2018上海中学自主招生试题

D.more too difficult
【答案】C
【分析】考察tooto句型，too修饰形容词，难多了表述为much too difficult.
65.I couldn ' t do my homework with all thatnoise.
A.going on
B.went on
C.goes on
【答案】A
【分析】考察反义疑问句，前肯后否，have sth done,反义疑问句的谓语动词用didn ' t.
64.This book is for a seven-year-old to read.
A.too much difficult
B.too more difficult
C.much too difficult
my boring ex-neighbor again .
When I reached the hotel, I went77to my room and rested there until it was time for dinner . Then I went down to the lounge and78a drink . I had barely raised the glass to my lips when an all too familiar voice greeted me. I had not escaped from my tiresome neighbor after all! He grasped me warmly by the hand and insisted that we79a table in the dinning-room,“This is a pleasant" he said, “I never expected to see you

2018年上海中学自主招数学试卷一、选择题（本大题共4小题，共12.0分。

在每小题列出的选项中，选出符合题目的一项）1. 已知x2+ax−12能分解成两个整数系数的一次因式的积，则整数a的个数有( )A. 0B. 2C. 4D. 62. 如图，D、E分别为△ABC的底边所在直线上的两点，BD=EC，过A作直线l，作DM//BA 交l于M，作EN//CA交l于N.设△ABM面积为S1，△ACN面积为S2，则( )A. S1>S2B. S1=S2C. S1<S2D. S1与S2的大小与过点A的直线位置有关3. 设p1、p2、q1、q2为实数，则p1p2=2(q1+q2)，若方程甲：x2+p1x+q1=0，乙：x2+ p2x+q2=0，则( )A. 甲必有实根，乙也必有实根B. 甲没有实根，乙也没有实根C. 甲、乙至少有一个有实根D. 甲、乙是否总有一个有实根不能确定4. 设a=121+223+325+⋯+100722013，b=123+225+327+⋯+100722015，则以下四个选项中最接近a−b的整数为( )A. 252B. 504C. 1007D. 2013二、填空题（本大题共8小题，共24.0分）5. 已知1a +1b=1a+b，则ba+ab的值等于______ ．6. 有______个实数x，可以使得√120−√x为整数．7. 如图，△ABC中，AB=AC，CD=BF，BD=CE，用含∠A的式子表示∠EDF，则∠EDF=______．8. 在直角坐标系中，抛物线y=x2+mx−34m2(m>0)与x轴交于A，B两点.若A，B两点到原点的距离分别为OA，OB，且满足1OB −1OA=23，则m的值等于_______．9. 定圆A的半径为72，动圆B的半径为r，r<72且r是一个整数，动圆B保持内切于圆A且沿着圆A的圆周滚动一圈，若动圆B开始滚动时的切点与结束时的切点是同一点，则r共有______个可能的值．10. 学生若干人租游船若干只，如果每船坐4人，就余下20人，如果每船坐8人，那么就有一船不空也不满，则学生共有______人．11. 对于各数互不相等的正整数组(a1,a2,…a n)(n是不小于2的正整数)，如果在i<j时有a i>a j，则称a i与a j是该数组的一个“逆序”，例如数组(2,4,3,1)中有逆序“2，1”、“4，3”、“4，1”、“3，1”，其逆序数为4，现若各数互不相同的正整数组(a1,a2,a3,a4,a5,a6)的逆序数为2，则(a6,a5,a4,a3,a2,a1)的逆序数为______．12. 若n为正整数，则使得关于x的不等式1121<nx+n<1019有唯一的整数解的n的最大值为______．三、解答题（本大题共2小题，共16.0分。

上海复旦附中自主招生英语试题(2)Sarah Alexander celebrated the start of her last year at Wells College the way many other seniors before her have. She ran across the picturesque to the shores of Cayuga Lake, where she jumped into the water.So did many of her fellow seniors. But dozens of students decided to stay away, especially the relatively few newly arrived male students.Wells College, which since 1868 had educated only women, began accepting men this year in hopes of bolstering its dwindling enrollment. For many students and alumnae, it was a crushing decision. After the college announced last October that it would go coeducational, about half of the students protested and two filed a lawsuit, which they later dropped.The students—33 men and 383 women – campus late month Both sexes are now trying to navigate new social landscape. Mr. Phillips said “You can’t do guy stuff. Every time you want to sit and watch sports or a game, it turns into a movie.” The women were “some what nasty.” I could see the dirty looks in their eyes,” he said. “But I was not going to let that stop me from coming.”Wells was a place where women did not have to fuss over their appearance or fight to be taken seriously by their professors. They could enjoy the camaraderie of their campus sisters and their playful traditions. Besides jumping into the lake, the women dance around the maypole each May and kiss the feet of the statue of Minerva, the Roman goddess of wisdom, before exams.Ms. Alexander said, “People told us we wouldn’t notice a difference, but from the moment men arrived on campus not could notice a difference. Waking up early to put on makeup, and that’s odd,” she said.Henry Wells, a founder of Wells Fargo and a friend of Cornell’s benefactor, Ezra C ornell established this college, when women were not considered capable of higher learning. “Give her the opportunity,” he wrote.Henry Wells, a founder of Wells Fargo and a friend of Cornell’s benefactor, Ezra Cornell established this college, when were not considered capable of higher learning. “Give her the opportunity,” he wrote.The great-great-great-great granddaughter of Henry Wells, Stephanie Redmond, 18, of Washington State, said that earlier this year a Wells student had tracked her down and asked her to support the protest. But Ms. Redmond said the move the move to admit men had encouraged her to enroll at Wells this year as a freshman. She plans on a career in engineering, a male-dominated field, and said attending an all-women’s college might have put her at a disadvantage.49.The primary reason for the Wells College to accept men is that .A.its enrollment rate is declineB.the campus is lack of vigor and vitalityC.it will face the destiny of being closed downD.all-women’s college might put a woman at a disadvantage50. A typical behavior for seniors to do is that .A.they jog along the picturesque campusB.they switch sports programs to a movieC.they celebrate their year by jumping into a lakeD.they swim in Cayuga Lake accompanied by friends51.The change after turning into a coed college is that .A.dirty looks in women’s eyes have disappearedB.women get up early to make upC.women are waking up early to studyD.women dance with men around the maypole52.The attitude of the author is that .A.she hares a tradition of all-women schoolsB.she calls on women in support the protestC.she dislikes the change and hopes to file a lawsuitD.she objectively describes the new and uneasy coeducation53.Which of the following statements is Not true?A.The enrollment of male students caused controversy,B.The grandchildren of the college founder benefited most.C.The current president of the college was also its graduate.D.The founder hoped to give women opportunities of higher education.But what is teacher quality? How can one measure it reliably?An analysis is issued a sample of data a Texas school district. Experts argue convincingly that teacher effectiveness should be measured by students’ gains on standardized tests: Mr. Smith is presumably a better teacher than Ms. Brown if his students consistently improve their test scores more than hers do.Though this approach is appealing, there are tricky issues. For example, what if Ms. Brown teaches in a school where students score so high there is little room for improvement?The authors try to correct for this problem, as well as other sorts of measurement issues, to generate a measurement of teacher effectiveness. The paper is primarily concerned with how this measure is related to other observable teacher characteristics.The first finding is that is a large variation in teacher effectiveness: some teachers consistently have a larger impact on their students’ achievement than others.Second, easily observable characteristics like having a master’s degree or a passing score on the teacher certification exam are not correlated with teacher effectiveness.Then what does matter? The most important single influence is experience: first-year teachers are much less effective than others. The second year is significantly better, and by the fourth year, most teachers hit their stride.It is not entirely clear whether this experience effect is learning by doing (the more you teach, the more effective you become) or survival of the fittest (those who are not good at teaching tend to drop out early).From my reading of the paper, both effects appear important and there is no simple answer. The data do suggest, however, that teacher effectiveness is pretty clear by the end of the second year, so the information to make an informed decision is available at that time.The authors also investigate the contentious issue of racial matching of students and teachers. Here they find strong evidence that minority teachers tend to be more effective with minority students. Again, it is unclear whether this is because of a role model effect (students respond better of their own race) or an empathy effect (teachers empathize better with students of their own race) or something else entirely.The authors also look at teacher mobility. There is some evidence that teachers who quit teaching or switch schools tend to be below average in effectiveness. This is consistent with the survival-of-the-fittest model.54.The schoolmaster could decide wisely whether to further employ the teacher by the end of the .A. the first yearB. the second yearC. the third yearD. the fourth year55.The phrase “hit their stride” most probably means “”.A. reach their normal levelB. become confidentC. walk with long stepsD. get bored56.The author of this passage holds the view that .A.teachers will perform better with time passingB.ineffective teachers should leave earlier rather than laterC.teacher’s effectiveness is apparent after a couple of yearsD.a master’s degree will improve teacher’s effectiveness57.Why do black teachers tend to be more effective with black students?A.Students feel secure, so they respond better.B.Teachers sympathize with students of their own race.C.There are entirely some other identified reasons.D.The reasons are far from clear and definite.58.Which of the following may serve as the best title?A.Tenure, Turnover and the Quality of TeachingB.Impact of Teacher Quality on Student LearningC.Different Sorts of Measurement IssuesD.Survival-of-the-fittest Model vs. Learning-by-doing Model上海复旦附中自主招生英语试题(2) ACBDCBACDA。

学生反馈： 没有多少超纲的题，而且大把时间都是学姐给介绍附中的学习生活。除了两张卷子其余 时间没有什么“观察我们做实验”或者面试这样子的情节。所以主要看分数。物理明显简单， 数学开始容易后面难，化学难，英语正常。还有初中的学姐特别贴心担心我们冷还准备了暖 宝宝。
2018 自招情况
参与人群：到场约 600+人，80+人冲考，给冲考（基本上早点去等候冲考的人都让进了， 大多数拿到邀请函的都是兰生复旦的因为很多穿着兰生复旦校服的人都来了）家长不可进校； 有准考证的先进校园，冲考 7：50 进入校园，在另外的考场参加考试；
2018 创生科技班
34
2018 仰晖计划实验班
35
36
37
控江中学
2017 自招情况
参与人群：1500+人考试，给冲考，冲考的大概 600+人； 活动安排： 上午过去直接进去报告厅一样的地方分批进去考试；
考试内容： 语数英合卷，75 分钟，9 页；理化合卷，6 页，60 分钟，一共 111 题，都是选择；数 学和化学有多选题，选全对 5 分，部分答对 2 分，选错不给分； 语文：全是选择没有阅读，主要考知识积累； 数学：有点难度，主要考察知识点：统计，圆，函数，方程，无理数，不等式； 英语：一篇完形填空一篇阅读选择很难..基本就是两三个不会的词，词汇量大的会好做 一点； 物理：考的一般；有一题算是数学物理综合题（两个人从 a 出发,一个走了三分钟拐弯， 速度是另一个人两倍，另一个人直走,最后在 c 相遇,求 a 到 c 可能的距离）； 化学：基本就是学校里的，不难；知识点分布：关于物质的类别、酸碱(这个方面比较 多)，还有一些实验题；
7、以下四句不是交中的民间校训是？ （每届同学都口口相传的话）（1 分）

