上海交通大学附属中学2016届高三英语下册开学摸底考试卷.

2016-2017学年上海交大附中高三（下）开学数学试卷一、填空题：（本大题共14小题，每小题5分，共70分）1．（5分）函数y＝tan3x的最小正周期为．2．（5分）计算＝．3．（5分）＝．4．（5分）若集合M＝{y|y＝﹣x2+5，x∈R}，N＝{y|y＝，x≥﹣2}，则M∩N＝．5．（5分）二项式（x+1）10的展开式中，x4的系数为．6．（5分）现有6位同学排成一排照相，其中甲、乙二人相邻的排法有种．7．（5分）若cos（π+α）＝﹣，π＜α＜2π，则sinα＝．8．（5分）若一个球的体积为，则它的表面积为．9．（5分）三棱锥O﹣ABC中，OA＝OB＝OC＝2，且∠BOC＝45°，则三棱锥O﹣ABC体积的最大值是．10．（5分）如图所示，在长方体ABCD﹣A1B1C1D1中，AD＝2，AB＝AE＝1，M为矩形AEHD 内一点，若∠MGF＝∠MGH，MG和平面EFGH所成角的正切值为，则点M到平面EFGH的距离为．11．（5分）若集合A1，A2满足A1∪A2＝A，则称（A1，A2）为集合A的一种分析，并规定：当且仅当A1＝A2时，（A1，A2）与（A2，A1）为集合A的同一种分析，则集合A＝{a1，a2，a3}的不同分析种数是．12．（5分）已知函数y＝a x+b（b＞0）是定义在R上的单调递增函数，图象经过点P（1，3），则的最小值为．13．（5分）已知函数f（x）是R上的减函数，且y＝f（x﹣2）的图象关于点（2，0）成中心对称．若u，v满足不等式组，则u2+v2的最小值为．14．（5分）已知x∈R，定义：A（x）表示不小于x的最小整数，如，若x＞0且A（2x•A（x））＝5，则x的取值范围为．二、选择题：15．（5分）在△ABC中，若，则△ABC一定是（）A．等腰三角形B．直角三角形C．等腰直角三角形D．等边三角形16．（5分）已知z∈C，“”是“z为纯虚数”的（）A．充分非必要条件B．必要非充分条件C．充要条件D．既不充分也不必要条件17．（5分）下列关于公差d＞0的等差数列{a n}的四个命题：p1：数列{a n}是递增数列；p2：数列{na n}是递增数列；p3：数列是递增数列；p4：数列{a n+3nd}是递增数列；其中真命题是（）A．p1，p2B．p3，p4C．p2，p3D．p1，p418．（5分）某工厂今年年初贷款a万元，年利率为r（按复利计算），从今年末起，每年年末偿还固定数量金额，5年内还清，则每年应还金额为（）万元．A．B．C．D．三、解答题：本大题共5小题，共90分.解答应写出必要的文字说明或推理、验算过程. 19．（10分）某地区有800名学员参加交通法规考试，考试成绩的频率分布直方图如图所示，其中成绩分组区间是：[75，80），[80，85），[85，90），[90，95），[95，100]，规定90分及以上为合格：（1）求图中a的值；（2）根据频率分布直方图估计该地区学员交通法规考试合格的概率；（3）若三个人参加交通法规考试，估计这三个人至少有两人合格的概率．20．（10分）如图，在三棱锥P﹣ABC中，P A⊥底面ABC，AB⊥BC，AB＝P A＝BC＝2．D，E分别为AB，AC的中点，过DE的平面与PB，PC相交于点M，N（M与P，B不重合，N与P，C不重合）．（Ⅰ）求证：MN∥BC；（Ⅱ）求直线AC与平面PBC所成角的大小；（Ⅲ）若直线EM与直线AP所成角的余弦值时，求MC的长．21．（10分）在平面直角坐标系中xOy中，动点E到定点（1，0）的距离与它到直线x＝﹣1的距离相等．（Ⅰ）求动点E的轨迹C的方程；（Ⅱ）设动直线l：y＝kx+b与曲线C相切于点P，与直线x＝﹣1相交于点Q．证明：以PQ为直径的圆恒过x轴上某定点．22．（15分）已知函数（a＞0，a≠1）是奇函数．（1）求实数m的值；（2）判断函数f（x）在（1，+∞）上的单调性，并给出证明；（3）当x∈（n，a﹣2）时，函数f（x）的值域是（1，+∞），求实数a与n的值．23．（15分）已知二次函数y＝f（x）的图象的顶点坐标为，且过坐标原点O，数列{a n}的前n项和为S n，点（n，S n）（n∈N*）在二次函数y＝f（x）的图象上．（1）求数列{a n}的表达式；（2）设b n＝a n•a n+1cos（n+1）π（n∈N*），数列{b n}的前n项和为T n，若T n≥m2对n∈N*恒成立，求实数m的取值范围；（3）在数列{a n}中是否存在这样的一些项，，，，…，…（1＝n1＜n2＜n3＜…＜n k＜…k∈N*），这些项能够依次构成以a1为首项，q（0＜q＜5，q∈N*）为公比的等比数列{}？若存在，写出n k关于k的表达式；若不存在，说明理由．2016-2017学年上海交大附中高三（下）开学数学试卷参考答案与试题解析一、填空题：（本大题共14小题，每小题5分，共70分）1．【解答】解：函数y＝tan3x的最小正周期为T＝＝．故答案为：．2．【解答】解：＝2×3﹣1×4＝2，故答案为：2．3．【解答】解：＝＝（+）＝，故答案为：4．【解答】解：由M中y＝﹣x2+5≤5，得到M＝（﹣∞，5]，由N中y＝，x≥﹣2，得到y≥0，即N＝[0，+∞），则M∩N＝[0，5]，故答案为：[0，5]5．【解答】解：二项式（x+1）10的展开式中，x4的系数为C104＝210，故答案为：106．【解答】解：先把甲乙二人捆绑在一起，看作一个复合元素，再和其他4人进行全排，故有＝240种，故答案为：2407．【解答】解：∵cos（π+α）＝﹣cosα＝﹣，∴cosα＝，又π＜α＜2π，∴sinα＝﹣＝﹣．故答案为：﹣．8．【解答】解：由得，所以S＝4πR2＝12π．9．【解答】解：将△BOC作为三棱锥的底面，∵OA＝OB＝OC＝2，且∠BOC＝45°，∴△BOS的面积为定值S＝＝，∴当OA⊥平面BOC时，该棱锥的高最大，体积就最大，此时三棱锥O﹣ABC体积的最大值V＝×S×h＝＝．故答案为：．10．【解答】解：取FG的中点N，作MO⊥EH于O，连接MN，ON，MH，OG，在长方体ABCD﹣A1B1C1D1中，AD＝2，AB＝AE＝1，M为矩形AEHD内一点，若∠MGF ＝∠MGH，可得△MNG≌△MGH，则△ONG≌△OGH，所以ON＝GH＝AB＝1，因为N是FG的中点，所以NG＝FG＝AD＝×2＝1，所以在Rt△ONG中，OG＝＝＝MG和平面EFGH所成角的正切值为，可得＝，则MO＝＝．则点M到平面EFGH的距离为：．故答案为：．11．【解答】解：当A1＝∅时必须A2＝A，分析种数为1；当A1有一个元素时，分析种数为C31•2；当A1有2个元素时，分析总数为C32•22；当A1＝A时，分析种数为C33•23．所以总的不同分析种数为1+C31•21+C32•22+C33•23＝（1+2）3＝27．故答案为：2712．【解答】解：∵函数y＝a x+b（b＞0）是定义在R上的单调递增函数，图象经过点P（1，3），∴a＞1，3＝a+b．∴＝（a﹣1+b）＝≥＝，当且仅当a＝，b＝时取等号．故答案为：13．【解答】解：∵y＝f（x﹣2）的图象关于点（2，0）成中心对称．∴y＝f（x）的图象关于点（0，0）成中心对称．即函数f（x）是奇函数，则不等式组，等价为，即，作出不等式组对应的平面区域如图，则u2+v2的几何意义为区域内的点到原点距离的平方，则由图象知原点到直线u＝1﹣v，即v+u﹣1＝0的距离最小，此时d＝，故u2+v2的最小值为d2＝，故答案为：14．【解答】解：当A（x）＝1时，0＜x≤1，可得4＜2x≤5，得2＜x≤，矛盾，故A（x）≠1，当A（x）＝2时，1＜x≤2，可得4＜4x≤5，得1＜x≤，符合题意，故A（x）＝2，当A（x）＝3时，2＜x≤3，可得4＜6x≤5，得＜x≤，矛盾，故A（x）≠3，由此可知，当A（x）≥4时也不合题意，故A（x）＝2∴正实数x的取值范围是（1，]故答案为：（1，]二、选择题：15．【解答】解：∵＝cos＝sin，⇒，则△ABC是等腰三角形，故选：A．16．【解答】解：对于复数z，若z+＝0，z不一定为纯虚数，可以为0，反之，若z为纯虚数，则z+＝0．∴“z+＝0”是“z为纯虚数”的必要非充分条件．故选：B．17．【解答】解：∵对于公差d＞0的等差数列{a n}，a n+1﹣a n＝d＞0，∴命题p1：数列{a n}是递增数列成立，是真命题．对于数列{na n}，第n+1项与第n项的差等于（n+1）a n+1﹣na n＝（n+1）d+a n，不一定是正实数，故p2不正确，是假命题．对于数列，第n+1项与第n项的差等于﹣＝＝，不一定是正实数，故p3不正确，是假命题．对于数列{a n+3nd}，第n+1项与第n项的差等于a n+1+3（n+1）d﹣a n﹣3nd＝4d＞0，故命题p4：数列{a n+3nd}是递增数列成立，是真命题．故选：D．18．【解答】解：假设每年偿还x元，由题意可得a（1+r）5＝x（1+r）4+x（1+r）3+…+x（1+r）+x，化为a（1+r）5＝x•，解得x＝．故选：B．三、解答题：本大题共5小题，共90分.解答应写出必要的文字说明或推理、验算过程. 19．【解答】解：（1）由频率分布直方图，知：（0.01+a+0.07+0.06+0.02）×5＝1，解得a＝0.04．（2）规定90分及以上为合格，根据频率分布直方图估计该地区学员交通法规考试合格的概率：p1＝（0.06+0.02）×5＝0.4．（3）三个人参加交通法规考试，估计这三个人至少有两人合格的概率：p2＝＝．20．【解答】解：（Ⅰ）证明：∵D，E分别为AB，AC的中点；∴DE∥BC，BC⊂平面PBC，DE⊄平面PBC；∴DE∥平面PBC，平面DENM∩平面PBC＝MN；∴DE∥MN；∴MN∥BC；（Ⅱ）如图，在平面P AB内作BZ∥P A，则根据：P A⊥底面ABC，及AB⊥BC即知，BC，BA，BZ两两垂直；∴以B为坐标原点，BC，BA，BZ所在直线为x，y，z轴建立如图所示空间直角坐标系，则：B（0，0，0），C（2，0，0），A（0，2，0），P（0，2，2）；∴，；设平面PBC的法向量为；则由得：，令z1＝1，得x1＝0，y1＝﹣1；∴；设直线AC和平面PBC所成角为α，则：sinα＝＝；又；∴；即直线AC和平面PBC所成角为；（Ⅲ）设M（0，y，z），M在棱PB上，则：；∴（0，y，z）＝λ（0，2，2）；∴M（0，2λ，2λ），E（1，1，0）；∴；因为直线EM与直线AP所成角的余弦值；设直线EM和直线AP所成角为θ；所以cosθ＝；∴8λ2﹣18λ+9＝0；解得，或（舍去）；∴M（0，）；∴．21．【解答】（Ⅰ）解：设动点E的坐标为（x，y），由抛物线定义知，动点E的轨迹是以（1，0）为焦点，x＝﹣1为准线的抛物线，∴动点E的轨迹C的方程为：y2＝4x；（Ⅱ）证明：设直线l的方程为：y＝kx+b（k≠0），由，消去x得：ky2﹣4y+4b＝0．∵直线l与抛物线相切，∴△＝16﹣16kb＝0，即．∴直线l的方程为y＝kx+．令x＝﹣1，得，∴Q（﹣1，），设切点坐标P（x0，y0），则，解得：P（），设M（m，0），则＝＝．当m＝1时，．∴以PQ为直径的圆恒过x轴上定点M（1，0）．22．【解答】解：（1）∵函数（a＞0，a≠1）是奇函数．∴f（﹣x）+f（x）＝0解得m＝﹣1．（2）由（1）及题设知：，设，∴当x1＞x2＞1时，∴t1＜t2．当a＞1时，log a t1＜log a t2，即f（x1）＜f（x2）．∴当a＞1时，f（x）在（1，+∞）上是减函数．同理当0＜a＜1时，f（x）在（1，+∞）上是增函数．（3）由题设知：函数f（x）的定义域为（1，+∞）∪（﹣∞，﹣1），∴①当n＜a﹣2≤﹣1时，有0＜a＜1．由（1）及（2）题设知：f（x）在为增函数，由其值域为（1，+∞）知（无解）；②当1≤n＜a﹣2时，有a＞3．由（1）及（2）题设知：f（x）在（n，a﹣2）为减函数，由其值域为（1，+∞）知得，n＝1．23．【解答】解：（Ⅰ）由题意得f（x）＝（x+1）2﹣，∴S n＝（n+1）2﹣＝n2+n（n∈N*），当n≥2时，a n＝s n﹣s n﹣1＝n2+n﹣[（n﹣1）2+（n﹣1）]＝，当n＝1时，a1＝s1＝1适合上式，∴数列{a n}的通项公式是：a n＝（n∈N*）；（Ⅱ）∵b n＝a n a n+1cos（n+1）π，（n∈N*），∴T n＝b1+b2+…+b n＝a1a2﹣a2a3+a3a4﹣a4a5+…+（﹣1）n﹣1a n a n+1，由（Ⅰ）得：数列{a n}是以1为首项，公差为的等差数列，①当n＝2m，m∈N*时，T n＝T2m＝a1a2﹣a2a3+a3a4﹣a4a5+…+（﹣1）n﹣1a n a n+1，＝a2（a1﹣a3）+a4（a3﹣a5）+…+a2m（a2m﹣1﹣a2m+1）＝﹣（a2+a4+…+a2m）＝﹣••m＝﹣（8m2+12m）＝﹣（2n2+6n），②当n＝2m﹣1，m∈N*时，T n＝T2m﹣1＝T2m﹣（﹣1）2m﹣1a2m a2m+1＝﹣（8m2+12m）+（16m2+16m+3）＝（8m2+4m+3）＝（2n2+6n+7），∴T n＝，要使T n≥tn2对n∈N*恒成立，只要使﹣（2n2+6n）≥tn2（n为正偶数）恒成立，即使﹣（2+）≥t对n为正偶数恒成立．∴t≤[﹣（2+）]min＝﹣；（Ⅲ）由a n＝知，数列{a n}中每一项都不可能是偶数，①如存在以a1为首项，公比q为2或4的数列{ank}，k∈N*，此时{ank}中每一项除第一项外都是偶数，故不存在以a1为首项，公比为偶数的数列{ank}；②q＝1时，显然不存在这样的数列{ank}，q＝3时，若存在以a1为首项，公比为3的数列{ank}，k∈N*，则an1＝1，n1＝1，ank＝3k﹣1＝，n k＝，∴存在满足条件的数列{a nk}，且n k＝，（k∈N*）．。

