广东省梅州市2012届5月高三总复习质检试卷(二,文数,试题word)无答案版
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试卷类型:B梅州市高三总复习质检试卷(2012.5)数学(理科)本试卷共4页,21小题,满分150分。
考试用时120分钟。
注意事项:1.答卷前,考生务必用黑色字迹钢笔或签字笔将自己的姓名和考生号、试室号、座位号填写在答题卡上。
用2B 铅笔将试卷类型(B )填涂在答题卡相应位置上。
将条形码横贴在答题卡右上角“条形码粘贴处”。
2.选择题每小题选出答案后,用2B 铅笔把答题卡上对应题目选项的答案信息点涂黑,如需改动,用橡皮擦干净后,再选涂其他答案,答案不能答在试卷上。
3.非选择题必须用黑色字迹的钢笔或签字笔作答,答案必须写在答题卡各题目指定区域内的相应位置上;如需改动,先划掉原来的答案,然后再写上新的答案;不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
4.作答选做题时,请先用2B 铅笔填涂选做题的题号对应的信息点,再作答。
漏涂、错涂、多涂的,答案无效。
5.考生必须保持答题卡的整洁。
考试结束后,将试卷和答题卡一并交回。
一、选择题:本大题共10个小题,每小题5分,满分50分.在每小题给出的四个选项中,只有一项是符合题目要求的. 1.设,a b ∈R ,若复数12i 1iz +=+,则z 在复平面上对应的点在A .第一象限B .第二象限C .第三象限D .第四象限 2.已知集合3{0},{3}1x M xN x x x +=<=--…,则集合{1}x x …等于A .M ∩NB .M NC .D 、3.如图,某几何体的正视图与侧视图都是边长为1的正方形,且体积为12,则该几何体的俯视图可以是4.设0ω>,函数sin()3y x πω=+的图象向右平移43π个单位后与原图象重合,则ω的最小值为 A .23B .43C .32D .35.平面向量,a b 共线的充要条件是A .,a b 方向相同B .,a b 两向量中至少有一个为零向量C .,b λλ∃∈=R aD .存在不全为零的实数12,λλ,12λλ+=0a b6.函数x x xxe e y e e--+=-的图象大致为A .B .C .D .7.将甲、乙、丙、丁四名实习老师分到三个不同的班,每个班至少分到一名老师,且甲、乙两名老师不能分到同一个班,则不同分法的种数为 A 、28 B 、24 C 、30 D 、36 8.非空集合G 关于运算满足:(1)对于任意a 、b ∈G ,都有a ⊕b ∈G ;(2)存在e ∈G ,使对一切a ∈G 都有a ⊕e=e ⊕a=a ,则称G 关于运算⊕为“融合集”,现在给出集合和运算::①G={非负整数},为整数的加法;②G={偶数},为整数的乘法;③G={平面向量},为平面向量的加法;④ G={虚数},为复数乘法,其中G为关于运算的“融洽集”的个数为A 、1个B 、2个C 、3个 D4个二、填空题:本大题共5小题,考生作答4小题,每小题5分,满分20分.(一)必做题(11~13小题)9.执行如图所示的程序框图,若输入x =10 ,则输出y 的值为 .10.设等差数列{}n a 的前n 项和为n S ,若972S =,则249a a a ++= .11、在区间[-1,]上随机取一个数x ,cos 2xπ的值介于0到12之间的概率为____12、抛物线y 2=4x 的焦点为F ,过点P 5,12⎛⎫⎪⎝⎭的直线交抛物线于A 、B 两点,且P 恰好为AB 的中点,则|AF |+|BF |=____ 13、观察下列各式:xxx由以上等式推测到一个一般的结论: 对于:(二)选做题(14、15题,考生只能从中选做一题) 14.(坐标系与参数方程选做题)在极坐标系中,直线cos()24πρθ-=与圆4ρ=的交点个数为 .15.(几何证明选讲选做题)如图所示,过O 外一点P 作一条直线与O交于,A B 两点,己知弦6A B =,点P 到O 的切线长4,PT =则PA = .三、解答题:本大题共6个小题,满分80分.解答应写出文字说明,证明过程或演算步骤. 16.(本小题满分12分)己知点(1,0),(0,1),(2sin cos )A B C θθ,. (1)若=1,其中O 为坐标原点,求sin2θ的值;(2)若,且θ在第三象限.求sin()3πθ+值.17.(本小题满分13分)一个社会调查机构就某社区居民的月收入调查了10 000人,并根据所得数据画了样本的频率分布直方图(如图).(1)为了分析居民的收入与年龄、学历、职业等方面的关系,要从这10000人中再用分层抽样方法抽出100人作进一步调查,求月收入在[1500,2000)(元)段应抽出的人数;(2)为了估计该社区3个居民中恰有2个月收入在[2000,3000)(元)的概率,采用随机模拟的方法:先由计算器算出0到9之间取整数值的随机数,我们用0,1,2,3,…表示收入在[2000,3000)(元)的居民,剩余的数字表示月收入不在[2000,3000)(元)的居民;再以每三个随机数为一组,代表统计的结果,经随机模拟产生了20组随机数如下: 907 966 191 925 271 932 812 458 569 683 431 257 393 027 556 488 730 113 537 989P第15题图第17题图150020002500300035004000据此估计,计算该社区3个居民中恰好有2个月收入在[2000,3000)(元)的概率. (3)任意抽取该社区6个居民,用ξ表示月收入在(2000,3000)(元)的人数,求ξ的数学期望。
2023届广东省梅州市高三下学期二模英语试题学校:___________姓名:___________班级:___________考号:___________一、阅读理解Master Gardener Volunteers WantedWhat is a Master Gardener?A master gardener is a citizen that is interested in gardening and can fulfill the training and volunteer hours necessary.Requirements vary by county and state,and the course is tailored for that specific region.You will receive special education on the soils in your area,the types of native plants,insect and disease issues,basic botany,and other information pertinent(相关的)to your gardening zone.The educational opportunity to learn specifics about where you garden will not only help you be-come a better gardener but is then passed along to the general public in lectures,clinics,and through newsletters.What Qualifications Must You Meet?Anyone can apply to be a Master Gardener——you don’t need to be an expert or have a degree.You do,however,need to:●Have certain experience or know a little about gardening or landscape management.●Be willing to share horticulture(园艺学)information with others.●Be willing to attend a training program and can devote time to volunteering and continuing education.Besides,to become a Master Gardener volunteer,each applicant needs to complete an application,prepare background screening paperwork and schedule an interview with Extension staff.What Does the Training Involve?Training sessions are offered one day a week over a three-month period and are led by expert educators in the region.Approximately60hours of classroom instruction and field study and50hours of volunteer internship(实习)work are required to complete the program and become certified.In order to remain a certified Master Gardener,30hours of volunteer work and10hours of continuing education or advanced training are required each year. 1.What does a Master Gardener do?A.Promote gardening practices abroad.experience of starting a library with the books that are thrown away.Gutierrez says he doesn’t reject technology that allows books to be read digitally.But he prefers to read the printed words on paper.“There is nothing more beautiful than having a book in your pocket,in your bag or inside your car.”4.How old was Gutierrez when he started saving books from the trash?A.In his twenties.B.In his thirties.C.In his forties.D.In his fifties, 5.What does the underlined word“They”in Paragraph3refer to?A.Luxury books.B.Garbage trucks.C.Public libraries.D.Poor areas. 6.What did the book Anna Karenina mean to Gutierrez?A.The beginning of his charity project.B.A window to the world.C.One of his greatest achievements in life.D.Some comfort in difficult times. 