2018年上海中学自主招数学试卷一.填空题1．已知，则的值等于．2．（3分）有个实数x，可以使得为整数．3．（3分）如图，△ABC中，AB＝AC，CD＝BF，BD＝CE，用含∠A的式子表示∠EDF，则∠EDF ＝．4．（3分）在直角坐标系中，抛物线（m＞0）与x轴交于A，B两点．若A，B两点到原点的距离分别为OA，OB，且满足，则m的值等于．5．（3分）定圆A的半径为72，动圆B的半径为r，r＜72且r是一个整数，动圆B保持内切于圆A且沿着圆A的圆周滚动一圈，若动圆B开始滚动时的切点与结束时的切点是同一点，则r共有个可能的值．6．（3分）学生若干人租游船若干只，如果每船坐4人，就余下20人，如果每船坐8人，那么就有一船不空也不满，则学生共有人．7．（3分）对于各数互不相等的正整数组（a1，a2，…a n）（n是不小于2的正整数），如果在i＜j时有a i＞a j，则称a i与a j是该数组的一个“逆序”，例如数组（2，4，3，1）中有逆序“2，1”、“4，3”、“4，1”、“3，1”，其逆序数为4，现若各数互不相同的正整数组（a1，a2，a3，a4，a5，a6）的逆序数为2，则（a6，a5，a4，a3，a2，a1）的逆序数为．8．（3分）若n为正整数，则使得关于x的不等式有唯一的整数解的n的最大值为．二、选择题（共4小题，每小题3分，满分12分）9．（3分）已知x2+ax﹣12能分解成两个整数系数的一次因式的积，则整数a的个数有（）A．0 B．2 C．4 D．610．（3分）如图，D、E分别为△ABC的底边所在直线上的两点，BD＝EC，过A作直线l，作DM∥BA交l于M，作EN∥CA交l于N．设△ABM面积为S1，△ACN面积为S2，则（）A．S1＞S2B．S1＝S2C．S1＜S2D．S1与S2的大小与过点A的直线位置有关11．（3分）设p1、p2、q1、q2为实数，则p1p2＝2（q1+q2），若方程甲：x2+p1x+q1＝0，乙：x2+p2x+q2＝0，则（）A．甲必有实根，乙也必有实根B．甲没有实根，乙也没有实根C．甲、乙至少有一个有实根D．甲、乙是否总有一个有实根不能确定12．（3分）设a＝+…，b＝+…，则以下四个选项中最接近a﹣b的整数为（）A．252 B．504 C．1007 D．2013三.解答题13．已知直角三角形ABC和ADC有公共斜边AC，M、N分别是AC，BD中点，且M、N不重合．（1）线段MN与BD是否垂直？请说明理由；（2）若∠BAC＝30°，∠CAD＝45°，AC＝4，求MN的长．14．是否存在m个不全相等的正数a1、a2、…、a m（m≥7），使得它们能全部被摆放在一个圆周上，每个数都等于其相邻两数的乘积？若存在，求出所有这样的m值；若不存在，说明理由．参考答案与试题解析一.填空题1．已知，则的值等于﹣1 ．【分析】由左边通分得＝，则有（a+b）2＝ab，然后把+通分得，配方后得，再把（a+b）2＝ab整体代入即可得到值．【解答】解：+＝＝，∵，∴＝，∴（a+b）2＝ab，∴+＝＝﹣1．2．（3分）有11 个实数x，可以使得为整数．【分析】由二次根式有意义可知x≥0，120﹣≥0，可得≥0．而为整数数只有11个，从而可知对应的x取值个数．【解答】解：∵有意义，∴x≥0，∴120∴≥0．∵为整数数，∴的值为0、1、2、…10，共11个整数．∴x取值对应有11个．故答案为：11．3．（3分）如图，△ABC中，AB＝AC，CD＝BF，BD＝CE，用含∠A的式子表示∠EDF，则∠EDF ＝90°﹣∠A．【分析】由等腰三角形两底角相等用∠A表示出∠B，由SAS证得△DBF≌△ECD得出∠BFD ＝∠CDE，由三角形的一个外角等于与它不相邻的两个内角的和得出∠FDC＝∠B+∠BFD，又∠FDC＝∠EDF+∠CDE，从而得解．【解答】解：∵AB＝AC，∴∠B＝∠C，∴∠B＝（180°﹣∠A）＝90°﹣∠A，在△DBF和△ECD中，，∴△DBF≌△ECD（SAS），∴∠BFD＝∠CDE，∵∠FDC＝∠B+∠BFD，∠FDC＝∠EDF+∠CDE，∴∠B＝∠EDF，∴∠EDF＝90°﹣∠A，故答案为：90°﹣∠A．4．（3分）在直角坐标系中，抛物线（m＞0）与x轴交于A，B两点．若A，B两点到原点的距离分别为OA，OB，且满足，则m的值等于 2 ．【分析】设方程x2+mx﹣m2＝0的两根分别为x1、x2，由一元二次方程根与系数的关系及m的取值范围判断出x1＜0，x2＞0，再由﹣＝求出OA＝|x1|＝﹣x1，OB＝x2，再把OA＝|x1|＝﹣x1，OB＝x2代入﹣＝即可求出m的值．【解答】解：设方程x2+mx﹣m2＝0的两根分别为x1、x2，且x1＜x2，则有x1+x2＝﹣m ＜0，x1x2＝﹣m2＜0，所以x1＜0，x2＞0，由﹣＝，可知OA＞OB，又m＞0，所以抛物线的对称轴在y轴的左侧，于是OA＝|x1|＝﹣x1，OB＝x2，所以+＝，即＝，故＝，解得m＝2．故答案为：25．（3分）定圆A的半径为72，动圆B的半径为r，r＜72且r是一个整数，动圆B保持内切于圆A且沿着圆A的圆周滚动一圈，若动圆B开始滚动时的切点与结束时的切点是同一点，则r共有11 个可能的值．【分析】利用⊙B运动的距离除以⊙B的周长即可得出答案；【解答】解：∵让动圆B沿着圆A的圆周滚动一圈回到原来的位置，∴⊙B滚动的路程为：2π（72﹣r），∴⊙B自转了＝﹣1（圈），∵r＜72且r是一个整数，∴r可以为1，2，3，4，6，8，9，12，18，24，36，共11个，故答案为：11．6．（3分）学生若干人租游船若干只，如果每船坐4人，就余下20人，如果每船坐8人，那么就有一船不空也不满，则学生共有44 人．【分析】设码头剩有x只船，则学生有（4x+20）人，根据如果每船坐8人，则有船不空也不满，可列不等式组求解．【解答】解：设码头剩有x只船，则学生有（4x+20）人，由题可得：解得：5＜x＜7，∵x只能为整数，∴x＝6当x＝6时，4x+20＝44．即共有学生44人．故答案是：44．7．（3分）对于各数互不相等的正整数组（a1，a2，…a n）（n是不小于2的正整数），如果在i＜j时有a i＞a j，则称a i与a j是该数组的一个“逆序”，例如数组（2，4，3，1）中有逆序“2，1”、“4，3”、“4，1”、“3，1”，其逆序数为4，现若各数互不相同的正整数组（a1，a2，a3，a4，a5，a6）的逆序数为2，则（a6，a5，a4，a3，a2，a1）的逆序数为13 ．【分析】根据题意，各数互不相等的正整数组（a1，a2，a3，a4，a5，a6）的逆序数为2，根据从6个数字中任选2个的所有组合数减去2得到所有可能的结果数．【解答】解：根据题意，各数互不相等的正整数组（a1，a2，a3，a4，a5，a6）的逆序数为2，从6个数字中任选2个共有15种组合，∵（a1，a2，a3，a4，a5，a6）的逆序数为2，∴（a6，a5，a4，a3，a2，a1）的逆序数是所有组合数减去2，即共有15﹣2＝13种结果，故答案为：13．8．（3分）若n为正整数，则使得关于x的不等式有唯一的整数解的n的最大值为220 ．【分析】先解关于x的不等式组，由题意可得出n的不等式，求出n的最大值．【解答】解：由题意得：，解得：，∵不等式有有唯一的整数解，∴，∴n≤220．∵n为正整数，∴n的最大值为220．故答案为：220．二、选择题（共4小题，每小题3分，满分12分）9．（3分）已知x2+ax﹣12能分解成两个整数系数的一次因式的积，则整数a的个数有（）A．0 B．2 C．4 D．6【分析】根据十字相乘法分解因式，﹣12可以分解成﹣1×12，1×（﹣12），﹣2×6，2×（﹣6），﹣3×4，3×（﹣4），a等于分成的两个数的和，然后计算即可得解．【解答】解：∵﹣1×12，1×（﹣12），﹣2×6，2×（﹣6），﹣3×4，3×（﹣4），∴a＝﹣1+12＝11，1+（﹣12）＝﹣11，﹣2+6＝4，2+（﹣6）＝﹣4，﹣3+4＝1，3+（﹣4）＝﹣1，即a＝±11，±4，±1共6个．故选：D．10．（3分）如图，D、E分别为△ABC的底边所在直线上的两点，BD＝EC，过A作直线l，作DM∥BA交l于M，作EN∥CA交l于N．设△ABM面积为S1，△ACN面积为S2，则（）A．S1＞S2B．S1＝S2C．S1＜S2D．S1与S2的大小与过点A的直线位置有关【分析】利用等高模型，用转化的思想解决问题即可．【解答】解：连接AD，AE．∵DM∥BA，EN∥CA，∴S1＝S△ADB，S2＝S△AEC，∵BD＝EC，∴S△ABD＝S△AEC，∴S1＝S2，故选：B．11．（3分）设p1、p2、q1、q2为实数，则p1p2＝2（q1+q2），若方程甲：x2+p1x+q1＝0，乙：x2+p2x+q2＝0，则（）A．甲必有实根，乙也必有实根B．甲没有实根，乙也没有实根C．甲、乙至少有一个有实根D．甲、乙是否总有一个有实根不能确定【分析】将两方程根的判别式相加可得出△1+△2＝（p1﹣p2）2≥0，由此可得出△1、△2中至少有一个大于等于0，即甲、乙至少有一个有实根．【解答】解：方程甲的根的判别式△1＝p12﹣4q1，方程乙的根的判别式△2＝p22﹣4q2，∴△1+△2＝p12﹣4q1+p22﹣4q2，＝（p12+p22）﹣4（q1+q2），＝p12+p22﹣2p1p2，＝（p1﹣p2）2≥0，∴△1、△2中至少有一个大于等于0，即甲、乙至少有一个有实根．故选：C．12．（3分）设a＝+…，b＝+…，则以下四个选项中最接近a﹣b的整数为（）A．252 B．504 C．1007 D．2013【分析】根据题意列出算式a﹣b＝++++……+﹣＝﹣，再进一步计算可得．【解答】解：a﹣b＝++++……+﹣＝﹣＝1007﹣＝＝＝503，∴最接近a﹣b的整数为504，故选：B．三.解答题13．已知直角三角形ABC和ADC有公共斜边AC，M、N分别是AC，BD中点，且M、N不重合．（1）线段MN与BD是否垂直？请说明理由；（2）若∠BAC＝30°，∠CAD＝45°，AC＝4，求MN的长．【分析】（1）根据题意画出图形，再作出辅助线构成等腰三角形，利用等腰三角形的性质进行证明；（2）注意要分二种情况讨论：即B、D在AC两侧和B、D在AC同侧．【解答】解：（1）线段MN与BD垂直．连接MB与MD，由直角三角形斜边上的中线等于斜边长的一半，可以知道MB＝，MD＝，所以MB＝MD．三角形MBD中，N是底边上的中点，等腰三角形的性质可以说明：MN垂直BD．（2）如图一：连接BM、MD，延长DM，过B作DM延长线的垂线段BE，∵M是AC的中点，∴MD⊥AC，△BCM是等边三角形，∴在Rt△BEM中，∠EMB＝30°，∵AC＝4，∴BM＝2，∴BE＝1，EM＝，MD＝2，从而可知BD＝＝2∴BN＝．由Rt△BMN可得：MN＝＝．如图二：连接BM、MD，延长AD，过B作垂线段BE，∵M、N分别是AC，BD中点，∴MD＝AC，MB AC，∴MD＝MB，∵∠BAC＝30°，∠CAD＝45°，∴∠BMC＝60°，∠DMC＝90°，∴∠BMD＝30°，∴∠BDM＝＝75°，∵∠MDA＝45°∴∠EDB＝180°﹣∠BDM﹣∠MDA＝60°，令ED＝x，则BE＝x，AD＝2，AB＝2，∴由Rt△ABE可得：（2）2＝（x）2+（x+2）2，解得x＝，则BD＝2，∵M、N分别是AC，BD中点，∴MD＝2 DN＝．由Rt△MND可得：MN＝＝．14．是否存在m个不全相等的正数a1、a2、…、a m（m≥7），使得它们能全部被摆放在一个圆周上，每个数都等于其相邻两数的乘积？若存在，求出所有这样的m值；若不存在，说明理由．【分析】设前两个数为a1，a2，则按照“每个数都等于其相邻两数的乘积“，依次列式，找出循环规律，则问题得解．【解答】解：设前两个数为a1，a2，则有a1•a3＝a2，∴a1＝，a3＝a2•a4，∴a4＝＝，a4＝a3•a5，∴a5＝＝＝，a5＝a4•a6，∴a6＝＝a6＝a7•a5，∴a7＝＝a1，a7＝a6•a8，∴a8＝a2，…∴每6个数为一个循环∵m≥7∴当m＝6k，（k≥2，且k为正整数）时，存在符合题意的m值．。

