嘉定区2012学年第一学期高三质量调研考试试卷理
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某某市嘉定区2012届高三上学期第一次质量调研(历史)考生注意:1.考试时间120分钟,试卷满分150分。
2.本考试设试卷和答题纸两部分,试卷包括试题与答题要求;所有答题做在答题纸上;做在试卷上一律不得分。
3.答题前,务必在答题纸上填写某某号和某某。
4.答题纸与试卷在试题编号上是一一对应的,答题时应特别注意,不能错位。
一、选择题(共70分)以下每小题2分,共58分。
每题只有一个正确选项。
1、“它是时代的产物,它兴盛于英吉利民族呼唤主权国家之时,它肩负着两个重大的历史使命——实现国家统一、确保国家独立。
”“它”是A 封建等级制B 等级君主制C 君主专制D 君主立宪制2、“美洲金银产地的发现,土著居民的被剿灭,……非洲变成商业性地猎获黑人的场所”,以上是欧洲哪一历史现象的主要因素A 资本原始积累B 自由资本主义C 垄断资本主义D 资本全球扩X3、康德曾说:“除了自由而外并不需要任何别的东西,而且还确乎是一切可以称之为自由的东西之中最无害的东西,那就是在一切事情上都有公开运用自己理性的自由。
”他评价的是A 文艺复兴B 某某改革C 启蒙运动D 马克思主义4、钱乘旦在《走向现代国家之路》一文中指出,“从血统上说,王位的新主人是詹姆士的女儿和女婿,这样就保留了斯图亚特的族谱,但王位的内容却因此起了变化。
”对“王位的内容”变化说法欠妥的是A 专制王权→某某某某B 个人专制→宪政体制C 王在法上→王在法下D 国王至上→议会至上5、王斯德主编的《世界通史》认为,“正是那场在大西洋岛国最先迸发、然后蔓延到整个欧美世界的技术、经济变革,开启了人类新文明的大门。
”这一“新文明”与中华文明首次发生激烈碰撞是在A 十八世纪上半期B 十八世纪下半期C 十九世纪上半期D 十九世纪下半期6、“代替那存在着阶级和阶级对立的资产阶级旧社会的,将是这样一个联合体,在那里,每个人的自由发展是一切人的自由发展的条件。
”依据以上《共产党宣言》的内容,推断该文献产生的历史背景是A 早期资产阶级革命时期B 工业社会来临时期C 第二次工业革命时期D 资本主义“大萧条”时期7、19世纪中后期,某国最高统治者面临国内严峻形势,被迫有所行动,但他同时在国务会议上宣布:“诸位请相信,凡是为保障地主利益能够做的一切,都做到了。
2012学年嘉定区高三年级第一次质量调研数学试卷(理)一.填空题(本大题共有14题,满分56分)考生应在答题纸相应编号的空格内直接填写结果,每个空格填对得4分,否则一律得零分.1.若i ii z +=11(i 为虚数单位),则=z ___________. 2.已知集合},0)1)(2({R ∈<-+=x x x x A ,},01{R ∈<+=x x x B ,则=B A _____________.3.函数1)cos (sin )(2++=x x x f 的最小正周期是___________.4.一组数据8,9,x ,11,12的平均数是10,则这组数据的方差是_________.5.在等差数列}{n a 中,101-=a ,从第9则公差d 的取值范围是__________________.6.执行如图所示的程序框图,则输出的a 的值为_____________.7.小王同学有4本不同的数学书,3本不同的物理书和3本不同的化学书,从中任取2本,则这2本书属于不同学科的概率为______________(结果用分数表示).8.一个圆锥的侧面展开图是一个半径为R 的半圆,则这个圆锥的体积是________. 9.点M 是曲线1212+=x y 上的一个动点,且点M 为线段OP 的中点,则动点P 的轨迹方程为__________________. 10.在△ABC 中,已知41tan =A ,53tan =B ,且△ABC 最大边的长为17,则△ABC 最小边的长为____________.11.将直线1l :01=-+y x ,2l :0=-+n y nx ,3l :0=-+n ny x (*N ∈n ,2≥n )围成的三角形面积记为n S ,则=∞→n n S lim ___________.12.已知a 、b 是平面内两个互相垂直的单位向量,若向量c 满足0)()(=-⋅-c b c a,则||c的最大值是___________.13.观察下列算式:113=, 5323+=,119733++=,(第6题图)1917151343+++=,… … … …若某数3m 按上述规律展开后,发现等式右边含有“2013”这个数,则=m _______. 14.设m 、R ∈n ,定义在区间],[n m 上的函数|)|4(log )(2x x f -=的值域是]2,0[,若关于t 的方程0121||=++⎪⎭⎫⎝⎛m t (R ∈t )有实数解,则n m +的取值范围是___________.二.选择题(本大题共有4题,满分20分)每题有且只有一个正确答案,考生应在答题纸的相应编号上,将代表答案的小方格涂黑,选对得5分,否则一律得零分.15.已知R ∈x ,条件p :x x <2,条件q :11≥x,则p 是q 的…………………( ) A .充分不必要条件 B .必要不充分条件C .充分必要条件D .既不充分也不必要条件 16.以下说法错误的是………………………………………………………………………( ) A .直角坐标平面内直线的倾斜角的取值范围是),0[πB .直角坐标平面内两条直线夹角的取值范围是⎥⎦⎤⎢⎣⎡2,0π C .平面内两个非零向量的夹角的取值范围是),0[πD .空间两条直线所成角的取值范围是⎥⎦⎤⎢⎣⎡2,0π 17.在平面直角坐标系内,设),(11y x M 、),(22y x N 为不同的两点,直线l 的方程为0=++c by ax , cby ax cby ax ++++=2211δ.有四个命题:①存在实数δ,使点N 在直线l 上;②若1=δ,则过M 、N 两点的直线与直线l 平行;③若1-=δ,则直线l 经过线段MN 的中点;④若1>δ,则点M 、N 在直线l 的同侧,且直线l 与线段MN 的延长线相交.上述命题中,全部真命题的序号是……………………………………………………………( ) A .① ② ③ B .② ③ ④ C .① ③ ④ D .① ② ③ ④ 18.设函数)(x f y =是定义在R 上以1为周期的函数,若函数x x f x g 2)()(-=在区间]3,2[上的值域为]6,2[-,则)(x g 在区间]12,12[-上的值域为……………………( )A .]6,2[-B .]28,24[-C .]32,22[-D .]34,20[-三.解答题(本大题共有5题,满分74分)解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤. 19.(本题满分12分)设复数i a z ⋅++-=)cos 1(2)sin4(22θθ,其中R ∈a ,),0(πθ∈,i 为虚数单位.若z 是方程0222=+-x x 的一个根,且z 在复平面内对应的点在第一象限,求θ与a 的值.20.(本题满分14分)本题共有2个小题,第1小题满分8分,第2小题满分6分.如图,在三棱锥ABC P -中,⊥PA 底面ABC ,BC AC ⊥,2===PA BC AC . (1)求异面直线AB 与PC 所成角的大小;(2)求三棱锥ABC P -的表面积S .21.(本题满分14分)本题共有2个小题,第1小题满分6分,第2小题满分8分.已知椭圆C :12222=+b y a x (0>>b a )经过)1,1(与⎪⎪⎭⎫ ⎝⎛23,26两点,过原点的直线l 与椭圆C 交于A 、B 两点,椭圆C 上一点M 满足||||MB MA =.(1)求椭圆C 的方程;(2)求证:222||2||1||1OM OB OA ++22.(本题满分16分)本题共有3个小题,第13小题满分6分.设数列}{n a 的前n 项和为n S ,已知q pS S n n +=+1(*N ∈n ,p 、q 为常数),21=a ,12=a ,p q a 33-=.(1)求p 、q 的值;(2)求数列}{n a 的通项公式;(3)是否存在正整数m ,n ,使得1221+<--+m m n n m S m S 成立?若存在,请求出所有符合条件的有序整数对),(n m ;若不存在,请说明理由.23.(本题满分18分)本题共有3个小题,第1小题满分4分,第2小题满分6分,第3小题满分8分.设R ∈a ,函数x a x x x f 2||)(+-⋅=.(1)若2=a ,求函数)(x f 在区间]3,0[上的最大值; (2)若2>a ,写出函数)(x f 的单调区间(不必证明);(3)若存在]4,2[-∈a ,使得关于x 的方程)()(a f t x f ⋅=有三个不相等的实数解,求实数t 的取值范围.P A B C2012学年嘉定区高三年级第一次质量调研 数学试卷(理)参考答案与评分标准一.填空题(每小题4分,满分56分)1.i -2 2.}12{-<<-x x 3.π 4.25.⎥⎦⎤ ⎝⎛710,45 6.37 7.1511 8.2433R π 9.2412+=x y 10.2 11.2112.213.45 14.)2,1[二.选择题(每小题5分,满分20分)15.A 16.C 17.B 18.D 三.解答题 19.(本题满分12分)方程0222=+-x x 的根为i x ±=1.………………(3分)因为z 在复平面内对应的点在第一象限,所以i z +=1,………………(5分)所以⎩⎨⎧=+=-1)cos 1(21sin 422θθa ,解得21cos -=θ,因为),0(πθ∈,所以32πθ=,……(8分)所以43sin 2=θ,所以4sin 4122=+=θa ,故2±=a .…………(11分)所以3πθ2=,2±=a .…………(12分)20.(本题满分14分,第1小题8分,第2小题6分) (1)取PA 中点E ,PB 中点F ,BC 中点G ,连结EF ,FG ,EG ,则EF ∥AB ,FG ∥PC , 所以EFG ∠就是异面直线AB 与PC 所成的角(或 其补角).…………(2分) 连结AG ,则522=+=CG AC AG ,……(3分)622=+=AG EA EG , …………(4分)又22==PC AB ,所以2==FG EF .…………(5分)在△EFG 中,212cos 222-=⋅-+=∠FG EF EG FG EF EFG ,……(7分) 故︒=∠120EFG .所以异面直线AB 与PC 所成角的大小为︒60.…………(8分)(2)因为⊥PA 底面ABC ,所以AB PA ⊥,BC PA ⊥,AC PA ⊥, 又AC BC ⊥,所以⊥BC 平面PAC ,所以PC BC ⊥,…………(2分) 所以△ABC 、△PAB 、△PBC 、△PAC 都是直角三角形.……(3分) 所以,24421212121+=⋅+⋅+⋅+⋅=AC PA PC BC AB PA BC AC S .……(6分) G P ABC FE21.(本题满分14分,第1小题6分,第2小题8分) (1)将)1,1(与⎪⎪⎭⎫⎝⎛23,26代入椭圆C 的方程,得 ⎪⎪⎩⎪⎪⎨⎧=+=+143231112222b a b a ,…………(2分) 解得32=a ,232=b .…………(5分)所以椭圆C 的方程为132322=+y x .…………(6分) (2)由||||MB MA =,知M 在线段AB 的垂直平分线上,由椭圆的对称性知A 、B 关于原点对称.①若点A 、B 在椭圆的短轴顶点上,则点M 在椭圆的长轴顶点上,此时2112211||2||1||122222222=⎪⎭⎫ ⎝⎛+=++=++b a a b b OM OB OA .……(1分) 同理,若点A 、B 在椭圆的长轴顶点上,则点M 在椭圆的短轴顶点上,此时2112211||2||1||122222222=⎪⎭⎫ ⎝⎛+=++=++b ab a a OM OB OA .……(2分) ②若点A 、B 、M 不是椭圆的顶点,设直线l 的方程为kx y =(0≠k ), 则直线OM 的方程为x ky 1-=.设),(11y x A ,),(22y x M , 由⎪⎩⎪⎨⎧=+=132322y x kx y ,解得221213k x +=,2221213k k y +=,……(4分) 所以2221212221)1(3||||k k y x OB OA ++=+==,同理可得2222)1(3||kk OM ++=, 所以2)1(3)2(2)1(321)1(321||2||1||1222222222=++++++++=++k k k k k k OM OB OA .……(7分) 综上,222||2||1||1OM OB OA ++为定值2.…………(8分)(1)由题意,得⎩⎨⎧+=+=q pS S q pa S 2312,……(2分)即⎩⎨⎧+=-++=q p p q q p 33323 ,解得⎪⎩⎪⎨⎧==221q p .…………(4分) (2)由(1)知,2211+=+n n S S ①当2≥n 时,2211+=-n n S S ② …………(1分)①-②,得n n a a 211=+(2≥n ),又1221a a =,…………(3分)所以数列}{n a 是首项为2,公比为21的等比数列.…………(4分)所以}{n a 的通项公式为221-⎪⎭⎫ ⎝⎛=n n a (*N ∈n ).…………(6分)(3)由(2),得⎪⎭⎫ ⎝⎛-=n n S 2114,…………(1分)由1221+<--+m m n n m S m S ,得122211421141+<-⎪⎭⎫ ⎝⎛--⎪⎭⎫ ⎝⎛-+m m n n m m ,即12222)4(42)4(+<-⋅--⋅-mm nn m m , 即12122)4(2+>-⋅-mn m .因为012>+m ,所以22)4(>⋅-nm , 所以4<m 且422)4(21+<⋅-<+m n m , (*)因为*N ∈m ,所以1=m 或2或3.……………………(2分)当1=m 时,由(*)得8232<⨯<n,所以1=n ; …………(3分)当2=m 时,由(*)得12222<⨯<n,所以1=n 或2; …………(4分)当3=m 时,由(*)得2022<<n,所以2=n 或3或4. …………(5分)综上可知,存在符合条件的正整数m 、n ,所有符合条件的有序整数对),(n m 为:)1,1(,)1,2(,)2,2(,)2,3(,)3,3(,)4,3(. …………(6分)(1)当2=a ,]3,0[∈x 时,⎪⎩⎪⎨⎧<≤+-≥=+-⋅=.20,4;2,2|2|)(22x x x x x x x x x f …(2分) 作函数图像(图像略),可知函数)(x f 在区间]3,0[上是增函数,所以)(x f 的最大值为9)3(=f .…………(4分)(2)⎪⎩⎪⎨⎧<++-≥-+=.,)2(,,)2()(22a x x a x a x x a x x f ……(1分) ①当a x ≥时,4)2(22)(22--⎪⎭⎫ ⎝⎛--=a a x x f , 因为2>a ,所以a a <-22, 所以)(x f 在),[∞+a 上单调递增.…………(3分)②当a x <时,4)2(22)(22++⎪⎭⎫ ⎝⎛+--=a a x x f , 因为2>a ,所以a a <+22,所以)(x f 在⎥⎦⎤ ⎝⎛+∞-22,a 上单调递增,在⎥⎦⎤⎢⎣⎡+a a ,22上单调递减.…………(5分)综上,函数)(x f 的单调递增区间是⎥⎦⎤⎝⎛+∞-22,a 和),[∞+a , 单调递减区间是⎥⎦⎤⎢⎣⎡+a a ,22.………………(6分) (3)①当22≤≤-a 时,022≤-a ,022≥+a ,所以)(x f 在),(∞+-∞上是增函数,关于x 的方程)()(a f t x f ⋅=不可能有三个不相等的实数解.…………(2分)②当42≤<a 时,由(1)知)(x f 在⎥⎦⎤ ⎝⎛+∞-22,a 和),[∞+a 上分别是增函数,在⎥⎦⎤⎢⎣⎡+a a ,22上是减函数,当且仅当4)2()(22+<⋅<a a f t a 时,方程)()(a f t x f ⋅=有三个不相等的实数解.即⎪⎭⎫⎝⎛+4+=+<<4818)2(12a a a a t .…………(5分)令aa a g 4)(+=,)(a g 在]4,2(∈a 时是增函数,故5)(max =a g .…………(7分)所以,实数t 的取值范围是⎪⎭⎫⎝⎛89,1.…………(8分)。
2011学年嘉定区高三第一次模拟考试物理试卷本试卷分第I 卷(1—4页)和第II 卷(4—10页)两部分。
全卷共10页。
满分150分。
考试时间120分钟。
请在答题纸上答题。
第Ⅰ卷(共56分)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。
答案写在答题纸上相应的位置。
)1.(12.1嘉定)下列单位中,不属于国际单位制中规定的基本单位的是[ ]A .千克B .伏特C .安培D .开尔文2.(12.1嘉定)如图所示,用细线将一块玻璃板水平地悬挂在弹簧秤下端,并使玻璃板贴在水面上,然后缓慢提起弹簧秤,在玻璃板脱离水面的一瞬间,弹簧秤读数会突然增大,主要原因是[ ] A .水分子做无规则热运动 B .玻璃板受到大气压力作用 C .水与玻璃间存在在万有引力作用 D .水与玻璃间存在分子引力作用3.(12.1嘉定)伟大的物理学家伽利略的科学研究方法,对于后来的科学研究具有重大的启蒙作用,至今仍具有重要意义。
以下哪项是伽利略探究物体下落规律的过程 [ ]A .猜想—问题—数学推理—实验验证—合理外推—得出结论B .问题—猜想—实验验证—数学推理—合理外推—得出结论C .问题—猜想—数学推理—实验验证—合理外推—得出结论D .猜想—问题—实验验证—数学推理—合理外推—得出结论4.(12.1嘉定)法国科学家库仑精心设计的库仑扭称仪器,能测出的物理量是 [ ]A .静电力的大小B .金属小球的电荷量C .元电荷的电荷量D .电场强度的大小5.(12.1嘉定)某质点做匀速圆周运动,线速度大小v 、周期T ,则在T2 时间内,速度改变量大小是[ ]A .0B .v 2C .vD .2v6.(12.1嘉定)一个门电路的两个输入端A 、B 与输出端Z 的波形如图所示,则可知该门电路是[ ]A .“与”门B .“或”门C .“与非”门D .“或非”门7.(12.1嘉定)下列涉及能量变化的过程中,不属于单向性过程的是[ ]A .摩擦生热B .简谐振动C .热传递D .气体自由膨胀8.(12.1嘉定)从同一水平直线上的两位置分别沿同方向抛出两小球A 和B ,其运动轨迹如图所示,不计空气阻力。
2023-2024学年上海嘉定区高三年级第一次质量调研数学试卷(考试时间120分钟,满分150分)一.填空题(本大题满分54分)本大题共有12题,只要求直接填写结果,前六题每题得4分,后六题每题得5分.1.不等式260x x --<的解集为.2.已知()2,1a = ,()1,2b =- ,则23a b +=.3.函数sin πy x =的最小正周期为.4.已知tan 2α=,则πtan 2α⎛⎫+= ⎪⎝⎭.5.双曲线22145x y -=的离心率为.6.已知事件A 和B 独立,()14P A =,()113P B =,则()P A B = .7.已知实数a 、b 满足6ab =-,则22a b +的最小值为.8.已知()612x +的二项展开式中系数最大的项为.9.关于x 的方程232=x x mx -+有三个不同的实数解,则实数m 的值为.10.已知11个大小相同的球,其中3个是红球,3个是黑球,5个是白球,从中随机取出4个形成一组,其中三种颜色都有的概率为.11.已知复平面上一个动点Z 对应复数z ,若4i 2z -≤,其中i 是虚数单位,则向量OZ扫过的面积为.12.正四棱台1111ABCD A B C D -,3AB =,111A B =,12AA =,M 是11C D 的中点,在直线1AA 、BC 上各取一个点P 、Q ,使得M 、P 、Q 三点共线,则线段PQ 的长度为.二.选择题(本大题满分18分)本大题共有4题,每题都给出四个结论,其中有且只有一个结论是正确的,前两题每题得4分,后两题每题得5分.13.直线倾斜角的取值范围为……()A.π02⎡⎫⎪⎢⎣⎭, B.π02⎡⎤⎢⎥⎣⎦, C.[)0,π D.[]0,π14.两位跳水运动员甲和乙,某次比赛中的得分如下表所示,则正确的选项为……()第一跳第二跳第三跳第四跳第五跳甲85.59686.475.994.4乙79.58095.794.0586.4A.甲和乙的中位数相等,甲的均分小于乙B.甲的均分大于乙,甲的方差大于乙C.甲的均分大于乙,甲的方差等于乙D.甲的均分大于乙,甲的方差小于乙15.已知等差数列{}n a ,公差为d ,12()f x x a x a =-+-,则下列命题正确的是……()A.函数()y f x =(x ∈R )可能是奇函数B.若函数()y f x =(x ∈R )是偶函数,则0d =C.若0d =,则函数()y f x =(x ∈R )是偶函数D.若0d ≠,则函数()y f x =(x ∈R )的图像是轴对称图形16.已知四面体ABCD ,AB BC =,AD CD =.分别对于下列三个条件:①AD BC ⊥;②AC BD =;③2222AB CD AC BD +=+,是AB CD ⊥的充要条件的共有几个……()A.0B.1C.2D.3三.解答题(本大题满分78分)本大题共有5题,解答下列各题必须写出必要的步骤.17.(本题满分14分)本题共有2个小题,第1小题6分,第2小题8分.已知三角形ABC ,1CA CB ⋅=- ,三角形的面积12S =,(1)求角C 的值;(2)若3sin cos 4A A =,求c .18.(本题满分14分)本题共有2个小题,第1小题6分,第2小题8分.已知数列{}n a 的前n 项和为n S ,2n S n n =+,其中n N ∈,1n ≥.(1)求{}n a 的通项公式;(2)求数列11n n a a +⎧⎫⎨⎬⎩⎭的前n 项和n H .19.(本题满分14分)本题共有2个小题,第1小题6分,第2小题8分.中国历史悠久,积累了许多房屋建筑的经验.房梁为柱体,或取整根树干而制为圆柱形状,或作适当裁减而制为长方体形状,例如下图所示.(图片引自梁思成《营造法式.注释》卷五)材质确定的梁的承重能力取决于截面形状,现代工程科学常用抗弯截面系数W 来刻画梁的承重能力.对于两个截面积相同的梁,称W 较大的梁的截面形状更好.