7.Which of the following sayings does Gutierrez’s story lead us to believe?A.Actions speak louder than words.B.A good book can shine a light upon the soul.C.One man’s trash is another man’s treasure.D.The palest ink is better than the best memory.Jobs that use both technical and creative thinking are among the fastest-growing and highest-paying ones,according to a new report from Burning Glass Technologies,a job market analytic company in Boston.It studied millions of job postings to better understand the skills companies require. What they discovered was that many want workers with experience in such new abilities as big-data gathering and analytic,or design using digital technology.Burning Glass came up with the term“hybrid jobs”to describe these kinds of positions,which require skills not normally found together.For example,these hybrid jobs might require people with skills in data science and advertising,or engineering and sales.“The jobs of the future don’t involve just one skill,“says Matt Sigelman,chief manager of Burning Glass.The company expects general job growth of about10%between2018and2028,but the hybrid jobs by21%.What’s more,hybrid jobs pay more than positions that call for a traditional set of skills.For example,a marketing manager mastering a database program gets paid41%more than a traditional one,with an average yearly salary of$100,000.Moreover,anengineer who improves her sales skills and becomes a consulting engineer fora software company can more than double her pay from$180,000to$400,000.While data shows that workers who fail to update their skills will be able to find fewer jobs,people in hybrid jobs are less likely to become out of date,with only12%possibility of being re-placed by machine,compared with42%for general jobs,says Burning Glass.Hybrid jobs are mostly not beginner roles,so they mainly go to workers with years of experience and,most importantly,more training after leaving college.That means workers,bosses and educators will have to think about how to better prepare people for these roles.8.Why did the company research into job advertisements?A.To understand the growth of best paid workers.B.To compare workers’experience with new abilities.C.To find out companies’requirements about skills.D.To tell the possible changes in future job market.9.Which of the following jobs can be hybrid?A.Data engineer.B.Machine operator.C.Marketing manager.D.Medical consultant.10.How much is a traditional marketing manager possibly paid every year?A.$180,000.B.$71,000.C.$41,000.D.$10,000. 11.Which of the following is the best title for this passage?A.Future Jobs Requiring“Hybrid”Skills.B.How to Get Trained for Jobs.C.Tips on Finding Fastest-Growing Jobs.D.The Jobs with Highest Pay.Art and science may seem like opposite things.One means the creative flow of ideas, and the other means cold,hard data—some people believe.In fact,the two have much in common.Now,a study finds art can help students remember better what they learned in science class.Mariale Hardiman,an education specialist at Johns Hopkins University,noticed that students who used art in the classroom listened more carefully.They might ask more questions.They might volunteer more ideas.What's more,students seemed to remember more of what they had been taught when their science lessons had involved(涉及)art.To prove that,Hardiman teamed up with some researchers and six local schools.In the experiment,the researchers worked with teachers in16fifth-grade classrooms.They provided traditional science lessons and art-focused ones.In a traditional science class, for example,students might read aloud from a book.In the art-focused one,they might sing the information instead.The team randomly assigned(随机分配)each of the350students to either a traditional science classroom or an art-focused one.Students then learned science using that way for the whole unit—about three weeks.When they changed to a new topic,they also changed to the other type of class.This way,each student had both an art-focused class and a traditional one. Every unit was taught in both ways,to different groups of students.This enabled the researchers to see how students did in both types of classes.The team found that students who started off in traditional classes performed better after they moved into an art-focused class.But those who started in an art-focused class did well even when they went back to a traditional science class.These students appeared to use some of the art techniques(技巧)after going back to a traditional class.Classroom teachers reported that many students continued to sing the songs that they learned after finishing the unit."The more we hear something,the more we retain it,"Hardiman says."It suggests that the arts may help students apply creative ways of learning on their own."12.Why did Mariale Hardiman do the study?A.To prove the importance of art at school.B.To know how to encourage students to ask questions.C.To find a way to help her students learn better.D.To see if art might improve science learning.13.What were the students required to do in the experiment?A.Learn three units in total.B.Choose what they'd like to learn.C.Learn two topics for three weeks.D.Take two types of classes.14.What does the underlined word“retain”in the last paragraph mean?A.Remember.B.Express.C.Improve.D.Finish.15.What is the text mainly about?A.Art helps students develop creativity.B.Art-focused classes interest students a lotF.Also,treat your team members respectfully as equals.G.Have a good sense of judgement on important aspects.