选择填空限时练(四)
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小学数学限时练习题一、选择题1. 下列哪个图形是四边形?A. 圆形B. 三角形C. 正方形D. 椭圆形2. 如果1个苹果=8元,那么5个苹果加2个苹果等于多少元?A. 48元B. 50元C. 56元D. 58元3. 以下哪个数是奇数?A. 20B. 31C. 42D. 544. 把18分解成几个连续的自然数之和?A. 4个B. 5个C. 6个D. 7个5. 如下图所示,小军从点A出发,依次经过B、C、D、E、F、G、H、I、J,到达点K。
请问他走了多少条边?(图形略)A. 6B. 7C. 8D. 9二、填空题1. 25 ÷ 5 = ______2. 小明家里有6个苹果,他吃掉了2个,还剩下______个。
3. 向下取整:13.7 = ______4. 从1到10数字的和是______。
5. 请计算以下数列的下一个数:2, 4, 6, 8, ______三、解答题1. 两只小猫的体重分别是2千克和3千克,请问它们的总体重是多少千克?2. 一个图书馆里有250本书,其中的三分之一是关于科学的书籍,其他的书籍是三分之一是有关历史的书籍,还有50本是关于文学的书籍。
请问图书馆里有多少本有关历史的书籍?3. 一个教室里有40个学生,其中的四分之一是女生。
请问有多少个男生?4. 请写出4的10次方的值。
5. 请用算式表示出以下问题的答案并计算:小明有8本书,他借给了2个同学各2本书,还剩下几本书?这些题目的答案如下:一、选择题1. C2. A3. B4. B5. C二、填空题1. 52. 43. 134. 555. 10三、解答题1. 5千克2. 75本3. 30个4. 10,0005. 2希望这些练习题对你的数学学习有所帮助。
如果还有其他问题,欢迎随时向我提问。
祝你学习进步!。
选择题限时练(四)(限时:40分钟)太阳辐照度是指太阳辐射经过大气层的吸收、散射、反射等作用后到达固体地球表面单位面积、单位时间内的辐射能量,是影响太阳能光伏电站输出功率的最直接、最显著的因素。
某研究小组测量制得广西桂林某时段(北京时间)不同天气状况下太阳辐照度变化曲线图。
据此完成1~3题。
1.该时段最接近()A.元宵节B.妇女节C.端午节D.国庆节2.曲线④代表的天气状况最有可能是()A.晴天B.阴转晴C.阴天D.多云3.为了保证电力系统的稳定供电,太阳能光伏电站可以配合建设的电站是()A.火电站B.水电站C.潮汐电站D.风力电站(2021·山东烟台二模)“空屋”是指长时间无人居住和打理的闲置房屋。
过去,日本的空屋大多出现在农村地区。
后来,即便在东京等大城市,空屋也越来越多。
2013年日本境内“空屋”达820万所,占全国房产总数的13.5%,有研究机构称,2033年日本空置房屋比例将升至20%。
为此,日本政府制定了“空屋银行”政策,以低价甚至免费形式鼓励人们入住乡镇空置房屋。
据此完成4~5题。
4.过去,日本的“空屋”大多出现在农村地区的主要原因是()A.本国人口迁往国外B.人口死亡率升高C.房屋简陋寿命较短D.城镇化的发展5.导致东京等大城市的“空屋”越来越多的主要原因有()①社会养老机构发达②受逆城市化影响③大城市房价高④老龄化严重,老龄人口死亡率高A.①②B.①③C.①④D.②④等时间交通图集时间与空间两个维度为一体,一般指从中心地出发,在单位时间内能够到达的空间范围。
读我国某城市市内交通1小时交通圈示意图,完成6~7题。
6.据图判断,该城市所在区域的环境特征最可能是()A.地势崎岖B.河流穿城而过C.东南部为山地D.气候干旱7.图示地区出现两块“时间飞地”,其布局最可信的是()A.地铁站B.高教园区C.中央商务区D.生态保护区(2021·山东济宁二模)某科研小组,对内蒙古乌兰布和沙漠中一绿洲防护林[(40°N,106°E)附近]进行小气候研究。
第四单元第1课社会危机四伏和庆历新政一、选择题(每小题2.5分,共75分)1.公元997年,宋廷岁收2 200多万缗,收支相抵还余大半;到王安石变法前两年,收入已高达11 000多万缗,收支却亏1 500多万缗,“民贫乏食”而反。
造成这种统治危机的根源是( )A.经济衰退B.起义频繁C.兵力不足D.吏治腐败2.(2012·九江高二检测)北宋统治者经常换防各地驻屯的军队,其主要目的是为了( )A.增强军队战斗力B.防止地方专权C.加强禁军D.防止武将专权3.北宋诗人苏舜卿曾这样描述:“游嬉于廛市间,以鬻巧绣画为业,衣服举措不类军兵。
”另一位北宋文士宋祁形容说:“卫兵入宿,不自持被,而使人持之;禁兵给粮不自荷,而雇人荷之。
”上述材料突出反映了北宋中期面临哪一社会问题( )A.冗官B.冗兵C.积贫D.积弱4.北宋中期,“三冗”问题出现的主要原因有( )①宋初为加强中央集权,增设官僚机构以分化各级官员权力②形成庞大军事体系,军费开支增加③对辽和西夏的战争耗费和高额赔款④地主兼并土地,隐瞒田产,逃避税收A.①②③④B.①③④C.①②④D.①②③5.北宋皇权的空前强化所产生的影响包括( )①皇权得到巩固②军队战斗力加强③政府工作效率提高④政府财政负担过重A.①②B.②③C.③④D.①④6.北宋政府过分集权所带来的恶果有( )①政府机构重叠,行政效率低下②官员冗滥,国家财政开支增大③军队指挥不灵,战斗力下降④地方财政困难,物质基础薄弱A.①②③B.②③④C.①③④D.①②③④7.范仲淹主持的庆历新政的中心内容是( )A.加强军队训练B.整顿吏治C.限制官僚特权D.改革科举制度8.庆历新政的失败在一定程度上说明( )A.北宋统治阶级内部矛盾十分尖锐B.北宋王朝十分腐朽C.变法内容不尽合理D.变法没有顺应历史潮流9.(2012·洛阳高二检测)对北宋中期形势的表述,正确的是( )①社会经济停滞不前②阶级矛盾尖锐③民族间矛盾尖锐④统治集团内部矛盾尖锐A.①②③B.②③④C.①②④D.①②③④10.北宋初年,宋太祖加强中央集权主要是因为()A.陈桥兵变B.五代的频繁更替C.唐末农民战争D.唐后期藩镇割据11.北宋前期统治者认为“富者田连阡陌,为国守财尔。
高中数学专题复习《平面解析几何三角形、圆相关》单元过关检测经典荟萃,匠心巨制!独家原创,欢迎下载!注意事项:1.答题前填写好自己的姓名、班级、考号等信息 2.请将答案正确填写在答题卡上 评卷人得分一、填空题1.如图,在ABC 中,090C ∠=, 060,20A AB ∠==,过C 作ABC 的外接圆的切线CD ,BD CD ⊥,BD 与外接圆交于点E ,则DE 的长为__________(汇编年普通高等学校招生统一考试重庆数学(理)试题(含答案))2.如图3,圆O 的半径为5cm ,点P 是弦AB 的中点,3OP =cm ,弦CD 过点P ,且13CP CD =,则CD 的长为 cm .(几何证明选讲选做题)评卷人得分二、解答题3.选修4—1 几何证明选讲P OAB C D图3如图,已知⊙O 的半径为1,MN 是⊙O 的直径,过M 点作⊙O 的切线AM ,C 是AM 的中点,AN 交⊙O 于B 点,若四边形BCON 是平行四边形.求AM 的长;4.如图,圆1O 与圆2O 内切于点A ,其半径分别为1r 与212()r r r >, 圆1O 的弦AB 交圆2O 于点C (1O 不在AB 上), 求证::AB AC 为定值。
证明:由弦切角定理可得11212,O B r AB AO CAO B AC O C r∴== 5.过圆O 外一点A 作圆O 的两条切线AT 、AS ,切点分别为T 、S ,过点A 作圆O 的割线APN ,证明:22AT PT PSAN NT NS=.[来源:学科网ZXXK] (汇编年3月苏、锡、常、镇四市高三数学教学情况调查一) 证明:AT 是圆O 的切线,∠ATP =∠ANT ,又∠TAP =∠NAT ,∴三角形ATP 与三角形ANT ,∴AT PT AN TN =同理AS PSAN NS= 两等式相乘222,AT AS PT PSAT PT PS AT AS AN NT NSAN NT NS∙∙∙==∴=∙∙. 6.已知:如图,在△ABC 中,∠ABC =90°,O 是AB 上一点,以O 为圆心,OB 为半径的圆与AB 交于点E,与21-A 第图AC 切于点D ,连结DB 、DE 、OC 。