建平中学$交大附中2016学年十月联合月考卷II. Grammar and VocabularySection A (10%)Directions: After reading the sentences or passages below, fill in the blanks to make the sentences or 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 other.The world’s (1)__________(famous)heart surgeon,the Egyptian Professor,Sir Magdi Yacoub,has transplanted more hearts than anyone else.To the countless people whose lives he has transformed and saved,he is a hero.Professor Yacoub (2)_____________(inspire) in his work by his father,who was a general surgeon.Now 66 years old,professor Yacoub still retains his energy and extraordinary enthusiasm for his career.For 43 years,he has dealt with desperate patients(3)__________combination pf poor diet,inactive lifestyle and stress overload have caused them to ask for his help.(4)_________ ___________all these experiences,he is very aware of the role of good nutrition and regular exercise in maintaining good health.He eats very well and swims early each morning.Professor Yacoub’s life is always hectic(狂热的).(5)____________a donor heart has suddenly been found,then an operation has to take place quickly.He works long hours;he says there are no regular hours for a heart surgeon,as the surgery _________take place when it needs to be carried out.For relaxation, professor Yacoub enjoys (7)___________(garden) even grows orchids,One dream of his is to go to the Amazon one day(8)________(see) the rare plants there.He is patron of the Chain of Hope charity,which aims to take medical expense to the developing world.Specialist teams give their time free and travel all over the world to places such as Mozambique and Jamaica to train local surgeons in techniques that (9)________ (save) lives .This charity also brings needy children to the West (10)___________necessary heart surgery.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.(A)Valuable By-Products of Space ResearchResearch that went into developing the highly specialized technology for space travel has resulted in many unexpected 21 applications back on earth. Out of the engineering that produced rocket motor, space suits, and other necessities of space flight came by products that no one had anticipated. Equipment and 22 designed for use in medicine, industry, and the home, these valuable by products of space research, called spin offs, have improved the quality of life on earth in many ways.Some of the best-known examples of spin-offs from space research are found in hospitals and doctors' offices. One such example is the sight switch, which was originally developed to allow astronauts to control their spacecraft without using their hands. It is now used by 23 people to operate devices using eye movements.Doctors have also benefited from the technology required to make electronic instruments small enough and durable enough for trips into space. From this technology have come hearing aids the size of an aspirin and television cameras small enough to be 24 to a surgeon's head to give medical students a close-up view of an operation.Biotelemetry, which was developed to 25 the physical signs of astronauts by checking their temperature, brain-wave activity, breathing rate, and heartbeat, offers doctors a new means of monitoring hospital patients. Biosensors attached to the body send data by wire or radio. This information is displayed on 26 for doctors to analyze.One of the most valuable 27 of aerospace technology to industry is a management technique called the systems approach. With the aid of computers, this technique brings together all the elements of a complex project, including people, money, and materials, to assure that everything is completed at the optimum time. It has been applied to a variety of situations 28 to space exploration. Among them are cancer research, hospital design, city planning, crime detection, pollution control, building construction, and transportation.The experience gained from developing NASA spacesuits was applied to the process of designing clothing for use in other 29 . Firefighters now have lighter and special fire blocking materials that are more 30 to cracking and burning. Spacers used for cushioning in moon boots were adapted for use in athletic shoes that are designed to reduce fatigue and injury.(B)If your parents take out a loan, remind them to make the payments on time. Otherwise it will become a(n) 31 record in their personal credit reports, which are playing a(n) 32 big role in people's daily lives. A story carried by Chongqing Morning Post in June, 33 this trend.According to the report, a Chongqing student borrowed money from the bank to 34 his university studies. After he graduated in 2005, he went to work in Shenzhen. Later, he wanted to buy a house using loans. But several banks turned down his loan 35 . The reason was that he had not paid back 1,500 yuan he borrowed from a bank when he was at university.A personal credit rating is becoming a(n) 36 “pass” in everyday life, as China establishes a nationwide credit database. Personal credit systems go back 150 years. In developed countries, enterprises and banks use them to decide whether or not to loan money or do other business with a person.A credit report 37 the credit worthiness of an individual, a company, or even a country. It is a(n)38 made by credit bureaus of a borrower's overall credit history and his or her ability to repay debt. A poor credit rating means a high risk of defaulting on a loan, and thus leads to the 39 of a loan by the lender.Today in China, credit history in banks is the major 40 of a credit report. But in the future, reports will include information about the payment of telephone bills, water use fees, electricity and natural gas bills, and taxes, according to officials of the People's Bank of China, the central bank.The secrets of long lifeA long healthy life is no accident. It begins with good genes, but it also depends on good ___41___. So what’s the formula for success? In a recent study, scientists have focused on groups living in several refions where exceptional longevity is the norm: Sardinia, Italy, Loma Linda, California, and the islands of Okinawa, Japan.SardiniansWhy do they live so long? __42__ is part of the answer. By 11 a.m. Tonino has already milked four cows, chopped wood and walked four miles with his sheep. Now, taking the day’s first break, he gathers his grown children, grandson, around the kitchen table. Giovanna, his wife, unties a handkerchief containing a paper-thin flatbread called carta da musica, pours some red wine, and cut slices of homemade cheese.These Sardinians also benefit from their __43__ history. According to Paolo Francalacci of the University of Sassari, 80 percent of them are __44__the first Sardinians, who arrived in the area 11,000 years ago. Genetic traits made stronger over generations may favor longevity. __45__, too, is a factor.The Sardinians diet is loaded with fruits and vegetables, milk and milk products, fish and wine. Most of these items are homegrown.AdventistsThe study found that the Ad ventists’ habit of consuming beans, soy milk, tomatoes, and other fruits __46__their risk of developing certain cancers. It also suggested that eating whole wheat bread, drinking five glasses of water a day, and, most __47__, consuming four servings of nuts a week reduced their risk of heart disease. And it found that not eating red meat had been helpful in avoiding both cancer and heart disease.OkinawansThe first thing you notice about Ushi Okushima is her __48__. It fills the room with pure joy. This rainy afternoon she sits comfortably wrapped in a blue kimono. Her thick hair is combed back from her suntanned face, revealing alert green, eyes. Not long ago, she started wearing perfume. When asked about the perfume, she __49__that she has a new boyfriend.__50__behavior for a young woman, perhaps, but Ushi is 103.With an average life expectancy of 78 years for men and 86 years for women, Okinawans are among the world’s longest lived people. This is undoubtedly due in part to Okinawans warm and __51__ climate and scenic beauty. Senior citizens living in these islands tend to enjoy years __52__disabilities. Okinawans have very low rates of cancer and heart disease compared to American seniors.A lean diet of food grown on the island and a philosophy of __53__--- may also be a factor. “eat until your stomach is80 percent full.” may also be factors. Ironically, this healthy way of eating was born of __54__.Ushi Okushima grew up barefoot and poor, her family grew sweet potatoes, which formed the core of every meal. During World War II, when the men of the island joined the army, Ushi and her friend Setsuko fled to the center of the island with their children. “We __55__ terrible hunger,” Setsuko re calls.（B）In today's American society, background checks have become a routine part of hiring process. Employers use them to assess ___56____ workers, judging whether they are qualified for the posts. Through background checks, employers can also make sure that the information applicants provide is ____57___, which suggests the applicants' moral quality.Then what do background checks investigate? Many ____58___ a review of the employee's___59____ history trying to confirm whether the employee has ever been fired or forced to resign. Employers also pay attention to the length of unemployment, afraid that long-time absence from___60____ may bring negative influence to the employee's performance. Sometimes, an applicant's residential history is also an issue. Jobs with state or local governments often require that the employee live in certain areas, ___61____the chances for them to have contact with ill-intentioned people. Besides, living near the work place is always ___62____as it saves time and fares on transportation. Another item which can't be ____63___ is the applicant's criminal history --- whether he has ever been arrested or put into prison. Although __64__ offences like traffic ticketing or queue jumping are usually pardoned, breaking a criminal law is rarely spared and, in most cases, is sure to result in the____65___ of the employment. Then comes the social history. A background check that involves the applicant's social history is generally needed for government posts or employment in finance and law industries that require greater self-dicipline. A small mistake in these ____66___ may result in huge loss. The investigation usually checks drug use, family relationships and social contacts, in order to avoid ___67____someone unsuitable for the posts. Background investigators who look into social history may interview neighbors and professional references recognized by the applicant.Finally in the field of education background, an application form may ask for copies of licenses or university diplomas to show the applicant's __68__ performances. In many instances, an education background check is so particular about ____69___ that investigators even confirm the date on which the employee earned his degree to determine if it ___70____ the information the employee provided on his application.56. A.efficient B.special C.potential D.ordinary57. A.truthful B.adequate C.meaningful petitive58. A.explain B.imply C.describe D.include59. A.health B employment C.study D.finance60. A.work B.school C.family cation61. A.standing B.reducing C.promoting D.offering62. A.difficult B.impossibleC.welcomeD.flexible63. A.developed B.estimated C.included D.neglected64. A.reasonable B.normal C.minor D.easy65. A.ending B.spreading C.continying D.protecting66. A.degrees B.checks C.contacts D.posts67. A.omitting B.rejecting C.hiring D.rewarding68 A.professional B.academic C.social D.athletic69. A.scores B.interests C.behaviors D.details70. A.refers to B.agrees with C.keeps up D.brings aboutBiology may not be everything, but genes apparently have a far greater influence on human behavior than is commonly thought. Similarities ranging from hobbies to bodily gesture are being found in pairs separated at birth. Many of these behaviors are “things you would never think of looking at if you were going to study the genetics of behavior,” says psychologist Thomas J. Bouchard, Jr. , director of the Minnesota Center for Twin and Adoption Research at the University of Minnesota.Bouchard reports that so far, exhaustive psychological tests and questionnaires have been completed with approximately 50 pairs of identical twins reared apart, 25pairs of fraternal twins reared apart and comparison groups of twins reared together. “We were amazed at the similarity in posture and expressive style,” says Bouchard. “It’s probably the feature of the st udy that’s grabbed us the most.” Twins tend to have similar mannerisms, gestures, speed and tempo in talking, habits and jokes. Many of the twins dressed in similar fashion--one male pair who had never previously met arrived in England sporting identical beards, haircuts, glasses and shirts.The most striking example of common psychopathology(精神病理学），however, came from a pair of twinsraised apart. One had been reared by his own(poor) family the other had been adopted into a “good solid upper-middle-class family.”Both are now considered to be antisocial personalities, suffering from lack of impulse co ntrol, and both have criminal histories. Although the twins share, on average, 50 percent ot their genes, Bouchard suggests that the overlap is probably considerably more with this pair.Personality similarities between the identical twins raised apart are almost the same as they are with identical twins raised together, according to the results of a test developed by University of Minnesota psychologist Auke Tellegen. His personality questionnaire contains scales such as “social closeness,””harm avoidance”and”well-being.”The researchers were especially surprised to find that”traditionalism”--a trait implying conservatism and respect for authority--can be inherited. In fact, says Bouchard, his and other studies have found about 11 personality traits that appear to have significant genetic input.Overall, the emerging findings of the Minnesota study constitute a powerful disproof of those who maintain that environmental influences are the primary shaping forces of personality. The textbooks are going to have to be rewritten, Bouchard predicts.80.Why does Bouchard say these behaviors are “things you would never think of looking at if you were going to study the genetics of behavior?”A. These behaviors seemed too unimportant for scientists to observe.B. These behaviors seemed too intimate to allow scientists to observe them.C. Psychologists assumed these external characteristics could not be biologically based.D. Psychologists assumed the causes of these behaviors were too complicated for current methods of observations.81.The word “identical”(in para.3) most probably means________.A. fashionableB. alikeC. complexD. identified82.According to the passage, Auke Tellegen agrees that _______________.A.some textbooks on genes and behavior will be rewritten quite soon.B.people’s behaviors and personalities depend at large on their genesC.his personality questionnaire can indicate people’s 11 personality traitsD.the environmental influences have great effect on peopl e’s personalities81.What does the passage mainly talk about?A.Twins generally share the same hobbies and gestures if they are raised apart.B.Genes have a greater influence on human behavior than is commonly thought.C.People from upper-middle-class family are the same as those from poor family.D.Twins tend to dress in similar fashion even when brought up in different families.Section CDirections: Complete the following passage by using the sentences given below. Each sentence can be used onlySports stars have a natural advantageScientists have identified the clear biological advantages that give the world’s sporting champions a head start in life before they have even begun their rigorous training programmes.The coach for the French Olympic team says:” we measure special attributes between the ages of 16 and 18. But only one in 10,000 people has the physical aspects needed to compete at the very top level in sporting events. _82____ . We take into account the height, strength and endurance of a person. We also regard mental application as important, how an individual reacts when the competition gets really tough.”Scientists say that medical evidence is playing an increasingly important role in the selection of athletes. A study of the 40-year dominance of Kenyan runners in long distance athletic events has revealed that 45 percent of them come from the Nandi tribe. What is remarkable is that this tribe makes up only 3 percent of the Kenyan population.__83_____. Athletic organizations consider these genetic factors a good indicator when selecting sthletes to produce superior running performances.__84____. For example, David Beckham’s bandy legs have been partly credited with helping to put a spin on the football when he takes a free kick for England. Other biological characteristics are more measurable. The Americantennis player, Andy Roddick, has the fastest serve in the game. He is able to arch his back so much that it increases the rotation of his arm to 130 degrees. This is 44 percent better than the average professional player and this allows them to drive the ball over the net at 240 kilometers per hour. Michael Phelps, the 14-times Olympic swimming champion has over-sized feet which act like flippers to propel him through the water.__85_____. Mia Hamm, probably the best all-round woman footballer in the world, produces less than one liter of sweat an hour when doing vigorous exercise, which is half the human average. When it comes to speed, take the example of woman racing driver, Liz Halliday. A normal person would take 300 milliseconds to make a reactive decision. She can do it in 260 milliseconds. It may not sound much quicker but at top race speeds, this makes a difference of three car lengths.The difference between success and failure is very small and all these biological factors are crucial in finding future champions.Hitting the right buttonIt has been found that in some countries,achievement in some subjects at school is not always good for boys as it is girls.It is possible that using computers may be a way to solve this problem.Many boys seem to have a natural liking for computers,but it can often be hard to leave the screen and concentrate on the work the teacher wants them to do.As computers are becoming more and more important in the world of education today,it is natural to assume that computers can help greatly with boys who do not do too well at school and need to raise their general educational standards.Many boys appear to be more confident than girls in using it.and they need to use computers more frequently ,especially at home.Researchers at universities now think that it could be a really good way of re-engaging under-achieving boys in the learning process,and teachers have indicated that it does work.They have found that,although lots of boys do not seem to like writing in the classroom,when they use a computer they are more wiling to compose longer pieces of writing and use different styles.The issue of unintelligible handwriting is no longer a problem,either,as the neatness and presentation standards rise when boys use a computer to print out their work.Many boys welcome the “hands on” approach of computer,However,researchers and teachers need to be careful th at boys don’t just “cut and paste”things that they have found on the internet, but haven’t read,and hand it in as a completed assignment.Some boys overestimate how good they are and think they can do things without any effort.They need to develop proper research skills and make their written work more structured.Other boys take short cuts,or look at internet sites they haven’t been asked to look at.They may not plan or think carefully about their work,or they may try to finish their work quickly.This tendency is not going to be completely cured by using computers.One way to get boys to concentrate properly on the work they have been asked to do may be to encourage them to use their computers at home.However,they also need to be set tasks that are interesting and relevant to them.As in all things,the interaction between the pupil,the teacher and the computer is crucial.Translation:1.你知道如何给别人留下美好的印象吗？（leave）2.知道那时我才意识到我也许是最后知道这件事的人。

上海交通大学附属中学2016-2017学年度第一学期高二摸底上海交通大学附属中学2019-2019学年度第一学期高二物理摸底考试试卷（满分100分,60分钟完成,答案一律写在答题纸上.）命题：陈勇勇审核：王晓敏考生注意：1．重力加速度g取10 m/s2。

2．第18、19题要求写出必要的文字说明、方程式和重要的演算步骤，只写出最后答案，而未写出主要演算过程的，不能得分，有数字计算的问题，答案中必须明确写出数值和单位。

一、单项选择题（本题共18分，每小题3分）1.关于一定质量的理想气体发生状态变化时，其状态量P、V、T的变化情况，不可能的是（）（A）P、V、T都增大（B）P减小，V和T增大（C）P和V减小，T增大（D）P和T 增大，V减小2.一水平弹簧振子在光滑水平面上做简谐振动，当它通过关于平衡位置对称的两个位置时，一定相同的物理量有（）（A）位移和速度（B）速度和加速度（C）加速度和动能（D）动能和弹性势能3.4.为h1，弹簧测力计示数为F1。

若吸走槽中的部分水银，待稳定后管内外水银面高度差为h2，弹簧测力计示数为F2，则（）（A）h2＞h1，F2＝F1（B）h2＜h1，F2＝F1（C）h2＞h1，F2＞F1（D）h2＜h1，F2＞F15.一木块静止在粗糙水平面上，现用一大小为F1的水平力拉动木块，经过时间t，其速度为v。

若将水平拉力的大小改为F2，物体从静止开始经过相等时间t，速度变为2v。

对以上两个过程，用W F1、W F2分别表示拉力F1、F2做的功，W f1、W f2分别表示前后两次克服摩擦力做的功，则（）（A）W F2＞4W F1，W f2＞2W f1（B）W F2＞4W F1，W f2＝2W f1（C）W F2＜4W F1，W f2＝2W f1（D）W F2＜4W F1，W f2＜2W f1二、多项选择题（本题共16分，每小题4分）6.如图是一种工具-石磨，下面磨盘固定，上面磨盘可绕过中心的竖直转轴，在推杆带动下在水平面内转动。

