2016-高一下学期期末考试试题

2016—2017学年高一年级第二学期期末考试考生注意：（1）本试题满分120分，考试时间100分钟（2）将各题答案按序号答在答题卡上，试卷考生自己保存第I卷第一部分：阅读理解（共20小题，每小题2分，满分40分）第一节（共15小题，每小题2分，满分30分）阅读下列短文，从每题所给的四个选项（A、B、C和D)中，选出最佳选项。

AThere are a lot of products out there that make your life ea sier. Some, however, are a little sillier than others — so much that they seem like joke products. Here are a few products tha t sound crazy, but actually rule.Sleep PhonesIt’s hard to imagine something sillier than a music-playing headband you wear while you sleep, but they exist —and are quite popular. Sleep Phones won’t give you the highe st quality sound in the world, but if you prefer to fall asleep to music, they’re far more comfortable than normal headphones. While they’re a bit expensive, they might be perfec t for you. There’s also a wireless version (版本) if you prefer. Onion GogglesIf cutting onion brings on the waterworks no matter what you t ry, it’s time for desperate measures. We tested a bunch of me thods for avoiding onion tears, and found the best solutions c ame down to cutting the onion under a vent (通风孔), or wearing these stylish and awesome goggles.Lock LacesThere’re some great ways to tie your shoes better, but if you l ong for the laceless shoes of your childhood days, Lock Lace s are a pretty good choice. They’re basically elastic (有弹性的) laces that remove the need to tie your shoes. Sure, peopl e will make fun of you, but you can make fun of them after the y trip over their own untied laces. Or you can make your own slip-on shoes with elastic tubing.2D-GlassesHate 3D-movies, but have to go to one? The difference between 2D-glasses and 3D-glasses lies in their lenses (镜片). Each lens of 2D-glasses blocks the same picture, so each eye gets the same picture, while each lens of 3D-glasses blocks a different picture, so each eye gets a different picture which the brain interprets as 3D. Now you have a pair of glasses that can save you from the headache caused by w earing 3D-glasses which are popular in our movie theaters. You can buy them or make a pair for yourself.1．What do we know about Sleep Phones?A. There are two versions.B. They’re comfortable but unhealthy.C. They give you the best quality sound.D. They’re cheaper than other headphones.2．The underlined part “b rings on the waterworks” in the text probably means _____.A. makes your eyes waterB. makes your fingers hurtC. destroys your water pipesD. adds to your washing work3．What is the advantage of Lock Laces?A. They are strong and lasting.B. They help you walk comfortably.C. They are stylish and eco-friendly.D. They save you from tying your shoes.4．Compared with 3D-glasses, 2D-glasses _____.A. are cheaper and thinnerB. won’t give you a headacheC. let you see a different pictureD. are more popular in movie theaters.BThe arts, especially music, should be part of every school's lessons at every grade level. Students would be much smart er if they had some musical experience. They could improve t heir classroom skills,such as paying attention and following di rections and so on. People develop all these skills when they l earn music. Making music also lets children use their imaginat ion. It provides students with a chance to try out their own ide as.Music not only makes children better students, but also gives them something positive to do. In a music program, children c an be part of a band instead of joining a gang (团伙). Parents can enjoy listening to their children's music instea d of seeing them glued to a computer or TV screen. In a scho ol band, students get to be part of a team. They can get along well with old friends and make new friends through music.Music builds self-confidence, too. It gives children a sense of achievement and success. Making music is something for them to be proud of, and it lets kids practice performing in front of an audience. Mu sic gives children an opportunity for self-expression, and that helps develop their self-confidence. Once again, music is important because it can make children better students, give them something positive to do, and build their character. That is why music should be offered in every s ingle grade in every school.5．According to the passage, music could make students sm arter by _______________.A. improving their classroom skills and paying attentionB. improving their classroom skills and imaginationC. improving their attention, direction and imaginationD. learning music, making music and trying out their own idea s6．What does the underlined phrase "glued to" in the second paragraph mean?A. unwilling to turn onB. always lookingC. unwilling to leaveD. always playing7．The third paragraph mainly tells us that music could _____ __________.A. give children self-expression and self-confidenceB. bring to children achievement and successC. give children something to be proud ofD. develop children's self-confidence8．What's the best title of this passage？A. Music is a must as a course at schoolB. Music builds children's self-confidenceC. Music makes students much smarterD. Learning music and making music.CThe spread of Western eating habits around the world is ba d for human health and for the environment. Those findings c ome from a new report in the journal Nature.David Tilman is a professor at the of . In the study, he examin ed information from 100 nations to show what people ate and how diet affected health. Mr. Tilman noted a movement begin ning in the 1960s. He found that as nations industrialized(工业化), population increased and earnings rose. More people began to adopt what has been called the Western diet. The Wes tern diet is high in sugar, fat, oil and meat. By eating these foo ds, people began to get fatter and sicker.“The food, let us say, in the 15 richest nations of the world, rig ht now contains about 400 or 500 extra calories(热量) a day that are eaten beyond what people need, and that le ads people to gain weight.”David Tillman says overweight people are at greater risk for di seases like diabetes, heart disease and some cancers. Diabet es is shooting to very high rates in the United States and acro ss Europe. Heart disease is a major cause of death in the We stern nations. Unfortunately when people become industrializ ed, if they adopt this Western diet, they are going to have thes e same health problems.A diet bad for human beings, it seems, is also bad for the envi ronment. As the world’s population grows, experts say more f orests and areas will become farmland for crops or grassland s for raising cattle. These areas will be needed to meet the inc reasing demand for food.Mr. Tilman calls the link between diet, the environment and hu man health, “a dilemma”, a situation where it is very difficult to decide what to do. He says one possible solution is leaving th e Western diet behind.9．Why did people get fatter in the 1960s?A. They ate foods high in calories.B. They adopted a western lifestyle.C. They set aside little time for exercise.D. They had a better life and became lazier.10.According to the text, overweight people may suffer the foll owing diseases EXCEPT_____.A. diabetesB. skin diseaseC. cancersD. he art disease11．What can we infer from Paragraph 5?A. There will be fewer and fewer forests.B. People won’t care about the environment.C. The world’s population will grow faster than ever.D. Raising cattle will be the most moneymaking business. 12．What is the purpose of the author in writing this passage ?A. To tell people effective ways to keep healthy.B. To call on people to give up the Western diet.C. To show the problems industrialized nations are facing.D. To draw people’s attention to environmental protection.DWhile astronauts in space get to do many exciting things, t hey miss out on ordinary things that we will take for granted—being able to walk on firm ground, hanging out with family and digging into a slice of hot steaming pizza. Though not much c an be done about the first two things, there may soon be a sol ution to the third one, thanks to this cool 3-D pizza printer. About a year ago, NASA offered $125,000 to Anjan Contracto r, a 3-D technology expert, to build a device that would allow astron auts to make pizza on demand. The mechanical engineer pro mised that his invention would produce pies in large quantities that looked, tasted and even smelledlike pizza made in common ovens.Late last year, the engineer presented a video of his first proto type(原型) that begins by creating a single slice of dough that is cook ed and printed at the same time. Then comes the tomato sau ce--a mix of tomato powder, oil and water and finally, a protein sli ce that resembles cheese. While the video doesn't show theb aking process, the inventor says that once the pizza is printed, it can be ready to be consumed in 7 seconds.While the pie in the video looks delicious enough to attract an y pizza lover, Anjan Contractor is far from ready for astronaut s. That's because he still has to find a solution to make the fo od container in the printer last for 30 years. Though that may sound unrealistic ,actually it is not.Anjan Contractor believes that the only way that is possible is that the water is removed from all the ingredients and then the y are reduced to the powder form. This, as you can imagine, will not be so easy. But, while the printer may not be ready for space, it certainly looks ready enough for people on earth. H opefully, NASA and Contractor will consider selling it to those not fortunate enough to go to Mars !13．NASA offered $125,000 to Anjan Contractor mainly to __ __.A. create some new type of 3-D printerB. attract more companies to work for NASAC. help astronauts in space enjoy fresh pizza one dayD. produce pizza in large quantities to earn great profits 14．The biggest challenge that Anjan Contractor is faced with now is probably that ____A. he has no money left to go on with his researchB. the pizza doesn't seem appetizing（令人开胃的） to pizza loversC. he has no way to make pizza that can last for thirty yearsD. he cannot make the food container last for decades 15．What's the best title of the passage?A. NASA is trying its best to help astronautsB. Astronauts may soon be able to enjoy steaming hot pizzaC. NASA is working on making pizza for common peopleD. A 3-D pizza printer has been used to make pizza第二节：七选五（共5小题，每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

IndБайду номын сангаасa
In India，Teachers' Day is celebrated on September 5，in hono r of Dr Sarvepalli Radhakrishnan，the second President of India.Because his birthday was September 5th.At schools on this day，students in India celebrate this day to showtheir respect and love to their teachers.
A．covered B．shared
C．compared D．equipped
6．It can be inferred from the passage that Mary ________．
A．was tired of her dog
B．cared about her dog very much
C．was so sad about her disease that she never thought of her dog
Although different countries celebrate Teachers' Day on different days，the activities people take to celebrate it just stay the same.
1．The best title of the passage is ________．
D．Mary took her dog for the evening walk every day when she was in hospital

