2017届上海市七宝中学高三综合测试五(5月)数学试题

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2017-2018学年上海市七宝中学高三10月月考数学试题

2017-2018七宝中学高三月考数学卷2016.10一. 填空题1. 已知函数()f x 的定义域是[1,2]-，则()()y f x f x =+-的定义域是2. 若25x y -<<<，则x y -的取值范围是3. 锐角△ABC 中，角,A B 所对的边长分别为,a b ，若2sin a B b =，则A =4. 二项式921()x x -的展开式中常数项为 (结果用数值表示) 5. 若函数cos(2)y x ϕ=+(||)2πϕ<的图像关于点4(,0)3π中心对称，则ϕ= 6. 若122log (42)0ax x a -+-<对任意x R ∈恒成立，则实数a 的取值范围是7. 已知0x >，0y >，1211x y +=+，则x y +的最小值为 8. 已知向量AB 与AC 的夹角为120，且||2AB = ，||3AC = ，若AP AB AC λ=+ ，且AP BC ⊥，则实数λ的值为9. 某微信群中甲、乙、丙、丁、戊五名成员先后抢4个不相同的红包，每人最多抢一个红包，且红包全被抢光，则甲乙两人都抢到红包的情况有种 10. 设函数()min{||,||}f x x x t =+的图像关于直线3x =-对称，其中min{,}a b 表示,a b 中的最小值，则实数t =11. 右侧程序框图的运行结果：S =12. 已知函数1,0()42,0xx x x f x x --⎧+>⎪=⎨-≤⎪⎩，若函数 (32)y f x a =--恰有三个不同的零点，则实数a 的取值范围是13. 等差数列{}n a 的前n 项和为n S ，已知31819992017(1)2016(5)sin()3a a π-+-=-， 31999182017(5)2016(1)cos()6a a π-+-=-，则2016S = 14. 正方体1111D C B A ABCD -的棱长为3，以顶点A 为球心，2为半径作一个球，则球面与正方体的表面相交所得到的所有弧长之和等于二. 选择题15. 无穷等比数列{}n a *()n N ∈的前n 项的和是n S ，则下列首项1a 中，使得1lim 2n n S →∞=的只可能是（） A.12 B. 12- C. 14 D. 14- 16. 已知函数()f x 和()g x 的定义域都是R ，则“()f x 和()g x 在R 上一增一减”是“函数()()()F x f x g x =-有唯一零点”的（）条件A. 充分非必要B. 必要非充分C. 充要D. 既不充分也不必要 17. 对于平面向量x 和给定的向量a ，记()2()f x x x a a =-⋅，若()()f x f y x y ⋅=⋅r r r r对任意向量,x y 恒成立，则a的坐标可能是（）A. 1)2-B.C. 31(,)44D. 1(2-18. 函数()sin(2)f x A x θ=+(0,||)2A πθ>≤部分图像如图所示，且0)()(==b f a f ，对不同的12,[,]x x a b ∈，若)()(21x f x f =，有3)(21=+x x f ，则（）A. )(x f 在5(,)1212ππ-上是减函数 B. )(x f 在5(,)1212ππ-上是增函数 C. )(x f 在5(,)36ππ上是减函数 D. )(x f 在5(,)36ππ上是增函数三. 解答题19. 已知函数()|2||23|f x x a x =-++，()|1|2g x x =--；（1）解不等式|()|5g x <；（2）若{|()2}y y y f x ∈=-是{||()|}y y y g x ∈=的充分条件，求实数a 的取值范围；20. 某厂生产某产品的年固定成本为250万元，每生产x 千件，需另投入成本()C x （万元），若年产量不足80千件，()C x 的图像是如图的抛物线，此时()0C x <的解集为(30,0)-，且()C x 的最小值是75-，若年产量不小于80千件，10000()511450C x x x=+-，每千件商品售价为50万元，通过市场分析，该厂生产的商品能全部售完；（1）写出年利润()L x （万元）关于年产量x （千件）的函数解析式；（2）年产量为多少千件时，该厂在这一商品的生产中所获利润最大？21. 如图，直三棱柱111ABC A B C -中，AC AB ⊥，122AB AA ==，M 是AB 的中点， △11A MC 是等腰三角形，D 为1CC 的中点，E 为BC 上一点；（1）若DE ∥平面11A MC ，求CEEB；（2）平面11A MC 将三棱柱111ABC A B C -分成两个部分，求含有点A 的那部分体积；22. 已知常数0a ≠，数列{}n a 的前n 项和为n S ，11a =，(1)nn S a a n n=+-；（1）求数列{}n a 的通项公式；（2）若3(1)n n n n b a =+-，且{}n b 是单调递增数列，求实数a 的取值范围；（3）若12a =，2016n n n a c a =+，对于任意给定的正整数k ，是否存在正整数p 、q ，使得k p q c c c =？若存在，求出p 、q 的值(只要写出一组即可)；若不存在，请说明理由；23. 已知函数()||f x x x a =-的定义域为D ，其中a 为常数；（1）若R D =，且()f x 是奇函数，求a 的值；（2）若1a ≤-，[1,0]D =-，函数()f x 的最小值是()g a ，求()g a 的最大值；（3）若0a >，在[0,]a 上存在n 个点i x (1,2,,.3)i n n =≥ ，满足10x =，n x a =，12n x x x <<< ，使得12231|()()||()()||()()|8n n f x f x f x f x f x f x --+-++-= ，求实数a 的取值范围；七宝中学2016第一学期高三10月考试数学试卷考试时间：120分钟满分：150分一、填空题(每题4分，共56分)： 1. 已知函数()f x 的定义域是[1 2]-，，则()()y f x f x =+-的定义域是 [1 1]-，. 2. 若25x y -<<<，则x y -的取值范围是 (7 0)-，3. 在锐角中ABC ∆，角 A B 、所对的边长分别为 a b 、. 若2sin a B b =，则A =6π.4. 二项式921()x x-的展开式中常数项为 (结果用数值表示)84-． 5. 若函数cos(2)(||)2y x πϕϕ=+<的图像关于点4(0)3π，中心对称，则ϕ= 6π-. 6. 若212log (42)0ax x a -+-<对任意x R ∈恒成立，则实数a 的取值范围是4a >.7. 已知0 0x y >>，，1211x y +=+，则x y +的最小值为. 8. 已知向量与AC 的夹角为120 ，且||2 ||3A B A C == ，，若AP AB AC λ=+ ，且AP BC ⊥ ，则实数λ的值为 1279. 某微信群中甲、乙、丙、丁、戊五名成员先后抢4个不相同的红包，每人最多抢一个红包，且红包全被抢光，则甲乙两人都抢到红包的情况有种22142443343472P P C P C P ===.10. 设函数()min{|| ||}f x x x t =+，的图像关于直线3x =-对称，其中min{ }a b ，表示 a b 、中的最小值. 则实数t = 6. 11. 右侧程序框图的运行结果：S = 1320.12. 已知函数10()420xx x x f x x --⎧+>=⎨-≤⎩，，，若函数(32)y f x a =--恰有三个不同的零点,则实数a 的取值范围是 23a <≤.13. 等差数列{}n a 的前n 项和为n S ，已知31819992017(1)2016(5)sin()3a a π-+-=-， 31999182017(5)2016(1)cos()6a a π-+-=-，则2016S = 6048.14. 正方体1111D C B A ABCD -的棱长为3，以顶点A 为球心，2为半径作一个球，则球面与正方体的表面相交所得到的所有弧长之和等于 52π.二、选择题(每题5分，共20分)：15. 无穷等比数列{}n a (*n N ∈)的前n 项的和是n S ，则下列首项1a 中，使得1lim 2n n S →∞=的只可能是 ( C )A ．12 B ．12- C ．14 D ．14-. 16. 已知函数()f x 和()g x 的定义域都是R ，则“()f x 和()g x 在R 上一增一减”是“函数()()()F x f x g x =-有唯一零点”的 ( D ) A.充分非必要条 B.必要非充分条件 C.充要条件 D.既非充分也非必要条件17. 对于平面向量x 和给定的向量a ，记()2()f x x x a a =-⋅．若()()f x f y x y ⋅=⋅r r r r 对任意向量 x y 、恒成立，则a 的坐标可能是 ( D )A．1 )2- B． C ．31( )44， D．1(2- 18. 函数()sin(2)(0 ||)2f x A x A πθθ=+>≤，部分图像如图所示，且0)()(==b f a f ，对不同的12 [ ]x x a b ∈，，，若)()(21x f x f =，有3)(21=+x x f ，则 ( B ) A.)(x f 在5( )1212ππ-，上是减函数 B.)(x f 在5( )1212ππ-，C.)(x f 在5( )36ππ，上是减函数D.)(x f 在5( )36ππ，上是增函数三、解答题：19. (12分)已知函数322)(++-=x a x x f ，()12g x x =--. (1)解不等式()5g x <；(2)若{|()2}y y y f x ∈=-是{||()|}y y y g x ∈=的充分条件，求实数a 的取值范围. 解：(1)由|()|||1|2|5g x x =--<得3|1|7x -<-<，∴|1|7x -<，解得68x -<<．所以原不等式的解集为{|68}x x -<<；(2)∵{|()}y y y f x ∈=是{||()|}y y y g x ∈=的充分条件，所以{|()}{||()|}y y f x y y g x =⊆=，又()223232f x x a x a =-++-≥+-，()||1|2|0g x x =--≥ 所以32a +≥，解得：1a ≥-或5a ≤-.20. (14分)某厂生产某种产品的年固定成本为250万元，每生产x 千件，需另投入成本()C x (万元)，若年产量不足80千件，()C x 的图像是如图的抛物线，此时()0C x <的解集为(30 0)-，，且()C x 的最小值是75-. 若年产量不小于80千件，10000()511450C x x x=+-. 每千件商品售价为50万元. 通过市场分析，该厂生产的商品能全部售完.(1)写出年利润()L x (万元)关于年产量x (千件)的函数解析式；(2)年产量为多少千件时，该厂在这一商品的生产中所获利润最大？解：(1)依题意，当080x <<(千件)时，设2()(30)C x a x x =+，则22575a -=-解得13a =，即21()(30)3C x x x =+，此时21()50[250()]402503L x x C x x x =-+=-+-当80x ≥(千件)时，10000()50[250()]1200()L x x C x x x=-+=-+∴2140250 0803()100001200() 80x x x L x x x x ⎧-+-<<⎪=⎨⎪-+≥⎩，，(2)当080x <<(千件)时，21()(60)9503L x x =--+，此时，max ()(60)950L x L ==；当80x ≥(千件)时，10000()1200()1000L x x x=-+≤(当且仅当100x =时等号成立) 此时，max ()(100)1000L x L ==，综上所述，当年产量100千件时，该厂在这一商品的生产中所获利润最大，为1000万元. 21. (14分)如图，直三棱柱111ABC A B C -中，AC AB ⊥，122AB AA ==，M 是AB 的中点，△11A MC 是等腰三角形，D 为1CC 的中点，E 为BC 上一点．(1)若DE ∥平面11A MC ，求CEEB； (2)平面11A MC 将三棱柱111ABC A B C -分成两个部分，求含有点A 的那部分体积．解：取BC 中点为N ，连结1 MN C N ，， ∵,M N 分别为,AB CB 中点 ∴MN ∥AC ∥11AC ，∴11,,,A M N C 四点共面，且平面11BCC B I 平面11A MNC 1C N =又DE Ü平面11BCC B ，且DE ∥平面11A MC ，∴DE ∥1C N ∵D 为1CC 的中点，∴E 是CN 的中点，∴13CE EB =．(2)因为三棱柱111ABC A B C -为直三棱柱，∴1AA ^平面ABC，又AC AB ⊥，则AC ⊥平面11ABB A∵122AB AA ==，又11A MC ∆是等腰三角形，所以111AM AC ==如图，将几何体11AA M CC N -补成三棱柱11AA M CC F - ∴几何体11AA M CC N -的体积为：1111111111111232232212V AM AA AC CF CC NF =⋅⋅⋅-⋅⋅⋅⋅=⨯⨯⨯⨯⨯⨯=MEDC 1B 1 A A 1B C NF22. (16分)已知常数0a ≠，数列{}n a 的前n 项和为n S ，11(1)nn S a a a n n==+-，. (1)求数列{}n a 的通项公式；(2)若3(1)n n n n b a =+-，且{}n b 是单调递增数列，求实数a 的取值范围； (3)若12a =，2016nn n a c a =+，对于任意给定的正整数k ，是否存在正整数 p q 、，使得k p q c c c =？若存在，求出 p q 、的值(只要写出一组即可)；若不存在，请说明理由. 解：(1)11(1)(1)nn n n S a a a n na S a n n n==+-⇒=+-， {1111(1)22(1)(1)n n n n n n n n na S a n nna na an a a a n a S an n ++++=+-⇒-=⇒-=+=++∴{}n a 是以11a =为首项，2d a =为公差的等差数列，∴12(1)n a a n =+- (2)11113(1)3(1)n n n n n n n n b b a a ++++<⇔+-<+-,即(1)[1(21)]3n n a n -+-<若n 为奇数，则31(1 3 5 )21n a n n +>-=- ，，，恒成立，考察31()21n f n n +=--，231314(43)34(2)()02321(23)(21)n n n n f n f n n n n n +++--++-=-+=<+-+-即(1)(3)(5)f f f >>> ，∴(1)4a f >=-；若n 为偶数，则31(2 4 6 )21n a n n -<=- ，，，恒成立，考察31()21n g n n -=-，231314(43)34(2)()02321(23)(21)n n n n g n g n n n n n +---++-=+=>+-+-即(2)(4)(6)g g g <<< ，∴8(2)3a g <=；综上所述，843a -<<；(3)由(1)2016n n n a n c n ==+，.假设对任意*k N ∈，总存在正整数 p q 、，使k p q c c c =，则(2016)201620162016k p q k q p k p q q k+=⋅⇒=+++-令1q k =+，则(2017)p k k =+(或2q k =，则22016p k =+；…) ∴(2017)1k k k k c c c ++=(或220162k k k c c c +=；…)23. (18分)已知函数()||f x x x a =-的定义域为D ，其中a 为常数. (1)若R D =，且()f x 是奇函数，求a 的值；(2)若1[10]a D ≤-=-，，，函数()f x 的最小值是()g a ，求()g a 的最大值； (3)若0a >，在[0,]a 上存在n 个点(1,2,,.3)i x i n n =≥ ，满足10x =，n x a =，12n x x x <<< ，使得12()()f x f x -23()()f x f x +-+ 1()()n n f x f x -+-8=，求实数a 的取值范围.解：(1)∵()f x 是奇函数，∴()()0f x f x +-=对任意x ∈R 恒成立， ∴||||x x a x x a -=+，即0ax =对任意x ∈R 恒成立，∴0a =；(2)2222() 24()||()24a a x x a f x x x a a a x x a ⎧--≥⎪=-=⎨⎪--+<⎩，，，11 ∵1a ≤-，∴[1 0][ )a -⊆+∞，，，∴22()()24a a f x x =--，[1 0]x ∈-， ①当21a -≤≤-时，1122a -≤≤-，()f x 在[1 ]2a -，上递减，在[ 0]2a ，递增，2min [()]4a f x =- ②当2a <-时，12a <-，()f x 在[1 0]-，上单调递增，min [()](1)1f x f a =-=+ 综上所述，2 21()41 2a a g a a a ⎧⎪--≤≤-=⎨⎪+<-⎩，，，若21a -≤≤-，则11()4g a -≤≤-；若2a <-，则()1g a <- ∴当1a =-时，max 1[()]4g a =- (3)∵0a >，且()f x 在[0 ]2a ，上单调递增，在[ ]2a a ，上单调递减， ∴max min ()()()(0)2a f x f f x f ==，而12231max min |()()||()()||()()|2[()()]n n f x f x f x f x f x f x f x f x --+-++-≤-要使满足条件的点存在，必须且只需2[()(0)]82a f f -≥，即282a ≥，解得4a ≥为所求.。

