青浦高级中学2015学年第一学期期中考试

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上海市青浦高级中学2024-2025学年高三上学期期中考试数学试卷

上海市青浦高级中学2024-2025学年高三上学期期中考试数学试卷

上海市青浦高级中学2024-2025学年高三上学期期中考试数学试卷一、填空题1.已知集合{14}A m m =-<<∣,13B y y x ⎧⎫==⎨⎬⎩⎭∣,则A B =2.已知复数z 满足:21i z =+(i 为虚数单位),则z =3.已知向量()1,2,3a =- ,()2,,b m n = ,若a b∥,则m n +=4.设等差数列{}n a 的前n 项和为n S ,若28515a a a +=-,则9S 等于5.已知圆C 的方程是22240x y x y +-+=,则圆心C 的坐标是.6.已知4cos 25πα⎛⎫-=- ⎪⎝⎭,则cos 2=α.7.1013x ⎛⎫+ ⎪⎝⎭的展开式中,各项系数中的最大值为.8.记n S 为数列{}n a 的前n 项和,已知434n n S a =+,则数列的通项公式n a =9.已知正实数a 、b 满足42a b ab ++=,则a b +的最小值为.10.设圆锥底面圆周上两点A 、B 间的距离为2,圆锥顶点到直线ABAB 和圆锥的轴的距离为1,则该圆锥的侧面积为.11.设R,Z a m ∈∈,若存在唯一的m 使得关于x 的不等式组21122x m x a -<<+有解,则a的取值范围是.12.对任意数集{}123,,A a a a =,满足表达式为321y x x x =+--且值域为A 的函数个数为p .记所有可能的p 的值组成集合B ,则集合B 中元素之和为.二、单选题13.“0x y >>”是“11x y x y->-”的()A .充分非必要条件B .必要非充分条件C .充要条件D .既非充分也非必要条件14.函数()21sin 1xf x x e ⎛⎫=- ⎪+⎝⎭图象的大致形状是()A .B .C .D .15.如图所示,在正方体1111ABCD A B C D -中,点P 为线段11A C 上的动点,则下列直线中,始终与直线BP 异面的是()A .1DD B .ACC .1AD D .1B C16.已知数列{}n a 的各项均为正数,其前n 项和为n S ,满足()91,2,n n a S n == ,给出下列四个结论:①{}n a 的第2项小于3;②{}n a 为等比数列;③{}n a 为递减数列;④{}n a 中存在小于1100的项其中正确结论的个数是()A .1B .2C .3D .4三、解答题17.如图,正四棱柱1111ABCD A B C D -的底面边长为1,高为2,AC BD 、相交于点O .(1)证明:直线1B O 与平面11AC D 平行;(2)求三棱锥11O A C D -的体积.18.33()log ()log (6)f x a x x =++-(1)若将函数()f x 图像向下移0m m >()后,图像经过()()3,0,5,0,求实数a ,m 的值.(2)若3a >-且0a ≠,求解不等式()(6)f x f x ≤-.19.为研究某种农产品价格变化的规律,收集得到了该农产品连续40天的价格变化数据,如下表所示.在描述价格变化时,用“+”表示“上涨”,即当天价格比前一天价格高;用“-”表示“下跌”,即当天价格比前一天价格低;用“0”表示“不变”,即当天价格与前一天价格相同.时段价格变化第1天到第20天-++0---++0+0--+-+00+第21天到第40天0++0---++0+0+---+0-+用频率估计概率.(1)试估计该农产品价格“上涨”的概率;(2)假设该农产品每天的价格变化是相互独立的.在未来的日子里任取4天,试估计该农产品价格在这4天中2天“上涨”、1天“下跌”、1天“不变”的概率;(3)假设该农产品每天的价格变化只受前一天价格变化的影响.判断第41天该农产品价格“上涨”“下跌”和“不变”的概率估计值哪个最大.(结论不要求证明)20.已知椭圆()2222Γ:10y x a b a b +=>>−2,0在Γ上.(1)求椭圆Γ的方程;(2)椭圆的上、下顶点分别为1B ,2B ,点C 在Γ上(C 异于椭圆的顶点),直线1B C 与x 轴相交于点D ,点0,2,若2B CD △的面积是1B CE △面积的两倍,求点C 的坐标;(3)过点−2,3的直线交Γ于P ,Q 两点,直线AP ,AQ 与y 轴的交点分别为M ,N ,证明:线段MN 的中点为定点.21.已知函数()e xf x ax =-和()lng x ax x =-,R a ∈.(1)求()f x 在点()0,1处的切线方程;(2)若函数()f x 和()g x 有相同的最小值,①求a 的值;②证明:存在直线y b =,其与两条曲线()y f x =和()y g x =共有三个不同的交点,并且从左到右的三个交点的横坐标成等差数列.。

2018-2019学年上海市青浦高级中学高一上学期期中考试物理卷学生

2018-2019学年上海市青浦高级中学高一上学期期中考试物理卷学生

2018-2019学年上海市青浦高级中学高一上学期期中考试物理卷一、单选题1. 下列说法正确的是()A. 研究地球绕太阳的公转时可以把地球看成质点B. 位移和路程都是反映运动过程中位置变化的物理量C. 参考系必须是静止不动的物体D. 火车在忻州站停车15分钟指的是时刻2.下列各力中不属于弹力的是( )A. 悬挂重物的细绳,对重物的拉力B. 水平桌面对放在其上的书本的支持力C. 按图钉时,手对图钉的压力D. 地球对人造卫星的吸引力3.现代战争是科技之战、信息之战,某集团军进行的一次实战演习过程,在基地导演部的大型显示屏上一览无余,如图1所示是蓝军由基地A分三路大军进攻红军基地B的显示,若用x1、x2和x3分别表示三路大军的位移,则由大屏幕的显示图可知( )A. x1>x2>x3B. x1<x2<x3C. x1=x2=x3D. 三者关系无法确定4.关于物体的重心,下列说法正确的是()A. 重心就是物体内最重的点B. 重心是重力的作用点,所以重心一定在物体上C. 任何有规则形状的物体,它的几何中心必然与重心重合D. 物体的重心在物体中的位置不因物体升高、降低、倾斜而发生改变5.下列关于摩擦力的说法正确的是()A. 摩擦力的大小一定与压力成正比B. 摩擦力的方向一定与物体运动的方向相反C. 摩擦力一定是阻力D. 运动的物体可能受到静摩擦力作用6.两个力F l和F2间的夹角为θ,两个力的合力为F. 以下说法正确的是()A. 若F l和F2大小不变,θ角越小,合力F就越小B. 合力F可能比分力中的任何一个力都小C. 合力F总比分力中的任何一个力都大D. 如果夹角θ不变,Fl大小不变,只要F2增大,合力F就必然增大7.在一居民住宅楼的电梯内的一位乘客观察到显示器指示的楼层为1−2……7共用去时间14s,则电梯在这段时间的平均速度大约是()A. 0.5m/sB. 1.5m/sC. 2.5m/sD. 3.5m/s8.某物体沿直线运动的v−t图象如图所示,由图可以看出物体①沿直线向一个方向运动②沿直线做往复运动③加速度大小不变④做匀变速直线运动上述说法正确的是()A. ①④B. ①③C. ②③D. ②④9.如图是物体做直线运动的v−t图象,由图可知,该物体( )A. 第1s内和第3s内的运方向相反B. 第3s内和第4s内的加速度相同C. 第1s内和第3s内的位移不相同D. 0∼2s内和0∼4s内的平均速度大小相等10.某一时刻a,b两物体以不同的速度经过某一点,并沿同一方向做匀加速直线运动,已知两物体的加速度相同,则在运动过程中( )A. a,b两物体速度之差与时间成正比B. a,b两物体速度之差与时间的平方成正比C. a,b两物体位移之差与时间成正比D. a,b两物体位移之差与时间的平方成正比11.两辆完全相同的汽车,沿水平直路一前一后匀速行驶,速度均为v0,若前车突然以恒定的加速度刹车,在前车刚停住时,后车以前车刹车的加速度开始刹车,已知前车在刹车过程中所行驶的距离为s,若要保持两车在上述情况中不相撞,则两车在匀速行驶时保持的距离至少应为( )A. sB. 2sC. 3sD. 4s12.以下各种运动的速度和加速度的关系可能存在的是()A.速度向东,正在减小,加速度向西,正在增大B.速度向东,正在增大,加速度向东,正在减小C.速度向东,正在增大,加速度向西,正在减小D.速度向东,正在减小,加速度向东,正在增大13. DIS实验系统是由________、__________和电脑等三部分组成的,在测量瞬时速度时,我们使用的传感器是________传感器,在已知挡光板宽度的条件下,它通过记录________,得出物体的运动速度。