二、完形填空29.A.accept B.expect C.hear D.notice 30.A.daughter B.patient C.speaker D.friend 31.A.health B.family C.silence D.love 32.A.lesson B.secret C.treatment D.wisdom 33.A.arms B.eyes C.mouths D.faces 34.A.observe B.smell C.review D.suggest 35.A.cutting B.pulling C.brushing D.losing三、用单词的适当形式完成短文四、告知信/通知46.假定你是李华,你的外国朋友Peter给你发邮件说最近经过多次尝试终于学会了做中国传统美食——饺子,开心不已。
试卷类型:B梅州市高三总复习质检试卷(2012.5)数学(文科)本试卷共4页,21小题,满分150分。
考试用时120分钟。
注意事项:1.答卷前,考生务必用黑色字迹钢笔或签字笔将自己的姓名和考生号、试室号、座位号填写在答题卡上。
用2B 铅笔将试卷类型(B )填涂在答题卡相应位置上。
将条形码横贴在答题卡右上角“条形码粘贴处”。
2.选择题每小题选出答案后,用2B 铅笔把答题卡上对应题目选项的答案信息点涂黑,如需改动,用橡皮擦干净后,再选涂其他答案,答案不能答在试卷上。
3.非选择题必须用黑色字迹的钢笔或签字笔作答,答案必须写在答题卡各题目指定区域内的相应位置上;如需改动,先划掉原来的答案,然后再写上新的答案;不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
4.作答选做题时,请先用2B 铅笔填涂选做题的题号对应的信息点,再作答。
漏涂、错涂、多涂的,答案无效。
5.考生必须保持答题卡的整洁。
考试结束后,将试卷和答题卡一并交回。
一、选择题:本大题共10个小题,每小题5分,满分50分.在每小题给出的四个选项中,只有一项是符合题目要求的. 1.设,a b ∈R ,若复数12i1iz +=+,则z 在复平面上对应的点在 A .第一象限 B .第二象限 C .第三象限 D .第四象限2.已知集合3{0},{3}1x M x N x x x +=<=--…,则集合{1}x x …等于 A .M N B .M N C .()M N R ð D .()M N R ð 3.设,b c 表示两条直线,,αβ表示两个平面,下列命题中的真命题是A .b b c c αα⊂⎫⇒⎬⎭B .b c b c αα⊂⎫⇒⎬⎭C .c c ααββ⎫⇒⊥⎬⊥⎭D .c c αβαβ⎫⇒⊥⎬⊥⎭4.设0ω>,函数sin()3y x πω=+的图象向右平移43π个单位后与原图象重合,则ω的最小值为 A .23 B .43 C .32D .3 5.平面向量,a b 共线的充要条件是A .,a b 方向相同B .,a b 两向量中至少有一个为零向量C .,b λλ∃∈=R aD .存在不全为零的实数12,λλ,12λλ+=0a b6.以双曲线2213x y -=的左焦点为焦点,顶点在原点的抛物线方程是A .24y x =B .24y x =-C .2y =-D .28y x =-7.函数x xx xe e y e e --+=-的图象大致为A .B .C .D .8.在区间[,]22ππ-上随机取一个数,cos x x 的值介于于0到12之间的概率为 A .13 B .2πC .12D .23 9.己知函数()f x 是(,)-∞+∞上的偶函数,若对于0x …,都有(2)()f x f x +=,且当0,2x ∈[)时,2()log (1)f x x =+,则(2008)(2009)f f -+的值为A .2-B .1-C .1D .210.设G 是一个至少含有两个数的数集,若对任意,a b G ∈,都有,,,aa b a b ab G b+-∈(除数0b ≠),则称G 是一个数域,例如有理数集Q 是数域.有下列命题:①数域必含有0,1两个数;②整数集是数域;③若有理数集M ⊆Q ,则数集M 必为数域;④数域必为无限集.其中正确命题的个数是A .1个B .2个C .3个D .4个二、填空题:本大题共5小题,考生作答4小题,每小题5分,满分20分. (一)必做题(11~13小题) 11.若0x >,则2x x+的最小值为 . 12.执行如图所示的程序框图,若输入x =10 ,则输出y 的值为 . 13.设等差数列{}n a 的前n 项和为n S ,若972S =,则249a a a ++= . (二)选做题(14、15题,考生只能从中选做一题)14.(坐标系与参数方程选做题)在极坐标系中,直线cos()24πρθ-=与圆4ρ=的交点个数为 .15.(几何证明选讲选做题)如图所示,过O 外一点P 作一条直线与O交于,A B 两点,己知弦6AB =,点P 到O 的切线长4,PT =则PA = .第15题图xx三、解答题:本大题共6个小题,满分80分.解答应写出文字说明,证明过程或演算步骤. 16.(本小题满分12分)己知点(1,0),(0,1),(2sin cos )A B C θθ,.(1)若(2)1OA OB OC += ,其中O 为坐标原点,求sin 2θ的值;(2)若||||AC BC = ,且θ在第三象限.求sin()3πθ+值.17.(本小题满分13分)一个社会调查机构就某社区居民的月收入调查了10 000人,并根据所得数据画了样本的频率分布直方图(如图).(1)为了分析居民的收入与年龄、学历、职业等方面的关系,要从这10 000人中再用分层抽样方法抽出100人作进一步调查,求月收入在[1500,2000)(元)段应抽出的人数;(2)估计该社区居民月收人的平均数;(3)为了估计该社区3个居民中恰有2个月收入在[2000,3000)(元)的概率,采用随机模拟的方法:先由计算器算出0到9之间取整数值的随机数,我们用0,1,2,3,…表示收入在[2000,3000)(元)的居民,剩余的数字表示月收入不在[2000,3000)(元)的居民;再以每三个随机数为一组,代表统计的结果,经随机模拟产生了20组随机数如下:907 966 191 925 271 932 812 458 569 683 431 257 393 027 556 488 730 113 537 989据此估计,计算该社区3个居民中恰好有2个月收入在[2000,3000)(元)的概率.18.(本小题满分14分)已知直三棱柱111ABC A B C -的三视图如图所示; (1)求此三棱柱的体积和表面积;(2)画出此三棱柱,并证明:11AC AB ⊥第17题图第18题图正视图侧视图俯视图19.(本小题14分)己知椭圆2222:1(0)x y C a b b +=>>,不等式||||1x y a b +…所表示的平面区域的面积为.(1)求椭圆C 的方程;(2)设椭圆C 的左项点为A ,上顶点为B ,圆M 过A B 、两点.当圆心M 与原点O 的 距离最小时,求圆M 的方程.20.(本小题14分)定义在R 上的函数()f x 满足:( ) ()()f x y f x f y += ,且当0x >时,()1f x >. (1)求(0)f 的值,并证明()f x 是定义域上的增函数:(2)数列{}n a 满足10a a =≠,1()()(1)(1,2,3,)n n f a f aa f a n +=-=⋯,求数列{}n a 的 通项公式及前n 项和n S .21.(本小题14分)已知函数()ln f x x ax =-.(1)当1a =时,求()f x 的最大值; (2)试讨论函数()y f x =的零点情况;(3)设,,(1,2,,)k k a b k n = 均为正数,若112212n n n a b a b a b b b b ++++++ …,求证:12121n bbbn a a a ⋅ ….。
2024届广东省梅州市高三下学期高考英语试题(二模)本试卷共8页,满分120分。
考试用时120分钟。
注意事项:1.答卷前,考生务必将自己的姓名、考生号、试室号和座位号填写在答题卡上。
用2B铅笔将试卷类型(A)填涂在答题卡相应位置上。
并在答题卡相应位置上填涂考生号。
因笔试不考听力,试卷从第二部分开始,试题序号从“21”开始2.作答选择题时,选出每小题答案后,用2B铅笔把答题卡对应题目选项的答案信息点涂黑:如需改动,用橡皮擦干净后,再选涂其他答案。
答案不能答在试卷上3.非选择题必须用黑色字迹的钢笔或签字笔作答,答案必须写在答题卡各题目指定区域内相应位置上;如需改动,先划掉原来的答案,然后再写上新答案:不准使用铅笔和涂改液。
不按以上要求作答无效。
4.考生必须保持答题卡的整洁。
考试结束后,将试卷和答题卡一并交回。
第二部分阅读(共两节,满分50分)第一节(共15小题;每小题2.5分,满分37.5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。
