hour and a quarter．【分析】略【解答】C【点评】略4．（1.5分）A．＄6．B．＄16．C．＄30．D．＄60．【分析】略【解答】C5．（1.5分）A．Looking for a timetable．B．Buying some furniture．C．Reserving a table．D．Window shopping．【分析】略【解答】C【点评】略6．（1.5分）A．Egyptian．B．Greek．C．German．D．American．【分析】略【解答】D【点评】略7．（1.5分）系统找不到该试题8．（1.5分）A．Dangerous．B．Brave．C．Rude．D．Modest．【分析】略【解答】B【点评】略9．（1.5分）A．A job．B．An article．C．A book．D．An author．【分析】略【解答】C【点评】略10．（1.5分）A．More sleep can get the man back onto the right track．B．Tiredness is a typical symptom of lack of exercise．C．The man should spend more time outdoors．D．People tend to work longer hours with artificial lighting．【解答】C【点评】略Section BDirections：In Section B，you will hear two short passages and one longer conversation，and you will be asked to questions on each of the passages. The passages will be read twice，but the questions will be spoken only once. When you hear a question，read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.11．（4.5分）（1）A．One case．B．Two cases．C．Three cases．D．Four cases．（2）A．They fled the scene in a white car．B．They ran off into a lane．C．They ran along the Seventh Ave．D．They left by the front entrance．（3）A． A safe．B．Cash．C．A bike．D．A metal pole．【分析】略【解答】BAB【点评】略12．（6分）（1）A．50 million．B．57 million．C．120 million．D．128 million（2）A．For financial aid．B．For accurate policy making．C．For economic growth．D．For knowing the level of education．（3）A．Some people are unwilling to be recorded．B．Most developing countries lack civil registration systems．C．All the developing countries have no registration system．。

2020年上海市七宝中学高三生物上学期期中考试试卷及答案解析一、选择题：本题共15小题，每小题2分，共30分。

每小题只有一个选项符合题目要求。

1. 下图是细胞呼吸过程的图解。

在人体细胞中不能发生的过程是（）A ① B. ① C. ① D. ①2. 细胞的发现将生命的奥秘生命本身浓缩到一个微观世界。

细胞学说是一代一代科学家经过努力，逐渐建立和完善起来的。

下列有关细胞学说的叙述，错误的是（）A. 细胞学说主要由德国科学家施莱登和施旺提出B. 建立细胞学说的意义在于揭示了生物体结构的统一性C. 细胞学说揭示了病毒、细菌、动物、植物都是由细胞构成的D. 细胞学说的建立支持所有生物有共同祖先的进化观点3. 不能用杂交育种方法来培育新品种的生物是（）A. 水稻B. 牛C. 小麦D. 大肠杆菌4. 神经细胞甲释放多巴胺会导致神经细胞乙产生兴奋，甲细胞膜上的多巴胺运载体可以把发挥作用后的多巴胺运回细胞甲。

某药物能够抑制多巴胺运载体的功能，干扰甲、乙细胞间的兴奋传递(如图)。

下列有关叙述错误的是（）A.①中多巴胺的释放过程依赖于细胞膜的流动性B.药物会导致突触间隙多巴胺的作用时间缩短C.①释放的多巴胺与①结合会导致细胞乙的膜电位改变D.多巴胺只能由细胞甲释放，作用于细胞乙使兴奋单向传递5. 下列有关叙述中，正确的说法有（）①减数分裂四分体时期，同源染色体的姐妹染色单体之间的局部交换可导致基因重组；①异卵双生兄弟间的性状差异主要是基因重组导致的；①染色体中一段片段的缺失或重复属于染色体结构变异；①白化病和先天性愚型都可以通过诊断致病基因来检测出；①人类的大多数疾病与基因有关，与生活方式和环境无关。