三种不同截面形状的梁的抗弯截面系数公式,如下表所列,圆形截面正方形截面矩形截面条件r 为圆半径a 为正方形边长h 为矩形的长,b 为矩形的宽,h b>抗弯截面系数31π4W r =3216W a =2316W bh =(1)假设上表中的三种梁的截面面积相等,请问哪一种梁的截面形状最好?并具体说明;(2)宋朝学者李诫在《营造法式》中提出了矩形截面的梁的截面长宽之比应定为3:2的观点.考虑梁取材于圆柱形的树木,设矩形截面的外接圆的直径为常数D ,如下图所示,请问:h b 为何值时,其抗弯截面系数取得最大值,并据此分析李诫的观点是否合理.20.(本题满分18分)本题共有3个小题,第1小题4分,第2小题6分,第3小题8分.抛物线24y x =上有一动点(),P s t ,0t >.过点P 作抛物线的切线l ,再过点P 作直线m ,使得m l ⊥,直线m 和抛物线的另一个交点为Q .(1)当1s =时,求切线l 的直线方程;(2)当直线l 与抛物线准线的交点在x 轴上时,求三角形OPQ 的面积(点O 是坐标原点);(3)求出线段PQ 关于s 的表达式,并求PQ 的最小值.21.(本题满分18分)本题共有3个小题,第1小题4分,第2小题6分,第3小题8分.已知()e x x f x =,()ln xg x x=.(1)求函数()y f x =、()y g x =的单调区间和极值;(2)请严格证明曲线()y f x =、()y g x =有唯一交点;(3)对于常数10,e a ⎛⎫∈ ⎪⎝⎭,若直线y a =和曲线()y f x =、()y g x =共有三个不同交点()1,x a 、()2,x a 、()3,x a ,其中123x x x <<,求证:1x 、2x 、3x 成等比数列.2023-2024学年第一学期高三年级质量调研数学参考答案一.填空题(本大题满分54分)本大题共有12题,只要求直接填写结果,前六题每题得4分,后六题每题得5分.(1)()2,3-(2)()1,8(3)2(4)12-(5)32(6)152(7)12(8)4240x (9)3-(10)611(11)83(12)275二.选择题(本大题满分18分)本大题共有4题,每题都给出四个结论,其中有且只有一个结论是正确的,前两题每题得4分,后两题每题得5分.(13)C(14)B(15)D(16)C三.解答题(本大题满分78分)本大题共有5题,解答下列各题必须写出必要的步骤.17.(本题满分14分)本题共有2个小题,第1小题6分,第2小题8分.解(1)1cos 1CA CB ab C ⋅=-⇒=-,1sin 12S ab C =⇒=,两式相除得:tan 1C =-,所以3π4C =.(2)sin cos sin 222A A A =⇒=,所以π6A =或π3(舍),所以π6A =所以π12B =,62sin 4B =由正弦定理得,sin sin a c C A =,sin sin b c C B=,所以22sin sin sin abc C A B=,由(1)ab =,所以22c =即c =18.(本题满分14分)本题共有2个小题,第1小题6分,第2小题8分.解(1)()()221112n n S n n S n n n -=+⇒=-+-≥()122n n n a S S n n -=-=≥,又112a S ==,所以2n a n =.(2)1111141n n a a n n +⎛⎫=- ⎪+⎝⎭,所以n H 111111142231n n ⎛⎫=-+-- ⎪+⎝⎭+……+,所以()1114141n nH n n ⎛⎫=- ⎪++⎝⎭=.19.(本题满分14分)本题共有2个小题,第1小题6分,第2小题8分.解:(1)假设截面面积均为正常数S,31π=44S W r r ===,321666S W a a ===,23166S W bh h ==,所以326W W =>==,又因为3<π,所以,所以21W W >,综上,321W W W >>,于是矩形截面的梁的截面形状最好.(2)()()322223110666b D b W bh b D b b -+==-=>,导函数22336b D W -+'=,所以当b =时,3W 取到最大值,此时h =: 2.83:2h b =≈,:3:2h b =的结论与抗弯系数理论的结论不同,但比较接近,是合理的,应肯定李诫从实践中总结的经验的实用价值.20.(本题满分18分)本题共有3个小题,第1小题4分,第2小题6分,第3小题8分.解(1)因为0st >,所以(),P s t在曲线y =y '=l,所以l的直线方程为)y x s -=-,将1s =代入,则l 的直线方程为1y x =+.(2)设()22,Q x y ,将()1,0-代入方程)y x s -=-,得1s =,而直线m的方程为)y x s -=-,将1s =代入,则直线m 的方程为3y x =-+,联立24y x =,则24120y y +-=,由韦达定理得124y y +=-,而12y t ===,所以26y =-,所以三角形OPQ 的面积()1326122S =⋅⋅--=⎡⎤⎣⎦.(3)设()22,Q x y,)y x s -=-联立方程24y x =,得2840y y s +--=,因为t =,所以2y =-,所以244x s s=++,因为(,P s,44,Q s s ⎛++- ⎝,所以()322116s PQ s +=.对于2133231s u s s s -+==+,55233321213332s u s s s ---⎛⎫'=-+=-- ⎪⎝⎭,因为2s =,0u '=;02s <<,0u '<;2s >,0u '>,所以2133min 22u -=+,2316=PQ u ,()213332min 131622163210842=PQ -⎛⎫+=+++= ⎪⎝⎭,min PQ =.21.(本题满分18分)本题共有3个小题,第1小题4分,第2小题6分,第3小题8分.解(1)对于()y f x =,()1xx f x e -'=,对于()y g x =,()21ln xg x x -'=,严格增区间(],1-∞;严格减区间[)1+∞,;严格增区间(]0e ,;严格减区间[)e +∞,;1x <1x =1x >()0f x '>()0f x '=()0f x '>极大值0e x <<e x =e x >()0g x '>()0g x '=()0g x '>极大值极大值为1e极大值为1e(2)对于函数()()y f x g x =-,()0,x ∈+∞,设()()()h x f x g x =-,()211ln e x x xh x x--'=-,当[]1,e x ∈时,()0h x '<,严格递减,()()111110e h h e e e e -⎛⎫=⋅-< ⎪⎝⎭,存在一个零点0x ;当()0,1x ∈时,()0f x >,()0g x <,()()()0h x f x g x =->,无零点;当()e,+x ∈∞时,由(1)得1()e g x <,ln 1xx<,所以1ln x x e <<<,所以()()ln ()f x f x g x <=,所以()()()0h x f x g x =-<,无零点;综上所述,曲线()y f x =、()y g x =有唯一交点,且横坐标()01,x e ∈.(3)因为()y f x =在()0,1上严格单调递增,值域为10,e ⎛⎫ ⎪⎝⎭,所以y a =和()y f x =在()0,1x ∈上有一个交点,同理y a =和()y f x =在()1,+∞上有另一个交点;因为()y g x =在()1,e 上严格单调递增,值域为10,e ⎛⎫ ⎪⎝⎭,所以y a =和()y g x =在()1,e 上有一个交点,同理y a =和()y g x =在(),e +∞上有另一个交点,由题意,共有三个不同交点,则上述四个交点中有两个重合,于是y a =和()y f x =交点横坐标为1x 、2x ,y a =和()y g x =交点横坐标为2x 、3x ,其中()10,1x ∈,()21,x e ∈,()3,x e ∈+∞,由题意12312223ln ln x x x x x x e e x x ===,而222ln 2ln ln x x x x e=,因为()10,1x ∈、()2ln 0,1x ∈,又因为()y f x =在()0,1上严格单调递增,所以12ln x x =即12x x e =,同理23ln x x =,综上,113322ln x x x e x x x ==,所以1x 、2x 、3x 成等比数列.。
2013年高三物理教学质量检测试卷(第三次) 第I 卷(共56分)考生注意:满分150分。
考试时间120分钟。
请在答题纸上答题。
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.下列现象中,与原子核内部变化有关的是 (A )α粒子散射现象 (B )天然放射现象 (C )光电效应现象 (D )原子发光现象2.用单色光做单缝衍射实验,在屏幕上出现衍射条纹后,仅减小缝宽,则 (A )无法发生明显衍射现象 (B )中央明条纹宽度增加 (C ) 中央明条纹宽度减小 (D )中央明条纹宽度不变3.关于分子引力f 引和分子斥力f 斥与分子间距离r 的关系的说法中,正确的是 (A )当r 越小时,f 引越大,f 斥越小 (B )当r 越大时,f 引越大,f 斥越小 (C )无论r 多大,f 引总是小于f 斥 (D )当r 增大时,f 引和f 斥都会减小4.某学生在体育场上抛出铅球,不计阻力,其离手后运动轨迹如图所示。
则关于各点速度和加速度说法中正确的是 (A )v B >v C(B )v A >v D (C )各点加速度不同 (D )各点加速度相同5.如图,物体M 的各表面光滑,上表面水平,放在固定的斜面上。
在M 的水平上表面放一光滑小球m ,后释放M ,则小球在碰到斜面前的运动轨迹是(A )沿斜面向下的直线 (B )竖直向下的直线 (C )无规则的曲线 (D )抛物线6.如图所示,A 、B 分别表示某一个门电路两个输入端的信号,Z 表示该门电路输出端的信号,则根据它们的波形可以判断该门电路是(A )“与”门 (B )“或”门(C )“非”门 (D )“与非”门7.用等长的两根绳吊起一重物,使重物保持静止状态,如图所示。
设两根绳子的张力大小为T ,两个张力的合力为F ,当悬挂点A 、B 同时缓缓向左、右移开,使两根绳之间的夹角α渐渐增大,则 (A )T 逐渐增大,F 也逐渐增大 (B )T 逐渐增大,F 逐渐减小 (C )T 逐渐增大,F 大小不变 (D )T 逐渐减小,F 也逐渐减小8.从地面以大小为v 1的初速度竖直向上抛出一个皮球,经过时间t 皮球落回地面,落地时皮球速度的大小为v 2。
嘉定区2011学年高三年级第一次质量调研试卷参考答案一、选择题(每题2分,共10分)1D 2D 3C 4C 5A二、选择题(每题3分,共36分)6D 7C 8B 9C 10C 11C 12A 13C 14B 15 A 16 D 17B三、选择题(每题4分,共20分)18BC 19AC 20AC 21 C 22 AD四.(8分)23.3s23p2(1分);不稳定(1分);分子(1分)。
24.N2O、NO、N2O3、NO2 N2O4、N2O5(1分)(漏2个就不得分)。
25.Al(OH)33++3OH- (1分);略(写出Fe2O3、Fe3O4、FeO均得分)(1分)。
26.bc(2分)(选对1个得1分,错选不得分)五、(8分)27.Fe2(SO4)3(1分)28.SnC12→SnC14(2分)2e29.Fe2(SO4)3+SnC12+2HC1→2FeSO4+SnC14+H2SO4(3分)(方程式1分、配平1分、电子转移方向数目1分)30.1:2(2分)六、(8分)31.>;D。
(2分)32. c(2分)33.防止合成塔中的催化剂中毒(1分);低温、高压。
(1分)(漏1个不得分)34. cd (2分)七、(14分)35. (2分)4、5 ;2、3(漏1个不得分)36.(2分)尖嘴,a+2037.(2分)淀粉碘化钾;用玻璃棒蘸取溶液,滴在(干的)pH试纸上,并与标准比色卡比较38.(1)1、2、4、5 (2分)(漏2个不得分)(2)AC(2分)(漏1个得1分,错选不得分)39.①温度计水银球位置没有放在蒸馏烧瓶的支管口②冷凝管中的水流方向错误③加热时在烧杯上没有垫石棉网(3分)40.蒸馏烧瓶、酒精灯(1分)(漏1个不得分)八、(10分)41. A Cl2 (2分)42. 干燥混合气体(1分)43. 除去过量氯气(1分)44. CD (2分)45. C (1分)46.分液AB (3分)九、(本题9分)47 (苯环或苯基);—OH(羟基);—COOH(羧基) (3)48①、②、③、④……………………………………………………共2分(漏1个扣1分)49……………………………2分50…2分(其他合理答案给分)十、(本题11分)51. C9H6O2(1分) 52. 4mol(1分)53. 2-氯甲苯(邻氯甲苯) ;取代反应(2分)54. (2分)55. 4;对甲基苯酚(2分)56.(共3分)4①②十一.(本题16分)57. 78% (2分)58. 0.2 (2分) 3.0g (2分)59. 75;(2分)NaHSO3: 0.1mol (2分)和Na2SO3: 0.05mol (2分)(没有过程不得分)60. ①22400a/(21-b) (2分)②7% (2分) (没有过程不得分)。
《狼图腾》 ——姜戎一部关于狼的史诗性著作,一部对中国历史进行独特解读的小说 姜戎:用半条命著《狼图腾》 1.北京某大学研究人员。
主攻政治经济学,偏重政治学。
2.1967年自愿赴内蒙古额仑草原插队 ,十一年间与狼亲密接触。
3.潜心研究30年,埋头写作整6年,写就一部全面研究狼,描绘狼,与狼共舞,人狼合一,以狼为叙事主体的小说。
4.2004年4月问世,长期占据国内畅书排行榜的首位。
《狼图腾》故事简介 故事的背景发生在20世纪60年代末,中国大陆内蒙古最后一块靠近边境的原始草原。
本书的主人公、一个叫陈阵的北京青年带进了草原。
他亲眼目睹蒙古的女人和小孩与偷袭羊群的狼徒手搏斗。
也曾误入狼群、并亲眼看见群狼怎样在头狼的指挥下,调兵遣将围猎几百只黄羊。
但是,人却抢了狼储存的食物。
为了报复人的贪婪,狼利用冬季风雪和夏季蚊灾的掩护,发动了两次大规模的偷袭军马群的残酷而壮烈的战役。
于是人又被激怒了。
来自于农耕民族的干部不顾蒙古牧民的反对,开始了大规模的围猎狼群的战斗。
狼在死亡前的尊严和牺牲精神震撼了陈阵。
陈和他的朋友亲自掏了一窝小狼,并且养了其中的一只。
他要通过一只小狼的成长,探索狼的习性和狼的哲学。
陈阵发现狼是动物中唯一不可驯服的、十分神秘的动物。
进而又发现蒙古民族不仅将狼作为自己民族的图腾崇拜的对象,而且,死后又将自己的尸体放到狼出没的地方,实施“天葬”。
蒙古牧民相信狼会将他们的灵魂带上“腾格里”。
陈阵和他的来自于北京的青年朋友,因为狼的缘故和牧民融为一片。
但是,他们无法阻挡来自于农耕文化和文革时期的错误政策对草原生态的破坏。
他们首先用现代武器杀狼,将仅存的狼驱赶到边境外。
进而,大片的开垦草原土地。
几年以后,草原上鼠害横行,大片的草原沙化。
在作品的最后,也就小说的尾声,来自于蒙古草原的沙尘暴已经遮天避日地肆虐北京,浮尘甚至飘过大海,在日本和韩国的天空游荡…… “旷世奇书” “精神盛宴”遇事机敏,处事果敢,善于智谋,坚毅顽强,团结一致,组织严密,纪律严明。
2011学年嘉定区高三年级第一次质量调研数学试卷(文)考生注意:1.答题前,务必在答题纸上将学校、班级、姓名等信息填写清楚,并贴好条形码.2.解答试卷必须在答题纸规定的相应位置书写,超出答题纸规定位置或写在试卷上的答案一律无效.3.本试卷共有23道试题,满分150分,考试时间120分钟.一.填空题(本大题满分56分)本大题共有14题,考生应在答题纸相应编号的空格内直接填写结果,每个空格填对得4分,否则一律得零分. 1.若C z ∈,且i z i 2)1(=⋅-,则=z ____________.2.在等差数列}{n a 中,35=a ,26-=a ,则}{n a 的前10项和=10S ___________. 3.函数xx x f 11)(=(0≥x )的反函数=-)(1x f ___________________.4.方程1)21(log 2-=-x 的解=x __________.5.在直角坐标系xOy 中,O 为坐标原点,点)1,2(A ,),5(y B ,若AB OA ⊥,则=y _____.6.已知集合}3||{<=x x A ,}023{2>+-=x x x B ,则集合A x x ∈{且}B A x ∉=___________________.7.若某校老、中、青教师的人数分别为80、160、240,现要用分层抽样的方法抽取容量为60的样本参加普通话测试,则应抽取的中年教师的人数为_____________.8.若双曲线122=-ky x 的焦点到渐近线的距离为22, 则实数k 的值为____________.9.在一个小组中有5名男同学,4名女同学,从中任意 挑选2名同学参加交通安全志愿者活动,那么选 到的2名都是女同学的概率为_____________ (结果用分数表示).10.如图所示的算法框图,则输出S 的值是_________.否1←S 结束开始10←k 输出S 1-←k k是k S S ⨯← 8≤k11.一个扇形的半径为3,中心角为2π,将扇形以一条半径所在直线为轴旋转一周所成的几何体的体积是_________________. 12.函数x x x f cos )(2-=,⎥⎦⎤⎢⎣⎡-∈2,2ππx 的值域是________________. 13.如图,在平面直角坐标系xOy 中,圆 222r y x =+(0>r )内切于正方形ABCD ,任取圆上一点P ,若OB b OA a OP ⋅+⋅=(a 、R b ∈),则a 、b 满足的一个等式是______________________.14.将正整数排成三角形数表:1 2,3 4,5,6 7,8,9,10……按上面三角形数表排成的规律,数表中第n 行所有数的和为______________.二.选择题(本大题满分20分)本大题共有4题,每题有且仅有一个正确答案,考生应在答题纸的相应编号上,将代表答案的小方格涂黑,选对得5分,否则一律得零分. 15.若集合}4,3,2,1{=P ,},50{R x x x Q ∈<<=,则“P x ∈”是“Q x ∈”的( )A .充分非必要条件B .必要非充分条件C .充分必要条件D .既不充分也不必要条件16.二次函数c bx ax y ++=2中,0<ac ,则函数的零点个数是( )A .1B .2C .0D .无法确定 17.若0<ab ,且0>+b a ,则以下不等式中正确的是( ) A .011<+ba B .b a -> C .22b a < D .||||b a > 18.直线01cos =-+y x θ(R ∈θ且πθk ≠,Z k ∈)与圆12222=+y x 的位置关系是( )A .相交B .相切C .相离D .无法确定A BC DOyx三.解答题(本大题满分74分)本大题共有5题,解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤. 19.(本题满分12分)本题共有2个小题,第1小题满分5分,第2小题满分7分. 如图,在直三棱柱111C B A ABC -中,2=AB ,41==AA AC ,︒=∠90ABC . (1)求三棱柱111C B A ABC -的表面积S ;(2)求异面直线B A 1与AC 所成角的大小(结果用反三角函数表示).20.(本题满分14分)本题共有2个小题,第1小题满分6分,第2小题满分8分. 如图,设A 是圆122=+y x 和x 轴正半轴的交点,P 、Q 是圆上的两点,O 是坐标原点,6π=∠AOP ,α=∠AOQ ,),0[πα∈.(1)若点Q 的坐标是⎪⎭⎫⎝⎛54,53,求⎪⎭⎫ ⎝⎛-6cos πα的值; (2)设函数OQ OP f ⋅=)(α,求)(αf 的值域.21.(本题满分14分)本题共有2个小题,第1小题满分5分,第2小题满分9分. 已知曲线C 的方程为122=+ay x (R a ∈). (1)讨论曲线C 所表示的轨迹形状;(2)若1-≠a 时,直线1-=x y 与曲线C 相交于两点M ,N ,且2||=MN ,求曲线C的方程.A B C A 1 B 1 C 1 Oy P QxA22.(本题满分16分)本题共有3个小题,第1小题满分4分,第2小题满分6分,第3小题满分6分.定义1x ,2x ,…,n x 的“倒平均数”为nx x x n+++ 21(*N n ∈).(1)若数列}{n a 前n 项的“倒平均数”为421+n ,求}{n a 的通项公式;(2)设数列}{n b 满足:当n 为奇数时,1=n b ,当n 为偶数时,2=n b .若n T 为}{n b 前n 项的倒平均数,求n n T ∞→lim ;(3)设函数x x x f 4)(2+-=,对(1)中的数列}{n a ,是否存在实数λ,使得当λ≤x 时,1)(+≤n a x f n对任意*N n ∈恒成立?若存在,求出最大的实数λ;若不存在,说明理由. 23.(本题满分18分)本题共有3个小题,第1小题满分4分,第2小题满分6分,第3小题满分8分.已知函数)(||)(a x x x f -⋅=. (1)判断)(x f 的奇偶性;(2)设函数)(x f 在区间]2,0[上的最小值为)(a m ,求)(a m 的表达式; (3)若4=a ,证明:方程04)(=+xx f 有两个不同的正数解.2011学年嘉定区高三年级第一次质量调研数学试卷(文)参考答案与评分标准一.填空题1.i +-1;2.5;3.1+x (1-≥x );4.1-;5.5-;6.}21{≤≤x x ;7.20;8.8;9.61;10.90;11.π18;12.⎥⎦⎤⎢⎣⎡-4,12π;13.2122=+b a ;14.23n n +. 二.选择题15.A ;16.B ;17.A ;18.C .三.解答题 19.(1)在△ABC 中,因为2=AB ,4=AC ,︒=∠90ABC ,所以32=BC .…………(1分)3221=⋅⋅=∆BC AB S ABC .………………(1分)所以侧S S S ABC +=∆21)(2AA AC BC AB S ABC ⋅+++=∆4)4322(34⋅+++=31224+=.…………(3分) (2)连结1BC ,因为AC ∥11C A ,所以11C BA ∠就是异面直线B A 1与AC 所成的角(或其补角).…………(1分)在△11BC A 中,521=B A ,721=BC ,411=C A ,…………(1分)由余弦定理,1052cos 111212112111=⋅⋅-+=∠C A B A BC C A B A C BA ,…………(3分) 所以105arccos11=∠C BA .