2019年上海南模中学高三三模(2019.05)
2019-2020学年上海市南洋模范中学高三生物三模试卷及参考答案
2019-2020学年上海市南洋模范中学高三生物三模试卷及参考答案一、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. 下列关于生长素发现过程的实验，说法不正确的是（）A.达尔文实验证明，胚芽鞘的感光部位是尖端B.鲍森·詹森的实验证明，胚芽鞘尖端产生的影响可以透过琼脂片传递给下部C.拜尔的实验证明，胚芽鞘的弯曲生长是由于生长素生长分布不均匀造成的D.温特实验证明，胚芽鞘尖端能产生促进生长的化学物质2. 2018年诺贝尔生理学或医学奖授予美国免疫学家詹姆斯·艾利森和日本免疫学家本庶佑，以表彰他们在癌症免疫治疗方面所作出的贡献。
下列叙述错误的是A. 癌变的细胞内，负责调节细胞周期的基因功能异常B. 细胞癌变后，细胞膜的成分发生改变，细胞间黏着性降低C. 人体免疫系统能够消灭癌细胞体现了免疫系统的防卫功能D. 人体免疫系统识别癌细胞的过程受到干扰会导致癌细胞“逃逸”3. 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4. 生物大分子通常都有一定的分子结构规律，即由一定的基本组成单位，按一定的排列顺序和连接方式形成多聚体，下列表述正确的是（）A.若该图为一段肽链的结构模式图，则1表示肽键，2表示中心碳原子，3的种类约有21种B.若该图为一段RNA的结构模式图，则1表示核糖，2表示磷酸基团，3的种类有4种C.若该图为一段单链DNA的结构模式图，则1表示磷酸基团，2表示脱氧核糖，3的种类有4种D.若该图表示多糖结构模式图，淀粉、纤维素和糖原的空间结构是相同的5. 如图表示人体细胞间信息传递的一种方式。
下列描述错误的是（）A. 该调节方式的信息传递速度缓慢、作用范围较广泛B. 若靶细胞属于垂体，则分泌细胞一定是下丘脑细胞C. 若分泌细胞是垂体细胞，则靶器官可能是甲状腺、性腺、肾上腺D. 体温调节和血糖平衡调节可能涉及这种调节方式6. 下列关于脂质功能的叙述错误的是（）A. 胆固醇在人体内参与血液中脂质的运输B. 磷脂是构成细胞膜和细胞器膜的重要成分C. 维生素D能有效地促进人和动物肠道对钙和磷的吸收D. 脂肪中含H比糖类多，是主要的能源物质7. 图1表示芽的生长与生长素浓度的关系，图2表示幼苗横放时，根的生长与生长素浓度的关系。
上海市2019届高三高考数学系列模拟卷(3)及答案解析
上海市2019届高考数学模拟试卷3考生注意：1．每位考生应同时领到试卷与答题纸两份材料，所有解答必须写在答题纸上规定位置，写在试卷上或答题纸上非规定位置一律无效；2．答卷前，考生务必将学校、姓名、学号等相关信息在答题纸上填写清楚； 3．本试卷共23道试题，满分150分，考试时间120分钟。
一、填空题（本大题满分56分，共14小题，每小题满分4分）集合{}2M x x =<，{}lg (1)N x y x ==-，则M N = 1.若知i 是虚数单位，使(1)ni +为实数的最小正整数n 为2.已3.若对于任意实数x ，不等式a x x >--+|1||2|恒成立，则实数a 的取值范围是4.在ABC ∆中，若120=∠A ，5=AB ，7=BC ，则三角形ABC 的面积=S5.若直线),(042R n m ny mx ∈=-+始终平分圆042422=---+y x y x 的周长，则mn 的取值范围是_________________6.设f n k ()=（其中n N ∈*），k 是2的小数点后第n 位数字，…74142135623.12=， 则{}f f f f …个[()]88的值等于____________7.已知矩阵sin cos 0sin cos 1ααββ+⎛⎫⎪+⎝⎭为单位向量，且,,2παβπ⎡⎫∈⎪⎢⎣⎭，()sin αβ-的值 8.一个圆锥的侧面展开图是圆心角为43π，半径为18 cm 的扇形，则圆锥母线与底面所成角的余弦值为________9.在矩形ABCD 中，AB =1BC =，E 是CD 上一点，且1AE AB ⋅=，则AE AC ⋅的值为10.设函数f x ()是定义在R 上的奇函数，若f x ()的最小正周期为3，且f ()11>，f m m ()2231=-+，则m 的取值范围是_________________11.若π220≤≤x ，则使x x 2cos 2sin 12=-成立的x 的取值范围是 12.已知集合{1,2,,}U n =，n *∈N ．设集合A 同时满足下列三个条件：①A U ⊆；②若x A ∈，则2x A ∉；③若U x C A ∈，则2U x C A ∉．当7n =时，满足条件的集合A 的个数为______13.对任意的120x x <<，若函数()f x a x =的大致图像为如图所示的一条折线（两侧的射线均平行于x 轴），试写出a 、b 条件是14.已知数列{}n a 满足11,2,n n n a n a a n ++⎧=⎨-⎩为奇数，为偶数，设222n n n b a a +=-，则数列{}n b 的通项公式为________________二、选择题（本大题满分20分，共4小题，每小题满分5分）15.“21a >” 是“方程2221x y a+=表示椭圆”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16.设3144322314)1()1(+++=++++x b x a x a x a x a x 22)1(++x b 413)1(b x b +++定义),,,(),,,(43214321b b b b a a a a f =，则),1,2,3,4(f 等于A ．)4,3,2,1(B ．)0,4,3,0(C ．)2,2,0,1(--D ．)1,4,3,0(--17.互不相等的三个正数321,,x x x 成等比数列，且P 1(1log a x ,1log b y )，P 2(2log a x ，2log b y )，)log ,(log 333y x P b a 三点共线(其中0a >，1a ≠，0b >，1b ≠)，则1y ，2y ，3yA. 等差数列，但不等比数列；B. 等比数列而非等差数列C. 等比数列，也可能成等差数列D. 既不是等比数列，又不是等差数列 18.设函数)sin()sin()sin()(2211n n x a x a x a x f ααα+⋅+++⋅++⋅= ，其中)2,,,,2,1(*≥∈=n N n n i i α为已知实常数，R x ∈，则下列A ．若0)2()0(==πf f ，则0)(=x f 对任意实数x 恒成立；B ．若0)0(=f ，则函数)(x f 为奇函数；C ．若0)2(=πf ，则函数)(x f 为偶函数；D ．当0)2()0(22≠+πf f 时，若0)()(21==x f x f ，则)(221Z k k x x ∈=-π．74分，共5小题）19.(本题满分12分）第（1）小题6分，第（2）小题6分.在直三棱柱111C B A ABC -中，1==AC AB ，090=∠BAC ，且异面直线B A 1与11C B 所成的角等于060，设a AA =1.（1）求a 的值；（2）设D 是11C B 上的任意一点，求D 到平面BC A 1的距离.20.(本题满分14分）第（1）小题7分，第（2）小题7分.已知函数.3cos 33cos 3sin )(2xx x x f +=（1）将)(x f 写成)sin(φω+x A +B 的形式，并求其图象对称中心的横坐标；（2）如果△ABC 的三边a 、b 、c 满足ac b =2，且边b 所对的角为x ，试求x 的范围及此时函数)(x f 的值域。
2019-2020学年上海市南洋模范中学高三英语第三次联考试题及答案解析
2019-2020学年上海市南洋模范中学高三英语第三次联考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A4 Best Drive--In Movie Theaters in the USColorado: Holiday Twin Drive--InAddress: 2206 S Overland Trail, Fort Collins, CO 80526, USAPhone: +1 970-221-1244The theater, open since 1968 and currently the most popular drive-in in the US, provides various special foods. The menu there even amazes meat-free customers. But please remember the outside food is forbidden here. Besides, the Rocky Mountains provide a pastoral (田园式的) backdrop to screenings, and sunsets usually don’t disappoint either. It also offers lots of unique events that go beyond the big screen.North Carolina: Hound’s Drive--InAddress: 114 Raven Cir, Kings Mountain, NC 28086, USAPhone: +1 704-739-4424Having only opened in 2016, it’s one of the newest theaters on the block. The drive-in features newer equipment and digital projection. People can bring their animal friends along.Florida: Fort Lauderdale Swap ShopAddress: 3291 W Sunrise Blvd, Fort Lauderdale, FL 33311, USAPhone: +1 954-791-7927The Florida favorite offers plenty ofways to have fun. With 14 screens, the self-proclaimed (自称的) world’s largest drive-in equals any indoor cinema in terms of capacity and programming. It also includes an 88-acre flea (跳蚤) market and a free Ferrari museum. It’s best to book tickets on the Internet ahead of time if you don’t want to wait in line.California: Mission Tiki Drive -InAddress: 10798 Ramona Ave, Montclair, CA 91763, USAPhone: +1 909-628-0511Let’s have fun in the old-school outdoor cinema in Montclair, California. Remember tickets are available atthe ticket office only. It alternates (交替) up to eight new releases on four screens and hosts almost daily swap meets where people can exchange things they no longer need. It also organizes classic car and lowrider meet-ups.1.What can people do in Holiday Twin Drive-In?A.Participate in somespecial activities.B.Enjoy the film with the latest equipment.C.Learn about the benefits of being meat free.D.Share home-made cookies while watching the film.2.Which of the following theaters is friendly to visitors with pets?A.Hound’s Drive- In.B.Mission Tiki Drive-In.C.Holiday Twin Drive-In.D.Fort Lauderdale Swap Shop.3.What do Fort Lauderdale Swap Shop and Mission Tiki Drive-In have in common?A.Both feature old-fashioned styles.B.Both allow booking tickets online.C.Both provide free museum exhibitions.D.Both offer chances to trade second-hand goods.BOnce small farmers in Masii, a remote village in Kenya, have picked their crops, all they can do is wait until a buyer trucks through. The system works fairly well for beans and corn, but mangoes-the area’s other main crop-spoil (腐烂) more quickly. If the trader is late, they rot.However, a simple coating could change that. A company, SmartTech, has created a product that doubles the shelf life of fresh produce, enabling farmers to access far-off, larger markets. More time forfresh produce on grocers’ shelves also means less food waste-a $2.6 trillion problem, according to the United Nations’ Food and Agriculture Organization (FAO).James Rogers, CEO of SmartTech, wanted to solve the problem for food much in the same way that oxide barriers preventing rust (锈) have achieved for steel. Fortunately, researchers have found when plants made the jump from water to land, they developed cutin(蜡质), a barrier which is made of fatty acids that link together to form a seal around the plant, helping keep water in.The cutin was such a grand strategy that today you’ll still find it across the plant kingdom. SmartTech discovered through researches that an orange can last longer than a strawberry not so much because of the thickness of its skin, but because of the difference in the arrangement of those cutin molecules (分子)on thesurface. After extensive trials, Rogers and his team developed a natural and tasteless protective coating from plant material-stems, leaves and skins. The product extends the sweet spot between ripening and rot. And best of all, the treated produce doesn’t require refrigeration.“SmartTech has huge potential to turn poor farmers in Africa into commercial farmers,” says Rogers. “That means more money in pockets, and more food in stomachs.” But whether the company can cost-effectively reach small farmers in far-off areas still remains a challenge.4. The author mentions the small farmers in Kenya to ________.A. stress their need for preserving produceB. show their challenge in harvesting cropsC. express their wish to reach larger marketsD. evaluate their loss caused by slow transport5. What can we learn about SmartTech’s product?A. It is financially supported by FAO.B. It is intended to replace refrigeration.C. It is designed to thicken produce’s skin.D. It is based on plants’own defence system.6. What will James Rogers probably focus on next?A. How to expand farms.B. How to earn more money.C. How to produce more tasty food.D. How to profit farmers in remote area.7. The main purpose of the passage is to ________.A. promote a productB. present a technologyC. advertise SmartTechD. introduce James RogersCThe COVID-19 vaccination（接种疫苗）rate in the US has fallen to newlows in recent weeks, threatening President Joe Biden’s goal of having 70 percent of American adults with at least one shot by July 4.With just less than one month from July 4, the current vaccination rate will put the US at somewhere between 67 percent and 68 percent of the adult population with at least one dose（剂量）by Independence Day. To reach 70 percent by July 4, around 1.6 percent of the population needs to get their first dose per week from nowuntil July 4.The Centers for Disease Control and Prevention（CDC）reported last week that 63 percent of adults hadreceived their first dose of a COVID-19 vaccine. That was up slightly from 62 percent from the report a week before. The additional 1 percent of adults completing their first dose is the lowest since the CDC started tracking the vaccination rate