AFree Community SwapContact:Catherine Crawford, (718)809-1603Jon Klar, (646)530-0381New Yorkers looking to reduce, reuse, and save money this year are invited to participate in Stop ‘N’ Swap, a free community event organized by local nonprofit GrowNYC.The average NYC household throws away about 2,000 pounds of waste a year. By reusing through events like Stop ’N’ Swap, NYC residents can take part in saving over 40 million pounds of material from landfill every year. Take a break from shopping, support a cleaner future, and join the ever -growing reuse community!WHAT: Free Stop ‘N’ Swap Community Reuse EventWHEN: February 19th, 12pm-3pmWHERE: Bronx Works Classic Community Center—286 East 156th Street, Bronx, NY 10451 The public is invited to bring clean and reusable items. No one is required to bring something to take something—you can simply show up with a bag and see what’s free for the taking. Books, toys, clothing, and electronics are just some of the offerings. Furniture and other large items are not accepted at the swap. Anything leftover at the end of the day is donated or recycled.Stop ‘N’ Swaps have developed a regular following among environmentally conscious New Yorkers. After almost two years without swaps, GrowNYC has set a goal of hosting one swap in each of the city’s 59 communitydistricts each year, providing opportunities to make NYC truly livable—a place where every person can enjoy a healthier life.21.What should you do to get more information from Catherine?A.Call (646)530-0381.B.Call (718)809-1603.C..D.Visit 286 East 156th Street, Bronx.22.What items are unacceptable at the Stop ‘N’ Swap?A.Dry-as-dust books.B.Old-fashioned clothes.C.Out-of-date electronics.D.Second-hand furniture.23.What is the aim of GrowNYC’s Stop ‘N’ Swaps?A.To make NYC a better place to live.B.To enrich New Yorkers’ community life.C.To reduce the cost of dealing with waste in NYC.D.To encourage districts to compete in sustainability.BAt first look, the playground at the Children’s Guild-Transformation Academy in Baltimore, Maryland, looks like any other. It has swings, slides, and places for children to climb and crawl. But the playground is not just a place for fun. It is also a place where students can learn, grow and gain independence. Everything—from the kind of surface it sits on, to the color of its sitting areas, to the placement of the surrounding fence—is specifically designed for kids with autism(自闭症).Mark Rapaport is the managing director of autism services at the Transformation Academy. He said the school accepts students aged 5 to 21 with autism spectrum disorder (ASD) and are lower functioning.Rapaport said the goal of Transformation Academy is to make the students as independent as possible in an effort to help them prepare for adult life. The school aims to provide help with developing communication and social skills, as well as practical abilities like cleaning or cooking.The playground designed by Maryland company rks@Play, using structures manufactured by Landscape Structures, Inc., took a month to develop, said Dan Hack. He works for rks@Play and helped lead the playground’s design. Hack said he and others spent weeks getting to know the students and understanding their needs before any building was started. The design process involved physical therapists, occupational therapists, and other specialists. The huge $500,000 project was funded with support from the state of Maryland and the nonprofit Orokawa Foundation.Parts of the playground that seem small are very important for children with autism and other disabilities. The surrounding fence extends into a wooded area to make it seem more open. And the ground under the play areas is made of soft, but solid materials to support students using wheelchairsor crutches. The benches on the outside of the playground look simple from far away, but are “one of our most inclusive sensory” elements, Hack said. They have many different colors that bring about feelings of calm and curiosity. They are also made with smooth material that can be felt and moved. The academy’s Rapaport said if a child starts to feel uneasy, they can sit down and feel the bench, which can help them relax.24.Why is the playground in Baltimore designed with special materials?A.To make it superior to other playgrounds.B.To better serve children with autism.C.To improve the quality of the playground.D.To make it easier for kids to climb and crawl.25.What can we learn from the playground project?A.It took a month to complete the project.B.The design process is simple and easy.C.The result of the project is uncertain.D.It’s a money-consuming project.26.What is the last paragraph mainly about?A.The scale and the structure of the playground.B.Ways for kids to free from the stress and relax themselves.C.The underlying logic and reasonable factors of the playground.D.The advantages of the playground for autism and disabled kids.27.Which best describes the playground in Baltimore?A.Advanced.B.Environmental-friendly.C.Functional.D.Convenient.CNew findings suggest that when it comes to learning, the snake may be quite a bit like humans. David Holtzman, a scientist at the University of Rochester, has found that snakes have a much greater capacity for learning than earlier studies had indicated.Holtzman’s study challenged 24 snakes to escape from a black plastic container the size of a child’s pool. Cards mounted on the container’s walls and tape on its floor