上海市闵行区七宝中学2017届高三上学期期中数学试卷含解析

2016—2017学年上海市闵行区七宝中学高三（上）期中数学试卷一.填空题1．已知集合A={x｜|x|≤2}，，则A∩B=．2．已知12cosθ﹣5sinθ=Acos（θ+φ）（A＞0），则tanφ=．3．已知函数f(x）=arcsin（2x+1）,则f﹣1（）= ．4．若函数f（x）=(a＞0且a≠1)的值域是［4，+∞)，则实数a的取值范围是．5．已知函数f（x）=3x﹣1,g（x）=x2﹣2x﹣1,若存在实数a、b使得f（a）=g（b），则b是取值范围是．6．已知函数f（x）=若f（2﹣a2）＞f（a）,则实数a的取值范围为．7．已知θ为锐角,且cos(θ+）=，则cosθ=．8．已知a＞0,b＞0且a+b=1，则（a+2）2+(b+2）2的最小值是．9．已知偶函数f（x）对任意x∈R都有f（x+4)﹣f(x）=2f（2）,则f=|x﹣1|+m｜x﹣2|+6｜x﹣3|在x=2时取得最小值,则实数m的取值范围是．11．已知f（x)=2sin（ωx）（ω＞0）在［﹣，］上单调递增，则ω的取值范围是．12．若定义在［﹣m，m]（m＞0）上的函数f（x）=+xcosx（a＞0，a≠1）的最大值和最小值分别是M、N，则M+N= ．13．在某一个圆中，长度为2、3、4的平行弦分别对应于圆心角α、β、α+β，其中α+β＜π，则这个圆的半径是．14．若正实数x,y满足x+2y+4=4xy,且不等式（x+2y)a2+2a+2xy﹣34≥0恒成立，则实数a的取值范围是．二.选择题15．函数的最小正周期为（）A．B．C．π D．2π16．已知y=f（x）是周期为2π的函数，当x∈[0,2π）时,f(x)=sin，则f（x）=的解集为（）A．{x｜x=2kπ+，k∈Z｝B．{x｜x=2kπ+，k∈Z}C．｛x｜x=2kπ±，k∈Z｝D．｛x|x=2kπ+（﹣1）k,k∈Z}17．“＜x＜”是“不等式｜x﹣1|＜1成立”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18．设函数f（x）=a x+b x﹣c x，其中c＞a＞0,c＞b＞0．若a，b，c是△ABC的三条边长，则下列结论中正确的是（）①对一切x∈(﹣∞,1）都有f（x）＞0；②存在x∈R+，使a x，b x，c x不能构成一个三角形的三条边长；③若△ABC为钝角三角形,则存在x∈（1，2），使f(x）=0．A．①②B．①③C．②③D．①②③三.解答题19．在△ABC中，角A、B、C的对边分别为a、b、c，且sinCcosB+sinBcosC=3sinAcosB;（1）求cosB的值；(2）若•=2，且b=2,求a+c的值．20．已知函数f（x）=，a，b∈R，a≠0,b≠0，f（1)=,且方程f(x）=x有且仅有一个实数解；（1)求a、b的值;(2）当x∈（，］时,不等式（x+1）•f（x）＞m（m ﹣x）﹣1恒成立，求实数m的范围．21．已知函数f（x）=sin(ωx+φ）（ω＞0,0＜φ＜π）的周期为π,图象的一个对称中心为（，0），将函数f（x)图象上的所有点的横坐标伸长为原来的2倍（纵坐标不变）,再将所得图象向右平移0.5π个单位长度后得到函数g（x）的图象；（1）求函数f（x)与g（x）的解析式；（2）当a≥1，求实数a与正整数n，使F（x）=f（x）+ag（x）在（0，nπ）恰有2019个零点．22．已知数列｛a n｝的前n项和为S n,且a1=a（a∈R），a n+1=,n∈N＊；（1）若0＜a n≤6，求证：0＜a n+1≤6;(2）若a=5，求S2016；（3）若a=（m∈N*）,求S4m+2的值．23．已知函数f（x）=ax2++5(常数a，b∈R）满足f （1）+f(﹣1）=14．（1）求出a的值，并就常数b的不同取值讨论函数f(x)奇偶性；（2）若f（x）在区间（﹣∞，﹣）上单调递减，求b的最小值；（3)在（2）的条件下，当b取最小值时，证明:f（x)恰有一个零点q且存在递增的正整数数列｛a n｝，使得=q+q+q+…+q+…成立．2016—2017学年上海市闵行区七宝中学高三（上）期中数学试卷参考答案与试题解析一。

上海市七宝中学2023届高三5月第一次模拟练习数学试题(2)