A.①①①B.①①C.①①①D.①①6. 通过单倍体育种将宽叶不抗病(AAbb)和窄叶抗病(aaBB)两个烟草品种培育成宽叶抗病(AABB)新品种。

下列关于育种过程的叙述正确的是A.将AAbb和aaBB杂交得到AaBb的过程实现了基因重组B.对F1的花药进行离体培养,利用了细胞的全能性C.需要用秋水仙素处理萌发的F1种子,使染色体加倍D.育种过程中淘汰了杂合个体,明显缩短了育种年限7. 细菌在分类上属于原核生物的原因是（）A.没有细胞结构B.单细胞C.没有核膜D.没有DNA8. 下列不一定发生在人体内环境中过程有A.正常机体内抗体与抗原的结合B.某种激素与激素受体结合C.肝脏细胞代谢产生的尿素运输到肾小球D.各种神经递质从突触前膜到达突触后膜9. 下列关于生物大分子的叙述，不正确的是（）A.核酸在生物体的遗传、变异和蛋白质的生物合成中具有极其重要的作用B.核酸是储存遗传信息的生物大分子C.淀粉、糖原、纤维素以及果糖、乳糖都是生物大分子D.生物大分子以碳链为骨架，所以C是生命的核心元素10. 如图是下丘脑及其直接或间接支配的有关腺体之间的关系示意图（+表示促进，-表示抑制），有关说法正确的是（）A.a产生的某种物质可影响动物的性行为B.b与c两者的分泌物在某些生理效应上可表现为协同作用C.c不仅具有感受刺激和传导兴奋的功能，而且有分泌功能D.a、b、c中，c对内环境稳态的维持影响最小11. RNase P是一种核酸内切酶，由RNA和蛋白质组成。

2018-2019学年七宝中学高三年级上学期期中考试数学试卷一、 填空题（本大题共有12题，满分54分） 1、集合{}=0,1,2018A 的真子集有 个 【答案】72、设全集{}{}2,4,31xU R M x x N x ==>=≥,则右图中影音部分 所表示的集合是 （用区间表示） 【答案】[]0,23、命题“若实数,a b 满足5a b +≤,则2a ≤或3b ≤”是 命题 （填“真”或“假”） 【答案】真4、某个时针的针长6cm ，则在本场考试内，该时针扫过的面积是_______________2cm 【答案】6π5、函数121()log 1axf x x x -=--是奇函数，则实数a 的值为____________________ 【答案】1- 6、函数ay x x=+在（1,2）上单调递增，则实数a 的取值范围为___________ 【答案】2a ≤7、在△ABC 中，角A,B,C 所对的边分别是a,b,c ，若ABC A c a ∆===则,3,2,3π的面积是 。

8、已知函数43)(x x f =，则)13(-x f ＜)1(2x f +的解集是【答案】()1,22,2⎡⎫+∞⎪⎢⎣⎭9、若关于x 的不等式x a x +-2＞1在][2,0上恒成立，则实数a 的取值范围为 【答案】1a <-或2a >10. 已知常数0a >，函数2()2x x f x ax =+的图像经过点6(,)5P p 、1(,)5Q q -，若216p q pq +=，则a =【答案】411. 已知函数3()33333x x f x x x -=--+-+，若22(3)(1)6f a f b +-=，则大值是【答案】3【解析】 3()33333x x f x x x -=--+-+()333333x x f x x x --=++-+()()6f x f x +-=2222310,31a b a b ∴+-=+=3≤≤= 12. 已知函数212()1(2)012xx f x f x x -<≤⎧⎪=⎨<≤⎪⎩，如果函数()()(1)g x f x k x =--恰有三个不同的零点，那么实数k 的取值范围是 【答案】11(,]715--【解析】如图AN AM k k k <≤，即21715k -<≤-二、选择题（本大题共有4题，满分20分）13、“函数()()f x x R ∈存在反函数”是“函数()f x 在R 上为单调函数”的 ( )A 、充分而不必要条件B 、必要而不充分条件C 、充分必要条件D 、既不充分也不必要条件【答案】B14、若函数()f x 的反函数()1f x -，则函数()1f x -与()11f x --的图像可能是 ()【答案】A15、在△ABC 中，角A 、B 、C 所对的边分别为a 、b 、c ，给出四个命题 （1）若sin 2sin 2A B =，则△ABC 为等腰三角形 （2）若sin cos A B =，则△ABC 为直角三角形 （3）若cos sin cos A B Ca b c==，则△ABC 为等腰直角三角形 （4）()()()cos cos cos 1A B B C C A ---=，则△ABC 为正三角形 以上正确命题的个数是（ ） A 、1B 、2C 、3D 、4【答案】B16、()f x 是定义在D D ，若()f x 的图像绕原点逆时针旋转6π后与原图像重合，则在以下各项中，f 的可能取值只能是（ ）A 、0B 、1C 、2D 、3【答案】C【解析】函数上的点与原点连线构成的线段与x 轴的夹角不能是30︒的整数倍三、解答题（本大题共有5题，满分76分）17、（本题满分14分，第1小题满分7分，第2小题满分7分）已知锐角α和钝角β的终边分别与单位圆交于,A B 两点，其中A 点坐标34(,)55（1） 求1sin 2cos 2αα+的值；（2） 若5sin()13αβ+=-，求点B 坐标。