上海复旦附中自主招生英语试题(3)A United Nations panel on climate change says global warming is causing extreme weather all over the world and is 41 on governments to come up with new ideas to curb gas emissions. Since much of the air pollution comes from coal-fired power plants, scientists in Denmark are trying to lower their nation’s energy needs with new types of smart streetlights.Our 42 industrialized world needs huge amounts of electrical energy, but our power plants still rely mostly on technology 43 as early as the 19th century—coal—powered plants, hydroelectric dams or somewhat never nuclear energy, all of which have their own 44 .But scientists say we can slow down global warming by 45 energy demands for street lights.These 46 features of the world’s urban areas re quire a lot of electricity.The U.S. Energy Information Administration estimates that in 2012, lighting for buildings, streets and highways in the U.S. used about 274 billion kilowatt hours.In a bid to make Copenhagen the world’s first carbon-neutral city by 2025, scientists in the Danish capital are testing a variety of new street lighting technologies.Kim Brostrom is the chief technical officer at the Danish Outdoor Lighting Lab.“We have installed nine kilometers of streets, we have 280 masts placed here, we have 50 different 47 , we have 10 different management systems, and we have a lot of different sensors and things out in the open area,” said Brostrom.Chief science officer Jakob Andersen says the lights can be managed 48 from a tablet computer or a smart phone.The main goal is to lower energy 49 when the light is not needed. So the lamp brightens up only when it 50 an approaching pedestrian, cyclist or vehicle. Some of them even have a backup wind generator or a solar cell.2.Diet Coke, diet Pepsi, diet pills, on-fat diet, vegetable diet… We are 51 by the word “diet” everywhere we look and listen. We have so easily been attracted by the promise and 52 of diet products that we have stopped thinking about what diet products are doing to us. We are paying for products that 53 us psychologically and physically(身体上).Diet products significantly weaken us psychologically. On one level, we are not allowing our brain to 54 that our weight problems lie not in actually losing the weight, but in controlling the 55 of fatty, high-calorie, unhealthy foods. Diet products allow us to jump over the thinking stage and go straight for the scale( 秤) instead. All we have to do is to swallow or 56 the word “diet” in food labels.On another level, diet products have greater psychological effects. Every time we have azero-calorie drink, we are telling ourselves without our 57 that we don’t have to work to get results. Diet products make people believe that gain comes without pain, and that life can be without resistance a(n) 58 .The danger of diet products lies not only in the psychological effects they have on us, but also in the physical harm that they cause. Diet foods can 59 harm our bodies because consuming them instead of healthy foods means we are preventing our bodies from having 60 nutrients(营养成分). Diet foods and diet pills 61 zero calorie only because the diet industry has created chemicals to produce these wonder products. Diet products may not be 62 , and the chemical that go into diet products are potentially dangerous.Now that we are aware of the effects that diet products have on us, it is time to 63 think about buying them. Losing weight lies in the power of minds, not in the power of chemicals. 64 we realize this, we will be much better able to resist diet products, and 65 prevent the psychological harm that comes from using them.51. A. confused B. surrounded C. mixed D. fascinated52. A. potential B. affection C. obligation D. calculation53. A. weaken B. harm C. enforce D. inspire54. A. admire B. argue C. deny D. admit55. A. assumption B. digestion C. dissolution D. consumption56. A. recognize B. foresee C. overlook D. research57. A. frustration B. ignorance C. awareness D. emphasis58. A. maintenance B. efficiency C. struggle D. setback59. A. indirectly B. inevitably C. incredibly D. innocently60. A. extra B. basic C. organic D. delicate61. A. contain B. persist C. exclude D. melt62. A. nutritional B. poisonous C. ridiculous D. sensitive63. A. strongly B. enthusiastically C. eagerly D. seriously64. A. Unless B. While C. Though D. Once65. A. therefore B. otherwise C. meanwhile D. furthermore3.It was a bitter cold evening in northern Virginia many years ago. The old man’s beard was glazed by winter’s frost while he waited for a ride across the river. The wait seemed endless. His body became numb and stiff from the frigid north wind.It was long before he heard the faint, steady rhythm of hooves (马蹄) along the frozen path. Anxiously watching several horsemen coming up, he let the first one pass by without any effort to get his attention, then another passed by, and another. Finally, the last rider drew near where the old man sat like a snow statue when old man caught his eyes and said, “Sir, would you mind giving an old man a ride to the other side?”Stopping his horse, the rider replied, “Sure! Jump aboard.” Seeing the old man unable to lift his half-frozen body from the ground, the horseman got down to help him. The horseman took him not just across the river, but to his destination just a few miles away.As they approached the tiny but cozy cottage, the horseman’s curiosity caused him to inquire,“Sir, I noticed you let several other riders pass by without making an effort to secure a ride. Then I came up and you immediately asked me for a ride. I am curious why, on such a bitter night, you would wait and ask the last rider. What if I had refused and left you here?”The old man looked the rider straight in the eyes an d replied, “I reckon I know people pretty good. I looked into the eyes of the other riders and immediately found no concern for my situation. It would have been useless even to ask them for a ride. But when I looked into your eyes, your gentle spirit would welcome the opportunity to give me assistance in my time of need.”Those heart-warming comments touched the horseman deeply. “I’m so grateful for what you have said,” he told the old man. “May I never get too busy in my own affairs that I fail to respond to the needs of others with kindness and compassion.”With that, Thomas Jefferson turned his horse around and made his way back to the White House.66.Why didn’t the old man ask the previous riders for a ride?A.Because he was waiting for the last rider.B.Because his efforts failed to get their attention.C.Because he assumed they had no concern for him.D.Because he was too numb to lift his half-frozen body.67.What caused the last rider to stop and help the old man?A. The old man’s poor situation.B. The old man’s warm comments.C. His own affairs.D. Kindness and sympathy.68.What do you know about the old man?A. He judged people by looking into their eyes.B. He lived in a cozy cottage a few miles away.C. He gave the last rider an opportunity to help.D. He recognized the president at first.69.Which can be the best title of this text?A. Look into your eyes.B. Compassion of a great man.C. The last rider to help.D. Return to the White House.4.International Book ClubHave you ever thought of joining a book club and buying new books through the post? Here at the International Book Club, we already have many members buying books from us by mail. Immediate benefits：●As a special offer, you may choose any reduced price books from our new members’ book list,to the value of $6 in total (plus postage and packing). By doing this, you will save pounds on the publishers’ prices.●Tick the box on your form to order a free watch.●If you reply within seven days, we will send you another free gift carefully chosen from ourbook list by our staff.●Order a DVD from the many on offer in our list, at half the recommended retail price.When you’ve joined：As a member, you’ll enjoy savings of between 30% and 50% off the publisher’s price onevery book you buy, and what’s more, they’ll come straight to your door. Your free club magazine arrives once a month, to keep you up to date with the latest bestsellers. This means that every year we offer over 1,000 books to choose from. On the Internet, you can find all our titles for the year on our exclusive members’ website.Being a member：All we are asking you to do while you are a member is to choose four books during your first year. After that, you can decide on the number of books you wish to take.In each of our monthly club magazines, our experienced staff choose a Club Choice book —a work of fiction or a reference title which they feel is particularly worth buying, and which is offered at an extra special price. However, if you do not want this book, just say so in the space provided on the form. We will always send the book if we do not receive this.So, return your application form today, but hurry —it’s not every day we can make you an offer like this. To apply to become a member, all you need to do is simply fill in the enclosed form and return it in the postage paid envelope supplied.Before you know it, your books will be with you. Please don’t send any money now, as we will send you your bill with the books. And remember, you have up to a fortnight to decide if you wish to keep the books you have ordered. You should then either return the books or send your payment.70.Which of the following doesn’t belong to the benefits of being a club member?A. Get four books for free in the first year.B. Order a free watch.C. Get a gift for nothing.D. Order a DVD at a low price.71.Every month the club provides a free club magazine in order to .A.let readers know the number of books to be soldB.keep readers well informed of recent bestselling booksC.make readers know the club’s developmentD.attract more and more readers to join the club72.If a book is worth $100, how much will a member probably save if he buys one?A. $20B. $40C. $60D. $7073.What should you do if you want to join the book club?A.Just fill in a form with personal information and send the club an email.B.Ask other club members to recommend you to the club.C.Fill in an application form with needed information and return it to the club.D.Apply for a membership card.5.In 1789 the U.S. government passed a law which said that the land of the American Indians could never be taken from them without their agreement. One hundred years later, however, the Indians only had a very small part of the land that originally belonged to them. How did this great injustice occur?After 1812 white settlers began to move west across North America. At first, the settlers and the Indians lived in peace. However, the number of settlers increased greatly every year, and slowly the Indians began to see the white settlers as a danger to their survival. To feed themselves,the settlers killed more and more wild animals. The Indians, who depended on these animals for food, had to struggle against starvation. The settlers also brought with them many diseases which were common in white society, but which were new for the Indians. Great numbers of Indians became sick and died. Between 1843 and 1854 the Indian population in one area of the country went down from 100,000 to 30,000.More land was needed for the increasing number of white settlers. In Washington, the old respect for the rights of the Indians disappeared. The old promises to the Indians were broken; the government began to move groups of Indians from their original homelands to other poorer parts of the country. Some Indians reacted angrily and violently to this treatment. They began to attack white settlers, and the Indian war began. For 30 years, until the late 1880s, different groups of Indians fought against the injustices of the white man. They had a few famous successes, but the result of the struggle was never in doubt. There were too many white soldiers, and they were too powerful. Many Indians were killed; the survivors were moved from their homelands to different area of the country. It was a terrible chapter in the history of a country that promised freedom and equality to everyone.74.It can be inferred from the passage that .A.in the U.S. there were many laws that provided the rights of American IndiansB.the law which was passed in 1789 by the U.S. government was not successfully carried outC.in the 19th century no injustices were done against the Indians by the U.S. governmentD.the majority of white settlers were openly opposed to the law passed in 178975.According to the passage which of the following is TRUE?A.The Indians believed that killing too many wild animals had disturbed the balance of nature.B.The government began to have a better understanding of the Indians in the fifties of the19th century.C.Between 1843 and 1854 about 70,000 Indians were killed in the battle.D.The whites carried serious diseases into where the Indians lived.76.It is implied in the passage that .A.the Indians had many great successes in the Indians warsB.the Indians had no doubt that they would win the warsC.after the war the Indians stayed where they were beforeD.the Indians were too weak to win the struggle77.What is the writer’s opinion about the treatment that the Indians received from the U.S. government?A.He believed that the government always respected the rights of the Indians.B.He believed that the government can’t be criticized for its treatment to the Indians.C.He believed that the government treated the Indians unjustly.D.He believed that the government’s unfair treatment against the Indians was not on purpose.6.The question of whether our government should promote science and technology or the liberal arts in higher education isn’t an either/or proposition(命题), although the current emphasis on preparing young Americans for STEM(science, technology, engineering, maths)-related fields can make it seem that way.The latest congressional report acknowledges the critical importance of technical training, but also asserts that the study of the humanities( 人文学科)and social sciences must remain central c omponents of America’s educational system at all levels. Both are critical to producing citizens who can participate effectively in our democratic society, become innovative(创新的)leaders, and benefit from the spiritual enrichment that the reflection on the great ideas of mankind over time provides.Parents and students who have invested heavily in higher education worry about graduates’ job prospects as technological advances and changes in domestic and global markets transform professions in ways that reduc e wages and cut jobs. Under these circumstances, it’s natural to look for what may appear to be the most “practical” way out of the problem “Major in a subject designed to get you a job” seems the obvious answer to some, though this ignores the fact that m any disciplines in the humanities characterized as “soft” often, in fact, lead to employment and success in the long run. Indeed, according to surveys, employers have expressed a preference for students who have received a broadly-based education that has taught them to write well, think critically, research creatively, and communicate easily.Moreover, students should be prepared not just for their first job, but for their 4th and 5th jobs, as there’s little reason to doubt that people entering the workforce today will be called upon to play many different roles over the course of their careers. The ones who will do the best in this new environment will be those whose educations have prepared them to be flexible. The ability to draw upon every available tool and insight—picked up from science, arts, and technology—to solve the problems of the future, and take advantage of the opportunities that present themselves, will be helpful to them and the United States.(Note: Answer the questions or complete the statements in NO MORE THAN TWELVE WORDS.)78.The latest congressional report suggests that .79.What is the main concern of students when they choose a major?80.What kind of job applicants do employers look for?81.What suggestions does the author give to college students?7.In order to study enzymes(酶), a small piece of potato is cut into very thin pieces. These thin pieces are placed in a little glass container and covered with water. Then a little of the proper chemical is added. Immediately, because of the enzyme present in the potato, the chemical starts joining with the oxygen in the air above the water. If the container is entirely closed, a partial vacuum(真空)is framed inside. If the container is now connected with a fine tube which is dipped in water, the water is sucked part way up the tube because of the vacuum.The scientists doing the experiment carefully notice how far up the tube is when water is sucked in a certain time. The higher it is sucked, the more of that particular enzyme and evenabout the way in which it operates. And all the time we are working with amounts far too small to see or weigh.1.What do the scientists want to find out in the experiment?a.Whether enzyme is present in the potato.b.What particular enzyme there is in the potato.c.How much enzyme there is in the potato.d.How enzyme works in the potato.A. a and bB. c and dC. b and dD. a and c2.The proper title for the passage is .A.How a Vacuum Is FormedB.How Enzyme Is StudiedC.How Enzyme Works in a PotatoD.How Much Enzyme There Is in the Potato3.Which of the following correctly shows how the experiment is done?A.Put very thin pieces or potato in a vacuum container.B.Connect the glass container with a tube through which oxygen is sent in.C.Add some chemical to the water before thin pieces of potato are put in.D.Place thin pieces of potato in a glass container, cover them with water and then close it.4.The result of the study shows that .A.the higher water is sucked, the less of enzyme in the potato isB.the more water is put into, the more of enzyme in the potato isC.the higher water is sucked, the more of enzyme in the potato isD.the lower water is sucked, the more of enzyme in the potato is上海复旦附中自主招生英语试题(3)1.FAJHB CDEIK2.BABDD ACCAB AADDA3.CDAB4.ABBC5.BDDC6.78. The humanities and STEM subjects should be given equal importance.79.Their chances of getting a good job.80.Those who have received a well-rounded education.81.Preparing themselves to be flexible; achieving every available tool and insight.7.BBDC。