交大附中实验东校2014学年第二学期开学摸底考高二英语试卷(2015-2)II. GrammarDirection：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.There is a wonderful story about a young girl who had no family and no one to love her. One day, ___21_____(feel) very sad and lonely, she was walking ____22____ a grassland when she noticed a small butterfly ___23____(catch) in a thorn (荆棘) bush. The young girl carefully released the butterfly. 24______ _______flying away, the little butterfly changed into a beautiful fairy. The young girl rubbed her eyes in disbelief."For your wonderful kindness," the good fairy said to the girl, "I will give you any wish you would like." The little girl thought for ___25_____ moment and then replied, "I want to be happy."The fairy leaned toward her and whispered in her ear. Then the fairy disappeared.____26____ the little girl grew up, there was no one in the land as happy as she. Everyone asked her secret of happiness. She would only smile and answer, "The secret of my happiness is that I listened to a good fairy ___27_____ I was a little girl."When she was very old and on her deathbed, the neighbors all gathered around her, and feared that her unbelievable secret of happiness ____28____(die) with her. "Tell us, please," they begged, "Tell us what the good fairy said." The lovely old woman simply smiled and said, "She told me that everyone, no matter how secure they seemed, no matter how old or young, how rich or poor, had need of me."21__________ 22__________ 23__________ 24______ _____25__________ 26__________ 27__________ 28__________III. 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.A.dangerousB. riskC. pleasureD. important AB. surviveAC. strengthen AD. hunted BC. mainly BD. possessed CD. threatThe days of the hunter are almost over in India. This is partly because there is practically nothing left to kill, and partly because some steps have been taken, ___29___ by banning tiger-shooting, to protect those animals which still ___30____.Some people say that Man is naturally a hunter. I disagree with this view. Surely our earliest forefathers, who at first __31_____ no weapons, spent their time digging for roots, and were no doubt themselves often ____32____ by meat-eating animals.I believe the main reason why the modern hunter kills is that he thinks people will admire his courage in overpowering ___33____ animals. Of course, there are some who truly believe that the killing is not really the ___34____ thing, and that the chief __35_____ lies in the joy ofthe hunter and the beauties of the wild countryside. There are also those for whom hunting in fact offers a chance to prove themselves and ___36___ death by design; these men go out after dangerous animals like tigers, even if they say they only do it to rid the countryside of a __37____. I can respect reasons like these, but they are clearly different from the need to ___38_____ your high opinion of yourself.IV. 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.You've been away from us for one year; you told us a lie which I came to know not long ago. On this special day for teachers across the country, I can __39__keep myself from telling your white lie to those who would lend me an ear.Do you still remember the happy__40__about six years ago? We fixed our eyes upon you at your arrival. You, a beautiful young lady, __41__us that you would live in our village.Soon after, we began to find you were part of your students and their simple honest parents. The villagers found their children _42__more time on their books _43__after doing their homework and housework. Yet they still_44__ that one day you might leave. You wore a smile all the time, which reduced to some degree their _45__ of your leaving. You went all out in the_46__ of your students, helping them not only in their studies but also in their tuitions. You often emphasized to us the_47__ of one's life, so that must have been what you were_48__ in those five years!One cold morning when class began, you entered the room _49__you had been crying bitterly . In your class, we _50_ but looked away from your eyes. You stopped for some time as if you were _51__ to find this right word. You said you would go away and would never be back to teach because your boyfriend wanted you more...On the following morning, we _52__ you the very best and the villagers gave you their thanks. The train took you away and your broken_53__ . The other day I happened to hear my parents chatting that you had lung cancer and left the world soon after you waved goodbye.39. A．forever B．seldom C．hardly D．soon40. A．scene B．condition C．sign D．sight41. A．promised B．answered C．permitted D．agreed42. A．shared B．spent C．paid D．devoted43. A．even B．ever C．soon D．still44. A．considered B．feared C．supposed D．doubted45. A．rule B．trouble C．question D．fear46. A．teaching B．middle C．course D．field47. A．way B．wealth C．value D．cost48. A．after B．for C．with D．against49. A．as if B．because C．even though D．before50. A．listened B．talked C．discussed D．studied51. A．thinking B．worrying C．crying D．trying52. A．hoped B．expected C．wished D．brought53. A．boy B．class C．heart D．memoryV. 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 read.AIf you are a human, you can't help but experience times when everything seems to be going wrong and you feel as if your life is completely out of control. It is during those “low times” that words of encouragement from family, friends, co-workers or even strangers can lighten your spirits. It is also during those times that destructive words can sink deeper and deeper into depression.For example, consider this story about a group of frogs who were traveling through the woods when two of them fell into a deep pit (深坑). All of the other frogs gathered around the pit. When they saw how deep the pit was, they told the two unfortunate frogs they would never get out.The two frogs ignored the comments and tried to jump out of the pit. The other frogs kept telling them to stop. Finally, one of the two frogs took heed of what the other frogs were saying and simply gave up. He fell down and died. The other frog continued to jump as hard as he could. Once again the crowd of frogs shouted at him to stop the pain. The more they shouted, the harder he jumped and finally he made it to safety.When he got out, the other frogs asked him why he continued to jump when they were all shouting at him to simply quit. The frog explained to them that he was a little bit deaf. He thought they were encouraging him the entire time.Every time you have a chance to say either something positive or negative to another human being, do choose the chance to say something positive! Don't let those opportunities get away from you. Your words have a large amount of power. Use them wisely. You really never know just how much they can mean to someone else.54.The first paragraph tells us that words play an important part especially when_______.A. we stay with our family, friends and co-workersB. we hear strangers say something to usC. we get through hard times in lifeD. we make some big mistakes55. The underlined phrase “took heed of” has the similar meaning with_______.A. acted according toB. had some doubtC. held on toD. got used to56.The more they shouted, the harder he jumped and finally he made it to safety.That’s because__________________.A. he struggled to prove that they were wrongB. he thought they were encouraging himC. he was angry with what they saidD. he didn’t want to let them down57. After reading the passage, readers should learn a lesson that____________.A. we can use encouraging words to help others outB. having a positive attitude is important in lifeC. never give up until we winD. we must believe in ourselves rather than othersBSome people don’t mind being fat. Other people can keep slim without any effort. But a lot of people do put on weight and don’t like it. The question is, what can they do about it?Some believe exercise can be helpful. But the trouble is that it only makes you want to eatmore. You might sweat out a couple of pounds playing tennis or climbing a mountain, but you put it all back on again with a big steak or bread and jam.A helpful way is food choosing. But what sort of food should you choose? Some believe that the less they eat, the slimmer they will be. They don’t eat anything until they become weak with hunger. Some stick to milk and bananas. You’ll find you need a lot of bananas, and unless you live where they grow, they aren’t cheap. Another says that if you eat things like hard-boiled eggs, and apples with their skins on which are hard for your stomach to digest , the more you eat, the thinner you get. This is because you use up the fat in your body to get the energy to digest the food.For most of us these methods are too extreme. The simplest way is just to cut down on the carbohydrate, which means not eating bread, potatoes, cakes, sugar, rice, and so on and eating anything else you like. It’s straight forward and often quite effective.Still others like to be more scientific. They get a table, which tells them that, for example, 100 grams of roast leg of lamb gives you 330 calories and a 50 gram helping of pudding gives you 130 calories.58. There seems nothing wrong with exercise except that ______.A．it makes you sweat B．it’s hard work C．it tires you out D．it makes you eat more 59. According to the passage, the best way to keep slim is ______.A．exercising B．hunger C．food-choosing D．eating milk and bananas60. The practical method suggested here means ______.A．sticking to bananas B．not eating many carbohydratesC．eating as little as possible D．eating things that are hard to digest61. Which of the following do you think is the best title for the passage?A．Don’t Eat Too Much B．Various Ways of Losing WeightC．Ways to Keep Fit D．Food and HealthVI. Directions: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Five years ago, David Smith wore an expensive suit to work every day. “I was a clothes addict,” he jokes. “I used to carry a fresh suit to work with me so I could change if my clothes got wrinkled.” Today David wears casual clothes-khaki pants and sports shirt-to the office. He hardly ever wears a necktie. “I’m working harder than ever,”David says, “and I need to feel comfortable.”More and more companies are allowing their office workers to wear casual clothes to work in the United States. The change from formal to casual office wear has been gradual. In the early 1990s, many companies allowed their employees to wear casual clothes on Friday (but only on Friday). This became known as “dress-down Friday” of “casual Friday”. “What started out as an extra one-day-a-week benefit for employees has really become an everyday thing.” said business consultant Maisly Jones.Why have so many companies started allowing their employees to wear casual clothes? One reason is that it’s easier for a company to attract new employees if it has a casual dress code. “A lot of young people don’t want to dress up for work,” says the owner of a software company, “so it’s hard to hire people if you have a conservative dress code.”Another reason is that people seem happier and more productive when they are wearing comfortable clothes. In a studyconducted by Levi Strauss and Company, 85 percent of employers said that they believe that casual dress improves employee morale. Only 4 percent of employers said that casual dress has a negative impact on productivity. Supporters of casual office wear also argue that a casual dress code helps them save money. “Suits are expensive, if you have to wear one every day,”one person said. “For the same amount of money, you can buy a lot more casual clothes.”62. Why did David Smith refer to himself as “a clothes addict,”?_______________________________________________________________________________63. David Smith wears casual clothes now, because _____________________________________64. The majority of the employees said casual dress_____________________________________65. According to this passage, what does it mean by a conservative dress code?VII. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.66.多亏了你的帮助，我才度过了人生的难关。

上海市交通大学附属中学2021届高三9月开学考试英语试题II。

Grammar and VocabularySection ADirections: After reading the passage 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.This is not the end of meatIt is true that some Americans have had to adapt to some changes during the pandemic. Some slaughter—houses shut down as the virus ran rampant through the workforce. One Tyson Foods pork—processing plant closed after more than 20% of (21）________ employees tested positive。

Hundreds of Wendy’s locations can out of burgers。

Grocery stores put limits on how much meat customers (22）________ buy. But while Eating Animals author Jonathan Sarfran Fore took to the New York Times to declare, ”The end of meat is here,”and others have noted the increased sales of plant—based meat products like Beyond Burgers, there is little evidence that any change in our eating habits will stick.（23) ________ history tells us is that Americans become upset about meat only when production is shown to be unsanitary（不卫生的），or when supply reduces and prices go up。