…………(1分) 即异面直线B A 1与AC 所成角的大小为105arccos .……(1分) 20.(1)由题意,点P 的坐标是⎪⎪⎭⎫⎝⎛21,23,点Q 的坐 标是)sin ,(cos αα,……(1分) 所以53cos =α,54sin =α,……(2分) 所以⎪⎭⎫⎝⎛-6cos πα6sin sin 6cos cos παπα+=1033421542353+=⨯+⨯=.……(3分) (2)由题意,αααααsin 21cos 23)sin ,(cos 21,23)(+=⋅⎪⎪⎭⎫⎝⎛=f ⎪⎭⎫ ⎝⎛+=3sin πα,……(3分)A B CA 1B 1C 1因为),0[πα∈,所以⎪⎭⎫⎢⎣⎡∈+34,33πππα,…………(2分) 所以⎥⎦⎤ ⎝⎛-∈⎪⎭⎫ ⎝⎛+1,233sin πα.即函数)(αf 的值域是⎥⎦⎤ ⎝⎛-1,23.…………(3分)21.(1)当0<a 时,曲线C 的轨迹是焦点在x 轴上的双曲线;……(1分) 当0=a 时,曲线C 的轨迹是两条平行的直线1=x 和1-=x ;……(1分) 当10<<a 时,曲线C 的轨迹是焦点在y 轴上的椭圆; …………(1分) 当1=a 时,曲线C 的轨迹是圆122=+y x ; …………(1分) 当1>a 时,曲线C 的轨迹是焦点在x 轴上的椭圆. …………(1分) (2)由⎩⎨⎧=+-=1122ay x x y ,得012)1(2=-+-+a ax x a ……① …………(2分)因为1-≠a ,所以方程①为一元二次方程,△04)1)(1(442>=-+-=a a a ,所以直线l 与曲线C 必有两个交点. …………(1分)设),(11y x M ,),(22y x N ,则1x ,2x 为方程①的两根,所以1221+=+a a x x ,1121+-=a a x x , …………(1分)所以221221221)(2)()(||x x y y x x MN -=-+-=21141224)(2221221=+-⋅-⎪⎭⎫⎝⎛+⋅=-+⋅=a a a a x x x x ,……(2分) 所以0322=-+a a ,解得1=a 或3-=a . ……(2分)因此曲线C 的方程为122=+y x 或1322=-y x . ……(1分)22.(1)设数列}{n a 的前n 项和为n S ,由题意,421+==n S n T n n , 所以n n S n 422+=. …………(1分)所以611==S a ,当2≥n 时,241+=-=-n S S a n n n ,而1a 也满足此式.……(2分) 所以}{n a 的通项公式为24+=n a n .…………(1分) (2)设数列}{n b 的前n 项和为n S ,则当n 为偶数时,23nS n =,……(1分) 当n 为奇数时,21312)1(3-=+-=n n S n . …………(1分) 所以⎪⎪⎩⎪⎪⎨⎧-=为奇数当为偶数当n n n n T n ,132,32. ……(3分)所以32lim =∞→n n T . ……(2分)(3)假设存在实数λ,使得当λ≤x 时,1)(+≤n a x f n对任意*N n ∈恒成立,则12442++≤+-n n x x 对任意*N n ∈恒成立,…………(1分) 令124++=n n c n ,因为0)2)(1(21>++=-+n n c c n n ,所以数列}{n c 是递增数列,…(1分)所以只要124c x x ≤+-,即0342≥+-x x , 解得1≤x 或3≥x .…………(2分)所以存在最大的实数1=λ,使得当λ≤x 时,1)(+≤n ax f n 对任意*N n ∈恒成立.(2分)23.(1)0=a 时,)(x f 是奇函数;……(2分)0≠a 时,)(x f 既不是奇函数也不是偶函数.……(2分)(2)当]2,0[∈x 时,42)(222a a x ax x x f -⎪⎭⎫ ⎝⎛-=-=,函数)(x f 图像的对称轴为直线2ax =.……(1分) 当02<a,即0<a 时,函数)(x f 在]2,0[上是增函数,所以0)0()(==f a m ;…(1分) 当220≤≤a,即40≤≤a 时,函数)(x f 在]2,0[a 上是减函数,在]2,2[a 上是增函数,所以4)2()(2a a f a m -==;……(1分)当22>a,即4>a 时,函数)(x f 在]2,0[上是减函数, 所以a f a m 24)2()(-==.……(1分)综上,⎪⎪⎩⎪⎪⎨⎧>-≤≤-<=4,2440,40,0)(2a a a aa a m .……(2分) (3)证法一:若4=a ,则0>x 时,x x x f 4)(2-=,方程可化为0442=+-xx x , 即x x x442+-=.……(2分) 令xx g 4)(=,x x x h 4)(2+-=,在同一直角坐标系中作出函数)(x g )(x h 在0>x 时的图像.…………(2分)因为2)2(=g ,4)2(=h ,所以)2()2(g h >,即当2=x 时O xy2函数)(x h 图像上的点在函数)(x g 图像点的上方.……(3分) 所以函数)(x g 与)(x h 的图像在第一象限有两个不同交点. 即方程04)(=+xx f 有两个不同的正数解.…………(1分) 证法二:若4=a ,则0>x 时,x x x f 4)(2-=,方程可化为0442=+-xx x , 即xx x 442-=-.…………(2分) 令xx g 4)(-=,在同一直角坐标系中作出函数)(x f ,)(x g 在0>x 时的图像.……(2分) 因为4)2(-=f ,2)2(-=g ,所以)2()2(-<-g f , 即当2=x 时,函数)(x f 图像上的点在 函数)(x g 图像点的上方.…………(3分)所以函数)(x f 与)(x g 的图像在第四象限有两个不同交点. 所以方程04)(=+xx f 有两个不同的正数解.…………(1分)y Ox2。
2023学年高三年级第一次质量调研英语试卷(满分140分考试时间120分钟)I.Listening ComprehensionSection A(10分)Directions:In Section A,you will hear fen short conversations between two speakers.At the end of each conversation,a question will be asked about what was said.The conversations and the questions will be spoken only once.After you hear a conversation and the question about it, read the four possible answers on your paper and decide which one is the best answer to the question you have heard.1.A.In a leadership training center. B.In a student consulting office.C.At an indoor basketball court.D.At a science development lab.2.A.Dietician and client. B.Waitress and diner.C.Boss and secretary.D.Librarian and reader.3.A.3,600dollars. B.6,000dollars. C.1,200dollars. D.4,800dollars.4.A.The park was closed due to a severe accident.B.The boy got injured in the roller coaster ride.C.A child was not feeling well after the ride.D.Many students thought the park was nasty.5.A.Buy electronic devices. B.Do some housework.C.Repair the car.D.Go window shopping.6.A.Schedules of a negotiation. B.Orders with the suppliers.yout of the presentation.D.Preparations for a meeting.7.A.She doesn't know the requirements of the essay.B.She feels stuck while proceeding with her essay.C.She has difficulty in drafting when walking.D.She is unable to give the man some ideas.8.A.Set fewer goals next year to avoid struggling.e up with a plan to motivate themselves.C.Monitor habit-forming behaviours for each other.D.Join an organization to check in on their progress.9.A.Dressing professionally improves his thinking.B.Wearing a tie helps him fit in the company.C.Looking handsome is what he pursues.D.Buying the shirt costs him a fortune.10.A.The man desires a room with a view of mountains.B.The hotel offers the man a tempting alternative.C.Few customers can receive an upgraded service.D.The woman demands the man give an apology.Section B(15分)Directions:In Section B,you will hear two passages and one longer conversation.After each passage conversation,you will be asked several questions.The passages and the conversation will be read twice,but the questions will be spoken only once.When you hear a question,read the four possible answers on your paper and decide which one is the best answer to the question you have heard.Questions11through13are based on the following passage.11.A.Increase of gravity. B.Physical training.C.Water resistance.D.Sense of isolation.12.A.8. B.17. C.Over200 D.About100.13.A.The training for astronauts is very demanding.B.It has been10years since China sent a man to space.C.Astronauts will change suits every six hours in space.D.Three months is the minimum training time for astronauts.Questions I4through16are based on the following passage.14.A.About10,000birds were killed.B.The blue sky was the key cause of the hitting.C.Birds were drawn by the lights from the building.D.MeCormick Place was closed because of the hitting.15.A.Draw curtains during the day. e materials that don't attract birds.C.Change colors of the building.D.Apply environment-friendly stickers.16.A.Unusual B.Inevitable. C.Beneficial. D.Tragic. Questions17through20are based on the following conversation.17.A.Preparations to make for the tutoring.B.Promises to their physics teachers.C.Solutions to their respective problems.D.Apologies to give for the dollhouse.18.A.She has missed half-an-hour training.B.She hasn't entered for the after-school tutoring.C.She has to hand in the assignment on Wednesday.D.She is unable to deal with the physics homework.19.A.It involves complex architectural planning.B.It requires buying expensive wood supplies.C.It needs some features like adding windows.D.It must be exactly like his sister's old dollhouse.20.A.Beg his sister for forgiveness. B.Check whether Mr.Brown has time.C.Hire a professional carpenter.D.Piece together the broken dollhouse. II.Grammar and VocabularySection A(10分)Directions:After reading the passage below,fill in the blanks to make the passages coherent and grammatically correct.For the blanks with a given word,fill in each blank with the proper form of the given word;for the other blanks,use one word that best fits each blankSeeing Math on the PageMath and literature are probably two of the subjects that bring students headaches.However, scientists wonder(21)_____the beauty of math can be found in literary works.Once Upon a Prime: The Wondrous Connections between Mathematics and Literature,a book published recently by UK mathematician Sarah Hart,(22)______(present)some interesting thoughts about"three".She argues that the beauty of this number is indeed evident in many works of western literature and languages in general.‘Three’is the minimum number(23)_____a two-dimensional shape can be defined.For example, three sticks can create a triangle,a stable structure.Many common phrases are in three words, such as"ready,set,go".Being the first things kids may learn,some nursery rhymes have a word (24)________(repeat)three times,such as"row,row,row your boat".In stories,there are usually three main characters,such as Harry,Ron and Hermione in the Harry Potter series.For a series of novels,there are usually three books(25)________________four,according to Hart.Why is it always the third son who behaves differently from his two older brothers,thus (26)_______(win)the princess?"The reason for this,"Hart explains,"is obvious.We require two repetitions to get to know the pattern,(27)__________the breaking of the pattern in the third character can surprise or amuse us."Similarly,another study by researchers at the University of Vermont also connected math and storytelling.They analyzed more than1,300fiction books and arranged for10,000words from the books(28)____________(rate)by50participants on a happiness scale of1to9.Then the ratings(29)_(categorize)into different graphs,which showed how the readers'emotions changed while reading.It turned out that each story fit perfectly into one of six basic graphs,a mathematical pattern.