A．－1 B．1 C．－2 D．2
6.具有线性相关关系的变量x，y，满足一组数据如右表所示.若 与 的回归直线方程为 ，则m的值是（ ）
0
1
2
3
-1
1
m
8
A. 4 B. C. 5 D. 6
7.若某程序框图如ห้องสมุดไป่ตู้图所示,则该程序运行后输出的B等于（ ）
A．63B．31C．127D．15
8.要得到函数 的图象，只需将函数 的图象( )
21.．解：
. …… 3分
（1）因为 ，所以 ，所以当 时， . …7分
（2）由 ，知 ，
因为 ，所以 ，因此 ，
所以
. …… 12分
22. 解：（1）
…… 4分
∴函数 的最小正周期 …… 5分
令 ，解得
∴函数 的单调递减区间是 …… 7分
（2）由 ，得 ，即
在△ 中，∵ ，∴ ，得 …… 9分
又∵ ，∴
2.现有 辆汽车通过某一段公路时的时速的频率分布直方图如图所示，时速在 的汽车大约有( )
A．80辆B． 辆C． 辆D． 辆
3.一条弦的长等于半径，则这条弦所对的圆心角是 ____弧度．()
A．π
4.已知 ， ，则 的值为( )
（A） （B） （C） （D）
5．已知平面向量 ， ， 与 垂直，则 是（ ）
15.若点P(3a－9，a＋2)在角α的终边上，且cosα≤0，sinα>0，则实数a的取值范围是__________．
16.在 中，内角 的对边分别为 ，若 ， ， ．则边 的长度为__________．
三、解答题（本大题共70分。解答应写出文字说明）
17. (本题满分10分)

2014年重庆一中高2016级高一下期期末考试数 学 试 题 卷 2014.7第Ⅰ卷(选择题，共50分)【试卷综评】本次试卷（1） 注重基础知识、基本技能的考查，符合高考命题的意图和宗旨。

让不同的考生掌握不同层次的数学，让几乎所有的考生都能感受到成功的喜悦。

注重基础知识的考查，这样让所有同学对数学学习有了更强的信心。

（2） 注重能力考查 初等数学的基础知识是学生进入高等学校继续学习的基础，也是参加社会实践的必备知识．考查学生基础知识的掌握程度，是高考的重要目标之一．要善于知识之间的联系，善于综合应用，支离破碎的知识是不能形成能力的．考查时，既要注重综合性，又兼顾到全面，更注意突出重点．一、选择题：(本大题共10个小题，每小题5分，共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；各题答案必须答在答题卡上相应的位置.1. 已知等差数列{}n a 中，282a a += ，5118a a +=，则其公差是（ ）A ． 6B ．3C ．2D ．1【知识点】等差数列的性质;等差数列的通项公式．【答案解析】D 解析 ：解：∵等差数列{a n }中5118a a +=，282a a +=∴511286,a a a a +-+=即66,1d d ==,故选：D.【思路点拨】将两式5118a a +=，282a a +=作差，根据等差数列的性质建立公差的等式，解之即可．2. 已知直线01)1(:1=+++y a ax l ，02:2=++ay x l ，则“2-=a ”是“21l l ⊥”的（ ）A ．充分不必要条件B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件【知识点】两直线垂直的充要条件.【答案解析】A 解析 ：解：因为21l l ⊥，则()110a a a ⨯++=，解得2-=a 或0a =，所以“2-=a ”是“21l l ⊥”的充分不必要条件.故选：A.【思路点拨】利用两直线垂直的充要条件解方程可得2-=a 或0a =，然后判断即可.3.学校为了解学生在课外读物方面的支出情况，抽取了n 个同学进行调查，结果显示这些同学的支出都在[10,50)（单位：元），其中支出在[)30,50（单位：元）的同学有67人，其频率分布直方图如右图所示，则n 的值为（ ）A ．100B ．120C ．130D ．3904.(原创)口袋中有形状和大小完全相同的四个球，球的编号分别为1,2,3,4，若从袋中随机抽取两个球，则取出的两个球的编号之和大于5的概率为（ ）5.如图. 程序输出的结果s=132 , 则判断框中应填（ ）A. i ≥10B. i ≥C. i ≤11D. i ≥12 【知识点】程序框图．【答案解析】B 解析 ：解：由题意，S 表示从12开始的逐渐减小的若干个整数的乘积，由于12×11=132，故此循环体需要执行两次所以每次执行后i 的值依次为11，10,由于i 的值为10时，就应该退出循环，再考察四个选项，B 符合题意 故选B【思路点拨】由框图可以得出，循环体中的运算是每执行一次s 就变成了s 乘以i ，i 的值变为i-2，故S 的值是从12开始的逐渐减小的若干个整数的乘积，由此规律解题计算出循环体执行几次，再求出退出循环的条件，对比四个选项得出正确答案．6.圆()221x a y -+=与直线y x =相切于第三象限，则a 的值是（ ）．A ．2B ．2-C ．．2【知识点】圆的标准方程；点到直线的距离公式.【答案解析】C 解析 ：解：由圆()221x a y -+=，得到圆心（a ，0），半径r=1， 根据题意得：圆心到直线y x =1，=解得：a =∵圆与直线相切于第三象限，∴a ＜0．即a =故选C ．【思路点拨】由圆方程找出圆心坐标与半径，根据题意得到圆心到切线的距离等于圆的半径，利用点到直线的距离公式列出关于a 的方程，求出方程的解即可得到a 的值．7.已知点(,)P x y 在不等式组⎪⎩⎪⎨⎧≥-+≤-≤-0220102y x y x 表示的平面区域上运动，则z x y =-的取值范围是（ ）A.[]2,1--B. []1,2-C. []2,1-D.[]1,2【知识点】简单的线性规划.【答案解析】B 解析 ：解：画可行域如图，画直线y x =，平移直线y x =过点A （0，1）时z 有最大值1；平移直线y x =过点B （2，0）时z 有最小值-2；则z y x =-的取值范围是[-2，1]故选B.【思路点拨】根据步骤：①画可行域②z 为目标函数纵截距③画直线0=y-x ，平移可得直线过A 或B 时z 有最值即可解决．【典型总结】本题主要考查了简单的线性规划，以及利用几何意义求最值．8.设{}n a 是公比为q 的等比数列，令1n n b a =+，*n N ∈，若数列{}n b 的连续四项在集合}{53,23,19,37,82--中，则q 等于( )A ．4-B ．3-C ．3-或2-D ．3-或4-9.已知在平面直角坐标系xoy 中，圆C 的方程为2223x y y +=-+，直线l 过点(1,0)且与直线10x y -+=垂直.若直线l 与圆C 交于A B 、两点，则OAB ∆的面积为（ ）A ．1B ．2 D ．【知识点】点到直线的距离公式;直线的方程;圆的方程;直线与圆的位置关系.【答案解析】A 解析 ：解：∵圆C 的方程为x 2+y 2=-2y+3，∴化成标准方程，可得x 2+（y+1）2=4， 由此可得圆的圆心为C （0，-1）、半径为2．∵直线x-y+1=0的斜率为1且与直线l 垂直，直线l 经过点（1，0）， ∴直线l 的斜率为k=-1，可得直线l 的方程为y=-（x-1），即x+y-1=0．因此，圆心C 到直线l 的距离d ==AB =又∵坐标原点O 到AB 的距离为d'2，=出圆心C 到l 的距离d =公式即可算出△OAB 的面积．10. (原创) 设集合},,)2(2|),{(222R y x m y x m y x A ∈≤+-≤=, },,122|),{(R y x m y x m y x B ∈+≤+≤=, 若A B φ＝，则实数m 的取值范围是（ ）A 21m ≤≤ B. 02m <<+C. 21m m <->D. 122m m <>+或【知识点】直线与圆的位置关系.【答案解析】D 解析 ：解：因为A B φ＝，则ÆA=或蛊A ，（1）当ÆA=时，必有22m m <，解得10m <<，满足题意.①0A {20}B {x y |0x y 1}m ===? 时，（，），（，），此时A B φ＝，满足题意；②当m 0＜时，有||m m --＜且＜；则有m m 2---＞，＞， 又由m 0＜，则22m 1+＞，可得A B φ＝，满足题意；③当m ³1m |m ，解可得：221122m m m m ><->+<-，又由m ³2m >第Ⅱ卷(非选择题，共100分)二、填空题：(本大题共5个小题，每小题5分，共25分)各题答案必须填写在答题卡相应的位置上.11. 在△ABC 中，角,,A B C 所对的边分别为,,a b c ，已知2a =，3c =，60B =︒．则b 60B =︒，∴由余弦定理得：222b a c 2accos B 49=+-=+-【思路点拨】利用余弦定理列出关系式，将a ，c 及cosB 代入计算即可求出b 的值．12.在区间[5,5]-内随机地取出一个数a ，使得221{|20}x x ax a ∈+->的概率为 ． 【知识点】几何概型．【答案解析】0.3解析 ：解：由题意221{|20}x x ax a ∈+->，故有22a a 0＞+-，解得1a 2＜＜-,由几何概率模型的知识知，总的测度，区间[5,5]-的长度为10，随机地取出一个数a ，使得221{|20}x x ax a ∈+->这个事件的测度为3故区间[5,5]-内随机地取出一个数a ，使得221{|20}x x ax a ∈+->的概率为0.3 故答案为0.3【思路点拨】由221{|20}x x ax a ∈+->代入得出关于参数a 的不等式，解之求得a 的范围，再由几何的概率模型的知识求出其概率．【典型总结】本题考查几何概率模型，求解本题的关键是正确理解221{|20}x x ax a ∈+->的意义，即得到参数a 所满足的不等式，从中解出事件所对应的概率.13.若直线)0,(022>=-+b a by ax 始终平分圆082422=---+y x y x 的周长，则ba 121+的最小值为【答案22x 2y 113（）（），-+-=∴圆的圆心是（2，1）,∵直线平分圆的周长，所以直线恒过圆心（2，1）,把（2，1）代入直线)0,(022>=-+b a by ax ，得1a b +=()111322b a a b b a b a b⎛⎫+=++=++ ⎪⎝⎭∵a ＞0，b ＞0，()1113222b a a b b a b a b ⎛⎫=++=++≥ ⎪⎝⎭故答案为：. 【思路点拨】先求出圆的圆心坐标，由于直线平分圆的周长，所以直线恒过圆心，从而有a b +=+)112a b a b ⎛⎫++ ⎪⎝⎭，利用基本不等式可求． 14. (原创)给出下列四个命题：①某班级一共有52名学生，现将该班学生随机编号，用系统抽样的方法抽取一个容量为4的样本，已知7号、33号、46号同学在样本中，那么样本中另一位同学的编号为23； ②一组有六个数的数据是1,2,3,3,4,5的平均数、众数、中位数都相同； ③根据具有线性相关关系的两个变量的统计数据所得的回归直线方程为y a bx =+中，2,1,3,b x y ===则1a =；其中正确的命题有 （请填上所有正确命题的序号）对于③，回归直线方程为y=ax+2的直线过点(),x y ，把（1，3）代入回归直线方程y=ax+2得a=1．③是真命题；故答案为：②③，【思路点拨】①利用系统抽样的特点可求得该次系统抽样的编号，从而可判断其正误；②利用平均数、众数、中位数的概念，可求得数据1、2、3、4、5的平均数、众数、中位数，从而可知其正误； ③利用回归直线过点(),x y ，即可求得a 的值，从而可知其正误.15. (原创) 数列{}n a 满足*1142(1),()32n n n n a a a n N a n ++==∈+－,则n a 的最小值是【知识点】构造新数列；等差数列的性质.【答案解析】8-解析 ：解：因为12(1)2n n n n a a a n++=+，整理得：112(1)2n n n n a a n a na ++=+-， 两边同时除以1n n a a +可得：12(1)21n n n n a a ++-=，则数列2n n a ⎧⎫⎨⎬⎩⎭是公差为1的等差数列，所以()12211n n n a a =+-⨯，即252n n a n =-，当3n ≥时，0n a >，当2n =时，8n a =-，故n a 的最小值是8-.故答案为：8-. 【思路点拨】先把原式变形构造新数列2n n a ⎧⎫⎨⎬⎩⎭进而判断即可. 三、解答题 ：(本大题6个小题，共75分)各题解答必须答在答题卡上相应题目指定的方框内(必须写出必要的文字说明、演算步骤或推理过程).16.（本小题满分13分）在等比数列{}n a 中，11a =，且14a ，22a ，3a 成等差数列.（1）求n a ； （2）令2log n n b a =，求数列{}n b 的前n 项和n S .【知识点】等差、等比数列的通项与性质；等差数列的前n 项和公式；对数的运算法则.【答案解析】（1）12n n a -=（2）(1)2n n n S -= 解析 ：解：（1）设{}n a 的公比为q ，由14a ，22a ，3a 成等差数列，得13244a a a +=. 又11a =，则244q q +=，解得2q =. ∴12n n a -=（*N n ∈ ）.（2）12log 21n n b n -==-，∴11n n b b +-=，{}n b 是首项为0，公差为1的等差数列，它的前n 项和(1)2n n n S -=. 【思路点拨】（1）设{a n }的公比为q ，根据等比数列的通项公式与等差中项的定义，建立关于q 的等式解出q=2，即可求出{a n }的通项公式．（2）根据（I ）中求出的{a n }的通项公式，利用对数的运算法则算出b n =n-1，从而证出{b n }是首项为0、公差为1的等差数列，再利用等差数列的前n 项和公式加以计算，可得数列{b n }的前n 项和S n 的表达式． 17. （本小题满分13分）在ABC ∆中，角,,A B C 对的边分别为,,a b c ，且2,60c C ==︒．(1)求sin sin a b A B++的值； (2)若a b ab +=，求ABC ∆的面积ABC S ∆．解析2=sinA sinB sin A sinB sinC sin60a b a b c ＝＝＝++︒sin A sinB a b +∴+【思路点拨】（1）根据正弦定理以及合比定理即可；（2）由余弦定理求出ab=4，然后根据三角形的面积公式求出答案．18. （本小题满分13分）某车间将10名技工平均分成甲、乙两组加工某种零件，在单位时 间内每个技工加工的合格零件数，按十位数字为茎，个位数字为叶得到的茎叶图如图所示．已知甲、乙 两组数据的平均数都为10. （1）求m ，n 的值； （2）分别求出甲、乙两组数据的方差2S 甲和2S 乙， 并由此分析两组技工的加工水平；（3）质检部门从该车间甲、乙两组技工中各随机抽取一名技工，对其加工的零件进行检测，若两人加工的合格零件数之和大于17，则称该车间“质量合格”，求该车间“质量合格” 的概率．（注：方差2222121[()()()n s x x x x x x n =-+-++-，x 为数据x 1，x 2，…，x n 的平均数）【知识点】古典概型及其概率计算公式；极差、方差与标准差． 【答案解析】（1）m=3,n=8 (2) 乙组更稳定些（3）45 解析 ：解：（1）m=3,n=8(2)2 5.2S 甲＝, 2S 乙＝2,所以两组技工水平基本相当，乙组更稳定些。