in mid-February.On average, fewer than 1 million shots are given out per day, a decline of more than two-thirds from the peak of 3.4 million in April, The Washington Post reported. In South Carolina, about 71,000 residents got a shot in the week leading up to June 3, compared to a high of nearly 300,000 in one week in early April, according to data from the CDC.The slowdown is moreprominentacross the South and Midwest. Twelve states have seen vaccinations fall to 15 daily shots per 10,000 residents. Less than a quarter of black Americans had received their first COVID-19 shot as of June 7.James Hildreth, CEO of Meharry Medical College, told Politico, “We need to make a stronger effort to bring the vaccine to the communities, rather than relying on the communities to come to vaccination centers.”The sharp decline in vaccination began in mid-April when federal officials temporarily stopped the use of the Johnson＆Johnson vaccine while they investigated rare blood-clotting（凝血）reactions.The “low-hanging fruit—thosepeople who ly want to get vaccinated without you telling them anything” have already been vaccinated, which has led to the slowdown, Dr Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said on a White House-organized call with community leaders last week, according to the Post.8. What can we learn from the text?A. Dr Anthony Fauci is in charge of the Centers for Disease Control and Prevention.B. In South Carolina, about 300,000 residents got a shot in the week leading up to June 3C. In mid-April federal officials temporarily suspended the Johnson＆Johnson vaccine.D. Less than one fourth of Americans had received their first COVID-19 shot by June 7.9. Which of the following can replace the underlined word “prominent” in Para. 5?A. Meaningful.B. Obvious.C. Inspiring.D. Complex.10. How can America increase the COVID-19 vaccination rate according to James Hildreth?A. By giving the vaccine shot at the communities.B. By offering the vaccine to the public for free.C. By frequently informing the public of the vaccine.D. By urging the communities to come to vaccination centers.11. What can be the best title for the text?A. Biden wishes to have 70% of adults with one shot by July 4B. CDC has been trackingthe vaccination rate since mid-FebruaryC. Some Americans need to get vaccinated without telling them toD. Biden’s July 4th vaccine goal may be missedDIf you believe in thermometers (温度计), you should believe in global warming. And if you believe in eating French fries with your hamburger, you should worry more about carbonemission.It won't happen overnight, but as the planet’s climate changes, the growth cycles of main crops will all be heavily affected. Here are three of the crops that might not beat the heat.The potato actually needs a great deal of beauty rest to develop properly. “They need a cool nighttime temperature in order to start growing the tuber, the part that we eat,” Nelson says.Temperature and altitude are two primary concerns in coffee growth, and farmers are stuck between a rock and a hard place. “We know that coffee grows in a certain temperature range,” Nelson says. “They've been moving up the mountains, but at some point you run out of mountains to move up.” Higher-grade strains of Arabica coffee in Central American regions are at particular risk due to the need for lower growing temperature, especially since diseases and pests are also becoming more of a factor as temperatures rise.Even if you're looking at the direct effects of temperature alone, rice is in trouble. “As nighttime temperatures go up, the rice is going to have a problem flowering and won't make as many seeds,” Nelson says. In addition to this direct heat consequence, rising sea levels will flood many rice paddies and destroy water salinity levels, while droughts will lower production, raise prices, and further shame westerners who are clumsy with chopsticks to be able to clear their plates once a new grain is adopted.12. What is the closest meaning to the underlined word “emission” in Paragraph 1?A. Mixture.B. Pollution.C. Giving off.D. Going down.13. What does the potatoes' development need according to Nelson?A. Cool temperature at night.B. Sudden rise of the temperature.C. Enough water and salt.D. Much sunshine and fresh air.14. The rice is difficult to flower,probably because ________.A. sea levels go up suddenlyB. many seeds can't be producedC. the temperature rises at nightD. both temperature and altitude rise15. What is the best title for the text?A. How Does Global Warming Affect WesternersB. How Does the Cool Temperature Affect RiceC. What Is the Real Reason For Crops’ GrowthD. Three Crops That Won't Survive Climate Changes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。
2019届上海市高考模拟卷(三)数学试题(解析版)
2019届上海市高考模拟卷（三）数学试题一、单选题1．设x ∈R ，则“|x －2|<1”是“x 2＋x －2>0”的( ) A ．充分不必要条件 B ．必要不充分条件 C ．充要条件 D ．既不充分也不必要条件【答案】A【解析】根据不等式的性质，结合充分条件和必要条件的定义进行判断即可． 【详解】解：由“|x ﹣2|＜1”得1＜x ＜3，由x 2+x ﹣2＞0得x ＞1或x ＜﹣2，即“|x ﹣2|＜1”是“x 2+x ﹣2＞0”的充分不必要条件，故选：A ．【考点】必要条件、充分条件与充要条件的判断．2．已知集合{(,)|||||1}P x y x y =+…，{}22(,)|1Q x y x y =+…，则有（ ）A ．P Q =B ．PQ C ．P Q P = D ．P Q Q ⋂=【答案】B【解析】根据两个集合分别表示的平面区域分析可得答案. 【详解】因为{(,)|||||1}P x y x y =+…表示四个顶点分别为(1,0),(0,1),(1,0),(0,1)--的正方形围成的区域(包括边界),而{}22(,)|1Q x y x y =+…表示的圆心为原点,半径为1的圆围成的区域(包括边界),所以P Q .故选:B 【点睛】本题考查了集合之间的真子集关系,属于基础题.3．将向量1a =(1x ，1y )，2a =(2x ，2y )，…n a =(n x ,n y )组成的系列称为向量列{n a }，并定义向量列{n a }的前n 项和12n n S a a a =++⋅⋅⋅+．如果一个向量列从第二项起,每一项与前一项的差都等于同一个向量，那么称这样的向量列为等差向量列。
若向量列{n a }是等差向量列，那么下述四个向量中，与21S 一定平行的向量是 ( ) A ．10a B ．11aC ．20aD ．21a【答案】B【解析】依题意，当{}n a 为等差向量列时，设每一项与前一项的差都等于d ，则可求出通项公式1(1)n a a n d =+- ，所以{}n a 前21项和211221111111()(20)2121021S a a a a a d a d a d a =+++=+++++=+= ，故与21S 平行的向量是11a ，选B.点睛: 本题主要考查新定义: 等差向量列的理解和应用, 属于中档题. 解题思路：设每一项与前一项的差都等于d ，运用类似等差数列的通项和求和公式，计算可得211121S a =，由向量共线定理，可得出结论. 考查类比的数学思想方法和向量共线定理的运用.4．设集合A ＝[0，12)，B ＝[12，1]，函数()()1,221,x x Af x x x B⎧+∈⎪=⎨⎪-∈⎩，若x 0∈A ，且f[f(x 0)]∈A ，则x 0的取值范围是( ) A ．(0，14] B ．(14，12) C ．(14，12] D ．[0，38]【答案】B 【解析】【详解】 ∵x 0∈A ，∴f(x 0)＝x 0＋12∈B. ∴f[f(x 0)]＝f(x 0＋12)＝2(1－x 0－12)＝1－2x 0. 又因为f[f(x 0)]∈A ，∴0≤1－2x 0<12， 解得14<x 0≤12，又0≤x 0<12.∴14<x 0<12，故选B.二、填空题5．函数sin cos cos sin 44y x x x x ππ⎛⎫⎛⎫=+++ ⎪ ⎪⎝⎭⎝⎭的最小正周期T =___________.【答案】π【解析】利用两角和的正弦公式化简函数表达式，由此求得函数的最小正周期. 【详解】依题意ππsin sin 244y x x x ⎛⎫⎛⎫=++=+ ⎪ ⎪⎝⎭⎝⎭，故函数的周期2ππ2T ==. 故填：π. 【点睛】本小题主要考查两角和的正弦公式，考查三角函数最小正周期的求法，属于基础题.6．若函数21()12x f x =，(0,)x ∈+∞，则其反函数1()f x -=_________.【答案】2log (1)1x +-,(1,)x ∈+∞【解析】计算二阶行列式化简()f x ,再根据求反函数的步骤可求得反函数. 【详解】因为21()12x f x =1221121x x +=⨯-⨯=-,因为x ∈(0,)+∞,所以()(1,)f x ∈+∞, 所以由121x y +=-得21log (1)x y +=+,所以2log (1)1x y =+-,交换,x y 可得2log (1)1y x =+-, 所以12()log (1)1fx x -=+-,(1,)x ∈+∞,故答案为:2log (1)1x +-, (1,)x ∈+∞. 【点睛】本题考查了二阶行列式的计算,反函数的求法,属于基础题.7．在614x x ⎛⎫- ⎪⎝⎭的展开式中，2x 的系数为 .【答案】1516【解析】614x x ⎛⎫- ⎪⎝⎭展开式的通项为6621661144rrr r r r r T C x C x x --+⎛⎫⎛⎫=-=- ⎪ ⎪⎝⎭⎝⎭，由622r -=得2r =，所以222236115416T C x x ⎛⎫=-= ⎪⎝⎭，所以该项系数为1516.【考点】二项式定理及二项展开式的通项.8．过原点且与圆22420x y x y ++-=相切的直线方程为_______. 【答案】20x y -=【解析】切线的斜率显然存在,设出切线方程,利用圆心到直线的距离等于半径,列方程可解得答案. 【详解】由22420x y x y ++-=得22(2)(1)5++-=x y ,所以圆心为(2,1)-,因为圆心到y 轴的距离为2,所以所求切线的斜率一定存在, 所以设所求切线方程为y kx =,即0kx y -=,=解得2k =,所以所求切线方程为20x y -=. 故答案为:20x y -=. 【点睛】本题考查了求圆的切线方程,属于基础题.9．我国古代数学名著《九章算术》有“米谷粒分”题：粮仓开仓放粮，有人送来米1534石，验得米内夹谷，抽样取米一把，数得254粒内夹谷28粒，则这批米内夹谷约为__________石；（结果四舍五入，精确到各位）． 【答案】169【解析】根据古典概型概率公式可得这批米内夹谷的概率约为28254，所以这批米内夹谷约为281534169254⨯≈石，故答案为169. 10．抛物线x 2=2py （p ＞0）的焦点为F ，其准线与双曲线-=1相交于A ，B 两点，若△ABF 为等边三角形，则p=___________. 【答案】6【解析】因为抛物线x 2=2py 的准线2py =-和双曲线-=1相交交点横坐标为=, 6.2x p p =∴=由等边三角形得解得【考点】本题主要考查抛物线的概念、标准方程、几何性质，考查分析问题解决问题的能力.11．若复数z x yi =+（x ，y ∈R ，i 为虚数单位）满足|||22|z z i =--，则33x y +的最小值为_______. 【答案】6【解析】根据复数模的计算公式将|||22|z z i =--化为2y x =-,将其代入到33x y +后,利用基本不等式可求得答案. 【详解】由|||22|z z i =--=化简得2x y +=,即2y x =-, 所以33x y +233x x -=+932363x x =+≥=⨯=,当且仅当 1.1x y ==时等号成立. 故答案为:6 【点睛】本题考查了复数的模的公式,基本不等式求最小值,属于基础题. 12．一个等差数列{}n a 中，2nna a 是一个与n 无关的常数，则此常数的集合为 ．【答案】11,2⎧⎫⎨⎬⎩⎭【解析】试题分析：设数列的首项为1a ，公差为d ，()()1211,21n n a a n d a a n d ∴=+-=+-1212n n a a d nd a a d nd-+∴=-+ 2n n a a 是一个与n 无关的常数10a d ∴-=或0d =，所以比值常数为11,2⎧⎫⎨⎬⎩⎭【考点】等差数列通项公式13．已知直三棱柱111ABC A B C -的6个顶点都在球O 的球面上，若3AB =，4AC =，AB AC ⊥，112AA =，则球的表面积为______.【答案】169π【解析】把直三棱柱111ABC A B C -的补成一个长方体，则直三棱柱111ABC A B C -的外接球和长方体的外接球是同一个球，由长方体的对角线长等于球的直径，求得球的半径，再利用球的表面积公式，即可求解． 【详解】由题意，直三棱柱111ABC A B C -的底面ABC ∆为直角三角形， 可把直三棱柱111ABC A B C -的补成一个长方体，则直三棱柱111ABC A B C -的外接球和长方体的外接球是同一个球， 又由长方体的对角线长等于球的直径，且13,4,12AB AC AA ===，即213R ===，即132R =， 所以球的表面积为221344()1692S R πππ==⨯=． 故答案为：169π 【点睛】本题主要考查了直三棱柱与球的组合体问题，以及球的表面积的计算，其中解答中根据组合体的结构特征，求得球的半径是解答的关键，着重考查了运算与求解能力，属于基础题．14．新一季“中国好声音”开唱，开场节目是四位导师各选一首自己的代表作供其他导师演唱，每人恰好都是唱别人的歌.假设四首歌已选定，则有______种不同演唱方式. 【答案】9【解析】将问题转化为四个元素填四个空的全错位排列后,再按照元素1的位置分3类讨论计算结果相加即可得到. 【详解】将四位导师抽象为四个元素,设为1,2,3,4,四首歌抽象为四个空位,设为1,2,3,4,依题意转化为四个元素填四个空的全错位排列,第一类:元素1填在2号空位,则元素2有3种填法,元素3,4填法唯一,此时共有3种填法; 第二类,元素1填在3号空位,则元素3有3种填法,元素2,4填法唯一,此时共有3种填法;第三类,元素1填在4号空位,则元素4有3种填法,元素2,3填法唯一,此时共有3种填法; 根据分类计算原理可得共有3+3+3=9种填法. 综上所述,共有9种不同的演唱方式. 故答案为:9 【点睛】本题考查了有限制条件的排列问题,属于中档题.15．若函数()2(1)y x x ax b =+++的图象关于点()20，成中心对称，则a b +=______. 【答案】3【解析】在函数()2(1)y x x ax b =+++的图象上取两点(1,0)-,(0,)b ,求出它们关于点(2,0)对称的点(5,0),(4,)b -后,代入()2(1)y x x ax b =+++,解方程组可得答案.【详解】在函数()2(1)y x x ax b =+++的图象上取两点(1,0)-,(0,)b ,则它们关于点(2,0)对称的点(5,0),(4,)b -也在函数()2(1)y x x ax b =+++的图象上, 即(51)(255)0(41)(164)a b a b b +++=⎧⎨+++=-⎩,即52510340a b a b +=-⎧⎨+=-⎩,解得7,10a b =-=,所以3a b +=. 