限时组合练(四)限时:60分钟 总分:100分第一部分 阅读理解(共两节,满分35分)第一节(共10小题;每小题2.5分,满分25分) 阅读下列短文,从每题所给的A、B、C和D四个选项中,选出最佳选项。
A(2019山东潍坊三月一模,B)Hawking was perhaps the most famous scientist in the world when he died in 2018 at age 76.His 1988 book, A Brief History of Time, sold ten million copies and made him an unlikely superstar even to people who sweated over high school science.Humor was always a big part of Hawking's effort to bring physics to the masses. In his 2010 book, The Grand Design, for instance, he recounts how, in 1277, the Catholic Church declared scientific laws such as gravity to be wrong, since they seemed against God's idea.“Interestingly,”the text adds jokingly, “Pope John was killed by the effects of the law of gravity a few months later when the roof of his palace fell in on him.”Hawking was only 21 when he was diagnosed with the disease ALS. For most people, the condition would have been a disaster. But Hawking rolled over hardship as if it were just a pebble under his wheelchair.“Life would be tragic,”he once said, “if it weren't funny.”He kept smiling even though he spent more than 50 years in a wheelchair.“He loved adventure and fun,”says Mlodinow, who once took Hawking on a punt-boat trip down the River Cam in Cambridge, England, despite the obvious danger of the boat turning over.“You know about when he went on the Vomit Comet? It's a plane that flies in a parabolic(抛物线的)path so you are weightless, like you are in space. A lot of people vomit, but he loved that sort of thing.”And he was 65 at the time.Hawking's greatest hit, humor-wise, was probably the cocktail party he threw in 2009. It was a “welcome reception for future time travelers,”he said, so naturally, he sent out the invitations the day after the party. No one showed up yet. “Maybe one daysomeone living in the future will find the information and use a wormhole time machine to come back to my party, proving that time travel will one day be possible,” Hawking explained. And if that happens, don't be surprised if Hawking is there too. After all, he never missed a chance to have fun.1.What can we learn about Pope John?A.He was not in favor of God.B.He was a scientist like Hawking.C.He was opposed to the law of gravity.D.He was killed due to the discovery of gravity.2.What drove Hawking to go on the Vomit Comet?A.His fondness of adventure.B.The invitation from his friend.C.The requirements of his work.D.His desire for recovery from ALS.3.What can be inferred from the last paragraph?A.The cocktail party was a great success.B.The possibility of time travel was not proved.C.Hawking was a man who enjoyed holding parties.D.The wormhole time machine was used at that time.答案 [语篇解读] 本文为人物介绍类记叙文。