2016---2017学年度下学期高一年级期末考试2017-7本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

考试时间120分钟，满分150分。

考试结束，将试题卷和答题卡一并交回。

注意事项：1．答第Ⅰ卷时，考生务必将自己的姓名、准考证号填写在答题卡上。

2．选出每小题答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号框。

不能答在试卷上，否则无效。

第Ⅰ卷第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项, 并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

第一部分：听力测试（共两节，满分30分，每小题1.5分）第一节（共5小题；每小题1．5分，满分7．5分）听下面 5 段对话, 每段对话后有一个小题, 从题中所给的A、B、C三个选项中选出最佳选项, 并标在试卷的相应位置。

听完每段对话后, 你都有 10 秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. What is the woman going to do tomorrow?A. Go swimming.B. Go fishing.C. Go to the hospital.2. How does the man find his job?A. Its pay is good.B. It is boringC. It is interesting and fun.3. What are the speakers talking about?A. A story.B. A book.C. A movie.4. Where does the conversation probably take place?A. At the airport.B. At the bus stop.C. At the train station.5. Where is the man going ?A. The classroom.B. The library.C. The cinema.第二节（共15小题；每小题1．5分，满分22．5分）听下面5段对话。

秘密★启用前2015-2016学年（春）高一期末测试卷数学试题数学试题共4页，满分150分。

考试时间120分钟。

注意事项：1.答题前，务必将自己的姓名、准考证号填写在答题卡规定的位置上。

2.答选择题时，必须使用2B 铅笔将答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦擦干净后，再选涂其他答案标号。

3.答非选择题时，必须使用0.5毫米黑色签字笔，将答案书写在答题卡规定的位置上。

4.所有题目必须在答题卡上作答，在试题卷上答题无效。

一、选择题：本大题共12小题，毎小题5分，共60分.在毎小)每给出的四个条选项中，只有一项是符合题目要求1、某工厂生产甲、乙、丙三种型号的产品，产品数量之比为2:3:5，现按型号用分层抽样的方方法随机抽出容量为n 的样本，若抽抽到12件甲，产品，则n = A 、50 B 、60 C 、70 D 、802、设,a b 是非零实数，且a b <，则下列不等式一定成立的是：A 、22a b <，B 、22ba ab >C 、11a b < D 、2211ba ab> 3、已知具有线性相关关系的两个变量,x y 的5对观察数据112255(,)(,)(,)x y x y x y ，若其中12345x x x x x <<<<，下列说法正确的是：A 、必存在a b R ∈、，使得(1,25)i i y b a i =+=B 、若,x y 高度正相关，则必存在,0a R b ∈>，使得(1,25)i i y b a i =+=C 、若,x y 正相关，则必有12345y y y y y <<<<D 、若12345y y y y y <<<<，则,x y 正相关4、等差数列{}n a 中，31140a a +=，则678a a a ++的值等于：A 、48B 、60C 、72D 、845、已知向量(2,1)a =，(,2)b x =-，若a b ⊥，则a b -=A 、(1,3)-B 、(3,1)--C 、(3,1)-D 、(1,3)6、执行如图所示的程序框图，若输入a 的值是1，则输出的结果是：A 、1B 、2C 、3D 、57、在区间[]0,10内任取一个a ，则对x R ∀∈,2280x ax -+≥的概率是：A 、15 B 、25 C 、35 D 、45 8、若甲乙丙三个人随机站成一排，则甲乙相邻且甲在乙的右边的概率是：A 、13 B 、12 C 、23 D 、349、若实数,x y 满足不等式组231402,1x y y x +-≤⎧⎪≥⎨⎪≥⎩且log a y x =，则a 的最大值为： A 、1 B 、2 C 、3 D 、410、设ABC ∆的内角C B A 、、所对的边分别为c b a 、、.已知1=a ，2=b ，2cos cos cos b A c A a C =+.则A = A 、34π B 、23π C 、3π D 、4π 11、某市出租车的收费标准如下：①不超过4千米的里程收费12元；②超过4千米的里程超过的部分按每千米2元收费〈对于其中不足1千米的部分，若其小鱼0.5千米，则不收费，否则按1千米收费〉：③当车程超过4千米时，另收燃油附加费1元12、如图所示，D 是BC 上的中点，En 是AC 上的一列动点，且111(1),22n n n n n E A a E B a E D +=--若10a =，则n a 等于： A 、11()2n - B 、111()2n -- C 、1()12n - D 、11()12n --二、填空题（本大题共4小题，每小题5分，共20分） 13、样本数据4,9,6,1,3,8的中位数是14、设ABC ∆的内角C B A 、、所对的边分别为c b a 、、.已知23C π=，2=b ，23ABC S ∆=.，则a = 15、下图是样本容量为200的频率分布直方图。