是 G 6.67 1011 Nm 2 / kg 2 。
正因为万有引力的存在，十九世纪四十年代 奥本 勒维耶 通过经典力学分析天王星轨
道的摄影后预测勒海王星的位置。十九世纪末天文学家根据对海王星的观察推测有其他行星 摄动天王星轨道。
我们相信，通过以上内容的阅读，你已经对匀速圆周运动有了一个初步的了解，接下来， 请回答以下问题：
二、问题：
1、判断以下说法是否正确：正确打“√”，错误打“ ” 1 360 2 ， 45 /4 ( )
2 匀速圆周运动的物体，周期越小，转的越快( ) 3 不同的匀速圆周运动中，相同时间内线速度大的物体一定比线速度小的物体转的圈 数多。( ) 4 对匀速圆周运动的物体进行受力分析的时候，向心力一定要画，因为它是客观存在 的。( ) 5 万有引力定律可以解释人造卫星绕地球做匀速圆周运动的原因，万有引力提供向心 力。( )
淋雨量问题涉及的主要因素有：单位体积降雨量 ，竖直雨速 v 雨，水平风速 v 风，人
的行走速度 v 人(当跑步时，v 人比较大)，行走的直线距离 L1 和人的淋浴面积。人可简化 为一个长方体模型，如图所示，可能被淋到的面为：S 顶，S 正(代表人的正面)，S 背 。若以 上条件均已知，则
(1) 在无风的情况下，即 v =0，人在雨中行走或跑步，S 顶，S 正，S 背三个面中，哪个面的 风
淋雨为 0？ (2) 请写出无风时，淋雨量不为 0 的各面的淋雨量的表达式。由此，在无风的情况，是 走还是跑才能被雨少淋？ (3) 若有风，且背面有风，求雨滴相对于地面的速度大小，并写出总淋雨量的表达式， 说明是走还是跑才能被雨少淋。
【例 4】
一、正文：
圆周运动
大家学习了有关物体运动的知识，但研究的基本都是直线运动，而直线运动是物体运动 的最简单形式，实际生活中，绝大部分物体的运动都不是直线运动，所以我们有必要对物体 运动的研究进行拓展，而今天我们要研究的是最简单曲线运动之一的圆周运动。 物体在以某点为圆心半径为 R 的圆周上运动，即物体运动时其轨迹是圆周的运动叫“圆周运 动”，它是一种最常见的曲线运动。例如吊扇、车轮、皮带轮等都做圆周运动。圆周运动分 为匀速圆周运动和变速圆周运动（如：竖直平面内绳/杆转动小球、竖直平面内的单摆运动）。 在圆周运动中，最常见和最简单的是匀速圆周运动（匀速圆周运动实际上是指速度大小始终 保持不变的圆周运动）

10
本部英语老师讲的《中国美食》。 体验课 5： 课程简介：同学们是不是在电视、网络等媒体上经常会听到“金融”两个字？那么到底什 么是“金融”呢？它和我们每天都接触的“钱（货币）”又有什么关系呢？今天这节课，就让我 们一起来了解一下金融中的一个小知识：货币。 体验课 6： 课程简介：苹果公司凭借 iPhone6 手机，首次成为中国智能手机市场的最大厂商。追捧 苹果公司产品的人越来越多，然而大家是否关注过那个“被咬了一口”的苹果 LOGO？为什么 这只“苹果”的造型如此完美？你可知 LOGO 中蕴藏的数学知识？你想亲手绘制苹果公司的 LOGO 吗？这节课，就让我们一起探究苹果公司 LOGO 背后的数学秘密。
考试内容： 数学：60 分钟，150 分，新知杯的难度，不可用计算器；
填空题先易后难；证明题（第一题是已知正五边形边长求对角线长，再求 sin18° 的值）（最后一题给了高中知识点再做题）； 语文：40 分钟，100 分；
1、找错别字；2、两句理解性课内默写、一句课外默写，比较难；3、填两个关于 狗的成语，比较难；4、作文根据泰戈尔的“我不能选择最好的，是最好的选择了我” 写一篇 400 字作文；5、其他：根据所给内容写一句比喻句、对对联、诗词赏析排句子 顺序、问将“三八国际妇女节”改成“女神节”你是否赞成及理由； 理化：40 分钟，100 分，题量大，可以用计算器；
考试内容： 3 小时五门五张卷子一起发，时间很充裕，题目很简单，理化略难于中考，比自招简单； 语文：1、文言常识（找错别字、诗人名字对应其称呼，不难）；2、古文（毛遂自荐， 难度一般）：加点字解释、句子翻译、文章结尾理解；3、现代文（议论文：论思考，难度高 于一般）4、材料分析（考概括、看图表，题型与中考“综合应用”相似）； 英语：语法大约 15 道（主要是定语从句）、完形填空、首字母、词性转换； 数学：简单，时间充裕，填空、选择、2 道大题一题 10 分（每道大题有三小问，8 个小 题一题 5 分，一道几何题，一道函数题）； 理化：比延安简单，和交附没法比，就是学校考试范围，有填空选择和计算，化学有流 程题，不用学自招就能考

3． AB∥CD ， AB = 15 ， CD = 10 ， AD = 3 ， CB = 4 ，求 SABCD __________． 【答案】 【解析】解：设 AE = x ， BC∥FD ， 则：： AF = AB − CD = 5 ， GF =AF − AE =5 − x ，
A= D2 A= E2 FD2 − EF 2 即： 9 − x2 = 16 − (5 − x)2 ，
= 1 + 1 2 4k +
2
(k
= 1, ,50)
，
故 a≤ 51 ， 101
故
1 2
<
a≤ 51 101
，故
amax
=
51 101
．
10． G 为重心， DE 过重心，求 S△ADE max 以及 S△ADE min ，并证明结论．
A
D
E
B
C
【答案】 【解析】假设△ABC 面积为 S1 ，△ADE 面积为 S2 ， 设 AD = mAB ， AE = nAC ，由于 G 为△ABC 重心，易知： 1 + 1 =3 ，
A
D
G
D
E
B
C
E
7．在直角坐标系中，正 △ABC
，
B(2, 0)
，C
9 2
,
0
，过点 O
作直线
OMN
， OM
=
MN
，求
M 的横坐标__________．
y A
MN
OB
Cx
17 【答案】
8 【解析】作 MH∥AC ， MG ⊥ BH ， 设 BH = x ，
OH = HC ⇒ 2 + x = 5 − x ， 2