金陵中学河西分校八(上)英语限时训练(四)一、选择填空(每小题1分,共15分)1. — What did you and your friends buy in the shop this afternoon?— ________. ________ of us had money for anything.A. Nothing; NoneB. None; No oneC. Nothing; NobodyD. None; Nothing2. — Listen! What's the noise outside?— It________ be some children playing football. But I'm not quite sure.A. mayB. mustC. shouldD. would3. — Could you please ________ here? There are many kids playing here.— Sorry, I didn't know that.A. to smokeB. not to smokeC. smokeD. not smoke4. My parents agreed ________ me ________ at home alone when they were away.A. to let; to stayB. letting; stayC. to let; stayD. letting; to stay5. The boy is so smart that he can ________ many difficult maths problems correctly.A. put outB. cut outC. work outD. give out6. —How is Susan now?— I hear a famous company her with a job, but she refused it.A. preventedB. offeredC. providedD. introduced7. — Not all people coming here are real bird lovers.— Yeah. Some try to make the place a better area ________ others just bring trouble.A. soB. becauseC. whileD. moreover8. — Is Jack good at singing?— Yes, we can often hear him ________ in the classroom.A. singB. singsC. to singD. singing9. Spring Bud Project is an organization that raises money ________ poor young girls return to school.A. helpingB. to helpC. invitingD. to inviteA. on; atB. on; inC. at; onD. at; in11. It snowed heavily last night. Grandpa made a snowman ________ the children in the morning.A. surpriseB. surprisedC. to surpriseD. surprising12. Our teacher often tells us ________ when we have trouble ________ a problem.A. to give up; solvingB. not to give up; working outC. to give up; to work outD. not to give up; to solve13. As is known to all, about seventy-five ________ of the earth ________ covered with water.A. per cent; areB. per cent; isC. per cents; areD. per cents; is14. He spoke loudly ________ everyone in the room ________ him clearly.A. to make; to hearB. to make; hearC. making; to hearD. making; hear15. ________ animals will be in danger and there will be space for them if we don't take any action.A. More and more; fewer and fewerB. Fewer and fewer; more and moreC. More and more; less and lessD. Less and less; more and more二、完形填空Many people live with animals. Some have dogs and cats. Some have fish. Dian Fossey was different from them. She had gorillas. The gorillas didn't live in her house. She lived in ___16___. What a special woman she was!Dian Fossey was born in San Francisco, California, in 1932. She loved ___17___. She went to college to become a veterinarian(兽医). One day, she took a trip to Africa. ___18___ she was there, she became interested in gorillas. Dian loved watching the gorillas. She decided to move there.Dian Fossey was known as the first person to have19contact(接触) with gorillas. She sat with the gorillas. She played with them. They never ___20___ her.Dian became interested in a baby gorilla. She was able to ___21___ him. She named him Digit. Dian was able to watch him grow. Digit liked Dian, too. A few years later, Digit was killed by hunters. Dian was very ___22___ about Digit's death. She decided to do something to ___23___ the gorillas.She started a ___24___ that tried to protect the gorillas. National Geographic wrote a story about Dian and her group. Many people ___25___ money to her to help save the gorillas. She said she would do more things to save gorillas.16. A. hers B. his C. theirs D. ours17. A. bird B. animals C. forests D. plants18. A. Although B. Because C.While D. Unless19. A. friendly B. strict C. serious D. careful20. A. win B. beat C. protect D. hurt21. A. stay away from B. get close to C. look out for D. catch up with22. A. pleased B. sad C. bored D. proud23. A. protect B. kill C. lose D. miss24. A. team B. group C. club D. center25. A.stole B. wrote C. sent D. received三、阅读理解(每小题1分,共5分)(A)Wetlands