2018上海中学自主招生试题
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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。
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。
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?。
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。
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.。
上海2018年自主招生物理模拟试题【含答案】一.单项选择题(共16分,每小题2分.每小题只有一个正确选项.)1.下列叙述中符合物理学史实的有()A.托马斯•杨通过对光的干涉现象的研究,证实了光具有波动性B.麦克斯韦建立了完整的电磁场理论,并通过实验证实了电磁波的存在C.查德威克通过对α粒子散射实验的研究,提出了原子的核式结构学说D.贝克勒尔发现了天然放射现象,并提出原子核是由质子和中子组成的2.在阳光下,竖直放置的肥皂膜上呈现彩色条纹,可以观察到()A.竖直方向的条纹,是由于不同频率的光各自在肥皂膜前后表面反射叠加的结果B.竖直方向的条纹,是由于相同频率的光在肥皂膜前后表面反射叠加的结果C.水平方向的条纹,是由于不同频率的光各自在肥皂膜前后表面反射叠加的结果D.水平方向的条纹,是由于相同频率的光在肥皂膜前后表面反射叠加的结果3.下列叙述正确的是()A.外界对物体做功,物体的内能一定增加B.热量不能由低温物体传递到高温物体C.温度升高,物体内每个分子的热运动速率都增大D.自然界中进行的涉及热现象的宏观过程都具有方向性4.分子运动是看不见、摸不着的,其运动特征不容易研究,但科学家可以通过布朗运动认识它,这种方法叫做“转换法”.下面给出的四个研究实例,其中采取的方法与上述研究分子运动的方法相同的是()A.牛顿通过对天体现象的研究,总结出万有引力定律B.爱因斯坦在普朗克量子学说的启发下提出了光子说C.欧姆在研究电流与电压、电阻关系时,先保持电阻不变研究电流与电压的关系;然后再保持电压不变研究电流与电阻的关系D.奥斯特通过放在通电直导线下方的小磁针发生偏转得出通电导线的周围存在磁场的结论5.两个相距较远(此时它们之间的分子力可以忽略)的分子在靠近的过程中()A.分子间的引力减小,斥力增大B.分子力先增大后减小,然后再增大C.分子势能先增大后减小D.分子势能先增大后减小,然后再增大6.为了探究能量转化和守恒,小明将小铁块绑在橡皮筋中部,并让橡皮筋穿入铁罐,两端分别固定在罐盖和罐底上,如图所示.让该装置从不太陡的斜面上A处滚下,到斜面上B 处停下,发现橡皮筋被卷紧了,接着铁罐居然能从B处自动滚了上去.下列关于该装置能量转化的判断正确的是()A.从A处滚到B处,主要是重力势能转化为动能B.从A处滚到B处,主要是弹性势能转化为动能C.从B处滚到最高处,主要是动能转化为重力势能D.从B处滚到最高处,主要是弹性势能转化为重力势能7.在秋收的打谷场上,脱粒后的谷粒用传送带送到平地上堆积起来形成圆锥体,随着堆积谷粒越来越多,圆锥体体积越来越大,简化如图所示.用力学知识分析得出圆锥体底角的变化情况应该是()A.不断增大B.保持不变C.不断减小D.先增大后减小8.图中A球系在绝缘细线的下端,B球固定在绝缘平面上,它们带电的种类以及位置已在图中标出.A球能保持静止的是()A.B.C.D.二.单项选择题(共24分,每小题3分.每小题只有一个正确选项.)9.n辆汽车从同一地点先后开出,在平直的公路上排成一直线行驶.各车均由静止出发先做加速度为a匀加速直线运动,达到同一速度v做匀速直线运动.