2015-2016学年度（下）调研检测2016.7高一物理试题卷本试题卷分为第一部分（选择题）和第二部分（非选择题）两部分，共6页。

考生作答时，须将答案答在答题卡上，在本试题卷、草稿纸上答题无效。

满分100分，考试时间90分钟。

第一部分（选择题，共39分）注意事项：1. 答题前，务必将自己的姓名、考号填写在答题卡规定的位置上。

并用2B 铅笔将答题卡考号对应数字标号涂黑。

2. 答选择题时，必须使用2B 铅笔将答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其它答案标号。

一、 选择题（本题共6小题，每小题3分，共18分。

每小题给出的四个选项中，只有一个．．．．选项符合题目要求）1．对于做匀速圆周运动的物体，下列说法中正确的是A ．线速度、加速度都不变B ．线速度、角速度都不变C ．角速度、加速度都不变D ．角速度、周期都不变 2．人造地球卫星绕地球做匀速圆周运动，离地面越远的卫星A ．向心加速度越大B ．线速度越大C ．周期越大D ．角速度越大3．如图所示，长为L =0.5 m 的轻质细杆OA ，其A 端固定有一小球，小球质量为5 kg ，小球以O 点为圆心在竖直平面内做圆周运动，通过最高点时速率为2 m/s ，g 取10m/s 2，则此时细杆OA 受到A ．40 N 的拉力B ．40 N 的压力C ．10 N 的拉力D ．10 N 的压力4．如图为一辆老式自行车，它的前轮直径是后轮直径的3倍，当该自行车在平直路面上匀速行驶(不打滑)时，前、后车轮边缘上的点相对于各自转轴做匀速圆周运动的向心加速度大小之比为A ．1∶3B ．3∶1C ．1∶9D ．9∶15．如图所示，初速度大小相等的A 、B 、C 三个小球，在同一水平面上，A 球竖直上抛，B 球以倾斜角θ斜向上抛出，C 球沿倾角为θ的光滑斜面上滑，不计空气阻力，它们上升的最大高度分别为h A 、h B 、h C ，则A ．h A =hB =hC B ．h B ＜h A <h CC ．h A = h C > h BD ．h A =h B >h C6．如图所示，B 为竖直面内的圆弧轨道的右端点，B 点与圆心O 的连线与竖直方向的夹角为θ，一小球从B 点右上方的A 点以速度v 0水平抛出，恰好沿B 点的切线方向进入圆弧轨道，已知重力加速度为g ，则A 、B 两点间的竖直高度为A ．220tan v g θB ．220tan 2v g θC ．20tan v g θD ．20tan 2v gθ二、 选择题(本题共7小题，每小题3分，共21分。

2016年高一下学期数学期末试卷（含答案）孝感高中2015—2016学年度高一下学期期末考试数学试题命题人：陈文科考试时间：120分钟分值：150分一、选择题（本大题共12个小题，每小题5分，共60分，在每小题所给出的四个选项中，只有一项是符合题目要求的）1．等差数列中，若,则的值为（）A．B．C．D．2．设为不重合的两个平面，为不重合的两条直线，则下列判断正确的是()A．若α⊥β，α∩β＝n，m⊥n，则m⊥αB．若mα，nβ，m∥n，则α∥βC．若m∥α，n∥β，m⊥n，则α⊥βD．若n⊥α，n⊥β，m⊥β，则m⊥α3．若两直线与平行，则它们之间的距离为（）A．B．C．D．4．在如图所示的长方体中，，,分别是的中点，则异面直线与所成角的余弦值是()A．B．C．D．5．已知点，若直线过点与线段相交，则直线的斜率的取值范围是（）A．B．C．D．6．在空间直角坐标系中，点，则两点间的距离为（）A．B．C．D．7．在中，角所对的边分别为，已知，若三角形有两解，则边的取值范围为（）A．B．C．D．8．半径为，圆心角为的扇形卷成一个圆锥，则它的体积为()A．B．C．D．9．过点作圆的两条切线，切点分别为，点为坐标原点，则的外接圆方程是（）A．B．C．D．10．一个几何体是由一个三棱柱截去一个四棱锥而成，它的三视图如图所示，则这个几何体的体积是() A．B．C．D．11．已知圆上到直线的距离为的点有且仅有个，则的取值范围是（）A．B．C．D．12．已知圆，设，若圆是的内切圆，则面积的最大值为（）A．B．C．D．二、填空题（本大题共4小题，每小题5分，共20分，把答案填在答题卡中的横线上）13．经过直线的交点且垂直于直线的直线方程为.14．已知满足条件()，若目标函数的最大值为，则的值为.15．已知点，点在圆上运动，则的最大值为.16．已知正方体的棱长为，下列说法：①对角线被平面和平面三等分；②以正方体的顶点为顶点的四面体的体积都是；③正方体的内切球，与各条棱相切的球，外接球的表面积之比为；④正方体与以为球心，为半径的球的公共部分的体积为；则正确的是.（写出所有正确的序号）三、解答题（本大题共6小题，满分70分，解答应写出文字说明、证明过程或演算步骤）17．（10分）设直线的方程为；（Ⅰ）若直线不经过第二象限，求实数的取值范围；（Ⅱ）若直线与坐标轴围成三角形的面积为，求实数的值. 18．（12分）在中，角的对边分别为．（Ⅰ）求的值；（Ⅱ）若，求的面积．19．（12分）如图1所示，在边长为的等边三角形中，分别是边上的点，，是的中点，与交于点，将沿折叠，得到如图2所示的三棱锥，其中；（Ⅰ）证明：平面；（Ⅱ）证明：平面；（III）当时，求三棱锥的体积．20．（12分）甲、乙两地相距，货车从甲地匀速行驶到乙地，速度不得超过，已知货车每小时的运输成本（单位：元）由可变成本和固定成本组成，可变成本是速度平方的倍，固定成本为元；（Ⅰ）将全程运输成本（元）表示为速度（）的函数，并指出这个函数的定义域；（Ⅱ）若，为了使全程运输成本最小，货车应以多大的速度行驶？21．（12分）已知点都在直线上，为直线与轴的交点，数列成等差数列，公差为；（Ⅰ）求数列，的通项公式；（Ⅱ）若=问是否存在,使得成立；若存在，求出的值，若不存在，说明理由；（III）求证：.22．（12分）已知，若由不等式组围成的区域为，设两曲线的交点为，且；（Ⅰ）求实数的取值范围；（Ⅱ）若，求的面积；（III）求的面积的最大值.孝感高中2015—2016学年度高一下学期期末考试数学答案一、选择题1~5BDADC6~10BCACD11~12BA二、填空题13.14.15.16.①③三、解答题17.解：（Ⅰ）由题意知：∴（Ⅱ）由题意知：令令∴∴，或18.（Ⅰ）（Ⅱ）由（Ⅰ）知由正弦定理知：∴∴19.（Ⅰ）在等边三角形ABC中，AD＝AE，∴A DDB＝AEEC. 在折叠后的三棱锥A&shy;BCF中也成立，∴DE∥BC.∵DE平面BCF，BC&#8834;平面BCF，∴DE∥平面BCF. （Ⅱ）在等边三角形ABC中，F是BC的中点，∴AF⊥FC，BF＝CF＝12.∵在三棱锥A&shy;BCF中，BC＝22，∴BC2＝BF2＋CF2，∴CF⊥BF.∵BF∩AF＝F，∴CF⊥平面由(1)可知GE∥CF，结合(2)可得GE⊥平面&shy;DFG＝13×12×DG×FG×GE＝13×12×13×13×32×13＝3324.20.（Ⅰ）可变成本为，固定成本为元，所用时间为，即。

2016-2017学年高一下学期期末考试第I卷（三部分，共115分）第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

请听下面5段对话，选出最佳选项。

1. What’s wrong with the man’s watch?A. It goes slowly.B. It goes too fast.C. It doesn’t work so metimes.2. When will the speakers meet?A. At 2:00.B. At 4:00.C. At 6:00.3. What is the relationship between the speakers?A. Neighbors.B. Teacher and student.C. Classmates.4. What will the woman do?A. Give Tom some medicine.B. Take Tom’s temperature.C. Have a look at Tom’s mouth.5. Why did the woman make Mr. Jones angry?A. She asked the answered question again.B. She didn’t finish her work in 20 minutes.C. She asked the same question three times.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

每段对话或独白后有几个小题,从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

答案2016学年下学期高一期末测试一、阅读理解（40分）1-3ACB 4-7A DBD 8-12 BCACA 13-15 C DA 16-20 CDEBG二、完形填空（30分）21-25 CBADB 26-30 CBCDA 31-35 AACBD 36-40BCDAB三、单项选择（10分）41--45 BBDAD 50—55 BCABC四、语法填空(1.5分)51.with 52. be made 53. to create 54. The 55. using 56 .as 57. gradually58. who 59.development 60. were五、单词拼写（10分）61.arrival 62. benefits 63. surrounded 64. wandering 65. argued66. reduces/ decreases 67. therefore 68. approached 69. modelled 70. convincing六、完成句子（10分）71.You may find it astonishing72. was she allowed to begin her project/research73. Rather than take/Instead of taking the plane all the way74. no wonder (the) tourism is increasing wherever there is a Disneyland/it is no wonder where there is a Disneyland, (the) tourism is increasing.75. according to a widely/universally accepted/acknowledged theory七、短文改错（10分）e 改为came 77.student改为students 78.paid 和visit之间加入a 79. or 改为and 80.删除in 和London 之间的the 81. where改为which 82. beautifully改为beautiful 83.But 后面的that 改为it 84. here改为there 85.excited改为exciting 八、书面表达(25分)Dear Editor，As more and more students are getting fond of western fast food which leads to obesity，I’m writing to talk something about this phenomenon.Although people hold different views about it, I don’t think western fast food is good for our health because they are rich in sugar and fat. In my opinion，the Chinese food is healthier. The Chinese food contains a lot of fruits and green vegetables which are high in vitamins and fibers. In addition, the Chinese food is very delicious and has various dishes，which provide us with all kinds of beneficial nutrition. That’s why many Chinese people enjoy it and keep fit as well. I think the Chinese food is the healthiest one in the world.What’s your opinion about it? I am expecting your reply!Best wishes！Yours SincerelyLi Hua。