故答案为:3 【点睛】本题考查了函数图象的对称中心的性质,属于基础题.16．在平面直角坐标系中，O 是坐标原点，两定点,A B 满足·2OA OB OAOB===，由点集{|,1,,}P OP OA OB R λμλμλμ=++≤∈所表示的区域的面积是__________．【答案】【解析】【详解】由|OA |＝|OB |＝OA ·OB ＝2，知cos ∠AOB ＝12，又0≤∠AOB ≤π，则∠AOB ＝3π，又A ，B 是两定点，可设A 1)，B (0,2)，P (x ，y )，由OP ＝λOA ＋μOB，可得{2x y λμ，＝＋⇒{26x y x λμ==-.因为|λ|＋|μ|≤1x＋2y x -≤1， 等价于由可行域可得S 0＝12×P 所表示的区域面积S ＝4S 0＝三、解答题17．已知(sin ,1)a α=，(cos ,2)b α=，0,2πα⎛⎫∈ ⎪⎝⎭. （1）若//a b ，求sin 2α的值； （2）在（1）的条件下，若5cos()13αβ+=，0,2πβ⎛⎫∈ ⎪⎝⎭，求sinβ的值. 【答案】(1)45,(2)65【解析】(1)由//a b 可得1tan 2α=,再由万能公式可得sin 2α的值, (2)利用sin sin()βαβα=+-sin()cos cos()sin αβααβα=+-+可得答案. 【详解】(1)因为 //a b ,所以2sin cos 0αα-=,即1tan 2α=, 所以2222sin cos 2tan sin 22sin cos sin cos tan 1ααααααααα===++2124215()12⨯==+. (2)由(1)知,cos 2sin αα= ,且(0,)2πα∈,所以22sin (2sin )1αα+=,所以21sin 5α=,所以sin α,cos α=, 又(0,)2πβ∈,所以(0,)αβπ+∈,所以12sin()13αβ+===, 所以sin sin()sin()cos cos()sin βαβααβααβα=+-=+-+1251313=-=【点睛】本题考查了向量平行的坐标表示,二倍角的正弦公式,同角公式,两角差的正弦公式,属于基础题.18．如图，正四棱锥P ABCD -内接于圆锥，圆锥的轴截面是边长为10cm 的正三角形.（1）求异面直线PA 与BC 所成角的大小；（2）若正四棱锥由圆锥削去一部分得到，则需要削去部分的体积为多少？（精确到30.1cm ）【答案】(1)arccos4,(2)382.3cm .【解析】(1)根据//AD BC 可知, PAD ∠就是异面直线P A 与BC 所成的角,在三角形PAD 中由余弦定理可求得,(2)用圆锥的体积减去正四棱锥的体积即可得到答案. 【详解】(1)在正四棱锥P ABCD -中,//AD BC ,所以PAD ∠就是异面直线P A 与BC 所成的角,在正方形ABCD 中,10AC =,所以AD =, 在三角形PAD 中,10PA PD ==,所以222cos2PA AD PD PAD PA AD +-∠=⨯⨯2224==,所以PAD ∠=,所以异面直线P A 与BC 所成角的大小为.(2)在直角三角形PAO 中,PO ===所以圆锥的体积211133V PO AO π=⋅⋅⋅=⨯25⨯=,正四棱锥P ABCD -的体积221133V PO AD =⋅⋅=⨯23=,所以需要削去部分的体积为12(2)333V V π-=-=-82.3≈. 所以需要削去部分的体积约为82.33cm . 【点睛】本题考查了正四棱锥的结构特征,异面直线所成角,椎体的体积公式,属于中档题. 19．首项为12的无穷等比数列{}n a 所有项的和为1，n S 为{}n a 的前n 项和，又()25log 1n n b S t +-=，常数*t N ∈，数列{}n c 满足n n n c a b =⋅.（1）求数列{}n a 的通项公式； （2）若{}n c 是递减数列，求t 的最小值. 【答案】(1)12n na =,(2)1【解析】(1)根据无穷等比数列{}n a 所有项的和为1,求出公比12q =,再根据等比数列的通项公式可得;(2)求出n S 后代入可得5n b n t =+,1(5)2n n c n t =+⋅,然后根据数列递减可得10n n c c +-<恒成立,由不等式恒成立可得答案.【详解】(1)设无穷等比数列{}n a 的公比为q ,则111a q =-,所以1211q=-,解得12q =,所以111111()222n n n n a a q--==⨯=, (2)因为11(1)22112n n S -=-112n =-,所以215log (11)2n n b t +-+=, 所以5n b n t =+,所以1(5)2n n n n c a b n t ==+⋅,因为{}n c 是递减数列, 所以1111(55)(5)22n n n n c c n t n t ++-=++⋅-+⋅11(55102)2n n t n t +=++--⋅ +11(55)2n n t =--⋅0< 恒成立,所以550n t --<恒成立,所以55t n >-+恒成立,因为()55f n n =-+为递减函数,所以1n =时,()f n 取得最大值(1)550f =-+=, 所以0t >,又因为*t N ∈,所以t 的最小值为1. 【点睛】本题考查了无穷等比数列的和,等比数列的通项公式和前n 项和,数列的单调性,属于中档题.20．设S 、T 是R 的两个非空子集，如果函数()y f x =满足：①{()|}T f x x S =∈；②对任意1x ，2x S ∈，当12x x <时，恒有()()12f x f x <，那么称函数()y f x =为集合S 到集合T 的“保序同构函数”.（1）试写出集合{|01}A x x =<<到集合R 的一个“保序同构函数”； （2）求证：不存在从集合Z 到集合Q 的“保序同构函数”； （3）已知2()1xf x x =+是集合[]0,s 到集合[]0,t 的“保序同构函数”，求s 和t 的最大值.【答案】(1) ()tan()2f x x ππ=-(01)x <<,(2)证明见解析,(3)s 的最大值为1,t 的最大值为12【解析】(1)直接由题意写出()tan()2f x x ππ=-(01)x <<即可;(2)用反证法证明即可;(3)用定义证明()f x 在[0,1]上递增,在[1,)+∞上递减后,可得1s ≤,(1)t f ≤. 【详解】(1)取()tan()2f x x ππ=-(01)x <<,该函数是集合{|01}A x x =<<到集合R 的一个“保序同构函数”; 证明:任取1201x x <<<, 则122222x x ππππππ-<-<-<,因为tan y x =在(,)22ππ-上为增函数,所以12tan()tan()22x x ππππ-<-, 即12()()f x f x <,由定义可知, 函数()tan()2f x x ππ=-是集合{|01}A x x =<<到集合R 的一个“保序同构函数”.(2)证明:假设存在一个从集合Z 到集合Q 的“保序同构函数”,由“保序同构函数”的定义可知,集合Z 和集合Q 中的元素必须是一一对应的,不妨设整数0和1在Q 中的像分别为a 和b ,根据保序性,因为0<1,所以a b <,又2a b +也是有理数,但是2a b+没有确定的原像,因为0和1之间没有另外的整数了,故假设不成立,故不存在从集合Z 到集合Q 的“保序同构函数”.(3)设120x x <<,则12122212()()11x x f x f x x x -=-++21122212()(1)(1)(1)x x x x x x --++, 所以当1201x x <<≤时,21120,10x x x x ->-<,所以12())0(f x f x -<,即12()()f x f x <,所以()f x 在[0,1]上递增,当211x x >≥时, 21120,10x x x x ->->,所以12())0(f x f x ->,即12()()f x f x >, 所以()f x 在[1,)+∞上递减, 因为2()1xf x x =+是集合[]0,s 到集合[]0,t 的“保序同构函数”,所以()f x 在[0,]s 上递增,所以1s ≤,所以s 的最大值为1,t 的最大值为11(1)112f ==+. 【点睛】本题考查了正切函数的单调性,函数单调性的定义,利用单调性求函数的最值,属于难题.。
2019-2020学年上海南洋模范高级中学高三生物第三次联考试题及参考答案
2019-2020学年上海南洋模范高级中学高三生物第三次联考试题及参考答案一、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. 对下列图示的生物学实验的叙述正确的有几项（）a．若图①表示将显微镜镜头由a转换成b，则视野中观察到的细胞数目减少b．若图①是显微镜下洋葱根尖某视野的图像，则向右移装片能观察清楚c细胞的特点c．若在显微镜下观察图①细胞质流动时，发现细胞质的流动方向是顺时针，则细胞质的实际流动方向是逆时针d．若图①是在显微镜下目镜为10×，物镜为10×，视野中被相连的64个分生组织细胞所充满的图像。
目镜不变，物镜换成40×时，则在视野中可检测到的分生组织细胞数为4个e．标本染色较深，观察时应选用凹面反光镜和大光圈f．若转换高倍镜，需要先升镜筒，以免镜头破坏玻片标本A.一项B.两项C.三项D.四项2. 灵菌红素具有抗肿瘤和抑制T细胞介导的免疫反应的功能。
科研人员在橡胶树内生菌ITBBB5-1中发现一个新细胞器——马阔囊胞，该囊胞位于杆状细菌末端。
电镜观察发现，灵菌红素位于马阔囊胞和其分泌的胞外小囊泡中。
下列说法错误的是（）A.橡胶树内生菌ITBBB5-1的核膜包含不连续的四层磷脂分子B.新型细胞器马阔囊胞可能具有储存和分泌灵菌红素的功能C.马阔囊胞分泌灵菌红素过程体现了生物膜的结构特点D.灵菌红素在癌症治疗和器官移植中具有潜在的应用价值3. 下列实例中，能说明生命活动离不开细胞的是（）①流感病人打喷嚏时，会有大量流感病毒随飞沫散布于空气中①手触碰到盛有沸水的电水壶会迅速缩回①体操运动员完成单杠动作离不开肌肉的收缩和舒张①人的胚胎发育过程中，细胞不断地进行分裂A.①①①B.①①①C.①①①D.①①①①4. 甲、乙两图为生物组织的呼吸方式实验装置图，图中植物呼吸作用释放的CO2被NaOH溶液吸收，使容器内气体压强减小，刻度管内的红墨水滴会发生移动。
2019-2020学年上海市南洋模范中学高三英语第三次联考试卷及答案
2019-2020学年上海市南洋模范中学高三英语第三次联考试卷及答案第一部分阅读（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AIn his 402nd anniversary year, Shakespeare is still rightly celebrated as a great language master and writer. But he was not the only great master of play writing to die in 1616, and he is certainly not the only writer to have left a lasting influence on theater.While less known worldwide, Tang Xianzu is considered one of Chinas greatest playwrights and is highly spoken of in that country of ancient literary and dramatic traditions.Tang was born in 1550 inLinchuan,Jiangxiprovince. Unlike Shakespeare's large body of plays,poems and sonnets (十四行诗), Tang wrote only four major plays: The Purple Hairpin, Peony Pavilion (《牡丹亭》), A Dream under the Southern bough, and Dream of Handan. The latter three were constructed around a dream narrative, a way through which Tang unlocked the emotional dimension of human desires and ambitions and explored human nature beyond the social and political limits of that time.Similar to Shakespeare, Tang's success rode the wave of a renaissance (复兴) in theater as an artistic practice. As in Shakespeare'sEngland, Tang's works became hugely popular inChinatoo. During Tang'sChina, his plays were enjoyed performed, and changed. Kunqu Opera, a form of musical drama, spread from southernChinato the whole nation and became a symbol of Chinese culture. Combining northern tune and southern music, kunqu Opera was known for its poetic language, music, dance movements and gestures. Tang's works benefited greatly from the popularity of kunqu Opera, and his plays are considered classics of kunqu Opera.While Tang and Shakespeare lived in a world away from each other, there are many things they share in common, such e humanity of their drama, their heroic figures, their love for poetic language, a lasting popularity and the anniversary during which we still celebrate them.1. Why is Shakespeare mentioned in the first paragraph?A. To describe Shakespeare's anniversary.B. To introduce the existence of Tang Xianzu.C. To explain the importance of Shakespeare.D. To suggest the less popularity of Tang Xianzu.2. What's possibly one of the main theme of Tang's works?A. Social reality.B. Female dreams.C. Human emotions.D. Political environment.3. What does the author mainly tell us in Paragraph 4?A. The influence of Kunqu Opera on Tang's works.B. Tang's success in copying Shakespeare's styles.C. The way Kunqu Opera became a symbol of Chinese culture.D. Tang's popularity for his poetic language and music.BIf you struggle to fall asleep quickly, you’re not alone! Fortunately, thereare plenty of solutions you can try. With a few changes, you can fall asleep fast every night!Keep your room dark. Turn off all the lights above your head when you go to bed. Any bright light can make you believe it is too early in the day for sleep. If you want to read or write before bed, try using a small book light. Now that blue lights can keep you awake, red ones are a great choice.If you can, keep noise in and around your room the lowest at night. If you have an old clock that ticks loudly and keeps you awake, replace it with a silent one. If you share your home with anyone else, request that they keep noises like talking, music, or TV shows at the lowest while you are trying to sleep. It is difficult to fall asleep if you live near a busy road or hear other boring sounds after bedtime. You could get a white noise machine or play recordings of nature sounds, like waves or whales’ singing. You could also listen to soft, relaxing music.Read a book in bed if you have difficulty in falling asleep. Staying in bed doing nothing when you’re having trouble falling asleep may keep you wide awake. While reading in bed may be slightly harmful to your eyes, it can distract (分散) you from your thoughts and help you feel sleepy. But remember to read from a print book rather than something with a screen. The light from electronic screens can keep you awake.Lowering your body temperature helps you sleep, so set the room temperature between 15.5℃-21℃could do the trick.4. What color1 book light should you choose toread before bed?A. Red.B. Blue.C. White.D. Orange.5. What is the author’s attitude towards reading in bed?A. Doubtful.B. Worried.C. Favorable.D. Uncaring.6. What can we inferred from the text?A. Reading on cellphones sometimes helps you fall asleep.B. The lower your temperature while sleeping is, the better.C. Bright lights are better for your reading before going to bed.D. Playing recordings like birds’ singing can improve your sleep.7. How does the author organize the text?A. By givingexamples.B. By asking questions.C. By offering suggestions.D. By listing research results.CBack about 20 months ago I started college and just struggled with