欲使汽车都匀速行驶时彼此间距均为s则各辆车依次启动的时间间隔为(不计汽车长度)()A.B.C.D.10.如图所示电路中,电源内阻r=R1=R2=R3.开关K接通后流过R1的电流是K接通前的()A.B.C.D.11.用a、b两束单色光分别照射同一双缝干涉装置,在距双缝恒定距离的屏上得到图示的干涉图样,其中甲图是a光照射时形成的,乙图是b光照射时形成的.则关于a、b两束单色光,下述正确的是()A.a光光子的能量较大B.在真空中a光传播的速度较大C.若用b光照射某金属时不能打出光电子,则用a光照射该金属时一定打不出光电子D.用a光照射一条狭缝,用b光照射另一条狭缝,屏上将呈现彩色干涉条纹12.弹簧秤挂在升降机的顶板上,下端挂一质量为2kg的物体.当升降机在竖直方向运动时,弹簧秤的示数始终是16N.如果从升降机的速度为3m/s时开始计时,则经过1s,升降机的位移可能是(g取10m/s2)()A.2m B.3m C.6m D.8m13.如图所示是伽利略设计的世界上第一个温度计示意图,上部是一个球形容器,里面有一定量的空气,下部是一根细管,细管插入带色液体中,制作时先给球形容器微微加热,跑出一些空气(可视为理想气体),插入液体时,带色液体能上升到管中某一高度,测量时上部的球形容器与被测物质接触.已知外界大气压为p0并保持不变,所测量温度为t1时,管内液面在a位置,管内气体分子的平均动能为Ek1,气体压强为p1;所测量温度为t2时管内液面上升到b位置,其他二个量分别为Ek2、p2.由此可知()A.t1<t2 B.p1<p2 C.Ek1>Ek2 D.Ek1<Ek214.如图,用三条细线悬挂的水平圆形线圈共有N匝,线圈由粗细均匀、单位长度质量为2克的导线绕制而成,三条细线呈对称分布,稳定时线圈平面水平,在线圈正下方放有一个圆柱形条形磁铁,磁铁的中轴线OO′垂直于线圈平面且通过其圆心O,测得线圈的导线所在处磁感应强度B的方向与水平线成60°角,线圈中通过的电流为0.1A,要使三条细线上的张力为零,重力加速度g取10m/s2.则磁感应强度B的大小应为()A.4T B.0.4T C.T D.0.4T15.一个用半导体材料制成的电阻器D,其电流I随它两端电压U的关系图象如图(a),将它与两个标准电阻R1、R2并联后接在电压恒为U的电源两端,三个用电器消耗的电功率相同,现将它们连接成如图(b)的电路,仍接在该电源的两端,设电阻器D和电阻R1、R2消耗的电功率分别是PD、P1、P2,它们之间的大小关系是()A.P1<P2 B.PD>P2 C.P1<PD D.P1<4P216.如图,两平行金属板水平放置并接到电源上,一个带电微粒P位于两板间恰好平衡,现用外力将P固定住(保持其电荷量不变),然后使两板各绕其中点转过α角,如图中虚线所示,再撤去外力以后,则P在两板间运动,其()A.重力势能将变大B.重力势能将变小C.电势能将变大D.电势能将变小三.多项选择题(共16分,每小题4分.每小题有二个或三个正确选项.全选对的,得4分;选对但不全的,得2分;有选错或不答的,得0分.)17.下面的各种核反应中能产生中子的是()A.用γ光子轰击2612Mg,生成物之一为2611NaB.用氘核轰击94Be,生成物之一为105BC.用质子轰击73Li,生成物之一为84BeD.用α粒子轰击73Li,生成物之一为105B18.一列向x轴正方向传播的简谐横波在t=0时的波形如图,A、B、C分别是x=0、x=1m和x=2m处的三个质点.已知该波波速为1m/s,则()A.在第1s内回复力对质点A做正功B.在第2s内回复力对质点B做负功C.在第1s内回复力对质点A和C做功相同D.在2s内回复力对质点B和C做功相同19.在正方形的四个顶点各有一根长直导线,四根导线相互平行,且与正方形平面垂直.现给每根导线通以大小相等的电流,每根导线中电流在正方形中心O产生的磁场磁感应强度大小为B,则正方形中心O的磁感应强度大小的可能值为()A.0 B.2B C.2 B D.4B20.