一、单选题二、多选题1. “垛积术”是我国古代数学的重要成就之一，宋元时期数学家朱世杰在《四元玉鉴》中记载了“三角形垛”，其中的“落一形”堆垛就是每层为“三角形数”的三角锥的堆垛（俯视如图所示，顶上一层1个球，下一层3个球，再下一层6个球，…）.若一“落一形”三角锥垛有6层，则该堆垛第6层的小球个数为（）A ．45B ．36C ．28D ．212.已知样本数据的平均数为､方差为，若样本数据，的平均数为，方差为，则（）A．B．C．D．3. 复数z 在复平面内对应的点的坐标为，则（）A．B．C．D．4.在的展开式中常数项为（）A ．721B ．-61C ．181D ．-595. 已知，且，则（）A．B．C．D．6. 已知正四棱台（上下底面都是正方形的四棱台）．下底面ABCD 边长为2，上底面边长为1，侧棱长为，则不正确的是（）A．它的表面积为B．侧棱与下底面所成的角为C．它的外接球的表面积为D ．它的体积比棱长为的正方体的体积大7.已知过椭圆的左焦点的直线与椭圆交于不同的两点，，与轴交于点，点，是线段的三等分点，则该椭圆的标准方程是（）A．B．C．D．8. 已知集合或，，则（）A．B．C．D．9. 下列抛物线中，焦点落在圆内部的是（）A．B．C．D．10.已知函数，则下列判断正确的是（）A．的最小正周期为B ．的图象关于点对称C ．的值域为D．的图象关于直线对称上海市七宝中学2023届高三5月第一次模拟练习数学试题(2)上海市七宝中学2023届高三5月第一次模拟练习数学试题(2)三、填空题四、解答题11. 已知是定义在上的连续函数，且满足，当时，，设（）A ．若，则B ．是偶函数C ．在上是增函数D．的解集是12. 已知复数，下列命题正确的是（）A．B ．若，则C．D ．若，则为实数13. 以抛物线：的顶点为圆心的圆交于两点，交的准线于两点.已知，，则等于__________．14. 已知向量夹角为，且，则__________．15. 已知二次函数的值域为，则函数的值域为______．16. 已知函数，．（1）讨论函数的单调性；（2）若，且关于的不等式在上恒成立，其中是自然对数的底数，求实数的取值范围．17. 为助力湖北新冠疫情后的经济复苏，某电商平台为某工厂的产品开设直播带货专场.为了对该产品进行合理定价，用不同的单价在平台试销，得到如下数据：单价（元/件）88.28.48.68.89销量（万件）908483807568（1）根据以上数据，求关于的线性回归方程；（2）若该产品成本是7元/件，假设该产品全部卖出，预测把单价定为多少时，工厂获得最大利润？（参考公式：回归方程，其中，）18. 已知椭圆C ：＋＝1(a ＞b ＞0)的左、右焦点分别为F 1，F 2，离心率为，点A 在椭圆C 上，|AF 1|＝2，∠F 1AF 2＝60°，过F 2与坐标轴不垂直的直线l 与椭圆C 交于P ，Q 两点，N 为线段PQ 的中点．(1)求椭圆C 的方程；(2)已知点M，且MN ⊥PQ ，求线段MN 所在的直线方程．19. 为了落实习主席提出的“绿水青山就是金山银山”的环境治理要求，某市计划自2014年初起开始实施绿化行动.实施绿化的第年(如2014年对应的)，绿化面积为平方公里，则连续五年，之间的数据如下表：1234513678（1）已知对于一组数据，，……，若其拟合直线方程，记，若越小则拟合效果越好.若根据表中数据，观察得出的拟合直线方程分别为，，使用判断哪条点线的拟合效果更好；（2）试用（1）中所求的拟合效果较好的直线，估计2024年的绿化面积.20. 设函数．（1）设，求的极值点；（2）若时，总有恒成立，求实数m的取值范围．21. 已知数列满足：．(1)证明数列为等差数列，并求数列的通项公式．(2)若，证明：．。

上海市七宝中学2017届高三5月月考英语试题(含答案)