2017-2018青浦高级中学高一英语期中考试

2017-2018青浦高级中学高一英语期中考试

上海市青浦高级中学2018学年第一学期期中考试高一英语试卷考试时间:90分钟满分:100 分II. Grammar and VocabularySection A (15%)Directions: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.16. Helen was much kinder to her youngest son than to the others, ______, of course, made theothers envy him.A. whoB. thatC. whatD. which17.What surprised everyone present at the meeting was not what he said but ______ he said it.A. the wayB. in the way thatC. in the wayD. the way which18. Williams felt himself to be senior ______ all of his colleagues.A. thanB. toC. overD. among19. Speaking without thinking is shooting without aiming.What's the sentence element of the underlined words?A. 谓语B. 宾语C. 状语D. 表语20. Mary was such a dependable mail carrier that people called her “Stagecoach” Mary.What's the sentence element of the underlined words?A. 表语B. 宾语补足语C. 宾语D. 状语21. Avoiding eye contact might be considered impolite, but staring at others is also consideredrude and should be avoided.What's the sentence element of the underlined words?A. 主语B. 宾语C. 表语D. 谓语22. I work in a business ______ almost everyone is dying for a golden chance.A. howB. whichC. whereD. that23. After graduation from college, her sister became a lawyer, ______ she wanted to be.A. whoB. thatC. whatD. which24. The Beatles, ______ many of you are old enough to remember, came from Liverpool.A. whatB. thatC. howD. as25. Look out! Don’t get too close to the house ______ roof is under repair.A. whoseB. whichC. of whichD. that26. Many people who had seen the film were afraid to go to the forest when they remembered thescenes ______ people were eaten by the tiger.A. thatB. by whichC. whichD. in which27. They talked and talked for a couple of hours of things and persons ______they rememberedin the university.A. whichB. thatC. whoD. whom28. Is this museum ______some German friends visited last Wednesday?A. thatB. whereC. in whichD. the one29. We tried but could not find any reason ______they were all against the plan.A. whichB. thatC. whyD. what30. On the train of metro line 2 I saw a student _____ I thought was a former classmate of yours.A. whoB. whomC. whichD. thatSection B (10%)Directions: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.Everyone is born with their own built-in burglar (窃贼) alarms, called the sense of sight and sound.31______, many of us go around with the alarm turned off.We don’t see the stranger 32______ outside the house next door.We don’t notice the sounds from the flat upstairs.(Weren’t they supposed to be on holiday?)The police can only do so much to 33______ crime. There never can be enough of them to guard every home in every town. So they need your help in 34______ with the burglars,the vandals (恣意破坏者), and the car thieves.Not, of course, by setting out to have a go every time you see something suspicious. It’ll always be the job of the police to arrest 35______.But by acting as a line of 36______ between them and your community, for instance, you probably know far more about your immediate 37______ than the police ever could.A stranger in someone’s garden would probably be far more 38______ to you than it would to even the local police, if, of course, you were on the look-out.That’s the whole idea behind the Neighborhood Watch schemes, springing up around the country to 39______ a spirit of watchfulness within a community, anything suspicious being reported to the police.It’s early days yet, but results so far are very 40______. The crime figures are already dropping in many of the areas running the scheme. And all due to people like you.III. Reading ComprehensionSection A (15%)Directions: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Last weekends, my kids along with a few other kids from the neighborhood volunteered to help me wash my car. My 10-year-old daughter came up with the idea of __41__ other people’s cars as well. It was pretty __42__ outside and I had no plans to continue to be in the bright sun. She __43__ wanted to give lemonade (柠檬汽水) to passersby for free. I had seen little kids serve and sell fresh lemonade for a small cost but not free. Although I felt __44__, I decided to help her. Then she asked me, “What if we __45__ this a smile car wash?” I couldn’t hold back my tears and __46__ her and the other kids to go outside the house and come up with creative ideas. While I kept myself busy in drying the car, the gang walked up to me with a(n) __47__ with beautiful images of smiles. Theyhad “Free Car Wash” written on it and the theme of their exercise was “smile”. It was pretty neat to see a team of kids ranging 5-11 years with the __48__ to do something for others.All that seemed __49__ and came right from their heart. Nothing seemed to __50__ to them: their playtime, the heat outside -- they just wanted to __51__ others and do something nice in the community!I helped them make some fresh lemonade and brought out some old __52__ to help clean cars. The passersby were __53__ and one even shouted back to them saying “God Bless You, my kids…” One of them even tried giving them 5 dollars, which they refused. A pretty heartwarming __54__ !I feel blessed by being __55__ by such wonderful and loving souls.41. A. decorating B. repairing C. washing D. drying42. A. dirty B. hot C. different D. quiet43. A. hardly B. therefore C. already D. further44. A. difficult B. popular C. confused D. worried45. A. order B. leave C. make D. show46. A. encouraged B. expected C. invited D. challenged47. A. board B. picture C. idea D. car48. A. need B. duty C. imagination D. skill49. A. important B. disappointing C. hopeful D. natural50. A. matter B. object C. belong D. refer51. A. relax B. try C. help D. smile52. A. friends B. clothes C. newspapers D. records53. A. amused B. amazed C. bored D. frightened54. A. scene B. gift C. story D. explanation55. A. known B. understood C. refused D. surroundedSection B (22%)Directions:Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just readALike human beings, dogs may catch cold because of cold weather, wet conditions or can also get it from other sick dogs. If a dog has a running nose and watery eyes, coughs or sneezes (打喷嚏), then it is quite probable that the dog has caught cold.A dog's cold can get over after a few days without treatment but it totally depends upon the owner to treat it with medications or improve its immune power (免疫力)to get rid of the cold naturally. Following are some of the things you can do if your dog gets a cold.You can improve its immune power by giving it proper nutrient diet. Healthy food can really do wonders. Try to give it food which is either suggested by the vet (兽医) or is healthy for your pet. Increase the intake of food which is rich in vitamins A, C and E.Keep your dog warm. The best place for your dog in winter is inside your house. Do not keep your dog outside when it is cold and wet. At home you can also keep the dog warm with the help of carpets. This will make him comfortable and help him to recover fast.Increase the fluid (流质)intake as it helps a lot. Water can be the best choice but you can also add broth (肉汤)in water which will give your dog strength. Warm water will make your dog morecomfortable and will also keep the dog away from the respiratory infections (呼吸道感染). Steam treatment is considered to be effective in getting rid of cold. It makes the nasal (鼻的) passage wet, which helps proper breathing. Just fill your bathroom with steam and leave your dog inside the bathroom for 15 minutes. Do it nearly 2 to 3 times a day and you will see your dog recovering.These are some of the things you can do to help your dog recover from cold. However, if you are not able to find any improvement in its health, then turn to the vet for help immediately. Take your dog for regular checkups so as to avoid complications (并发症).56. From the first paragraph we know about ________.A. the difficulty in keeping a dog as a petB. characteristics of sick dogsC. the similarities between dogs and human beingsD. causes and symptoms (症状)of cold in dogs57. When your dog catches cold, you should feed it on ________.A. its favorite foodB. the suggested food by the vetC. some meat and waterD. food rich in vitamin B58. When a dog catches cold, it is wrong to ________.A. keep it inside during cold and wet weatherB. leave it inside the bathroom full of steamC. let it eat too much solid foodD. keep it sleeping on rugs at home59. It can be learnt from the text that ________.A. a dog’s cold can always disappear naturallyB. it’s quite easy to make a sick dog recover from coldC. treating a dog’s cold sometimes needs a vet's helpD. cold in dogs won’t spread between each other.BWant to find a job? Now read the following advertisements.FAIRMONT HOTELFive waiters and Ten Waitresses---Aged under 22---At least high school graduate---Good looking; men at least 1.72 meters tall and women 1.65---Those knowing foreign languages preferred---Paid 1600---2200 dollars per monthOne Secretary---Aged under 30---Female preferred---Good at writing and skilled at computerIf interested, call 465-4768 or write to: Mr. Jack Hundris Room 0825, Fairmont Hotel567 Wood Street, San Markers, 78003Fax: 6954828WILSON BOOKSTOREAccountant (会计)---Aged between 25 and 40---With an experience of at least two years---With a degree and an accountant certificate(证书)---Paid 3000-4000 dollars monthly---With a knowledge of computerSalesclerk---Basic education of 12 years or more---Good at computer---Paid 1800-2200 dollars monthlyTel: 447-4398Fax: 348526960. If you don’t know how to use a computer, you can just apply for the position as ________.A. a secretaryB. a waiter or a waitressC. an accountantD. a salesclerk61. If you want to get the position of accountant in Wilson Bookstore, you have to satisfy thefollowing conditions EXCEPT ________.A. being a womanB. knowing well how to use a computerC. having been an accountantD. having an accountant certificate62. If you want to try for a job in Fairmont Hotel, you ________.A. have to be a woman and know foreign languagesB. should be a university graduateC. have to be taller than 1.72 metersD. should be younger than 30 years oldCWhen I was small and my grandmother died, I couldn’t understand why I had no tears. But that night when my dad tried to cheer me up, my laugh turned into crying.. So it came as no surprise to learn that researchers believe crying and laughing come from the same part of the brain. Just as laughing has many health advantages, scientists are discovering that so, too, does crying.Whatever it takes for us to reduce pressure is important to our emotional (情感的) health, and crying seems to work well. One study found that 85 percent of women and 73 percent of men report feeling better after crying.Besides, tears attract help from other people. Researchers agree that when we cry, people around us become kinder and friendly and they are more ready to provide support and comfort. Tears also enable us to understand our emotions better; sometimes we don't even know we're very sad until we cry. We learn about our emotions through crying, and then we can deal with them.Just as crying can be healthy, not crying--- holding back tears of anger, pain or suffering--- can be bad for physical health, Studies have shown that too much control of emotions can lead to high blood pressure, heart problems and some other illnesses. If you have a health problem, doctors will certainly not ask you to cry. But when you feel like crying, don't fight it. It's a natural --- and healthy --- emotional response (反应).63. Why didn't the author cry when her grandmother died?A. The author doesn’t give the explanation.B. Because she did not love her grandmother.C. Because she was too shy to cry at that time.D. Because her father did not allow her to feel too sad.64. It can be inferred from the text that ________.A. there are two ways to keep healthyB. crying does more good to health than laughingC. emotional health has close connection with physical healthD. crying and laughing play the same roles65. According to the author, which of the following statements is true?A. Crying is the best way to get help from others.B. Fighting back tears may cause some health problems.C. We will never know our deep feelings unless we cry.D. We must cry if we want to reduce pressure.66. What might be the most suitable title for the text?A. Power of TearsB. How to Keep HealthyC. Why We CryD. A New Scientific Discovery第Ⅱ卷(共23分)I. Verb filling (8%)Directions: Filling in the blanks with the verbs given in their proper tenses or forms.67. According the timetable, the next flight for Beijing __________ (leave) at 9:10 a.m.68. This is not the first time that he __________ (be) late for school.69. Cars are moving slowly because the main road __________ (repair).70. Take your time to reflect before __________ (draw) a final conclusion.71.In the physics exam last week, Doris got better marks than we __________ (expect).72. She’s crazy. She wastes so much valuable time __________ (shop) on-line.73. Rather than __________ (ride) on a crowded bus, he always prefers to go to school on a bicycle74. The letter he looked forward to __________ (reach) him at last.II. Translation (15%)Directions: Translate the following sentences into English, using the words given in the brackets.75.缺乏睡眠或锻炼会导致疲劳。