2020年上海市七宝实验中学高三英语上学期期中考试试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AA Lifelong Devotion to Keeping People FedYuan Longping is a Chinese agricultural scientist and educator, known for developing the hybrid rice varieties.Yuan graduated from the Southwest Agriculture Institute in 1953 andbegan his teaching career at an agriculture school.In the 1960s, when a serious food shortage sweptChina, Yuan decided to devote himself to studying how to increase the yields of rice. He then began a lifelong connection with rice.Yuan succeeded in growing the world’s first high-yielding hybrid rice varieties in 1973, which could reach a yield of over 500 kg per mu (about 0.067 hectares), rising from the previous yield of only 300 kg per mu. For the next four decades, he continued to work on research and development of hybrid rice, achieving increasingly higher outputs. In 2020, hybrid rice developed by Yuan’s team achieved 1,500 kilograms per mu in two growing seasons, a new world record.InChina, where rice is the main food for the majority of the 1.4 billion people, the planting area of hybrid rice has reached 16 million hectares, or 57 % of the total planting area of rice, helping feed an extra 80 million people a year.Hybrid rice has also been grown in over 40 countries, including theU.S.,Brazil,India,Vietnam, thePhilippinesandMadagascar. The total planting area of the hybrid rice has reached 8 million hectares overseas.Even after a great success, Yuan never held himself back from making new breakthroughs. In 2017, his team started to grow seawater rice inQingdao. The rice was designed to grow in saline-alkaline land and survive even after being completely in seawater. His team planned to develop a type of seawater rice that could be planted in 6.67 million hectares of saline-alkaline land acrossChinato boost the country’s rice harvest by about 20 %. In 2018, Yuan’s team was invited to plant the saline-alkaline tolerant rice in experimental fields inDubai, which achieved huge success. In June 2020, his team started to grow seawater rice on a farm at an altitude of 2,800 meters in northwestChina’sQinghaiProvince. The experiment succeeded.Yuan had two dreams — to “enjoy the cool under the rice crops taller than men” and that hybrid rice could be grown all over the world to help solve the global food shortage.1. What made Yuan Longping decide to study rice?A. A serious food shortage.B. Agriculture development.C. His interest in the rice experiment.D. His wish to plant the tallest rice in the world.2. From the passage, we know that Yuan Longping ________.A. developed a variety of hybrid riceB. worked as a scientist after graduationC. started to grow seawater rice inDubaiin 2017D. grew the first high-yielding hybrid rice varieties in 19533. We can infer from the passage that Yuan Longping’s most outstanding qualities are________.A. modest and outgoingB. honest and creativeC. generous and optimisticD. responsible and devotedBLearning to say “yes, and”When I first heard about the improvisation (即兴交流) class, I was hesitating. As a quiet and shy girl, I feared improvising in front of strangers. However,I knew I wanted to work as a science communicator after finishing my Ph.D., so it seemed like a perfect opportunity to learn how to speak and communicate with others effectively. I signed up, knowing the experience would give me help.During our first class, we learned an important concept of improvisation: “yes, and.” It means that, as improvisers, we’d better accept what fellow performers say. If someone says that rhinos (犀牛) are librarians, for example, then rhinos are librarians. We do not question the logic; we say “yes” and then continue with the scene as if nothing is wrong.The first few scenes were hard, but as weeks turned into months, I became more comfortable andeven started to enjoy our classes. I became better at listening, relating to my conversation partners, and communicating clearly in the moment. Once when I was giving a presentation about my science, an audience member surprised me with a question that didn’t grow out of the information I’d presented. Instead of getting confused and nervous, I took the “yes, and” approach—accepting the question and letting my mind focus on why it was asked. That helped me find an appropriate answer. I got pretty excited about it.The benefits of improvisation go beyond communication. Before attending the class, I would get stuck when my experiments produced unexpected data, thinking that I had made a mistake. But now, instead of getting discouraged, I will stay open to the possibility that the results are real, keep exploring the data and end upidentifying a new type of cell—one that isn’t behaving as expected.I think all scientists can benefit from this lesson. If the data say rhinos are librarians, then it’s worth findingout whether rhinos are, in fact, librarians. As scientists, our job isn’t to challenge data that support a preconceived (先入为主的) story, but to say “yes, and.”4. Why did the author attend the improvisation class?A. To get a different experience.B. To finish her Ph.D. at university.C. To give up her job as a science communicator.D. To improve her speaking and communicating ability.5. What was the author’s change after attending the improvisation class?A. She formed her own idea quickly.B. She came up with lots of creative responses.C. She paid more attention to the logic of answers.D. She became a good listener before giving an