第I卷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. See a film with the man B. Offer the man some helpC. Listen to some great musicD. Say thanks to the man.2. A. At 1:00 pm B. At 3:00 pm C. At 4:00 pm D. At 5:00 pm3. A. On his way B. In a restaurant C. At home D. On a train4. A. A gay stole his clothes B. He found his clothes uglyC. Someone said he was uglyD. The clothes in the supermarket are ugly5. A. Ask for something cheaper B. Buy the vase she really likesC. Protect herself from being hurtD. Bargain with the shop assistant6. A. 147 pounds B. 150 pounds C. 153 pounds D. 163 pounds7. A. To get a haircut B. To attend a party C. To do some shopping D. To drive her home8. A. Use a computer in the lab B. Take a chemistry courseC. Help him revise his reportD. Get her computer repaired9. A. It spoke highly of the mayor B. It misinterpreted the mayor’s speechC. It made the mayor’s view clearerD. It carried the mayor’s speech accurately10. A. Germany B. France C. West Africa D. SpainSection BDirections: In Section B, you will hear several longer conversation(s) and short passage(s), and you will be asked several questions on each of the conversation(s)and short passage(s). The conversation(s)and the passage(s)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. He was Mrs. Beach’s neighborB. He used to work at Ms. Beach’s bookstoreC. He has followed Ms. Beach’s way of doing businessD. He came from Britain12. A. She died B. The Germans made her give it upC. Her business went from bad to worseD. She decided to start a new business13. A. In 1951 B. In 1962 C. In 1964 D. In 1919Questions 14 through 16 are based on the following passage.14. A. 0.1 cm B. 1cm C. 0.01 mm D. 0.1mm15. A. There was a hole in it B. It got hurt by something hardC. It went off Bill Beaver’s eyeD. It sometimes didn’t work well16. A. It was made by handB. It was made by a special robotC. There was some blood during the operationD. The doctors didn’t take part during the opersationQuestions 17 through 20 are based on the following conversation.17. A. It couldn’t be doneB. It couldn’t be doneC. It was very difficultD. It was boring18. A. He didn’t like physical educationB. He had so little physical energyC. He was unable to sit still in classD. He can’t use skateboard at school19. A. He had a different schoolB. He let students plan P. E. classes on their ownC. He was kind to every studentD. He showed some techniques during classes20. A. It was robot-like with new tricksB. He was more professionalC. He created it by himselfD. It is smoother than others’II. Grammar and V ocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.I have often though it would be a blessing(21)_________each human being were stricken blind and deaf for a few days at some time during his early adult life. Darkness would make him more appreciative of sight; silence would teach him the joys of sound.Now and then I have tested my seeing friends to discover what they see. Recently I was visited by a very good friend who had just returned from a long walk in the woods, and I asked her what she had o bserved. “Nothing in particular,” she replied. I (22)_______be suspicious if I had not been accustomed to such responses, for long ago I became convened that (23)____seeing see little.How was it possible, I asked myself, (24)__________(walk)for an hour through the woods and see nothing worthy of note? I who cannot see find hundreds of things to interest me(25)_______mere touch. I feel the delight of a flower, and something of the miracle of nature is revealed to me. Occasionally, if I am very fortunate, I place my hand gently in a small tree and feel the happy tremble of a bird in full song. I am delighted to have cool waters of a river (26)_________(rush)through my open fingers.To me the feast of seasons is a thrilling and unending drama, the action of (27)_________streams through my fingertips. At times my heart cries out, (28)________(thrill)to see al these things. If I can get so much pleasure by mere touch, how much more beauty must be revealed by sight? Yet, those who, have eyes apparently, see little. The view of color and action that fill the world(29)___________(take) for granted.It is human, perhaps, to appreciate little that which we have and to long for that which we have not, (30)________it is a great pity that in the world of light the gift of sight is used only as mere convenience rather than as a means of adding fullness to life.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.By now, how the immune system is affected by stress has been discovered. In one study, ___31___500 couples, those who showed very unfriendly behavior during a 30-minute discussion about marriage problems had lower immune functioning for 24-hour period following the experiment than people who showed less ___32___behavior. It is not just stress that can do damage. One researcher though that if the same cold virus was put under two different noses, the person who is depressed or anxious would be more likely to develop the cold. How can stress and related emotions contribute to poor health?These feelings can cause the __33___of substances that damage or weaken our immure cells. Negative emotion can also cause our bodies to produce fewer substances that __34___help fight off disease. If stress, depression, anger and other negative feelings can make you more likely to get sick, can the ___35____be true? Will you have a stronger immune__36___and greater health if you are happier, less stressed? Experts believe that the answer is yes. There are studies showing that by __-37___certain mind-body techniques that help reduce stress and improve outlook, cancer patients can live longer. And cancer patients aren’t the only ones who can benefit. Research has found that when patients with chronic pain use ____38___therapies and other techniques to deal with discomfort, they reduced their visits to the doctors by 36%. Relaxation produces better health through deep rhythmic breathing, muscle loosening and a slower heart rate. When some of the pressure is taken out of the body, they entire immune system will ___39___much better. Relaxation decreases blood pressure and heart rate. That is important because a body that is ___40___under pressure will exhaust.III. Reading Comprehension Section ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Why do people go to university? There is a popular notion that a college education is something to be endured in order to become __41___to obtain certain kinds of jobs or to go to graduate school. This is not what we are trying to do at Harvard, nor would we wish to have many students here who took such a(n)___42___view of a college career. There are several goals we aim to reach in our undergraduate program.The most obvious one is to give knowledge—fairly___43___knowldege in one field and a more general knowledge of a variety of other subject areas which you may choose according to your interest. But if acquiring knowledge is a self-evident part of a college education, it is __44___the most important. Remarkably few of the facts you learn here will remain in your___45___for many years, and some of those that do will even be proved___46___by new knowledge.__47___, we can instill(灌输)certain attitudes of mind-a willingness to accept uncertainly and the lack of definite truths; independence of mind, and a respect for facts and for the uncomfortable conclusions which facts sometimes lead to.In addition to these ___48___qualities, a college education should try to lay a foundation for the creative use of ___49___time. Some of this capacity can be stimulated in the classroom—in courses in the humanities and the arts. Yet, at least as much __50___will occur outside the lecture hall---on athletic fields, in music rooms, student theaters, concert hails, and so forth.These are some of the __51___of a liberal college education as I see them. I cannot resist concluding with a few private thoughts about our new careers at Harvard.To begin with, I hope that we will think__52___about what we want to accomplish here. It would be __53___for you to set your sights on some limited goal, such as getting good grades or merely getting into one or another graduate school.Second, I hope that you will give some thought to what you can do for others during your stay here. There are many problems waiting for your help, and many people who could __14___your efforts.My final bit of advice. Whatever else we do, let us remember not to take ourselves too seriously. However great our problems may seem, however urgent our complaints, they are overshadowed(黯然失色)by the __55__of countless other people on our planet.41. A. fascinated B. qualified C. determined D. required42. A. optimistic B. strong C. narrow D. sensitive43. A. concentrated B. expanded C. informed D. illustrated44. A. by far B. far from C. free from D. without doubt45. A. memory B. position C. evaluation D. foundation46. A. useful B. essential C. false D. common47. A. Besides B. However C. Therefore D. Somehow48. A. physical B. inborn C. emotional D. intellectual49. A. business B. study C. experiment D. leisure50. A. appreciation B. stimulation C. participation D. exposure51. A. benefits B. aims C. problems D. achievements52. A. broadly B. honestly C. freely D. continually53. A. fantastic B. magic C. tragic D. basic54. A. suffer from B. profit from C. reflect on D. complain about55. A. inspiration B. difference C. ambitions D. difficultiesSection BDirections: 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 read.(A)The Tide Rises, the Tide FallsBy Henry Wadsworth LongfellowThe tide rises, the tide falls,Along the sea — sands damp and brownThe traveler hastens toward the town,And the tide rises, the tide falls.Darkness settles on roofs and walls,But the sea, the sea in the darkness calls;The little waves, with their soft, white hands,Efface the footprints in the sands,And the tide rises, the tide falls.The morning breaks; the steeds in their stallsStamp and neigh, as the hostler calls;The day returns, but never moreReturns the traveler to the shore,And the tide rises, the tide falls.56. What is the figurative meaning (寓意)of the title “The Tide Rises, the Tide Falls” indicate?A. the change of the oceanB. the sequence of human historyC. the coming and going of travelersD. the eternity of the natural world57. In stanza 1, which line is parallel to “The morning breaks: the steeds in their stalls”?A. The tide rises, the tide fallsB. The twilight darkens, the curlew callsC. Alone the sea-sands damp and brownD. The traveler hastens toward the town58. In stanza 2, the word “Efface” in line 4 is the closest to _________in meaning.A. drawB. engraveC. eraseD. impress59. In stanza 3, “The day returns, but nevermore; Returns the traveler to the shore”, the poet possibly means ________.A. Time hustles; people bustleB. The traveler comes to the town just onceC. People will die while time goes onD. If time had feelings, people would stay(B)Predicting the future is alwa ys risky. But it’s probably safe to say that at least a few historians will one day speak of the 20th century as America’s “Disney ear”. Today, it’s certainly difficult to think of any other single thing that represents modern America as powerfully as the company that created Mickey Mouse. Globally, brands like Coca-Cola and McDonald's may be more widely known, but neither concludes 20th-century America in quite the same way as Disney.The reasons for Disney's success are quite a lot, but ultimately the credit belongs to one person - the man who created the cartoon and built the company from nothing, Walt Disney. Ironically, he could not draw particularly well. But he was a genius in other aspects. In business, his greatest skills were his insight and his management ability. After setting himself up in Hollywood, he single-handedly pioneered the concepts of branding and merchandising -- something his company still does brilliantly today.But what really distinguished Disney was his ability to identify with his audiences. Disney always made sure that his films championed the "little guy", and made him feel proud to be American. This he achieved by creating characters that reflected the hopes and fears of ordinary people. Some celebrated American achievements---He achieved this by creating characters that reflected the hopes and fears of ordinary people. Some Mickey Mouse, was “inspired by Charles Lindbergh’s flight across the Atlantic. Others, like the There Little Pigs and Snow White and the Seven Dwarves, show ed how, through hard wok and helping one’s fellow man or Americans could survive social and economic crises like the Great Depression.Disney's other great virtue was the fact that his company -- unlike other big corporations--- had a human face. His Hollywood studio -- the public heard -- operated just like a democracy, where everyone was on first name terms and had a say in how things should be run. He was also regarded as a great patriot because not only did his cartoons praise America, but, during World War II, his studios made training films for American soldiers.The reality, of course, was less idyllic. As the public would later learn, Disney's patriotism had an unpleasant side. After a strike by cartoonists in 1941, he became convinced that Hollywood had been infiltrated by Communists . He agreed to work for the FB1 as a mole, identifying and spying on colleagues whom he suspected were subversives.But, apart from his affiliations with the FBI, Disney was more or less the genuine article. A new book, The Magic Kingdom: Walt Disney and the American Way of Life, by Steven Watts, confirms that he was very definitely on the side of ordinary Americans—in the 30s and 40s he voted for Franklin Roosevelt, believing he was a champion of the workers. Also, Disney was not an apologist for the FBI, as some have suggested. In fact, he was always suspicious of large, bureaucratic organizations, as is evidenced in films like That Darned Cat, in which he portrayed FB1 agents as bungling incompetents.By the time he died in 1966, Walt Disney was as icon like Thomas Edison and the Wright Brothers. To business people and filmmakers, he was a role model; to the public at large, he was "Uncle Walt" -- the man who had entertained them all their lives, the man who represented them all their lives, the man who represented all that was good about America.60. Walt Disney is believed to possess the following abilities EXCEPT______________.A . painting B. creativity C. management D. merchandising61. According to the passage, what was the pleasant side of Disney’s patriotism?A. He sided with ordinary Americans in his filmsB. He supported Arnorlca’s was efforts in his own wayC. He had doubts about large, bureaucratic organizationsD. He voted for Franklin Roosevelt in the 30s and 40s62. In the sixth paragraph the sentence “Disney was more or lets the genuine article” means that _________.A. Disney was a creative and capable personB. Disney once agreed to work for the FB1C. Disney ran his company in a democratic wayD. Disney was sympathetic with ordinary people(C)For most thinkers since the Greek philosophers, it was self-evident that there is something called human nature, something that constitutes the essence of man. There were various views about what constitutes it, but there was agreement that such an essence exists---that is to say, that there is something by virtue of which man is man. Thus man was defined as a rational being, as a social animal, an animal that can make tools, or a symbol-making animal.More recently, this traditional view has begun to be questioned. One reason for this change was the increasing emphasis given to the historical approach to man. An examination of the history of humanity suggested that man in our time is so different from man in previous times that it seemed unrealistic to assume that men in every age have had in common something that can be called “human nature.” The historical approach was reinforced, particularly in the United States, by studies in the field of cultural anthropology (人类学). The study of primitive peoples has discovered such a diversity of customs, values, feelings, and thoughts that many anthropologists arrived at the concept that man is born as a blank sheet of paper on which each culture writes its text. Another factor contributing to the tendency to deny the assumption of a fixed human nature was that the concept has so often been abused as a shield behind which the most inhuman acts are committed. In the name of human nature, for example, Aristotle and most thinkers up to the eighteenth century defended slavery. Or in order to prove the rationality and necessity of the capitalist form of society, scholars have tried to make a case for acquisitiveness, competitiveness, and selfishness as natural human characters. Popularly, one refers cynically to “human nature” in accepting the inevitability of such undesirable human behavior as greed, murder, cheating and lying.Another reason for skepticism about the concept of human nature probably lies in the influence of evolutionary thinking. Once man came to be seen as developing in the process of evolution, the idea of a substance which is contained in his essence seemed untenable. Yet I believe it is precisely from an evolutionary standpoint that we can expect new insight into the problem of the nature of man.63. Most philosophers believed that human nature ________.A. is the quality distinguishing man from other animalsB. consists of competitiveness and selfishnessC. is something partly innate and partly acquiredD. consists of rationality and undesirable behavior64. The traditional view of “human nature” was strongly challenged by ________.A. the emergence of the evolutionary theoryB. the historical approach to manC. new insight into human behaviorD. the philosophical analysis of slavery65. The author mentioned Aristotle, a great ancient thinker, in order to ________.A. emphasize that he contributed a lot to defining the concept of “human nature”B. show that the concept of “human nature” was used to justify social evilsC. prove that he had a profound influence on the concept of “human nature”D. support the idea that some human characters are inherited.66. According to the passage, anthropologists believe that human beings ________.A. have some characters in commonB. are born with diverse culturesC. are born without a fixed natureD. change their characters as they grow upSection CDirections: Complete the following passage by using the sentences given below. Each sentence can be used only once. Note that there are two more sentences than you need.1) In a few years you will be able to order a transcript of your entire genetic code for less than $1,000. ____67____Two different university laboratories have developed test that will reveal the enti rety of a baby’s genetic code using just a blood sample from the mother plus a drop of saliva(唾液)from the father.2) Prenatal(出生前的) whole-genome sequencing will provide volumes of information beyond the currently available tests exclusively for genetic dis orders such as Down’s syndrome or Tay-Saches disease. The three billion units of code furnished in the new tests will also dwarf(使……相形见的) the relative trickle(零散)of information provided by consumer gene-testing services such as 23andMe, which currently look only at perhaps about one million locations in the genome.3)____68____Without careful panning, the new prenatal genetics might rob a child of the chance to make decisions best left until adulthood---whether or not to learn, for instance, if a mutation(突变)predicts the inevitability of Huntington’s disease 20 years hence.4)_____69_____. Similar laissez0faire(放住)action to prenatal whole-genome testing could portend(预示)tragedy.5)Ultimately certain agency will need to develop a comprehensive policy on prenatal whole genome testing. Bioethics scholars wrote an analysis last summer that calls on the medical community to develop a guide to the most relevant genomic data for future parents. ___70___Without access to a much higher level of refined expertise, the secrets of our offspring’s genetic code will continue to remain an unnerving cipher---or worse.IV. Summary WritingDirections: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.Rocks Tell TimeEarth’s surface is constantly changing, and its rocks are evidence of past geologic events. The age of rocks can be determined in various ways. By using relative-dating principles and noting the position of layers within a rock, it is also possible to reconstruct the sequence(顺序)of geologic events that have occurred at a site.One way scientists do this is by using the principle of uniformitarianism, which states that the processes affecting the earth today are the same ones that affected it in the past. For example, at an active volcano, today, lava can be observed to cool and form layers of basalt(玄武岩). Therefore, any time one sees layers of basalt, it can be assumed that they likely formed from lava cooling after a volcanic eruption.Second, the principle of original horizontality states that most sedimentary(由沉淀物所生成的)rock is deposited in a horizontal position, which means they form layers. The principle of superposition can be used to interpret the relative ages of these layers: In a sequence of undisturbed sedimentary layers or lava flows, the oldest layers are at the bottom. These principles allow scientists to determine the relative age of a rock compared with another rock. They can also compare the ages of rock layers in different areas. This type of comparison has enabled them to create a list of earth’s rock layers from youngest to oldest, called a geologic column.Another way to test a rock’s age is by using radioactivity. Radioactive parts of elements in rocks decay into other elements at a constant pace called a half-life. By comparing the amount of the originai element with the amount present today, scientists can come up with an absolute age for a rock. These ages are compiled into a history of earth. Long stretches of time on earth are called eras. Earth’s rock history includes the Paleozoic, Mesozoic, and Cenozoic eras.The scientists who interpret the stories told by rocks are called structural geologists and stratigraphers(地层学家). Structural geologists c arefully observe and interpret layer of rock. They study the way in which the earth’s crust is deformed by mountain-building processes. They also study clues at the earth’s surface that reveal the underlying structure and geologic history of an area. Stratigaphers compare vertical sequences of rock layers form different areas to piece together the geologic history of a region.71._____________________________第II卷V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72．在我看来，中国人是世界上最喜欢谈论国内外大事的民族。