are any land that is flooded with shallow water all or most of the time. They are a natural water holding system.There are many types of wetlands. Among them, bogs, marshes and swamps are the three n types. The different types of wetlands have different kinds of plants. Only mosses (苔藓) and a few other kinds of plants can grow in bogs. Grassy plants like cattails(香蒲) and reeds (芦苇) are the most common plants in a marsh. A swamp is a forest whose ground is underwater all or most of the time. Unlike bogs or marshes, a swamp is full of trees and bushes. It's not a good idea to go exploring a swamp without a guide. There are hidden pools of water, thick mud, and sometimes big crocodiles looking for their next meal.Hungry crocodiles aren't the only animals that make the wetlands their home. Otters, turtles, frogs, snakes and many other animals do too. The water is home to many kinds of fish and crabs. Birds, including ducks, geese and cranes, use wetlands seasonally during their long migrations.Wetlands are important because they provide habitats for plants and animals. A wetland system can also protect shorelines, make polluted waters clean, prevent floods, and restore underground water supplies.According to WWF, more than half of the world's wetlands have disappeared since the beginning of the 20th century. If this continues, countless plant and animal species will surely die- out. Without wetlands, cities have to spend more money treating water. Don't feel helpless. Try to do your part to protect them right now. Here are some ideas.26. According to the passage, which of the following is TRUE?A. Wetlands are a man-made water holding system.B. There are three types of wetlands in the world.C. People cannot meet with big crocodiles in wetlands.D. Wetlands can protect shorelines and prevent floods.27. What is the writer probably going to talk about after Paragraph 5?A.What are the different types of wetlands?B. What will happen if wetlands disappear?C. What actions can people take to protect wetlands?D. What other kinds of plants and animals live in wetlands?(B)Some of the greatest problems we face today are the destruction(破坏) of our environment. Brown clouds, polluted water, endangered wild animals... these problems seem so huge.So my family do what we can. We take cloth bags to stores instead of using plastic bags. We walk where we don't have to drive ...But does it do any good? When I am the only one in line at the market with cloth bags, am I doing any good? Does my walking to stores make any real difference to the world?I recently learned something about flamingos(火烈鸟) which like to get together in groups of a thousand or more. Every year, when the time comes for migration, a few of them first take off from the lake. But none of the others seem to notice, so the small group returns. However, the next day they try again. This time a few more fly along with them, but most of them still pay no attention, so they return again. They try for several times. Every time a few more birds join in but, since the thousands of others still take no notice, the great migration plan is once more stopped.Then one day something changes. The same small group of birds once again starts flying and a small number more join in just as before, then more. Finally, they all take flight and the migration really