provided the snakes with visual and touchable signals to find their goal: holes in the container’s bottom that offer a dark, comfortable spot to hide.Simply falling into a hole isn’t the only proof that the snakes are learning something, though. “Speed to find that goal is one of the measures which shows they’re learning,” Holtzman says. “On average, they take over 700 seconds to find the correct hole on the first day of training, and then go down to about 400 seconds by the fourth day of training. Some are actually very fast and find it in less than 30 seconds.”Studies dating back to the 1950s interpreted snakes’ awkwardness with mazes(迷宫) as a poorreflection on their intelligence. “Early attempts to study snake intelligence were problematic because the studies used mazes as testing arenas(场地)——as though snakes might be expected to run through mazes in the same way mice run through mazes,” says Peter Kareiva, a professor of zoology. “Snakes do not encounter anything like mazes in nature, and they do not learn how to run mazes in laboratory conditions.”Holtzman also found a few age-based differences in the signals the snakes use. Young snakes appear to be more adaptable and resourceful, using a variety of clues to find their way to the exit. But their elders seem to rely much more heavily on visual clues. “Actually, one of the amazing findings from our studies is that snakes do use vision in locating places,” says Holtzman. “They don’t just rely on the chemical clues picked up by sticking their tongues out, as many snake biologists assume.”28.What is the function of the cards and tape?A.To direct the snakes to the exits.B.To protect the snakes from bright lights.C.To cover the holes at the container’s bottom.D.To make the container a comfortable spot to stay.29.What do the data in paragraph 3 show about the snakes according to Holtzman?A.They are skillful escapers.B.They are good learners.C.They communicate with each other.D.They adapt to environments quickly.30.What was the problem with early attempts to study snake intelligence?A.They chose the wrong testing arenas.B.They failed to do tests in laboratory conditions.C.They referred to studies dating back to the 1950s.D.They compared snakes with a different kind of animal.31.What astonishes Holtzman about snakes?A.They rely on sight to find their way.B.They leave chemical clues everywhere.C.The young beat their elders in many ways.D.Their tongues are unable to recognize chemical clues.DResearch led by ecologist Bart Hoekstra of the University of Amsterdam shows that birds are affected by the mass use of fireworks on New Year’s Eve up to a distance of 10km (6 miles) away.With data from weather radars and bird counts an international team of researchers revealed how many birds take off immediately after the start of the fireworks, at what distance from fireworksthis occurs and which species groups mainly react.“Birds take off as a result of an acute flight response due to sudden noise and light. We already knew that many water birds react strongly, but now we also see the effect on other birds throughout the Netherlands,” says ecologist Bart Hoekstra of the University of Amsterdam. In the scientific journal Frontier s in Ecology and the Environment, he researchers therefore argue for large fireworks-free zones.Last year, other researchers at IBED discovered that geese are so affected by fireworks that they spend an average of 10% longer looking for food than normal during at least the next 11 days. They apparently need that time to restore their energy to their former condition, after fleeing from the fireworks.Because 62% of all birds in the Netherlands live within a radius of 2.5 km of inhabited areas, the consequences of fireworks are high for all birds throughout the country. “Flying requires a lot of energy, so ideally birds should be disturbed as little as possible during the cold winter months. Measures to ensure this are especially important in open areas such as grasslands, where many larger birds spend the winter. The effects of fireworks on birds are less pronounced near forests and semi-open habitats. In addition, smaller birds such as tits and finches live there, which are less likely to fly away from disturbance.”The authors argue for fireworks-free zones in areas where large birds live. Hoekstra: “These buffer zones could be smaller in areas where light and sound travel less far, such as near forests. Furthermore, fireworks should mainly be lit at central locations in built-up areas, as far away from birds as possible. It would be best for birds if we moved towards light shows without sound, such as drone shows or decorative fireworks without very loud bangs.”32.What can we learn about the research?A.It’s the first one about fireworks’ effects on birds.B.It’s conducted by collecting data from weather radars.C.It shows the extent of the fireworks’ influence on birds.D.It keeps track of birds throughout Netherlands and