上海市青浦高级中学高二化学上学期期中考试试题新人教版

上海市青浦高级中学高二化学上学期期中考试试题新人教版

青浦高级中学2013学年第一学期期中考试高二化学试题试卷说明:1.本试卷考试时间为90分钟,满分为100分2.可能用到的相对原子质量:O-16 Al-27 Fe-56 Mg-24 H-1一、单选题:(每小题2分,共50分)1.下列有关金属的描述正确的是 ( C )A、金属都是银白色、都有金属光泽,能导电、导热,有延展性B、金属在常温下都是固体C、短周期中,导电导热性最好的金属是AlD、在周期表中金属的种类比非金属少2. 常温能被浓硝酸钝化的黑色金属是 ( C )A、MgB、AlC、FeD、Cu3.下列物质中,不属于合金的是( D )A、硬铝B、黄铜C、钢铁D、水银4.下列实验中能得到Fe2O3的是( D )A、铁在纯氧中燃烧B、红热的铁和水蒸气反应C、灼烧并蒸干F e2(S O4)3溶液D、加热氢氧化铁固体5.把铁片投入下列某溶液中,铁片溶解且其质量减轻,也没有气体产生。

该溶液是( B )A、 H2SO4B、 Fe2(SO4)3C、FeSO4D、CuSO46.上海世博园地区的一座大型钢铁厂搬迁后,附近居民将不再受到该厂产生的棕红色烟的困扰。

你估计这一空气污染物可能含有( B )A、FeO粉尘B、Fe2O3粉尘C、FeS粉尘D、Fe3O4 粉尘7.下列物质不能通过化合反应得到的是 ( C )A、Fe(OH)3B、FeCl2C、Al(OH)3D、FeS8.随着人们生活节奏的加快,方便的小包装食品已被广泛接受。

为了延长食品的保质期,防止食品氧化变质,在包装袋中可以放入的化学物质是( B )A、无水硫酸铜B、硫酸亚铁C、食盐D、生石灰9.下列各组物质中,滴入KSCN溶液显红色的是 ( D )A、过量铜粉和硫酸铁溶液B、过量铁粉与稀硫酸C、少量的铁粉与盐酸D、氯水与氯化亚铁溶液10.下列物质反应时,不会产生H2的是 ( B )A、Al + 盐酸B、Al + HNO3(浓常温)C、Al + NaOH溶液D、Al +热H2O 11.用一张已除去表面氧化膜的铝箔紧紧包裹在试管外壁(如图),将试管浸入硝酸汞溶液中,片刻取出,然后置于空气中,不久铝箔表面生出“白毛”,红墨水柱右端上升。

上海中学2015学年第一学期数学期中考试(理科)151106

上海中学2015学年第一学期数学期中考试(理科)151106

上海中学2015学年第一学期高三数学(理科)期中考试答题纸一、填空题(每题4分,共56分)1.____________2.____________.3.__________4.__________5.____________6.___________.7.____________8.____________9.__________10.___________.11._________.12___________. 13.__________.14.___________.二、选择题((每题5分,共20分)15._______16.______.17._______.18______.三.解答题19. (本题满分12分)20. (本题满分12分)(1)(2)21. (本题满分16分)(1)(2)22. (本题满分16分)(1)(2) 23.(本题满分18分)(1)(2)(3)上海中学2015学年第一学期期中考试数 学 试 题(理科)2015.11.06一.填空题(每题4分,共56分)1. 已知f(x)=⎩⎨⎧>≤+,0,2,0,12x x x x 若f(x)=10,则x=_________.2. 已知函数a x f x++=131)(为奇函数,则方程41)(=x f 的解是_________. 3. 已知钝角α的顶点在坐标原点,始边与x 轴的正半轴重合,角α的终边与圆心在原点的单位圆(半径为1的圆)交于第二象限内的点A(x A ,53),则sin 2α=_________.4. 设f(x)是定义在R 上的奇函数,且对任意实数x 满足f(x+2)=f(x),当0<x<1时,f(x)=1-x 2,则f(-23)+f(1)=_______ .5. 已知cos(x-)43,2(,102)4πππ∈=x ,则cos2x=__________.6.若函数y=ax 与y=xb-在(0,+∞)上都是减函数,则函数y=ax 2+bx 在(0,+∞)上是单调递_______函数.7. 在∆ABC 中,若12tan 2tan =+BA ,则tan 2C 的最小值为__________.8. 设函数f(x)=xx+12,区间M=[a,b],(a<b),集合N={y M x x f y ∈=),(},则使得M=N 的实数对(a,b)有________对.9. 若关于x 的方程2x|x|-a|x|=1有三个不同的实数解,则实数a 的取值范围是___________ .10. 当x ∈[0,2π],满足方程2log 3(tanx)=log 2(sinx)的所有解是__________ . 11. 设f 0(x)=|x|-2015,f n (x)=|f n-1(x)|-1(,n ∈N*),则函数y=f 2015(x)的零点个数为______. 12. 对于具有相同定义域D 的函数f(x)和g(x),若存在实常数k 和b,使得函数f(x)和g(x)对其定义域D 上的任何实数x 分别满足:f(x)≥kx+b 和g(x)≤kx+b,则称直线L:y=kx+b 为f(x)和g(x)的“隔离直线”。