2016-2017学年上海交大附中高二（下）期末英语试卷II. Grammar and VocabularySection ADirections：After reading the passage below，fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word，fill in each blank with the proper form of the given word；for the other blanks，use one word that best fits each blank.1．To Kill A Mockingbird （Excerpt I）By Harper LeeI was fairly sure Boo Radley was inside that house，but I couldn't prove it，and felt it best to keep my mouth shut or I would be accused （21）believing in Hot Steams，phenomena I was immune to in the daytime．Jem parceled out our roles：I was Mrs．Radley，and （22）I had to do was come out and sweep the porch．Dill was old Mr．Radley：he walked up and down the sidewalk and coughed when Jem spoke to him．Jem，naturally，was Boo：he went under the front steps and screamed from time to time．（23）the summer progressed，so did our game．We polished and perfected it，and added dialogue and plot until we had manufactured a small play upon which we rang changes every day．Dill was a villain's villain：he could get into any character part （24）（assign）him，and appear tall if height was part of the cruelty required．He was as good as his worst performance；his worst performance was Gothic．I reluctantly played various ladies who entered the script．I never thought it as much fun as Tarzan，and I played that summer with more than vague anxiety （25）Jem's assurances that Boo Radley was dead and nothing would get me，with him and Calpurnia there in the daytime and Atticus home at night．Jem was a born hero．It was a blue little drama，（26）（weave）from bits and pieces of gossip and neighborhood legend：Mrs．Radley had been beautiful until she married Mr Radley and lost all her money．She also lost most of her teeth，her hair，and her rightforefinger；she sat in the living room and cried most the time，（27）．Boo slowly whittled（消减）away all the furniture in the house．The three of us were the boys （28）got into trouble；I was the judge，for a change；Dill led Jem away and crammed him beneath the steps，poking him with the brushbroom．Jem would reappear as needed in the shapes of the sheriff，various townsfolk，and Miss Stephanie Crawford，who had more to say about the Radleys than anybody in Maycomb．When it was time to play Boo's big scene，Jem would sneak into the house，steal the scissors from the sewing﹣machine drawer when Calpurnia's back （29）（turn），then sit in the swing and cup up newspapers．Dill would walk by，cough at Jem，and Jem would pretend a plunge into Dill's thing．From （30）．I stood it looked real．2．What the Bible Says About MoneyMost people know Sean Hyman form his regular appearances on Fox Business，CNBC，and Bloomberg Television，but what they don't know is that Sean is a former minister，and that his secret to （31）（invest）is hidden within the Bible．Perhaps （32）can explain why，despite his mysterious ability to predict accuate moves in the stock market，Sean is often laughed at for his unique strategy for investing．For example，a few months ago Sean appeared on Bloomberg Television．At that time，Best Buy （33）（drop）to all﹣time lows of﹩16 a share．Sean predicted the stock（34）go down to﹩11a share，and would then quickly rebound to ﹩25 per share，and after that would restore to 40 per share over the next ye ar．Another commentator on the show actually challenged Sean for his prediction，saying"﹩40 on Best Busy？If that's the case Apple is going to﹩1500．That's the most ridiculous thing I have ever heard!（Editor's Note：At the time，Apple was trading at﹩650per share．）Within a few weeks，Sean would receive the last laugh．Best Buy dropped down to﹩11.20 a shar eand has since rebounded to﹩30 ashare，（35）（continue）its path to﹩40…．exactly as Sean predicted．（Ironically，Apple has dropped down to about﹩400 per share．）During a recent private dinner with Sean，once he （36）（bless）the food，I wasted no time （37）（ask）him what his secret is for investing so successfully．I expected Sean to say that it was his years of experience at Charles Schwab or perhaps one of the complicated algorithms（算法）he uses for timing the stock market．（38）when Sean responded that his secret was the Bible，I was thoroughly shocked．Yes，I knew Swan was a Christian．However，people usually keep their faith separate from things like…investing．But not Swan．For Sean，the Bible is his foundation for investing．He explained to me （39）there is actually a"Bible Money Code"hidden into Scripture．Certain investment Giants，Sean says，such as Warren Buffett and John Templeton，（40）（already use）this code to store up billions．Finally，Sean used the teachings of King Solomon and Jesus of Nazareth to show how anyone can get out of debt…make sound investments…and morally build substantial wealth．Section B 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.3．A．aspects B．astonishingly C．realization D．adapted E．inevitably F．peersG．collections H．pause I．feast J．instincts K．exposedHere is a lesson that we're going to be taught again and again in the coming years：Most animals are not just animals．They're also （41）of microbes （微生物）．If you really want to understand the animal，you also have to understand the world of microbes inside them．In other words，zoology is ecology．Consider the western corn rootworm﹣﹣﹣﹣a beetle that's a serious pest of cornin the US．The adults have strong preferences for laying eggs in corn fields，so that their underground larvae （幼虫）hatch into a （42）of corn roots．This life cycle depends on a continuous year﹣on﹣year supply of corn．Farmers can use this dependency against the rootworm，by planting soybean and corn in alternate years．These rotations （轮流）mean that rootworms lay eggs into corn fields but their larvae hatch among soybean，and die．But the rootworms have （43）to this strategy by reducing their strong（44）for laying eggs in corn．These"rotation﹣resistant"females might lay among soybean fields，so their larvae hatch into a crop of corn．There are almost certainly genetic differences that separate the rotation﹣resistant rootworms from their normal （45）．Researchers at the University of Illinois began to study the genes of the bacteria in its gut （肠）and found some answers，after focusing on the rootworm's own genes and found that the results were mostly inconclusive．"The bad guy in the story﹣﹣﹣﹣the western corn rootworm﹣﹣﹣was actually part of a multi﹣species plot，"says Joe Spencer，who was part of the study．"No wonder it was hard to figure out what was happening．We were only looking at the most obvious （46）of the story．"If you really want to understand the animal，you also have to understand the microbes．The rootworm's gut bacteria are effectively another one of its organs，but an（47）flexible on that can change dramatically when （48）to a new food source．This allows the insects to adapt very quickly to environmental challenges，far more quickly than if they could only rely on mutations （突变）in their own genes．Spencer says，"Modern agriculture has always underestimated the ability of pests to avoid pest control，and I think the （49）that pest insects are not alone in their efforts should give us some（50）．There is a brand new tiny world out there inside every creature，and we need to start thinking seriously about it．"Reading Comprehension .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.4．In a development that would have seemed hardly possible just over a decade ago，many of us have gained constant access to information．If we need to find out the score of a ballgame，learn how to perform a complicated mathematical task，or simply remember the name of the actress in the movie we are viewing，we need only turn to our （51）or smart phones and we can find the answers immediately．It has become such an ordinary （52）to look up the answer to any question the moment it occurs．It can feel like going through withdrawal when we can't find out something immediately．We are seldom offline unless by choice and the Internet，with its search engines like Baidu and Google and the information stored there，has become an （53）memory source that we can access at any time．Storing information externally is nothing particularly（54），even before the invention of computers．In any group relationship，people typically develop a transactive（交换式）memory，which is a combination of memory stores held directly by individuals and the memory stores they can （55）because they are in touch with someone who knows that information．Like（56）computers that can address each other's memories，people in groups form transactive memory systems．In a rec arch led by Besty Sparrow of Columbia University，researchers have （57）whether having online access to search engines has become a primary transactivc memory source in itself．If asked the question whether there are any countries with only one color in their flag，for example，do we think about flags﹣or immediately think to go online to find out the answer？In one experiment，the participants were asked to read 40memorable unimportant statements of the type that they could （58）online （e．g．，an ostrich's eye is bigger than its brain）．Then they were asked to type the statements intocomputer to assure memory．Half the participants believed the computer would save what was typed and the other half believed the item would be（59）．After the reading and typing task，participants wrote down as many of the statements as they could （60）．It turned out that participants who believed the computer would erase what they had typed had（61）recall than those who regarded the computer as the memory source．The Internet has become a primary form of transactive memory，and processes of human memory are （62）to the new computing and communication technology．Just as we learn through transactive memory who knows what in our families and offices，we are learning what the computer"knows"and when we should attend to where we have stored information in our computer﹣based memories．The importance of the information from the Internet is almost（63）to that of all the knowledge we gain from our friends and coworkers﹣and lose if they are out of touch．The experience of losing our Internet connection becomes more and more like losing a（64）．We must always remain （65）to know what the Internet knows．51．A．televisions B．newspapers C．dictionaries D．laptops 52．A．practice B．custom C．regulation D．routine 53．A．additional B．external C．aggressiv e D．significant 54．A．traditional B．new C．amazing D．unique 55．A．obtain B．create C．access D．exchange 56．A．professional B．updated C．feasible D．linked 57．A．explored B．discussed C．experienced D．investigated 58．A．track down B．look up C．take in D．bring about 59．A．disappeared B．increased C．erased D．broken 60．A．guess B．remember C．claim D．announce 61．A．better B．high C．temporary D．shorter 62．A．contributing B．adding C．tending D．adapting 63．A．peculiar B．beneficial C．equal D．superior64．A．assistant B．library C．friend D．dictionary 65．A．backed up B．taken ou t C．called off D．plugged inSection B Directions：Read the following four 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 read.5．It doesn't matter if books are delivered in print or by smart phone；the main thing is to get lost in reading them．Reading books is vital for human development．Why should we bother reading a book？All children say this occasionally．Many of the 12 million adults in Britain with reading difficulties repeat it to themselves daily．In a world of advanced technology，increasing time poverty and decreasing attention should they invest precious time sinking into a good book？The discovery that our brains are physically changed by the experience of reading is something many of us will understand instinctively，as we think back to the way an extraordinary book had a transformative effect on the way we viewed the world．This transformation only takes place when we lose ourselves in a book，abandoning the emotional and mental chatter of the real world．That's why studies have found this kind of deep reading makes us more sensitive to the inner lives of others．Reasoningly，we know that reading is the foundation stone of all education，and therefore an essential basis of the knowledge economy．So reading is﹣or should be ﹣an aspect of public policy．But perhaps even more significant is its emotional role as the starting point for individual voyages of personal development and pleasure．Books can open up emotional，imaginative and historical landscapes that equal and extend the corridors of the web．They can help create and strengthen our sense of self．If reading were to decline significantly，it would change the very nature of our species．However，technology throws up as many solutions as it does challenges：for every door it closes，another opens．So the ability，offered by devices like e﹣readers，smart phones and tables，to carry an entire library in your hand is anamazing opportunity．Publishers need to use every new piece of technology to embed （嵌入）long﹣form reading within our culture66．According to the author，what attitude do the British hold towards reading？A．No child in Britain likes reading nowadays．B．Many people in Britain are at a loss as to the function of reading．C．British people are more interested in others'lives．D．British people consider reading a waste of time．67．Which one in NOT the reason why we should read？A．Reading can promote the development of human species．B．Without reading，education does not happen．C．Reading can physically change our brain．D．Reading can lead to personal pleasure．68．When will the transformative effect of reading happen？A．When we forget ourselves．B．When the real world doesn't matter to us．C．When books open up a new landscape to us．D．When we are buried in deep reading．69．Why should reading be an aspect of public policy？A．Because otherwise no one bothers to read．B．Because reading can bring economic benefit indirectly．C．Because reading is the starting point of individual voyage．D．Because books are the extension of the web．6．So many girls are raised thinking that the world is perfect and they will grow up to be a princess．I know that when I have my daughter，I'll probably tell her stories of Peria，Ancient Egypt and Sparta．I don't really want my daughter to grow up to be a Princess；I want her to grow up to be a Spartan woman．I don't want to be the father who tells his daughter all of these tales of happy endings，and she gets older only to find out they were all lies．Most of those stories from our youth were great，I think there was some truth to them，but I don't think it was explained all that well．I can remember stories，those things my mother saidShe told me fairy tales，before I went to bedSpoke of happy endings，then tacked me in real tightShe turned my night light on，and kissed my face good nightMy mind would fill with visions，of perfect paradiseShe told me everything，she said he'd be so niceHe'd ride up on his horse and，take me away on nightI'd be so happy with him，we'd ride clean out of sightShe never said that we would，curse，cry and scream and lieShe never said that maybe，someday he'd say goodbye﹣﹣Anita Baker Fairy Tales I always loved that song as a child．Now，take for example，Cinderella，Belle，Ariel，Jasmine，Mulan，Pocahontas，and Nala．I'm going to break this down in a way that will relate this to the real world in the most realiest way ever．Cinderella﹣She lived in a city with mad people．She basically got treated like garbage from her family because she was pretty．But Cinderella was one chick in that whole city．That's the only woman in die city who ended up getting a Prince．Remember the scene at the ball？How many of those women showed up looking for a Prince and the shoe didn't fit？Think about that in today's terms：So many women want a Barack，but there's only one Michelle out of all those women in the world．That was the same for Cinderella story，you can't possibly think that everyone can find a Prince．Belle﹣Many of you know how I feel about"faith﹣based"relationships．Faith is the belief in things not seen．She had to learn to love a Beast in order to get her Prince．But think about how many women will turn to Gaston because he looks good on paper and miss out on their Prince．Your mother told you not to bring home any ugly babies．The Beast never had a chance．Ariel﹣Ariel had to learn to shut the heck up to get a man．Jasmine﹣She was looking for love，and her dad was trying get $30，000 by getting her casted on Teen Mom．She ended up dating a homeless guy who was convinced he was a Prince．Turn out he was a nice guy，but she had to learn to trust a man with her heart and that's hard work．Mulan﹣She had to pretend to be a man to get a man．Pocahontas﹣She had to fight a war and teach white folks （who would later end up killing off all her peoples）to survive．Nala﹣Spartan．That's all you can say，she had to go get her man who had forgotten who he was and ran away from his home．Then she managed to get pregnant on the first night!That's Spartan．But you've got to ask yourself，arc most of the women we know as strong willed as these fairy tale women were？And while we're thinking about all of this，let's think about the men．Cinderella's Prince﹣He had to try and slide a glass slipper on a bunch of rathchets and hoppers just to find his Princess．Ariel's Prince﹣He had to kill a super﹣saiyan sea monster to get his Princess．Aladdin﹣He had to go into the desert，get a genie，a magic carpet，a parrot and kill a wizard to get with Princess Jasmine．Simba﹣He had to go back to the place where his pops was murdered and fight his Uncle，which required him to not only beat a bunch of hyenas，but then he got fire thrown in his eyes．Ask yourself another question，do you really think the men of today are trying to do all that for their Princess？The reality of life is that while your mother told you that you'd grow up to be a Princess，they never told you that Princes sow their royal oats before settling down．You'll have to wait for him to finish sowing and decide he wants to be a Prince，ask Kate Middleton．Your mother told you that you could one day be the Princess，but she never told you that the Prince would have options．Your mother told you that a man was going to sweep you off your feet，but she never told you that most mendon't chase women any more．You're going to have to figure out how to make him sit still．In real life we can count all the happy endings we know on our hands．Maybe your mother should have told you this when you went to bed at night：When you get older you're going to find a man to marry and you'll get to pick out the best wedding dress in the world．People will come from far to see it．You'll have to take your dress though．It will be free，you know we love free．It will be beautiful and it will make you look like a Princess．In fact，it will be televised for everyone to see．The whole world will be matching．But baby？There is only one Vera Wang dress and there's a nasty b*tch that wants it more than you do．So if you truly want that fairy tale wedding，and you want the best wedding dress in the world，you are going to need to kill that b*tch and take what's yours．Now get some rest we got work to do in the morning．There's only room enough for one Princess．70．How many women characters in the fairy tales are mentioned in the passage？A.7B.8C.10D.1171．Who finally found Jasmine after experiencing so many hardships？A．Gaston B．Aladdin C．Simba D．Spartan72．Which of the following is the best title for this passage？A．Never Have All the Eggs in One Basket．B．Prince and Princess Tie the Knot by Killing the Wizard．C．There Always Exists a Stepmother in Fairy Tales．D．The Real Truth Behind Fairy Tale Relationships．7．Years ago，social scientists introduced the broken﹣windows theory of crime control，which assumed that if a neighborhood looked orderly and cared for﹣with no broken windows﹣potential wrong doers would be discouraged from committing crimes there．Now psychologists have proposed a similar theory，which suggests that people can behave morally when their environment smells as clean as it looks．It's the Macbeth principle of morality，says Katie Liljenquist，professor of organizational leadership at Brigham Young University's Marriott School ofManagement and lead author of the new study，to be published in Psychological Science．"There is a strong link between moral and physical purity that people associate at an essential level．People feel guilty by immoral choices and try to wash away their evil，"says Liljenquist．"To some degree，washing actually is effective in relieving guilt．What we wondered was whether you could regulate moral behavior through cleanliness．We found that we could．"In two separate experiments，researchers were able to influence participants'behavior by exposing them to"cleanliness"in the form of a common cleaning agent's smell﹣in this case，orange﹣scented Windex （清新剂）．It turned out that people who sat in a room sprayed with Windex were more likely to act fairly and charitably than those in unscented air．The first experiment involved an anonymous （faceless）game of trust．The 28 study participants were told they would be"receivers，"with whom a group of anonymous"senders"had been instructed to invest money．Participants were told that each sender had been given $ 4 and told that any part of it invested with receivers would be three times．The job of the receiver，then，was to decide what portion of the profits to return to the sender．In reality，there was no sender，and each study participant received 12，makingitseemasthoughthesendershadentrustedthemwiththefull 4 they had been given．But would the receivers return that trust or exploit their unidentified investors？On average，those in the plain﹣smelling room returned 2.5tothesender，pocketingthelion'sshareofthemoney．ButthosebathedinthescentofWindexsentbacka naverageof 5.5，returning the senders'blind faith．The scientists insist they didn't overdo it with the Windex，just a few spritzes（喷）﹣so we can rule out brain﹣cell death or intoxication（陶醉）﹣induced generosity as reasons why those receivers gave back so much of the stolen property．Rather，Liljenquist says，"a moral awareness was awakened in a clean﹣smelling environment．"In the second experiment，researchers aimed to handle people's tendency towardcharity．Ninety﹣nine participants were assigned to either a Windex﹣scented room or a neutral﹣smelling room and given a packet of tasks to complete．Included in the packet was a flyer requesting volunteers and donations to the charity Habitat for Humanity．As expected，people in the Windex﹣sprayed room preferred to volunteer and give money than those in the unscented room﹣22% of those in the clean group said they wanted to donate money，compared with 6% of the controls．According to co﹣author Adam Galinsky，a social psychologist at Northwestern University's Kellogg School of Management，society relies on incentives（刺激，动机），in the form of rewards and punishments，to encourage people to adjust to certain standards of behavior．"Economists and even psychologists haven't been paying much attention to the fact that small changes in our environment can have dramatic effects on behavior．We underemphasize these subtle environmental cues，"he says．73．In what situation could crimes rates be dramatically reduced according to the broken﹣windows theory？A．People lived in a clean environment．B．People stayed in a pleasant smelling surroundings．C．Teenagers are born and bred in a well﹣raised family．D．Teenagers live and study along with virtuous peers in a wealthy community．74．What did participants in the plain﹣smelling room do in the first experiment？A．They contributed all the money they gain to the"senders"．B．They put a small amount of the gains into their own pocket．C．They put the largest share of the gains into their own pocket．D．They put all the gains from the investment into their own pocket．75．According to the scientists who conducted the experiments，the participants'fair and charitable behavior could be attributed to．A．the special kind of odor which made them feel pleasantB．intoxication provided by the citrus﹣scented WindexC．the unscented air the participants breathedD．common cleaning agents'odor76．The scientists in the experiments might agree that it is more beneficial for factory owners to provide．A．a good educational program for their employees．B．rich bonus for their employees．C．a good welfare system for their employees．D．a clean smelling environment．Section C Directions：Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there is one sentence more than you need.8．A．Poland is a developed and democratic country，with a high﹣income economy，and a very high standard of living．B．Poland's swift rise in PISA rankings is largely the result of the high scores of these supposedly non﹣academic children．C．The country may have one of the highest school﹣graduation rates in the world，but children appear miserable．D．The PISA for Development initiative aims to encourage and facilitate PISA participation of interested and motivated low﹣and﹣middle﹣income countries E．Poland has made some dramatic gains in education in the past decade．F．Classrooms tend to be free of the high﹣tech devices of their schools back home．Best and BrightestBAMA Companies has been making pies and biscuits in Oklahoma since 1920s．But the company is struggling to find Okies with the skills to fill even its most basic factory jobs．Graduates of local schools are often unable to read or do simple maths．This is why the company recently decided to open a new factory in Poland﹣its first in Europe．（77）．Before 2000half of the country's rural adults had finished only primary school．Yet international rankings now put the country's students well ahead of America's in science and maths．What is Poland doing right？And what is America doing wrong？Amanda Ripley，an American journalist，seeks to answer such questions in The Smart kids in the World，her new book about the schools that are working around the globe．If most exams quantify students'ability to memorize material，the PISA test aims to assess their effectiveness at problem﹣solving．Since 2000 it has been administered to millions of teenagers in more than 40countries，with surprising results．Pupils in Finland，South Korea，Japan and Canada consistently score much higher than their peers in Germany，Britain，America and France．To understand what is happening in these classrooms，Mrs Ripley follows three American teenagers who spend a year as foreign﹣exchange students in Finland，Poland and South Korea．In each country，the Americans are startled by how hard their new peers work and how seriously they take their studies．Maths classes tend to be more sophisticated．（78）．And teachers in every subject exhibit the authority of Professionals．Ms．Ripley credits Poland's swift turnaround to Miroslaw Handke，the former minister of education．When he entered the post in 1997，Poland's economy was growing but Poles seemed fated do the low﹣skilled jobs that other Europeans did not want．So he launched an impressive program of school reforms，with a new core curriculum and standardized tests．Yet his most effective change was also his vaguest：he expected the best work from all of his pupils．He decided to keep all Polish children in the same schools until they were 16，delaying the moment when some would have entered vocational tracks．（79）Not every story of academic success is a happy one．In South Korea Ms．Ripley finds a"Culture of educational masochism（受虐狂），"where pupils study at all hours in the hope of securing a precious spot in one of country's three distinguished universities．（80）．Even so，South Korea offers some good lessons for how。