如图所示,子弹水平射入放在光滑水平地面上静止的木块后不再穿出,此时木块动能增加了6J,那么此过程产生的内能可能为()A.10J B.8J C.6J D.4J四.填空题(共20分,每小题4分.)本大题中第22、23题为分叉题,分A、B两类,考生可任选一类答题.若两类试题均做,一律按A类题计分.21.已知1个铜原子的质量为a,铜的摩尔质量为b,密度为ρ,则1个铜原子所占的体积是,阿伏加德罗常数是.22.如图,质量为M的小车静止在光滑水平面上,车厢内有一质量为m的物体以速度v0开始向左运动,与车厢壁来回碰撞几次之后静止于车厢中,这时小车的速度大小为,方向.23.同步卫星轨道半径为r,运行速率为v1,加速度为a1.地球赤道上的物体随地球自转的向心加速度为a2,第一宇宙速度为v2,地球半径为R.则a1:a2= ,v1:v2= .24.从地面竖直上抛一物体,质量m=0.5kg,上抛初速度v0=10m/s,物体上升的最大高度H=4m,设物体在整个运动过程中所受的空气阻力大小不变,以地面为重力势能零点,重力加速度g取10m/s2.可得空气阻力f= N,在整个运动过程中物体离地面高度h= m处,其动能与重力势能相等.25.如图,ef、gh为水平放置的足够长的平行光滑导轨,导轨间距为L=1m,导轨左端连接一个R=1.5Ω的电阻,将一根质量m=0.2kg、电阻r=0.5Ω的金属棒cd垂直地放置导轨上,且与导轨接触良好,导轨的电阻不计.整个装置放在磁感应强度为B=2T的匀强磁场中,磁场方向垂直于导轨平面向下.现对金属棒施加一水平向右的拉力F,使棒从静止开始向右运动.施加的水平外力的功率恒为P=18W,则金属棒达到的稳定速度v1= m/s,金属棒从开始运动到速度v2=2m/s的过程中电阻R产生的热量为6.45J,则该过程所需的时间t= s.26.如图,河宽L=60m,一只小船在河的正中央航行,经过O点时发现在距船S=40m的下游有一瀑布,为了使小船在A点安全靠岸,在O点立即调整好船头的指向,不至被冲进瀑布中.若河水的流速大小恒为5m/s,则小船的最小航行速率为m/s.若河水的流速与到河岸的最短距离x成正比,即v水=kx(x≤,k为一常量),小船在O点调整船头垂直河岸,让小船保持航行速率不变到达A点,则小船在平行河岸方向做运动.五.实验题(共24分)27.现将电池组、滑线变阻器、带铁芯的线圈A、线圈B、电流计及开关如图连接.在开关闭合、线圈A放在线圈B中的情况下,某同学发现当他将滑动变阻器的滑片P向右加速滑动时,电流计指针向右偏转.由此可以推断()A.因为线圈A、线圈B的绕线方向未知,故无法判断电流计指针偏转的方向B.线圈A中铁芯向上拔出或断开开关,电流计指针向右偏转C.滑动变阻器的滑片P匀速向右滑动,电流计指针静止在中央D.线圈A向上移动,电流计指针向左偏转28.某同学利用“非”门电路设计了一个路灯自动控制门电路.天黑了,让路灯自动接通;天亮了,让路灯自动熄灭.图中RG是一个光敏电阻,当有光线照射时,光敏电阻的阻值会显著减小.R是可调电阻,起分压作用.虚线框内为“非”门电路,它能将输入的高压信号转变为低压信号,或将低压信号转变为高压信号.J为路灯总开关控制继电器,它在获得高电压时才动作(图中未画路灯电路).(1)在图中虚线框内画出“非”门符号;(2)当天黑时,RG变,非门电路获得电压,J得到电压.(填“大”、“小”或“高”、“低”);(3)如果路灯开关自动接通时天色还比较亮,现要调节自动控制装置,使得它在天色较黑时才会自动接通开关,应将R调(填“大”或“小”)一些.29.伽利略曾经提出和解决了这样一个问题:一根细绳悬挂在黑暗的城堡中,人们看不到它的上端,只能摸到它的下端.为了测出细绳的长度,可以在细绳的下端系一个金属球,使之在竖直平面内做小角度的摆动.