数学-高一-上海市青浦一中高一上学期期中考试数学试卷

数学-高一-上海市青浦一中高一上学期期中考试数学试卷

2016-2017学年上海市青浦一中高一(上)期中数学试卷一、填空题(每小题3分,共36分)1.不等式|x+3|>1的解集是.2.已知a,b∈R,则“a>1,b>1”是“a+b>2”的条件.3.已知集合A={x|∈N*,x∈Z},用列举法表示为.4.命题“设x,y∈Z,若x,y是奇数,则x+y是偶数”的等价命题是.5.设全集U={1,3,5,7},集合M={1,|a﹣5|},C U M={5,7},则a的值为.6.已知﹣1<a<b<2,则a﹣b的范围是.7.已知x,y∈R+,且x+4y=1,则x•y的最大值为.8.设x>0,则的最小值为.9.已知集合A={x|x2﹣3x﹣10=0},B={x|mx﹣1=0},且A∪B=A,则实数m的值是.10.若不等式(a﹣b)x+a+2b>0的解是x>,则不等式ax<b的解为.11.已知a>0,若不等式|x﹣4|+|x﹣3|<a在实数集R上的解集不是空集,则a的取值范围是.12.非空集合G关于运算⊕满足:(1)对任意a,b∈G,都有a+b∈G;(2)存在e∈G使得对于一切a∈G都有a⊕e=e⊕a=a,则称G是关于运算⊕的融洽集,现有下列集合与运算:①G是非负整数集,⊕:实数的加法;②G是偶数集,⊕:实数的乘法;③G是所有二次三项式构成的集合,⊕:多项式的乘法;④G={x|x=a+b,a,b∈Q},⊕:实数的乘法;其中属于融洽集的是(请填写编号)二、选择题(每小题3分,共12分)13.三国时期赵爽在《勾股方圆图注》中对勾股定理的证明可用现代数学表述为如图所示,我们教材中利用该图作为“()”的几何解释.A.如果a>b,b>c,那么a>cB.如果a>b>0,那么a2>b2C.对任意实数a和b,有a2+b2≥2ab,当且仅当a=b时等号成立D.如果a>b,c>0那么ac>bc14.已知a,b,c满足c<b<a且ac<0,则下列选项中不一定能成立的是()A.ab>ac B.c(b﹣a)>0 C.cb2<ca2D.ac(a﹣c)<015.设实数x,y为任意的正数,且+=1,求使m≤2x+y恒成立的m的取值范围是()A.(﹣∞,8]B.(﹣∞,8)C.(8,+∞)D.[8,+∞)16.设[x]表示不超过x的最大整数(例如:[5.5]=5,=﹣6),则不等式[x]2﹣5[x]+6≤0的解集为()A.(2,3)B.[2,4)C.[2,3]D.(2,3]三、解答题(满分52分)17.(8分)已知集合A={x|x2﹣mx+m2﹣19=0},B={x|x2﹣5x+6=0},C={2,﹣4},若A∩B ≠∅,A∩C=∅,求实数m的值.18.(10分)若集合A={x|ax2﹣3x+2=0,a∈R}有且仅有两个子集,求实数a的取值范围.19.(10分)已知命题甲:关于x的不等式x2+(a﹣1)x+a2≤0的解集为空集;命题乙:方程x2+ax﹣(a﹣4)=0有两个不相等的实根.(1)若甲,乙都是真命题,求实数a的取值范围;(2)若甲,乙中有且只有一个是假命题,求实数a的取值范围.20.(12分)如图,要设计一张矩形广告,该广告含有大小相等的左右两个矩形栏目(即图中阴影部分),这两栏的面积之和为18000cm2,四周空白的宽度为10cm,两栏之间的中缝空白的宽度为5cm.(1)设矩形栏目宽度为xcm,求矩形广告面积S(x)的表达式(2)怎样确定广告的高与宽的尺寸(单位:cm),能使矩形广告面积最小?21.(12分)已知集合M={x|x2﹣4x+3<0},N={x||x﹣3|≤1}.(1)求出集合M,N;(2)试定义一种新集合运算△,使M△N={x|1<x<2};(3)若有P={x|||≥},按(2)的运算,求出(N△M)△P.2016-2017学年上海市青浦一中高一(上)期中数学试卷参考答案与试题解析一、填空题(每小题3分,共36分)1.(2015秋•上海校级期中)不等式|x+3|>1的解集是(﹣∞,﹣4)∪(﹣2,+∞).【考点】绝对值不等式的解法.【专题】不等式的解法及应用.【分析】直接转化绝对值不等式,求解即可.【解答】解:不等式|x+3|>1等价于x+3>1或x+3<﹣1,解得x∈(﹣∞,﹣4)∪(﹣2,+∞).故答案为:(﹣∞,﹣4)∪(﹣2,+∞).【点评】本题考查绝对值不等式的解法,考查计算能力.2.(2016秋•青浦区校级期中)已知a,b∈R,则“a>1,b>1”是“a+b>2”的充分不必要条件.【考点】必要条件、充分条件与充要条件的判断.【专题】对应思想;转化法;简易逻辑.【分析】根据充分必要条件的定义判断即可.【解答】解:若a>1,b>1,则a+b>2,是充分条件,若a+b>2,则推不出a>1,b>1,比如:a=0,b=3也可以,故答案为:充分不必要.【点评】本题考查了充分必要条件,考查不等式问题,是一道基础题.3.(2016秋•青浦区校级期中)已知集合A={x|∈N*,x∈Z},用列举法表示为{﹣1,2,3,4} .【考点】集合的表示法.【专题】计算题;集合.【分析】利用已知条件,化简求解即可.【解答】解:集合A={x|∈N*,x∈Z},可知,=2,=3,=6,则x=﹣1,2,3,4.集合A={x|∈N*,x∈Z}={﹣1,2,3,4}.故答案为:{﹣1,2,3,4}.【点评】本题考查集合的表示方法,是基础题.4.(2016秋•青浦区校级期中)命题“设x,y∈Z,若x,y是奇数,则x+y是偶数”的等价命题是设x,y∈Z,若x+y不是偶数,则x,y不都是奇数.【考点】命题的真假判断与应用;四种命题间的逆否关系.【专题】转化思想;定义法;简易逻辑.【分析】原命题与其逆否命题的真假性相同,为等价命题,根据原命题写出逆否命题,可得答案.【解答】解:原命题与其逆否命题的真假性相同,为等价命题,故命题“设x,y∈Z,若x,y是奇数,则x+y是偶数”的等价命题是:“设x,y∈Z,若x+y 不是偶数,则x,y不都是奇数“;故答案为:设x,y∈Z,若x+y不是偶数,则x,y不都是奇数【点评】本题以命题的真假判断与应用为载体,考查了四种命题及其真假关系,难度不大,属于基础题.5.(2010•河西区一模)设全集U={1,3,5,7},集合M={1,|a﹣5|},C U M={5,7},则a的值为2或8.【考点】补集及其运算.【专题】计算题.【分析】题目给出了全集U={1,3,5,7},给出了全集的子集M及M的补集,由M∪(C U M)=U可求a的值.【解答】解:由U={1,3,5,7},且C U M={5,7},所以,M={1,3},又集合M={1,|a﹣5|},所以|a﹣5|=3.所以,实数a的值为2或8.故答案为:2或8【点评】本题考查了补集及其运算,解答此题的关键是一个集合与其补集的并集等于全集,此题是基础题.6.(2016秋•青浦区校级期中)已知﹣1<a<b<2,则a﹣b的范围是﹣3<a﹣b<0.【考点】不等式的基本性质.【专题】转化思想;转化法;不等式.【分析】根据不等式的基本性质,可得﹣2<b<1,进而﹣3<a﹣b<2,结合a<b,则a﹣b <0,可得答案.【解答】解:∵﹣1<a<b<2,∴a﹣b<0,﹣2<b<1,∴﹣3<a﹣b<2,综上可得:﹣3<a﹣b<0;故答案为:﹣3<a﹣b<0【点评】本题考查的知识点是不等式的基本性质,难度不大,属于基础题.7.(2007•上海)已知x,y∈R+,且x+4y=1,则x•y的最大值为.【考点】基本不等式.【专题】计算题.【分析】变形为x与4y的乘积,利用基本不等式求最大值【解答】解:,当且仅当x=4y=时取等号.故应填.【点评】考查利用基本不等式求最值,此为和定积最大型.8.(2016秋•青浦区校级期中)设x>0,则的最小值为2﹣1.【考点】基本不等式.【专题】转化法;函数的性质及应用;不等式的解法及应用.【分析】可令t=x+1(t>1),则==t+﹣1,再由基本不等式可得最小值.【解答】解:由x>0,可得x+1>1,可令t=x+1(t>1),即x=t﹣1,则==t+﹣1≥2﹣1=2﹣1.当且仅当t=,即x=﹣1,取得最小值.故答案为:2﹣1.【点评】本题考查函数最值的求法,注意运用换元法和基本不等式,考查运算化简能力,属于中档题.9.(2016秋•青浦区校级期中)已知集合A={x|x2﹣3x﹣10=0},B={x|mx﹣1=0},且A∪B=A,则实数m的值是0或或..【考点】集合的包含关系判断及应用.【专题】定义法;集合.【分析】求出集合A的元素,根据A∪B=A,建立条件关系即可求实数m的值.【解答】解:由题意:集合A={x|x2﹣3x﹣10=0}={﹣2,5},集合B={x|mx﹣1=0},∵A∪B=A,∴B⊆A当B=∅时,满足题意,此时方程mx﹣1=0无解,解得:m=0.当C≠∅时,此时方程mx﹣1=0有解,x=,要使B⊆A,则满足或,解得:m=或m=.综上可得:实数m的值:0或或.故答案为:0或或.【点评】本题主要考查集合的基本运算,比较基础.属于基础题.10.(2015秋•上海校级期中)若不等式(a﹣b)x+a+2b>0的解是x>,则不等式ax<b的解为{x|x<﹣1} .【考点】其他不等式的解法.【专题】不等式的解法及应用.【分析】由题意可得a>b,=,求得=﹣1,a>0,从而求得不等式ax<b 的解集.【解答】解:由于不等式(a﹣b)x+a+2b>0的解是,∴a>b,=,求得=﹣1,a>0,故不等式ax<b,即x<=﹣1,即x<﹣1,故答案为:{x|x<﹣1}.【点评】本题主要考查一次不等式的解法,体现了转化的数学思想,属于基础题.11.(2015秋•上海校级期中)已知a>0,若不等式|x﹣4|+|x﹣3|<a在实数集R上的解集不是空集,则a的取值范围是(1,+∞).【考点】绝对值不等式的解法.【专题】不等式的解法及应用.【分析】法一:利用绝对值不等式的性质:|a|+|b|≥|a﹣b|(当且仅当a与b同号取等号),求出原不等式左边的最小值,让a大于求出的最小值,即可得到满足题意的实数a的取值范围.法二:由绝对值的几何意义知|x﹣4|+|x﹣3|表示实数轴上的点到﹣3和到4两点的距离之和,故范围可求出,由题意a大于|x﹣4|+|x﹣3|的最小值即可.【解答】解:法一:∵|x﹣4|+|x﹣3|≥|x﹣4+3﹣x|=1,∴|x﹣4|+|x﹣3|的最小值为1,又不等式|x﹣4|+|x﹣3|≤a的解集不是空集,∴a>1.法二:由绝对值的几何意义知|x﹣4|+|x﹣3|表示实数轴上的点到﹣3和到4两点的距离之和,故|x﹣4|+|x﹣3|≥1,由题意,不等式|x﹣4|+|x13|<a在实数集上的解不为空集,只要a>(|x﹣4|+|x13|)min即可,即a>1,故答案为:(1,+∞)【点评】本题考查绝对值不等式的性质及其解法,这类题目是高考的热点,难度不是很大,要注意不等号进行放缩的方向.12.