“The idea that one would(30)_____choose between mathematics and literature is something of a tragedy,"Hart says,"The two fields are fundamentally linked".Section B(10分)Directions:After reading the passage below,fill in each blank with a proper word given in the box.Each word can be used only once.Note that there is one more word than you need.A.ballooning.B.frost-intolerant.C.directly.D.contributors.E.eruptedF.conditions.G.shadedH.sensor-equippedI.engineeringJ.situatedK.properlyFarm of the Future in the SkyFive storeys off the ground at Colorado State University,a highly unlikely garden grows under a long row of rooftop solar panels.It's late November at9am,when the temperature is-2℃and the wind is cutting.Not long before my arrival,researchers had pulled the last__31__crops out of the soil under the panels.In their place,cool-season foods like leafy greens still grow, __32_from the intense sunlight up there.This is no ordinary green roof,but an expansive and___33____outdoor laboratory.The idea behind it is explained by Jennifer Bousselot,the director of the rooftop farm.Solar panels tend to get too hot on conventional roof tops,and that heat reduces their efficiency while plants help cool them off."If you have plants under there,"Bousselot said,"they create ideal___34____for solar panels to operate.Also,the shade of the panels encourages the growth of plants.A win-win solution."Therefore,the overall goal of the rooftop farm is to grow more food for___35___urban populations while generating clean energy and making buildings more energy efficient.Without the sun beating down__36_on a bare roof,green roofs boost a building's energy efficiency by about10percent.That is,you don't need to run as much air-conditioning to__37___cool the place during a heat wave.This innovative approach can also maximize land use,making urban spaces not just consumers of resources,but also active___38___to both energy and agricultural production.However,being__39___on a rooftop comes with more challenges than a typical farming site. The wind loads on a roof make it challenging to install a tracking system and irrigation(灌溉)is also trickier.The expenses are substantially increased due to higher__40___costs and the difficulties of moving and installing all the sensors and materials high in the air.It is obviously early days for rooftop farms,but some effects were already evident.Instead of being big,dead spaces,roofs may act as booming ecosystems.III.Reading ComprehensionSection A(15分)Directions:For each blank in the following passage there are four words or phrases marked A,B, C and D.Fill in each blank with the word or phrase that best fits the context.“So…tell me about yourself.”The toughest job interview question may seem like a softball from the interviewer's perspective:It seems___41____because it feels like a free pass:no request for real-life examples, no technical challenge,not even the feared"What's your biggest fault?"Just…tell me anything.Receiving such an open invitation invites more___42____than opportunities,because you'regiven no framework for your response—just a blank,clue-free paper.I often see this__43situation in my point-making workshops:communicating without a point.What your prospective employer most needs from you is a point("T am an important asset(资产)to the company"),not a___44___("All about me").But how do you get from the interviewer's broad question to a specific and___45___point?Start with realizing that your interviewer already knows your job history thanks to your resume(简历).So you should be more than your___46__.Remember that interviews are more about making strong___47__than proving qualifications.This is a two-step process that will require some homework.First,identify what the organization specifically needs from this role. Second,__48_your response to position yourself as the best person to fill that need.Identifying the organization's need means examining the job description like a treasure map. Phrases like“required,”"must have,"and"highly desired"mean what they say,so___49__those in your planning.Items further down the list or labeled"preferred"may be less important,even if you meet those standards.The__50___of a job description can be telling as well.Descriptions that sound personal,or come right out and say"sense of humor preferred"indicate a workplace where people like to have fun.__51_,a very formal job posting might indicate a conservative workplace where people are expected to be serious about the work.Pulling from these soures,write down the three personal qualities they're most looking for like“self-starter,""team player,"or"interest in healthcare".Now change the___52___slightly to "I'm aself-starter"or“At work,my approach is.…."Then pick a story from your professional life that53__you filling that particular need of the job.Feel free to add details,but don't__54___the primary elements.Assume they can smell a lie from a mile away,whether they can or can't.In this way,you should do more than just widen eyes in the room.Why?Because you've matched who you are and your personal story with the company's brand and primary need.You didn't just tell them about you;you pointed out why you___55___to them.41.A.hard B.Easy C.huge D.small42.A.missions B.joys. ments D.risks43.A,unlikely B.favourable. C.problematic petent44.A.book report B.phone call. C.desk lamp D.lunch break45.A.declared B.tailored. C.rejected D.assessed46.A.profile B.criterion C.dimension D.nickname47.A.transitions B.judgments C.matches D.distributions48.A.stabilize B.customize C.memorize D.authorize49.A.diversify B.approve C.delete D,highlight50.A.tone B.format C.picture D.length51.A.For instance B.By contrast C.After all D.In addition52.A.blogging working C.messaging D.wording53.A.illustrates B.suspends C.dismisses D.circulates54.A.make up B.put off C.break down D.get through55.A.submitted B.extended C.mattered D.shifted Section B(22分)Directions:Read the following three passages.Each passage is followed by several questions or unfinished statements.For each of them there are four choices marked A,B,C and D.Choose the one that fits best according to the information given in the passage you have just read.(A)To us,the kitchen was a mysterious place.Our kitchen at home was so simple:an old Sparks oven,a refrigerator,a sink,and a table.At the New Eastern,it was a busy factory.Almost an entire wall wastaken up by a line of huge black woks(锅).This was my father's stage.He strode(大步走)the length of the four woks,each one fired up by gas flames underneath.Beneath him,blocks of wood, raised off the ground an inch or two,served to give his legs and feet some spring.The sink was the size of a bathtub(浴);the refrigerator had glass doors and stretched three times as wide as the one at home.Every appliance was bigger,and there were things we never saw anywhere else,like the big metal oven in which my father hung long poles holding large pieces of pork.We could hear the fire roaring from the bottom of it.My dad would go about his business, and then,always at exactly the right time,he'd wander over,lift off the top,and take out several poles of barbecued pork—bright red,with black at the tips.If I happened by at that magical moment,I'd stop.“Yeet-gow!”I'd say.And he'd skillfully chop off a piece of the juicy,sweet meat.“One dollar!"he'd shout,and then hand it over.My father made the best food in town.There was nothing he wouldn't try.He was once proud of a rock candy he invented and determined to sell at the front counter of the New Eastern.We,of course,served as his guinea pigs—we couldn't bring ourselves to tell him the sad truth:The candy was so hard that it was uneatable.I rolled a piece around my mouth.“Tastes good,Ba-Ba,”I said. Then,when he looked away,I spat it out.Sometimes,he liked to invent stories to us.Watching my little sister Shirley biting on an apple, he'd lean over.“Don't eat the seed,"he said,"or an apple tree will grow inside you."“What?”“Yes.Right inside your stomach,an apple tree!”56.It can be learned from paragraph1and2that____________.A.the author's father can repair springsB.the author enjoys observing in the kitchenC.the author helps to cook difficult dishesD.the author's family lives in a busy factory57.How does the author develop the idea that"the kitchen is a mysterious place"?A.By describing how his father manages various tasks in the kitchen.B.By classifying the kitchen appliances into different categories.C.By contrasting the restaurant kitchen with the kitchen at home.D.By explaining why large pieces of pork were placed in the oven.58.The author mentions the incident of a rock candy in paragraph3_____________.A.to highlight how he disliked the food his father madeB.to illustrate why they often kept secrets from his fatherC.to emphasize the troubled relationship with his fatherD.to show the family's support for his father's experiments59.Which of the following words can best describe the author's father?A.dynamic and playfulB.strict and innovativeC.talented and greedyD.hardworking and outdated60.It can be learned from“THE ATTACK”that_______.A.Sandra asks Marcus for his password.B.Marcus steals the key corporate data.C.The attacker gains Marcus's trust first.D.Sandra is a senior director of the bank.61.Which of the following best fits the"?"in step④of“THE DEFENSE"?A.LESSONB.HEALTHC.PROGRAMD.FINANCE62.Which of the following is covered in the case?A.What loss the company has sufferedB.How Marcus regretted receiving the callC.What Natalie has found about the domainD.How effectively Ray responded to the attack(C)New research confirms that human footprints found in New Mexico are probably the oldest direct evidence of human presence in the Americas,a finding that upends what many scientists knew about human habitation and migration(迁徙).The footprints were discovered at the edge of an ancient lakebed in White Sands national park.According to the new paper published in the journal Science,they date back to between21, 000and23,000years ago.Actually,the estimated age of the footprints was first reported in Science in2021,but some researchers raised concerns about the dates.Questions focused on whether seeds of water plants used for the original dating may have absorbed ancient carbon from the lake—which could,in theory,throw off radiocarbon dating by thousands of years.But the new study presents two additional lines of evidence for the older date range.It uses two entirely different materials found at the site,ancient pollen(花粉)and stone grains.The reported age of the footprints challenges the once conventional wisdom that humans did not reach the Americas until a few thousand years before rising sea levels covered the Bering land bridge between Russia and Alaska,perhaps about15,000years ago.