①在上述设想中,要达到测出细绳长度的目的,需要测量或知道的物理量是下列选项中的(填序号字母).A.金属球的质量m B.金属球的直径dC.金属球全振动的次数”和对应的时间t D.当地的重力加速度g②利用①中测量或知道的物理量得到的细绳长度表达式为l= .30.某同学要测量一节干电池的电动势和内阻,实验器材仅有一个理想电压表、一个电阻箱、一个开关和导线若干,该同学进行实验,测得的数据如表所示.实验次数 1 2 3 4 5R(Ω) 2.0 4.0 6.0 8.0 10.0U(V) 1.00 1.19 1.27 1.31 1.35U/R(A)0.50 0.30 0.21 0.16 0.13(1)根据表中提供的数据,画出该同学的实验电路图;(2)根据表中提供的数据,若利用图象确定电池的电动势和内阻,则应作图象;(A)U﹣(B)R﹣U (C)R﹣(D)﹣U(3)根据(2)中你选择的图象,电池的电动势是该图象的,电池的内阻是该图象的.六.计算题(共50分)31.如图甲所示,在一端封闭、长约1m的玻璃管内注满清水,水中放一个蜡烛做的蜡块,将玻璃管的开口端用胶塞塞紧.然后将这个玻璃管倒罩,在蜡块沿玻璃管上升的同时,将玻璃管水平向右移动.假设从某时刻开始计时,蜡块在玻璃管内每1s上升的距离都是10cm,玻璃管向右匀加速平移,每1s通过的水平位移依次是2.5cm、7.5cm、12.5cm、17.5cm.图乙中,y表示蜡块竖直方向的位移,x表示蜡块随玻璃管通过的水平位移,t=0时蜡块位于坐标原点.(1)请在图乙中描绘出蜡块4s内的轨迹.(2)求出玻璃管向右平移的加速度a.(3)求t=3s时蜡块的速度大小及方向.32.扣在水平桌面上的热杯盖有时会发生被顶起的现象.截面积为S的热杯盖扣在水平桌面上,开始时内部封闭气体的温度为T0,压强为大气压强p0.当封闭气体温度上升2%时,杯盖恰好被整体顶起,放出少许气体后又落回桌面,其内部压强立即减为p0,此时温度尚未下降.再经过一段时间,内部气体温度下降到T0.整个过程中封闭气体均可视为理想气体.求:(1)当温度上升2%且尚未放气时,封闭气体的压强;(2)当温度下降到T0时,竖直向上提起杯盖所需的最小力.33.质量为0.1kg的带正电小球处在竖直向上、范围足够大的匀强电场中,由地面静止起开始运动,6秒末电场突然消失,再经过6秒小球落回到出发点.不计空气阻力.重力加速度g取10m/s2,取地面处的重力势能和电势能为零.求:(1)小球上升过程中小球电势能的变化量;(2)小球运动过程中的最大机械能和最大动能;(3)若6秒末原电场并未消失,而是大小不变,方向竖直向下,当小球的动能和重力势能相等时,小球离地的高度.34.如图所示,两条平行金属导轨间距2m,固定在倾角为37°的绝缘斜面上,导轨上端连接一个定值电阻R.导体棒a和b放在导轨上,与导轨垂直并良好接触,a为光滑导体棒而b与导轨有摩擦,动摩擦因数为.斜面上水平虚线PQ以下区域内,存在着垂直穿过斜面向上、大小为0.5T的匀强磁场.现对a棒施以平行导轨斜向上的拉力F,使它沿导轨由静止起匀加速向上运动,加速度为1m/s2.当a棒运动到磁场的上边界PQ处时(放在导轨下端的b棒仍保持静止),撤去拉力,a棒将继续沿导轨向上运动一小段距离后再向下滑动.当a 棒再次滑回到磁场边界PQ处进入磁场时,恰沿导轨受力平衡.已知a棒、b棒和定值电阻R的阻值均为1Ω,b棒的质量为0.1kg,重力加速度g取10m/s2,导轨电阻不计.求:(1)a棒沿导轨向上运动过程中,a、b棒中的电流强度之比;(2)a棒沿导轨向上运动到磁场的上边界PQ处所允许的最大速度;(3)若a棒以第(2)问中的最大速度运动到磁场的上边界PQ处,a棒在磁场中沿导轨向上开始运动时所受的拉力F0;(4)若a棒以第(2)问中的最大速度运动到磁场的上边界PQ处过程中,流过定值电阻R 的电量.上海2018年自主招生物理模拟试题参考答案与试题解析一.单项选择题(共16分,每小题2分.