上海市宝山区吴淞中学2018自招考试试卷试卷分析51. I can still remember the sitting-room my father and I used to sit in the evening.A. whatB. whichC. thatD. where【答案】D【分析】考察定语从句，本题缺少地点状语，used to sit in the sitting-room, 故选D.52. Mary eating fish, but he doesn't eating fish today.A. Likes; feel likeB. feels like; likeC. would like; likeD. Likes; would like【答案】A【分析】like doing喜欢做某事;feel like doing=would like to do 想要做某事.53. At the good news, all the people present at the meeting couldn't help but for the victory.A. cheeringB. cheerC. cheeredD. to cheer【答案】B【分析】can’t help but do固定搭配只能做........ can’t help doing 情不自禁做某事can’t help do 不能帮助做某事54. A medical team which _ 10 doctors and 15 nurses will be sent to the earthquake hit area to help carry out the rescue work.A. is made up ofB. is consisted ofC. composes ofD. contains of【答案】A【分析】be made up of由........组成=consist of=be composed of55. Peoples opinion on what makes a happy life from person to person.A. developsB. variesC. showsD. improves【答案】B【分析】vary......from从.....到......范围内变化.56.Being a great gardener, he was trained to gardening at an early age.A. take onB. take inC. take upD. take out【答案】C【分析】考察短语take up doing开始从事某事take on: 承担take in : 吸收，欺骗take out: 取出57. A red sky at night usually fine weather the following day, which is believed by the local People.A.turnsB. indicatesC. forcesD. starts【答案】B【分析】由句意可知，indicate 表明。