opinion.6. The author mentions applying the “yes, and” approach to her scientific experiments to ______.A. explain the process of using the methodB. prove the benefits of the improvisation classC. share her own research experiences with readersD. attract fellow scientists to attend the improvisation class7. What can be inferred about scientists from the last paragraph?A. They should attend the improvisation class.B. They should question all preconceived ideas.C. They should carry on research by admitting earlier data.D. They should try to improve their professional knowledge.CIf you think you’d like to live on Mars, you may have that possibility by 2023. A Dutch company called Mars One will soon advertise for people interested in colonizing (开拓) Mars. Ifyou have all the necessary skills, you could be one of the first colonists. Are you ready for the challenge?You won’t have to pay for the mission to Mars. Mars One has already received money from some donors and is hoping to get more from TV viewers who will become interested in the show where all applicants have a debatefor the rare chances.The main responsibility of the first colonists is to create an artificial environment on Mars where there is no air to breathe and no land to farm. Scientists know it’s quite possible because something similar has already been done inAntarctica.Another problem is that space travel to Mars takes nearly a year to get to Mars and the colonists will live the rest of their lives there. When a human lives in an environment without gravity or with low gravity for a long time, the systems in the body weaken. Luckily, spinning (旋转) the spaceship can create artificial gravity, and artificial gravity can ease these problems. It will also be difficult for Mars colonists to be far from home, living in small spaces, and seeing the same people over and over. Colonists with depression could put the mission in danger. Fortunately, a few years ago, a joint Russian and European project called the Mars500 Mission studied people’s reactions in a Mars-like environment. It is viewed as a great success because scientists were able to see how people handle emotional and physical stresses.Recent studies show that seven percent of people would want to go on such an adventure.Mars One will soon start accepting its first colonists. Are you interested?8. What do we know about the applicants to Mars from the first two paragraphs?A. They will land on Mars in 2023.B. They can get money from donors.C. They will compete in a TV show.D. They do not need special skills.9. What will the first colonists do to solve the basic living problems on Mars?A. Create earth-like conditions.B. Build labs inAntarctica.C. Spin the spaceship.D. Start the Mars500Mission.10. What can the life of the first colonists be like according to the passage?A. Difficult and dangerous.B. Different but adaptable.C. Challenging and unbearable .D. Acceptable but depressing.11. What’s the best title for the text?A. Mars: our final destination?B. Ready to be Mars’ colonists?C. Space travel: a thrilling adventure?D. Are you a qualified Mars astronaut?DSome of the oldest art in human history is being damaged, scientists say. And climate change may be speeding up its loss. Newresearch reports that ancient rock art in Indonesian caves is degrading over time, as bits of rock slowly break off from the walls. It's a huge loss for human history.Salt crystals（结晶）building up on the walls are a key part of the problem, the study suggests. These salt crystals go into the cave walls, changing sizes as temperatures rise and fall. This process causes the rock to slowly break down.Salt crystals may become larger when exposed to repeated changes between wet conditions and periods of drought. These kinds of changes are expected to become more obvious as the climate continues to warm.In particular, the researchers say, climate change may cause more intense El Nino（厄尔尼诺）events in the future. These events can strengthen the kinds of conditions that help salt crystals form Scientists are still debating the exact influence of climate change on El Nino, a natural climate cycle that drives changing patterns of warming and cooling in thePacific Ocean.The new study, led by Jillian Huntley, examined 11 ancient cave art sites in South Sulawesi, Indonesia. The researchers found evidence of salt formation at all 11 sites. It's merely a small part There are more than 300 known eave art sites around the region. The researchers note that salt crystals may indeed be part of the problem, adding that climate change is a growing threat, one that deserves more attention.12. What is the main cause of the rocks breaking off from the wall?A. Weather patterns.B. Salt crystals.C. Wet conditions.D. Drought Periods.13. Which of the following may researchers agree with?A. El Nino events prevent salt crystals forming.B. Climate change makes little difference to El Nino.C.Salt crystals may become much larger in wet conditions.D. Constant warm weather may cause salt crystals to change size.14. Which word best describes Huntley's attitude to climate change?A. Worried.B. Curious.C. Doubtful.D. Positive.15. What can we learn from thelast paragraph?A. The formation and patterns of salt crystals.B. The impact of climate change on ancient rock arts.C. The historical value of ancient rock art in cave sites.D. The threats of human activities to ancient eave art sites.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。