“This is a subject that's always been controversial because it's so significant.It's about how we understand the last chapter of the peopling of the world,”said Thomas Urban,an archaeologist(考古学家)at Comell University,who was involved in the2021study but not the new one.Thomas Stafford,an independent archaeological geologist in New Mexico,who was not involved in the study,said he“was a bit suspicious before”but now is convinced.The new study isolated about75,000grams of pure pollen from the same stone layer that contained the footprints. "Dating pollen is laborious but worthwhile,"said Kathleen Springer,a research geologist at the US Geological Survey and a co-author of the new paper.Ancient footprints of any kind can provide archaeologists with a quick look of a moment in time.While some archeological sites in the Americas point to similar date ranges—including necklaces carved from giant animal remains in Brazil—scientists still question whether such objects really indicate human presence.“White Sands is unique because there's no question these footprints were left by people,"said Jennifer Raff,a scientist at the University of Kansas,who was not involved in the study.63.The underlined word"upends”(paragraph1)is closest in meaning to“_______".prisesB.connectsC.challengespares64.According to the passage,what is special about the new research?A.It shows the footprints were made by the Russians.B.It offers more convincing lines of evidence for dating.C.It confirms that the ancient humans enjoyed living by the lake.D.It reveals the footprints are much younger than previously thought.65.It can be inferred from the last paragraph that_____________.A.necklaces are valuable objects for archaeologists to date animalsB.human footprints are often sure signs of human presenceC.ancient objects in Brazil are excluded from the studyD.White Sands is one important archaeological site66.Which of the following might be the best title of the passage?A.Scientists Discovers New Species of Humans in AmericasB.Humans Reached Americas15,000Years Earlier Than BelievedC.American Archaeologists Unearthed Valuable Manmade ObjectsD.New Research Confirms Early Human Presence in AmericasSection C(8分)Directions:Read the following passage.Fill in each blank with a proper sentence given in the box.Each sentence can be used only once.Note that there are two more sentences than you needA.The key is to look for places where improvements were done poorly.B.An experienced agent is probably going to have a better eye than the buyer.C.Is buying one of these quick-turnaround properties a good idea?D.Set aside money for any problems that may crop up or ask the seller to cover them.E.How do you know if the previous owner has moved out of the house?F.Flippers sometimes skip getting permits for the work they do.What to Know If Buying a Flipped HouseHouse flipping is hardly new.For someone who is working in the real estate market,a flipped or recently renovated(翻新的)home can be very appealing.But how about you,the home-hunter?_____67____You certainly don't need to avoid flipped properties.A flipped property does have some strong selling points.A lot of its features and fixtures have been replaced or improved.Certainly, you'll save on the time and trouble of doing the renovation yourself.But there are some things to watch out for if you're considering buying one.____68____For example,Alice recently toured a flipped house whose kitchen drawer was blocked by the refrigerator and the dishwasher wasn't installed correctly-things that would prevent people from being able to function in there.Addressing issues like these can become costly,especially if you haven't factored them into your budget.Don't neglect your right to a professional inspection.____69_____So getting an expert to go take a thorough look at the property is crucial,to make sure everything is up to code.It's going to be really important to do your sewer(下水道)and separate roof inspections.Flipped houses may seem up-to-date on the surface,but shiny new finishes can sometimes mask substandard work. Finally,flipped properties are rarely advertised as such.Therefore,it is crucial to work with aknowledgeable real estate agent.____70____When he tours a house that he suspects is being flipped,he'll check who owned the home previously,and will reach out to other agents in his network to see if anyone has experience buying from them.IV.Summary writing(10分)Directions:Read the following passage.Summarize the main idea and the main point(s)of the passage in no more e your own words as far as possible.Dealing with One Missed WorkoutIt's a common dilemma(图局)for anyone on a training plan:You miss one workout and become awashed with guilt.To make up for it,you add those extra miles to your next workout. But according to the professionals,this isn't the right way to go about it."A single workout is not going to make or break a training plan.The key to training is consistency over time,"says John Raglin,PhD,professor in the Department of Kinesiology at Indiana University Bloomington.When you miss a workout,the temptation is to think,"Oh,I've got to do more tomorrow". But when you try to catch up on your workouts,you run a couple of risks:"Certainly an injury,but also becoming over-tired,which could ruin your training after that,"says Raglin.This is a phenomenon called'non-functional overreaching',"he says.Eventually,this could lead to overtraining syndrome(综合症),which is characterized by a decrease in performance later due to a long-term increase in training load without adequate recovery.So how do you move forward if you skipped a run or five?Well first,people download generalized training plans without understanding that they are meant to be adapted to life.There is a whole host of life stressors—job,kids,friendships,travel—and exercise is just another type of stress.Actually,when things get chaotic in your life,it may be necessary to just let go.Next,if you missed a workout,you have to ask yourself why:"Was it just because your schedule got out of hand or because you were feeling overly exhausted?"Understanding why you missed the workout can offer some insights into how to tailor your program to suit your lifestyle.V.Translation(15分)Directions:Translate the following sentences into English,using the words given in the brackets.72.门后挂着毛巾和睡衣,方便客人使用。
嘉定区2011学年度高三年级第一次质量调研生命科学学科试卷(完卷时间:120分钟,满分150分)2012年1月考生注意:1.本试卷分为第Ⅰ卷和第Ⅱ卷两部分。
全卷共11页。
2.考生应用钢笔或圆珠笔将答案直接写在答题纸上...........,写在试卷上不给分。
第I 卷 (共60分)一、单选题(共60分,每题2分。
每小题只有一个正确选项。
)1.下列各组物质中,由相同种类元素组成的是A .磷脂、脂肪酸、脂肪酶B .淀粉、半乳糖、糖原C .氨基酸、核苷酸、丙酮酸D .DNA 、脱氧核糖、胰岛素2.A 、B 两种酶用同一种蛋白酶处理,酶活性与处理时间的关系如下图所示。
下列分析错误的是A. A 酶能够抗该种蛋白酶降解B. A 酶不可能是具有催化功能的RNAC. B 酶的化学本质为蛋白质D. B 酶活性的改变是因为其分子结构的改变3.下列与激素作用无关的实例是A.草莓果实自然发育成熟B.人舌尖触到蔗糖时感觉甜C.自然生长的雪松树冠呈塔形D.饥饿时人体血糖仍维持正常水平4.据右图回答问题:如果环境剧变或某种植物病害暴发,哪种植物的生存几率最大?A .栽培小麦B .栽培玉米C .野生小麦D .野生玉米5.下列符合现代生物进化理论的叙述是A .物种的形成可以不经过生殖隔离B .生物进化过程的实质在于有利变异的保存C .基因突变产生的有利变异决定生物进化的方向D .自然选择通过作用于个体而影响种群的基因频率6.心理学家研究发现,轻松和愉快会使T 细胞提高对病毒、肿瘤的监控,间接引起抗体生成能力的升高。
这表明不健康的心态会导致A .细胞免疫提高,体液免疫降低B .细胞免疫降低,体液免疫提高C .细胞免疫提高,体液免疫提高D .细胞免疫降低,体液免疫降低7.下列选项中前者为科枝成果,后者为应用原理的是A .单克隆抗体,基因重组B .八倍体小黑麦,染色体畸变C .转基因抗虫棉,基因突变D .无子番茄,染色体畸变8. 下列生殖方式中所产生的后代基因型不同于母体的是A .酵母菌出芽生殖B .花药离体培养C .根霉孢子生殖D .马铃薯块茎繁殖9.SARS 病毒、蓝藻、蝴蝶都属于生物,下面哪项是它们的共同特征①具有细胞结构 ②含生物大分子如核酸、蛋白质 ③能独立完成新陈代谢④都能适应一定的环境 ⑤能繁殖后代A .①②③④⑤B .②③④⑤C .③④⑤D .②④⑤10.将某一个细胞中的磷脂分子全部抽提出来,并将它在空气和水界面上铺成单分子层。
2024学年上海市嘉定区市级名校物理高三第一学期期中质量检测模拟试题注意事项:1.答题前,考生先将自己的姓名、准考证号码填写清楚,将条形码准确粘贴在条形码区域内。
2.答题时请按要求用笔。
3.请按照题号顺序在答题卡各题目的答题区域内作答,超出答题区域书写的答案无效;在草稿纸、试卷上答题无效。
4.作图可先使用铅笔画出,确定后必须用黑色字迹的签字笔描黑。
5.保持卡面清洁,不要折暴、不要弄破、弄皱,不准使用涂改液、修正带、刮纸刀。
一、单项选择题:本题共6小题,每小题4分,共24分。
在每小题给出的四个选项中,只有一项是符合题目要求的。
1、做匀减速直线运动的物体经4s停止,若在第1s内的位移是14m,则最后1s内位移是()A.4.5m B.3.5m C.2m D.1m2、质量为m = 2kg的物体沿水平面向右做直线运动,t = 0时刻受到一个水平向左的恒力F,如图甲所示,此后物体的v− t图像如图乙所示,取水平向右为正方向,g = 10m/s2,则()A.物体与水平面间的动摩擦因数为μ = 0.5B.10s末恒力F的功率为6 WC.10s末物体恰好回到计时起点位置D.10s内物体克服摩擦力做功34 J3、如图所示,两个完全相同的小球分别从水平地面上A点和A点正上方的O点抛出,O点抛出小球做平抛运动,A点斜抛出的小球能达到的最高点与O点等高,且两球同时落到水平面上的B点,关于两球的运动,下列说法正确的是A.两小球应该是同时抛出B.两小球着地速度大小相等C.两小球着地前瞬间时刻,重力的瞬时功率相等D.两小球做抛体运动过程重力做功相等4、在学校体育器材室里,篮球水平放在如图所示的球架上.已知球架的宽度为0.15m,每个篮球的质量为0.4kg,直径为0.25m,不计球与球架之间的摩擦,则每个篮球对球架一侧的压力大小为(重力加速度g=10m/s2)A.4N B.5N C.2.5N D.3N5、某卫星在距月球表面高度为h的轨道上做匀速圆周运动,其运行的周期为T,最终在月球表面实现软着陆.若以R表示月球的半径,引力常量为G,忽略月球自转及地球对卫星的影响,下列说法不正确的是()A.该卫星绕月运行时的向心加速度为22 4R T πB3 2()R R h π+C.月球的质量为2324()R hGTπ+D.物体在月球表面自由下落的加速度大小为23224()R hR Tπ+6、如图所示,质量为m、带电量为q的油滴从空中自由下落时间t1后进入水平放置的带电极板间,再经过t2速度为第一次变为零,则油滴在极板间运动时油滴的加速度大小为(不计空气阻力) ()A .gt 1/(t 1+t 2)B .g(t 1+t 2)/t 2C .gt 1/t 2D .g t 2/t 1二、多项选择题:本题共4小题,每小题5分,共20分。