2016学年度第二学期高一年级英语学科期末试卷（考试时间：120分钟满分：150分）第I卷 (共110分)I. Listening Comprehension（25分）Section A (10×1=10分)Directions: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a qu estion will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a c onversation and the question about it, read the four possible a nswers on your paper, and decide which one is the best answ er to the question you have heard.1. A. They are talking about the runners. B. They a re running in the village.C. They are listening to the radio.D. They are watching the opening ceremony.2. A. Cindy will arrive at 4:20 p.m. B. Cindy will arrive at 4:05 p.m.C. Cindy will arrive at 4:35 p.m.D. Cindy willarrive at 4:15 p.m.3. A. To a river. B. To a lake. C. To a park. D. To the ocean.4. A. The man has been in for 20 years.B. The man has been in for 30 years.C. The man has been in for 60 years.D. The man has been in for 35 years.5. A. She will try to help the man. B. She is unwilling to help the man.C. She doesn’t like French.D. She speaks French well.6. A. In an airport. B. In a car. C. Near a statio n. D. On a bus.7. A. Making poses. B. How to look natu ral.C. Mending cameras.D. Taking photographs.8. A. There’re not enough oranges. B. There’r e altogether 10 oranges.C. There’re altogether 10 children.D. There’re altogether 8 oranges..9. A. A student. B. A teacher. C. An interviewe r. D. An eye doctor10.A. Driving. B. Reading. C. Shopp ing. D. Parking.Section B(10×1.5=15分)Directions: In Section B, you will hear several longer conversa tion(s) and short passage(s), and you will be asked several qu estions on each of the conversation(s) and the passage(s). Th e conversation(s) and the passage(s) will be read twice, but th e questions will be spoken only once. When you hear a questi on, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. It costs too much. B. It doesn’t work very well.C. It bends in some situations.D. It is not safe.12. A. In newspapers. B. In business halls.C. On the Internet.D. In shops.13. A. A good material B. A ne w iPhone.C. A safe choice.D. A cell phone problem.Questions 14 through 16 are based on the following passage.14. A. They’re special. B. They’re short.C. They’re strange.D. They’re easy to r emember.15. A. . B. . C. Chicago D. .16. A. Because of the shiny, bright and unreal nature of .B. Because of the fruit that grows in that city’s climate.C. Because it is warm and sunny.D. Because it is the music industry center.Questions 17 through 20 are based on the following conversa tion.17. A. Moving to a unit. B. Selling a unit.C. Furnishing a unit.D. Renting a unit.18. A. She thinks it’s nice but a little bit smaller for her.B. She is satisfied with the unit.C. She wants the unit to be furnished.D. She wants the security deposit a little lower.19. A. She has to furnish it by herself. B. She need s to wash her clothes by hands.C. She can park her car in the garage.D. She will live on the first floor.20. A. 450 yuan. B. 900 yuan. C. 1350 yuan.D. 2250 yuan.II. Grammar and VocabularySection A(10×2=20分)Directions: Read the following passage. Fill in the blanks to m ake the passage coherent. For the blanks with a given word, fi ll in each blank with the proper form of the given word. For the other blanks, fill in each blank with one proper word. Make su re that your answers are grammatically correct.Many restaurants have “take out” service. But this restaurant i n , , (21) ___________ (become) famous for its special “take in ” service. Actually the name of the restaurant is “Take In” too. Instead of cooking the meals in its own kitchen--- which doesn’t exit ---- it allows customers (22) __________ (order) various dishes fr om 20 other restaurants in the city.(23) ___________ (sponsor) by American Express and Wolt , (24) _________ popular food delivery app, “Take In” is a popula r restaurant that opened at the beginning of November 2016.(25) _________ you have probably already guessed, the name “Take In” is a clever play on words. The whole point of orderi ng take-out is to avoid (26) ___________ (go) to a restaurant, and if yo u are going to dress up to go out, you (27) __________ as well go straight to your favorite restaurant instead of ordering food from it somewhere else. But here is the idea (28) _________ it ----- when you go out with a group of friends and you can not dec ide where to go for dinner, because everyone wants to order s omething else, “Take In” is the perfect solution. You can have a pizza, (29) __________ your friends enjoy Japanese, Chines e or even a burger.If customers want to try the “take in” experience, they can use the Wolt app, just as they would from the comfort of their own homes. (30) __________ they order and pay for their meals, al l they have to do is to wait for someone to deliver it to the rest aurant.Section B (10分)Directions: Complete the following passage by using the word s in the box. Each word can only be used once. Note that ther e is one word more than you need.Do you want to stop struggling and being frustrated in your language learning? Do you want to gain an improved underst anding of what it takes to get better at learning a second lang uage so you can move forward faster and more effectively? D o you want to see how this can be done? The language learni ng strategies you ___31___are fundamental to your success. Many language learnerssettle for a lot less than they can achieve sometimes becaus e they have settled on the wrong understandings, methods or tools, sometimes because they lack ___32___in their own cap acities and sometimes because there is lack of ___33___in wh at they really want from their lives and sometimes.In these pages you can find many insights into what you ca n do NOW to improve your language learning. In addition, we make ___34___free of charge on a fortnightly basis new insigh ts and strategies that you can use to transform your learning s o that you make continued and ___35___ progress. You can fi nd out what actually works for you so you do the things that w ork, not the things you think should work but in fact may not. One ___36___ I have made time and time again is that the quality of your speaking in a second or foreign language will b e ___37___by the quality of your listening. This will no doubt b e a surprise to many people, as most language teaching does not appear to take this on board. Instead, many learners and teachers think that studying the grammar and the vocabulary will give the learners their ___38___ results. There is a lot mor e to successful language learning than that.If you are interested in finding out about some great langua ge learning strategies and how you can improve your speakin g and your language learning, ___39___ yourself now for the f ree fortnightly insights. You can also read a book that I have r ecently published, Language Learning Unlocked, in which you will find a lot more ___40___discussion and practices that can positively improve your learning of languages.III． Reading ComprehensionSection A (15分)Directions: For each blank in the following passage there are f our words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Children have lost touch with nature and the outdoors in just one generation! Recently a campaign encouraging children to put away __41__ and play outside has been organized. The c ampaign, said to be the biggest ever, has been launched with the __42__ of a documentary film, Project Wild Thing. It tells t he story of how, __43__ an attempt to get his daughter and so n outside, film-maker David Bond __44__ as marketing director for nature. The call to renew a connection with nature comes from about 400 organizations, from playgroups to the National Health Ser vice. Children are being __45__ to take back their “wild time”, swapping (交换) 30 minutes of screen use for outdoor activities. The organi zers __46__ that giving up 30 minutes of television and compu ter games each day in exchange for outdoor play will increase the __47__ of fitness and alertness and improve children’s we ll-being.According to the chairman Andy Simpson, right now, time s pent outdoors is down, activity levels are declining and the ability to identify common species has been __48__. “With many more parents becoming __49__ the dominance of screen time in their children’s lives, and growing scientific evidence that a decline in __50__ time is bad news for the health and happin ess of our children, we all need to become marketing director s for nature. We want parents to see what this magical wonde r product does for their kids’ development, independence and creativity, by giving wild time a go” said Mr. Simpson.In Mr. Bond’s opinion, the reasons why kids, __51__ they liv e in cities or the countryside, have become __52__ from natur e and the outdoors are complex. “We need to make more spa ce for wild time in children’s daily routine, __53__ this generati on of kids to have the sort of experiences that many of us took for granted. It’s all about finding __54__ on your doorstep and discovering the sights, sounds and __55__ of nature一maybe in a back garden, a local park, or just green space at t he end of the road.”41. A. subjects B. screensC. stagesD. scenes42. A. outcome B. directionC. exposureD. release43. A. by B. on C. forD. ins D. regards45. A. pulled B. forced C. urgedD. warned46. A. allow B. admit C. acquireD. argue47. A. amountsB. levelsC. degreesD. standards48. A. developedB. shownC. testedD. lost49. A. delighted with B. guilty of C. concer ned about D. desperate for50. A. free B. active C. spareD. normal51. A. while B. though C. asD. whether52. A. escaped B. disconnectedC. sufferedD. protected53. A. freeing B. forbiddingC. seekingD. serving54. A. imagination B. fortuneC. wildnessD. solutionures D. smellsSection B（11×2=22分）Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. Fo r each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information give n in the passage you have just read.(A)Mr. Richards was quite good at shooting with a rifle (来福枪), and he had taken part in several competitions in his small town. He had never actually won a prize, but each time he ha d done well and once he had come in fourth.Then he had to go to a big city on business for a month, and a s he had nothing much to do in the evenings, he joined the loc al rifle club, and spent several pleasant evenings shooting the re.The rifle club had a very good first team, which used to take part in a lot of important shooting competitions. One of these took place while Mr. Richards wa s with them, and of course he went to see it. But one of the m embers of the club’s team suddenly fell ill just before the matc h, and the captain had to choose somebody else to take his place in a hurry. He had heard that Mr. Richards had taken part in several competitions already, and he had seen for himself at the club that, although he was not up to the standard of the club’s first team, he was quite a good shot. He therefore invite d him to take the sick man’s place.Mr. Richards felt greatly honored to be asked to shoot for suc h a good team, but he also felt very nervous, because he was afraid of making a fool of himself and letting down his team. In fact, he was so nervous that he could not keep his hand fro m trembling while he was shooting, with the result that he did very badly in the competition. When he took his score card to his captain, he said , “After seeing my score , I feel like going outside and shooting myself. ”The captain looked at the card for a few minutes and then sai d, “Well, you had better take two bullets with you if you do that .”56. How did it happen that Mr. Richards took part in the comp etition for the club’s first team?A. He was a member of the club’s first team.B. He was a first-rate shot in competitions.C. He wanted to take the sick man’s place.D. He took part in the competition at the invitation of the captain.57. How did Mr. Richards feel after the competition?A. He felt uncomfortable.B. He was very much shocked.C. He felt very much ashamed.D. He was very angry with himself58. According to the passage, which of the following was true of Mr. Richards?A. He joined the local club to compete with other members.B. He was a man who had a strong sense of self-respect.C. He always came in first in all the competitions he took part in.D. He was full of confidence before the competition.59. What does the last sentence “You had better take two bull ets with you if you do that.” mean?A. One bullet is not powerful enough to kill a person.B.The quality of the bullets is very bad. You had better take a n extra one.C. You are such a bad shot that you might miss the target whi le trying to kill yourself.D. There are two bullets left in your rifle. You had better use them up.（B）Psychologists have found that only about two percent of adult s use their creativity, compared with ten percent of seven-year-old children. When five-year-olds were tested, the results soared to ninety percent! Curiosit y and inventiveness are daily occurrences for the small child, but somehow most of us lose the freedom and flexibility (灵活性) of the child as we grow older. The need to “follow direction s” and “do-it-right,” plus the many societal constraints we put on ourselves, prevent us from using our creative potential.It is never too late to tap our creative potential. Some of us, h owever, find it difficult to think in imaginative and flexible ways because of our set pattern of approaching problems. When w e are inflexible in our approach to situations, we close our min ds to creative possibilities.Being creative does n’t necessarily mean being a genius. It me ans looking at situations in a new way or putting something to gether in a new form that makes sense. Spontaneity（自发性） is one of the key elements of creativity.If you were to ask someone, “What's half of eight?” and receiv ed the answer, “Zero,” you might laugh and say, “That's wrong!” But the figure 8 can be visualized as two zeros, one on top of the other; it can also be seen as two 3's standing face to fa ce.The ability to visualize our environment in new ways opens ou r perspective and allows us to make all kinds of discoveries. If each of us asked the question “Why?” more often and investi gated “other” alternatives to problem solving, our lives would be more interesting and exciting.60. According to the essay, ___________________.A. we tend to be more creative as we grow oldB. adults do not use their creativity so often as children doC. we don't lose our creativity as we grow oldD. people are born with different creative potentials61. Being creative means being ________________A. able to approach problems in new waysB. able to solv e problemsC. inclined to ask whyD. a genius62. We are less creative than we can be because __________ _____A. we often think it too late to tap our creative potentialsB. set patterns of doing things close our minds to new possibil itiesC. creativity is not encouraged by societyD. education kills creativity(C)Was your school noisy or peaceful? It might not seem importa nt, but a growing body of research suggests that sounds can have an impact on learning, performance and creativity. Whether background sounds are beneficial or not seems to d epend on what kind of noise it is — and the volume. In a serie s of studies published last year, Ravi Mehta from the College of Business at and his colleagues tested people's creativity w hile exposed to a soundtrack made up of background noises — such as coffee-shop chatter and construction-site drilling — at different volumes. They found that people we re more creative when the background noises were played at a medium level than when volume was low. Loud background noise, however, damaged their creativity.This makes sense for a couple of reasons, says psychologist Dr Nick Perham, at Cardiff Metropolitan University in the , wh o studies the effect of sounds on learning but was not involve d in the study. Firstly, he says, sounds that are most disturbin g tend to be very variable. A general hum (嗡嗡声) in the background suggests a steady-state sound with not much variation. "So there's not much there to capture your attention — nothing disturbing the subjects," he says. At the same time, the background noise might caus e the subjects to be in a slightly heightened state of arousal (觉醒), says Perham. "Medium arousal is best for good performa nce. So it might be that a general hum in the background give s an ideal level of arousal." With that in mind, Perham suggest s there may be some benefits to playing music or other sound s in an art class or other situations where creativity is key. Many teachers all over the world already play music to studen ts in class. Many are inspired by the belief that hearing music can improve IQ in tasks, the so-called Mozart effect. While the evidence actually suggests it's a stretch to say classical music improves brainpower, researc hers do think pleasant sounds before a task can sometimes lif t your mood and help you perform well, says Perham, who ha s done his own studies on the phenomenon. The key appears to be that you enjoy what you’re hearing. "If you like the musi c or you like the sound — even listening to a Stephen King no vel — then you did better. It didn’t matter about the music," he says.63. Which of the following is true according to the studies byRavi Mehta and Nick Perham?A. It’s better not to expose people to any background noise w hile at work.B. Construction-site drilling should be forbidden where there is a school.C. Noises will harm people’s health however low their volume s are.D. A certain level of noise may do good to people’s creativity.64. According to Dr Nick Perham, it can be inferred that in an art class teachers had better ______.A. keep the classroom quietB. play music at a steady and medium volumeC. broadcast classical musicD. vary the volume of the music constantly65. In the last paragraph. the underlined part “it’s a stretch" is used to______.A. prove the usefulness of pleasing soundsB. confirm the belief of Mozart effectC. challenge the importance of soft musicD. cast doubt on the power of music in raising IQ66. Which of the following might be the best title for this passage?A. Learning Power: Noise and Music WorkB. Noise Meeting Music: A Blessing?C. Noise or Music: Creativity in DangerD. Brainpower: More Music and Less NoiseSection C （4×2=8分）Directions: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be us ed only once. Note that there are two more sentences than yo u need.Over the last 10 years, the number of university students see king help for mental or emotional problems has grown sharply . _____67___ Nearly half of all students who sought help in recent years said they felt anxious. __ __68____ An additional 40 percent of students said they felt depressed—very, very sad. ____69____ One reason could simply be a change in America n culture. In the , people are increasingly comfortable talking about mental health issues and bringing their problems to trai ned experts. Another reason could be related to the current g eneration of young people attending university today. But one reason is surely higher education itself.____70____ But college is a difficult time when students want to make friends, find their identity and succeed academically.“College being a place with high demands, lots of competition and lots of concern about being able to get a good job after c ollege, certainly increases the level of stress that students experience.”IV. Summary Writing (10分)Directions: Read the following passage. Summarize the main idea and the main points of the passage in no more than 60 w ords. Use your own words as far as possible.Now another American education icon may be disappearing: t he hardbound (精装的) textbook. More and more school districts are replacing tra ditional textbooks with electronic ones. Electronic textbooks ar e usually accessed either through an online server or are dow nloaded to student laptops.In North Texas, Plano and Irving schools are introducing e-books into a few classrooms, and school officials also are co nsidering them. But no local district appears to be going as far as Forney. The district most likely would be the first in the sta te to use e-books in every classroom for grades five to twelve.Officials point out several reasons for turning to e-books. For one, they are easier to update. Thus the publisher s are able to find ways to do online textbooks and they can go back and change information. Using e-books will better prepare students for college and the workpla ce.Rapid district growth is another reason. The number of the stu dents in the district is expected to double within five years. It’sdifficult to know textbook needs in advance and some studen ts wait months for their books. But e-books can be uploaded onto a “blank” laptop in a few hours. Cost may eventually be a deciding cause for choosing e-books, but there are no big savings yet. Even if they get it ele ctronically, they still have to pay for the book because they’re buying the instructional material. That may change as more a nd more districts move toward e-books.Today’ students have little trouble adjusting to laptops and e-books, said Connie Cooley, who has taught at the of for five years. But she said it could worry teachers.“It’s harder for people who are right around my age and older.” said Ms. Cooley, 36. “I’m laptop-savvy, so I was ready for it, but those that aren’t are a little wo rrying.第II 卷 (共40分)I. Translation（3+3+4+5=15分）Directions: Translate the following sentences into English, usi ng the words given in the brackets.71. 在英语考试中，你越仔细，你犯的错误就越少。