everything, such as classes and friends. I quickly became depressed and angry at myself for not being about to do better in school, in addition to lack of friends due to poor social and communication skills.This went on for months until my 19th birthday. My parents sent me a cake, which was a great cake. But I remember having this large cake and ly no one to share it with. I ended throwing out the cake after having one piece, with about 90 % of it leftover. That night I was depressed that I decided to go outside to the freezing temperature of the winter and run. I put my earphones in, went outside and ran about 2 miles at 11 p.m. on my birthday.When I got back inside I was content. I was proud of what I was able to do. The next night I did the same. I wasn’t quick or fit but you know that I went outside and did something. This continued for about 2 months until I finally worked up the courage to go to the gym, where I started swimming again as I used to in high school. A month went by and I started lifting weights and continually running.Looking back I can see that exercise helped cure my depression but it didn’t only do that. At the gym I met new friends and back at my dorm I grew confidence to go to the end of the hall seeing people playing Super Smash Brothers and ask if I could join.So go forward to present now. I exercise every day and look forward to that hour and a half I get daily to do what I love with people who love it as well. I hope this helps someone who may be or have been in a similar situation.8. What made the author decide to run at night?A. His l9th birthday.B. His parents’ cake.C. His loneliness.D. His friends.9. Which of the following best describes the author?A. Traditional.B. Determined.C. Humorous.D. Generous.10. What is the biggest benefit of the author’s running?A. Regaining his confidence.B. Losing his weight.C. Playing with his brothers.D. Joining other activities.11. Why do you think the author wrote this passage?A. To recall his life in college.B. To show his gratitude to his parents.C. To emphasize the importance of friendship.D. To share his experience of dealing with hardship.DMark Twain,the famous American writer,was once traveling in France.He went by trainto Dijon.He was very tired and wanted to sleep.He therefore asked the conductor to wake him up when the train came to Dijon.But first he explained he was a very heavy sleeper,“I may possibly protest(抗议)loudly when you try to wake me up,” he said to the conductor.“But don’t take any notice of what I say.Just put me off the train anyway.”Then Mark Twain went to ter,when he woke up it was night time and the train had reached Paris already.He realized at once that the conductor had forgotten to wake him up at Dijon.He was so angry that he ran to the conductor and began to shout at him.“I have never been so angry in my life,” Mark Twain said.The conductor looked at him calmly(平静地).“You are not half so angry as the American whom I put off the train atDijon,” he said.12. Mark Twain knew that he was a heavy sleeper,so ________.A. he protested loudly to the conductorB. he did not sleep before he arrived inDijonC. he told the conductor to wake him up no matter how loudly he might protestD. he slept lightly that time13. The conductor didn’t wake up Mark Twain atDijonbecause ________.A. he didn’t take Mark Twain’s words seriouslyB. he forgot Mark Twain’s words when the train came toDijonC. he did not want to bear his protestD. he mistook another American traveler for Mark Twain14. The American whom the conductor put off the train ________.A. did not want to get off atDijonB. wanted to get off atParisC. wanted to get off atDijonD. did not want to get off atParis15. Which of the following is TRUE?A. The conductor didn’t take Mark Twain’s words seriously.B. The conductor did take Mark Twain’s words seriously.C. The conductor was a heavy sleeper.D. Mark Twain must get off atParis.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。
2019-2020学年上海南洋模范高级中学高三英语第三次联考试题及答案
2019-2020学年上海南洋模范高级中学高三英语第三次联考试题及答案第一部分阅读（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ANo one knows when the first printing press was invented or who invented it. but the oldest known printed text originated in China during the first millennium (千年) AD.The Diamond Sutra (《金刚经》), a Buddhist book from Dunhuang, China during the Tang Dynasty, is said to be the oldest known printed book.The Diamond Sutrawas created with a method known as block printing (雕版印刷), which used boards of hand-carved wood blocks in reverse.It was said that the moveable type was developed by Bi Sheng. He was fromYingshan,Hubei,China, living from 970 to 1051 AD. His method replaced panels of printing blocks with moveable individual Chinese characters that could be reused. The first moveable Chinese Characters were carved into clay and baked into hard blocks that were then arranged onto an iron frame that was pressed against an iron plate.The earliest mention of Bi Sheng’s printing press is in the bookDream Pool Essays, written in 1086 by Shen Kuo, who noted that his nephews came into possession of Bi Sheng’s typefaces (字体) after his death. Shen Kuo explained that Bi Sheng did not use wood because the texture is inconsistent (不一致的) and absorbs wetness too easily.By the time of the Southern Song Dynasty, which ruled from 1127 to 1279 AD, books had become popular in society and helped create a scholarly class of citizens who had the capabilities to become civil servants. Large printed book collections also became a status symbol for the wealthy class.1. When was Bi Sheng’s printing press first introduced in history?A. After Bi Sheng died and his nephews owned his typefaces.B. When books became popular in the Southern Song Dynasty.C. After the block printing was replaced by the moveable type printing.D. WhenThe Diamond Sutrawas printed into a book.2. What can we infer from the passage?A. Shen Kuo made great contributions to printing.B. The moveable type printing was invented earlier than block printing.C. Printed books were hard to get in the Song Dynasty.D. By the Southern Song Dynasty, books had helped people get to higher social positions.3. Why does the author write this passage?A. To show that Buddhism was popular in the Tang Dynasty.B. To introduce the early history of printing.C. To memorize Bi Sheng, developing the moveable type printing.D. To indicate the advantages of moveable type printing.BIt was the first day of spring here but it didn't feel like it. The COVID-19 epidemic (流行病) was sweeping the globe and everywhere there were feelings of fear and loneliness. “Social Distancing” had become the new norm. Here the schools had been closed, the restaurant dining rooms had been shut, and people had been told to work from home whenever they could. Even the sheltered workshop where my oldest son worked had been closed until further notice. People had made a run on the stores and large areas of the shelves were bare. On the news the numbers of the sick and dead continued to rise. It felt like there was a weight on the souls of everyone in the world.My family were staying at home as much as possible and as I looked out of my window I wondered how long this crisis would last. It was then, however, that I saw something that lifted that weight off of my soul, made me smile, and made my heart feel happy again. On the street below my house there was an old friend of mine from high school who was a teacher there. With him was my younger son's former aide from the high school as well. They were delivering the school lunches door to door to the hungry children who were stuck at home. Watching them made me think of something everyone's childhood television neighbor, Mr. Roger's once said: "In the bad times, always look for the helpers."I have no doubt that this crisis will pass as all the crisis before. But it is our choice on whether it brings out the best in us or the worst in us. Let it bring out the best in you. Use it to strengthen your faith. Use it to free yourself from fear. Use it to grow kinder, more giving, and more loving. Become a helper to all those in need and you will be a happy person today and all the days to come.4. Why didn't the author like the first day of spring?A. He had to work at home instead of at office.B. There wasn't social distance between each other.C. There was an epidemic everywhere in the world.D. His own company had been closed for a long time.5. How did people feel in the face of the epidemic?A. Disappointed.B. TenseC. Confident.D. Cheerful.6. What made the author happy?A. Seeing someone delivering lunches from door to door.B. Talking with his old friend in the street.C. Watching a childhood television at home.D. Staying together with his family.7. What do Mr. Roger's words actually mean?A. It's not necessary for us to find helpers in bad times.B. In good times we needn't do much to help others.C. We should ask more people to help us in bad times.D. We are supposed to help each other in bad times.CPeople saved a 20-foot orca (虎鲸) that was stuck between rocks on an Alaskan shore by continuously pouring water over it and protecting it from birds who circled above the defenseless whale.The whale was ultimately saved after a six-hour, labor-intensive life-saving operation. Someone spotted the large whale on