begins. What a spectacular(壮观的) sight it must be -thousands of flamingos taking off into the sky at once!A few can make a difference. Even if you're the one to take the first step, and continue trying, others will someday take notice and together we will solve even our greatest problems.28. Why does the small group of flamingos return to the lake?A. Because they are very tired.B. Because they can't find food in other places.C. Because they don't know where to go.D. Because the others don't fly along with them.29. What’s the writer's purpose of writing this article?A. To show that the writer loves to see the migration of flamingos.B. To introduce how flamingos migrate to readers.C. To tell readers to continue trying and it can make a difference.D. To show that we face lots of serious problems today.30. Where would you most probably read this passage?A. A guidebook.B. A movie poster.C. A personal blog (博客).D. A science magazine.四、词汇(每小题2分,共30分)(A)根据汉语提示、音标或首字母提示写单词,使句意完整31. They finally___________ (卖) their house at a good price.32. I invited Tom to dinner and he happily___________(接受) my invitation.33. The man can't sleep well at night and it leads to___________ / ˈsɪəriəs/ problems to his health.34. Don't take p___________ him. He is pretending(假装) to be poor.35. Don't be too strict with yourself. After all, none of us is___________(完美的).36. Our_____(政府) is taking some action to improve people's living conditions.37. My teacher asked me to___________(描述) this picture with my own words.38. The students come from different places. Do you know all their ___________(地址)?(B)用所给词的适当形式填空39. We don't need to hurry because there is still a little time ___________(leave).40. My grandfather likes sleeping with the windows___________(close) in summer.41. The film is very interesting and I lost myself in it from___________(begin) to end.42. He treats everyone with ___________(kind), so he has lots of friends.43. --Is John in his bedroom now? --Yes. He may___________(make) his bed.44. The doctor did everything he could___________(save) the child who was hurt in the accident.45. A nurse took her arm and___________(lead) her to a chair.五、句型转换,每空一词。
选择填空限时练(四)
(推荐时间:45分钟)
一、选择题
1. 已知集合A ={y |x 2+y 2=1}和集合B ={y |y =x 2},则A ∩B 等于
( )
A .(0,1)
B .[0,1]
C .(0,+∞)
D .{(0,1),(1,0)}
答案 B
2. 复数(3+4i)i(其中i 为虚数单位)在复平面上对应的点位于
( )
A .第一象限
B .第二象限
C .第三象限
D .第四象限
答案 B
解析 因为(3+4i)·i =-4+3i ,
所以在复平面上对应的点位于第二象限,选B. 3.“α=2k π-π
4
(k ∈Z )”是“tan α=-1”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 由α=2k π-π
4(k ∈Z )可得tan α=-1;
而由tan α=-1得α=k π-π
4
(k ∈Z ),故选A.
4. 一个几何体的三视图如图所示,则此几何体的体积是
( )
A .112
B .80
C .72
D .64
答案 B
解析 依题意得,该几何体的下半部分是一个棱长为4的正方体,上半部分是一个底面
是边长为4的正方形,高为3的四棱锥,故该几何体的体积为43+1
3×4×4×3=80.故
选B.
5. 将参加夏令营的500名学生编号为:001,002,…,500,采用系统抽样的方法抽取一个
容量为50的样本,且随机抽得的号码为003,这500名学生分住在三个营区,从001到200在第一营区,从201到355在第二营区,从356到500在第三营区,三个营区被抽中的人数为
( )
A .20,15,15
B .20,16,14
C .12,14,16
D .21,15,14
答案 B
解析 根据系统抽样特点,被抽到号码l =10k +3,k ∈N .第353号被抽到,因此第二营区应有16人,所以三个营区被抽中的人数为20,16,14.
6. 要得到函数y =sin ⎝
⎛⎭⎫2x -π
3的图象,只需将函数y =sin 2x 的图象
( )
A .向左平移π
12个单位
B .向右平移π
12个单位
C .向左平移π
6个单位
D .向右平移π
6个单位
答案 D
解析 要得到函数y =sin ⎝⎛⎭⎫2x -π3,只需将函数y =sin 2x 中的x 减去π
6,即得到y =sin 2⎝⎛⎭⎫x -π6=sin ⎝
⎛⎭⎫2x -π
3. 7. 设数列{a n }是等差数列,若a 3+a 4+a 5=12,则a 1+a 2+…+a 7=
( )
A .14
B .21
C .28
D .35
答案 C
解析 由a 3+a 4+a 5=12得a 4=4,
所以a 1+a 2+a 3+…+a 7=7(a 1+a 7)2
=7a 4=28.