上海市嘉定区2012届高三第三次模拟考试英语试题2012嘉定三模(可编辑)上海市嘉定区2011―2012学年度高三第三次质量调研英语试题 (120分钟完成; 总分:150分)第I卷 (共 105 分) I. Listening Comprehension Section ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard. 1. A. At home. B. On the farm. C. In a restaurant. D. In a supermarket. 2. A. $6. B. $4.5.C. $5.D. $4. 3.A. A worker at McDonald’s.B. A student.C. Atutor. D. A salesman in a market. 4.A. She didn’t receive th e E-mail.B. She is too busyto check the E-mail. C. Her computer broke down.D. She has replied to his E-mail. 5. A. It’s certainthat they will come to the lecture. B. They won’t come if they don’t call first. C. She is worried aboutit. D. There are plenty of seats for all the people. 6. A. She wishes the teacher could talk more.B. She thinks the teacher has an accent.C. She didn’t always catch the teacher.D. She thinks the teacher should talk louder. 7. A. Shewill pick up Jack at 2:00 in the af ternoon. B. She won’t be able to meet Jack atthe airport. C. She doesn’t want to meet Jack at the airport.D. She doesn’t know when Jack will arrive. 8. A. She is looking for a job in the summer. B. She is eager to go home for the vacation. C. She doesn’t know where to go in summer. D. She doesn’t want to go home in summer. 9. A. The woman goes to work by bike every day. B. The woman used to go to work by bike. C. The woman has bought a new bike. D. The man’s bikewas stolen. 10. A. The man wants to help the woman to find the lunch box. B. The man doesn’t know what todo. C. The man will buy lunch for the woman.D. The man will give the woman a treatment. Section B Directions: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard. Questions 11 through 13 are based on the following passage. 11. A. Keep a high level of care for the people. B. Pay for damage done by dogs.C. Provide medical care for dogs.D. Buy insurance for dog owners.12. A. The owner of the car.B. The owner of the dog.C. The insurance company.D. The government.13. A. Dogs are welcome in public places. B. Keeping dogs means askingfor trouble. C. Many car accidents are caused by dogs.D. People care much about dogs. Questions 14 through 16 are based on the following passage. 14. A. Information research.B. Research for advertising.C. Market research.。
嘉定区2011学年度高三年级第一次质量调研英语试卷2012.1(120分钟完成; 总分:150分)第I卷(共 105 分)I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. At 2:30. B. At 2:00. C. At 1:30. D. At 1:00.2. A. In Beijing. B. In Shanghai. C. In Shenzhen. D. In Chengdu.3. A. She would like to talk at another time. B. She would like the man to continue.C. She wants the man to go away.D. She doesn’t know what to do.4. A. She is annoyed. B. She is upset.C. She is understanding.D. She is bored.5. A. A railway porter. B. A telephone operator.C. A bus conductor.D. A postal clerk.6. A. A math teacher and his colleague. B. A teacher and his student.C. A student and his classmate.D. A librarian and a student.7. A. The man no longer smokes.B. The man refuses to listen to his doctor’s advice.C. The man usually follows his wife’s advice.D. The man is under pressure from his wife.8. A. The man can stay in her brother’s apartment.B. The man should have booked a less expensive hotel.C. Her brother can find an apartment for the man.D. Her brother can help the man find a cheaper hotel.9. A. Reading should come before listening.B. It’s most helpful to read English newspapers every day.C. It’s more effective to combine listening with reading.D. Priority should be given to listening.10. A. The man can’t come for the appointment at 3:15.B. The man wants to change the date of the appointment.C. The man is glad he can get in touch with the doctor.D. The man was confused about the date of the appointment.Section BDirections:In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken onlyonce. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. He will be an intelligent student. B. He may not be an intelligent student.C. He will score better in exams.D. He will not be a good student.12. A. Through his teachers. B. Through his deeds in the classroom.C. Through his appearance.D. Through his reaction to different situations.13. A. Not to judge a boy by taking notes.B. Not to make the mistake of thinking a young man stupid.C. Not to overestimate a student’s intelligence.D. Not to judge a person’s intelligence by his appearance.Questions 14 through 16 are based on the following passage.14. A. Positive thinking can make people healthy.B. A better attitude results in a better operation.C. Researchers have observed 16 patients’ recovery during the past 30 years.D. Great attention has been paid to how attitudes affect health.15. A. The painting was once thought to be worth around $25 million.B. The painting is one of the most expensive pictures ever sold at auction.C. The painting was purchased through TV.D. The quality of the painting has not been seen on the market for more than 10 years.16. A. The kindergarten fired the teacher.B. The mother demanded an unreasonable apology from the teacher.C. The teacher frightened a South Korean boy.D. The kindergarten punished a boy so severely.Section CDirections:In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Ⅱ. Grammar and VocabularySection ADirections:Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one that best completes the sentence.25. After 20 years in an African country, I returned home and found it changed______recognition.A. overB. beyondC. more thanD. out of26. ______ the cliffs rose out of the ground, there were often narrow tracks winding upwards.A. BecauseB. As long asC. WhereD. Only if27. ______a wave of frustration, she felt at a loss as to how to respond to his angry words.A. Overcoming withB. Overcame byC. In order to overcomeD. Overcome with28. In China, no other organization than the CPC.(人大)make any law.A. willB. shouldC. shallD. must29. You don’t think she is more anxious to go there alone than you are, ______?A. do youB. are youC. isn’t sheD. don’t you30. The best job is______ which uses your skill in doing something together with your interest inthe subject.A. thatB. oneC. suchD. this31. ______criticize my son, I______ help him find a more effective way to learn English.A. Rather than; prefer toB. Other than; would ratherC. Rather than; would like toD. Better than; had better32. So little______ with each other that almost no progress was made at the Copenhagen ClimateConference.A. the world leaders sharedB. did the world leaders shareC. shared by the world leadersD. share did the world leaders33. ______all by herself for many years, the old lady is sometimes very difficult______.A. Having lived; to be got along withB. Living; to get on well withC. Having lived; to get along withD. Living; to get along34. Another cultural reason ____ doing journalism is tough here is _____ people don’t want tostick their necks out.A. that; becauseB. why; becauseC. for which; whyD. why; that35. China, together with some other ASEAN(东盟)countries, ______against the overpoliticizing of the differences over the South China Sea.A. areB. wereC. isD. had been36. Unfortunately, his parents forced him to be a lawyer, _____ was against his own wishes.A. whoB. asC. whichD. what37. At the news that her daughter was missing, a _____ look appeared on the mother’s face.A. frighteningB. frightenedC. frightfulD. fright38. How nice it______ to be back home again after such a long absence!A. is feltB. feelsC. will be feltD. is feeling39. Many factors contribute to____, but the most destructive is the role that humans have played.A. animals to dieB. dying animalsC. animals died outD. animals dying out40. President Obama claimed that the rise of China could be a big threat and the worldneeds______.A. to be reshapedB. to reshapeC. to be reshapingD. reshapedSection BDirections:Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.By now you know that getting your money’s worth is not just a matter of luck. It is more often the 41 of buying skill. Nevertheless, even the smartest consumers are sometimes fooled into thinking they are getting their money’s worth when they are not. At one time or another, almost everyone experiences deception (欺骗)in the market place. The deception may not be 42 . But, whether or not, any kind of deception hurts consumers’ feelings as well as their pocket books. Some kinds of deception even endanger their health and safety as well. Obviously, consumers need protection against the marketing of unsafe goods and false or misleading advertising. Fortunately, there are both public and 43 agencies working to meet the need. Government’s job in free enterprise system is to protect the public 44 . The public is composed entirely of consumers. When it comes to protecting consumers, therefore, government has the most influence. Because most consumer products are sold 45 , the major responsibility for consumer protection is 46 by federal government. That responsibility, however, is shared by many agencies. For example, the US Postal Service works to uncover and stop dishonest schemes operated by mail. The National Highway Safety Bureau is47 with all aspects of automobile safety. Certain federal agencies, however, have consumer protection as one of their chief 48 . Most federal agencies are known by their initials. FDA stands for the Food and Drug Administration, which probably does more to protect consumers than any other agency. Its major concern is the safety, purity, and labeling of foods, drugs, and cosmetics. These are the products for which consumers spends a(n) 49 38% of their incomes.