(2016秋•青浦区校级期中)非空集合G关于运算⊕满足:(1)对任意a,b∈G,都有a+b∈G;(2)存在e∈G使得对于一切a∈G都有a⊕e=e⊕a=a,则称G是关于运算⊕的融洽集,现有下列集合与运算:①G是非负整数集,⊕:实数的加法;②G是偶数集,⊕:实数的乘法;③G是所有二次三项式构成的集合,⊕:多项式的乘法;④G={x|x=a+b,a,b∈Q},⊕:实数的乘法;其中属于融洽集的是①④(请填写编号)【考点】元素与集合关系的判断.【专题】新定义;集合思想;集合.【分析】逐一验证几个选项是否分别满足“融洽集”的两个条件,若两个条件都满足,是“融洽集”,有一个不满足,则不是“融洽集”.【解答】解:①对于任意非负整数a,b知道:a+b仍为非负整数,所以a⊕b∈G;取e=0,及任意非负整数a,则a+0=0+a=a,因此G对于⊕为整数的加法运算来说是“融洽集”;②对于任意偶数a,b知道:a+b仍为偶数,故有a+b∈G;但是不存在e∈G,使对一切a ∈G都有a⊕e=e⊕a=a,故②的G不是“融洽集”.③对于G={二次三项式},若a、b∈G时,a,b的两个同类项系数,则其积不再为二次三项式,故G不是和谐集,故③不正确;④G={x|x=a+b,a,b∈Q},设x1=a+b,x2=c+d,则设x1+x2=(a+c)+(b+d),属于集合G,取e=1,a×1=1×a=a,因此G对于⊕实数的乘法运算来说是“融洽集”,故④中的G是“融洽集”.故答案为①④.【点评】本题考查了对新定义“融洽集”理解能力,及对有关知识的掌握情况.关键是看所给的数集是否满足“融洽集”的两个条件.二、选择题(每小题3分,共12分)13.(2016秋•青浦区校级期中)三国时期赵爽在《勾股方圆图注》中对勾股定理的证明可用现代数学表述为如图所示,我们教材中利用该图作为“()”的几何解释.A.如果a>b,b>c,那么a>cB.如果a>b>0,那么a2>b2C.对任意实数a和b,有a2+b2≥2ab,当且仅当a=b时等号成立D.如果a>b,c>0那么ac>bc【考点】基本不等式.【专题】不等式的解法及应用.【分析】可将直角三角形的两直角边长度取作a,b,斜边为c(c2=a2+b2),可得外围的正方形的面积为c2,也就是a2+b2,四个阴影面积之和刚好为2ab,可得对任意正实数a和b,有a2+b2≥2ab,即可得出.【解答】解:可将直角三角形的两直角边长度取作a,b,斜边为c(c2=a2+b2),则外围的正方形的面积为c2,也就是a2+b2,四个阴影面积之和刚好为2ab,对任意正实数a和b,有a2+b2≥2ab,当且仅当a=b时等号成立.故选:C.【点评】本题考查了基本不等式的性质、正方形的面积计算公式,考查了推理能力,属于基础题.14.(2016秋•青浦区校级期中)已知a,b,c满足c<b<a且ac<0,则下列选项中不一定能成立的是()A.ab>ac B.c(b﹣a)>0 C.cb2<ca2D.ac(a﹣c)<0【考点】命题的真假判断与应用.【专题】探究型;定义法;不等式.【分析】根据不等式的基本性质,实数的性质,逐一分析给定四个命题的真假,可得答案.【解答】解:∵c<b<a且ac<0,故c<0,a>0,∴ab>ac一定成立,又∵b﹣a<0,∴c(b﹣a)>0一定成立,b2与a2的大小无法确定,故cb2<ca2不一定成立,∵a﹣c>0,∴ac(a﹣c)<0一定成立,故选:C【点评】本题以命题的真假判断与应用为载体,考查了不等式的基本性质,实数的性质,难度不大,属于基础题.15.(2016秋•青浦区校级期中)设实数x,y为任意的正数,且+=1,求使m≤2x+y恒成立的m的取值范围是()A.(﹣∞,8]B.(﹣∞,8)C.(8,+∞)D.[8,+∞)【考点】基本不等式.【专题】转化思想;转化法;不等式的解法及应用.【分析】不等式2x+y≥m恒成立⇔(2x+y)min≥m.利用“乘1法”和基本不等式的性质即可得出.【解答】解:∵x>0,y>0且+=1,∴2x+y=(2x+y)(+)=4++≥4+2=8,当且仅当y=2x=4时取等号.∵不等式2x+y≥m恒成立⇔(2x+y)min≥m.∴m∈(﹣∞,8],故选:A.【点评】本题考查了“乘1法”和基本不等式的性质、恒成立问题的等价转化方法,属于中档题.16.(2010•浦东新区校级模拟)设[x]表示不超过x的最大整数(例如:[5.5]=5,=﹣6),则不等式[x]2﹣5[x]+6≤0的解集为()A.(2,3)B.[2,4)C.[2,3]D.(2,3]【考点】一元二次不等式的应用.【专题】计算题;压轴题.【分析】先将[x]看成整体,利用不等式[x]2﹣5[x]+6≤0求出[x]的范围,然后根据新定义[x]表示不超过x的最大整数,得到x的范围.【解答】解:不等式[x]2﹣5[x]+6≤0可化为:([x]﹣2)([x]﹣3)≤0解得:2≤[x]≤3,所以解集为2≤[x]≤3,根据[x]表示不超过x的最大整数得不等式的解集为:2≤x<4故选B.【点评】考查学生理解新定义的能力,一元二次不等式,不等式的解法等基础知识,考查运算求解能力,考查整体思想、化归与转化思想.属于基础题.三、解答题(满分52分)17.(8分)(2015秋•上海校级期中)已知集合A={x|x2﹣mx+m2﹣19=0},B={x|x2﹣5x+6=0},C={2,﹣4},若A∩B≠∅,A∩C=∅,求实数m的值.【考点】交集及其运算.【专题】集合.【分析】由A,B,C,以及A∩B≠∅,A∩C=∅,确定出m的值即可.【解答】解:由B中方程变形得:(x﹣2)(x﹣3)=0,解得:x=2或x=3,即B={2,3},∵A={x|x2﹣mx+m2﹣19=0},C={2,﹣4},且A∩B≠∅,A∩C=∅,∴将x=3代入集合A中方程得:m2﹣2m﹣10=0,即(m﹣5)(m+2)=0,解得:m=5或m=﹣2,当m=5时,A={x|x2﹣5x+6=0}={2,3},此时A∩C={2},不合题意,舍去;当m=﹣2时,A={x|x2+2x﹣15=0}={3,﹣5},满足题意,则m的值为﹣2.【点评】此题考查了交集及其运算,熟练掌握交集的定义是解本题的关键.18.(10分)(2016秋•青浦区校级期中)若集合A={x|ax2﹣3x+2=0,a∈R}有且仅有两个子集,求实数a的取值范围.【考点】子集与真子集.【专题】集合思想;转化法;集合.【分析】用描述法表示的集合元素个数问题,用到一元方程解的个数,用判别式与零的关系,当方程有一个解时,判别式等于零.【解答】解:因为集合A={x|ax2﹣3x+2=0}的子集只有两个,所以A中只含一个元素.当a=0时,A={};当a≠0时,若集合A只有一个元素,由一元二次方程判别式△=9﹣8a=0得a=,综上,当a=0或a=时,集合A只有一个元素.故答案为:0或.【点评】解题时容易漏掉a≠0的情况,当方程,不等式,函数最高次项系数带有参数时,要根据情况进行讨论.19.(10分)(2016秋•青浦区校级期中)已知命题甲:关于x的不等式x2+(a﹣1)x+a2≤0的解集为空集;命题乙:方程x2+ax﹣(a﹣4)=0有两个不相等的实根.(1)若甲,乙都是真命题,求实数a的取值范围;(2)若甲,乙中有且只有一个是假命题,求实数a的取值范围.【考点】命题的真假判断与应用.【专题】转化思想;转化法;简易逻辑.【分析】命题甲:;命题乙:a<﹣4,a>2;进而可得:(1)甲,乙都是真命题,(2)甲,乙中有且只有一个是假命题,的实数a的取值范围.【解答】解:命题甲:由不等式x2+(a﹣1)x+a2≤0的解集为空集,得△=(a﹣1)2﹣4a2<0…(1分)解得:…(1分)命题乙:由方程有两个不相等的实根得△=2a2+4(a﹣4)>0,…(1分)解得:a<﹣4,a>2;…(1分)(1)甲,乙都是真命题的条件是a∈(﹣∞,﹣4)∪(2,+∞)…(2分)(2)甲,乙中有且只有一个是假命题的条件是,或,故…(4分)【点评】本题以命题的真假判断与应用为载体,考查了复合命题的真假判断,二次不等式的解法,方程根的个数及其判断,难度中档.20.(12分)(2016秋•青浦区校级期中)如图,要设计一张矩形广告,该广告含有大小相等的左右两个矩形栏目(即图中阴影部分),这两栏的面积之和为18000cm2,四周空白的宽度为10cm,两栏之间的中缝空白的宽度为5cm.(1)设矩形栏目宽度为xcm,求矩形广告面积S(x)的表达式(2)怎样确定广告的高与宽的尺寸(单位:cm),能使矩形广告面积最小?高中数学-打印版校对打印版 【考点】基本不等式在最值问题中的应用.【专题】应用题;函数思想;演绎法;函数的性质及应用.【分析】(1)设矩形栏目宽度为xcm ,高为,利用两栏的面积之和为18000cm 2,建立方程,即可写出矩形广告面积S (x )的表达式;(2)根据基本不等式的性质求得广告面积的最小值.根据等号成立的条件确定广告的高和宽.【解答】解:(1)设矩形栏目宽度为xcm ,高为…(2分)…(4分)(2)根据题意得:等号成立的条件是:x=75,y=120…(2分)答:当广告的高为75cm ,宽为120cm 时,矩形广告的面积最小.…(1分)【点评】本题主要考查了基本不等式在最值问题中的应用.基本不等式在解决生活问题中常被用到,也是高考应用题中热点,平时应用注意这方面的训练.21.(12分)(2015秋•上海校级期中)已知集合M={x |x 2﹣4x +3<0},N={x ||x ﹣3|≤1}.(1)求出集合M ,N ;(2)试定义一种新集合运算△,使M △N={x |1<x <2};(3)若有P={x |||≥},按(2)的运算,求出(N △M )△P . 【考点】子集与交集、并集运算的转换.【专题】计算题;集合.【分析】(1)利用不等式的解法,求出集合M ,N ; (2)M △N 中的元素都在M 中但不在N 中;(3)P={x |||≥}=(2.5,3.5],按(2)的运算,即可求出(N △M )△P .【解答】解:(1)M={x |x 2﹣4x +3<0}={x |1<x <3},N={x ||x ﹣3|≤1}={x |2≤x ≤4}.(2)M △N 中的元素都在M 中但不在N 中,∴定义M △N={x |x ∈M 且x ∉N }.(3)P={x |||≥}=(2.5,3.5],∵N △M={x |3≤x ≤4},∴(N △M )△P={x |3≤x ≤4}.【点评】本题考查集合的运算,考查学生解不等式的能力,属于中档题.。