2016-2017学年第二学期高一年级期末考试说明：1.本试卷满分135分，考试时间120分钟。

2.答卷前，考生要务必填写答题卷上的有关项目。

3.选择题选出答案后，用黑色2B铅笔在答题卡上涂黑，不能答在试卷上。

4.非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卷各题目指定区域内；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。

5.考生必须保持答题卷的整洁，考试结束后，只交回答题卷以及选择题答题卡。

一、阅读理解（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A.B.C和D项中，选出最佳选项，并在答题卡上将该项涂黑。

AMr. Lee was in bed and was trying to go to sleep when he hea rd the bell ring. He turned on the light and looked at his clock. It was twelve o'clock. "Who can it be at this time of night?" He thought. He decided to go and find out. So he got off bed, puton his dressing gown (浴袍) and went to the door. When he opened the door, there wa s nobody there. "That is very strange." Then he went back to his bedroom, took off his dressing gown, got back into bed, tu rned off the light and tried to go to sleep. A few minutes later he heard the bell again. Mr. Lee jumped out of bed very quickl y and rushed to the door. He opened it, but again he found no one there. He closed the door and tried not to feel angry. The n he saw a piece of paper on the floor. He picked it up. There were some words on it : "It is now after midnight(午夜), so it is April Fools’ Day. April fool to you!""Oh, it was the English boy next door!" Mr. Lee exclaimed (惊叫) and almost smiled. He went back to bed and fell asleep at once. The bell did not ring again.1. When did Mr. Lee go to bed?A. before twelve o'clockB. after twelve o'clockC. when the bell rangD. when he saw the boy2. Why did he rush to the door when he heard the bell ring the second time?A. He wanted to open the door for the visitorB. He wanted to find out who the visitor was.C. He was afraid of the ringD. He was waiting for someone.3. From this passage, we learn that we can _______ on April F ools’ Day.A. say "Hello" to each otherB. dance and sing at nightC. play jokes on each otherD. send presents to children 【答案】1. A 2. B 3. C【解析】本文是一篇记叙文。