上海高考生&上海试卷联合推送建平中学$交大附中2016学年十月联合月考卷II. Grammar and VocabularySection A (10%)Directions: After reading the sentences or passages below, fill in the blanks to make the sentences or passagescoherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of thegiven word; for the other blanks, use one word that best fits each other.The world's (1)__________(famous)heart surgeon,the Egyptian Professor,Sir Magdi Yacoub,has transplantedmore hearts than anyone else.To the countless people whose lives he has transformed and saved,he is a hero.ProfessorYacoub (2)_____________(inspire) in his work by his father,who was a general surgeon.Now 66 years old,professor Yacoub still retains his energy and extraordinary enthusiasm for his career.For 43years,he has dealt with desperate patients(3)__________combination pf poor diet,inactive lifestyle and stress overloadhave caused them to ask for his help.(4)_________ ___________all these experiences,he is very aware of therole of good nutrition and regular exercise in maintaining good health.He eats very well and swims early eachmorning.Professor Yacoub's life is always hectic(狂热的).(5)____________a donor heart has suddenly beenfound,then anoperation has to take place quickly.He works long hours;he says there are no regular hours for a heart surgeon,as thesurgery _________take place when it needs to be carried out.For relaxation, professor Yacoub enjoys (7)___________(garden) even grows orchids,One dream of his is to goto the Amazon one day(8)________(see) the rare plants there.He is patron of the Chain of Hope charity,which aims totake medical expense to the developing world.Specialist teams give their time free and travel all over the world toplaces such as Mozambique and Jamaica to train local surgeons in techniques that (9)________ (save) lives .Thischarity also brings needy children to the West (10)___________necessary heart surgery.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note thatthere is one word more than you need.(A)Valuable By-Products of Space Research页11 共/ 页1 第上海高考生&上海试卷联合推送Research that went into developing the highly specialized technology for space travel has resulted in manyunexpected 21 applications back on earth. Out of the engineering that produced rocket motor, space suits,and other necessities of space flight came by products that no one had anticipated. Equipment and22designed for use in medicine, industry, and the home, these valuable by products of space research, called spin offs,have improved the quality of life on earth in many ways.Some of the best-known examples of spin-offs from space research are found in hospitals and doctors' offices. Onesuch example is the sight switch, which was originally developed to allow astronauts to control their spacecraft withoutusing their hands. It is now used by 23 people to operate devices using eye movements.Doctors have also benefited from the technology required to make electronic instruments small enough and durableenough for trips into space. From this technology have come hearing aids the size of an aspirin and television camerassmall enough to be 24 to a surgeon's head to give medical students a close-up view of an operation.Biotelemetry, which was developed to 25 the physical signs of astronauts by checking theirtemperature, brain-wave activity, breathing rate, and heartbeat, offers doctors a new means of monitoring hospitalpatients. Biosensors attached to the body send data by wire or radio. This information is displayed on 26 fordoctors to analyze.One of the most valuable 27 of aerospace technology to industry is a managementtechnique calledthe systems approach. With the aid of computers, this technique brings together all the elements of a complex project,including people, money, and materials, to assure that everything is completed at the optimum time. It has been appliedto a variety of situations 28 to space exploration. Among them are cancer research, hospital design, cityplanning, crime detection, pollution control, building construction, and transportation.The experience gained from developing NASA spacesuits was applied to the process of designing clothing for usein other 29 . Firefighters now have lighter and special fire blocking materials that are more 30to cracking and burning. Spacers used for cushioning in moon boots were adapted for use in athletic shoes that aredesigned to reduce fatigue and injury.(B)页11 共/ 页2 第上海高考生&上海试卷联合推送If your parents take out a loan, remind them to make the payments on time. Otherwise it will become a(n) 31big role in people's daily lives. A story 32 record in their personal credit reports, which are playing a(n)this trend. 33 carried by Chongqing Morning Post in June,university his 34 borrowed money from the bank to student According to the report, a Chongqingstudies. After he graduated in 2005, he went to work in Shenzhen. Later, he wanted to buy a house using loans. But. The reason was that he had not paid back 1,500 yuan he borrowed 35 several banks turned down his loanfrom a bank when he was at university.“pass”in everyday life, as China establishes a nationwide 36 A personal credit rating is becoming a(n)credit database. Personal credit systems go back 150 years. In developed countries, enterprises and banks use them todecide whether or not to loan money or do other business with a person. a(n) country. It is a the credit worthiness of an individual, company, or even a report A credit 37made by credit bureaus of a borrower's overall credit history and his or her ability to repay debt. A poor credit 38of a loan by the lender. 39 rating means a high risk of defaulting on a loan, and thus leads to theof a credit report. But in the future, reports will 40 Today in China, credit history in banks is the majorinclude information about the payment of telephone bills, water use fees, electricity and natural gas bills, and taxes,according to officials of the People's Bank of China, the central bank.The secrets of long life. So what's the A long healthy life is no accident. It begins with good genes, but it also depends on good ___41___formula for success? In a recent study, scientists have focused on groups living in several refions where exceptionallongevity is the norm: Sardinia, Italy, Loma Linda, California, and the islands of Okinawa, Japan. Sardinians页11 共/ 页3 第上海高考生&上海试卷联合推送Why do they live so long? __42__ is part of the answer. By 11 a.m. Tonino has already milked four cows, choppedwood and walked four miles with his sheep. Now, taking the day's first break, he gathers his grown children,grandson, around the kitchen table. Giovanna, his wife, unties a handkerchief containing a paper-thin flatbread calledcarta da musica, pours some red wine, and cut slices of homemade cheese.These Sardinians also benefit from their __43__ history. According to Paolo Francalacci of the University of Sassari,80 percent of them are __44__the first Sardinians, who arrived in the area 11,000 years ago. Genetic traits madestronger over generations may favor longevity. __45__, too, is a factor.The Sardinians diet is loaded with fruits andvegetables, milk and milk products, fish and wine. Most of these items are homegrown.AdventistsThe study found that the Adventists' habit of consuming beans, soy milk, tomatoes, and other fruits__46__their riskof developing certain cancers. It also suggested that eating whole wheat bread, drinking five glasses of water a day,and, most __47__, consuming four servings of nuts a week reduced their risk of heart disease. And itfound that noteating red meat had been helpful in avoiding both cancer and heart disease.OkinawansThe first thing you notice about Ushi Okushima is her __48__. It fills the room with pure joy. This rainy afternoon shesits comfortably wrapped in a blue kimono. Her thick hair is combed back from her suntanned face, revealing alertgreen, eyes. Not long ago, she started wearing perfume. When asked about the perfume, she __49__that she has a newboyfriend.__50__behavior for a young woman, perhaps, but Ushi is 103.With an average life expectancy of 78 years for men and 86 years for women, Okinawans are among the world'slongest lived people. This is undoubtedly due in part to Okinawans warm and __51__ climate and scenic beauty.Senior citizens living in these islands tend to enjoy years __52__disabilities. Okinawans have very low rates of cancerand heart disease compared to American seniors.A lean diet of food grown on the island and a philosophy of __53__--- may also be a factor. “eat until your stomach is80 percent full.”may also be factors. Ironically, this healthy way of eating was born of __54__.Ushi Okushima grewup barefoot and poor, her family grew sweet potatoes, which formed the core of every meal. During World War II,when the men of the island joined the army, Ushi and her friend Setsuko fled to the center of the island with their页11 共/ 页4 第联合推送上海高考生&上海试卷（B）In today's American society, background checks have become a routine part of hiring process.Employers use them to assess ___56____ workers, judging whether they are qualified for the posts.Through background checks, employers can also make sure that the information applicants provide is____57___, which suggests the applicants' moral quality.Then what do background checks investigate? Many ____58___ a review of the employee's___59____ history trying to confirm whether the employee has ever been fired or forced to resign.Employers also pay attention to the length of unemployment, afraid that long-time absence from___60____ may bring negative influence to the employee's performance. Sometimes, an applicant'sresidential history is also an issue. Jobs with state or local governments often require that the employeelive in certain areas, ___61____the chances for them to have contact withill-intentioned people.Besides, living near the work place is always ___62____as it saves time and fares on transportation.Another item which can't be ____63___ is the applicant's criminal history --- whether he has ever beenarrested or put into prison. Although __64__ offences like traffic ticketing or queue jumping areusually pardoned, breaking a criminal law is rarely spared and, in most cases, is sure to result in the____65___ of the employment. Then comes the social history. A background check that involves theapplicant's social history is generally needed for government posts or employment in finance and lawindustries that require greater self-dicipline. A small mistake in these ____66___ may result in hugeloss. The investigation usually checks drug use, family relationships and social contacts, in order toavoid ___67____someone unsuitable for the posts. Background investigators who look into socialhistory may interview neighbors and professional references recognized by the applicant.Finally in the field of education background, an application form may ask for copies of licenses oruniversity diplomas to show the applicant's __68__ performances. In many instances, an educationbackground check is so particular about ____69___ that investigators even confirm the date on whichthe employee earned his degree to determine if it ___70____ the information the employee provided onhis application.56.A.efficientB.specialC.potentialD.ordinarypetitive58.A.explainB.implyC.describeD.include59.A.healthBemploymentC.studyD.finance页11 共/ 页5 第联合推送上海高考生&上海试卷educationD.C.family60.A.workB.schoolofferingD.C.promotingB.61.A.reducingstandingimpossibledifficult 62.A.B.flexibleD.welcomeC.neglectedestimatedD.developed63.A.C.includedB.A.64.B.normalD.easyC.minorreasonableA.endingcontinyingC.D.protectingB.spreading65.A.degrees66.D.contactsC.postsB.checksA.rejectingB.omitting67.hiringrewardingC.D.A.D.68professionalathleticacademicC.socialB.A.interestsB.69.scoresD.C.detailsbehaviorsA.brings about70.keeps uprefers toC.agrees withB.D.is behavior than influence on human but genes apparently have a far greater may Biology not be everything,commonly thought. Similarities ranging from hobbies to bodily gesture are being found in pairs separated at birth. Manyof these behaviors are “things you would never think of looking at if you were going to study the genetics of behavior,”Bouchard, Jr. , director of the Minnesota Center for Twin and Adoption Research at says psychologist Thomas J.the University of Minnesota.with completed have been psychological far, exhaustive tests and questionnaires Bouchard reports that soapproximately 50 pairs of identical twins reared apart, 25pairs of fraternal twins reared apart andcomparison groups oftwins reared together. “We were amazed at the similarity in posture and expressive style,”says Bouchard. “It's probablyudy that's grabbed us the most.”Twins tend to have similar mannerisms, gestures, speed and tempo thefeature of the stin talking, habits and jokes. Many of the twins dressed in similar fashion--one male pair who had never previously metarrived in England sporting identical beards, haircuts, glasses and shirts.however, came from a pair of twins 精神病理学），The most striking example of common psychopathology(-middle-raised apart. One had been reared by his own(poor) family the other had been adopted into a “good solid upperntrol, and both class family.”Both are now considered to be antisocial personalities,suffering from lack of impulse cohave criminal histories. Although the twins share, on average, 50 percent ot their genes, Bouchard suggests that theoverlap is probably considerably more with this pair.Personality similarities between the identical twins raised apart are almost the same as they are with identical twinsraised together, according to the results of a test developed by University of Minnesota psychologist Auke Tellegen.being.”The -“social closeness,””harm avoidance”and”wellscales His personality questionnaire contains such asfor and respect trait that”traditionalism”--a implying conservatism to researchers were especiallysurprised findauthority--can be inherited. In fact, says Bouchard, his and other studies have found about 11 personality traits thatappear to have significant genetic input.Overall, the emerging findings of the Minnesota study constitute a powerful disproof of those who maintain thatenvironmental influences are the primary shaping forces of personality. The textbooks are going to have to be rewritten,Bouchard predicts.Why does Bouchard say these behaviors are “things you would never think of looking at if you were going to study 80. the genetics of behavior?”页11 共/ 页6 第上海高考生&上海试卷联合推送A. These behaviors seemed too unimportant for scientists to observe.B. These behaviors seemed too intimate to allow scientists to observe them.C. Psychologists assumed these external characteristics could not be biologically based.D. Psychologists assumed the causes of these behaviors were too complicated for current methodsof observations.81.The word “identical”(in para.3) most probably means________.A. fashionableB. alikeC. complexD. identified82.According to the passage, Auke Tellegen agrees that _______________.A.some textbooks on genes and behavior will be rewritten quite soon.B.people's behaviors and personalities depend at large on their genesC.his personality questionnaire can indicate people's 11 personality traitsD.the environmental influences have great effect on people's personalities81.What does the passage mainly talk about?A.Twins generally share the same hobbies and gestures if they are raised apart.B.Genes have a greater influence on human behavior than is commonly thought.C.People from upper-middle-class family are the same as those from poor family.D.Twins tend to dress in similar fashion even when brought up in different families.Section CDirections: Complete the following passage by using the sentences given below. Each sentence can be used onlyonce. Note that there are two more sentences than you need.Sports stars have a natural advantageScientists have identified the clear biological advantages that give the world's sporting champions a head start inlife before they have even begun their rigorous training programmes.The coach for the French Olympic team says:”we measure special attributes between the ages of 16 and 18. Butonly one in 10,000 people has the physical aspects needed to compete at the very top level in sporting events. _82____ .We take into account the height, strength and endurance of a person. We also regard mental application as important,how an individual reacts when the competition gets really tough.”Scientists say that medical evidence is playing an increasingly important role in the selection of athletes. A study ofthe 40-year dominance of Kenyan runners in long distance athletic events has revealed that 45 percent of them comefrom the Nandi tribe. What is remarkable is that this tribe makes up only 3 percent of the Kenyanpopulation.__83_____.Athletic organizations consider these genetic factors a good indicator when selecting sthletes to produce superiorrunning performances.__84____. For example, David Beckham's bandy legs have been partly credited with helping to put a spin on thefootball when he takes a free kick for England. Other biological characteristics are more measurable. The American页11 共/ 页7 第上海高考生&上海试卷联合推送tennis player, Andy Roddick, has the fastest serve in the game. He is able to arch his back so much that it increases therotation of his arm to 130 degrees. This is 44 percent better than the average professional player and this allows themto drive the ball over the net at 240 kilometers per hour. Michael Phelps, the 14-times Olympic swimming championhas over-sized feet which act like flippers to propel him through the water.__85_____. Mia Hamm, probably the best all-round woman footballer in the world, produces less than one liter ofsweat an hour when doing vigorous exercise, which is half the human average. When it comes to speed, take the exampleof woman racing driver, Liz Halliday. A normal person would take 300 milliseconds to make a reactive decision. Shecan do it in 260 milliseconds. It may not sound much quicker but at top race speeds, this makes a difference of three carlengths.The difference between success and failure is very small and all these biological factors are crucial in finding futurechampions.Hitting the right buttonIt has been found that in some countries,achievement in some subjects at school is not always goodfor boys as it is girls.It is possible that using computers may be a way to solve this problem.Many boys seem to have a natural liking for computers,but it can often be hard to leave the screenand concentrate on the work the teacher wants them to do.As computers are becoming more and more important in the world of education today,it is naturalto assume that computers can help greatly with boys who do not do too well at school and need to raisetheir general educational standards.Many boys appear to be more confident than girls in using it.andthey need to use computers more frequently ,especially at home.Researchers at universities now think that it could be a really good way ofre-engaging under-achieving boys in the learning process,and teachers have indicated that it does work.They have foundthat,although lots of boys do not seem to like writing in the classroom,when they use a computer theyare more wiling to compose longer pieces of writing and use different styles.The issue of unintelligiblehandwriting is no longer a problem,either,as the neatness and presentation standards rise when boys usea computer to print out their work.Many boys welcome the “hands on”approach ofcomputer,However,researchers and teachersneed to be careful that boys don't just “cut and paste”things that they have found on the internet, buthaven't read,and hand it in as a completed assignment.Some boys overestimate how good they are andthink they can do things without any effort.They need to develop proper research skills and make theirwritten work more structured.Other boys take short cuts,or look at internet sites they haven't beenasked to look at.They may not plan or think carefully about their work,or they may try to finish theirwork quickly.This tendency is not going to be completely cured by using computers.One way to getboys to concentrate properly on the work they have been asked to do may be to encourage them to usetheir computers at home.However,they also need to be set tasks that are interesting and relevant tothem.As in all things,the interaction between the pupil,the teacher and the computer is crucial.页11 共/ 页8 第上海高考生&上海试卷联合推送Translation:你知道如何给别人留下美好的印象吗？（leave）1.知道那时我才意识到我也许是最后知道这件事的人。