上海市青浦区2015学年第一学期高三期终学习质量调研测试数学试题带答案

上海市青浦区2015学年第一学期高三期终学习质量调研测试数学试题带答案

上海市青浦区2015学年第一学期高三期终学习质量调研测试数学试题带答案青浦区2015学年第一学期高三期终学习质量调研测试学生注意:(满分150分,答题时间120分钟)数学试题Q.2016.01.051.本试卷包括试题纸和答题纸两部分.2.在试题纸上答题无效,必须在答题纸上的规定位置按照要求答题.3.可使用符合规定的计算器答题.一.填空题(本大题满分56分)本大题共有14题,考生应在答题纸相应编号的空格内直接填写结果,每个空格填对得4分,否则一律得零分. 1.方程组??3x?5y?6?0的增广矩阵是_____________.?4x?3y?7?02.已知3i?2是关于x的方程2x2?px?q?0的一个根,则实数p?q?_____________.?1x?1,x?0??23.函数f(x)??若f(a)?a,则实数a的取值范围是.?1,x?0,??x0????图像的一条对称轴是直线x?4.已知函数f(x)?sin(2x??),5.函数f(x)?lg(2?3)的定义域为.6.已知函数f(x)?x?2,若f(a)?f(b),且0?a?b,则ab的取值范围是.2?8,则?? .xxB?{(x,y)y?3?4x?x}, 7.已知A?{(x,y)y?x?b},满足A?B??,则实数b的取值范围是. 8.执行如图所示的程序框图,输出结果为. 9.平面直角坐标系中,方程x?y?1的曲线围成的封闭图形绕y轴旋转一周所形成的几何体的体积为.10.将两颗质地均匀的骰子抛掷一次,记第一颗骰子出现的点数是m,记第二颗骰子出现的点数是n,向量2开始n=1,S=0 n≤2015 否是????a??m?2,2?n?,向量b??1,1?,则向量a?b的概率..1 S?S?n(n?2)输出S 结束是.高三数学试卷20160105 1 / 9n←n+2 第8题11.已知平面向量???OA?、???OB?、???OC?满足???OA?????OB??0,且???OA?????OC??1,???OB??3,则???CA?????CB?的最大值是.12.如图,将自然数按如下规则“放置”在平面直角坐标系中,使其满足条件:①每个自然数“放置”在一个“整点”(横纵坐标均为整数的点)上;②0在原点,1在?0,1?点,2在?1,1?点,3在?1,0?点,4在?1,?1?点,5在?0,?1?点,?,即所有自然数按顺时针“缠绕”在以“0”为中心的“桩”上,则放置数字?2n?1?2,n?N*的整点坐标是.13.设?ABC的内角A、B、C所对的边a、b、c成等比数列,则ba?ab的取值范围_______.14.若函数f(x)是定义在R 上的奇函数,当x?0 时f(x)?1(x?a2?x?2a22?3a2),若对任意的x?R,f(x?1)?f(x),则实数a的取值范围是________________.二.选择题(本大题满分20分)本大题共有4题,每题有且只有一个正确答案,考生应在答题纸的相应编号上,将代表答案的小方格涂黑,选对得5分,否则一律得零分. 15.a?14是“直线(a?1)x?3ay?1?0与直线(a?1)x?(a?1)y?3?0相互垂直”的?????????????????????????????????(). (A)充分而不必要条件(B)必要而不充分条件(C)充要条件(D)既不充分也不必要条件16.复数z?a?i1?i(a?R, i是虚数单位)在复平面上对应的点不可能位于???(). (A)第一象限(B)第二象限(C)第三象限(D)第四象限17.已知?an?是等比数列,给出以下四个命题:①?2a3n?1?是等比数列;②?an?an?1?是等比数列;③?anan?1?是等比数列;④?lgan?是等比数列,下列命题中正确的个数是?????????????????????????????????().(A)1个(B)2个(C)3个(D)4个2?2px(p?0)与双曲线x2y218.已知抛物线ya2?b2?1(a?0,b?0)有相同的焦点F,点A是两曲线的一个交点,且AF?x轴,若l为双曲线一、三象限的一条渐近线,则l的倾斜角所在的区间可能是?????????????????????????().高三数学试卷20160105 2 / 9(A)?0,???? (B)?6?????????, (C)???,? (D)?64??43??????,? ?32?三.解答题(本大题满分74分)本大题共有5题,解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤.19.(本题满分12分)本题共2小题,第(1)小题6分,第(2)小题6分. 如图所示,在四棱锥P?ABCD中,AB?平面PAD,AB∥CD且2AB?CD,PD?PA,点H为线段AD 的中点,若PPH?1,AD?2,PB与平面ABCD所成角的大小为45?.(1)证明:PH?平面ABCD;(2)求四棱锥P?ABCD的体积.20.(本题满分14分)本题共2小题,第(1)小题6分,第(2)小题8分.已知椭圆M的对称轴为坐标轴,且抛物线y2?4x的焦点F 是椭圆M的一个焦点,以F为圆心,以椭圆M的短半轴长为半径的圆与直线l:x?22y?2?0相切.(1)求椭圆M的方程;(2)已知直线y?x?m与椭圆M交于A、B两点,且椭圆M 上存在点P满足DH A 第19题图CB????????????OP?OA?OB,求m的值.高三数学试卷20160105 3 / 921.(本题满分14分)本题共2小题,第(1)小题4分,第(2)小题10分.如图,有一块平行四边形绿地ABCD,经测量BC?2百米,CD?1百米,?BCD?120?,拟过线段BC上一点E设计一条直路EF(点F在四边形ABCD的边上,不计路的宽度),将绿地分为面积之比为1︰3的左右两部分,分别种植不同的花卉,设EC?x百米,EF?y百米.(1)当点F与点D重合时,试确定点E的位置;(2)试求x的值,使路EF的长度y最短.C E BD 第21题图A22.(本题满分16分)本题共3小题,第(1)小题4分,第(2)小题4分,第(3)小题8分.设数列?an?的所有项都是不等于1的正数,?an?的前n项和为Sn,已知点*(其中常数k?0,且k?1)数列,又bn?log1an.Pn(an,Sn),n?N 在直线y?kx?b上2(1)求证数列?an?是等比数列;(2)如果bn?3?n,求实数k、b的值;(3)若果存在t,s?N*,s?t使得点?t,bs?和?s,bt?都在直线在y?2x?1上,是否存在自然数M,当n?M(n?N*)时,an?1恒成立?若存在,求出M的最小值;若不存在,请说明理由.高三数学试卷20160105 4 / 923.(本题满分18分)本题共3小题,第(1)小题4分,第(2)小题6分,第(3)小题8分.已知函数f(x),g(x)满足关系g(x)?f(x)?f(x??),其中?是常数. (1)设f(x)?cosx?sinx,???2,求g(x)的解析式;(2)设计一个函数f(x)及一个?的值,使得g(x)?2cosx(cosx?3sinx);(3)当f(x)?sinx?cosx,???2时,存在x1,x2?R,对任意x?R,g(x1)?g(x)?g(x2)恒成立,求x1?x2的最小值.高三数学试卷20160105 5 / 9青浦区2015学年第一学期高三期终学习质量调研测试参考答案及评分标准2016.01一.填空题(本大题满分56分)本大题共有14题,考生应在答题纸相应编号的空格内直接填写结果,每个空格填对得4分,否则一律得零分. 1.??35?6??; 2. ;3.;4.;5.(??,0) (??,?1)34?4?437?210081;9. ?;10. ;6201736.(0,2);7.1?22?b?3;8.11.3;12. ??n,n?1?;13. [2,5);14. ?66. ?a?66二.选择题(本大题满分20分)本大题共有4题,每题有且只有一个正确答案,考生应在答题纸的相应编号上,将代表答案的小方格涂黑,选对得5分,否则一律得零分. 15. A ;16. A ;17.B ;18. D .三.解答题(本大题满分74分)本大题共有5题,解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤.19.(本题满分12分)本题共2小题,第(1)小题6分,第(2)小题6分.19. 解:(1)证明:?AB?平面PAD,PH?平面PAD,AB?PH 又?PAD中,PD?PA,点H为线段AD的中点,PH?AD?PH?AD???PH?AB?PH?平面ABCD ?AD?AB?A?(2)?PH?1,AD?2?AH?DH?26,又PH?AD,?PA?PD?,22连结BH,可得?PBH是PB与平面ABCD所成角,又PB 与平面ABCD所成角的大小为45?,?BH?1,在Rt?ABH 中,AB?2,21111?VP?ABCD?S梯形ABCDPH??(AB?CD)?AD?PH?.分332220.(本题满分14分)本题共2小题,第(1)小题6分,第(2)小题8分. 解:(1)因为抛物线y?4x的焦点F是椭圆M的一个焦点,即F(1,0)2x2y222又椭圆M的对称轴为坐标轴,所以设椭圆方程为2?2?1,a?b?0,且a?b?1ab高三数学试卷20160105 6 / 9百度搜索“就爱阅读”,专业资料、生活学习,尽在就爱阅读网,您的在线图书馆!。