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.There are many ways of defining success. It is accurate to say that each of us has our own50 of success, and that each of us is 51 for setting our own goals and52 whether we have met these goals satisfactorily. Because each of us possesses unique differences in genetic ability and favorable environments in which to express these abilities, it is necessarily true that we must define success broadly.For some people, simply being able to live their life with a minimum of misery and suffering is considered 53 .Think of the peace of mind of the poor shepherd who tends his sheep, enjoying his simple life with his family in the beauty of 54 , and who is respected because he does a good job of 55 the goals expected of and accepted by him and his society. On the other hand, it seems that 56 some people appear to be rich in 57 possessions, many of them seem to be miserable and consider themselves unsuccessful when 58 their own goals of success. Because not all ventures can be successful, oneshould not set 59 goals for achieving success, but if one has self-confidence and ability it would be unfortunate to set one’s goals at too low a60 of achievement.A wise counselor once said to a young man who was 61 frustration and disappointment with his own professional success, “You 62 set your goal to reach the moon in order to have success in traveling. Sometimes one can be very successful 63 by taking a walk in the park, or riding the subway downtown,” the counselor added,“You have not really failed and spoilt your chances for success until you have been unsuccessful at 64you really like, and to which you have given your best effort.”50. A. purpose B. decision C. concept D. name51. A. helpful B. charged C. free D. responsible52. A. thinking B. determining C. knowing D. learning53. A. development B. life C. a success D. progress54. A. nature B. environment C. surrounding D. scenery55. A. realizing B. carrying out C. achieving D. completing56. A. as though B. even that C. as if D. even though57. A. spiritual B. mental C. ideal D. material58. A. judged by B. supposed to C. depended on D. relied on59. A. untrue B. unrealistic C. wrong D. false60. A. condition B. situation C. position D. standard61. A. experiencing B. considering C. feeling D. thinking62. A. mustn’t B. do not have to C. shouldn’t D. can’t63. A. nearly B. mostly C. merely D. frequently64. A. something B. anything C. nothing D. everything Section BDirections: Read the following four passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.AThe rise of the so-cal led “boomerang generation” is revealed in official figures showing that almost one in five graduates in their late 20s now live with their parents.By contrast, only one in eight university graduates had failed to fly the nest by the same age 20 years ago. It also found that grown-up sons are twice as likely as their sisters to still be living with their parents in their late 20s. With nearly a quarter of men approaching 30 still living at home, the findings are bound to lead to claims of a “generation of mummy’s boys”.Young professionals in their late 20s or early 30s have been nicknamed the “boomerang generation” because of the trend toward returning to the family home having initially left to study. Recent research has suggested that young people in Britain are twice as likely to choose to live with their parents in their late 20s than their counterparts elsewhere in Europe.Growing housing prices, rising student debts and the effects of recession(衰退)on the job market have forced a wave of young people to move back into the family home at an age when they would normally be moving out. But commentators warned that the phenomenon may have more to do with young people facing “dire” prospects than simply a desire to save money.While the proportion of those of university or college age moving out from the family home has continued to rise in the last 20 years, among those in their mid and late 20s the trend has been reversed. Overall 1.7 million people aged from 22 to 29 now share a roof with their parents,including more than 760,000 in their late 20s. In 1988, 22.7 per cent of men aged 25 to 29 were still living with their parents but last year the proportion was 24.5 per cent.65. What is the main idea of the passage?A. The economic crisis has shown its effect on the young generation.B. More young professionals are returning home to live.C. British parents are suffering more loads from their grown-up children.D. Britain is suffering more than any other country in Europe.66. Which of the following statements is TRUE?A. Male children seem to be more independent than females.B. Eighty percent of university graduates were able to live independently two decades ago.C. The grown-up children choose to live with their parents only to save money.D. More and more children are moving out at university age.67. What does the underlined word “dire” probably mean?A. promising.B. inconvenient.C. very bad.D. hopeful.68. The following factors may account for the phenomenon except ___________.A. that living prices have risen a lotB. that it’s difficult to land a jobC. that education has already cost them a lotD. that parents can help them moreBIt’s great f un to explore new places—it feels like an adventure, even when you know you’re not the first to have been there. But make sure not to get lost or waste time going round in circles.● Do the map reading if you’re being driven somewhere. It’ll be easier if you keep turning the map so it follows the direction you’re traveling in. Keep looking ahead so that you can give the driver lots of warning before having to make a turn or you’ll ha ve to move to the back seat.● Get a group of friends together and go exploring. You'll need a good map, a compass (指南针), a raincoat, a cell phone to call for help in case you get lost, and a bit of spare cash for emergencies. Tell someone where you’re goi ng before you set out and let them know what time you expect to be back. The test is in not getting lost, not in seeing how fast you can go, so always stick together, waiting for slower friends to catch up.● See if your school or a club organizes orientee ring activities, in which you need a map and a compass to find your way. This can be done as a sport, with teams trying to find the way from A to B (and B to C, etc.) in the fastest time, or simply as a spare-time activity. Either way, it’s not only good fun, but a great way to keep fit.69. Sitting beside the driver, you should___________.A. direct the driver when necessaryB. look ahead to see where there’s a turnC. move to the back seat if feeling uncomfortableD. keep looking at the map to find a place to go to70. Why do you need to tell someone your exploration plan before setting out?A. To get information when in danger.B. To be saved in case of an accident.C. To share the fun with him/her in exploration.D. To tell him/her what’s going o n with the group members.71. Orienteering activities can______________.A. make people work fastB. help people stay healthyC. help people organize other activitiesD. make people get prepared for sportsCIs early childhood education really necessary? Early childhood education primarily focuses on learning through playing to develop the child’s physical, sensory, communicational and social development. Early childhood education has become a concern of the government, who pushes poor children to be formally trained before they are old enough for kindergarten.There are good reasons for the government to push early childhood education. Studies have shown that orphaned children who did not receive good care and education become developmentally delayed causing failure in school, and even in life. Further studies show that poor children who take part in Head Start programs are more prepared for school, less likely to end up in Special Education classes, and are less likely to receive public help or go to prison.There are also negative parts to putting a child in formal education programs too early. Time Magazine online explains that “the younger the child the less his chances of catching up with first-grade work.” I have personally witnessed many children of my generation who went to Head Start programs become frustrated and bored with school before they finished high school. Yet parents have been sure that the earlier the child starts school, the better off he or she is, so they push to start children earlier.Actually while early formal education of poor children does show great gains in the early elementary years, studies also show that this head start is really a “false start”, as the gains are lost in middle and high school years. It seems that environm ent is a bigger factor on life’s success than early education. Head Start programs have not achieved its original goal in closing the achievement gap in poor and middle school children. Perhaps it is time to find other ways to close that gap.72. The purpose of the government valuing the early childhood education is ________.A. to develop the children’s communicationB. to give orphaned children good care and educationC. to get the children prepared for the kindergartenD. to train the children formally and regularly73. According to the studies, which of the following is True?A. Children with good early education may have a rich life.B. The orphaned children are usually unhappy in their life.C. Children without early education can do well at school.D. Head Start programs are helpful to the poor children.74. The underlined sentence “the younger the child the less his chances of catching up withfirst-grade work. ” suggests that _____________.A. the early childhood education is helpless to the child’s gradeB. it is good for the young children to receive early educationC. the early education can help the children follow the gradeD. the younger the children are, the cleverer they will be75. The author’s attitude toward the early childhood education i s _________.A. puzzlingB. negativeC. indifferentD. approvingSection CDirections: Read the following text and choose the most suitable heading from A-F for each paragraph. There is one extra heading which you do not need.Robot, it is a word that seems very modern, a word that creates a strong mental picture, a picture of something that looks and acts like a human. Robots are not human, of course, they areThe word robot, and robots themselves, are less than 100 years old. But humans have been dreaming of real and imaginary copies of themselves for thousands of years. Early people madeWhat is the future of robots? The goal of scientists is to create a true human-like robot. Some experts have described this robot of the future as one that can act independently with the physical world through its own senses and actions. Humans have the ability to see, hear, speak and solve problems. Engineers