the Prince of Wales Island near the coast of British Columbia on the morning of July 29th. The Coast Guard was called around 9 a.m. local time. Chance Strickland, the captain of a private yacht in Alaska, and his crew anchored and began life-saving action that were videoed by Aroon Melane and posted on the Internet.Strickland could hear the orca calling out to killer whales swimming in the area. People on other boats stopped with water and buckets to pour water over the animal. “There were tears coming out of its eyes,” Mr. Strickland told the local newspaper. “It was pretty sad.”The group of people formed a chain that passed buckets of seawater back and forth and poured the water on the orca, which seemed to liven it up. It made a noise and raised its tail when it got water.The National Oceanic and Atmospheric Administration (NOAA) was called in, which can be seen on the video using a machine to spray amist of seawater on the orca, which doubled as a way to keep the whale cool and scare the large group of birds that were hoping to feast on the beast.Melane said in her video that the orca was stranded (搁浅) for about six hours until the tide came in andswept it back into the ocean. The group efforts of Strickland’s crew and the NOAA saved the 13-year-old killerwhale.8. Why did birds circle above the orca?A. They were eager to eat it.B. They wished to protect it.C. They were attracted by the people.D. They wanted to find a place to rest.9. What did Strickland do immediately after finding the whale?A. Posted pictures online.B. Called friends for help.C. Took action to save it.D. Videoed the trapped animal.10. Why did the whale make a noise and raise its tail?A. To express its eager for water.B. To extend its thanks to people.C. To call out to its fellow whales.D. To show its power and sadness.11. Which can be the best title for the text?A. Killer Whale Got SavedB. The Orca Inspired KindnessC. Combined Efforts WantedD. Animals and Humans UnitedDMichele Gentile, an Italian bookseller, is offering free books to children in exchange for plastic bottles to recycle.Michele owns Ex Libris Cafe in Polla，a small town in southern Italy. He said he thought of the recycling program, because he wanted to inspire children in the small town to read and pay attention to the environment.''My goal is to spread the passion and love for books among those people in Italy who do not usually read while at the time helping the environment," Gentile explained.The idea for the initiative (倡议) came after Gentile collaborated with a nearby middle school on an aluminum recycling project. Working together, the schoolchildren and Gentile collected enough cans to purchase books for an entire classroom. His new program too off from there and has already spread into northern Italy: Gentile's hopes his work will continue to make headlines and become a worldwide initiative.The free books come from customers in Gentile's shop who have donated money to purchase a ''suspended" book. The idea comes from a World War II practice in which customers would buy two Coffees: one for themselves and another for the next person in line. Gentile has been using the extra books as part of his recycling initiative, While Gentile's program is a great way to recycle and get kids to read, it also brings awareness to the growing problem of plastic waste. Single-use plastics make up around 26 percent of all the plastics in the world, only 14 percent of which are recycled. Plastics that end up in landfills take around 500 years to decompose (分解),is amajor concern for environmentalists.Cutting down on plastic waste is important if we want to better the environment for future generations, and recycling programs like Gentile's book giveaway are a great way to meet that goal.12. What is the purpose of Gentile's book giveaway?A. To sell more coffee and books.B. To attract more customers.C. To collect money for a new project.D. To inspire reading and recycling.13. How did Gentile come up with the idea?A. Working with a school to recycle cans.B. Seeing school kids don't like reading.C. Donating books for a local school.D. Buying a “suspended” book for a child.14. Who pay for the books of the project?A. The local government.B. Gentile himself.C. Some publishers.D. His customers.15. Whichof the following is the best title for the text?A. An Italian's Reading InitiativeB. Recycling Can Get Kids Free BooksC. Michele's Way of Doing BusinessD. A New Way to Deal with Plastic Waste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。
上海市南洋模范中学2019届高三下学期3月月考数学试题(解析版)
2018学年南模中学高三年级三月份月考卷数学2019.3.6一、填空题。
1.已知全集，若集合，则_________.【答案】【解析】【分析】求出集合A，即可求解∁U A【详解】全集U＝R，集合A＝{x|x＞1或x<0}则＝故答案为【点睛】本题考查集合的基本运算，补集的求法，分式不等式解法，准确计算是关键，是基础题．2.双曲线的焦距为__________.【答案】6【解析】【分析】将双曲线的方程化为标准方程，求得a，b，c，可得焦距2c的值．【详解】双曲线2x2﹣y2＝6即为1，可得a，b，c3，即焦距为2c＝6．故答案为：6．【点睛】本题考查双曲线的简单几何性质，焦距的求法，注意将双曲线的方程化为标准方程，运用双曲线的基本量的关系，考查运算能力，属于基础题．3.已知二项展开式中的第五项系数为，则正实数_____.【答案】【解析】【分析】由二项式定理的通项公式可得：，解出即可得出．【详解】T5x﹣2，∴，a＞0．解得a．故答案为：．【点睛】本题考查了二项式定理的应用，考查了推理能力与计算能力，准确计算是关键，属于基础题．4.已知函数的图像与它的反函数的图像重合，则实数的值为___.【答案】-3【解析】【分析】先求反函数：y，利用函数f（x）（a）图象与它的反函数图象重合，即为同一个函数即可得出．【详解】由y（a），解得x（y≠3），把x与y互换可得：y，∵函数f（x）（a）图象与它的反函数图象重合，∴﹣a＝3，解得a＝﹣3．故答案为：﹣3．【点睛】本题考查了反函数的求法及其性质，考查了推理能力与计算能力，属于中档题．5.设，满足约束条件，则目标函数的最大值为_____.【答案】14【解析】【分析】画出可行域，通过向上平移基准直线到可行域边界的位置，由此求得目标函数的最大值.【详解】画出可行域如下图所示，由图可知，目标函数在点处取得最大值，且最大值为.【点睛】本小题主要考查利用线性规划求线性目标函数的最大值.这种类型题目的主要思路是：首先根据题目所给的约束条件，画出可行域；其次是求得线性目标函数的基准函数；接着画出基准函数对应的基准直线；然后通过平移基准直线到可行域边界的位置；最后求出所求的最值.属于基础题.6.从集合中随机选取一个数记为，从集合中随机选取一个数记为，则直线不经过第三象限的概率为_____.【答案】【解析】【分析】将试验发生包含的事件（k，b）的所有可能的结果列举，满足条件的事件直线不经过第三象限，符合条件的（k，b）有2种结果，根据古典概型概率公式得到结果．【详解】试验发生包含的事件（k，b）的取值所有可能的结果有：（﹣1，﹣2）；（﹣1，1）；（﹣1，2）；（1，﹣2）；（1，1）；（1，2）；（2，﹣2）；（2，1）；（2，2）共9种结果．而当时，直线不经过第三象限，符合条件的（k，b）有2种结果，∴直线不过第三象限的概率P，故答案为．【点睛】本题考查古典概型，古典概型要求能够列举出所有事件和发生事件的个数，属于基础题．7.设，是双曲线的两个焦点，是双曲线上的一点，且，则的周长为___. 【答案】24【解析】【分析】先由双曲线的方程求出|F1F2|＝10，再由3|PF1|＝4|PF2|，运用双曲线的定义，求出|PF1|＝8，|PF2|＝6，由此能求出△PF1F2的周长．【详解】双曲线x21的a＝1，c5，两个焦点F1（﹣5，0），F2（5，0），即|F1F2|＝10，由3|PF1|＝4|PF2|，设|PF2|＝x，则|PF1|x，由双曲线的定义知，x﹣x＝2，解得x＝6．∴|PF1|＝8，|PF2|＝6，|F1F2|＝10，则△PF1F2的周长为|PF1|+|PF2|+|F1F2|＝8+6+10＝24．故答案为：24．【点睛】本题考查双曲线的定义和性质的应用，考查三角形周长的计算，熟练运用定义是关键，属于基础题．8.已知四面体中，，，分别为，的中点，且异面直线与所成的角为，则____. 【答案】1或【解析】【分析】取BD中点O，连结EO、FO，推导出EO＝FO＝1，，或，由此能求出EF．【详解】取BD中点O，连结EO、FO，∵四面体ABCD中，AB＝CD＝2，E、F分别为BC、AD的中点，且异面直线AB与CD所成的角为，∴EO∥CD，且EO，FO∥AB，且FO1，∴∠EOF是异面直线AB与CD所成的角或其补角，∴，或，当∠EOF时，△EOF是等边三角形，∴EF＝1．当时，EF．故答案为：1或．【点睛】本题考查异面直线所成角的应用，注意做平行线找到角是关键，解题时要认真审题，注意空间思维能力的培养，是易错题9.已知函数是定义在上的奇函数，当时，，则时，不等式的解集为____. 【答案】【解析】【分析】由奇函数的性质可得x＞0时的解析式，再解不等式即可．【详解】∵函数f（x）是定义在R上的奇函数，∴当x＞0时，﹣x＜0，∴f（﹣x）＝x2﹣6，由奇函数可得f（x）＝﹣x2+6，∴不等式f（x）＜x可化为，解得x＞2∴x＞0时，不等式f（x）＜x的解集为：（2，+∞）故答案为：（2，+∞）【点睛】本题考查函数的奇偶性，涉及不等式的解法，熟记奇函数得定义是关键，属基础题．10.关于的方程在上的解的个数是____.【答案】7【解析】【分析】化简y=从而作函数的图像，从而可解【详解】化简y=,作函数在上的图像如下：结合图像可知，两个图像共有7 个交点故答案为7【点睛】本题考查函数与方程，函数的性质，三角函数，准确作图是关键，是中档题11.任意实数，，定义，设函数，数列是公比大于0的等比数列，且，，则____.【答案】4【解析】【分析】f（x）＝，及其数列{a n}是公比大于0的等比数列，且＝1，对公比q分类讨论，再利用对数的运算性质即可得出．【详解】由题，∵数列{a n}是公比大于0的等比数列，且，①1＜q时，，，…，∈（0，1），，，∈（1，+∞），1．∴，分别为：，，…，，1，q，…，q4．∵∴0++…+＝，∴q4q q2．∴2．左边小于0，右边大于0，不成立，舍去．②0＜q＜1时，1，∴，分别为：，，…，，1，q，…，q4，，，…，∈（1，+∞），，，∈（0，1），∵∴log2q2．∴2．∴4，∴a1＝4．③q＝1时，＝…＝＝…＝＝1，不满足舍去．综上可得：＝4．故答案为：4．【点睛】本题考查了等比数列的通项公式及其性质、对数的运算性质，考查了分类讨论方法、推理能力与计算能力，属于难题．12.以正方形的四个顶点分别作为椭圆的两个焦点和短轴的两个端点，，，是椭圆上的任意三点（异于椭圆顶点），若存在锐角，使，（0为坐标原点）则直线，的斜率乘积为___. 【答案】或-2【解析】设椭圆方程为，A（，），B（，），从而得到的坐标表示，然后，再根据M点在该椭圆上，建立关系式，结合A、B点在也该椭圆上，得到，，从而得到相应的结果，同理当椭圆方程为可得答案【详解】由题意可设椭圆方程为，又设A（，），B（，），因为M点在该椭圆上，∴，则又因为A、B点在也该椭圆上，∴，∴，即直线OA、OB的斜率乘积为，同理当椭圆方程为时直线OA、OB的斜率乘积为﹣2．故答案为：或﹣2．【点睛】本题重点考查椭圆综合，平面向量的坐标运算，注意审题仔细，要注意分类讨论椭圆的焦点位置，属于中档题．二、选择题。
2019届上海市南洋模范中学三模数学试题(解析版)
∴ ＝ ．
∴异面直线A1C与DD1所成角的大小为 ；
【点睛】
本题考查三棱锥的体积的求法，考查异面直线所成角的求法，是中档题，解题时要认真审题，注空间思维能力的培养．
18．已知函数 ．
（1）若不等式 的解集为 ，求a的值；
（2）在（1）的条件下，若存在 ，使 ，求t的取值范围．
可得
，代入曲线方程，可得
2x02﹣y02＝1，即为2（2x）2﹣（2y）2＝1，
即为8x2﹣4y2＝1．
故答案为：8x2﹣4y2＝1．
【点睛】
本题考查中点的轨迹方程的求法，注意运用代入法和中点坐标公式，考查参数方程和普通方程的互化，注意运用同角的平方关系，考查运算能力，属于中档题．
12．在等差数列 中，首项 ，公差 ，若某学生对其中连续10项进行求和，在遗漏掉一项的情况下，求得余下9项的和为185，则此连续10项的和为．
14．已知数列 的通项公式为 ，则这个数列的前n项和 _____．
【答案】
【解析】分n为奇数、偶数两种情况讨论，利用分组求和法计算即得结论．
【详解】
当n为偶数时，Sn＝[（﹣1+2）+（﹣3+4）+…+（﹣n+1+n）]+（2+22+…+2n）
＝
＝2n+1+ ﹣2；
当n为奇数时，Sn＝[（﹣1+2）+（﹣3+4）+…+（﹣n+2+n﹣1）﹣n]+（2+22+…+2n）
不等式f（x）＜6的解集为（﹣1，3），
∴|2x﹣a|＜6﹣a的解集为（﹣1，3），
2019-2020学年上海南洋模范高级中学高三生物第三次联考试题及参考答案
2019-2020学年上海南洋模范高级中学高三生物第三次联考试题及参考答案一、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. 根据细胞的功能推测，下列叙述中错误的是A.唾液腺细胞比心肌细胞具有更多的高尔基体B.白细胞比红细胞具有更多的溶酶体C.植物根尖分生区细胞比叶肉细胞具有更多的叶绿体D.合成性激素的卵巢细胞比皮肤的表皮细胞具有更多的内质网2. 下列四组生物中，都属于原核生物的是（）A. 黑藻、大肠杆菌、乳酸杆菌B. 水绵、肺炎双球菌、酵母菌C. 小球藻、HIV、破伤风芽胞杆菌D. 发菜、醋酸杆菌、硝化细菌3. 将生理状态相同、大小相似的多只家兔均分为甲、乙2组，2组家兔分别注射一定浓度的胰岛素溶液和肾上腺素溶液，一段时间后检测发现甲组家兔血糖浓度下降，乙组家兔血糖浓度升高。
下列分析错误的是（）A. 因缺少对照，该实验不能得出血糖浓度受激素影响的结论B. 实验开始前，应分别测量甲、乙两组小鼠初始血糖浓度C. 实验过程中，甲组家兔可能会出现行动迟缓甚至昏迷等症状D. 肾上腺素可能具有促进肝糖原分解，升高血糖的功能4. 认识细胞这个基本生命系统，首先要分析它的物质组成与功能。
下列化合物与其功能不符的是（）A. 自由水是细胞内的良好溶剂B. 脂肪是细胞内良好的储能物质C. 糖类是细胞内唯一能源物质D. 无机盐对维持生物体生命活动有重要作用5. 下列说法中正确的有（）①2N的生物体减数分裂的第二次分裂一定不存在同源染色体①生物的基因型相同表现型一定相同①遗传物质是RNA的生物一定是病毒①基因在染色体上都是成对存在的①人主要的遗传物质是DNA，大多分布在细胞核中①除病毒外，生物体的遗传物质中嘌呤碱基与嘧啶碱基相等A. —种B. 两种C. 三种D. 四种6. 下列实验不能用紫色洋葱鳞片叶(外或内)表皮细胞作为实验材料的是A. 观察植物细胞的质壁分离和复原实验B. 观察DNA和RNA在细胞中的分布实验C. 用高倍镜观察细胞中的线粒体实验D. 观察植物细胞的有丝分裂实验7. 下列关于兴奋传导的叙述，正确的是A. 突触小体可完成“电信号→化学信号→电信号”的转变B. 兴奋在神经元之间传递是从突触前膜到突触后膜C. 神经递质作用于突触后膜，只能使突触后膜产生兴奋D. 神经纤维内部局部电流的方向与兴奋传导的方向相反8. 钙、磷代谢调节激素分别通过对各自靶细胞的作用，维持血钙、血磷水平和骨代谢之间的稳态，其作用关系如图。
2019年上海市高三高考仿真模拟考试英语试卷(三)及解析