beyond.33.Why did geese spend more time looking for food?A.To find a place without fireworks.B.To store more food in case.C.To find a new source of energy.D.To make up for the lost energy.34.What does the underlined word “pronounced” in Para.4mean?A.Predictable.B.Noticeable.C.Admirable.D.Avoidable.35.What can be the best title for the passage?A.Fireworks in the world B.Fireworks-free zonesThese problems will drive you mad.in New York. One afternoon, I 41 a train with a load of hot-off-the-press catalogues(目录簿), our first to list every one of our titles. I was on my way to 42 my aunt, who’d agreed to 43 them to her friends.Back then, I was much less 44 ; somehow I made it on the train but I hadn’t had time to buya 45 . I figured I’d buy one on board. When the conductor came to stand next to me, I opened my46 and found nothing inside. They didn’t 47 credit cards back then. I was told to get off at the next station. 48 , the man next to me handed $15 to the conductor. I was beyond grateful and 49 : I promised him I would send him a check, which he 50 . I made him write down his address, though.Later, I wrote a check, 51 it in a letter, and sent it off. I expressed my 52 again and included my email address. Soon he emailed me and we 53 a lasting friendship.That 54 action has stayed with me. Thinking about that day, I 55 myself to be much kinder to strangers and to focus on the good in people.41.A.came across B.rushed onto C.passed byD.looked for42.A.visit B.help C.rescueD.introduce43.A.return B.explain C.connectD.distribute44.A.determined B.objective C.organizedD.professional45.A.ticket B.card C.giftD.book46.A.parcel B.wallet C.envelopeD.bottle47.A.cancel B.reject C.provideD.accept48.A.Naturally B.Unexpectedly C.DoubtfullyD.Disagreeably49.A.embarrassed B.disturbed C.annoyedD.dissatisfied50.A.gave away B.checked out C.laughed offD.sent back51.A.lost B.unfolded C.noticedD.enclosed52.A.appreciation B.admiration C.amazementSouthern Lionremember the rule. Share it fair!”答案第二部分:阅读理解第一节(共15小题;每小题2.5分,满分37.5分)21-25 BDABD26-30 CCABA31-35 ACDBC第二节(共5小题;每小题2.5分,满分12.5分)36-40 CEBGD第三部分:语言运用(共两节,满分30分)第一节完形填空(共15小题;每小题1分,满分15分)41-45 BADCA46-50 BDBAC51-55 DACBD第二节(共10小题;每小题1.5分,满分15分)(形式不对不给分)56.dates57.where58.was introduced59.its60.a61.mainly62.like63.combination64.making65.to share第四部分写作(共三节,满分40分)第一节(满分15分)One possible version:Dear Chris,I’m Li Hua, chairman of the School Cooking Club. I’m writing to tell you that we intend to throw a party, featuring “My Specialty Dish” next Saturday night p.m.p.m.p.m. to 8 p.m. at the dining hall. And I sincerely invite you to join us and have some fun.During the party, all participants will cook a “specialty dish” that they are good at and share with everybody how it is made. Then will come the most-anticipated part—everyone sharing these delicious dishes. I’m pretty sure you will enjoy this party very much.Looking forward to your attending.Yours,Li Hua第二节(满分25分)One possible version:First Doobie uses a knife to smooth Duksie’s lines in the icing. Then he draws three lines on the cake. The cake now bears a striking resemblance to the badge of his dad’s vehicle, its three equal parts. Just as the children celebrate their cake-cutting victory, Mama K emerges from her house,bearing a tray with three glasses of strawberry juice. Maya excitedly points out Doobie’s achievement, proudly claiming his master y of fair sharing. Mama K’s eyes shine with delight as she comments the children for their fairness and praises Doobie for his exceptional problem-solving skills.With Mama K’s encouragement, Maya takes charge, expertly cutting along Doobie’s lines to make three equal slices. Each piece falls into place, their sizes perfectly matched. In a playful display of satisfaction, the children put the slices upon one another, witnessing the unity of their equal proportions. The sight brings smiles of joy to their faces. Amidst the children’s laughter, Doobie’s dad pulls up to pick up the children, and Doobie runs off to meet him. He can’t wait to tell his dad how the badge on the truck has helped him to solve a very tricky problem!。
2012年普通高等学校招生全国统一考试(广东卷)A理科综合本试卷共10页,36小题,满分300分。
考试用时150分钟。
可能用到的相对原子质量:H 1 C 12 N 14 O 16 Al 27 S 32 Cl 35.5 K 39 Ca 40一、单项选择题:本大题共16小题,每小题4分,共64分。
在每小题给出的四个选项中,只有一个选项符合题目要求,选对的得4分,选错或不答的得0分。
1.有关生物膜结构与功能的叙述,正确的是A.膜载体蛋白的合成不需要ATPB.葡萄糖跨膜运输不需要载体蛋白C.线粒体外膜与内膜的主要功能不同D.变形虫和草履虫的细胞膜基本组成成分不同2.培育草莓脱毒苗所采用的主要技术是A.组织培养B.细胞杂交C.显微注射D.核移植3.分析下表,可推测注:“+”显色,“++”显色更深;“-”不显色.A.甲溶液含有淀粉酶B.乙溶液含有还原糖C.混合溶液不含淀粉D.混合溶液含有淀粉酶4.有关土壤动物研究的叙述,正确的是A.土壤动物群落不存在分层现象B.土壤动物中间关系主要是互利共生C.土壤盐碱度不同,土壤动物群落结构有差异D.随机扫取表层土取样,可以调查土壤小动物类群丰富度5、有关人体免疫的叙述,正确的是A 机体主要依赖免疫调节维持内环境稳态B 病原微生物侵袭,可引起机体产生特异性免疫C 特异性免疫过程中,只有T 细胞产生记忆细胞D 如果神经中枢受损,机体的特异性免疫功能完全丧失6、科学家用人工合成的染色体片段,成功替代了酵母菌的第6号和第9号染色体的部分片段,得到的重组酵母菌能存活 , 未见明显异常 ,关于该重组酵母菌的叙述,错误的是 A 还可能发生变异 B 表现型仍受环境的影响 C 增加了酵母菌的遗传多样性 D 改变了酵母菌的进化方向7、化学与生活息息相关,下列说法不正确的是 A 用食醋可除去热水壶内壁的水垢 B 淀粉,油脂 和蛋白质都是高分子化合物 C 自行车钢价生锈主要是电化学腐蚀所致D 新型复合材料使用手机,电脑能电子产品更轻巧,使用和新潮 8、在水溶液中能大量共存的一组是A 2e F + 3Al + C l O -Cl - B K + 2C u + OH - 3N O -C 4N H + N a + B r - 24SO -D 2M g + H + 23S i O - 24SO - 9 下列实验能达到目的的是 A 用溴水鉴别苯和正己烷B 用BaCl 2溶液鉴别24SO - 和 23SO -C 用浓HNO 3与Cu 反应制备NO 2D 将混有HCL 的Cl 2通入饱和NaHCO 3溶液中除去HCl 10 、下列应用不涉及氧化还原反应的是A Na 2O 2用作呼吸面具的供氧剂B 工业上电解熔融状态Al 2O 3制备AlC 工业上利用合成氨实现人工固氮D 实验室用NH 4Cl 和Ca(OH)2制备NH 3 11、设n A 为阿伏伽德罗常数的数值 ,下列说法正确的是 A 常温下,4gCH 4 含有n A 个C-H 共价键B 1 mol Fe 与总量的稀HNO 3 反应,转移2 n A 个电子C 1 L 0.1 mol ·1L -NaHCO 3液含有0.1n A 个HCO 3D 常温常压下,22.4L 的NO 2 和CO 2合气体含有2 n A 个O 原子12、下列陈述ⅠⅡ正确并且有因果关系的是13、清晨,草叶上的露珠是由空气中的水汽凝结成德水珠,这一物理过程中,水分子间的A 引力消失,斥力增大,B 斥力消失,引力增大C 引力、斥力都减小D 引力、斥力都增大14.景颇族的祖先发明的点火器如图1所示,用牛角做套筒,木质推杆前端粘着艾绒。