上海市七宝中学2017-2018学年下学期高三3月月考数学试题

2017-2018年七宝中学高三下3月月考2018.03一. 填空题1. 已知集合{|3}{|1}A x x x x =≥<-，则C A =R2. 复数1i z i=-（其中i 为虚数单位）的模为 3. 某学校有8个社团，甲、乙两位同学各自参加其中一个社团，且他俩参加各个社团的可能性相同，则这两位同学参加同一个社团的概率为4. 从编号0，1，2，⋅⋅⋅，79的80件产品中，采用系统抽样的方法抽取容量是5的样本，若编号为28的产品在样本中，则该样本中产品的最大编号为5. 设奇函数()f x 的定义域为[5,5]-，若当[0,5]x ∈时，()f x 的图像如图，则不等式()0f x <的解是6. 若12log 11a a <-，则a 的取值范围是 7. 在平面直角坐标系xOy 中，设A 是半圆22:2O x y +=（0x ≥）上一点，直线OA 的倾斜角为45°，过点A 作x 轴的垂线，垂足为H ，过H 作OA 的平行线交半圆于点B ，则直线AB 的方程是8. 在ABC ∆中，D 是BC 的中点，8AD =，20BC =，则AB AC ⋅的值为9. 设x 、y 、z 是实数，9x 、12y 、15z 成等比数列，且1x 、1y 、1z 成等差数列，则x z z x + 的值是10. 设实数a 、b 、c 满足221a b c +≤≤，则a b c ++的最小值为11. 若不等式2(1)[3(1)1]0mx m x m --+-≥对任意(0,)m ∈+∞恒成立，则实数x 的值为12. 设等差数列{}n a 的公差为d ，前n 项和为n S ，且11a ≥，2424a ≥，12168S ≤，则29a d -的取值范围是二. 选择题13. 若函数2()21xx f x =-+，则该函数在(,)-∞+∞上是（） A. 单调递减无最小值 B. 单调递减有最小值 C. 单调递增无最大值 D. 单调递增有最大值14. “22a -≤≤”是“实系数一元二次方程210x ax ++=有虚根”的（）条件A. 必要不充分B. 充分不必要C. 充要D. 既不充分也不必要15. 已知a 、b 是单位向量，0a b ⋅=，若向量c 满足||1c a b --=，则||c 的取值范围是（）A. 1]B. 2]C. 1]D. 2]+16. 将半径都为1的4个钢球完全装入形状为正四面体的容器里，这个正四面体的高的最小值为（）A.3 B. 23+ C. 43+ D. 3三. 解答题17. 在ABC ∆中，已知9AB AC ⋅=，16AB BC ⋅=-，求：（1）AB 的值；（2）sin()sin A B C-的值.18. 如图，在直棱柱1111ABCD A B C D -中，AD ∥BC ，90BAD ∠=︒，AC BD ⊥，1BC =，13AD AA ==.（1）证明：1AC B D ⊥；（2）求直线11B C 与平面1ACD 所成角的正弦值.19. 将52名志愿者分成A 、B 两组参加义务植树活动，A 组种植150捆白杨树苗，B 组种植200捆沙棘树苗，假定A 、B 两组同时开始种植.（1）根据历年统计，每名志愿者种植一捆白杨树苗用时25小时，种植一捆沙棘树苗用时12小时，应如何分配A 、B 两组的人数，使植树活动持续时间最短？（2）在按（1）分配的人数种植1小时后发现，每名志愿者种植一捆白杨树苗用时仍为25小时，而每名志愿者种植一捆沙棘树苗实际用时23小时，于是从A 组抽调6名志愿者加入B 组继续种植，求植树活动所持续的时间.20. 已知左焦点为(1,0)F -的椭圆过点(1,3E ，过点(1,1)P 分别作斜率为1k 、2k 的椭圆的动弦AB 、CD ，设M 、N 分别为线段AB 、CD 的中点.（1）求椭圆的标准方程；（2）若P 为线段AB 的中点，求1k ；（3）若121k k +=，求证：直线MN 恒过定点，并求出定点坐标.21. 已知数列{}n a 满足212n a a a n ++⋅⋅⋅+=（n ∈*N ）.（1）求数列{}n a 的通项公式；（2）对任意给定的k ∈*N ，是否存在,p r ∈*N （k p r <<）使1ka 、1p a 、1r a 成等差数列？若存在，用k 分别表示p 和r （只要写出一组），若不存在，请说明理由；（3）证明：存在无穷多个三边成等比数列且互不相似的三角形，其边长为1n a 、2n a 、3n a .参考答案1、[)1,3-2、23、184、765、()(]2,02,5-6、4a >7、1y =+ 8、36- 9、3415 10、12- 11、1x = 12、2498,16⎡⎤⎢⎥⎣⎦ 13-16、AAAC17、（1）5；（2）72518、（1）证明略;（2）7 19、（1）A 组20人，B 组32人；（2）277小时 20、（1）22132x y +=；（2）23-；（3）20,3⎛⎫- ⎪⎝⎭ 21、（1）21n a n =-；（2）21p k =-，2452r k k =-+；（3）证明略。