2015届上海市青浦区高三上学期期终学习质量调研数学试卷(带解析)

2015届上海市青浦区高三上学期期终学习质量调研数学试卷(带解析)

试卷第1页,共7页绝密★启用前2015届上海市青浦区高三上学期期终学习质量调研数学试卷(带解析)试卷副标题考试范围:xxx ;考试时间:167分钟;命题人:xxx学校:___________姓名:___________班级:___________考号:___________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第I 卷(选择题)一、选择题(题型注释)1、设函数,函数,则方程实数根的个数是( ).A .个B .个C .个D .个2、设为正实数,则“”是“”成立的( ).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3、设是两条不同的直线,是两个不同的平面,则下面四个命题中错误的是( ).试卷第2页,共7页A .若,则//B .若,则C .若,则//或D .若//,则4、已知,则向量与向量的夹角为( ).A .B .C .D .试卷第3页,共7页第II 卷(非选择题)二、填空题(题型注释)5、当和取遍所有实数时,恒成立,则的最小值为 .6、设函数在上有定义,对于任意给定正数,定义函数,则称函数为的“孪生函数”,若给定函数,,则= .7、已知正实数满足,则的最小值为 .8、已知,则无穷数列前项和的极限为 .9、若甲乙两人从门课程中各选修门,则甲乙所选的课程中恰有门相同的选法有 种.10、抛物线的动弦的长为,则弦中点到轴的最短距离是 .11、已知函数对任意的满足,且当时,.若有4个零点,则实数的取值范围是 .12、函数的反函数为,如果函数的图像过点,那么函数的图像一定过点 .试卷第4页,共7页13、平面截半径为的球所得的截面圆的面积为,则球心到平面的距离为____ .14、已知函数与,它们的图像有一个横坐标为的交点,则的值是 .15、直线的倾斜角.16、展开式中有理项的个数是 .17、设是等差数列的前项和,若,则.18、若复数(为虚数单位),则的值为_____________.三、解答题(题型注释)19、(本题满分18分)本题共3小题,第(1)小题6分,第(2)小题6分,第(3)小题6分.已知函数.试卷第5页,共7页(1)指出的基本性质(结论不要求证明)并作出函数的图像;(2)关于的不等式恒成立,求实数的取值范围; (3)关于的方程()恰有6个不同的实数解,求的取值范围.20、(本题满分16分)本题共3小题,第(1)小题4分,第(2)小题4分,第(3)小题8分.已知数列是公差不为的等差数列,数列是等比数列,且,,数列的前项和为,记点.(1)求数列的通项公式;(2)证明:点在同一直线上,并求出直线方程;(3)若对恒成立,求的最小值.21、(本题满分12分)本题共2小题,第(1)小题6分,第(2)小题6分. 如图所示,在长方体中,,,,为棱上一点.试卷第6页,共7页(1)若,求异面直线和所成角的正切值;(2)若,求证平面.22、(本题满分14分)本题共2小题,第(1)小题8分,第(2)小题6分. 如图,摩天轮上一点在时刻距离地面高度满足,,已知某摩天轮的半径为米,点距地面的高度为米,摩天轮做匀速转动,每分钟转一圈,点的起始位置在摩天轮的最低点处.(1)根据条件写出(米)关于(分钟)的解析式; (2)在摩天轮转动的一圈内,有多长时间点距离地面超过米?23、(本题满分14分)本题共2小题,第(1)小题6分,第(2)小题8分.如图所示的“8”字形曲线是由两个关于轴对称的半圆和一个双曲线的一部分组成的图形,其中上半个圆所在圆方程是,双曲线的左、右顶点、是该圆与轴的交点,双曲线与半圆相交于与轴平行的直径的两端点.试卷第7页,共7页(1)试求双曲线的标准方程;(2)记双曲线的左、右焦点为、,试在“8”字形曲线上求点,使得是直角.参考答案1、2、3、4、5、6、7、8、9、10、11、12、13、14、15、16、17、18、19、(1)见图象,(2),(3)20、(1),(2)(3)21、(1),(2)证明略,22、(1)(2)23、(1),(2)满足条件的点有4个,分别为.【解析】1、试题分析:首先画出函数的图象,特别是当时,,当时,,当时,...,在画出对数函数的图象,两曲线交于点,则方程实数根的个数有2个 .考点:1.函数的零点;2.把函数零点问题转化为两曲线的交点问题;2、试题分析:已知为正实数,若,因为,则有,反过来,若,则,则“”是“”成立的充要条件 .考点:充要条件;3、试题分析:命题(A )中若,则或,但,则.正确,命题(B )中若 ,则正确,命题(C )中若 ,则//或正确,命题(D )若,则直线错误,因为//,则与平面可能平行,可能相交;选择.考点:空间直线与平面的位置关系;4、试题分析:由,则,向量与向量的夹角为,选 .考点:平面向量的数量积和向量夹角;5、试题分析:首先把题目中的字母更改一下,当和取遍所有实数,这时设,令,则点的轨迹为直线;设,令,则点的轨迹为圆在第一象限的四分之一圆弧,而表示圆弧上一点与直线上一点的距离的平方,画出图形可以看出,当取圆弧上一点时,点到直线的距离最小,此时,取最大值为8,要使当和取遍所有实数时,恒成立,则的最小值为.考点:1.直线和圆的参数方程;2.两点间的距离;6、试题分析:由“孪生函数”定义可知:给定函数,,则,即,则考点:自定义信息题;7、试题分析:由于,则,利用均值不等式,(当且仅当时取等号),则,所以的最小值为考点:均值不等式;8、试题分析:根据通项公式可知:........,则无穷数列前项和的极限为考点:无穷递缩等比数列的各项和公式;9、试题分析:甲乙所限课程有两门相同,从6门选2门,有种选法,余下4门课程,甲有4种选法,乙有3种选法,共有种选法考点:排列、组合、计数原理;10、试题分析:要使弦中点到轴的距离最短,只需使弦轴,则点纵坐标为3,把代入中得,则弦中点到轴的最短距离是. 考点:抛物线中的最值问题;11、试题分析:函数对任意的满足,说明函数是偶函数,若有4个零点,当时,,有两个零点,则只需.考点:1.偶函数图象的性质;2.函数的零点;3.数形结合思想;12、试题分析:由于函数的图像过点,则它的反函数图象过,则,对于函数,令,则,则的图像一定过点.考点:互为反函数图像关系;13、试题分析:由于截面圆的面积为,则截面圆的半径为,又球的半径为,由于球的半径、截面圆的半径,球心到界面距离满足勾股定理,则球心到平面的距离为考点:1.球和截面;2.球心与截面圆心连线垂直截面,球的半径、截面圆的半径,球心距满足勾股定理;14、试题分析:当时,函数过点,则也过点,则,因,.考点:已知三角函数值求角;15、试题分析:由于直线方程化为,斜率为,由于直线的倾斜角的范围是,则直线的倾斜角为考点:直线的倾斜角与斜率;直线的倾斜角的范围;16、试题分析:,当时是有理项,展开式中有理项的个数是.考点:二项式定理和通项公式;17、试题分析:【法一】由于,【法二】即:;考点:等差数列前项和公式和性质;18、试题分析:[法一],[法二]先求出,则,考点:1.复数的运算与复数的模;19、试题分析:明确绝对值的含义,首先化简绝对值符号,当时,,,则,,,同理:当,,当时,,当时,,求出的解析式,画出函数在每一段的图象,可以看出函数函数是偶函数,数形结合后,写出单调区间及最值;第二步先用换元法令,把不等式后,先求的最大值,然后写出的范围;第三步先观察的图象可知,关于的方程()恰有6个不同的实数解即有6个不同的解,要使方程有6个不同实根,只需,,这时只需研究一元二次方程的根的分布问题即可,何时一元二次方程的一根为2,另一根在呢?设,首先一根为2满足,另一根在满足,消去求出的取值范围即可 .试题解析:(1),,是偶函数,在区间和上单调递增,在区间和上单调递减,的最大值是,无最小值,值域为作图如下:因为关于的不等式恒成立,令,则,即不等式在上恒成立,当时,,不等式化为,又(3)关于的方程()恰有6个不同的实数解即有6个不同的解,数形结合可知必有和,,令,则关于的方程有一根为2,另一根在间,考点:1.含绝对值符号的函数式化为分段函数;2.极端原理;3.数形结合;20、试题分析:先根据题意列方程组,求出等比数列的公比及等差数列的公差,得到两数列的通项公式,第二步证明点在一条直线上,只需证明具有线性关系,满足直线方程,通过消元法可达目的,第三步恒成立问题,通过对的单调性的讨论,研究的单调性,从而求出取值范围,进而找出的最小值.试题解析:(1)设等差数列的公差为,等比数列的公比为,由题设可得....(1),...........(2),联立(1)(2)得方程组,解方程组得:或,因为数列是公差不为0的等差数列,所以,即,,,令,两式消去得,即点,在同一条直线上。