2015-2016学年上海交大附中高三（上）摸底数学试卷一、填空题（本大题共14题，每题4分，满分56分）1．已知全集U=R，集合A={x|x≤﹣2，x∈R}，B={x|x＜1，x∈R}，则（∁U A）∩B=．2．已知互异的复数a，b满足ab≠0，集合{a，b}={a2，b2}，则a+b= ．3．若不等式ax2+5x﹣2＞0的解集是，则不等式ax2﹣5x+（a2﹣1）＞0的解集是．4．设等差数列{a n}的前n项和为S n，若S10=10，S20=30，则S30= ．5．在△ABC中，已知角A，B，C所对的边分别为a，b，c，且c（acosB﹣bcosA）=2b2，则= ．6．若点A（2，3）与点B（1，y0）位于直线l：x﹣2y+5=0的两侧，则y0的取值范围是．7．将一枚质地均匀的一元硬币抛3次，恰好出现一次正面的概率是．8．已知b∈R，若（1+bi）（2﹣i）为纯虚数，则|1+bi|= ．9．已知，且x+2y=1，则的最小值是．10．已知一圆锥的底面是半径为1cm的圆，若圆锥的侧面积是底面积的3倍，则该圆锥的体积是cm3．11．抛物线y2=4x的焦点为F，过点P（2，0）的直线与该抛物线相交于A，B两点，直线AF，BF分别交抛物线于点C，D．若直线AB，CD的斜率分别为k1，k2，则= ．12．已知f（x）=x2﹣3x+4，若f（x）的定义域和值域都是[a，b]，则a+b= ．13．关于函数f（x）=cos（2x﹣）+cos（2x+），有下列说法（1）y=f（x）的最大值为；（2）y=f（x）是以π为最小正周期的函数；（3）y=f（x）在区间（，）上单调递减；（4）将函数y=cos2x的图象向左平移个单位后，将与已知函数的图象重合．其中正确说法的序号是．14．定义在实数集R上的函数f（x），如果存在函数g（x）=Ax+B（A、B为常数），使得f（x）≥g （x）对一切实数x都成立，那么称g（x）为函数f（x）的一个承托函数．给出如下四个命题：①对于给定的函数f（x），其承托函数可能不存在，也可能有无数个；②定义域和值域都是R的函数f（x）不存在承托函数；③g（x）=2x为函数f（x）=|3x|的一个承托函数；④为函数f（x）=x2的一个承托函数．其中正确的命题有．二、选择题（本大题共4题，每题5分，满分20分）15．在（1+x）6（2+y）4的展开式中，含x4y3项的系数为（）A．210 B．120 C．80 D．6016．已知a、b、c是△ABC的三边长，且满足=0，则△ABC一定是（）A．等腰非等边三角形 B．等边三角形C．直角三角形D．等腰直角三角形17．甲乙两人进行相棋比赛，甲获胜的概率是0.4，两人下成和棋的概率是0.2，则甲不输的概率是（）A．0.6 B．0.8 C．0.2 D．0.418．圆ρ=（cosθ+sinθ）的圆心坐标是（）A．（1，）B．（，）C．（，）D．（2，）三．解答题（本大题共五题，满分74分，12+14+14+16+18=74）19．已知角α的终边经过点P（，﹣）．（1）求sinα的值．（2）求式•的值．20．已知函数f（x）=|3x+2|．（Ⅰ）解不等式f（x）＜4﹣|x﹣1|；（Ⅱ）已知m+n=1（m，n＞0），若|x﹣a|﹣f（x）≤+（a＞0）恒成立，求实数a的取值范围．21．如图，在直三棱柱ABC﹣A1B1C1中，∠ACB=90°，AC=BC=CC1=2．（1）证明：AB1⊥BC1；（2）求点B到平面AB1C1的距离；（3）求二面角C1﹣AB1﹣A1的大小．22．已知F1，F2为椭圆E的左右焦点，点P（1，）为其上一点，且有|PF1|+|PF2|=4（Ⅰ）求椭圆C的标准方程；（Ⅱ）过F1的直线l1与椭圆E交于A，B两点，过F2与l1平行的直线l2与椭圆E交于C，D两点，求四边形ABCD的面积S ABCD的最大值．23．给定数列{c n}，如果存在常数p、q使得c n+1=pc n+q对任意n∈N*都成立，则称{c n}为“M类数列”．（1）若{a n}是公差为d的等差数列，判断{a n}是否为“M类数列”，并说明理由；（2）若{a n}是“M类数列”且满足：a1=2，a n+a n+1=3•2n．①求a2、a3的值及{a n}的通项公式；②设数列{b n}满足：对任意的正整数n，都有a1b n+a2b n﹣1+a3b n﹣2+…+a n b1=3•2n+1﹣4n﹣6，且集合M={n|≥λ，n∈N*}中有且仅有3个元素，试求实数λ的取值范围．2015-2016学年上海交大附中高三（上）摸底数学试卷参考答案与试题解析一、填空题（本大题共14题，每题4分，满分56分）1．已知全集U=R，集合A={x|x≤﹣2，x∈R}，B={x|x＜1，x∈R}，则（∁U A）∩B={x|﹣2＜x＜1} ．【考点】交、并、补集的混合运算．【专题】集合．【分析】根据全集U及A求出A的补集，找出A补集与B的交集即可．【解答】解：∵全集U=R，集合A={x|x≤﹣2}，∴∁U A={x|x＞﹣2}，∵B={x|x＜1}，∴（∁U A）∩B={x|﹣2＜x＜1}．故答案为：{x|﹣2＜x＜1}【点评】此题考查了交、并、补集的混合运算，熟练掌握各自的定义是解本题的关键．2．已知互异的复数a，b满足ab≠0，集合{a，b}={a2，b2}，则a+b= ﹣1 ．【考点】集合的相等．【专题】集合．【分析】根据集合相等的条件，得到元素关系，即可得到结论．【解答】解：根据集合相等的条件可知，若{a，b}={a2，b2}，则①或②，由①得，∵ab≠0，∴a≠0且b≠0，即a=1，b=1，此时集合{1，1}不满足条件．若b=a2，a=b2，则两式相减得a2﹣b2=b﹣a，∵互异的复数a，b，∴b﹣a≠0，即a+b=﹣1，故答案为：﹣1．【点评】本题主要考查集合相等的应用，根据集合相等得到元素相同是解决本题的关键，注意要进行分类讨论．3．若不等式ax2+5x﹣2＞0的解集是，则不等式ax2﹣5x+（a2﹣1）＞0的解集是．【考点】一元二次不等式的应用．【分析】先由二次不等式的解集形式，判断出，2是方程ax2+5x﹣2=0的两个根，利用韦达定理求出a的值，再代入不等式ax2﹣5x+a2﹣1＞0易解出其解集．【解答】解：∵ax2+5x﹣2＞0的解集是，∴a＜0，且，2是方程ax2+5x﹣2=0的两根韦达定理×2=，解得 a=﹣2；则不等式ax2﹣5x+a2﹣1＞0即为﹣2x2﹣5x+3＞0，解得故不等式ax2﹣5x+a2﹣1＞0的解集．故答案为：【点评】本题考查的知识点是一元二次不等式的解法，及“三个二次”（三个二次指的是：二次函数，一元二次不等式，一元二次方程）之间的关系，“三个二次”之间的关系及应用是数形结合思想的典型代表．4．设等差数列{a n}的前n项和为S n，若S10=10，S20=30，则S30= 60 ．【考点】等差数列的性质．【专题】计算题；等差数列与等比数列．【分析】由给出的数列是等差数列，可知数列的第一个10项和，第二个10项和，…仍然构成等差数列，结合S10=10，S20=30，列式求解S30的值．【解答】解：∵数列{a n}是等差数列，则S10，S20﹣S10，S30﹣S20仍然构成等差数列，由S10=10，S20=30，得2×20=10+S30﹣30，∴S30=60．故答案为：60．【点评】本题考查了等差数列的性质，考查了等差数列的前n项和，关键是对性质的理解与运用，是中档题．5．在△ABC中，已知角A，B，C所对的边分别为a，b，c，且c（acosB﹣bcosA）=2b2，则=．【考点】余弦定理；正弦定理．【专题】解三角形．【分析】由条件利用正弦定理和余弦定理代入进行化简即可．【解答】解：∵c（acosB﹣bcosA）=2b2，∴由余弦定理可得ac•﹣bc•=2b2，即a2+c2﹣b2﹣b2﹣c2+a2=4b2，即a2=3b2，则a=b，∴=．再利用正弦定理可得=，故答案为：【点评】本题主要考查正弦定理和余弦定理的应用，比较基础．要求熟练掌握相应的公式．6．若点A（2，3）与点B（1，y0）位于直线l：x﹣2y+5=0的两侧，则y0的取值范围是（3，+∞）．【考点】二元一次不等式（组）与平面区域；直线的斜率．【专题】直线与圆．【分析】由不等式与平面区域的关系可得y0的不等式，解不等式可得．【解答】解：∵点A（2，3）与点B（1，y0）位于直线l：x﹣2y+5=0的两侧，∴（2﹣2×3+5）（1﹣2y0+5）＜0，解得y0＞3故答案为：（3，+∞）【点评】本题考查不等式与平面区域，属基础题．7．将一枚质地均匀的一元硬币抛3次，恰好出现一次正面的概率是．【考点】相互独立事件的概率乘法公式．【专题】计算题．【分析】掷一枚硬币，正面向上的概率是，将一枚质地均匀的一元硬币抛3次，相当于做了三次独立重复试验，利用独立重复试验的概率公式写出结果．【解答】解：由题意知掷一枚硬币，正面向上的概率是，将一枚质地均匀的一元硬币抛3次，相当于做了三次独立重复试验，∴恰好出现一次正面的概率是故答案为：【点评】本题考查独立重复试验的概率公式，解题的关键是看出试验符合什么条件，注意应用概率的公式，本题是一个基础题．8．已知b∈R，若（1+bi）（2﹣i）为纯虚数，则|1+bi|= ．【考点】复数求模．【专题】数系的扩充和复数．【分析】通过化简可知（1+bi）（2﹣i）=（2+b）+（2b﹣1）i，利用纯虚数的定义计算即可．【解答】解：∵（1+bi）（2﹣i）=（2+b）+（2b﹣1）i为纯虚数，∴，解得b=﹣2，∴|1+bi|===，故答案为：．【点评】本题考查复数求模，弄清纯虚数的概念是解决本题的关键，注意解题方法的积累，属于基础题．9．已知，且x+2y=1，则的最小值是．【考点】两向量的和或差的模的最值．【专题】计算题．【分析】根据要求的向量可以表示成两个向量的和的形式，把两个向量的系数用一个字母来表示，求向量的模长，利用二次函数的最值，做出结果．【解答】解：∵x+2y=1∴•===84y2﹣72y+16∴当y=时，原式=，故答案为：，【点评】本题考查向量的模长的最值，本题解题的关键是表示出向量的模长，再用函数求最值的方法来求解，这是这一类题目共同的特征．10．已知一圆锥的底面是半径为1cm的圆，若圆锥的侧面积是底面积的3倍，则该圆锥的体积是cm3．【考点】棱柱、棱锥、棱台的体积．【专题】空间位置关系与距离．【分析】由已知中，圆锥的底面半径为1，侧面积是底面积的3倍，分析圆锥的母线长，进而求出圆锥的高，结合圆锥的体积公式即可获得问题的解答．【解答】解：∵圆锥的底面半径r=1cm，侧面积是底面积的3倍，∴圆锥的母线长l=3cm，故圆锥的高h==2cm，故圆锥的体积V=Sh=πr2•h==cm3，故答案为：．【点评】本题考查的是圆锥的体积求解问题．在解答的过程当中充分体现了圆锥体积公式的应用以及转化思想的应用．值得同学们体会反思．11．抛物线y2=4x的焦点为F，过点P（2，0）的直线与该抛物线相交于A，B两点，直线AF，BF分别交抛物线于点C，D．若直线AB，CD的斜率分别为k1，k2，则= ．【考点】直线与圆锥曲线的关系．【专题】直线与圆；圆锥曲线的定义、性质与方程．【分析】设AF的方程是y=（x﹣1），与抛物线方程联立，求出C的坐标，同理求出D的坐标，可得k2，即可求出．【解答】解：设A（x1，y1），B（x2，y2），C（x3，y3），D（x4，y4），∴AF的方程是y=（x﹣1）设k0=，则AF：y=k0（x﹣1），与抛物线方程联立，可得k02x2﹣（2k02+4）x+k02=0，利用韦达定理x3x1=1∴x3=，∴y3=k0（x3﹣1）=﹣即C（，﹣）同理D（，﹣）∴k2==2k1，∴=．故答案为：．【点评】本题考查直线与抛物线的位置关系，考查斜率的计算，考查学生的计算能力，属于中档题．12．已知f（x）=x2﹣3x+4，若f（x）的定义域和值域都是[a，b]，则a+b= 5 ．【考点】函数的值域；函数的定义域及其求法．【专题】函数的性质及应用．【分析】因为定义域和值域都是[a，b]，说明函数最大值和最小值分别是a和b，所以根据对称轴进行分类讨论即可．【解答】解：∵f（x）=x2﹣3x+4=+1，∴x=2是函数的对称轴，根据对称轴进行分类讨论：①当b＜2时，函数在区间[a，b]上递减，又∵值域也是[a，b]，∴得方程组即，两式相减得（a+b）（a﹣b）﹣3（a﹣b）=b﹣a，又∵a≠b，∴a+b=，由，得3a2﹣8a+4=0，∴a=∴b=2，但f（2）=1≠，故舍去．②当a＜2＜b时，得f（2）=1=a，又∵f（1）=＜2，∴f（b）=b，得，∴b=（舍）或b=4，∴a+b=5③当a＞2时，函数在区间[a，b]上递增，又∵值域是[a，b]，∴得方程组，即a，b是方程x2﹣3x+4=x的两根，即a，b是方程3x2﹣16x+16=0的两根，∴，但a＞2，故应舍去．故答案为：5【点评】本题考查了二次函数的单调区间以及最值问题，属于基础题．13．关于函数f（x）=cos（2x﹣）+cos（2x+），有下列说法（1）y=f（x）的最大值为；（2）y=f（x）是以π为最小正周期的函数；（3）y=f（x）在区间（，）上单调递减；（4）将函数y=cos2x的图象向左平移个单位后，将与已知函数的图象重合．其中正确说法的序号是（1）（2）（3）．【考点】两角和与差的余弦函数．【专题】三角函数的图像与性质．【分析】由三角函数公式化简可得f（x）=sin（2x+），由三角函数的性质逐个选项验证可得．【解答】解：化简可得f（x）=cos（2x﹣）+cos（2x+）=cos（2x+﹣）+cos（2x+）=sin（2x+）+cos（2x+）=sin（2x++）=sin（2x+）∴函数f（x）的最大值为，（1）正确；函数的周期T==π，（2）正确；由2kπ+＜2x+＜2kπ+可得kπ+＜x＜kπ+，当k=0时可得函数y=f（x）在区间（，）上单调递减，（3）正确；（4）y=cos2x的图象向左平移个单位后，可得y=cos2（x+）=cos（2x+）≠sin（2x+），错误；综上可知（1）（2）（3）正确，故答案为：（1）（2）（3）．【点评】本题考查三角函数的图象和性质，涉及两角和与差的三角函数公式和诱导公式，属中档题．14．定义在实数集R上的函数f（x），如果存在函数g（x）=Ax+B（A、B为常数），使得f（x）≥g （x）对一切实数x都成立，那么称g（x）为函数f（x）的一个承托函数．给出如下四个命题：①对于给定的函数f（x），其承托函数可能不存在，也可能有无数个；②定义域和值域都是R的函数f（x）不存在承托函数；③g（x）=2x为函数f（x）=|3x|的一个承托函数；④为函数f（x）=x2的一个承托函数．其中正确的命题有①③．【考点】函数最值的应用．【专题】压轴题；新定义．【分析】函数g（x）=Ax+B（A，B为常数）是函数f（x）的一个承托函数，即说明函数f（x）的图象恒在函数g（x）的上方（至多有一个交点）①举例可以说明，如f（x）=cosx，则g（x）=B（B ＜﹣1）就是它的一个承托函数，且有无数个，反例如y=tanx或y=lgx就没有承托函数；②f（x）=2x+3的定义域和值域都是R，存在一个承托函数y=2x+1，故命题②不正确；③要说明g（x）=2x为函数f（x）=|3x|的一个承托函数；即证明F（x）=e x﹣2x 的图象恒在x轴上方；④举反例即可．【解答】解：①如f（x）=sinx，则g（x）=B（B＜﹣1）就是它的一个承托函数，且有无数个，再如y=tanx．y=lgx就没有承托函数，∴命题①正确；②f（x）=2x+3的定义域和值域都是R，存在一个承托函数y=2x+1，故命题②不正确；③令F（x）═|3x|﹣2x=，可见在x≥0时，函数F（x）单调递增，最小值F（0）=0，在x＜0时，函数F（x）单调递减，最小值大于F（0）=0，∴F（x）≥0在R上恒成立，符合定义∴命题③正确；④x=1时，g（1）=，f（1）=1，显然g（1）＜f（1），当x=时，g（）=，f（）=，显然g（）＞f（），命题④不正确．故答案为：①③【点评】本题是新定义题，考查对题意的理解和转化的能力，要说明一个命题是正确的，必须给出证明，如③，对于存在性命题的探讨，只需举例说明即可，如①，对于不正确的命题，举反例即可，如②③，属于中档题．二、选择题（本大题共4题，每题5分，满分20分）15．在（1+x）6（2+y）4的展开式中，含x4y3项的系数为（）A．210 B．120 C．80 D．60【考点】二项式定理的应用．【专题】二项式定理．【分析】利用二项展开式的通项公式求得（1+x）6（2+y）4的展开式中，含x4y3 的项，可得含x4y3项的系数．【解答】解：在（1+x）6（2+y）4的展开式中，含x4y3 的项为•x3••2•y3=120x4y3，故含x4y3项的系数为120，故选：B．【点评】本题主要考查二项式定理的应用，二项展开式的通项公式，二项式系数的性质，属于基础题．16．已知a、b、c是△ABC的三边长，且满足=0，则△ABC一定是（）A．等腰非等边三角形 B．等边三角形C．直角三角形D．等腰直角三角形【考点】高阶矩阵．【专题】选作题；矩阵和变换．【分析】方程化为2a2+2b2+2c2﹣2ab﹣2bc﹣2ca=0，配方可得结论．【解答】解：方程化为2a2+2b2+2c2﹣2ab﹣2bc﹣2ca=0，所以（a﹣b）2+（b﹣c）2+（a﹣c）2=0，所以a=b=c，故选：B．【点评】本题考查高阶矩阵，考查学生的计算能力，比较基础．17．甲乙两人进行相棋比赛，甲获胜的概率是0.4，两人下成和棋的概率是0.2，则甲不输的概率是（）A．0.6 B．0.8 C．0.2 D．0.4【考点】概率的基本性质．【专题】计算题．【分析】欲求甲不输的概率，利用等量关系：甲获胜的概率是0.4，两人下成和棋的概率是0.2，把相关数值代入即可求解．【解答】解，根据题意，甲获胜的概率是0.4，两人下成和棋的概率是0.2所以甲不输的概率为0.4+0.2=0.6．故选A．【点评】本题考查了等可能事件的概率，解答本题的关键是要判断出“甲获胜的概率，和棋的概率和乙获胜的概率的和是1”．18．圆ρ=（cosθ+sinθ）的圆心坐标是（）A．（1，）B．（，）C．（，）D．（2，）【考点】简单曲线的极坐标方程．【专题】坐标系和参数方程．【分析】利用化为直角坐标方程，进而得出．【解答】解：圆ρ=（cosθ+sinθ）即（cosθ+sinθ），∴，化为．∴圆心坐标是，∴=1，θ=arctan1=．极坐标为．【点评】本题考查了极坐标与直角坐标方程的互化，属于基础题．三．解答题（本大题共五题，满分74分，12+14+14+16+18=74）19．已知角α的终边经过点P （，﹣）． （1）求sin α的值．（2）求式•的值．【考点】任意角的三角函数的定义；运用诱导公式化简求值． 【专题】计算题．【分析】（1）求出|OP|，利用三角函数的定义，直接求出sin α的值．（2）利用诱导公式化简表达式，根据角的终边所在象限，求出cos α=，可得结果．【解答】解：（1）∵|OP|=，∴点P 在单位圆上． 由正弦函数的定义得sin α=﹣（2）原式==..由余弦的定义可知，cos α=即所求式的值为【点评】本题考查任意角的三角函数的定义，运用诱导公式化简求值，考查计算能力，推理能力，是基础题．20．已知函数f （x ）=|3x+2|． （Ⅰ）解不等式f （x ）＜4﹣|x ﹣1|；（Ⅱ）已知m+n=1（m ，n ＞0），若|x ﹣a|﹣f （x ）≤+（a ＞0）恒成立，求实数a 的取值范围． 【考点】绝对值不等式的解法． 【专题】不等式的解法及应用．【分析】（Ⅰ）把要解的不等式等价转化为与之等价的三个不等式组，求出每个不等式组的解集，再取并集，即得所求．（Ⅱ）由条件利用基本不等式求得+≥4，结合题意可得|x﹣a|﹣|3x+2|≤4恒成立．令g（x）=|x ﹣a|﹣|3x+2|，利用单调性求得它的最大值，再由此最大值小于或等于4，求得a的范围．【解答】解：（Ⅰ）不等式f（x）＜4﹣|x﹣1|，即|3x+2|+|x﹣1|＜4，∴①，或②，或③．解①求得﹣＜x＜﹣，解②求得﹣≤x＜，解③求得x∈∅．综上可得，不等式的解集为（﹣，）．（Ⅱ）已知m+n=1（m，n＞0），∴+=（m+n）（+）=2++≥2+2=4，当且仅当m=n=时，取等号．再根据|x﹣a|﹣f（x）≤+（a＞0）恒成立，可得|x﹣a|﹣f（x）≤4，即|x﹣a|﹣|3x+2|≤4．设g（x）=|x﹣a|﹣|3x+2|=，故函数g（x）的最大值为g（﹣）=+a，再由+a≤4，求得 0＜a≤．【点评】本题主要考查绝对值不等式的解法，函数的恒成立问题，基本不等式的应用，体现了转化、分类讨论的数学思想，属于中档题．21．如图，在直三棱柱ABC﹣A1B1C1中，∠ACB=90°，AC=BC=CC1=2．（1）证明：AB1⊥BC1；（2）求点B到平面AB1C1的距离；（3）求二面角C1﹣AB1﹣A1的大小．【考点】二面角的平面角及求法；点、线、面间的距离计算．【专题】综合题．【分析】（1）以C点为坐标原点，CA，CB，CC1为X，Y，Z轴正方向建立空间坐标系，分别求出AB1与BC1的方向向量，代入数量积公式，得到其数量积为0，即可得到AB1⊥BC1；（2）求出平面AB1C1的一个法向量，则AB的方向向量，代入到公式，即可求出点B到平面AB1C1的距离；（3）结合（2）的结合，再求出平面AB1A1的一个法向量，代入向量夹角公式，即可得到二面角C1﹣AB1﹣A1的大小．【解答】证明：（1）如图建立直角坐标系，其为C为坐标原点，题意A（2，0，0），B（0，2，0），A1（2，0，2），B1（0，2，2），C1（0，0，2）．∵，∴∴AB1⊥BC1解：（2）设的一个法向量，由得令∵，∴点B到平面AB1C1的距离．（3）解设是平面A1AB1的一个法向量由∴令∵，∴二面角C1﹣AB﹣A1的大小为60°．【点评】本题考查的知识点是二面角的平面角及求法，点到面的距离，异面直线的夹角，其中建立适当的空间坐标系，将问题转化为向量夹角及向量长度问题是解答本题的关键．22．已知F1，F2为椭圆E的左右焦点，点P（1，）为其上一点，且有|PF1|+|PF2|=4（Ⅰ）求椭圆C的标准方程；（Ⅱ）过F1的直线l1与椭圆E交于A，B两点，过F2与l1平行的直线l2与椭圆E交于C，D两点，求四边形ABCD的面积S ABCD的最大值．【考点】直线与圆锥曲线的综合问题．【专题】圆锥曲线中的最值与范围问题．【分析】（I）设椭圆E的标准方程为，由已知|PF1|+|PF2|=4，，由此能求出椭圆E的标准方程．（II）由题意可知，四边形ABCD为平行四边形，S△ABCD=4S△OAB，设直线AB的方程为x=my﹣1，且A（x1，y1），B（x2，y2），由，得（3m2+4）y2﹣6my﹣9=0，由此利用弦长公式能求出S△BCD的最大值．【解答】解：（I）设椭圆E的标准方程为，由已知|PF1|+|PF2|=4，得2a=4，∴a=2，…又点P（1，）在椭圆上，∴，∴b=，椭圆E的标准方程为=1．…（II）由题意可知，四边形ABCD为平行四边形，∴S▱ABCD=4S△OAB，设直线AB的方程为x=my﹣1，且A（x1，y1），B（x2，y2），由，得（3m2+4）y2﹣6my﹣9=0，∴y1+y2=，y1y2=﹣，…S△OAB=+=|OF1||y1﹣y2|===6，…令m2+1=t，则t≥1，S△OAB=6=6，…又∵g（t）=9t+在[1，+∞）上单调递增∴g（t）≥g（1）=10，∴S△OAB的最大值为．∴S▱ABCD的最大值为6．…【点评】本题考查椭圆方程的求法，考查三角形面积的最大值的求法，解题时要认真审题，注意椭圆弦长公式的合理运用．23．给定数列{c n}，如果存在常数p、q使得c n+1=pc n+q对任意n∈N*都成立，则称{c n}为“M类数列”．（1）若{a n}是公差为d的等差数列，判断{a n}是否为“M类数列”，并说明理由；（2）若{a n}是“M类数列”且满足：a1=2，a n+a n+1=3•2n．①求a2、a3的值及{a n}的通项公式；②设数列{b n}满足：对任意的正整数n，都有a1b n+a2b n﹣1+a3b n﹣2+…+a n b1=3•2n+1﹣4n﹣6，且集合M={n|≥λ，n∈N*}中有且仅有3个元素，试求实数λ的取值范围．【考点】数列的应用．【专题】点列、递归数列与数学归纳法．【分析】（1）通过a n+1=a n+d与c n+1=pc n+q比较可知p=1、q=d，进而可得结论；（2）①通过a1=2、a n+a n+1=3•2n计算出a2、a3的值，进而利用数列{a n}是“M类数列”代入计算可知数列{a n}是以首项、公比均为2的等比数列，计算可得结论；②通过①可知2b n+22b n﹣1+23b n﹣+…+2n b1=3•2n+1﹣4n﹣6，利用2b n=（2b n+22b n﹣1+23b n﹣2+…+2n b1）﹣（22b n﹣1+23b n﹣2+…+2n b1）计算可知2b n=2n﹣1，从而M={n|≥λ，n∈N*}，分别计算出当n=1、2、3时λ的值，进而可得结论．【解答】（1）结论：公差为d的等差数列是“M类数列”．理由如下：∵数列{a n}是公差为d的等差数列，∴a n+1=a n+d，此时p=1、q=d，即公差为d的等差数列是“M类数列”；（2）①∵a1=2，a n+a n+1=3•2n，∴a2=3•2﹣a1=4， =8，又∵数列{a n}是“M类数列”，∴，即，解得：p=2，q=0，即a n+1=2a n，又∵a1=2，∴数列{a n}是以首项、公比均为2的等比数列，∴数列{a n}的通项公式a n=2n；②由①可知a1b n+a2b n﹣1+a3b n﹣2+…+a n b1=3•2n+1﹣4n﹣6，即2b n+22b n﹣1+23b n﹣2+…+2n b1=3•2n+1﹣4n﹣6，∴2b n﹣1+22b n﹣2+23b n﹣3+…+2n﹣1b1=3•2n﹣4（n﹣1）﹣6=3•2n﹣4n﹣2，∴22b n﹣1+23b n﹣2+…+2n b1=3•2n+1﹣8n﹣4，∴2b n=（2b n+22b n﹣1+23b n﹣2+…+2n b1）﹣（22b n﹣1+23b n﹣2+…+2n b1）=（3•2n+1﹣4n﹣6）﹣（3•2n+1﹣8n﹣4）=4n﹣2，即b n=2n﹣1，∴集合M={n|≥λ，n∈N*}={n|≥λ，n∈N*}，当n=1时，λ≤=；当n=2时，λ≤=；当n=3时，λ≤=；当n≥4时，λ≤=；又∵集合M={n|≥λ，n∈N*}中有且仅有3个元素，∴＜λ≤，故实数λ的取值范围是（，]．【点评】本题是一道关于数列与不等式的综合题，考查数列的通项，考查运算求解能力，注意解题方法的积累，属于难题．。