2012梅州市高三总复习第一次质检试卷--语文一、本大题4小题,每小题3分,共12分。
⒈下列词语中加点的字,每对读音都不相同的一组是A.悱.恻/斐.然弹劾./遗骸.哄.抢/哄.堂B.噱.头/戏谑.提挈./地契.济.济/济.世C.癖.好/譬.如蓦.然/粮秣.拮据./根据.D.逡.巡/钦.慕嬗.变/赡.养偏裨./裨.益⒉下面语段中加点的词语,使用不恰当的一项是三聚氰胺、苏丹红、地沟油、漂白蘑菇……层出不穷....的食品安全事件完全超出人们的想象,商家不可信,专家能信吗? 但近年来,近似于骗子的“养生专家”、被发现收了企业红包的“代言人专家”以及说出类似“北京交通拥堵的原因是自行车太多了”等匪夷所思....言论的专家,实在让人失望。
甚至,对一些“官方说法”“官方澄清”,人们也开始将信将疑....。
最典型的当数每年统计部门公布的平均工资水平及收入增长速度,几乎一边倒地遭到置疑..。
A.层出不穷 B.匪夷所思 C.将信将疑 D.置疑⒊下列句子中,没有语病的一项是A.针对该地区严峻的毒品犯罪形势,四国联合巡逻执法将把打击跨国毒品犯罪作为重要任务之一。
B.“贾君鹏,你妈妈喊你吃饭”这个帖子可能因为太好玩了,很快网友们转至各大网站,很多不明真相的网友纷纷问“贾君鹏是何许人也”,但没有任何人出来解答。
C.老百姓对一个政党评价的好坏,最大的因素就是腐败。
对病人来说,治不好肿瘤保不住性命;对政党而言,治不了腐败保不住政权。
D.“新生代农民工”自从被列入政府重点关注的对象之后,各级政府积极行动,将关心新生代农民工成长作为新一年度工作重点。
⒋把下列句子组成语意连贯的语段,排序最恰当的一项是①在后工业化的时代,人类正在步入一个“风险社会”②它是人类发展、特别是科技进步造成的③这是权力的基本职责所在,更是职业的底线道德所在④为大发展、大跨越欢呼时,社会管理者尤其需要保持警惕、完善制度⑤做好应对“文明的风险”的准备⑥这样的风险更多地来自人类自身,是所谓“人造风险”或“文明的风险”⑦种种事故验证了德国社会学家贝克一个这样的结论A.⑦②⑥①④⑤③ B.①⑥④⑤③⑦② C.⑦①⑥②④⑤③ D.①②④⑤⑥⑦③二、本大题7小题,共35分。
文学类文本阅读专题广东省梅州市2021届高三5月总复习质检语文试卷(二)现代文阅读Ⅱ(本题共4小题,16分)阅读下面的文字,完成6~9题。
蟋蟀葫芦①水上勉②三年前的冬天老舍先生曾光临舍下。
日中文化交流协会办事处打电话来说,正在访日的老舍先生想到我家来拜访,问我方便不方便。
③我说,请原谅,我对中国的情况一无所知,老舍先生我也不大熟悉,他的地位究竟相当于日本的哪一位作家呢?那个人告诉我,老舍先生在中国已是文坛泰斗了,地位相当于日本的志贺直哉④。
我那攥着听筒的手颤抖起来。
我家很少有贵客临门,顿时紧张起来。
三天后,老舍先生偕同一位高个子、长脸的中年作家,带着一位女翻译到舍下来了。
我乍一看到老舍先生,吃了一惊。
因为他给我的印象是那么质朴,像是个农村出身的人。
也许是旅途劳累的关系,他的脸色不大好。
他在门口脱下淡褐色夹大衣,里面穿的西服不怎么讲究。
略旧的深蓝色裤子不够笔挺,虽结着黑领带,衬衫的领口却随随便便,我总觉得先生的外貌有点儿像我那位在若狭去世的叔叔。
我松了口气,紧张情绪顿时消失,就把先生迎入客厅。
老舍先生在沙发上坐下来,胳膊肘放在扶手上,弓着背,定睛看着我。
大概那位女翻译已经向他介绍过我的情况,他眼睛里流露出和蔼可亲的神色,为突然造访而向我表示歉意。
说实在的,和老舍先生会面,我想向他请教一下蟋蟀葫芦的事。
先生默默地定睛看着我。
我毕恭毕敬地问道:“老舍先生,我看到过一个据说是从中国的旧货铺买来的葫芦。
似乎是养蟋蟀用的,让它们相斗来解闷。
中国是不是从前就有这样的习俗呢?”“有过的。
”老舍先生通过翻译回答道,他的表情好像一瞬间略为严肃了。
“那么,今天……民间还有这个习俗吗?”“不,那是过去的事。
您见到的罐子,恐怕也有年头了吧?”“老舍先生,我生在日本的若狭这个地方,小时候养蜘蛛玩过。
蜘蛛天生好斗,打得可欢啦,看着挺有趣儿……蟋蟀也像蜘蛛那样好斗吗?”“好斗。
中国的诸侯在近臣中设专人饲养蟋蟀,并且以斗蟋蟀取乐。
梅州高三数学试题及答案一、选择题(每题4分,共40分)1. 若函数f(x)=\(\sin x + \sqrt{3}\cos x\),则f(π/6)的值为:A. \(\sqrt{3}\)B. \(\sqrt{2}\)C. 2D. 32. 已知数列{an}满足a1=1,an+1=2an+1,求a5的值为:A. 15B. 31C. 63D. 1273. 若直线l:y=2x+b与椭圆C:x^2/4 + y^2/2 = 1相交于点A和点B,且AB的中点为(1,1),则b的值为:A. 0B. 2C. -2D. -44. 对于双曲线x^2/a^2 - y^2/b^2 = 1,若其渐近线方程为y=±(b/a)x,则双曲线的离心率为:A. \(\sqrt{2}\)B. \(\sqrt{3}\)C. 2D. 35. 已知函数f(x)=x^3-3x+1,求f'(x)的导数为:A. 3x^2-3B. x^2-3x+1C. 3x^2+3x-3D. x^3-3x^2+16. 若向量a=(2,-1),向量b=(-1,2),则向量a与向量b的点积为:A. -3B. 3C. -1D. 17. 已知三角形ABC的内角A、B、C满足A+B=2C,且sinA=2sinBsinC,则三角形ABC的面积为:A. \(\frac{1}{2}\)B. \(\frac{\sqrt{3}}{2}\)C. \(\frac{\sqrt{2}}{2}\)D. \(\frac{\sqrt{6}}{2}\)8. 对于函数f(x)=\(\frac{1}{x}\),若f(2x)=2f(x),则x的值为:A. 1B. -1C. 2D. -29. 若复数z满足|z|=1,且z的实部为1/2,则z的虚部为:A. \(\frac{\sqrt{3}}{2}\)B. \(-\frac{\sqrt{3}}{2}\)C. \(\frac{1}{2}\)D. \(-\frac{1}{2}\)10. 已知等比数列{an}的前三项和为7,且a2=2,则该数列的公比q 为:A. 2B. \(\frac{1}{2}\)C. 3D. \(\frac{1}{3}\)二、填空题(每题4分,共20分)11. 已知等差数列{an}的前n项和为Sn,若S5=75,则a3的值为______。
梅州市高三总复习质检试卷(2013.5)数学(理科)一、选择题(40分)1、已知集合A ={3,2a },集合B ={3,b ,1-a },A B ={1},则A B =A 、{0,1,3}B 、{1,2,4}C 、{0,1,2,3}D 、{0,1,2,3,4} 2、复数11z i=-(i 为虚数单位)的共轭复数z 是 A 、1-i B 、1+i C 、1122i + D 、1122i - 3、为了研究一片大约一万株树木的生长情况,随机测量了其中100株树木的底部周长(单位:cm ),根据所得数据画出的样本频率分布直方图如图,那么在这片树木中底部周长大于100cm 的株树大约中A 、3000B 、6000C 、7000D 、80004、已知a =(-3,2),b =(-1,1),向量λa +b与a -2b 垂直,则实数λ的值为A 、-17B 、17C 、-16D 、165、下列曲线中,离心率为62的是 A 、22124x y -= B 、22142x y -= C 、22146x y -= D 、22164x y -= 6、函数f (x )=x |x +a |+b 是奇函数的充要条件是A 、a ·b =0B 、a +b =0C 、a 2+b 2=0D 、a =b7、一个三棱锥的三视图是三个直角三角形,如图所示,则该三棱锥的外接球表面积为A 、29πB 、30πC 、292π D 、216π8、若m 是一个给定的正整数,如果两个整数a 、b 用m 除所得的余数相同,则称a 与b 对m 校同余,记作例如:,则r 可能为 A 、5 B 、4 C 、3 D 、2二、填空题(30分)(一)必做题(9-13题)9、函数12log 2x y =+的定义域是_____10、右边是一个算法的程序框图,当输入的值x 为5时,则其输出的结果是____11、已知x ,y 满足2420x x y x y c ≥⎧⎪+≤⎨⎪-++≥⎩,且目标函数z =3x +y 的最小值为5,则c 的值为____12、不等|x +3|-|x -1|≤a 2-3a 对任意实数x 恒成立,则实数a 的取值范围为____13、已知,则由函数f (x )的图像与x 轴、直线x =e 所围成的封闭图形的面积为____(二)选做题(14、15题)14、(坐标与参数方程选做题)在极坐标中,已知点P 为方程(cos sin )1ρθθ+=所表示的曲线上上一动点(2,)3Q π,则|PQ |的最小值为___15、(几何证明选讲选做题)如图,PA 切圆O 于点A ,割线PBC 经过圆心O ,OB =PB =1,OA 绕点O 逆时针旋转60°到OD ,则PD 的长为____三、解答题(80分)16、(本小题满分12分) 已知函数2()2cos 23sin cos f x x x x =+。
试卷类型:B
梅州市高三总复习质检试卷(2012.5)
数学(文科)
一、选择题:本大题共10个小题,每小题5分,满分50分.在每小题给出的四个选项中,
只有一项是符合题目要求的. 1.设,a b ∈R ,若复数12i
1i
z +=
+,则z 在复平面上对应的点在 A .第一象限 B .第二象限 C .第三象限 D .第四象限
2.已知集合3
{0},{3}1
x M x N x x x +=<=--…,则集合{1}x x …等于 A .M N B .M N C .()M N R ð D .()M N R ð 3.设,b c 表示两条直线,,αβ表示两个平面,下列命题中的真命题是
A .b b c c αα⊂⎫⇒⎬⎭
B .b c b c αα⊂⎫⇒⎬⎭
C .c c ααββ⎫⇒⊥⎬⊥⎭
D .c c αβαβ⎫⇒⊥⎬⊥⎭
4.设0ω>,函数sin(3y x πω=+的图象向右平移43
π
个单位后与原图象重合,则ω的最
小值为 A .