2015-2016学年河南省南阳市高一（下）期末数学试卷一、选择题（每题5分）1．（5分）学校为了解高二年级1201名学生对某项教改试验的意见，打算从中抽取一个容量为40的样本，考虑用系统抽样，则分段的间隔k为（）A．10 B．20 C．30 D．402．（5分）cos1050°的值为（）A．B．﹣C．D．﹣3．（5分）如图是南阳市某中学在会操比赛中七位评委为甲、乙两班打出的分数的茎叶图（其中m为数字0﹣9中的一个），去掉一个最高分和一个最低分后，甲、乙两个班级的平均分分别为，，则一定有（）A．＞B．＜C．=D．，的大小不确定4．（5分）若sin（π﹣α）﹣cos（π+α）=，则sin（﹣α）cos（+α）等于（）A．B．﹣C．D．﹣5．（5分）已知单位向量，满足|3﹣2|=，则|3+|=（）A．1 B．4 C．2 D．6．（5分）若某公司从5位大学毕业生甲、乙、丙、丁、戊中录用3人，这5人被录用的机会均等，则甲、乙同时被录用的概率为（）A．B．C．D．7．（5分）下列说法中，正确的个数为（）（1）（2）已知向量=（6，2）与=（﹣3，k）的夹角是钝角，则k的取值范围是k ＜0（3）若向量能作为平面内所有向量的一组基底（4）若，则在上的投影为．A．1个 B．2个 C．3个 D．4个8．（5分）函数f（x）=Asin（ωx+φ）（A＞0，ω＞0）的图象如图所示，则以下步骤可以得到函数f（x）的图象的是（）A．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的2倍，然后再向左平移个单位B．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的2倍，然后再向右平移个单位C．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的，然后再向右平移个单位D．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的，然后再向左平移个单位9．（5分）运行如图所示的程序框图，则输出的S的值为（）A．B．C．D．10．（5分）△ABC中，若cos（2B+C）+2sinAsinB=0，则△ABC中一定是（）A．锐角三角形B．钝角三角形C．直角三角形D．等腰三角形11．（5分）已知函数f（x）=cosωx（sinωx+cosωx）（ω＞0），如果存在实数x0，使得对任意的实数x，都有f（x0）≤f（x）≤f（x0+2016π）成立，则ω的最小值为（）A．B．C．D．12．（5分）已知△ABC内一点O满足=，若△ABC内任意投一个点，则该点△OAC内的概率为（）A．B．C．D．二、填空题（每题5分）13．（5分）从某小区抽取100户居民进行月用电量调查，发现其用电量都在50至350度之间，频率分布直方图如图所示，在这些用户中，用电量落在区间[150，250）内的户数为．14．（5分）如图所示，在半径为7，圆心角为的扇形铁皮ADE上截去一个半径为3的小扇形ABC，则剩下扇环的面积为．15．（5分）在等腰直角三角形ABC中，已知AB=AC=1，E，F分别是边AB，AC 上的点，且=m，=n，其中m，n∈（0，1）且m+2n=1，若EF，BC的中点分别为M，N，则||的最小值是．16．（5分）已知定义域为R的奇函数f（x）满足：当x＞0时，f（x）=lnx，则函数g（x）=f（x）﹣sin4x的零点的个数为．三、解答题17．（10分）已知向量=（3，﹣4），=（6，﹣3），=（5﹣x，﹣3﹣y），=（4，1）（1）若四边形ABCD是平行四边形，求x，y的值；（2）若△ABC为等腰直角三角形，且∠B为直角，求x，y的值．18．（12分）某地区2009年至2015年农村居民家庭人均纯收入y（单位：千元）的数据如表：（1）求y关于t的线性回归方程；（2）利用（Ⅰ）中的回归方程，分析2009年至2015年该地区农村居民家庭人均纯收入的变化情况，并预测该地区2017年农村居民家庭人均纯收入．附：回归直线的斜率和截距的最小二乘估计公式分别为：．．参考数据：（﹣3）×（﹣1.4）+（﹣2）×（﹣1）+（﹣1）×（﹣0.7）+1×0.5+2×0.9+3×1.6=14．19．（12分）已知向量=（cosx，sinx），=（sinx，sinx），x∈R设函数f（x）=﹣（1）求函数f（x）的最小正周期；（2）求函数f（x）在[0，]上的最大值和最小值．20．（12分）某小组共有A、B、C、D、E五位同学，他们的身高（单位：米）以及体重指标（单位：千克/米2）如表所示：（Ⅰ）从该小组身高低于1.80的同学中任选2人，求选到的2人身高都在1.78以下的概率（Ⅱ）从该小组同学中任选2人，求选到的2人的身高都在1.70以上且体重指标都在[18.5，23.9）中的概率．21．（12分）在△ABC中，已知tanA，tanB是关于x的方程x2+（x+1）p+1=0的两个实根．（1）求角C；（2）求实数p的取值集合．22．（12分）函数y=Asin（ωx+φ）（A＞0，ω＞0，|φ|＜）在x∈（0，7π）内取到一个最大值和一个最小值，且当x=π时，y有最大值3，当x=6π时，y有最小值﹣3．（1）求此函数解析式；（2）写出该函数的单调递增区间；（3）是否存在实数m，满足不等式Asin（）＞Asin （）？若存在，求出m值（或范围），若不存在，请说明理由．2015-2016学年河南省南阳市高一（下）期末数学试卷参考答案与试题解析一、选择题（每题5分）1．（5分）学校为了解高二年级1201名学生对某项教改试验的意见，打算从中抽取一个容量为40的样本，考虑用系统抽样，则分段的间隔k为（）A．10 B．20 C．30 D．40【解答】解：了解1201名学生对学校某项教改试验的意见，打算从中抽取一个容量为40的样本，∵1201除以40不是整数，∴先随机的去掉1个人，再除以40，得到每一段有30个人，则分段的间隔k为30．故选：C．2．（5分）cos1050°的值为（）A．B．﹣C．D．﹣【解答】解：cos1050°=cos（﹣3×360°+1050°）=cos（﹣30°）=cos30°=，故选：A．3．（5分）如图是南阳市某中学在会操比赛中七位评委为甲、乙两班打出的分数的茎叶图（其中m为数字0﹣9中的一个），去掉一个最高分和一个最低分后，甲、乙两个班级的平均分分别为，，则一定有（）A．＞B．＜C．=D．，的大小不确定【解答】解：去掉一个最高分和一个最低分后，=（81+85+85+84+85）=84，=（84+84+86+84+87）=85．∴＜．故选：B．4．（5分）若sin（π﹣α）﹣cos（π+α）=，则sin（﹣α）cos（+α）等于（）A．B．﹣C．D．﹣【解答】解：∵sin（π﹣α）﹣cos（π+α）=sinα+cosα=，∴平方可得sinα cosα=﹣，则sin（﹣α）cos（+α）=﹣cosα•（﹣sinα）=sinα cosα=﹣，故选：B．5．（5分）已知单位向量，满足|3﹣2|=，则|3+|=（）A．1 B．4 C．2 D．【解答】解：∵，是单位向量，∴||=||=1，又|3﹣2|=，∴9﹣12•+4=7，即9﹣12•+4=7，∴•=；∴=9+6•+=9+6×+1=13，∴|3+|=．故选：D．6．（5分）若某公司从5位大学毕业生甲、乙、丙、丁、戊中录用3人，这5人被录用的机会均等，则甲、乙同时被录用的概率为（）A．B．C．D．【解答】解：从甲、乙、丙、丁、戊中录用3人，共有C53=10种方法，其中甲、乙同时被录用，则剩余的一人从丙、丁、戊选，共有3种方法，故甲、乙同时被录用的概率为，故选：A．7．（5分）下列说法中，正确的个数为（）（1）（2）已知向量=（6，2）与=（﹣3，k）的夹角是钝角，则k的取值范围是k ＜0（3）若向量能作为平面内所有向量的一组基底（4）若，则在上的投影为．A．1个 B．2个 C．3个 D．4个【解答】解：（1）根据向量的加法运算法则可得，，所以（1）正确．（2）当k=﹣1时，，此时向量共线且方向相反，此时向量夹角为180°，但不是钝角，所以（2）错误．（3）因为，所以向量共线，所以向量不能作为平面内所有向量的一组基底，所以（3）错误．（4）当方向相同时，在上的投影为．当方向相反时，在上的投影为﹣．所以（4）错误．故正确是（1）．故选：A．8．（5分）函数f（x）=Asin（ωx+φ）（A＞0，ω＞0）的图象如图所示，则以下步骤可以得到函数f（x）的图象的是（）A．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的2倍，然后再向左平移个单位B．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的2倍，然后再向右平移个单位C．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的，然后再向右平移个单位D．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的，然后再向左平移个单位【解答】解：根据函数f（x）=Asin（ωx+φ）（A＞0，ω＞0）的图象，可得A=1，•=﹣，∴ω=2．再根据五点法作图可得2×+φ=，∴φ=，∴f（x）=sin（2x+）．将y=sinx的图象上的点纵坐标不变，横坐标变成原来的，可得y=sin2x的图象；然后把所的图象上的点的横坐标再向左平移个单位，可得y=sin2（x+）=sin （2x+）的图象，故选：D．9．（5分）运行如图所示的程序框图，则输出的S的值为（）A．B．C．D．【解答】解：模拟执行程序，可得：该程序的作用是利用循环计算S=cos cos cos cos的值并输出，由于：S=cos cos cos cos=×（cos cos cos cos）=×（cos cos cos）=×（cos cos）=×cos==．故选：C．10．（5分）△ABC中，若cos（2B+C）+2sinAsinB=0，则△ABC中一定是（）A．