每小题只有一个正确选项.)1.下列叙述中符合物理学史实的有()A.托马斯•杨通过对光的干涉现象的研究,证实了光具有波动性B.麦克斯韦建立了完整的电磁场理论,并通过实验证实了电磁波的存在C.查德威克通过对α粒子散射实验的研究,提出了原子的核式结构学说D.贝克勒尔发现了天然放射现象,并提出原子核是由质子和中子组成的【考点】1U:物理学史.【分析】根据物理学史和常识解答,记住著名物理学家的主要贡献即可【解答】解:A、托马斯•杨通过对光的干涉现象的研究,证实了光具有波动性,故A正确.B、麦克斯韦依据电磁场理论预言了电磁波的存在,赫兹通过实验给予了证,故B错误.C、卢瑟福根据α粒子散射实验现象提出原子核式结构模型,故C错误.D、贝克勒尔发现了天然放射现象,揭示了原子核具有复杂的结构,没有提出原子核是由质子和中子组成的,故D错误.故选:A2.在阳光下,竖直放置的肥皂膜上呈现彩色条纹,可以观察到()A.竖直方向的条纹,是由于不同频率的光各自在肥皂膜前后表面反射叠加的结果B.竖直方向的条纹,是由于相同频率的光在肥皂膜前后表面反射叠加的结果C.水平方向的条纹,是由于不同频率的光各自在肥皂膜前后表面反射叠加的结果D.水平方向的条纹,是由于相同频率的光在肥皂膜前后表面反射叠加的结果【考点】H9:光的干涉.【分析】当光源发出的光照射到肥皂膜上时,从膜的前后两面分别反射两列光为相干光,当光程差为波长的整数倍时呈现亮条纹,当光程差为半个波长的奇数倍时呈现暗条纹.【解答】解:薄膜干涉为前后两个面反射回来的光发生干涉形成干涉条纹,故从肥皂薄膜的观察到水平干涉条纹,用复色光时出现彩色条纹,即不同频率的光各自在肥皂膜前后表面反射叠加的结果.故C正确,A、B、D错误.故选C.3.下列叙述正确的是()A.外界对物体做功,物体的内能一定增加B.热量不能由低温物体传递到高温物体C.温度升高,物体内每个分子的热运动速率都增大D.自然界中进行的涉及热现象的宏观过程都具有方向性【考点】8F:热力学第一定律;8H:热力学第二定律.【分析】改变物体内能的方式有两种:做功和热传递,热量不能自发由低温物体传递到高温物体,第二类永动机不可能制成,因为它违背了热力学第二定律.温度是分子的平均动能的标志,是大量分子运动的统计规律.【解答】解:A、根据热力学第一定律可知,影响内能的方式有做功和热传递,外界对物体做功,物体的内能不一定增加,故A错误;B、根据热力学第二定律,热量不能自发由低温物体传递到高温物体,但在一定的条件下,热量可能从低温物体传递到高温物体,如冰箱、空调等,但要消耗其他的能量,故B错误;C、温度是分子的平均动能的标志,温度升高,物体内的分子的平均动能增大,但不是每个分子的热运动速率都增大,故C错误;D、根据热力学第二定律可知,自然界中进行的涉及热现象的宏观过程都具有方向性,故D 正确;故选:D4.分子运动是看不见、摸不着的,其运动特征不容易研究,但科学家可以通过布朗运动认识它,这种方法叫做“转换法”.下面给出的四个研究实例,其中采取的方法与上述研究分子运动的方法相同的是()A.牛顿通过对天体现象的研究,总结出万有引力定律B.爱因斯坦在普朗克量子学说的启发下提出了光子说C.欧姆在研究电流与电压、电阻关系时,先保持电阻不变研究电流与电压的关系;然后再保持电压不变研究电流与电阻的关系D.奥斯特通过放在通电直导线下方的小磁针发生偏转得出通电导线的周围存在磁场的结论【考点】1U:物理学史.【分析】本题根据转换法的定义及物理学史结合进行解答.【解答】解:A、牛顿通过对天体运动的研究,根据开普勒定律、牛顿第二定律、第三定律,直接得出万有引力定律,这种方法不是转换法.故A错误.B、爱因斯坦在普朗克量子学说的启发下提出了光子说,采用的是类比法.故B错误.C、欧姆在研究电流与电压、电阻关系时,采用的控制变量法得到了欧姆定律.