2016-2017学年上海市交大附中高三（上）摸底数学试卷一、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．设全集U={1，3，5，7}，集合M={1，|a﹣5|}，∁U M={5，7}，则a的值为．2．若复数z满足2z+=3﹣2i，其中i为虚数单位，则z=．3．已知双曲线的中心在坐标原点，一个焦点为F（10，0），两条渐近线的方程为y=±，则该双曲线的标准方程为．4．行列式的第2行第3列元素的代数余子式的值为．5．若变量x，y满足约束条件，则z=3x﹣y的最小值为．6．五位同学排成一排，其中甲、乙必须在一起，而丙、丁不能在一起的排法有种．7．已知{a n}为等差数列，S n为其前n项和．若a1+a9=18，a4=7，则S8=．8．若（x2+1）（2x+1）9=a0+a1（x+2）+a2（x+2）2+…+a11（x+2）11，则a0+a1+…+a11的值为．9．一个由半球和四棱锥组成的几何体，其三视图如图所示．则该几何体的体积为．10．函数f（x）=为奇函数，则实数a的值为．11．已知关于x的方程|x|=ax+1有一个负根，但没有正根，则实数a的取值范围是．12．设O为坐标原点，P是以F为焦点的抛物线y2=2px（p＞0）上任意一点，M 是线段PF上的点，且|PM|=2|MF|，则直线OM的斜率的最大值为．13．已知函数f（x）=sin（ωx+φ）（ω＞0，|φ|≤），x=﹣为f（x）的零点，x=为y=f（x）图象的对称轴，且f（x）在（，）单调，则ω的最大值为．14．在平面直角坐标系中，当P（x，y）不是原点时，定义P的“伴随点”为P′（，）；当P是原点时，定义P的“伴随点“为它自身，平面曲线C上所有点的“伴随点”所构成的曲线C′定义为曲线C的“伴随曲线”．现有下列命题：①若点A的“伴随点”是点A′，则点A′的“伴随点”是点A；②单位圆的“伴随曲线”是它自身；③若曲线C关于x轴对称，则其“伴随曲线”C′关于y轴对称；④一条直线的“伴随曲线”是一条直线．其中的真命题是（写出所有真命题的序列）．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，填上正确的答案，选对得5分，否则一律得零分．15．钱大姐常说“好货不便宜”，她这句话的意思是：“好货”是“不便宜”的（）A．充分条件B．必要条件C．充分必要条件D．既非充分又非必要条件16．若D′是平面α外一点，则下列命题正确的是（）A．过D′只能作一条直线与平面α相交B．过D′可作无数条直线与平面α垂直C．过D′只能作一条直线与平面α平行D．过D′可作无数条直线与平面α平行17．已知函数f（x）=sinϖx+cosωx（ω＞0）的图象与x轴交点的横坐标依次构成一个公差为的等差数列，把函数f（x）的图象沿x轴向左平移个单位，得到函数g（x）的图象，则（）A．g（x）是奇函数B．g（x）关于直线x=﹣对称C．g（x）在[，]上是增函数D．当x∈[，]时，g（x）的值域是[2，1]18．已知符号函数sgnx=，f（x）是R上的增函数，g（x）=f（x）﹣f（ax）（a＞1），则（）A．sgn[g（x）]=sgnx B．sgn[g（x）]=﹣sgnx C．sgn[g（x）]=sgn[f（x）] D．sgn[g（x）]=﹣sgn[f（x）]三、解答题（本大题满分74分）19．△ABC的内角A，B，C的对边分别为a，b，c，已知2cosC（acosB+bcosA）=c．（Ⅰ）求C；（Ⅱ）若c=，△ABC的面积为，求△ABC的周长．20．如图，在四棱锥P﹣ABCD中，AD∥BC，∠ADC=∠PAB=90°，BC=CD=AD．E 为棱AD的中点，异面直线PA与CD所成的角为90°．（Ⅰ）在平面PAB内找一点M，使得直线CM∥平面PBE，并说明理由；（Ⅱ）若二面角P﹣CD﹣A的大小为45°，求直线PA与平面PCE所成角的正弦值．21．已知a≥3，函数F（x）=min{2|x﹣1|，x2﹣2ax+4a﹣2}，其中min（p，q）=（Ⅰ）求使得等式F（x）=x2﹣2ax+4a﹣2成立的x的取值范围（Ⅱ）（i）求F（x）的最小值m（a）（ii）求F（x）在[0，6]上的最大值M（a）22．（16分）各项均为正数的数列{b n}的前n项和为S n，且对任意正整数n，都有2S n=b n（b n+1）．（1）求数列{b n}的通项公式；（2）如果等比数列{a n}共有2015项，其首项与公比均为2，在数列{a n}的每相邻两项a k与a k+1之间插入k个（﹣1）k b k（k∈N*）后，得到一个新的数列{c n}．求数列{c n}中所有项的和；（3）如果存在n∈N*，使不等式成立，求实数λ的范围．23．（18分）如图，已知双曲线C1：，曲线C2：|y|=|x|+1，P是平面内一点，若存在过点P的直线与C1，C2都有公共点，则称P为“C1﹣C2型点”（1）在正确证明C1的左焦点是“C1﹣C2型点“时，要使用一条过该焦点的直线，试写出一条这样的直线的方程（不要求验证）；（2）设直线y=kx与C2有公共点，求证|k|＞1，进而证明原点不是“C1﹣C2型点”；（3）求证：圆x2+y2=内的点都不是“C1﹣C2型点”2016-2017学年上海市交大附中高三（上）摸底数学试卷参考答案与试题解析一、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．设全集U={1，3，5，7}，集合M={1，|a﹣5|}，∁U M={5，7}，则a的值为2或8．【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：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．2．若复数z满足2z+=3﹣2i，其中i为虚数单位，则z=1﹣2i．【分析】设复数z=a+bi，（a、b是实数），则=a﹣bi，代入已知等式，再根据复数相等的含义可得a、b的值，从而得到复数z的值．解：设z=a+bi，（a、b是实数），则=a﹣bi，∵2z+=3﹣2i，∴2a+2bi+a﹣bi=3﹣2i，∴3a=3，b=﹣2，解得a=1，b=﹣2，则z=1﹣2i故答案为：1﹣2i．【点评】本题给出一个复数乘以虚数单位后得到的复数，求这个复数的值，着重考查了复数的四则运算和复数相等的含义，属于基础题．3．已知双曲线的中心在坐标原点，一个焦点为F（10，0），两条渐近线的方程为y=±，则该双曲线的标准方程为．【分析】由题意得，c=10，=，100=a2+b2，解出a和b的值，即得所求的双曲线的标准方程．解：由题意得，c=10，=，100=a2+b2，∴a=6，b=8，故该双曲线的标准方程为，故答案为．【点评】本题考查双曲线的定义和双曲线的标准方程，以及双曲线的简单性质的应用．4．行列式的第2行第3列元素的代数余子式的值为﹣4．【分析】根据余子式的定义可知，在行列式中划去第2行第3列后所余下的2阶行列式为第3行第3列元素的代数余子式，求出值即可．解：由题意得第2行第3列元素的代数余子式M23==﹣8+4=﹣4故答案为：﹣4．【点评】此题考查学生掌握三阶行列式的余子式的定义，会进行矩阵的运算，是一道基础题．5．若变量x，y满足约束条件，则z=3x﹣y的最小值为﹣7．【分析】由约束条件作出可行域，由图得到最优解，求出最优解的坐标，数形结合得答案．解：x，y满足约束条件对应的平面区域如图：当直线y=3x﹣z经过C时使得z最小，解得，所以C（﹣2，1），所以z=3x﹣y的最小值为﹣2×3﹣1=﹣7；故答案为：﹣7．【点评】本题考查了简单的线性规划，关键是正确画出平面区域，利用z的几何意义求最值；考查了数形结合的解题思想方法，是中档题．6．五位同学排成一排，其中甲、乙必须在一起，而丙、丁不能在一起的排法有24种．【分析】根据题意，先使用捆绑法，将甲乙看成一个“元素”，再将丙、丁单独排列，进而将若甲、乙与第5个元素分类讨论，分析丙丁之间的不同情况，由乘法原理，计算可得答案．解：根据题意，先将甲乙看成一个“元素”，有2种不同的排法，将丙、丁单独排列，也有2种不同的排法，若甲、乙与第5个元素只有一个在丙丁之间，则有2×C21=4种情况，若甲、乙与第5个元素都在丙丁之间，有2种不同的排法，则不同的排法共有2×2×（2+4）=24种情况；故答案为：24．【点评】本题考查排列、组合的综合运用，涉及相邻与不能相邻的特殊要求，注意处理这几种情况的特殊方法．7．已知{a n}为等差数列，S n为其前n项和．若a1+a9=18，a4=7，则S8=64．【分析】由等差数列的性质可得：a1+a9=18=2a5，解得a5．可得S8==4（a4+a5）．解：由等差数列的性质可得：a1+a9=18=2a5，解得a5=9．又a4=7，则S8==4（a4+a5）=4×（9+7）=64．故答案为：7=64．【点评】本题考查了等差数列的性质及其求和公式，考查了推理能力与计算能力，属于中档题．8．若（x2+1）（2x+1）9=a0+a1（x+2）+a2（x+2）2+…+a11（x+2）11，则a0+a1+…+a11的值为﹣2．【分析】本题通过赋值法进行求解，在题干所给的式子中令x=﹣1，即可得到所求的结果．解：∵（x2+1）（2x+1）9=a0+a1（x+2）+a2（x+2）2+…+a11（x+2）11∴在上式中，令x=﹣1：（（﹣1）2+1）（2（﹣1）+1）2=a0+a1+…+a11即a0+a1+…+a11=﹣2故答案为：﹣2【点评】本题通过赋值法进行求解，另外此种方法在函数的求值问题也常用到，属于基础题．9．一个由半球和四棱锥组成的几何体，其三视图如图所示．则该几何体的体积为．【分析】由已知中的三视图可得：该几何体上部是一个半球，下部是一个四棱锥，进而可得答案．解：由三视图可知，上面是半径为的半球，体积为V==，下面是底面积为1，高为1的四棱锥，体积，所以该几何体的体积为．故答案为．【点评】本题考查的知识点是由三视图，求体积和表面积，根据已知的三视图，判断几何体的形状是解答的关键．10．函数f（x）=为奇函数，则实数a的值为1或﹣1．【分析】函数f（x）=为奇函数，可得=﹣，化简即可得出结论．解：∵函数f（x）=为奇函数，∴=﹣，∴=﹣，∴a=1或﹣1．故答案为1或﹣1．【点评】本题考查了奇函数的性质，考查学生的计算能力，属于基础题．11．已知关于x的方程|x|=ax+1有一个负根，但没有正根，则实数a的取值范围是a≥1．【分析】构造函数y=|x|，y=ax+1，在坐标系内作出函数图象，通过数形结合求出a的范围．解：令y=|x|，y=ax+1，在坐标系内作出函数图象，方程|x|=ax+1有一个负根，但没有正根，由图象可知a≥1故答案为：a≥1【点评】本题考查根的存在性及根的个数判断，考查数形结合思想，计算能力，是基础题．12．设O为坐标原点，P是以F为焦点的抛物线y2=2px（p＞0）上任意一点，M 是线段PF上的点，且|PM|=2|MF|，则直线OM的斜率的最大值为．【分析】根据体积，建立方程组，求出M的坐标，可得直线OM的斜率，利用基本不等式可得结论．解：设P（2pt，2pt），M（x，y），则，∴x=，y=，∴k OM==≤=，当且仅当t=时取等号，∴直线OM的斜率的最大值为．故答案为：．【点评】本题考查抛物线的方程及运用，考查直线的斜率的最大值，考查基本不等式，考查运算能力，属于中档题．13．已知函数f（x）=sin（ωx+φ）（ω＞0，|φ|≤），x=﹣为f（x）的零点，x=为y=f（x）图象的对称轴，且f（x）在（，）单调，则ω的最大值为9．【分析】先跟据正弦函数的零点以及它的图象的对称性，判断ω为奇数，由f（x）在（，）单调，分f（x）在（，）单调递增、单调递减两种情况，分别求得ω的最大值，综合可得它的最大值．解：∵函数f（x）=sin（ωx+φ）（ω＞0，|φ|≤），x=﹣为f（x）的零点，x=为y=f（x）图象的对称轴，∴ω（﹣）+φ=nπ，n∈Z，且ω•+φ=n′π+，n′∈Z，∴相减可得ω•=（n′﹣n）π+=kπ+，k∈Z，即ω=2k+1，即ω为奇数．∵f（x）在（，）单调，（1）若f（x）在（，）单调递增，则ω•+φ≥2kπ﹣，且ω•+φ≤2kπ+，k∈Z，即﹣ω•﹣φ≤﹣2kπ+①，且ω•+φ≤2kπ+，k∈Z ②，把①②可得ωπ≤π，∴ω≤12，故有奇数ω的最大值为11．当ω=11时，﹣+φ=kπ，k∈Z，∵|φ|≤，∴φ=﹣．此时f（x）=sin（11x﹣）在（，）上不单调，不满足题意．当ω=9时，﹣+φ=kπ，k∈Z，∵|φ|≤，∴φ=，此时f（x）=sin（9x+）在（，）上单调递减，不满足题意；故此时ω无解．（2）若f（x）在（，）单调递减，则ω•+φ≥2kπ+，且ω•+φ≤2kπ+，k∈Z，即﹣ω•﹣φ≤﹣2kπ﹣③，且ω•+φ≤2kπ+，k∈Z ④，把③④可得ωπ≤π，∴ω≤12，故有奇数ω的最大值为11．当ω=11时，﹣+φ=kπ，k∈Z，∵|φ|≤，∴φ=﹣．此时f（x）=sin（11x﹣）在（，）上不单调，不满足题意．当ω=9时，﹣+φ=kπ，k∈Z，∵|φ|≤，∴φ=，此时f（x）=sin（9x+）在（，）上单调递减，满足题意；故ω的最大值为9．故答案为：9．【点评】本题主要考查正弦函数的零点以及它的图象的对称性，正弦函数的单调性的应用，属于中档题．14．在平面直角坐标系中，当P（x，y）不是原点时，定义P的“伴随点”为P′（，）；当P是原点时，定义P的“伴随点“为它自身，平面曲线C上所有点的“伴随点”所构成的曲线C′定义为曲线C的“伴随曲线”．现有下列命题：①若点A的“伴随点”是点A′，则点A′的“伴随点”是点A；②单位圆的“伴随曲线”是它自身；③若曲线C关于x轴对称，则其“伴随曲线”C′关于y轴对称；④一条直线的“伴随曲线”是一条直线．其中的真命题是②③（写出所有真命题的序列）．【分析】利用新定义，对4个命题分别进行判断，即可得出结论．解：①若点A（x，y）的“伴随点”是点A′（，），则点A′（，）的“伴随点”是点（﹣x，﹣y），故不正确；②由①可知，单位圆的“伴随曲线”是它自身，故正确；③若曲线C关于x轴对称，点A（x，y）关于x轴的对称点为（x，﹣y），“伴随点”是点A′（﹣，），则其“伴随曲线”C′关于y轴对称，故正确；④设直线方程为y=kx+b（b≠0），点A（x，y）的“伴随点”是点A′（m，n），则∵点A（x，y）的“伴随点”是点A′（，），∴，∴x=﹣，y=∵m=，∴代入整理可得n﹣1=0表示圆，故不正确．