上海市七宝中学2017-2018学年高三模拟考试理数试题 Word版含解析

上海市七宝中学2017-2018学年高三模拟考试理数试题一、填空题（本大题共14小题，每题4分，满分56分．）1.函数y =______________. 【答案】(0,1] 【解析】试题分析：由0log 5.0≥x 得10≤<x ，应填答案(0,1]. 考点：对数不等式的解法．2.已知{}2,M y y x x R ==∈，{}222,,N x x y x y R =+=∈，则M N =_____.【答案】⎢⎣【解析】试题分析：因02≥=x y ,而2222≤-=y x ,故22≤≤-x ,所以]2,0[=N M .考点：集合的交集运算．3.在41(1)(1)x x++的展开式中2x 项的系数为______________.【答案】10考点：二项式定理及通项公式的运用．4.已知地球的半径为R ，在北纬045东经030有一座城市A ，在北纬045西经060有一座城市B ，则坐飞机从城市A 飞到B 的最短距离是______________.（飞机的飞行高度忽略不计）【答案】3R π【解析】试题分析：已知纬圆所在的纬度为045,则纬圆的半径为R 22,纬圆周的两点B A ,的弦长为R R AB =⋅=222,所以点B A ,所在的球的大圆面上弧所对的圆心角为3π,则大圆的弧长为R 3π.考点：球面距离及计算．【易错点晴】球面距离的定义是经过球心的大圆上的劣弧的长.解答本题的关键是求出经过B A ,大圆的圆心角AOB ∠,为此先求045纬圆上这两点B A ,连线段的长AB ,即纬圆上的弦长AB .求的长时借助纬度的概念,求出了球心与纬圆面之间的距离=d R 22与纬圆的半径相等.由经度的定义可知0190=∠B AO ,所以R R AB =⋅=222,这样AOB ∆就是等边三角形,所以点B A ,所在的球的大圆面上弧所对的圆心角为3π,则大圆的弧长为R 3π,即球面距离是R 3π.5.已知一随机变量ξ的分布列如下表，则随机变量ξ的方差D ξ=______________.【答案】11 【解析】试题分析：因为3)840(41)(,20)64160(41)(2=++==++=x E x E ,所以11920)()(22=-=-=x E x E D ξ.考点：数学期望和方差的计算． 6.在极坐标系中，点(2,),(2,)2A B ππ，C 为曲线2cos ρθ=的对称中心，则三角形ABC 面积等于________. 【答案】3 【解析】试题分析：将点B A ,化为直角坐标为)2,0(),0,2(B A -,极坐标方程化为直角坐标为0222=-+x y x ,所以圆心为)0,1(C ,所以ABC ∆的面积为32321=⨯⨯=S . 考点：极坐标方程及运用．7.高三（1）班班委会由4名男生和3名女生组成，现从中任选3人参加上海市某社区敬老服务工作，则选出的人中至少有一名女生的概率是______________.（结果用最简分数表示）【答案】3135【解析】试题分析：从7名学生中选3名的种数为3512356737=⨯⨯⨯⨯=C ,其中无女生的种数为41434==C C ,所以至少含有一个女生的概率为35313541=-=P . 考点：古典概型的计算公式及排列数组合数公式的运用．8.在复数范围内，若方程22012690x x ++=的一个根为α，则α=______________.考点：复数的模及计算．9.将()f x =sin cos xx 的图象按(,0)(0)n a a =->平移，所得图象对应的函数为偶函数，则a 的最小值为______________. 【答案】56π 【解析】试题分析：因为()f x =sin cos xx )6cos(sin cos 3π+=-=x x x ,所以按向量平移后所得的函数为)6cos()(π++=a x x g ,由题设可得1)60cos()0(±=++=πa g ,即ππk a =+6,也即6ππ-=k a ,所以a 的最小值为56π.考点：行列式的计算及三角函数的图象和性质．10.已知()y f x =是定义在R 上的增函数，且()y f x =的图象关于点(6,0)对称，若实数,x y满足不等式22(6)(836)0f x x f y y -+-+≤，则22x y +的取值范围是______________. 【答案】[16,36]考点：函数的单调性和圆的方程的等知识的综合运用．11.函数()f x 对任意12,[,]x x m n ∈都有1212()()f x f x x x -≤-，则称()f x 为在区间[,]m n 上的可控函数，区间[,]m n 称为函数()f x 的“可控”区间，写出函数2()21f x x x =++的一个“可控”区间是________. 【答案】1[,0]2-的子集都可以【解析】试题分析：因为)](1)(2[)()(212121x x x x x f x f -++=-,由可控函数的定义可得1|1)(2|21≤++x x ,即0121≤+≤-x x ,所以区间[,]m n 应为]0,21[-的一个子区间.考点：定义新概念和综合运用所学知识．【易错点晴】本题以函数的形式为背景，考查的是不等式的有关知识及推理判断的能力.结论的开放性和不确定性是本题的一大特色.解答时应充分依据题设条件,合理有效地利用好可控函数及可控区间等新信息和新定义,并以此为基础进行推理论证,从而写出满足题设条件的答案.解答本题时,借助绝对值不等式的性质进行巧妙推证,从而探寻出符合题设条件的一可控区间的区间.12.椭圆22221(0)43x y a a b+=>的左焦点为F ，直线x m =与椭圆相交于点,A B ，当FAB ∆的周长最大时，FAB ∆的面积是______________.【答案】acb S 23=考点：椭圆的定义和几何性质．13.用符号(]x 表示小于x 的最大整数，如(]3,( 1.2]2π=-=-，有下列命题：①若函数()(],f x x x x R =-∈，则()f x 的值域为[1,0)-；②若(1,4)x ∈，则方程1(]5x x -=有三个根；③若数列{}n a 是等差数列，则数列{}(]n a 也是等差数列；④若57,{,3,}32x y ∈，则(](]2x y∙=的概率为29P =. 则下列正确命题的序号是______________. 【答案】①②④ 【解析】试题分析：由定义0](1<-≤-x x ,所以其值域为[1,0)-,故①正确；由于5.0](=-x x ,因此可求得2.3,2.2,2.1=x ,所以②正确；对于③,如取数列7.4,9.2,1.1成等差数列,但4]7.4(,2]9.2(,1]1.1(===不成等差数列；对于④很容易验证是正确的.故应填①②④.考点：函数的性质及分析问题解决问题的能力．【易错点晴】本题以符号函数为背景，考查的是函数与方程、等差数列和等比数列、概率等许多有关知识和运算求解及推理判断的能力.定义新概念运用新信息是解答本题的一大特色.解答时应充分依据题设条件,对题设中提供的几个命题进行分析推断最后作出真假命题的判断.对于命题,举出一个反例,进行了推断从而说明它是假命题.运用反例是否定一个命题是真命题的有效方式和方法.14.设()cos 2()cxf x ax bx x R =++∈，,,a b c R ∈且为常数，若存在一公差大于0的等差数列{}n x（*n N ∈），使得{()}n f x 为一公比大于1的等比数列，请写出满足条件的一组,,a b c 的值【答案】0,0,0a b c ≠=>（答案不唯一，一组即可）【解析】试题分析：由题设可取1,0,1===c b a ,此时x x x f 2cos )(+=,存在数列25,23,2πππ,满足题设,应填答案1,0,1===c b a .考点：函数与等差等比数列以及分析探究的能力．【易错点晴】本题以函数的形式为背景，考查的是等差数列和等比数列的有关知识及推理判断的能力.开放性是本题的一大特色.解答时应充分依据题设条件,想方设法构造出一个满足题设条件的数列.由于本题是一道结论开放型的问题,因此它的答案是不唯一的,所以在求解时只要求出一组符合题目要求的数据即可.如本题的解答时取1,0,1===c b a ,函数xx x f 2cos )(+=,取数列}25,23,2{πππ,则253322)25(,2)23(,2)2(ππππππ===f f f 成等比数列,故答案应填1,0,1===c b a . 二、选择题（本大题共4个小题，每小题5分，共20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.）15.若直线l 的一个法向量(3,1)n =，则直线l 的一个方向向量d 和倾斜角α分别为（） A ．(1,3);arctan3d α== B ．(1,3);arctan(3)d α=-=- C ．(1,3);arctan3d απ==- D ．(1,3);arctan3d απ=-=- 【答案】D 【解析】试题分析：由题设可知直线l 的一个方向向量是)3,1(-=,其斜率3-=k ,即3tan -=α,故3arctan -=πα,应选D.考点：直线的法向量和反正切函数．16.在ABC ∆中，“cos cos cos 0A B C ∙∙<”是“ABC ∆为钝角三角形”的（） A ．充分必要条件 B ．必要不充分条件 C ．充分不必要条件 D ．既不充分也不必要条件【答案】A试题分析：由题设条件可知C B A cos ,cos ,cos 中必有一个是负数,即三个内角中必有一个是钝角,所以是钝角三角形,是充分条件;反之,若三角形是钝角三角形,则C B A cos ,cos ,cos 的积必为负数,即是必要条件,应选答案A. 考点：解三角形．【易错点晴】本题以解三角形的问题的形式为背景，考查的是充分必要条件的有关知识及推理判断的能力. 解答好本题的关键是搞清楚钝角三角形的概念是什么?其外延是什么?其实钝角三角形的概念是有一个内角是钝角即可了.解答这个问题的过程中常常会出现三个内角都是钝角的错误,将锐角三角形的概念和钝角三角形的概念混淆在一起,从而误判得出不正确的答案.17.定义域是一切实数的函数()y f x =，其图象是连续不断的，且存在常数()R λλ∈使得()()0f x f x λλ++=对任意实数x 都成立，则称()f x 是一个“λ—半随函数”.有下列关于“λ—半随函数”的结论：①()0f x =是常数函数中唯一一个“λ—半随函数”；② “12—半随函数”至少有一个零点；③2()f x x =是一个“λ—半随函数”；其中正确结论的个数是（）A ．1个B ．2个C ．3个D ．0个【答案】A考点：函数及新定义的概念的灵活运用．【易错点晴】本题以函数的形式为背景，考查的是函数的零点等有关知识及推理判断的能力. 命题的真假的判断及分析求解的能力是解答好本题的关键,本题给出的三个命题的真假的判断成为解答这道试题的重中之重.对于命题①,实数λ的取值是不唯一的,因此该命题是假命题；对于命题②,运用定义可得结论,显然这个方程0)(21)21(=-=+x f x f 的解是不唯一的,所以是真命题；对于命题③找不到实数λ满足题设,因此是假命题整个求解过程充满了推理和判断.18.已知数据123,,,,n x x x x 是上海普通职工n （3n ≥，*n N ∈）个人的年收入，设这n 个数据的中位数为x ，平均数为y ，方差为z ，如果再加上世界首富的年收入1n x +，则这1n +个数据中，下列说法正确的是（）A ．年收入平均数大大增大，中位数一定变大，方差可能不变；B ．年收入平均数大大增大，中位数可能不变，方差变大；C ．年收入平均数大大增大，中位数可能不变，方差也不变；D ．年收入平均数可能不变，中位数可能不变，方差可能不变. 【答案】B 【解析】试题分析：由题设可知选择支中的A,C,D 都是不正确的，所以应选B. 考点：中位数平均数方差等概念的理解和计算．三、解答题（本大题共5小题，共74分.解答应写出文字说明、证明过程或演算步骤.） 19.（本题满分12分，其中第1小题6分，第2小题6分）在直三棱柱111ABC A B C -中，1AB AC ==，090BAC ∠=，且异面直线1A B 与11B C 所成的角等于060，设1AA a =. （1）求a 的值；（2）求直线11B C 到平面1A BC 的距离.【答案】(1)1；(2)3．【解析】试题分析：(1)运用平几的勾股定理等知识求解；(2)运用等积法求解. 试题解析：（1）∵11//BC B C ，∴1A BC ∠就是异面直线1A B 与11B C 所成的角，即0160A BC ∠=,又连接1AC ，AB AC =，则11A B AC = ∴1A BC ∆为等边三角形，由1AB AC ==，090BAC ∠=BC ⇒=∴11A B a =⇒==.（2）易知11//B C 平面1A BC ，又D 是11B C 上的任意一点，所以点D 到平面1A BC 的距离等于点1B 到平面1A BC 的距离. 设其为d ，连接1B C ，则由三棱锥11B A BC -的体积等于三棱锥11C A B B -的体积，求d ，11A B B ∆的面积12S =，1A BC ∆的面积'242S ==，又1CA A A ⊥，CA AB ⊥，∴CA ⊥平面11A B C ，所以'11333S AC S d d ∙∙=∙∙⇒=，即11B C 到平面1A BC 的距离等于3. 考点：空间的直线与平面的位置关系及几何体的体积公式．【易错点晴】立体几何是高中数学的重要内容之一,也是上海市历届高考必考的题型之一.本题考查是空间的直线与直线所成角的计算问题和直线与平面的距离的计算问题.解答时第一问充分借助已知条件中异面直线所成角的概念,通过解直角三角形而获解.关于第二问中直线与平面之间的距离问题,解答时巧妙运用转化的思想,将其转化为三棱锥的高的问题来处理,使得问题的求解过程简捷明快.20.（本小题满分14分，其中第1小题6分，第2小题8分）某海域有,A B 两个岛屿，B 岛在A 岛正东4海里处，经多年观察研究发现，某种鱼群洄游的路线是曲线C ，曾有渔船在距A 岛、B 岛距离和为8海里处发出过鱼群。

2017届上海市七宝中学高三5月模拟理科数学试题及答案

七宝中学高三数学模拟试题（理科）一、填空题（本题满分56分）本大题共有14题，要求在答题纸相应题序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．为虚数单位，复数的虚部是＿＿＿＿．2．设函数若函数存在两个零点，则实数的取值范围是＿＿．3．在极坐标系中，为曲线上的点，为曲线上的点，则线段长度的最小值是＿＿．4.阅读如右图所示的程序框图，如果输入的的值为6，那么运行相应程序，输出的的值为＿＿．5．若，则方程的解为＿＿＿＿．6．已知正方形的四个顶点分别为，，，，点分别在线段上运动，且，设与交于点，则点的轨迹方程是＿＿＿．7．年龄在60岁（含60岁）以上的人称为老龄人，某小区的老龄人有350人，他们的健康状况如下表：其中健康指数的含义是：2代表“健康”，1代表“基本健康”，0代表“不健康，但生活能够自理”，-1代表“生活不能自理”.按健康指数大于0和不大于0进行分层抽样，从该小区的老龄人中抽取5位，并随机地访问其中的3位.则被访问的3位老龄人中恰有1位老龄人的健康指数不大于0的概率是_____（用分数作答）.8．已知数列{}的通项公式为，则+++的最简表达式为_____.9 ．平面的斜线交于点，过定点的动直线与垂直，且交于点，则动点的轨迹是_________________.10．祖暅原理对平面图形也成立，即夹在两条平行线间的两个平面图形被任意一条平行于这两条直线的直线截得的线段总相等，则这两个平面图形面积相等.利用这个结论解答问题：函数、与直线所围成的图形的面积为_______.11．对于任意正整数，定义“n的双阶乘n!!”如下：对于n是偶数时，n!!=n·(n－2)·(n－4)……6×4×2；对于n是奇数时，n!!=n·(n －2)·(n－4)……5×3×1．现有如下四个命题：①(2017!!)·(2017!!)=2017!；②2017!!=21007·1007!；③2017!!的个位数是0；④2017!!的个位数不是5．正确的命题是________．12．已知关于t的一元二次方程.当方程有实根时，则t的取值范围______.13．已知是内部一点，，记、、的面积分别为、、，则________.14. 在平面直角坐标系中，对于任意相邻三点都不共线的有序整点列（整点即横纵坐标都是整数的点）：与：，其中，若同时满足：①两点列的起点和终点分别相同；②线段，其中，则称与互为正交点列.则：的正交点列为二、选择题（本题满分20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，必须把答题纸上相应题序内的正确结论代号涂黑，选对得 5分，否则一律得零分．15．已知集合，则集合的非空真子集数为（）（A）14 （B） 512 （C）511 （D）510 16．已知函数.若存在，使成立，则称为函数的一个“生成点”.函数的“生成点”共有（）（Ａ） 1个（Ｂ）2个（Ｃ）3个（Ｄ）4个17. 如图，梯形中，,,, ,将沿对角线折起．设折起后点的位置为，使二面角为直二面角.给出下面四个命题：①；②三棱锥的体积为；③平面；④平面平面.其中正确命题的序号是（）（A）①②（B）③④（C）①③（D）②④18．已知动点在椭圆上，为椭圆的右焦点，若点满足且，则的最小值为（）（Ａ）（Ｂ）（Ｃ）（Ｄ）三、解答题：（本题满分74分）本大题共有5题，解答下列各题必须在答题纸的规定区域（对应的题号）内写出必要的步骤．19．（本题12分）圆形广场的有南北两个大门在中轴线上，东、西各有一栋建筑物与北门的距离分别为30米和40米，且以北门为顶点（视大门和建筑物为点）的角为，求广场的直径（保留两位小数）.20．（本题14分）本题共有2小题，第1小题满分6分，第2小题满分8分.设底面直径和高都是4厘米的圆柱的内切球为.（1）求球的体积和表面积；（2）与底面距离为1的平面和球的截面圆为，是圆内的一条弦，其长为，求两点间的球面距离.21．（本题14分）本题共有3小题，第1小题满分3分，第2小题满分5分，第3小题满分6分.如图，设椭圆两顶点，短轴长为4，焦距为2，过点的直线与椭圆交于两点．设直线与直线交于点.（1）求椭圆的方程；（2）求线段中点的轨迹方程；（3）求证：点的横坐标为定值.22．（本题16分）本题共有3小题，第1小题满分2分，第2小题满分6分，第3小题满分8分.数列满足,且，是的前和.（1）求；（2）求；（3）求.23．（本题18分）本题共有3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，为常数，且.（1）证明函数的图象关于直线对称；（2）当时，讨论方程解的个数；（3）若满足，但，则称为函数的二阶周期点，则是否有两个二阶周期点，说明理由.七宝中学５月高三数学模拟试题（理科）理科答案1、；2、；3、2；4、5；5、或；6、；7、3/5；8、；9、直线；10、1；11、①②③；12、；13、1：2：3；14、 DBBA 19．设南、北门分别为点A、B，东、西建筑物分别为点C、D.在中，，. 5分由于为的外接圆直径，所以.所以广场直径约为41.63米. 12分20．（1），…… 3分…… 6分（2），…… 12分所以AB两点间的球面距离为. …… 14分21．（1）椭圆方程为. …… 3分（2）设，，，则①，②①②得，…… 5分因，所以，即（）. ……8分用代入法求解酌情给分。