8. 某程序的框图如图所示,则运行该程序后输出的B 值是
( )
A .5
B .11
C .23
D .47
答案 C
解析 第一次循环:B =2×2+1=5,A =4; 第二次循环:B =2×5+1=11,A =5; 第三次循环:B =2×11+1=23,A =6; 第四次循环:输出B =23,选C.
9. 已知定义在R 上的函数f (x ),其导函数f ′(x )的图象如图所示,则
下列叙述正确的是
( )
A .f (b )>f (c )>f (d )
B .f (b )>f (a )>f (e )
C .f (c )>f (b )>f (a )
D .f (c )>f (e )>f (d ) 答案 C
解析 根据函数f (x )的特征图象可得:f (c )>f (b )>f (a ). 10.若实数x ,y 满足不等式组:⎩⎪⎨⎪
⎧
x -y ≥-1,x +y ≥1,
3x -y ≤3,
则该约束条件所围成的平面区域的面积是
( )
A .3 B.5
2
C .2
D .2 2
答案 C
解析 可行域为直角三角形,其面积为S =1
2
×22×2=2.
11.如图,过抛物线y 2=2px (p >0)的焦点F 的直线l 交抛物线于点A 、B ,
交其准线于点C ,若|BC |=2|BF |,且|AF |=3,则此抛物线方程为 ( )
A .y 2=9x
B .y 2=6x
C .y 2=3x
D .y 2=3x
答案 C
解析 如图,∵|BC |=2|BF |, ∴由抛物线的定义可知∠BCD =30°, |AE |=|AF |=3,∴|AC |=6. 即F 为AC 的中点,
∴p =|FF ′|=12|EA |=3
2
,故抛物线方程为y 2=3x .
12.已知函数y =f (x )是定义在R 上且以3为周期的奇函数,当x ∈⎝⎛⎭
⎫0,3
2时,f (x )=ln(x 2-x +1),则函数f (x )在区间[0,6]上的零点个数为
( )
A .3
B .5
C .7
D .9
答案 C
解析 当x ∈⎝⎛⎭⎫-32,0时,-x ∈⎝⎛⎭⎫0,3
2, f (x )=-f (-x )=-ln(x 2+x +1);
则f (x )在区间⎝⎛⎭⎫-32,32上有3个零点(在区间⎣⎡⎭
⎫0,3
2上有2个零点). 根据函数周期性,可得f (x )在⎝⎛⎭⎫32,92上也有3个零点,在⎝⎛⎦⎤9
2,6上有2个零点.故函数f (x )在区间[0,6]上一共有7个零点. 二、填空题 13.二项式⎝
⎛⎭
⎫x -
2x 6
的展开式中的常数项为________. 答案 -160
解析 T r +1=C r 6(x )6-r ⎝
⎛⎭⎫-2x r =C r 6(-2)r x 3-r . 所以常数项为T 4=C 36(-2)3
=-160.
14.向量a =(-1,1)在向量b =(3,4)方向上的投影为________.
答案 15
解析 设向量a =(-1,1)与b =(3,4)的夹角为θ,则向量a 在向量b 方向上的投影为|a |·cos θ=a ·b |b |=(-1,1)·(3,4)32+42
=15.
15.某中学从6名品学兼优的同学中选出4名去进行为期三天的环保知识宣传活动,每人一
天,要求星期天有2人参加,星期五、星期六各有1人参加,则不同的选派方案的种数有________. 答案 180
解析 第一步,从6人中选出4人有C 46种不同的方法,
第二步,从选出的4人中选2人安排在星期天有C 24种不同的方法, 第三步,安排剩余的两人有A 22种不同的方法,
所以共有C 46C 24A 22=15×6×2=180种不同的选派方案.
16.下面四个命题:
①已知函数f (x )=sin x ,在区间[0,π]上任取一点x 0,则使得f (x 0)>12的概率为23;
②函数y =sin 2x 的图象向左平移π
3个单位得到函数y =sin ⎝⎛⎭⎫2x +π3的图象; ③命题“∀x ∈R ,x 2-x +1≥34”的否定是“∃x 0∈R ,x 20-x 0
+1<3
4”; ④若函数f (x )是定义在R 上的奇函数,则f (x +4)=f (x ),则f (2 012)=0. 其中所有正确命题的序号是________. 答案 ①③④
解析 ②错误,应该向左平移π
6;
①使得f (x 0)>1
2的概率为p =56π-16ππ=23;
④f (2 012)=f (0)=0.。