2019 年上海市高三高考仿真模拟考试英语试卷（三）★祝考试顺利★I. Listening ComprehensionSection A (10%)Directions : In Section A, you will hear ten short conversations betweentwo speakers. At the end of each conversation，a question will be asked about -what was said. The conversations and the questions will be spokenonly 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. A waitress.B. An actress.C. A policewoman.D. A driver.【答案】 C2.A. In a furniture store.B. In a restaurant.C. At a bank.D. In a factory.【答案】 B3.A. The good weather tomorrow.B. The vacation plan.C. Getting up early in the morning.D. The possible heavy traffic.【答案】 B4.A. 100 dollars.B. 200 dollars.C. 300 dollars.D. 400 dollars.【答案】 A5.A. She works in a very nice restaurant.B. Restaurant food is dirty and has made her ill.C. Her job involves a lot of business dinners.D. She feels tired when preparing meals at home.【答案】 C6.A. She is at home now.C. She lost her hotel card.【答案】 B7.A. He is asking for leave.C. He is quitting his job. money.【答案】 C8.B. She is a tourist there.D. She doesn ’t know the man.B. He is asking for reasons. D. He is investing time andA. She would rather stay at home listening to CDs.B. She likes to listen to new music CDs.C. She wants the man to buy CDs for her.D. She can get new music CDs for free.【答案】 B9.A. Next Tuesday.B. Next Wednesday.C. Next Thursday.D. NextFriday.【答案】 A10.A. China.B. France.C. Italy.D. Japan.【答案】 ASection B (15%)Directions: In Section B, you will hear several longer conversation (s)and short passage (s), and you will be asked several questions on eachof the conversation (s) and the passage (s). The conversation(s) and thepassage (s) will be read twice ， but the questions will be spoken only once. Whenyou hear a question ，read the four possible answers on your paper anddecide which one is the best answer to the question you have heard.Questions are based on the following passage.11..A. A rental apartment usually has a kitchen and a bathroom.B. Rental apartments have no more than two bedrooms.C. One-room apartments are too small to have a bathroom.D. A living room is essential for all the rental apartments12.A. According to the number of bedrooms.B. The prices of all houses or apartments are fixed.C. Based on the location and the quality.D. The owners decide the prices themselves.13.A. Security deposit is equal to two months’ rent.B. It costs you a month’s rent to repair the damage.C. You are required by law to pay rent for a full year.D. You can renew the agreement by reducing the rent.【答案】 11. A 12. C13. AQuestions are based on the following passage.14.A. By staying alert to see something happening in nature.B. By possessing two essential characteristics of great physicists.C. By totally understanding the tricky make-up of the world.D. By succeeding in transferring the skills into the wider social area.15.A. His contributions have advanced progress in the society.B. He suggested and created many modern power systems.C. He laid out important principles in his scientific works.D. His contributed to helping people evolve and survive.16.A. Develop the observation of natural phenomena.B. Help humankind to survive in the world.C. Drive important changes to the society.D. Inspire many other great physicists.【答案】 14. D 15. B16. BQuestions are based on the following passage.17. A. Draw. B. Fold paper. C. Sing. D. Tell stories.18.A. At the age of four.B. At the age of five.C. At the age of six.D. At the age of seven.【答案】 17. B18. BQuestions are based on the following passage.19.A. His college life is too boring.B. Some principles of science are too difficult for him to understand.C. Students can’t quite follow his teaching.D. He can ’t concentrate when talking about some basics.20.A. Freshmen are usually highly motivated.B. Jane White teaches chemistry in college.C. Susan is popular with her students.D. The man will try something new.【答案】 19. C20. DII.Grammar andVocabulary Section A (10%)Directions : After reading the passage below, fill in the blanks to makethe 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.What is an insect? Insects of all kinds have existed on earth formillions of years. Sometimes we think of all insects as pests.Humanlife, however,would have a difficult time continuing without insects,___21___ they pollinate plants and are a food source for many animals. Besides,insects, especially the social ___22___，are fascinating.One very interesting and useful social insect is the honey bee. Bees___23___ (consider) social insects because they live and work together. Thebee lives in a beehive with other worker bees, and with the queen, who canlay thousands of eggs a day. The worker bees make wax used ___24___(create) new cells inside the hive. Humans use this valuable beeswax___25___ candles ，cosmetics,expensive furniture polish,and other products. They also produce honey, a valuable food for humans (as well as for bees).Another fascinating social insect is ___26___ant. Many types of ants live in colonies underground. There thousands of them build and maintaintheir“city ”. They also cooperate to provide food,sometimes in a manner that looks like human. For example,some ants actually raise their own food. One type of ant“farmer ” keeps and cares for tiny insects that suck sweet sap ( 汁液 )from plants.Ant farmers milk them from the sap,just like actual farmers milk cows. The sap is then given as food to young ants and to thequeen, ___27___main duty is to lay eggs. Another type of ant that produces its own food does so by gardening. These farmer ants take pieces of leaves into the colony and chew them up. The soft ， ___28___ (chew)up leaves then sprout (涌出 )a fungus that the worker ants use to feed the queen and young ants.There are many other ways that ants cooperate to maintain and protect their colonies.There are also many other kinds of social insects. ___29___makes them all so fascinating is their organization. ___30___each insect has certain tasks to perform,the entire hive or colony appears to function as one living organism.【答案】 21. because22. ones23. are considered24.to create25.in 26. the27. whose28. chewed29. What30. Although【解析】【分析】这是一篇说明文。
2019-2020学年上海市上南中学高三英语三模试题及答案
2019-2020学年上海市上南中学高三英语三模试题及答案第一部分阅读（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AAs the MOOC craze continues to explode, anyone interested in taking an online course faces a tricky question: Which course to take? Here are five aspects that you should consider before you start.(1)What is your learning style?Many MOOCs are video-based. Other courses use presentation formats. Some also require participation in group work. If you want to stay motivated during your course, think about how you enjoy learning.Are you a visual learner, preferring to use images to understand a topic? If so, a video-based course will work well for you. If you are a verbal learner who gains new information by speaking and writing, try a text-based course with lots of note-taking. Social learners, meanwhile, will thrive in forum discussions and project-based assessment.(2)Are you ready to become a full-time student?Be realistic about the time that you can commit to your online studies. Participating in an online course can take as much time and commitment as a class-based program. Check the course requirements and make a plan around your current schedule.(3) Does the course really meet your needs?Whether you are interested in a professional qualification or want to take a personal development course like yoga, there is a MOOC for you. It's easy to get caught up in the excitement of taking lots of free courses in everything that you ever wanted to learn. Before you start a course, think about the end goal. Is the course aimed at beginners or advanced learners? Why do you need this qualification?(4) Do you need a support group?Some people learn best from seeing how others approach the problem. If you are such as learner, you will need to supplement your online lessons with an in-person support group.(5) What kind of certification will you get?Take time to find out what kind of certification is available upon completion of the course, and how you can prove your learning to others - for example, certificates, transcripts or digital badges.1. What kind of MOOC's does the author recommend to verbal learners?A. A video-based course.B. A text-based course.C. A forum-based discussion.D. A project-based assessment.2. What kind of learners need an in-person support group?A. Learners who prefer individual work.B. Learners who are in great need of a certificate.C. Learners who are too busy to become a full-time student.D. Learners who learn best from observing how others address the problem.3. What is the passage mainly about?A. Picking the right MOOC's for you.B. Deciding your learning style.C. Taking the right course you need.D. Choosing a suitable support group.BIn the U. S., speaking more than one language fluently is not very common except in Los Angeles, California.The city has one of the largest population in the U. S. of young people between the ages of 18 and 34. This generation is often called millennials (新千年一代). More than half of millennials in Los Angeles are bilingual (双语的), which means they speak more than one language.Maria Elena Burgos is cooking a Mexican breakfast. She says making Mexican food is just one of the many traditions in her home. Another is speaking Spanish to her children.