上海市七宝中学2017-2018学年高三上学期期中考试数学理试题 Word版无答案

2017-2018学年七宝中学高三第一学期期中考试理科数学一、填空题1、设集合{}2M x x x ==，{}lg 0N x x =≤，则MN =___________.2、已知1122(1,)(2,)(,)n n P a P a P n a ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅、、是直线上的一列点，且12a =-，2 1.2a =-，则这个数列{}n a 的通项公式是___________.3、设02πθ<<，向量(sin 2,cos )a θθ=，(cos ,1)b θ=，若a b ，则tan θ=___________.4、函数y =定义域是___________.5、已知单位向量1e 与2e 的夹角为α，且1cos 3α=，向量1232a e e =-与123b e e =-的夹角为β，则cos β=___________. 6、函数213,(10)xy x -=-≤≤的反函数是___________.7、方程lg(42)lg 2lg3x x +=+的解是___________.8、 ,a b 是不等的两正数，若11lim2n n n nn a b a b ++→∞-=+，则b 的取值范围是___________. 9、数列{}n a 中，已知111212,(),2n n a a a a a n N *+==++⋅⋅⋅⋅⋅⋅+∈，则{}n a 的前n 项和n S =___________.10、若向量a 与b 夹角为3π，4,(2)(3)72b a b a b =+-=-，则a =___________. 11、若三数,1,a c 成等差，且22,1,a c 成等比，则22lim()n n a c a c →∞++值为___________. 12、已知菱形ABCD 的边长为2，120BAD ∠=，点,E F 分别在边,BC DC 上，3,BC DE DC DF λ==，若1AE AF ⋅=，则λ的值为___________.13、已知()f x 是定义在[]4,4-上的奇函数，1()(2)3g x f x =-+，当[)(]2,00,2x ∈-时，1(),(0)021xg x g ==-，则方程12()log (1)g x x =+的解的个数为___________. 14、已知函数()sin f x x =，若存在12,,,n x x x ⋅⋅⋅满足120,m x x x n n N π*≤<<⋅⋅⋅<≤∈，且12231()()()()()()12,(2,)m m f x f x f x f x f x f x m m N *--+-+⋅⋅⋅+-=≥∈，当m 取最小值时，n 的最小值为___________. 二、选择题15、定义在R 上的偶函数()f x 满足：对任意的(]1212,,0,()x x x x ∈-∞≠，有[]1212()()()0x x f x f x -->，则当n N *∈时，有A. (1)()(1)f n f n f n +<-<-B. (1)()(1)f n f n f n -<-<+C. ()(1)(1)f n f n f n -<-<+D. (1)(1)()f n f n f n +<-<- 16、函数()cos()f x x ωϕ=+的部分图像如图所示，则()f x 的单调递减区间为A. 13,,44k k k Z ππ⎛⎫-+∈ ⎪⎝⎭ B. 132,2,44k k k Z ππ⎛⎫-+∈ ⎪⎝⎭ C. 13,,44k k k Z ⎛⎫-+∈ ⎪⎝⎭ D. 132,2,44k k k Z ⎛⎫-+∈ ⎪⎝⎭17、已知两个不相等的非零向量,a b ，两组向量12345,,,,x x x x x 和12345,,,,y y y y y 均由2个a 和3个b 排列而成，记1122334455S x y x y x y x y x y =⋅+⋅+⋅+⋅+⋅，min S 表示S 所有可能取值中的最小值，则下列中(1) S 有5个不同的值；(2)若a b ⊥则min S 与a 无关；(3)若a b 则min S 与b 无关；(4)若4b a >，则min 0S >；(5)若2b a =，2min 8S a =，则a 与b 的夹角为4π。