故C错误.D、奥斯特通过放在通电直导线下方的小磁针发生偏转,根据小磁针的偏转得出通电导线的周围存在磁场的结论,是一种转换法.故D正确.故选D5.两个相距较远(此时它们之间的分子力可以忽略)的分子在靠近的过程中()A.分子间的引力减小,斥力增大B.分子力先增大后减小,然后再增大C.分子势能先增大后减小D.分子势能先增大后减小,然后再增大【考点】86:分子间的相互作用力;87:分子势能.【分析】开始时由于两分子之间的距离大于r0,因此分子力为引力当相互靠近时分子力做正功,当分子间距小于r0,分子力为斥力,相互靠近时,分子力做负功.【解答】解:A、开始时由于两分子之间的距离大于r0,分子力表现为引力,该力先增大后减小;当分子间距小于r0,分子力为斥力,随二者距离的减小而增大.故A错误,B正确;C、开始时由于两分子之间的距离大于r0,因此分子力为引力当相互靠近时分子力做正功,分子势能减小;当分子间距小于r0,分子力为斥力,相互靠近时,分子力做负功分子势能增大;故CD都错误;故选:B.6.为了探究能量转化和守恒,小明将小铁块绑在橡皮筋中部,并让橡皮筋穿入铁罐,两端分别固定在罐盖和罐底上,如图所示.让该装置从不太陡的斜面上A处滚下,到斜面上B 处停下,发现橡皮筋被卷紧了,接着铁罐居然能从B处自动滚了上去.下列关于该装置能量转化的判断正确的是()A.从A处滚到B处,主要是重力势能转化为动能B.从A处滚到B处,主要是弹性势能转化为动能C.从B处滚到最高处,主要是动能转化为重力势能D.从B处滚到最高处,主要是弹性势能转化为重力势能【考点】6C:机械能守恒定律.【分析】对系统,有动能、重力势能、弹性势能发生相互转换,根据能量守恒定律判断能量之间的转化.【解答】解:从A处滚到B处,初动能为零,末动能为零,重力势能转化为弹性势能.从B 处滚到最高处,初末动能为零,弹性势能转化为重力势能.故D正确,A、B、C错误.故选D.7.在秋收的打谷场上,脱粒后的谷粒用传送带送到平地上堆积起来形成圆锥体,随着堆积谷粒越来越多,圆锥体体积越来越大,简化如图所示.用力学知识分析得出圆锥体底角的变化情况应该是()A.不断增大B.保持不变C.不断减小D.先增大后减小【考点】2H:共点力平衡的条件及其应用;2G:力的合成与分解的运用.【分析】开始时,圆锥体底角逐渐增加,当谷粒的重力的下滑分量与最大静摩擦力等大后,坡角就达到了最大值.【解答】解:谷粒受重力、支持力和静摩擦力;开始时,圆锥体底角逐渐增加,故重力的下滑分力mgsinθ不断变大,而最大静摩擦力(约等于滑动摩擦力)μmgcosθ逐渐减小,当两者相等,即mgsinθ=μmgcosθ,tanθ=μ时,坡角达到最大值,此后坡角保持不变;故选B.8.图中A球系在绝缘细线的下端,B球固定在绝缘平面上,它们带电的种类以及位置已在图中标出.A球能保持静止的是()A.B.C.D.【考点】A4:库仑定律.【分析】对A球进行受力分析,由于A球能保持静止,根据共点力平衡状态解决问题.【解答】解:A、对A球进行受力分析:根据力的合成,可知道三个力合力可以为0,故A正确.B、对A球进行受力分析:根据力的合成,可知道任意两个力的合力的方向不可能与第三个力方向相反.故B错误.C、对A球进行受力分析:根据力的合成,可知道任意两个力的合力的方向不可能与第三个力方向相反.故C错误.D、对A球进行受力分析:根据力的合成,可知道三个力合力可以为0,故D正确.故选AD.二.单项选择题(共24分,每小题3分.每小题只有一个正确选项.)9.n辆汽车从同一地点先后开出,在平直的公路上排成一直线行驶.各车均由静止出发先做加速度为a匀加速直线运动,达到同一速度v做匀速直线运动.欲使汽车都匀速行驶时彼此间距均为s则各辆车依次启动的时间间隔为(不计汽车长度)()A.B.C.D.【考点】1G:匀变速直线运动规律的综合运用.【分析】设某辆车从静止开始做匀加速直线运动经过时间t速度恰好达到v,其前面一辆车运动时间为t+△t,根据两车的位移差为s即可求解.【解答】解:设某辆车从静止开始做匀加速直线运动经过时间t速度恰好达到v,其前面一辆车运动时间为t+△t,则s1=at2,s1+s=at2+v•△t.联立上述方程得各辆车依次启动的时间间隔△t=,故D项正确.。