“We want them to be bilingual. We want to keep the Spanish somewhere in their learning too, not only at home.”When Ms Burgos first came to the United States from Mexico, she learned English. She knew her children would learn English quickly. So she wanted them to speak Spanish at home and study the language at school.She says being bilingual will give them more opportunities in the future. Knowing Spanish also means the children can talk with their s in Mexico.“When we had our children, one of the decisions we as parents made was to name them with a name that was easily pronounced in English and Spanish.”Elizabeth wants to know her family’s culture.” “The culture-to go back to our roots because that’s part of who we are.”Monica wants to pass on the culture to her children“It’s nice to know our culture and then to be able to pass it onto our children and grand-children and everyone to let them know where we come from.”And, Monica says she does not speak only English and Spanish. She has even learned some Korean in school.4. Which of the following is a tradition of Maria?A. Cooking breakfast for her s.B. Talking with her children in Spanish.C. Talking with her s in Spanish.D. Forcing her children to speak Spanish.5. What can be inferred from Monica’s words?A. She doesn’t care where she comes from.B. She looks forward to learning Spanish.C. Everyone should know his own culture.D. She doesn’t like American culture.6. Which of the following is mentioned about children speaking more languages?A. It can give children more chances in the future.B. It can make children feel proud before their friends.C. It can give the children a chance to go to a good college.D. It can let children go to the places where they want to go.7. What’s the main purpose of this passage?A. To entertain the readers with a funny story.B. To inform the readers of a shocking experiment result.C. To encourage more persons to learn a second language.D. To tell a truth that many people in Los Angeles are bilingual.CHave you ever thrown a camel? Camels are large and heavy animals so it would be hard to throw. But in the French-speaking Democratic Republic ofthe Congo, “to throw a camel” is a way of saying “to make a spelling mistake”.In the past, a phrase like that was not accepted by the French government as an official French term. But recently, the French Ministry of Culture worked on a new kind of dictionary that accepts the idea that many people outside of France speak the language. The language has changed over time and is different in places like Ivory Coast in West Africa or Quebec in Cana-da, compared to how it is in ParisA new online dictionary, called the French speakers’ dictionary, includes new French words from around theworld. It was released on March 18—just in time for International French Speaker’s Day on March 20.Supporters say the new Internet dictionary is more democratic than earlier French dictionaries that only showed the way highly educated French people spoke. The new dictionary includes unofficial words like “pourriel”, which means an unwanted email if you are in Canada. It is a word based on “courriel”, which just means an email.French President Emmanuel Macron proposed the idea of the dictionary in 2018. It now contains about 600.000 terms, Roselyne Bachelot is the French Culture Minister. She said the dictionary is not just for France's 67 million citizens, but for the 300 million French speakers worldwide.The aim, supporters say, is to recognize the way language changes. Words and expressions included in the dictionary come from over 50 countries—even from the United States Some people in the southern U. S. state of Louisiana speak French.People can see the dictionary on a website or with an app. Users can also send in new words they think should be included. Official dictionaries produced by the French Academy in Paris were first published hundreds of years ago and are regularly updated.8. What do we mean if we say a man “throws a camel” in French?A. He talks big.B. He is very strong.C. He makes a joke.D. He misspells a word.9. What is the purpose of the publication date of the new online dictionary?A. To celebrate an event.B. To honor foreign users.C. To draw more attention.D. To meet an urgent need.10. Where does the word “pourriel” come from?A. French.B. An email.C. A holiday.D. Canada.11. What can people do with the new dictionary?A. Update it regularly.B. Recommend new words to it.C. Change the meaning of its words.D. Regard it as an official dictionary.DA new study has discovered that meditation (冥想) and oxygen sport together reduce depression. The Rutgers University study found that this mind and body combination, done twice a week for only two months,reduced the symptoms for a group of students by 40 percent.“We are excited by the findings because we saw such a meaningful improvement in both clinically depressed and non-depressed students,” said lead author Dr. Brandon Alderman. “It is the first time that both of these twobehavioral ways have been looked at together for dealing with depression.”Researchers believe the two activities have an interactive effect on combatingdepression. Alderman and Dr. Tracey Shors discovered that a combination of mental and physical training (MAP) enabled students with major depressive disorder not to let problems or negative thoughts defeat them.Rutgers researchers say those who participated in the study began with 30 minutes of focused attention meditation followed by 30 minutes of oxygen sport. They were told that if their thoughts drifted to the past or the future they should refocus on their breathing, enabling those with depression to accept moment-to-moment changes in attention.Shors, who studies the productionof new brain cells in the hippocampus—part of the brain involved in memory and learning—says scientists have shown in animal models that oxygen sport exercise keeps a large number of certain cells alive.The idea for the human intervention (干预) came fromher laboratory studies, she says, with the main goal of helping individuals acquire new skills so that they can learn to recover from stressful life events.By learning to focus their attention and exercise, people who are fighting depression can acquire new learning skills that can help them process information and reduce the overwhelming recollection of memories from the past, Shors says.“We know these treatments can be practiced over a lifetime and that they will be effective in improving mental health.” said Alderman. “The good news is that this intervention can be practiced by anyone at any time and at no cost.”12. What made the research so different?A. Adopting a way of meaningful talk.B. Combining the two behavioral ways to treat depression.C. Treating depression with special medicine.D. Comparing the depressed with the non-depressed.13. The underlined word “combating” in Paragraph 3 can be replaced by ______.A. fightingB. identifyingC. distinguishingD. examining14. What did the participants do in the research?A. They did oxygen sport half an hour before thinking.B. They thought quietly and then took exercise.C. They took exercise longer than they thought.D. They took exercise while thinking quietly.15. What is Shors’ main purpose of her studies?A. To find out certain brain cells of humans.B. To study the production of new brain cells.C. To offer people a new method to treat stress.D. To decide the links between stress and exercise.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。
上海南洋模范中学2019高三上学期年中考试-数学理
上海南洋模范中学2019高三上学期年中考试-数学理期中考试数学理试卷【一】填空题〔本部分共14道题，每题4分，总分值56分〕1、集合}1|{≤=x x A ，}|{a x x B ≥=，且R B A =⋃，那么实数a 的取值范围是2、函数xx y --=21的定义域为3、“1>x ”是“02>-x x ”的条件4、函数)1(321>-=+-x y x 的反函数为5、函数xx y 2+=，]2,0()0,2[⋃-∈x 的单调递减区间为 6、假设函数()f x ax b =+的零点为2x =，那么函数2()g x bx ax =-的零点是0x =和x =7、【理科】一盒中有7件正品，3件次品，无放回地每次取一件产品，直至取到正品、抽取次数ξ的概率分布律如下表：那么抽取次数ξ的数学期望E ξ=8、【理科】圆的极坐标方程为)3cos(2πθρ+=，那么该圆的圆心的极坐标是9、【理科】直线047=-+y x 与曲线⎩⎨⎧==θθ2cos sin y x 〔θ为参数〕的交点坐标是 10、在)2,0(π内，使|cos |sin x x ≥成立的x 的取值范围为11、函数x x y 2arccos )1arcsin(+-=的值域为12、)(x f 是偶函数，且)(x f 在),0[+∞上是增函数，如果)2()1(-≤+x f ax f 在]1,21[∈x 上恒成立，那么实数a 的取值范围是13、函数21-=+x a y )1,0(≠>a a 的图像恒过定点A ，假设点A 在直线01=++ny mx 上)0,0(>>n m ，那么nm 12+的最小值是 14、设函数2)(2-=x x g )(R x ∈，⎩⎨⎧≥-<++=)(,)()(,4)()(x g x x x g x g x x x g x f ，那么)(x f 的值域为【二】选择题〔本部分共4道题，每题4分，总分值16分〕15、假设函数)sin()(ϕ+=x x f 是偶函数，那么ϕ可取的一个值为〔〕A 、πϕ-=B 、2πϕ-=C 、4πϕ-=D 、8πϕ-=16、函数|lg |)(x x f =、假设b a <<0，且)()(b f a f =，那么b a 2+的取值范围是〔〕A 、),22(+∞B 、),22[+∞C 、),3(+∞D 、),3[+∞17、为了得到函数)32sin(π-=x y 的图像，只需把函数)62sin(π+=x y 的图像〔〕A 、向左平移4π个长度单位B 、向右平移4π个长度单位C 、向左平移2π个长度单位D 、向右平移2π个长度单位18、假设点)0)(,(0000≠y x y x P 在函数)(x f y =的图像上，)(1x f y -=为函数)(x f y =的反函数、设1P ),(00x y ，2P ),(00x y -，3P ),(00x y -，4P ),(00x y --，那么有〔〕 A 、点1P 、2P 、3P 、4P 有可能都在函数)(1x f y -=的图像上 B 、只有点2P 不可能在函数)(1x f y -=的图像上 C 、只有点3P 不可能在函数)(1x f y -=的图像上D 、点2P 、3P 都不可能在函数)(1x f y -=的图像上南洋模范中学2018学年第一学期高三年级期中考试数学试卷——答题卷【一】填空题〔本部分共14道题，每题4分，总分值56分〕1、2、3、4、5、6、7、【理科】【文科】8、【理科】【文科】9、【理科】【文科】10、11、12、13、14、【二】选择题〔本部分共4道题，每题4分，总分值16分〕15、16、17、18、【三】解答题〔本部分共6道题，总分值78分〕19、〔此题总分值12分〕函数)2sin(21cos cos sin 2sin 21)(2ϕπϕϕ+-+=x x x f )0(πϕ<<，其图象过点)21,6(π、 〔1〕求ϕ的值；〔2〕将函数)(x f y =的图象上各点的横坐标缩短到原来的21，纵坐标不变，得到函数)(x g y =的图象，求函数)(x g 在]4,0[π上的最大值和最小值、20、〔此题总分值12分〕设函数|2|)(2a x x x f -+=〔a R x ,∈为实数〕.