2018年上海复旦附中自主招生英语试题选择题31.They are fed up the old routine.A. withB. ofC. atD. on32.He is such a(n) teacher that has devoted all his and energy to his students.A. conscientiousB. consciousC. academicD. scientific33.We are looking for someone with a real sense of to the job.A. committeeB. commitmentC. communityD. commission34.Since you are to the seafood, you’d better avoid eating it.A. sensibleB. sentimentalC. sensitiveD. sensory35.During the celebration, fireworks have been at the bay.A. set outB. set aboutC. set upD. set off36.There are fewer working hours in the executive jobs, the job stress is comparatively higher.A. thatB. whereC. whichD.what37.They declared the war, for they believed that country had the weapons of mass destruction.A. liberatedB. counteredC. approvedD. proliferated38.The journalist reported the of children labors who had worked many days on end.A. expansionB. expeditionC. exploitationD. explorationWhat is the thing called happiness? For centuries, people were too busy pursuing it 39 much time analyzing it. Now a pioneering band of researchers has finally bagged the elusive quarry or at least taken its measure. Using such sophisticated new tools 40 the five-item Life Satisfaction Scale and the seven-point Delighted-terrible Scale (On a scale of one to seven, how do you feel about your life?), social psychologists have plumbed the heart of happiness. And their answer to the age-old 41 is that it all depends.Happiness, that is, 42 what makes you feel happy, which is why psychologists often call it “subjective well-being.” But from43 studies of various age and population groups in the United States and abroad, they have reached some 44 at the top of the charts is not, as many might expect, success, youth, good looks or any of those 45 assets. The clear winner is relationship, close ones, followed by happy marriage. Supportive, intimate connections with other people seem 46 important. Using simple survey questions, psychologist David Myers found that the 47 happy people are those in unhappy marriages. Happiest are those who married 48 their “best friend.”39. A. to spendB. spendingC. has spentD. have spent40. A. likeB. alikeC. asD. for instance41. A. psychologyB. mysteryC. solutionD. trick42. A. results inB. leans againstC. depends onD. arrives at43. A. realisticB. idealisticC. objectiveD. individualistic44. A. endlesslyB. contradictorilyC. harmoniouslyD. consistently45. A. enviableB. reliableC. inevitableD. endurable46. A. vastlyB. tremendouslyC. swiftlyD. basicallyD. D. off上海复旦附中自主招生英语试题(1)AABCD BDDAABCC DBBCB上海复旦附中自主招生英语试题(2)Sarah Alexander celebrated the start of her last year at Wells College the way many other seniors before her have. She ran across the picturesque to the shores of Cayuga Lake, where she jumped into the water.So did many of her fellow seniors. But dozens of students decided to stay away, especially the relatively few newly arrived male students.Wells College, which since 1868 had educated only women, began accepting men this year in hopes of bolstering its dwindling enrollment. For many students and alumnae, it was a crushing decision. After the college announced last October that it would go coeducational, about half of the students protested and two filed a lawsuit, which they later dropped.The students —33 men and 383 women – campus late month Both sexes are now trying to navigate new social landscape. Mr. Phillips said “You can’t do guy stuff. Every time you want to sit and watch sports or a game, it turns into a movie.” The women were “some what nasty.” I could see the dirty looks in their eyes,” he said. “But I was not going to let that stop me from coming.”Wells was a place where women did not have to fuss over their appearance or47. worstA. mostB. bestC. least 48. A. toB. withC. forfight to be taken seriously by their professors. They could enjoy the camaraderie of their campus sisters and their playful traditions. Besides jumping into the lake, the women dance around the maypole each May and kiss the feet of the statue of Minerva, the Roman goddess of wisdom, before exams.Ms. Alexander said, “People told us we wouldn’t notice a difference, but from the moment men arrived on campus not could notice a difference. Waking up early to put on makeup, and that’s odd,” she said.Henry Wells, a founder of Wells Fargo and a friend of Cornell’s benefactor, Ezra Cornell established this college, when women were not considered capable of higher learning. “Give her the opportunity,” he wrote.Henry Wells, a founder of Wells Fargo and a friend of Cornell’s benefactor, Ezra Cornell established this college, when were not considered capable of higher learning. “Give her the opportunity,” he wrote.The great-great-great-great granddaughter of Henry Wells, Stephanie Redmond, 18, of Washington State, said that earlier this year a Wells student had tracked her down and asked her to support the protest. But Ms. Redmond said the move the move to admit men had encouraged her to enroll at Wells this year as a freshman. She plans on a career in engineering, a male-dominated field, and said attending an all-women’s college might have put her at a disadvantage.49.The primary reason for the Wells College to accept men is that .A.its enrollment rate is declineB.the campus is lack of vigor and vitalityC.it will face the destiny of being closed downD.all-women’s college might put a woman at a disadvantage50. A typical behavior for seniors to do is that .A.they jog along the picturesque campusB.they switch sports programs to a movieC.they celebrate their year by jumping into a lakeD.they swim in Cayuga Lake accompanied by friends51.The change after turning into a coed college is that .A.dirty looks in women’s eyes have disappearedB.women get up early to make upC.women are waking up early to studyD.women dance with men around the maypole52.The attitude of the author is that .A.she hares a tradition of all-women schoolsB.she calls on women in support the protestC.she dislikes the change and hopes to file a lawsuitD.she objectively describes the new and uneasy coeducation53.Which of the following statements is Not true?A.The enrollment of male students caused controversy,B.The grandchildren of the college founder benefited most.C.The current president of the college was also its graduate.D.The founder hoped to give women opportunities of higher education.But what is teacher quality? How can one measure it reliably?An analysis is issued a sample of data a Texas school district. Experts argue convincingly that teacher effectiveness should be measured by students’ gains on standardized tests: Mr. Smith is presumably a better teacher than Ms. Brown if his students consistently improve their test scores more than hers do.Though this approach is appealing, there are tricky issues. For example, what if Ms. Brown teaches in a school where students score so high there is little room for improvement?The authors try to correct for this problem, as well as other sorts of measurement issues, to generate a measurement of teacher effectiveness. The paper is primarily concerned with how this measure is related to other observable teacher characteristics.The first finding is that is a large variation in teacher effectiveness: some teachers consistently have a larger impact on their students’ achievement than others.Second, easily observable characteristics like having a master’s degree or a passing score on the teacher certification exam are not correlated with teacher effectiveness.Then what does matter? The most important single influence is experience: first-year teachers are much less effective than others. The second year is significantly better, and by the fourth year, most teachers hit their stride.It is not entirely clear whether this experience effect is learning by doing (the more you teach, the more effective you become) or survival of the fittest (those who are not good at teaching tend to drop out early).From my reading of the paper, both effects appear important and there is no simple answer. The data do suggest, however, that teacher effectiveness is pretty clear by the end of the second year, so the information to make an informed decision is available at that time.The authors also investigate the contentious issue of racial matching of students and teachers. Here they find strong evidence that minority teachers tend to be more effective with minority students. Again, it is unclear whether this is because of a role model effect (students respond better of their own race) or an empathy effect (teachers empathize better with students of their own race) or something else entirely.The authors also look at teacher mobility. There is some evidence that teachers who quit teaching or switch schools tend to be below average in effectiveness. This is consistent with the survival-of-the-fittest model.54.The schoolmaster could decide wisely whether to further employ the teacher by the end of the .A. the first yearB. the second yearC. the third yearD. the fourth year55.The phrase “hit their stride” most probably means “”.A. reach their normal levelB. become confident1.A. increasinglyF.callingG.dependent senses B. lowering C. common D. solutions E. individually H. shortcomings I. consumption J. introduced K.C. walk with long stepsD. get bored56.The author of this passage holds the view that _ .A.teachers will perform better with time passingB.ineffective teachers should leave earlier rather than laterC.teacher’s effectiveness is apparent after a couple of yearsD.a master’s degree will improve teacher’s effectiveness57.Why do black teachers tend to be more effective with black students?A.Students feel secure, so they respond better.B.Teachers sympathize with students of their own race.C.There are entirely some other identified reasons.D.The reasons are far from clear and definite.58.Which of the following may serve as the best title?A.Tenure, Turnover and the Quality of TeachingB.Impact of Teacher Quality on Student LearningC.Different Sorts of Measurement IssuesD.Survival-of-the-fittest Model vs. Learning-by-doing Model上海复旦附中自主招生英语试题(2)ACBDCBACDA上海复旦附中自主招生英语试题(3)A United Nations panel on climate change says global warming is causing extreme weather all over the world and is 41 on governments to come up with new ideas to curb gas emissions. Since much of the air pollution comes from coal-fired power plants, scientists in Denmark are trying to lower their nation’s energy needs with new types of smart streetlights.Our 42 industrialized world needs huge amounts of electrical energy, but our power plants still rely mostly on technology 43 as early as the 19th century—coal—powered plants, hydroelectric dams or somewhat never nuclear energy, all of which have their own 44 .But scientists say we can slow down global warming by 45 energy demands for street lights.These 46 features of the world’s urban areas require a lot of electricity.The U.S. Energy Information Administration estimates that in 2012, lighting for buildings, streets and highways in the U.S. used about 274 billion kilowatt hours.In a bid to make Copenhagen the world’s first carbon-neutral city by 2025,scientists in the Danish capital are testing a variety of new street lighting technologies.Kim Brostrom is the chief technical officer at the Danish Outdoor Lighting Lab.“We have installed nine kilometers of streets, we have 280 masts placed here, we have 50 different 47 , we have 10 different management systems, and we have alot of different sensors and things out in the open area,” said Brostrom.Chief science officer Jakob Andersen says the lights can be managed 48 from a tablet computer or a smart phone.The main goal is to lower energy 49 when the light is not needed. So the lamp brightens up only when it 50 an approaching pedestrian, cyclist or vehicle. Some of them even have a backup wind generator or a solar cell.2.Diet Coke, diet Pepsi, diet pills, on-fat diet, vegetable diet… We are 51 by the word “diet” everywhere we look and listen. We have so easily been attracted bythe promise and 52 of diet products that we have stopped thinking about what diet products are doing to us. We are paying for products that 53 us psychologically and physically(身体上).Diet products significantly weaken us psychologically. On one level, we are not allowing our brain to 54 that our weight problems lie not in actually losing the weight, but in controlling the 55 of fatty, high-calorie, unhealthy foods. Diet products allow us to jump over the thinking stage and go straight for the scale( 秤) instead. All we have to do is to swallow or 56__ the word “diet” in food labels.On another level, diet products have greater psychological effects. Every time we have a zero-calorie drink, we are telling ourselves without our 57 that we do n’t have to work to get results. Diet products make people believe that gain comes without pain, and that life can be without resistance a(n) 58 .The danger of diet products lies not only in the psychological effects they have on us, but also in the physical harm that they cause. Diet foods can 59 harm our bodies because consuming them instead of healthy foods means we are preventing our bodies from having 60 nutrients( 营养成分). Diet foods and diet pills 61 zero calorie only because the diet industry has created chemicals to produce these wonder products. Diet products may not be 62 , and the chemical that go into diet products are potentially dangerous.Now that we are aware of the effects that diet products have on us, it is time to63 think about buying them. Losing weight lies in the power of minds, not in the power of chemicals. 64 we realize this, we will be much better able to resist diet products, and 65 prevent the psychological harm that comes from using them.51. A. confused B. surrounded C. mixed D. fascinated52. A. potential B. affection C. obligation D. calculation53. A. weaken B. harm C. enforce D. inspire54. A. admire B. argue C. deny D. admit55. A. assumption B. digestion C. dissolution D.consumption56. A. recognize B. foresee C. overlook D. research57. A. frustration B. ignorance C. awareness D. emphasis58. A. maintenance B. efficiency C. struggle D. setback59. A. indirectly B. inevitably C. incredibly D. innocently60. A. extra B. basic C. organic D. delicate61. A. contain B. persist C. exclude D. melt62. A. nutritional B. poisonous C. ridiculous D. sensitive63. A. strongly B. enthusiastically C. eagerly D. seriously64. A. Unless B. While C. Though D. Once65. A. therefore B. otherwise C. meanwhile D. furthermore3.It was a bitter cold evening in northern Virginia many years ago. The old man’s beard was glazed by winter’s frost while he waited for a ride across the river. The wait seemed endless. His body became numb and stiff from the frigid north wind.It was long before he heard the faint, steady rhythm of hooves (马蹄) along the frozen path. Anxiously watching several horsemen coming up, he let the first one pass by without any effort to get his attention, then another passed by, and another. Finally, the last rider drew near where the old man sat like a snow statue when old man caught his eyes and said, “Sir, would you mind giving an old man a ride to the other side?”Stopping his horse, the rider replied, “Sure! Jump aboard.” Seeing the old man unable to lift his half-frozen body from the ground, the horseman got down to help him. The horseman took him not just across the river, but to his destination just a few miles away.As they approached the tiny but c ozy cottage, the horseman’s curiosity caused him to inquire, “Sir, I noticed you let several other riders pass by without making an effort to secure a ride. Then I came up and you immediately asked me for a ride. I am curious why, on such a bitter night, you would wait and ask the last rider. What if I had refused and left you here?”The old man looked the rider straight in the eyes and replied, “I reckon I know people pretty good. I looked into the eyes of the other riders and immediately found no concern for my situation. It would have been useless even to ask them for a ride. But when I looked into your eyes, your gentle spirit would welcome the opportunity to give me assistance in my time of need.”Those heart-warming comments touched the horseman deeply. “I’m so grateful for what you have said,” he told the old man. “May I never get too busy in my own affairs that I fail to respond to the needs of others with kindness and compassion.”With that, Thomas Jefferson turned his horse around and made his way back to the White House.66.Why didn’t the old man ask the previous riders for a ride?A.Because he was waiting for the last rider.B.Because his efforts failed to get their attention.C.Because he assumed they had no concern for him.D.Because he was too numb to lift his half-frozen body.67.What caused the last rider to stop and help the old man?A. The old man’s poor situation.B. The old man’s warm comments.C. His own affairs.D. Kindness and sympathy.68.What do you know about the old man?A. He judged people by looking into their eyes.B. He lived in a cozy cottage a few miles away.C. He gave the last rider an opportunity to help.D. He recognized the president at first.69.Which can be the best title of this text?A. Look into your eyes.B. Compassion of a great man.C. The last rider to help.D. Return to the White House.4.International Book ClubHave you ever thought of joining a book club and buying new books through the post? Here at the International Book Club, we already have many members buying books from us by mail.Immediate benefits：●As a special offer, you may choose any reduced price books from our newmembers’ book list, to the value of $6 in total (plus postage and packing). By doing this, you will save pounds on the publishers’ prices.●Tick the box on your form to order a free watch.●If you reply within seven days, we will send you another free gift carefullychosen from our book list by our staff.●Order a DVD from the many on offer in our list, at half the recommended retailprice.When you’ve joined：As a member, you’ll enjoy savings of between 30% and 50% off the publisher’s price on every book you buy, and what’s more, they’ll come straight to your door. Your free club magazine arrives once a month, to keep you up to date with the latest bestsellers. This means that every year we offer over 1,000 books to choose from. On the Internet, you can find all our titles for the year on our exclusive members’ website. Being a member：All we are asking you to do while you are a member is to choose four books during your first year. After that, you can decide on the number of books you wish to take.In each of our monthly club magazines, our experienced staff choose a Club Choice book — a work of fiction or a reference title which they feel is particularlyworth buying, and which is offered at an extra special price. However, if you do not want this book, just say so in the space provided on the form. We will always send the book if we do not receive this.So, return your application form today, but hurry —it’s not every day we can make you an offer like this. To apply to become a member, all you need to do is simply fill in the enclosed form and return it in the postage paid envelope supplied.Before you know it, you r books will be with you. Please don’t send any money now, as we will send you your bill with the books. And remember, you have up to a fortnight to decide if you wish to keep the books you have ordered. You should then either return the books or send your payment.70.Which of the following doesn’t belong to the benefits of being a club member?A. Get four books for free in the first year.B. Order a free watch.C. Get a gift for nothing.D. Order a DVD at a low price.71.Every month the club provides a free club magazine in order to .A.let readers know the number of books to be soldB.keep readers well informed of recent bestselling booksC.make readers know the club’s developmentD.attract more and more readers to join the club72.If a book is worth $100, how much will a member probably save if he buys one?A. $20B. $40C. $60D. $7073.What should you do if you want to join the book club?A.Just fill in a form with personal information and send the club an email.B.Ask other club members to recommend you to the club.C.Fill in an application form with needed information and return it to the club.D.Apply for a membership card.5.In 1789 the U.S. government passed a law which said that the land of the American Indians could never be taken from them without their agreement. One hundred years later, however, the Indians only had a very small part of the land that originally belonged to them. How did this great injustice occur?After 1812 white settlers began to move west across North America. At first, the settlers and the Indians lived in peace. However, the number of settlers increased greatly every year, and slowly the Indians began to see the white settlers as a danger to their survival. To feed themselves, the settlers killed more and more wild animals. The Indians, who depended on these animals for food, had to struggle against starvation. The settlers also brought with them many diseases which were common in white society, but which were new for the Indians. Great numbers of Indians became sick and died. Between 1843 and 1854 the Indian population in one area of the country went down from 100,000 to 30,000.More land was needed for the increasing number of white settlers. In Washington, the old respect for the rights of the Indians disappeared. The old promises to the Indians were broken; the government began to move groups of Indians from theiroriginal homelands to other poorer parts of the country. Some Indians reacted angrily and violently to this treatment. They began to attack white settlers, and the Indian war began. For 30 years, until the late 1880s, different groups of Indians fought against the injustices of the white man. They had a few famous successes, but the result of the struggle was never in doubt. There were too many white soldiers, and they were too powerful. Many Indians were killed; the survivors were moved from their homelands to different area of the country. It was a terrible chapter in the history of a country that promised freedom and equality to everyone.74.It can be inferred from the passage that .A.in the U.S. there were many laws that provided the rights of American IndiansB.the law which was passed in 1789 by the U.S. government was not successfully carried outC.in the 19th century no injustices were done against the Indians by the U.S. governmentD.the majority of white settlers were openly opposed to the law passed in 178975.According to the passage which of the following is TRUE?A.The Indians believed that killing too many wild animals had disturbed the balance of nature.B.The government began to have a better understanding of the Indians in the fifties of the 19th century.C.Between 1843 and 1854 about 70,000 Indians were killed in the battle.D.The whites carried serious diseases into where the Indians lived.76.It is implied in the passage that .A.the Indians had many great successes in the Indians warsB.the Indians had no doubt that they would win the warsC.after the war the Indians stayed where they were beforeD.the Indians were too weak to win the struggle77.What is the writer’s opinion about the treatment that the Indians received from the U.S. government?A.He believed that the government always respected the rights of the Indians.B.He believed that the government can’t be criticized for its treatment to the Indians.C.He believed that the government treated the Indians unjustly.D.He believed that the government’s unfair treatment against the Indians was not on purpose.6.The question of whether our government should promote science and technology or the liberal arts in higher education isn’t an either/or proposition(命题), although the current emphasis on preparing young Americans for STEM(science, technology, engineering, maths)-related fields can make it seem that way.The latest congressional report acknowledges the critical importance of technical training, but also asserts that the study of the humanities(人文学科)and socialsciences must remain central components of America’s educational system at all levels. Both are critical to producing citizens who can participate effectively in our democratic society, become innovative(创新的)leaders, and benefit from the spiritual enrichment that the reflection on the great ideas of mankind over time provides.Parents and students who have invested heavily in higher education worry about graduates’ job prospects as technological advances and changes in domestic and global markets transform professions in ways that reduce wages and cut jobs. Under these circumstances, it’s natural to look for what may appear to be the most “practical” way out of the problem “Major in a subject designed to get you a job” seems the obvious answer to some, though this ignores the fact that many disciplines in the humanities characterized as “soft” often, in fact, lead to employment and success in the long run. Indeed, according to surveys, employers have expressed a preference for students who have received a broadly-based education that has taught them to write well, think critically, research creatively, and communicate easily.Moreover, students should be prepared not just for their first job, but for their 4th and 5th jobs, as there’s little reason to doubt that people entering the workforce today will be called upon to play many different roles over the course of their careers. The ones who will do the best in this new environment will be those whose educations have prepared them to be flexible. The ability to draw upon every available tool and insight—picked up from science, arts, and technology—to solve the problems of the future, and take advantage of the opportunities that present themselves, will be helpful to them and the United States.(Note: Answer the questions or complete the statements in NO MORE THAN TWELVE WORDS.)78.The latest congressional report suggests that.79.What is the main concern of students when they choose a major?80.What kind of job applicants do employers look for?81.What suggestions does the author give to college students?7.In order to study enzymes(酶), a small piece of potato is cut into very thin pieces. These thin pieces are placed in a little glass container and covered with water. Then a little of the proper chemical is added. Immediately, because of the enzyme present in the potato, the chemical starts joining with the oxygen in the air above the water. If the container is entirely closed, a partial vacuum(真空)is framed inside. If the container is now connected with a fine tube which is dipped in water, the water is sucked part way up the tube because of the vacuum.The scientists doing the experiment carefully notice how far up the tube is when water is sucked in a certain time. The higher it is sucked, the more of that particular enzyme and even about the way in which it operates. And all the time we are working with amounts far too small to see or weigh.1.What do the scientists want to find out in the experiment?。