2018上海中学自主招生试题
1、因式分解:411623++-x x x =____________
2、设0>>b a ,ab b a 422=+,则b a b a -+=____________
3、若012=-+x x ,则3223++x x =_________
4、已知))(()(412a c b a c b --=-,且0≠a ,则a
c b +=___________
5、一个袋子里装有两个红球和一个白球(仅颜色不同),第一次从中取出一个球,记下颜色后放回,摇匀,第二次从中取出一个球,则两次都是红球的概率是_________
6、直线33:+-=x y l 与x 、y 轴交于点A 、B ,AOB ∆关于直线AB 对称得到ACB ∆,则点C 的坐标是______
7、一张矩形纸片ABCD ,9=AD ,12=AB ,将纸片折叠,使A 、C 两点重合,折痕长是_______
8、任何给一个正整数n ,如果n 是偶数,就将它减半(即2
n ),如果n 是奇数,则将它乘以3加1(即13+n )。
不断重复这样的运算,现在请你研究:如果对正整数n (首项)按照上述规则施行变换(注:1可以多次出现)后的第八项为1,则n 所有可能取值为_________;
9、正六边形ABCDEF 的面积是6平方厘米,联结AC 、CE 、EA 、BD 、DF 、FB ,求阴影部分小正六边形的面积为____________;
10、已知)4()4(221m x m x y -+-+=与mx y =2在x 取任意实数时,至少有一个是正数,求m 的取值范围___________
11、已知a 、b 、c 是互不相等的实数,x 是任意实数,
化简:()()()()()()()()()
b c a c c x b a b c b x c a b a a x ---+---+---222=_________
12、已知实数a 、b 满足122=++b ab a ,22b a ab t --=,则t 的取值范围是________;
13、(1)求边长为1的正五边形对角线长;(2)求 18sin ;
14、(1)()c bx ax x x f +++=23,()()()33210≤-=-=-<f f f ,求c 的取值范围;
(2)()d cx bx ax x x f ++++=234,()101=f ,()202=f ,()303=f ,求()()610-+f f
15、我们学过直线与圆的位置关系,根据材料完成问题(1)(1) 类似给出背景知识:
平面α:0=+++d Cz By Ax ;
球:()()()22
22R c z b y a x =-+-+-; 点()c b a ,,到平面0=+++d Cz By Ax 的距离公式:222C B A D
Cc Bb Aa d +++++=;
球心到平面的距离为d ,当R d <时,球与平面相交,当R d =时,球与平面相切,当R d >时,球与平面相离;
问题(1):若实数m 、n 、k 满足1=++k n m ,求222k n m ++的最小值;
问题(2):解方程:)(2
121z y x z y x ++=-+-+。
答案
1、()()()12431+--x x x
2、3
3、4
4、2
5、9
4 6、⎪⎪⎭
⎫ ⎝⎛23,23 7、4
45 8、128、2、16、20、3、21 9、22cm
10、4<m
11、1
12、3
13-≤≤-t 13、(1)215+ (2)4
15- 14、(1)96≤<c (2)8104
15、(1)31 (2)⎪⎩⎪⎨⎧===321z y x。