〔1〕假设)(x f 为偶函数，求实数a 的值；〔2〕设2>a ，求函数)(x f 的最小值.21、〔此题总分值12分〕ABC ∆的三个内角C B A ,,的对边分别为c b a ,,、〔1〕假设当θ=A 时，2cos 2cos C B A ++取到最大值，求θ的值； 〔2〕设A 的对边长1=a ，当2cos 2cos C B A ++取到最大值时，求ABC ∆面积的最大值、 22、〔此题总分值12分〕xx x x x x x x x f cos sin 1sin cos 1cos sin 1sin cos 1)(+---+---+=，定义域为D 、 〔1〕化简)(x f ，并求定义域D ；〔2〕是否存在x ，使得)(2tan x f x ⋅与x x sin 2tan 12+相等？假设存在，求x 的值；假设不存在，请说明理由、23、〔此题总分值14分〕函数)1,0(112log )(≠>+--=a a x mx m x f a 是奇函数，定义域为区间D 、〔1〕求实数m 的值，并写出区间D ；〔2〕假设底数1>a ，试判断函数)(x f y =在定义域D 内的单调性，并说明理由；〔3〕当D A b a A x ⊂=∈),,[时，函数值组成的集合为),1[+∞，求实数b a ,的值、24、〔此题总分值16分〕函数)(x f ，如果存在给定的实数对),(b a ，使得b x a f x a f =-⋅+)()(恒成立，那么称)(x f 为“-Γ函数”.〔1〕判断函数x x f x x f 3)(,)(21==是否是“-Γ函数”；〔2〕假设x x f tan )(3=是一个“-Γ函数”，求出所有满足条件的有序实数对),(b a ； 〔3〕假设定义域为R 的函数)(x f 是“-Γ函数”，且存在满足条件的有序实数对)1,0(和)4,1(，当]1,0[∈x 时，)(x f 的值域为]2,1[，求当]2012,2012[-∈x 时函数)(x f 的值域、南洋模范中学2018学年第一学期高三年级期中考试数学试卷——参考答案【一】填空题〔本部分共14道题，每题4分，总分值56分〕1、1≤a2、),2()2,1[+∞⋃3、充分非必要4、)23)(3(log 12-<<-+-=x x y 5、)0,2[-和]2,0(6、21-7、【理科】118【文科】6365 8、【理科】)3,1(π-【文科】69、【理科】)21,21(【文科】2 10、]43,4[ππ11、],6[ππ12、]0,2[-13、223+14、),2(]0,49[+∞⋃- 【二】选择题〔本部分共4道题，每题4分，总分值16分〕15、B16、C17、B18、D【三】解答题〔本部分共6道题，总分值78分〕19、解：〔1〕将函数)(x f y =，整理化简为)2cos(21)(ϕ-=x x f ，因其图象过点)21,6(π，可得1)3cos(=-ϕπ，又πϕ<<0，所以3πϕ=、〔2〕由〔1〕知)32cos(21)(π-=x x f ，将函数)(x f y =的图像上各点的横坐标缩短到原来的21，纵坐标不变，得到函数)(x g y =的图象，可知)34cos(21)2()(π-==x x f x g ，因为]4,0[π∈x ，所以]32,3[34πππ-∈-x ，故1)34cos(21≤-≤-πx 、所以)(x g y =在]4,0[π上的最大值和最小值分别为21和41-. 20、解：〔1〕由)()(x f x f =-，即|2||2|a x a x +=-，解得0=a ；〔2〕⎪⎪⎩⎪⎪⎨⎧<+-≥-+=2,22,2)(22a x a x x a x a x x x f ， 当2a x ≥时，)1()1(2)(22+-+=-+=a x a x x x f ，由2>a ，2a x ≥得1>x ， 故)(x f 在2a x ≥时单调递增，)(x f 的最小值为4)2(2a a f =； 当2a x <时，)1()1(2)(22-+-=+-=a x a x x x f ，故当21a x <<时，)(x f 单调递增， 当1<x 时，)(x f 单调递减，那么)(x f 的最小值为1)1(-=a f ； 由04)2()1(422>-=--a a a ，知)(x f 的最小值为1-a 、 21、解：〔1〕因为2cos 2cos C B A ++2sin 2cos A A +=2sin 22sin 212A A +-= 23)212(sin 22+--=A ，故当212sin =A 时，原式取到最大值， 即三角形的内角3πθ==A 时，最大值为23、〔2〕由〔1〕结论可得3π=A ，此时⇒=-+=212cos 222bc a c b A bc c b =-+122、 又bc c b 222≥+，因此1122≤⇔≥-+=bc bc bc c b ，当且仅当c b =时等号成立、 所以4323121sin 21=⨯⨯≤=∆A bc S ABC ，故ABC ∆面积的最大为43、22、解：〔1〕2sin 2cos 2cos 2sin 22sin 22cos 2sin 22cos 2cos sin 1sin cos 122x x x x x x x x x x x x -=--=---+ ，=∴)(x f x x x x x x x x x sin 22cos 2sin 2sin 2cos 2cos 2sin 2sin 2cos 22-=+-=--，又因为⎩⎨⎧≠+-≠--0cos sin 10cos sin 1x x x x ， 即⎪⎪⎩⎪⎪⎨⎧≠-≠+22)4sin(22)4sin(ππx x ，解得：定义域为πk x x D ≠=|{且},22Z k k x ∈+≠ππ、〔2〕假设)(2tan x f x ⋅x x sin 2tan 12+=，那么x x sin 2tan 2-x x sin 2tan 12+=，所以12tan 12tan 22-=+x x ，即1si n -=x ，此时22ππ-=k x ，Z k ∈，即为存在的x 值、23、解：〔1〕因为)(x f y =是奇函数，所以对任意D x ∈，有0)()(=+-x f x f ， 即0112log 112log =+--++-+-x mx m x mx m a a 、化简得01)12()1(222=+---m x m ，又此方程有无穷多解，必有⎪⎩⎪⎨⎧=--=-01)12(0122m m ，解得1=m 、所以11log )(+-=x x x f a ，)1,1(-=D 、 〔2〕当1>a 时，函数11log )(+-=x x x f a 在)1,1(-=D 上是单调减函数、 理由：设11+-=x x t ，因112-+=x t 在)1,1(-=D 上是单调减函数，于是，当1>a 时，函数11log )(+-=x x x f a 在)1,1(-=D 上是单调减函数、 〔3〕1,10,),[≤<<<∴⊂=b a a D b a A ，所以根据〔2〕，当10<<a 时，函数11log )(+-=x x x f a 在A 上是增函数、即1)(=a f ，111log =+-∴aa a ，解得12-=a 〔12--=a 舍去〕、 假设1<b ，那么函数)(x f y =在A 上的函数值组成的集合为)11log ,1[b b a +-，不符合题意，所以必有1=b ，因此，所求实数b a ,的值是12-=a ，1=b 、24、解：〔1〕假设x x f =)(1是“-Γ函数”，那么存在常数),(b a ，使得b x a x a =-+))((、 即b a x -=22时，对R x ∈恒成立、而b a x -=22最多有两个解，矛盾， 因此x x f =)(1不是“-Γ函数”、 假设x x f 3)(2=是“-Γ函数”，那么存在常数b a ,使得a x a x a 2333=⋅-+， 即存在常数对)3,(2a a 满足条件、因此x x f 3)(2=是“-Γ函数”、〔2〕x x f tan )(3=是一个“-Γ函数”，设有序实数对),(b a 满足： 那么b x a x a =-⋅+)tan()tan(恒成立、 当Z k k a ∈+=,2ππ时，x x a x a 2cot )tan()tan(-=-⋅+，不是常数、 因此Z k k a ∈+≠,2ππ，当Z m m x ∈+≠,2ππ时， 那么有b xa x a x a x a x a x a =--=⋅-+⨯⋅+-2222tan tan 1tan tan tan tan 1tan tan tan tan 1tan tan ， 即0)(tan tan )1tan (222=-+-⋅b a x a b 恒成立、即⇒⎩⎨⎧==⇒⎪⎩⎪⎨⎧=-=-⋅11tan 0tan 01tan 222b a b a a b Z k b k a ∈⎪⎩⎪⎨⎧=±=,14ππ， 当Z m m x ∈+=,2ππ,4ππ±=k a 时，1cot )tan()tan(2==-⋅+a x a x a 成立、因此满足x x f tan )(3=是一个“-Γ函数”，),(b a ))(1,4(Z k k ∈±=ππ、(3)函数)(x f 是“-Γ函数”，且存在满足条件的有序实数对)1,0(和)4,1(，于是,4)1()1(,1)()(=-⋅+=-⋅x f x f x f x f即]1,0[2]2,1[,4)2()(4)1()1(∈-∈=-⇔=-⋅+x x x f x f x f x f 时，，]4,2[)2(4)(∈-=x f x f ，.]2,0[∈∴x 时，]4,1[)(∈x f )(4)2()2(4)()(1)(4)1()1(1)()(x f x f x f x f x f x f x f x f x f x f =+⇒⎪⎪⎩⎪⎪⎨⎧+=-=-⇒⎩⎨⎧=-⋅+=-⋅. ].2,2[)(,]2012,2010[],2,2[)(,]22,2[],2,16[)(,]6,4[],16,4[)(]4,2[201220102226∈∈∈+∈∈∈∈∈+x f x x f k k x x f x x f x k k 时时依次类推可知时时， 因此]2,1[)(]2012,0[2012∈∈x f x 时，,].1,2[)(]2,1[)(],2012,0[,)(1)(,]0,2012[20122012-∈⇒∈-∈--=-∈x f x f x x f x f x 时综上可知当]2012,2012[-∈x 时函数)(x f 的值域为]2[22012-2012，、。
上海市南洋模范中学2018-2019学年高三上学期第三次月考试卷数学含答案
上海市南洋模范中学2018-2019学年高三上学期第三次月考试卷数学含答案 班级__________ 座号_____ 姓名__________ 分数__________一、选择题（本大题共12小题，每小题5分，共60分.每小题给出的四个选项中，只有一项是符合题目要求的.）1． 已知e 为自然对数的底数，若对任意的1[,1]x e∈，总存在唯一的[1,1]y ∈-，使得2ln 1y x x a y e -++= 成立，则实数a 的取值范围是（ ）A.1[,]e eB.2(,]e eC.2(,)e +∞D.21(,)e e e+【命题意图】本题考查导数与函数的单调性，函数的最值的关系，函数与方程的关系等基础知识，意在考查运用转化与化归思想、综合分析问题与解决问题的能力．2． 在数列{}n a 中，115a =，*1332()n n a a n N +=-∈，则该数列中相邻两项的乘积为负数的项是 （ ）A ．21a 和22aB ．22a 和23aC ．23a 和24aD ．24a 和25a 3． 沿一个正方体三个面的对角线截得几何体如图所示，则该几何体的侧视图为（ ）A ．B ．C ．D ．4． 函数f （x ）＝sin （ωx ＋φ）（ω＞0，－π2≤φ≤π2）的部分图象如图所示，则φω的值为（ ）A.18 B ．14C.12D ．15． 已知圆M 过定点)1,0(且圆心M 在抛物线y x 22=上运动，若x 轴截圆M 所得的弦为||PQ ，则弦长||PQ 等于（ ）A ．2B ．3C ．4D ．与点位置有关的值【命题意图】本题考查了抛物线的标准方程、圆的几何性质，对数形结合能力与逻辑推理运算能力要求较高，难度较大.6． 已知抛物线C ：24y x =的焦点为F ，定点(0,2)A ，若射线FA 与抛物线C 交于点M ，与抛 物线C 的准线交于点N ，则||:||MN FN 的值是（ ）A ．B ．C ．1:D (1 7． 如图是某几何体的三视图，正视图是等腰梯形，俯视图中的曲线是两个同心的半圆组成的半圆环，侧视图是直角梯形．则该几何体表面积等于（ ）A ．12+B ．12+23πC ．12+24πD ．12+π8． 设函数()''y f x =是()'y f x =的导数.某同学经过探究发现，任意一个三次函数()()320f x ax bx cx d a =+++≠都有对称中心()()00,x f x ，其中0x 满足()0''0f x =.已知函数()3211533212f x x x x =-+-，则1232016...2017201720172017f f f f ⎛⎫⎛⎫⎛⎫⎛⎫++++= ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭（ ）A ．2013B ．2014 C ．2015 D ．20161111] 9． 集合{}{}2|ln 0,|9A x x B x x =≥=<,则AB =（ ）A ．()1,3B ．[)1,3C ．[]1,+∞D ．[],3e 10．“24x ππ-<≤”是“tan 1x ≤”的（ ） A.充分不必要条件 B.必要不充分条件 C.充要条件D.既不充分也不必要条件【命题意图】本题主要考查充分必要条件的概念与判定方法，正切函数的性质和图象，重点是单调性. 11．棱长为2的正方体被一个平面截去一部分后所得的几何体的三视图如图所示，则该几何体的表面积为（ ）A ．B ．18C ．D ．12．由直线与曲线所围成的封闭图形的面积为（ ）A B1C D二、填空题（本大题共4小题，每小题5分，共20分.把答案填写在横线上）13．函数()2log f x x =在点()1,2A 处切线的斜率为 ▲ ．14．1F ，2F 分别为双曲线22221x y a b-=（a ，0b >）的左、右焦点，点P 在双曲线上，满足120PF PF ⋅=，若12PF F ∆______________.【命题意图】本题考查双曲线的几何性质，直角三角形内切圆半径与外接圆半径的计算等基础知识，意在考查基本运算能力及推理能力．15．圆上的点（2，1）关于直线x+y=0的对称点仍在圆上，且圆与直线x ﹣y+1=0相交所得的弦长为，则圆的方程为 ．16．在（1+2x ）10的展开式中，x 2项的系数为 （结果用数值表示）．三、解答题（本大共6小题，共70分。
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南模中学高三三模数学试卷
2019.05
一. 填空题
1. 若集合{|310}A x x =+>，{||1|2}B x x =-<，则A B =I
2. 若复数z 满足
1i
i z -=-，其中i 为虚数单位，则z = 3. 若函数1
()1f x x =+（0x >）的反函数为1()f x -，则不等式1()2f x ->的解集为
4. 试写出71
()x x
-展开式中系数最大的项
5.
若函数4y =a ，最大值为b ，则2lim 34n n n n
n a b a b →∞-=-
6. 已知平面上三点A 、B 、C
满足||AB =u u u r
，||BC =u u u r
||CA =u u u r
，则 AB BC BC CA CA AB ⋅+⋅+⋅u u u r u u u r u u u r u u u r u u u r u u u r
的值等于
7. 设P
是曲线tan x y θθ⎧=
⎪⎨⎪=⎩
（θ为参数）上的一动点，O 为坐标原点，M 为线段OP 的中 点，则点M 的轨迹的普通方程为
8. 在等差数列{}n a 中，首项13a =，公差2d =，若某学生对其中连续10项进行求和，在 遗漏掉一项的情况下，求得余下9项的和为185，则此连续10项的和为
9. 从集合{1,2,3,4,5,6,7,8,9,10}A =中任取两个数，欲使取到的一个数大k 于，另一个数小 于k （k A ∈）的概率为
2
5
，则k = 10. 已知数列{}n a 的通项公式为(1)2n n
n a n =-⋅+（*n ∈N ），则这个数列的前n 项和为
n S =
11. 已知函数1
()f x x x
=-
，数列{}n a 是公比大于0的等比数列，且61a =， 1239101()()()()()f a f a f a f a f a a +++⋅⋅⋅++=-，则1a =
12. 定义在R 上的奇函数()f x ，当0x ≥时，1
2log (1)[0,1)()1|3|[1,)
x x f x x x +∈⎧⎪=⎨⎪--∈+∞⎩，则关于x 的
函数()()F x f x a =-（01a <<）的所有零点之和为 （结果用a 表示）
二. 选择题
13. 已知非零向量a r 、b r ，“函数2
()()f x ax b =+r r 为偶函数”是“a b ⊥r r ”的（ ）条件
A. 充分非必要
B. 必要非充分
C. 充要
D. 既不充分也不必要
14. 若a 、b 表示两条直线，α表示平面，下列命题中的真命题为（ ） A. 若a α⊥，a b ⊥，则b ∥α B. 若a ∥α，a b ⊥，则b α⊥ C. 若a α⊥，b α⊆，则a b ⊥ D. 若a ∥α，b ∥α，则a ∥b 15. 抛物线24y x =的焦点为F ，点(,)P x y 为抛物线上的动点，又点(1,0)A -，则||
||
PF PA 的 最小值是（ ） A.
1
2
B. 22
C. 32
D. 233
16. 已知1x 、2x 是关于x 的方程220x mx m m ++-=的两个不相等的实数根，则经过两点
211(,)A x x 、2
22
(,)B x x 的直线与圆22(1)(1)1x y -++=的位置关系是（ ） A. 相离 B. 相切 C. 相交 D. 随m 的变化而变化
三. 解答题
17. 如图，长方体1111ABCD A B C D -中，2AB BC ==，13AA =. （1）求四棱锥1A ABCD -的体积； （2）求异面直线1A C 与1DD 所成角的大小.
18. 已知函数()|2|f x x a a =-+.
（1）若不等式()6f x <的解集为(1,3)-，求a 的值；
（2）在（1）的条件下，若存在0x ∈R ，使00()()f x t f x ≤--，求t 的取值范围.
19. 某景区欲建两条圆形观景步道1M 、2M （宽度忽略不计）
，如图所示，已知AB AC ⊥，
60AB AC AD ===（单位：米），要求圆1M 与AB 、AD 分别相切于点B 、D ，圆2M
与AC 、AD 分别相切于点C 、D . （1）若3
BAD π
∠=
，求圆1M 、2M 的半径（结果精确到0.1米）；
（2）若观景步道1M 、2M 的造价分别为每米0.8千元与每米0.9千米，则当BAD ∠多大时，总造价最低？最低总造价是多少？（结果分别精确到0.1°和0.1千元）
20. 已知椭圆2222:1x y C a b +=（0a b >>）的右焦点为(1,0)F ，且点3
(1,)2
P 在椭圆C 上.
（1）求椭圆C 的标准方程；
（2）过椭圆22
122:153
x y C a b +=-上异于其顶点的任意一点Q 作圆224:3O x y +=的两条切
线，切点分别为M 、N （M 、N 不在坐标轴上），若直线MN 在x 轴、y 轴上的截距分
别为m 、n ，证明：
22
11
3m n +
为定值； （3）若1P 、2P 是椭圆22
2223:1x y C a b
+=上不同的两点，12PP x ⊥轴，圆E 过1P 、2P ，且椭
圆2C 上任意一点都不在圆E 内，则称圆E 为该椭圆的一个内圆，试问：椭圆2C 是否存在过左焦点1F 的内切圆？若存在，求出圆心E 的坐标，若不存在，请说明理由.
21. 若{}n c 是递增数列，数列{}n a 满足：对任意*n ∈N ，存在*m ∈N ，使得1
0m n
m n a c a c +-≤-，
则称{}n a 是{}n c 的“分隔数列”.
（1）设2n c n =，1n a n =+，证明：数列{}n a 是{}n c 的分隔数列；
（2）设4n c n =-，n S 是{}n c 的前n 项和，32n n d c -=，判断数列{}n S 是否是数列{}n d 的分隔数列，并说明理由；
（3）设1n n c aq -=，n T 是{}n c 的前n 项和，若数列{}n T 是{}n c 的分隔数列，求实数a 、q 的取值范围.
参考答案
一. 填空题
1. 1(,3)3-
2. 1i -
3. 3(1,)2
4.
35x 5. 12
6. 8-
7. 22841x y -=
8. 200
9. 4或7
10. 1
1122212
2222
n n n n n k S n n k
++--⎧+-=-⎪⎪=⎨⎪+-=⎪⎩，*k ∈N
11. 2 12. 12n -
二. 选择题
13. C 14. C 15. B 16. C
三. 解答题
17.（1）4；（2
）. 18.（1）2a =；（2）8t ≥.
19.（1
）1r =
，260(2r =；（2）54.1°，867.1.
20.（1）22143x y +=；（2）3
4
；（3
）(2E -. 21.（1）证明略；（2）不是，反例：4n =时，m 无解；（3）0
2a q >⎧⎨≥⎩
.。