23 B .43 C .3
2
D .3 5.平面向量,a b 共线的充要条件是
A .,a b 方向相同
B .,a b 两向量中至少有一个为零向量
C .,b λλ∃∈=R a
D .存在不全为零的实数12,λλ,12λλ+=0a b
6.以双曲线2
213
x y -=的左焦点为焦点,顶点在原点的抛物线方程是
A .24y x =
B .24y x =- C
.2y =- D .28y x =-
7.函数x x
x x
e e y e e --+=-的图象大致为
A .
B .
C .
D .
x
x
8.在区间[,22ππ
-
上随机取一个数,cos x x 的值介于于0到1
2之间的概率为 A .13 B .2π
C .12
D .23
9.己知函数()f x 是(,)-∞+∞上的偶函数,若对于0x …,都有 (2)()f x f x +=,且当
0,2x ∈[)
时,2()log (1)f x x =+,则(2008)(2009)f f -+的值为 A .2- B .1- C .1 D .2
10.设G 是一个至少含有两个数的数集,若对任意,a b G ∈,都有,,,
a
a b a b ab G b
+-∈(除数0b ≠),则称G 是一个数域,例如有理数集Q 是数域.有下列命题:①数域必含有0,1两个数;②整数集是数域;③若有理数集M ⊆Q ,则数集M 必为数域;④数域必为无限集.其中正确命题的个数是
A .1个
B .2个
C .3个
D .4个 二、填空题:本大题共5小题,考生作答4小题,每小题5分,满分20分.
(一)必做题(11~13小题) 11.若0x >,则2
x x
+
的最小值为 . 12.执行如图所示的程序框图,若输入x =10 ,则输出y 的值为 .
13.设等差数列{}n a 的前n 项和为n S ,若972S =,则
249a a a ++= .
(二)选做题(14、15题,考生只能从中选做一题) 14.(坐标系与参数方程选做题)在极坐标系中,直线
cos(24
π
ρθ-=与圆4ρ=的交点个数为 .
15.(几何证明选讲选做题)如图所示,过O 外一点P 直线与O 交于,A B 两点,己知弦6AB =,点P 到O 线长4,PT =则PA = .
三、解答题:本大题共6个小题,满分80分.解答应写出文字说明,证明过程或演算步骤. 16.(本小题满分12分)
己知点(1,0),(0,1),(2sin cos )A B C θθ,
. (1)若(2)1OA OB OC +=,其中O 为坐标原点,求sin 2θ的值; (2)若||||AC BC =,且θ在第三象限.求sin()3
π
θ+值.
O 第15题图
一个社会调查机构就某社区居民的月收入调查了10 000人,并根据所得数据画了样本的频率分布直方图(如图).
(1)为了分析居民的收入与年龄、学历、职业等方面的关系,要从这10 000人中再用分层抽样方法抽出100人作进一步调查,求月收入在[1500,2000)(元)段应抽出的人数;
(2)估计该社区居民月收人的平均数;
(3)为了估计该社区3个居民中恰有2个月收入在
[2000,3000)(元)的概率,采用随机模拟的方法:先由计算器算出0到9之间取整数值的
随机数,我们用0,1,2,3,…表示收入在[2000,3000)(元)的居民,剩余的数字表示月收入不在[2000,3000)(元)的居民;再以每三个随机数为一组,代表统计的结果,经随机模拟产生了20组随机数如下:
907 966 191 925 271 932 812 458 569 683 431 257 393 027 556 488 730 113 537 989
据此估计,计算该社区3个居民中恰好有2个月收入在[2000,3000)(元)的概率.
第17题图
已知直三棱柱111ABC A B C -的三视图如图所示; (1)求此三棱柱的体积和表面积;
(2)画出此三棱柱,并证明:11AC AB ⊥
19.(本小题14分)
己知椭圆2222:1(0)x y C a b
b +=>>,不等式||||1x y a b +…所表示的平面区域的面积为.
(1)求椭圆C 的方程;
(2)设椭圆C 的左项点为A ,上顶点为B ,圆M 过A B 、两点.当圆心M 与原点O 的
距离最小时,求圆M
的方程.
第18题图
正视图
侧视图俯视图
20.(本小题14分)
定义在R 上的函数()f x 满足:( ) ()()f x y f x f y += ,且当0x >时,()1f x >. (1)求(0)f 的值,并证明()f x 是定义域上的增函数:
(2)数列{}n a 满足10a a =≠,1()()(1)(1,2,3,)n n f a f aa f a n +=-=⋯,求数列{}n a 的 通项公式及前n 项和n S .
21.(本小题14分)
已知函数()ln f x x ax =-.
(1)当1a =时,求()f x 的最大值; (2)试讨论函数()y f x =的零点情况;
(3)设,,(1,2,,)
k k a b k n =均为正数,若112212n n n a b a b a b b b b ++++++…,
求证:12
121n b b
b
n a a a ⋅….。