have built robots that have one or two of these abilities. But it takes a numberThe biggest problem in creating a human-like robot is copying human intelligence. The way the human mind works is almost impossible to copy. A simple computer can do mathematical problems far beyond the ability of even the smartest human mind. But the human mind is better than a thousand supercomputers at speaking, hearing and problem-solving. Several American and Japanese companies are working to develop the senses of sight and touch for robots. TheHowever, the most important human ability--the most difficult to copy--is problem-solving. An intelligent robot must be able to change the way it acts when it faces an unexpected situation. Humans do it all the time. Computers must do it for robots. This means computers must have a huge base of information about many things. They must be able to find quickly the needed information in their systems. And they must make choices about how to act. So far, this is beyond the ability of computers.Section DDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.From now on, never spend your precious time thinking of reasons for your failures and shortcomings. Instead, realize that the seeds of success were planted within you when you were born. Only you have the power to make those seeds grow.The seeds, and the power to grow them, are contained in the most awesome machine ever created: the human mind. Success is a choice and not a chance. You were born a winner. You were born rich. You can be a success only if you make the right choice.You cannot be successful without first developing your self-esteem. Your level ofself-esteem is always based on the degree of control that you are able to exercise over yourself, and thus over your life. People with low self-esteem are people who do not believe that they have any power, or responsibility for their lives. They are the perennial (长期的) victims and martyrs. They are leaves tossed (摇摆) by the winds of chance blown about with any sudden change in the weather.You can exercise control over your life only to the degree that you believe that you are responsible for everything that happens in your life. Failures think that everything happens by accident and chance. Successful people realize that they are responsible.Everything happens as a result of something. If we can identify the cause, we can control the effect. We are responsible for what we choose to think and believe. One generally rises to the level that one expects. We are responsible for setting our expectations. Our success is dependent upon our level of confidence.If you associate with positive-thinking people, you are definitely going to achieve success. On the contrary, the opposite happens. We are responsible for finding, planting, and nurturing the seeds that contain future victory, born from setbacks.In short, in all areas of your life, whether they be financial, physical, emotional, or spiritual, you are responsible. Once you recognize this, accept it, and firmly believe it, you are on the road to success.(Answer the questions or complete the statements in NO MORE THAN 12 WORDS)81. Why are people with low self-esteem compared to leaves?_________________________________________________________.82. What do losers think about their failures?_______________________________________________________.83. According to the writer, whether one will succeed ____________________________.84. The writer holds the view that he who connects with negative-thinking people will __________________________________________.第II卷(共 45 分)I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1、许多街道都是以名人或大城市命名的。
2012学年嘉定区高三年级第一次质量调研数学试卷(理)一.填空题(本大题共有14题,满分56分)考生应在答题纸相应编号的空格内直接填写结果,每个空格填对得4分,否则一律得零分.1.若i ii z +=11(i 为虚数单位),则=z ___________. 2.已知集合},0)1)(2({R ∈<-+=x x x x A ,},01{R ∈<+=x x x B ,则=B A _____________.3.函数1)cos (sin )(2++=x x x f 的最小正周期是___________.4.一组数据8,9,x ,11,12的平均数是10,则这组数据的方差是_________.5.在等差数列}{n a 中,101-=a ,从第9则公差d 的取值范围是__________________.6.执行如图所示的程序框图,则输出的a 的值为_____________.7.小王同学有4本不同的数学书,3本不同的物理书和3本不同的化学书,从中任取2本,则这2本书属于不同学科的概率为______________(结果用分数表示).8.一个圆锥的侧面展开图是一个半径为R 的半圆,则这个圆锥的体积是________. 9.点M 是曲线1212+=x y 上的一个动点,且点M 为线段OP 的中点,则动点P 的轨迹方程为__________________. 10.在△ABC 中,已知41tan =A ,53tan =B ,且△ABC 最大边的长为17,则△ABC 最小边的长为____________.11.将直线1l :01=-+y x ,2l :0=-+n y nx ,3l :0=-+n ny x (*N ∈n ,2≥n )围成的三角形面积记为n S ,则=∞→n n S lim ___________.12.已知a 、b 是平面内两个互相垂直的单位向量,若向量c 满足0)()(=-⋅-c b c a,则||c的最大值是___________.13.观察下列算式:113=, 5323+=,119733++=,(第6题图)1917151343+++=,… … … …若某数3m 按上述规律展开后,发现等式右边含有“2013”这个数,则=m _______. 14.设m 、R ∈n ,定义在区间],[n m 上的函数|)|4(log )(2x x f -=的值域是]2,0[,若关于t 的方程0121||=++⎪⎭⎫⎝⎛m t (R ∈t )有实数解,则n m +的取值范围是___________.二.选择题(本大题共有4题,满分20分)每题有且只有一个正确答案,考生应在答题纸的相应编号上,将代表答案的小方格涂黑,选对得5分,否则一律得零分.15.已知R ∈x ,条件p :x x <2,条件q :11≥x,则p 是q 的…………………( ) A .充分不必要条件 B .必要不充分条件C .充分必要条件D .既不充分也不必要条件 16.以下说法错误的是………………………………………………………………………( ) A .直角坐标平面内直线的倾斜角的取值范围是),0[πB .直角坐标平面内两条直线夹角的取值范围是⎥⎦⎤⎢⎣⎡2,0π C .平面内两个非零向量的夹角的取值范围是),0[πD .空间两条直线所成角的取值范围是⎥⎦⎤⎢⎣⎡2,0π 17.在平面直角坐标系内,设),(11y x M 、),(22y x N 为不同的两点,直线l 的方程为0=++c by ax , cby ax cby ax ++++=2211δ.有四个命题:①存在实数δ,使点N 在直线l 上;②若1=δ,则过M 、N 两点的直线与直线l 平行;③若1-=δ,则直线l 经过线段MN 的中点;④若1>δ,则点M 、N 在直线l 的同侧,且直线l 与线段MN 的延长线相交.上述命题中,全部真命题的序号是……………………………………………………………( ) A .① ② ③ B .② ③ ④ C .① ③ ④ D .① ② ③ ④ 18.设函数)(x f y =是定义在R 上以1为周期的函数,若函数x x f x g 2)()(-=在区间]3,2[上的值域为]6,2[-,则)(x g 在区间]12,12[-上的值域为……………………( )A .]6,2[-B .]28,24[-C .]32,22[-D .]34,20[-三.解答题(本大题共有5题,满分74分)解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤. 19.(本题满分12分)设复数i a z ⋅++-=)cos 1(2)sin4(22θθ,其中R ∈a ,),0(πθ∈,i 为虚数单位.若z 是方程0222=+-x x 的一个根,且z 在复平面内对应的点在第一象限,求θ与a 的值.20.(本题满分14分)本题共有2个小题,第1小题满分8分,第2小题满分6分.如图,在三棱锥ABC P -中,⊥PA 底面ABC ,BC AC ⊥,2===PA BC AC . (1)求异面直线AB 与PC 所成角的大小;(2)求三棱锥ABC P -的表面积S .21.(本题满分14分)本题共有2个小题,第1小题满分6分,第2小题满分8分.已知椭圆C :12222=+b y a x (0>>b a )经过)1,1(与⎪⎪⎭⎫ ⎝⎛23,26两点,过原点的直线l 与椭圆C 交于A 、B 两点,椭圆C 上一点M 满足||||MB MA =.(1)求椭圆C 的方程;(2)求证:222||2||1||1OM OB OA ++22.(本题满分16分)本题共有3个小题,第13小题满分6分.设数列}{n a 的前n 项和为n S ,已知q pS S n n +=+1(*N ∈n ,p 、q 为常数),21=a ,12=a ,p q a 33-=.(1)求p 、q 的值;(2)求数列}{n a 的通项公式;(3)是否存在正整数m ,n ,使得1221+<--+m m n n m S m S 成立?若存在,请求出所有符合条件的有序整数对),(n m ;若不存在,请说明理由.23.(本题满分18分)本题共有3个小题,第1小题满分4分,第2小题满分6分,第3小题满分8分.设R ∈a ,函数x a x x x f 2||)(+-⋅=.(1)若2=a ,求函数)(x f 在区间]3,0[上的最大值; (2)若2>a ,写出函数)(x f 的单调区间(不必证明);(3)若存在]4,2[-∈a ,使得关于x 的方程)()(a f t x f ⋅=有三个不相等的实数解,求实数t 的取值范围.P A B C2012学年嘉定区高三年级第一次质量调研 数学试卷(理)参考答案与评分标准一.填空题(每小题4分,满分56分)1.i -2 2.}12{-<<-x x 3.π 4.25.⎥⎦⎤ ⎝⎛710,45 6.37 7.1511 8.2433R π 9.2412+=x y 10.2 11.2112.213.45 14.)2,1[二.选择题(每小题5分,满分20分)15.A 16.C 17.B 18.D 三.解答题 19.(本题满分12分)方程0222=+-x x 的根为i x ±=1.………………(3分)因为z 在复平面内对应的点在第一象限,所以i z +=1,………………(5分)所以⎩⎨⎧=+=-1)cos 1(21sin 422θθa ,解得21cos -=θ,因为),0(πθ∈,所以32πθ=,……(8分)所以43sin 2=θ,所以4sin 4122=+=θa ,故2±=a .…………(11分)所以3πθ2=,2±=a .…………(12分)20.(本题满分14分,第1小题8分,第2小题6分) (1)取PA 中点E ,PB 中点F ,BC 中点G ,连结EF ,FG ,EG ,则EF ∥AB ,FG ∥PC , 所以EFG ∠就是异面直线AB 与PC 所成的角(或 其补角).…………(2分) 连结AG ,则522=+=CG AC AG ,……(3分)622=+=AG EA EG , …………(4分)又22==PC AB ,所以2==FG EF .…………(5分)在△EFG 中,212cos 222-=⋅-+=∠FG EF EG FG EF EFG ,……(7分) 故︒=∠120EFG .所以异面直线AB 与PC 所成角的大小为︒60.…………(8分)(2)因为⊥PA 底面ABC ,所以AB PA ⊥,BC PA ⊥,AC PA ⊥, 又AC BC ⊥,所以⊥BC 平面PAC ,所以PC BC ⊥,…………(2分) 所以△ABC 、△PAB 、△PBC 、△PAC 都是直角三角形.……(3分) 所以,24421212121+=⋅+⋅+⋅+⋅=AC PA PC BC AB PA BC AC S .……(6分) G P ABC FE21.(本题满分14分,第1小题6分,第2小题8分) (1)将)1,1(与⎪⎪⎭⎫⎝⎛23,26代入椭圆C 的方程,得 ⎪⎪⎩⎪⎪⎨⎧=+=+143231112222b a b a ,…………(2分) 解得32=a ,232=b .…………(5分)所以椭圆C 的方程为132322=+y x .…………(6分) (2)由||||MB MA =,知M 在线段AB 的垂直平分线上,由椭圆的对称性知A 、B 关于原点对称.①若点A 、B 在椭圆的短轴顶点上,则点M 在椭圆的长轴顶点上,此时2112211||2||1||122222222=⎪⎭⎫ ⎝⎛+=++=++b a a b b OM OB OA .……(1分) 同理,若点A 、B 在椭圆的长轴顶点上,则点M 在椭圆的短轴顶点上,此时2112211||2||1||122222222=⎪⎭⎫ ⎝⎛+=++=++b ab a a OM OB OA .……(2分) ②若点A 、B 、M 不是椭圆的顶点,设直线l 的方程为kx y =(0≠k ), 则直线OM 的方程为x ky 1-=.设),(11y x A ,),(22y x M , 由⎪⎩⎪⎨⎧=+=132322y x kx y ,解得221213k x +=,2221213k k y +=,……(4分) 所以2221212221)1(3||||k k y x OB OA ++=+==,同理可得2222)1(3||kk OM ++=, 所以2)1(3)2(2)1(321)1(321||2||1||1222222222=++++++++=++k k k k k k OM OB OA .……(7分) 综上,222||2||1||1OM OB OA ++为定值2.…………(8分)(1)由题意,得⎩⎨⎧+=+=q pS S q pa S 2312,……(2分)即⎩⎨⎧+=-++=q p p q q p 33323 ,解得⎪⎩⎪⎨⎧==221q p .…………(4分) (2)由(1)知,2211+=+n n S S ①当2≥n 时,2211+=-n n S S ② …………(1分)①-②,得n n a a 211=+(2≥n ),又1221a a =,…………(3分)所以数列}{n a 是首项为2,公比为21的等比数列.…………(4分)所以}{n a 的通项公式为221-⎪⎭⎫ ⎝⎛=n n a (*N ∈n ).…………(6分)(3)由(2),得⎪⎭⎫ ⎝⎛-=n n S 2114,…………(1分)由1221+<--+m m n n m S m S ,得122211421141+<-⎪⎭⎫ ⎝⎛--⎪⎭⎫ ⎝⎛-+m m n n m m ,即12222)4(42)4(+<-⋅--⋅-mm nn m m , 即12122)4(2+>-⋅-mn m .因为012>+m ,所以22)4(>⋅-nm , 所以4<m 且422)4(21+<⋅-<+m n m , (*)因为*N ∈m ,所以1=m 或2或3.……………………(2分)当1=m 时,由(*)得8232<⨯<n,所以1=n ; …………(3分)当2=m 时,由(*)得12222<⨯<n,所以1=n 或2; …………(4分)当3=m 时,由(*)得2022<<n,所以2=n 或3或4. …………(5分)综上可知,存在符合条件的正整数m 、n ,所有符合条件的有序整数对),(n m 为:)1,1(,)1,2(,)2,2(,)2,3(,)3,3(,)4,3(. …………(6分)(1)当2=a ,]3,0[∈x 时,⎪⎩⎪⎨⎧<≤+-≥=+-⋅=.20,4;2,2|2|)(22x x x x x x x x x f …(2分) 作函数图像(图像略),可知函数)(x f 在区间]3,0[上是增函数,所以)(x f 的最大值为9)3(=f .…………(4分)(2)⎪⎩⎪⎨⎧<++-≥-+=.,)2(,,)2()(22a x x a x a x x a x x f ……(1分) ①当a x ≥时,4)2(22)(22--⎪⎭⎫ ⎝⎛--=a a x x f , 因为2>a ,所以a a <-22, 所以)(x f 在),[∞+a 上单调递增.…………(3分)②当a x <时,4)2(22)(22++⎪⎭⎫ ⎝⎛+--=a a x x f , 因为2>a ,所以a a <+22,所以)(x f 在⎥⎦⎤ ⎝⎛+∞-22,a 上单调递增,在⎥⎦⎤⎢⎣⎡+a a ,22上单调递减.…………(5分)综上,函数)(x f 的单调递增区间是⎥⎦⎤⎝⎛+∞-22,a 和),[∞+a , 单调递减区间是⎥⎦⎤⎢⎣⎡+a a ,22.………………(6分) (3)①当22≤≤-a 时,022≤-a ,022≥+a ,所以)(x f 在),(∞+-∞上是增函数,关于x 的方程)()(a f t x f ⋅=不可能有三个不相等的实数解.…………(2分)②当42≤<a 时,由(1)知)(x f 在⎥⎦⎤ ⎝⎛+∞-22,a 和),[∞+a 上分别是增函数,在⎥⎦⎤⎢⎣⎡+a a ,22上是减函数,当且仅当4)2()(22+<⋅<a a f t a 时,方程)()(a f t x f ⋅=有三个不相等的实数解.即⎪⎭⎫⎝⎛+4+=+<<4818)2(12a a a a t .…………(5分)令aa a g 4)(+=,)(a g 在]4,2(∈a 时是增函数,故5)(max =a g .…………(7分)所以,实数t 的取值范围是⎪⎭⎫⎝⎛89,1.…………(8分)。