锐角三角形B．钝角三角形C．直角三角形D．等腰三角形【解答】解：∵cos（2B+C）+2sinAsinB=0，即cos（B+B+C）+2sinAsinB=0．∴cosBcos（B+C）﹣sinBsin（B+C）+2sinAsinB=0，即cosBcos（π﹣A）﹣sinBsin（π﹣A）+2sinAsinB=0．∴﹣cosBcosA﹣sinBsinA+2sinAsinB=0，即﹣cosBcosA+sinBsinA=0．即﹣cos（A+B）=0，cos（A+B）=0．∴A+B=，∴C=，故△ABC形状一定是直角三角形．故选：C．11．（5分）已知函数f（x）=cosωx（sinωx+cosωx）（ω＞0），如果存在实数x0，使得对任意的实数x，都有f（x0）≤f（x）≤f（x0+2016π）成立，则ω的最小值为（）A．B．C．D．【解答】解：由题意可得，f（x0）是函数f（x）的最小值，f（x0+2016π）是函数f（x）的最大值．显然要使结论成立，只需保证区间[x0，x0+2016π]能够包含函数的至少一个完整的单调区间即可．又f（x）=cosωx（sinωx+cosωx）=sin2ωx+=sin（2ωx+）+，故2016π≥•，求得ω≥，故则ω的最小值为，故选：D．12．（5分）已知△ABC内一点O满足=，若△ABC内任意投一个点，则该点△OAC内的概率为（）A．B．C．D．【解答】解：以，为邻边作平行四边形OBDC，则+=∵=，∴3=，作AB的两个三等分点E，F，则==，∴O到AC的距离是E到AC距离的一半，B到AC的距离是O到AC距离的3倍，如图∴S=S△ABC．△AOC故△ABC内任意投一个点，则该点△OAC内的概率为，故选：C．二、填空题（每题5分）13．（5分）从某小区抽取100户居民进行月用电量调查，发现其用电量都在50至350度之间，频率分布直方图如图所示，在这些用户中，用电量落在区间[150，250）内的户数为52．【解答】解：由用电量落在区间[150，250）内频率为：1﹣（0.0024+0.0036+0.0024+0.0012）×50=0.52，∴用电量落在区间[150，250）内的户数为：100×0.52=52．故答案为：52．14．（5分）如图所示，在半径为7，圆心角为的扇形铁皮ADE上截去一个半径为3的小扇形ABC，则剩下扇环的面积为5π．【解答】解：S=S ADE﹣S ABC=×72×﹣×32×=5π．留下故答案为：5π．15．（5分）在等腰直角三角形ABC中，已知AB=AC=1，E，F分别是边AB，AC 上的点，且=m，=n，其中m，n∈（0，1）且m+2n=1，若EF，BC的中点分别为M，N，则||的最小值是．【解答】解：如图所示，建立直角坐标系B（1，0），C（0，1）．∵=m，=n，其中m，n∈（0，1），∴=m（1，0）=（m，0），=（0，n）．∴==．==∴==．又m，n∈（0，1），m+2n=1．∴n∈．∴===≥，当且仅当n=，m=时取等号．故答案为：．16．（5分）已知定义域为R的奇函数f（x）满足：当x＞0时，f（x）=lnx，则函数g（x）=f（x）﹣sin4x的零点的个数为7．【解答】解：函数f（x）=sin4x是奇函数，且它的周期为=，∵g（x）=f（x）﹣sin4x=0，∴函数g（x）=f（x）﹣sin4x的零点的个数为相当于f（x）=sin4x的零点个数，即f（x）与sin4x的交点个数，∴画出二者图象，由数形结合，可知，在（﹣∞，0）有3个交点，0处有一个交点，（0，+∞）有3个交点，故共有7个交点．∴函数g（x）=f（x）﹣sin4x的零点的个数为7个，故答案为：7．三、解答题17．（10分）已知向量=（3，﹣4），=（6，﹣3），=（5﹣x，﹣3﹣y），=（4，1）（1）若四边形ABCD是平行四边形，求x，y的值；（2）若△ABC为等腰直角三角形，且∠B为直角，求x，y的值．【解答】解：（1）∵=（3，﹣4），=（6，﹣3），=（5﹣x，﹣3﹣y），∴=（1，5），=（﹣1﹣x，﹣y），由=，得x=﹣2，y=﹣5；（2）∵=（3，1），=（﹣x﹣1，﹣y），∵∠B为直角，则⊥，∴3（﹣x﹣1）﹣y=0，又||=||，∴（x+1）2+y2=10，再由y=3（﹣x﹣1），解得：或．18．（12分）某地区2009年至2015年农村居民家庭人均纯收入y（单位：千元）的数据如表：（1）求y关于t的线性回归方程；（2）利用（Ⅰ）中的回归方程，分析2009年至2015年该地区农村居民家庭人均纯收入的变化情况，并预测该地区2017年农村居民家庭人均纯收入．附：回归直线的斜率和截距的最小二乘估计公式分别为：．．参考数据：（﹣3）×（﹣1.4）+（﹣2）×（﹣1）+（﹣1）×（﹣0.7）+1×0.5+2×0.9+3×1.6=14．【解答】解：（1）由所给数据计算得==4，==4.4，（t i﹣）2=9+4+1+0+1+4+9=28，（t i﹣）（y i﹣）=（﹣3）×（﹣1.4）+（﹣2）×（﹣1）+（﹣1）×（﹣0.7）+1×0.5+2×0.9+3×1.6=14．，…4分==0.5，=4.3﹣0.5×4=2.3，所求回归方程为y=0.5t+2.3…8分（2）由（1）知，b=0.5＞0，故2009年至2015年该地区居民家庭人均纯收入逐年增加，平均每年增加0.5千元．将2017年的年份代号t=9代入（1）的回归方程，得y=6.8，故预测该地区2017年该地区居民家庭人均纯收入约为6.8千元．…12分．19．（12分）已知向量=（cosx，sinx），=（sinx，sinx），x∈R设函数f（x）=﹣（1）求函数f（x）的最小正周期；（2）求函数f（x）在[0，]上的最大值和最小值．【解答】解：（1）由向量=（cosx，sinx），=（sinx，sinx），x∈R，得f（x）=﹣==．∴函数f（x）的最小正周期T=；（2）当x∈[0，]时，，由正弦曲线y=sinx在[，]上的图象可知当即时f（x）取最大值1．当即x=0时f（x）取最小值．函数f（x）在[0，]上的最大值和最小值分别为1，．20．（12分）某小组共有A、B、C、D、E五位同学，他们的身高（单位：米）以及体重指标（单位：千克/米2）如表所示：（Ⅰ）从该小组身高低于1.80的同学中任选2人，求选到的2人身高都在1.78以下的概率（Ⅱ）从该小组同学中任选2人，求选到的2人的身高都在1.70以上且体重指标都在[18.5，23.9）中的概率．【解答】（Ⅰ）从身高低于1.80的同学中任选2人，其一切可能的结果组成的基本事件有：（A，B），（A，C），（A，D），（B，C），（B，D），（C，D）共6个．由于每个同学被选到的机会均等，因此这些基本事件的出现是等可能的．选到的2人身高都在1.78以下的事件有：（A，B），（A，C），（B，C）共3个．因此选到的2人身高都在1.78以下的概率为p=；（Ⅱ）从该小组同学中任选2人，其一切可能的结果组成的基本事件有：（A，B），（A，C），（A，D），（A，E），（B，C），（B，D），（B，E），（C，D），（C，E），（D，E）共10个．由于每个同学被选到的机会均等，因此这些基本事件的出现是等可能的．选到的2人的身高都在1.70以上且体重指标都在[18.5，23.9）中的事件有：（C，D）（C，E），（D，E）共3个．因此选到的2人的身高都在 1.70以上且体重指标都在[18.5，23.9）中的概率p=．21．（12分）在△ABC中，已知tanA，tanB是关于x的方程x2+（x+1）p+1=0的两个实根．（1）求角C；（2）求实数p的取值集合．【解答】（本题满分为12分）解：（1）根据题意，则有tanA+tanB=﹣p，tanAtanB=p+1，而，又A，B是△ABC的内角，所以，则．…（4分）（2）在△ABC中由（1）知，则，即tanA，tanB∈（0，1），…（6分）则关于x的方程x2+（p+1）x+1=x2+px+p+1=0在区间（0，1）上有两个实根，…（7分）设f（x）=x2+px+p+1，则函数f（x）与x轴有两个交点，且交点在（0，1）内；又函数f（x）的图象是开口向上的抛物线，且对称轴方程为x=﹣，故其图象满足：，…（9分）解之得：．…（11分）所以实数p的取值集合为．…（12分）22．（12分）函数y=Asin（ωx+φ）（A＞0，ω＞0，|φ|＜）在x∈（0，7π）内取到一个最大值和一个最小值，且当x=π时，y有最大值3，当x=6π时，y有最小值﹣3．（1）求此函数解析式；（2）写出该函数的单调递增区间；（3）是否存在实数m，满足不等式Asin（）＞Asin（）？若存在，求出m值（或范围），若不存在，请说明理由．【解答】解：（1）∵当x=π时，y有最大值3，当x=6π时，y有最小值﹣3．∴A=[3﹣（﹣3）]=3，=5π，∴T=10π=，∴ω==，∵当x=π时，y有最大值3，∴π+ϕ=，∴ϕ=，∴y=3sin（x+），（2）令2kπ﹣≤x+≤2kπ+得10kπ﹣4π≤x≤10kπ+π，k∈Z∴函数的单调递增区间为：{x|10kπ﹣4π≤x≤10kπ+π k∈Z}；（3）∵ω=，ϕ=，∴ω+ϕ=+∈（0，），ω+ϕ=+∈（0，），而y=sint在（0，）上是增函数∴+＞+，∴＞∴，∴解得：．∴m的取值范围是．赠送初中数学几何模型【模型三】双垂型：图形特征：运用举例：1.在Rt△ABC中，∠ACB＝90°，以斜边AB为底边向外作等腰三角形PAB，连接PC. （1）如图，当∠APB＝90°时，若AC=5，PC＝62，求BC的长；（2）当∠APB＝90°时，若AB=45APBC的面积是36，求△ACB的周长.P2.已知：如图，B、C、E三点在一条直线上，AB＝AD，BC＝CD.（1）若∠B＝90°，AB＝6，BC＝23，求∠A的值；（2）若∠BAD＋∠BCD＝180°，cos∠DCE＝35，求ABBC的值.3.如图，在四边形ABCD中，AB=AD，∠DAB=∠BCD=90°，（1）若AB=3，BC+CD=5，求四边形ABCD的面积（2）若p= BC+CD，四边形ABCD的面积为S，试探究S与p之间的关系。