解析
试题分析：
考点：考查了牛顿第二定律以及动能定理的应用 点评：动能定理在使用的时候一定要注意 分清楚物体运动的始末状态
如图所示，质量为 m带电量为+ q的小滑块以大小为 v 0的初速度从A点进入宽度为 d的AB绝缘水平面。当滑块运动至中点C
时，速度大小为
，从此刻起在AB区域内加上一个水平向左的强度不变的有界匀强电场（区域外不存在电场）。若
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考点：本题考查了动能定理的应用， 点评：解题的重点在于能否理解物体的运动过程，能正确的选择合适的过程建立动能定理表达式。
如图所示，在高出水平地面
的光滑平台上放置一质量
、由两种不同材料连接成一体的薄板A，其右段长度
答案
B,C
解析
试题分析：规定初速度方向为正方向，初速度
，碰撞后速度
，
，负号表示
速度变化量的方向与初速度方向相反，所以碰撞前后小球速度变化量的大小为12m/s。故A错误。故B正确。运用动能定理研 究碰撞过程，由于初、末动能相等，所以
碰撞过程中墙对小球做功的大小W为0。故C正确。D错误。 故选BC、 考点：动能定理的应用；运动的合成和分解。 点评：对于矢量的加减，我们要考虑方向，动能定理是一个标量等式，对于动能定理的研究，则无需考虑方向。
(1)滑块第一次经过B点时速度的大小； (2)滑块刚刚滑上圆弧形轨道时，对轨道上B点压力的大小； (3)滑块在从B运动到C的过程中克服摩擦力所做的功.
答案
（1）v B="4." 0 m/s（2）N="21" N（3）
解析
试题分析：(1)滑块由A到B的过程中，应用动能定理得： (3分)

2018年上海市华师大二附中自主招生数学试卷一、选择题（共10小题，每小题3分，满分30分）1．（3分）已知关于x的多项式ax7+bx5+x2+x+12（a、b为常数），且当x＝2时，该多项式的值为﹣8，则当x＝﹣2时，该多项式的值为．2．（3分）已知关于x的方程x2+（a﹣2）x+a+1＝0的两实根x1、x2满足，则实数a＝．3．（3分）已知当甲船位于A处时获悉，在其正东方向相距10海里的B处有一艘渔船遇险等待营救，甲船立即前往救援，同时把消息告知在甲船的南偏西30°，相距10海里C 处的乙船，试问乙船应该朝北偏东度的方向沿直线前往B处救援．4．（3分）关于x、y的方程组有组解．5．（3分）已知a、b、c均大于零，且a2+2ab+2ac+4bc＝20，则a+b+c的最小值是．6．（3分）已知二次函数y＝2x2﹣px+5，当x≥﹣2时，y随x的增加而增加，那么当x＝p 时，对应的y的值的取值范围为．7．（3分）如图所示，正方形ABCD的面积设为1，E和F分别是AB和BC的中点，则图中阴影部分的面积是．8．（3分）在直角梯形ABCD中，∠ABC＝∠BAD＝90°，AB＝16，对角线AC与交BD于点E，过E作EF⊥AB于点F，O为边AB的中点，且FE+EO＝8，则AD+BC＝．9．（3分）陈老师从拉面的制作受到启发，设计了一个数学问题：如图，在数轴上截取从原点到1的对应点的线段AB，对折后（点A与B重合）再均匀地拉成1个单位长度的线段，这一过程称为一次操作（如在第一次操作后，原线段AB上的和均变成，变成1，等）．那么在线段AB上（除A，B）的点中，在第n次操作后，恰好被拉到与1重合的点所对应的数为．10．（3分）定义min{a，b，c}表示实数a、b、c中的最小值，若x、y是任意正实数，则M ＝min{x，，y}的最大值是．二、解答题（共2小题，满分0分）11．四个不同的三位整数的首位数字相同，并且它们的和能被它们中的三个数整除，求这些数．12．如图，已知P A切⊙O于A，∠APO＝30°，AH⊥PO于H，任作割线PBC交⊙O于点B、C，计算的值．2018年上海市华师大二附中自主招生数学试卷参考答案与试题解析一、选择题（共10小题，每小题3分，满分30分）1．（3分）已知关于x的多项式ax7+bx5+x2+x+12（a、b为常数），且当x＝2时，该多项式的值为﹣8，则当x＝﹣2时，该多项式的值为40．【解答】解：∵当x＝2时，ax7+bx5+x2+x+12＝a×27+b×25+22+2+12＝﹣8，∴a×27+b×25＝﹣26．当x＝﹣2时，ax7+bx5+x2+x+12＝a×（﹣2）7+b×（﹣2）5+（﹣2）2+（﹣2）+12＝﹣a×27﹣b×25+22﹣2+12＝﹣（a×27+b×25）+4﹣2+12＝26+14＝40．故答案为40．2．（3分）已知关于x的方程x2+（a﹣2）x+a+1＝0的两实根x1、x2满足，则实数a＝3﹣．【解答】解：∵关于x的方程x2+（a﹣2）x+a+1＝0的两实根为x1、x2，∴△＝（a﹣2）2﹣4（a+1）≥0，即a（a﹣8）≥0，∴当a≥0时，a﹣8≥0，即a≥8；当a＜0时，a﹣8＜0，即a＜8，所以a＜0．∴a≥8或a＜0，∴x1+x2＝2﹣a，x1•x2＝a+1，∵x12+x22＝4，（x1+x2）2﹣2x1•x2＝（2﹣a）2﹣2（a+1）＝4，∴（x1+x2）2﹣2x1•x2＝（2﹣a）2﹣2（a+1）＝4，解得a＝3±．∵3＜＜4，∴6＜3+＜7（不合题意舍去），3﹣＜0；∴a＝3﹣．故答案为：a＝3﹣．3．（3分）已知当甲船位于A处时获悉，在其正东方向相距10海里的B处有一艘渔船遇险等待营救，甲船立即前往救援，同时把消息告知在甲船的南偏西30°，相距10海里C 处的乙船，试问乙船应该朝北偏东60度的方向沿直线前往B处救援．【解答】解：如图，连接BC．由题意，可知∠BAS＝90°，AB＝10海里，∠SAC＝30°，AC＝10海里．∴∠BAC＝∠BAS+∠SAC＝120°，∵AB＝AC，∴∠ACB＝∠B＝30°．∵AB∥CD，∴∠BCD＝∠B＝30°，∴∠NCB＝90°﹣∠BCD＝60°．故答案为60．4．（3分）关于x、y的方程组有2组解．【解答】解：把y＝1两边平方得到y2•x＝1，则x＝y﹣2，把x＝y﹣2代入方程x x﹣y＝y x+y得y﹣2（x﹣y）＝y x+y，当y＝1时，x＝1，当y≠1，则﹣2（x﹣y）＝x+y，所以y＝3x，x＝，∴＝，解得y＝，∴x＝．经检验方程组的解为或．故答案为2．5．（3分）已知a、b、c均大于零，且a2+2ab+2ac+4bc＝20，则a+b+c的最小值是2．【解答】解：（a+b+c）2﹣b2﹣c2+2bc＝20，（a+b+c）2＝（b﹣c）2+20，∵（b﹣c）2≥0，∴（b﹣c）2+20≥20，∵（a+b+c）2≥20．且a、b、c均大于零，∴a+b+c≥2，既a+b+c的最小值是2．故答案为：2．6．（3分）已知二次函数y＝2x2﹣px+5，当x≥﹣2时，y随x的增加而增加，那么当x＝p 时，对应的y的值的取值范围为y≥69．【解答】解：∵当x≥﹣2时，y随x的增加而增加，a＞0，∴x＝﹣＝≤﹣2，∴p≤﹣8，∴当x＝p时，y＝2p2﹣p2+5＝p2+5，∴对应的y的值的取值范围为：y≥69．故答案为：y≥69．7．（3分）如图所示，正方形ABCD的面积设为1，E和F分别是AB和BC的中点，则图中阴影部分的面积是．【解答】解：设DE，DF分别交AC于N，M，∵四边形ABCD是正方形，∴AB＝BC＝CD＝AD，AD∥BC，∴△AMD∽△CMF，∴，∵F是BC的中点，∴AD＝BC＝2FC，∴＝2，同理：△AEN∽△CDN，∵E是AB的中点，∴＝2，∴AN＝MN＝CM＝AC，∵S△ACD＝S正方形ABCD＝×1＝，∴S△DMN＝S△ACD＝×＝，S△ADM＝S△ACD＝×＝，∵，∴S△CFM＝×＝，同理：S△AEN＝，∴S阴影＝S正方形ABCD﹣S△AEN﹣S△CFM﹣S△DMN＝1﹣﹣﹣＝．8．（3分）在直角梯形ABCD中，∠ABC＝∠BAD＝90°，AB＝16，对角线AC与交BD于点E，过E作EF⊥AB于点F，O为边AB的中点，且FE+EO＝8，则AD+BC＝16．【解答】解：设EF＝x，BF＝y，∵FE+EO＝8，∴OE＝8﹣x，而AB＝16，O为边AB的中点，∴OF＝8﹣y，∵EF⊥AB，∴∠OFE＝90°，∴OE2＝OF2+EF2，即（8﹣x）2＝（8﹣y）2+x2，∴16x＝16y﹣y2，又∵∠ABC＝∠BAD＝90°，即AD∥EF∥BC，∴△BEF∽△BDA，△AEF∽△ACB，∴，，∴①，②，①+②得，，∴AD+BC＝16x •＝16，故答案为：16．9．（3分）陈老师从拉面的制作受到启发，设计了一个数学问题：如图，在数轴上截取从原点到1的对应点的线段AB，对折后（点A与B重合）再均匀地拉成1个单位长度的线段，这一过程称为一次操作（如在第一次操作后，原线段AB 上的和均变成，变成1，等）．那么在线段AB上（除A，B）的点中，在第n次操作后，恰好被拉到与1重合的点所对应的数为，，，…，．【解答】解：根据题意，得1 2 34操作次数变化点重合点11由上图表格，可以推出第n次操作后，恰好被拉到与1重合的点所对应的数的通式为，．所以原题答案为，，…，．10．（3分）定义min{a，b，c}表示实数a、b、c中的最小值，若x、y是任意正实数，则M ＝min{x，，y}的最大值是．【解答】解：依题设≥M，x≥M，y+≥M，∴，，M，∴M2≤2，y＝，y+＝，∴M＝，M的最大值是．故答案为：．二、解答题（共2小题，满分0分）11．四个不同的三位整数的首位数字相同，并且它们的和能被它们中的三个数整除，求这些数．【解答】解：先设这四个数为x1，x2，x3，x4，且它们的和能被其中的x2，x3，x4整除，x2＜x3＜x4；则根据题意有：（x1+x2+x3+x4）÷x2＝1+（x1+x3+x4）÷x2＝N（自然数），即（x1+x3+x4）÷x2＝N﹣1，因为他们的首位数字相同，所以N﹣1应该在3附近，又因为x2＜x3＜x4，所以（x1+x3+x4）÷x2＝4，同理（x1+x2+x4）÷x3＝3，（x1+x2+x3）÷x4＝2；则4x3＝5x2＝3x4；由5x2＝3x4可得2x2＝3（x4﹣x2），因为x4和x2的首位数字相同，所以x4﹣x2最大为99，即x2最大为148，且由4x3＝5x2＝3x4可以知道，x2应该能被12整除，故x2可以为108，120，132，144；进而求出x3为135，150…，x4为180，200…；所以x2只能取为x2＝108，从而x3＝135，x4＝180，x1＝117，即这四个数是117，108，135，180．12．如图，已知P A切⊙O于A，∠APO＝30°，AH⊥PO于H，任作割线PBC交⊙O于点B、C，计算的值．【解答】解：连接OB、OC、OA，如图，∵P A为⊙O的切线，∴OA⊥P A，即∠P AO＝90°，而AH⊥OP，∴∠PHA＝90°，∴Rt△P AH∽Rt△POA，∴P A：PO＝PH：P A，即P A2＝PH•PO，又∵PBC为⊙O的割线，∴P A2＝PB•PC，∴PH•PO＝PB•PC，∴△PBH∽△POC，∴∠PBH＝∠POC，＝，即＝①，∴点H、B、C、O四点共圆，∴∠HOB＝∠HCB，∴△PBO∽△PHC，∴＝，即＝②，由①②得＝，即＝，∴＝＝，∴＝，∴＝＝，∵在Rt△OAP中，∠APO＝30°，则OP＝2OA，∴＝．。