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青浦高级中学2015学年第一学期期中考试II. Grammar and Vocabulary (26%)Section ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)The good effects of an economic crisisWhile an economic crisis results in untold misery for countries and their people, a new study of health in Cuba has suggested there could be a silver lining during hard times.Researchers imply that people(25)_______lose weight during an economic crisis due to a reduction in eating and increasing physical activity.Their dramatic findings were based on a study in Cuba, where the population suffered food and fuel shortages(26)_________(follow) the economic crisis of the early 1990s.(27)_______resulted in an average decrease of 4to 5 kg(8 to 11ibs) in weight and subsequent rapid declines in deaths from heart disease by a third. Whole population trends in food consumption and transport policies (29)__________(link) to physical activity could reduce the burden of two major illnesses, said the researchers.―during the deepest period of the economic crisis in Cuba, from 1991 to 1995, food was scarce and access to gas was greatly reduced, virtually(30)_______(eliminate) motorized transport. This caused the industrial and agricultural sectors to shift to manual intensive labor,‖ said Prof Manuel Franco, (31)_____led the international team of researchers from Spain, Cuba and the United states.―so far, no country or regional population(32)______(reduce) the occurrence of fatness through public health campaigns or targeted treatment programmes successfully.‖(B)The answer is blowing in the windBritain is in the middle of a serious energy crisis! At the moment, more than 90%of Britain ‗s energy needs are met by burning fossil fuels or produced in nuclear power stations. Unfortunately, these are not renewable sources of energy. More importantly, these methods of electricity generation are harmful to the environment. What can we use as an alternative form of energy? (33)__________answer is all around us. Wind power!Wind power is an alternative energy source (34)__________has been used for many years in countries like Holland and Denmark. Strangely enough, even though it is one of power. All we need to do now is to set up some wind farms.Wind farms are actually groups of electricity-generating wind turbines. Wind turbines make hardly any noise and they are not unpleasant(36)___________(look) at. Now, there is still one thing you may worry. Because wind farms are so big and occupy a lot of space, do they influence us ? Actually, they are often located on unoccupied sites. Building wind farms at sea is also possible. Offshore wind farms also mean that much larger turbines can be built, (38)_______ objections from the public.A typical wind farm with several wind turbines will produce enough energy(39)________(meet) the annual electricity needs of about 1500 homes. At the moment, there are only around sixty wind farms in Britain . As this number increases, we may well see wind power (40)________(supply) as much as 20% of B ritain‘s electricity demands.So , why delay? Isn‘t it about time we stared building more wind farms in Britain and protecting our environment for future generations?Section BDirections:Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need. (** 友情提示:本题共十个空,请A tragic photo has made ___41___ around the world and awoken people to the Syrian refugee crisis.The photo shows the lifeless body of a baby boy lying ___42_____on the beach, his face sunken into the wet sand, his name was Aylan Kurdi. He had climbed aboard a smuggler‘s boat to escape war-torn Syria, in hopes of ___43_____with his aunt in Canada. But violent waves __44____ Aylan and his family into the Mediterranean sea. The shocking photo become refugee. But why do these Syrians____45_____ everything to run away from their country?After World War 1, France took control of part of the territory, today known as Syria and Lebanon . French colonialists formed a border around different ethnic and religious groups. Not all of these groups got along. Anti-government protests began in March 2011, and increased in extent after government decided to ______46____down. The protests had become a civil war by early 2012.Civilians have____47____ tremendously in syria‘s cruel conflict. Fighting and bombing have destroyed _____48__neighborhoods and towns. More than 250000 people have been killed. Half of the country‘s 22million citizens have been hom eless, with 4 million ____49____as refugees.Most Syrian refugees end up in camps in neighboring countries such as Turkey, Iraq, Jordan and Lebanon. But those places have been overcrowded and ___50___.many of these refugees hope to resettle in europe. But often, as in the case of little Aylan Kurdi, their voyages ends only in tragedy.III. Reading Comprehension(47%)Section ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.It‘s a basic commodity on menus, from fine teahouse to Starbucks: green tea. But the drink, which is experiencing a resurgence(再起,复活) of ____51_____, once fell out favor in the west.Green tea is believed to have___52_____-in China one thousand years ago, where it was recognized for its health benefits. And scientists continue to discover to discover new uses for the drink. Some studies suggest it can help ___53____cholesterol(胆固醇),protect against cancer and perhaps even fight tooth decay.Supported by the health food craze, green tea sales are ___54_____rising rapidly. The tea association of the USA reports that green tea sales jumped more than 60percent in the last decade. And in Canada, government data shows that _____55___-for green tea imports increased more than four times. Nowadays, green tea seems to be everywhere. In shops, you can buy green tea leaves prepared in a variety of ways: fried, aged, powdered or steamed.The funny things, _56___green t ea‘s healthy reputation, the drink was once considered as dangerous. Where did this nonsense come from? _____57____ the Victorian, of course. The Victorians lived in a period of English history around Queen Victoria‘s ruling period, in the 19th century. That‘s when some of the silliest theories about green tea arouse. One 1882 book described weird experiment to illustrate the risks of green tea. ____58_____a dose of green tea below a frog‘s abdomen(腹部),and you could cause loss of the abilities to move a body part in its back legs, the book claimed. And injecting the drink into a dog would cause it to lose control of its legs and tail. The book went so far as to report that green tea could kill someone, if it were applied to the certain kind of nerve. At the time, a green tea __59______ was sweeping England. Even Charlotte Bronte, an English literary master, refused to touch the drink, ____60___its bad effects it would have on her nerves.Some of the fear was well founded, though. English consumers___61____ brighter leaves over dull olive---colored ones. As a result, tea sellers would __62____dye their products, using anything they can get –including poisons like ―Prussian blue‖ cyanide(氰化物)。

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