故答案为：②③．【点评】此题考查点的坐标规律，读懂题目信息，理解“伴随点”的定义是解题的关键．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，填上正确的答案，选对得5分，否则一律得零分．15．钱大姐常说“好货不便宜”，她这句话的意思是：“好货”是“不便宜”的（）A．充分条件B．必要条件C．充分必要条件D．既非充分又非必要条件【分析】“好货不便宜”，其条件是：此货是好货，结论是此货不便宜，根据充要条件的定义进行判断即可，解：若p⇒q为真命题，则命题p是命题q的充分条件；“好货不便宜”，其条件是：此货是好货，结论是此货不便宜，由条件⇒结论．故“好货”是“不便宜”的充分条件．故选：A．【点评】本题考查了必要条件、充分条件与充要条件的判断，属于基础题．16．若D′是平面α外一点，则下列命题正确的是（）A．过D′只能作一条直线与平面α相交B．过D′可作无数条直线与平面α垂直C．过D′只能作一条直线与平面α平行D．过D′可作无数条直线与平面α平行【分析】将点和线放置在正方体中，视平面α为正方体中的平面ABCD，结合正方体中的线面关系对选支进行判定，取出反例说明不正确的，正确的证明一下即可．解：观察正方体，A、过D′可以能作不止一条直线与平面α相交，故A错；B、过D′只可作一数条直线与平面α垂直，故B错；C、过D′能作不止一条直线与平面α平行，故C错；D、过平面外一点有且只有一个平面与已知平面平行，且这个平面内的任一条直线都与已知平面平行，故D对．故选：D．【点评】本题主要考查了空间中直线与平面之间的位置关系，考查空间想象能力17．已知函数f（x）=sinϖx+cosωx（ω＞0）的图象与x轴交点的横坐标依次构成一个公差为的等差数列，把函数f（x）的图象沿x轴向左平移个单位，得到函数g（x）的图象，则（）A．g（x）是奇函数B．g（x）关于直线x=﹣对称C．g（x）在[，]上是增函数D．当x∈[，]时，g（x）的值域是[2，1]【分析】将函数化简，图象与x轴交点的横坐标依次构成一个公差为的等差数列，可知周期为π，由周期求出ω，向左平移个单位可得g（x）的解析式，再利用三角函数图象及性质，可得结论．解：f（x）=sinϖx+cosωx（ω＞0），化简得：f（x）=2sin（ϖx+），∵图象与x轴交点的横坐标依次构成一个公差为的等差数列，可知周期为π∴T=π=，解得ω=2．那么：f（x）=2sin（2x+），图象沿x轴向左平移个单位，得：2sin[2（x+）+]=2cos2x．∴g（x）=2cos2x，故g（x）是偶函数，在区间[0，]单调减函数．所以A，C 不对．对称轴方程为x=（k=Z），检验B不对．当x∈[，]时，那么2x∈[，]，g（x）的最大值为1，最小值为﹣2，故值域为[﹣2，1]．D正确．故选：D．【点评】本题考查了三角函数的辅助角公式的化简和图象的平移，三角函数的性18．已知符号函数sgnx=，f（x）是R上的增函数，g（x）=f（x）﹣f（ax）（a＞1），则（）A．sgn[g（x）]=sgnx B．sgn[g（x）]=﹣sgnx C．sgn[g（x）]=sgn[f（x）] D．sgn[g（x）]=﹣sgn[f（x）]【分析】直接利用特殊法，设出函数f（x），以及a的值，判断选项即可．解：由于本题是选择题，可以采用特殊法，符号函数sgnx=，f（x）是R上的增函数，g（x）=f（x）﹣f（ax）（a＞1），不妨令f（x）=x，a=2，则g（x）=f（x）﹣f（ax）=﹣x，sgn[g（x）]=﹣sgnx．所以A不正确，B正确，sgn[f（x）]=sgnx，C不正确；D正确；对于D，令f（x）=x+1，a=2，则g（x）=f（x）﹣f（ax）=﹣x，sgn[f（x）]=sgn（x+1）=；sgn[g（x）]=sgn（﹣x）=，﹣sgn[f（x）]=﹣sgn（x+1）=；所以D不正确；故选：B．【点评】本题考查函数表达式的比较，选取特殊值法是解决本题的关键，注意解题方法的积累，属于中档题．三、解答题（本大题满分74分）19．△ABC的内角A，B，C的对边分别为a，b，c，已知2cosC（acosB+bcosA）=c．（Ⅰ）求C；（Ⅱ）若c=，△ABC的面积为，求△ABC的周长．【分析】（Ⅰ）已知等式利用正弦定理化简，整理后利用两角和与差的正弦函数公式及诱导公式化简，根据sinC不为0求出cosC的值，即可确定出出C的度数；（2）利用余弦定理列出关系式，利用三角形面积公式列出关系式，求出a+b的值，即可求△ABC的周长．解：（Ⅰ）∵在△ABC中，0＜C＜π，∴sinC≠0已知等式利用正弦定理化简得：2cosC（sinAcosB+sinBcosA）=sinC，整理得：2cosCsin（A+B）=sinC，即2cosCsin（π﹣（A+B））=sinC2cosCsinC=sinC∴cosC=，∴C=；（Ⅱ）由余弦定理得7=a2+b2﹣2ab•，∴（a+b）2﹣3ab=7，∵S=absinC=ab=，∴ab=6，∴（a+b）2﹣18=7，∴a+b=5，∴△ABC的周长为5+．【点评】此题考查了正弦、余弦定理，三角形的面积公式，以及三角函数的恒等变形，熟练掌握定理及公式是解本题的关键．20．如图，在四棱锥P﹣ABCD中，AD∥BC，∠ADC=∠PAB=90°，BC=CD=AD．E 为棱AD的中点，异面直线PA与CD所成的角为90°．（Ⅰ）在平面PAB内找一点M，使得直线CM∥平面PBE，并说明理由；（Ⅱ）若二面角P﹣CD﹣A的大小为45°，求直线PA与平面PCE所成角的正弦值．【分析】（I）延长AB交直线CD于点M，由点E为AD的中点，可得AE=ED=AD，由BC=CD=AD，可得ED=BC，已知ED∥BC．可得四边形BCDE为平行四边形，即EB∥CD．利用线面平行的判定定理证明得直线CM∥平面PBE即可．（II）如图所示，由∠ADC=∠PAB=90°，异面直线PA与CD所成的角为90°AB∩CD=M，可得AP⊥平面ABCD．由CD⊥PD，PA⊥AD．因此∠PDA是二面角P﹣CD ﹣A的平面角，大小为45°．PA=AD．不妨设AD=2，则BC=CD=AD=1．可得P （0，0，2），E（0，1，0），C（﹣1，2，0），利用法向量的性质、向量夹角公式、线面角计算公式即可得出．解：（I）延长AB交直线CD于点M，∵点E为AD的中点，∴AE=ED=AD，∵BC=CD=AD，∴ED=BC，∵AD∥BC，即ED∥BC．∴四边形BCDE为平行四边形，即EB∥CD．∵AB∩CD=M，∴M∈CD，∴CM∥BE，∵BE⊂平面PBE，∴CM∥平面PBE，∵M∈AB，AB⊂平面PAB，∴M∈平面PAB，故在平面PAB内可以找到一点M（M=AB∩CD），使得直线CM ∥平面PBE．（II）如图所示，∵∠ADC=∠PAB=90°，异面直线PA与CD所成的角为90°，AB ∩CD=M，∴AP⊥平面ABCD．∴CD⊥PD，PA⊥AD．因此∠PDA是二面角P﹣CD﹣A的平面角，大小为45°．∴PA=AD．不妨设AD=2，则BC=CD=AD=1．∴P（0，0，2），E（0，1，0），C（﹣1，2，0），∴=（﹣1，1，0），=（0，1，﹣2），=（0，0，2），设平面PCE的法向量为=（x，y，z），则，可得：．令y=2，则x=2，z=1，∴=（2，2，1）．设直线PA与平面PCE所成角为θ，则sinθ====．【点评】本题考查了空间位置关系、空间角计算公式、法向量的性质，考查了空间想象能力、推理能力与计算能力，属于中档题．21．已知a≥3，函数F（x）=min{2|x﹣1|，x2﹣2ax+4a﹣2}，其中min（p，q）=（Ⅰ）求使得等式F（x）=x2﹣2ax+4a﹣2成立的x的取值范围（Ⅱ）（i）求F（x）的最小值m（a）（ii）求F（x）在[0，6]上的最大值M（a）【分析】（Ⅰ）由a≥3，讨论x≤1时，x＞1，去掉绝对值，化简x2﹣2ax+4a﹣2﹣2|x﹣1|，判断符号，即可得到F（x）=x2﹣2ax+4a﹣2成立的x的取值范围；（Ⅱ）（i）设f（x）=2|x﹣1|，g（x）=x2﹣2ax+4a﹣2，求得f（x）和g（x）的最小值，再由新定义，可得F（x）的最小值；（ii）分别对当0≤x≤2时，当2＜x≤6时，讨论F（x）的最大值，即可得到F （x）在[0，6]上的最大值M（a）．解：（Ⅰ）由a≥3，故x≤1时，x2﹣2ax+4a﹣2﹣2|x﹣1|=x2+2（a﹣1）（2﹣x）＞0；当x＞1时，x2﹣2ax+4a﹣2﹣2|x﹣1|=x2﹣（2+2a）x+4a=（x﹣2）（x﹣2a），则等式F（x）=x2﹣2ax+4a﹣2成立的x的取值范围是[2，2a]；（Ⅱ）（i）设f（x）=2|x﹣1|，g（x）=x2﹣2ax+4a﹣2，则f（x）min=f（1）=0，g（x）min=g（a）=﹣a2+4a﹣2．由﹣a2+4a﹣2=0，解得a1=2+，a2=2﹣（负的舍去），由F（x）的定义可得m（a）=min{f（1），g（a）}，即m（a）=；（ii）当0≤x≤2时，F（x）≤f（x）≤max{f（0），f（2）}=2=F（2）；当2＜x≤6时，f（x）≤g（x）≤max{g（2），g（6）}=max{2，34﹣8a}=max{f（2），f（6）}．则M（a）=．【点评】本题考查新定义的理解和运用，考查分类讨论的思想方法，以及二次函数的最值的求法，不等式的性质，考查化简整理的运算能力，属于中档题．22．（16分）各项均为正数的数列{b n}的前n项和为S n，且对任意正整数n，都有2S n=b n（b n+1）．（1）求数列{b n}的通项公式；（2）如果等比数列{a n}共有2015项，其首项与公比均为2，在数列{a n}的每相邻两项a k与a k+1之间插入k个（﹣1）k b k（k∈N*）后，得到一个新的数列{c n}．求数列{c n}中所有项的和；（3）如果存在n∈N*，使不等式成立，求实数λ的范围．【分析】（1）运用数列的通项和前n项和的关系，结合等差数列的定义和通项公式，即可得到；（2）运用等比数列的求和公式和数列求和方法：分组求和，即可得到所求；（3）运用参数分离可得，运用基本不等式和单调性，分别求出不等式左右两边的最值，即可得到所求范围．解：（1）当n=1时，由2S1=b1（b1+1）得b1=1，当n≥2时，由2S n=b n（b n+1），2S n﹣1=b n﹣1（b n﹣1+1）得（b n+b n﹣1）（b n﹣b n﹣1）=b n+b n﹣1因数列{b n}的各项均为正数，所以b n﹣b n﹣1=1，所以数列{b n}是首项与公差均为1的等差数列，所以数列{b n}的通项公式为b n=n．（2）数列{a n}的通项公式为，数列{c n}共有2015+1+2+…+2014=1008×2015项，=（2+22+…+22015）+（﹣1+22﹣32+42﹣…20132+20142）其所有项的和为S1008×2015=2（22015﹣1）+[3+7+…+4027]=22016﹣2+×1007=22016+2015×1007﹣2=22016+2029103；（3）由，得，记因为，当取等号，所以取不到，当n=3时，的最小值为（n∈N*）递减，的最大值为B1=6，所以如果存在n∈N*，使不等式成立实数λ应满足A3≤λ≤B1，即实数λ的范围应为．【点评】本题考查数列的通项和前n项和的关系，主要考查等差数列和等比数列的通项和求和公式的运用，同时考查不等式存在性问题转化为求最值问题，具有一定的难度和综合性．23．（18分）如图，已知双曲线C1：，曲线C2：|y|=|x|+1，P是平面内一点，若存在过点P的直线与C1，C2都有公共点，则称P为“C1﹣C2型点”（1）在正确证明C1的左焦点是“C1﹣C2型点“时，要使用一条过该焦点的直线，试写出一条这样的直线的方程（不要求验证）；（2）设直线y=kx与C2有公共点，求证|k|＞1，进而证明原点不是“C1﹣C2型点”；（3）求证：圆x2+y2=内的点都不是“C1﹣C2型点”【分析】（1）由双曲线方程可知，双曲线的左焦点为（），当过左焦点的直线的斜率不存在时满足左焦点是“C1﹣C2型点”，当斜率存在时，要保证斜率的绝对值大于等于该焦点与（0，1）连线的斜率；（2）由直线y=kx与C2有公共点联立方程组有实数解得到|k|＞1，分过原点的直线斜率不存在和斜率存在两种情况说明过远点的直线不可能同时与C1和C2有公共点；（3）由给出的圆的方程得到圆的图形夹在直线y=x±1与y=﹣x±1之间，进而说明当|k|≤1时过圆内的点且斜率为k的直线与C2无公共点，当|k|＞1时，过圆内的点且斜率为k的直线与C2有公共点，再由圆心到直线的距离小于半径列式得出k的范围，结果与|k|＞1矛盾．从而证明了结论．【解答】（1）解：C1的左焦点为（），写出的直线方程可以是以下形式：或，其中．（2）证明：因为直线y=kx与C2有公共点，所以方程组有实数解，因此|kx|=|x|+1，得．若原点是“C1﹣C2型点”，则存在过原点的直线与C1、C2都有公共点．考虑过原点与C2有公共点的直线x=0或y=kx（|k|＞1）．显然直线x=0与C1无公共点．如果直线为y=kx（|k|＞1），则由方程组，得，矛盾．所以直线y=kx（|k|＞1）与C1也无公共点．因此原点不是“C1﹣C2型点”．（3）证明：记圆O：，取圆O内的一点Q，设有经过Q的直线l与C1，C2都有公共点，显然l不与x轴垂直，故可设l：y=kx+b．若|k|≤1，由于圆O夹在两组平行线y=x±1与y=﹣x±1之间，因此圆O也夹在直线y=kx±1与y=﹣kx±1之间，从而过Q且以k为斜率的直线l与C2无公共点，矛盾，所以|k|＞1．因为l与C1由公共点，所以方程组有实数解，得（1﹣2k2）x2﹣4kbx﹣2b2﹣2=0．因为|k|＞1，所以1﹣2k2≠0，因此△=（4kb）2﹣4（1﹣2k2）（﹣2b2﹣2）=8（b2+1﹣2k2）≥0，即b2≥2k2﹣1．因为圆O的圆心（0，0）到直线l的距离，所以，从而，得k2＜1，与|k|＞1矛盾．因此，圆内的点不是“C1﹣C2型点”．【点评】本题考查了双曲线的简单几何性质，考查了点到直线的距离公式，考查了直线与圆锥曲线的关系，直线与圆锥曲线联系在一起的综合题在高考中多以高档题、压轴题出现，主要涉及位置关系的判定，弦长问题、最值问题、对称问题、轨迹问题等．突出考查了数形结合、分类讨论、函数与方程、等价转化等数学思想方法．属难题．。