2018-2019年最新上海中学自主招生语文模拟精品试卷（第一套）（满分：100分考试时间：90分钟）一、语文基础知识（18分，每小题3分）1．下列词语中加点的字，读音全都正确的一组是（）A．连累(lěi) 角(jué)色河间相(xiàng) 冠冕(miǎn)堂皇B专横(hèng) 忖(cǔn)度涮(shuàn) 羊肉妄加揣(chuāi)测C．笑靥(yè) 顷(qīng)刻汗涔(cén)涔休戚(qì)相关D慨叹(kǎi) 俨(yǎn)然刽子手(kuàì) 刎(wěn)颈之交2、下列各项中字形全对的是（）A、橘子州偌大急躁光阴荏苒B、蒙敝犄角慰籍书生意气C、敷衍磕绊笔竿艰难跋涉D、翱翔斑斓屏蔽自怨自艾3、依次填入下列各句横线上的词语，最恰当．．的一项是（）⑴虽然他尽了最大的努力，还是没能住对方凌厉的攻势，痛失奖杯。

⑵那些见利忘义，损人利己的人，不仅为正人君子所，还很可能滑向犯罪的深渊。

⑶我认为，真正的阅读有灵魂的参与，它是一种个人化的精神行为。

A.遏制不耻必需B.遏止不耻必需C.遏制不齿必须D.遏止不齿必须4、下列句中加点的成语，使用恰当的一句是（）A、故宫博物院的珍宝馆里，陈列着各种奇珍异宝、古玩文物，令人应接不暇。

B、任何研究工作都必须从积累资料做起，如果不掌握第一手资料，研究工作只能是空中楼阁．．．．。

C、电影中几处看来是闲笔，实际上却是独树一帜之处。

D、这部精彩的电视剧播出时，几乎万人空巷，人们在家里守着荧屏，街上显得静悄悄的。

5、下列句子中，没有语病的一项是（）A 大学毕业选择工作那年，我瞒着父母和姑姑毅然去了西藏支援边疆教育。

B北京奥运会火炬接力的主题是“和谐之旅”，它向世界表达了中国人民对内致力于构建和谐社会，对外努力建设和平繁荣的美好世界。

C他不仅是社会的一员，同时还是宇宙的一员。

他是社会组织的公民，同时还是孟子所说的“天民”。

2018年交大附中自招真题卷整理【例1】已知甲、乙、丙三个电荷，依次排列在同一直线上，且都处于静止状态，由此可以判断（）A. 甲、乙、丙带同种电荷B. 甲、丙带同种电荷，甲、乙带异种电荷C. 甲、丙带同种电荷，甲、乙可能带同种电荷，也可能带异种电荷D. 无论甲、乙、丙带何种电荷，均可能使它们同时静止【例2】如图所示，作用在杠杆一端且始终与杠杆垂直的力F，将杠杆缓慢地由位置A拉至位置B，在这个过程中，力F的大小（）A.变小B. 不变C. 变大D.先变大后变小【例3】人们常常用充气泵为金鱼缸内的水补充氧气，如图所示为充气泵气室的工作原理图。

设大气压强为P0，气室中的气体压强为P，气体通过阀门S1、S2与空气导管相连接，下列选项中正确的是（）A. 当橡皮碗被拉伸时，P>P0，S1开通,S2关闭B. 当橡皮碗被拉伸时，P<P0，S1开通，S2关闭C. 当橡皮碗被压缩时，P>P0，S1关闭，S2开通D. 当橡皮碗被压缩时，P<P0，S1关闭，S2开通【例4】如图所示，静止的传送带上有一木块A正在匀速下滑,当传送带突然向上开动时，木块滑到底部所需的时间t与传送带静止不动时所需时间t0相比（）A.t=t0B.t>t0C.t<t0D. 无法判断【例5】某旅客在火车车厢内以1.5米/秒的速度行走。

当车厢静止时，他从车厢头走到车厢尾需要20秒。

当火车以10米/秒的速度向前匀速行驶时，则他从车厢头走到车厢尾需要的时间是______秒，站在地面上的人看见该旅客通过的路程为______米。

【例6】如图所示，将一块重为3N，体积为100cm3的石块，用细线系着浸没在装有水的圆柱形容器中，容器中水的深度由10cm上升到12cm。

则石块所受浮力大小为______牛；细线松动，石块沉到容器底静止后，容器对水平地面的压强为______帕(容器的重力和容器壁的厚度，g=10N/kg)。

【例7】把一根粗糙的木棒按图所示的方式放在分开的两手的食指上。

得到△ACB ，则点 C 的坐标是
【答案】
3 (,
3)
22
【解析】如右图所示易得
CAD BAO 60
过C 作CD x 轴于点 D 在△ACD 中 AC 1 易解得
AD 1 ， CD 3
22Leabharlann 即 C( 3 , 3 )22
7、一张矩形纸片 ABCD ， AD 9， AB 12 ，将纸片折叠，使 A 、 C 两点重 合，折痕的长是
y1 x0 0
故4 m 0 m 4 0
4
则 0 解得4 m 4 0 m 4 （2）当m 0 时，同理解得m 0 （3）当m 0 时， y1 0 恒成立
综上所述， m 4
11、已知a 、b 、c 是互不相等的实数， x 是任意实数，
2018 上海市上海中学自招部分真题
1、因式分解： 6x3 11x2 x 4 【答案】(x 1)(3 x 4)(2 x 1) 【解析】试根法易得 x 1时，上式值为 0. 利用长除法可得 原式= (x 1)(6 x2 5 x 4) = (x 1)(3 x 4)(2 x 1)
化简： x a2 x b2 x c2 a ba c c ba b c ac b
【答案】1
x a2 b c x b2 c a x c2a b
=
a bb cc a
【答案】 45
4
【解析】如右图所示
易得 AC 92 122 15
所以OC 15
2
△C△OF∽ ABC
所以 OF OC 解得OF 45 即 EF 45
AB BC
8

2018年上海中学自主招数学试卷一.填空题1．已知1a +1b =1a+b ，则b a+a b 的值等于 ． 2．有 个实数x ，可以使得√120−√x 为整数．3．如图，△ABC 中，AB ＝AC ，CD ＝BF ，BD ＝CE ，用含∠A 的式子表示∠EDF ，则∠EDF＝ ．4．在直角坐标系中，抛物线y =x 2+mx −34m 2（m ＞0）与x 轴交于A ，B 两点．若A ，B两点到原点的距离分别为OA ，OB ，且满足1OB −1OA =23，则m 的值等于 ． 5．定圆A 的半径为72，动圆B 的半径为r ，r ＜72且r 是一个整数，动圆B 保持内切于圆A且沿着圆A 的圆周滚动一圈，若动圆B 开始滚动时的切点与结束时的切点是同一点，则r 共有 个可能的值．6．学生若干人租游船若干只，如果每船坐4人，就余下20人，如果每船坐8人，那么就有一船不空也不满，则学生共有 人．7．对于各数互不相等的正整数组（a 1，a 2，…a n ）（n 是不小于2的正整数），如果在i ＜j时有a i ＞a j ，则称a i 与a j 是该数组的一个“逆序”，例如数组（2，4，3，1）中有逆序“2，1”、“4，3”、“4，1”、“3，1”，其逆序数为4，现若各数互不相同的正整数组（a 1，a 2，a 3，a 4，a 5，a 6）的逆序数为2，则（a 6，a 5，a 4，a 3，a 2，a 1）的逆序数为 ．8．若n 为正整数，则使得关于x 的不等式1121＜n x+n ＜1019有唯一的整数解的n 的最大值为 ．二、选择题（共4小题，每小题3分，满分12分）9．已知x 2+ax ﹣12能分解成两个整数系数的一次因式的积，则整数a 的个数有（ ）A ．0B ．2C ．4D ．6 10．如图，D 、E 分别为△ABC 的底边所在直线上的两点，BD ＝EC ，过A 作直线l ，作DM∥BA交l于M，作EN∥CA交l于N．设△ABM面积为S1，△ACN面积为S2，则（）A．S1＞S2B．S1＝S2C．S1＜S2D．S1与S2的大小与过点A的直线位置有关11．设p1、p2、q1、q2为实数，则p1p2＝2（q1+q2），若方程甲：x2+p1x+q1＝0，乙：x2+p2x+q2＝0，则（）A．甲必有实根，乙也必有实根B．甲没有实根，乙也没有实根C．甲、乙至少有一个有实根D．甲、乙是否总有一个有实根不能确定12．设a=121+223+325+⋯+100722013，b=123+225+327+⋯+100722015，则以下四个选项中最接近a﹣b的整数为（）A．252B．504C．1007D．2013三.解答题13．已知直角三角形ABC和ADC有公共斜边AC，M、N分别是AC，BD中点，且M、N 不重合．（1）线段MN与BD是否垂直？请说明理由；（2）若∠BAC＝30°，∠CAD＝45°，AC＝4，求MN的长．14．是否存在m个不全相等的正数a1、a2、…、a m（m≥7），使得它们能全部被摆放在一个圆周上，每个数都等于其相邻两数的乘积？若存在，求出所有这样的m值；若不存在，说明理由．。