2017年上海市七宝中学高考数学模拟试卷(5月份)及参考答案

2017年上海市七宝中学高考数学模拟试卷（5月份）一.填空题1．已知定义在[﹣1，1]上的函数f（x）值域为[﹣2，0]，则y=f（cosx）的值域为．2．5051﹣1被7除后的余数为．3．已知直线l的参数方程是（t为参数），则它的普通方程是．4．一名工人维护3台独立的游戏机，一天内3台需要维护的概率分别为0.9、0.8和0.85，则一天内至少有一台游戏机不需要维护的概率为（结果用小数表示）5．地球的半径为R，在北纬45°东经30°有一座城市A，在北纬45°西经60°有一座城市B，则坐飞机从A城市飞到B城市的最短距离是．（飞机的飞行高度忽略不计）6．如果复数z满足|z+i|+|z﹣i|=2（i是虚数单位），则|z|的最大值为．7．已知定义在R上的增函数y=f（x）满足f（x）+f（4﹣x）=0，若实数a、b满足不等式f（a）+f（b）≥0，则a2+b2的最小值是．8．已知点P是棱长为1的正方体ABCD﹣A1B1C1D1的底面A1B1C1D1上一点（包括边界），则的取值范围是．9．椭圆（a＞0）的左焦点为F，直线x=m与椭圆相交于点A、B，则△FAB的周长的最大值是．10．已知函数，（a＞0），若对任意x1∈[0，2]，总存在x2∈[0，2]，使g（x1）=f（x2）成立，则实数a的取值范围是．11．在直角坐标平面上，已知点A（0，2），B（0，1），D（t，0）（t＞0）．点M 是线段AD上的动点，如果|AM|≤2|BM|恒成立，则正实数t的最小值是．12．设ω为正实数，若存在a，b（π≤a＜b≤2π），使得cosωa+cosωb=2，则ω的取值范围是．二.选择题13．若z∈C，i为虚数单位，且，则复数z等于（）A．B．C．D．14．设M={a|a=x2﹣y2，x，y∈Z}，则对任意的整数n，形如4n，4n+1，4n+2，4n+3的数中，不是集合M中的元素是（）A．4n B．4n+1 C．4n+2 D．4n+315．直线l在平面α内，直线m平行于平面α，且与直线l异面，动点P在平面α上，且到直线l、m距离相等，则点P的轨迹为（）A．直线B．椭圆C．抛物线D．双曲线16．设集合A=[0，），B=[，1]，函数f （x）=，若x0∈A，且f[f （x0）]∈A，则x0的取值范围是（）A．（0，]B．[，]C．（，）D．[0，]三.简答题17．如图，正四棱柱ABCD﹣A1B1C1D1中，O是BD的中点，E是棱CC1上任意一点．（1）证明：BD⊥A1E；（2）如果AB=2，，OE⊥A1E，求AA1的长．18．如图，某污水处理厂要在一个矩形ABCD的池底水平铺设污水净化管道（直角△EFG，E是直角顶点）来处理污水，管道越长，污水净化效果越好，设计要求管道的接口E是AB的中点，F、G分别落在AD、BC上，且AB=20m，，设∠GEB=θ．（1）试将污水管道的长度l表示成θ的函数，并写出定义域；（2）当θ为何值时，污水净化效果最好，并求此时管道的长度．19．若函数y=f（x）对定义域的每一个值x1，在其定义域均存在唯一的x2，满足f（x1）f（x2）=1，则称该函数为“依赖函数”．（1）判断，y=2x是否为“依赖函数”；（2）若函数y=a+sinx（a＞1），为依赖函数，求a的值，并给出证明．20．已知椭圆（a＞b＞0）长轴的两顶点为A、B，左右焦点分别为F1、F2，焦距为2c且a=2c，过F1且垂直于x轴的直线被椭圆C截得的线段长为3．（1）求椭圆C的方程；（2）在双曲线上取点Q（异于顶点），直线OQ与椭圆C交于点P，若直线AP、BP、AQ、BQ的斜率分别为k1、k2、k3、k4，试证明：k1+k2+k3+k4为定值；（3）在椭圆C外的抛物线K：y2=4x上取一点E，若EF1、EF2的斜率分别为、，求的取值范围．21．设T n为数列{a n}的前n项的积，即T n=a1•a2…•a n．（1）若T n=n2，求数列{a n}的通项公式；（2）若数列{a n}满足T n=（1﹣a n）（n∈N*），证明数列{}为等差数列，并求{a n}的通项公式；（3）数列{a n}共有100项，且满足以下条件：①a1•a2…•a100=2；②a1•a2…•a k+a k+1•a k+2…a100=k+2（1≤k≤99，k∈N*）．（Ⅰ）求a5的值；（Ⅱ）试问符合条件的数列共有多少个？为什么？2017年上海市七宝中学高考数学模拟试卷（5月份）参考答案与试题解析一.填空题1．（2017•闵行区校级模拟）已知定义在[﹣1，1]上的函数f（x）值域为[﹣2，0]，则y=f（cosx）的值域为[﹣2，0] ．【解答】解：∵f（x）的定义域是[﹣1，1]，值域是[﹣2，0]，而cosx∈[﹣1，1]，故f（cosx）的值域是[﹣2，0]，故答案为：[﹣2，0]．2．（2017•闵行区校级模拟）5051﹣1被7除后的余数为0．【解答】解：5051﹣1=（49+1）51﹣1=•4951+•4950+•4949+…+•49+﹣1，显然，除了最后两项外，其余的各项都能被7整除，故它除以7的余数为﹣1=0，故答案为：0．3．（2017•闵行区校级模拟）已知直线l的参数方程是（t为参数），则它的普通方程是3x﹣4y+5=0．【解答】解：直线l的参数方程是（t为参数），可得，可得3x﹣4y+5=0．故答案为：3x﹣4y+5=0．4．（2017•闵行区校级模拟）一名工人维护3台独立的游戏机，一天内3台需要维护的概率分别为0.9、0.8和0.85，则一天内至少有一台游戏机不需要维护的概率为0.388（结果用小数表示）【解答】解：一天内至少有一台游戏机不需要维护的对立事件是三台都需要维护，∴一天内至少有一台游戏机不需要维护的概率：p=1﹣0.9×0.8×0.85=0.388．故答案为：0.388．5．（2016•上海模拟）地球的半径为R，在北纬45°东经30°有一座城市A，在北纬45°西经60°有一座城市B，则坐飞机从A城市飞到B城市的最短距离是．（飞机的飞行高度忽略不计）【解答】解：由已知地球半径为R，则北纬45°的纬线圈半径为R，又∵两座城市的经度分别为东经30°和西经60°，故连接两座城市的弦长L=R=R，则A，B两地与地球球心O连线的夹角∠AOB=，则A、B两地之间的距离是．故答案为：．6．（2015•浦东新区三模）如果复数z满足|z+i|+|z﹣i|=2（i是虚数单位），则|z|的最大值为1．【解答】解：复数z满足|z+i|+|z﹣i|=2（i是虚数单位），复数z的几何意义是到虚轴上的点到（0，1），（0，﹣1）的距离之和，|z|的最大值为：1，故答案为：1．7．（2017•闵行区校级模拟）已知定义在R上的增函数y=f（x）满足f（x）+f（4﹣x）=0，若实数a、b满足不等式f（a）+f（b）≥0，则a2+b2的最小值是8．【解答】解：∵f（x）=﹣f（4﹣x），∴﹣f（x）=f（4﹣x），∴f（a）+f（b）≥0可化为f（a）≥﹣f（b）=f（4﹣b），又∵f（x）在R上单调递增，∴a≥4﹣b，即a+b﹣4≥0，a2+b2表示点（0，0）到点（a，b）的距离平方，∴a2+b2的最小值是点（0，0）到直线a+b﹣4＞0的距离平方．故答案为：88．（2017•闵行区校级模拟）已知点P是棱长为1的正方体ABCD﹣A1B1C1D1的底面A1B1C1D1上一点（包括边界），则的取值范围是．【解答】解：如图所示，建立空间直角坐标系．A1（0，0，0），A（0，0，1），C（1，1，1），设P（x，y，0），（x，y∈[0，1]）．=（﹣x，﹣y，1），=（1﹣x，1﹣y，1），∴=﹣x（1﹣x）﹣y（1﹣y）+1=++=f（x，y）．当x=，y=时，f（x，y）取得最小值．当点P取（0，0，0），（1，0，0），（0，1，0），（1，1，0），f（x，y）取得最大值1．∴f（x，y）∈．故答案为：．9．（2017•闵行区校级模拟）椭圆（a＞0）的左焦点为F，直线x=m与椭圆相交于点A、B，则△FAB的周长的最大值是8a．【解答】解：如图，设椭圆的右焦点为M，由椭圆的方程得椭圆的长轴为2×2a=4a，△FAB的周长AF+FB+AB≤FA+AM+FB+BM=2×2a+2×2a=8a，故答案为：8a10．（2017•闵行区校级模拟）已知函数，（a＞0），若对任意x 1∈[0，2]，总存在x 2∈[0，2]，使g （x 1）=f （x 2）成立，则实数a 的取值范围是．【解答】解：函数=﹣4+，（a ＞0），x 2∈[0，2]，x 2+1∈[1，3]， ∴∈[3，9]，∴﹣4+∈[﹣1，5]，即f （x 2）∈[﹣1，5]；又x 1∈[0，2]，x 1∈[0，]，sin （x 1）∈[0，1]，∴g （x ）=asin （x 1）+2a ∈[a ，3a ]；对任意x 1∈[0，2]，总存在x 2∈[0，2]，使g （x 1）=f （x 2）成立，等价于，解得﹣1≤a ≤；又a ＞0，∴实数a 的取值范围是0＜a ≤．故答案为：（0，]．11．（2013•宁波二模）在直角坐标平面上，已知点A （0，2），B （0，1），D （t ，0）（t ＞0）．点M 是线段AD 上的动点，如果|AM |≤2|BM |恒成立，则正实数t的最小值是．【解答】解：设M （x ，y ），则由A 、M 、D 三点共线可得，整理可得y=，由两点间的距离公式，结合|AM |≤2|BM |恒成立可得x 2+（y ﹣2）2≤4[x 2+（y ﹣1）2]，整理可得3x2+3y2﹣4y≥0，代入y=化简可得（3t2+12）x2﹣16tx+4t2≥0恒成立，∵3t2+12＞0，由二次函数的性质可得△=（﹣16t）2﹣4（3t2+12）•4t2≤0，整理可得3t4﹣4t2≥0，即，解得t≥，或t≤（因为t＞0，故舍去）故正实数t的最小值是：故答案为：12．（2017•闵行区校级模拟）设ω为正实数，若存在a，b（π≤a＜b≤2π），使得cosωa+cosωb=2，则ω的取值范围是{2}∪[3，+∞）．【解答】解：要cosωa+cosωb=2，则有cosωa=cosωb=1；余弦函数y=cosx图象如下：可知，当x=2kπ时，cosx=1，∵cosωa+cosωb=2，π≤a＜b≤2π），∴必有ωa=2kπ，ωb=2kπ+nπ，（k，n∈N+∴），得到k+1≤ω≤2k（k∈N+①k=1时，ω=2，②k=2时，3≤ω≤4，③k=3时，4≤ω≤6，④k=4时，5≤ω≤8，…可得ω的取值范围为{2}∪[3，+∞）．二.选择题13．（2017•闵行区校级模拟）若z∈C，i为虚数单位，且，则复数z等于（）A．B．C．D．【解答】解：设z=a+bi（a，b∈R），且，则+i=﹣i，∴=，=﹣，联立解得a=，b=﹣．∴z=﹣i，故选：B．14．（2017•闵行区校级模拟）设M={a|a=x2﹣y2，x，y∈Z}，则对任意的整数n，形如4n，4n+1，4n+2，4n+3的数中，不是集合M中的元素是（）A．4n B．4n+1 C．4n+2 D．4n+3【解答】解：∵4n=（n+1）2﹣（n﹣1）2，∴4n∈M，∵4n+1=（2n+1）2﹣（2n）2，∴4n+1∈M，∵4n+3=（2n+2）2﹣（2n+1）2，∴4n+3∈M，若4n+2∈M，则存在x，y∈Z使得x2﹣y2=4n+2，∴4n+2=（x+y）（x﹣y），∵x+y和x﹣y的奇偶性相同，若x+y和x﹣y都是奇数，则（x+y）（x﹣y）为奇数，而4n+2是偶数；若x+y和x﹣y都是偶数，则（x+y）（x﹣y）能被4整除，而4n+2不能被4整除，∴4n+2∉M．故选C．15．（2017•闵行区校级模拟）直线l在平面α内，直线m平行于平面α，且与直线l异面，动点P在平面α上，且到直线l、m距离相等，则点P的轨迹为（）A．直线B．椭圆C．抛物线D．双曲线【解答】解：设直线m在平面α的射影为直线n，则l与n相交，不妨设l与n垂直，设直线m与平面α的距离为d，在平面α内，以l，n为x轴，y轴建立平面坐标系，则P到直线l的距离为|y|，P到直线n的距离为|x|，∴P到直线m的距离为，∴|y|=，即y2﹣x2=d2，∴P点轨迹为双曲线．故选：D．16．（2016•上海模拟）设集合A=[0，），B=[，1]，函数f （x）=，若x0∈A，且f[f （x0）]∈A，则x0的取值范围是（）A．（0，]B．[，]C．（，）D．[0，]【解答】解：∵0≤x0＜，∴f（x0）=x0 +∈[，1]⊆B，∴f[f（x0）]=2（1﹣f（x0））=2[1﹣（x0+）]=2（﹣x0）．∵f[f（x0）]∈A，∴0≤2（﹣x0）＜，∴＜x0≤．又∵0≤x0＜，∴＜x0＜．故选C．三.简答题17．（2017•闵行区校级模拟）如图，正四棱柱ABCD﹣A1B1C1D1中，O是BD的中点，E是棱CC1上任意一点．（1）证明：BD⊥A1E；（2）如果AB=2，，OE⊥A1E，求AA1的长．【解答】解：（1）证明：连结AC，A1C1，∵AA1⊥平面ABCD，BD⊂平面ABCD，∴AA 1⊥BD，∵四边形ABCD是正方形，∴AC⊥BD，又AC∩AA1=A，AC⊂平面ACC1A1，AA1⊂平面ACC1A1，∴BD⊥平面ACC1A1，又A1E⊂平面ACC1A1，∴BD⊥A1E．（2）∵AB=2，∴AO=CO=，A1C1=2，设AA1=a，则C1E=a﹣，∴OE2=2，A1O2=a2+2，A1E2=（a﹣）2+8=a2﹣2a+10，∵OE⊥A1E，∴A 1O2=OE2+A1E2，即a2+2=2+a2﹣2a+10，解得a=．∴AA1=．18．（2017•闵行区校级模拟）如图，某污水处理厂要在一个矩形ABCD的池底水平铺设污水净化管道（直角△EFG，E是直角顶点）来处理污水，管道越长，污水净化效果越好，设计要求管道的接口E是AB的中点，F、G分别落在AD、BC 上，且AB=20m，，设∠GEB=θ．（1）试将污水管道的长度l表示成θ的函数，并写出定义域；（2）当θ为何值时，污水净化效果最好，并求此时管道的长度．【解答】解：（1）由题意，∠GEB=θ．∠GEF=90°．则∠AEF=90°﹣θ，E是AB的中点，AB=20m，，∴EG=，EF==．FG==则定义域：；（2）由（1）可知则，；化简可得l=，令t=sinθ+cosθ=sin（）．∵；∴∈[，]，可得sin（）∈[，1]则：t∈[，]可得：sinθcosθ=，且t≠1．那么：l===．当t=时，长度l取得最大值为；此时：t=sin（）=，即=或∴或，故得或时，污水净化效果最好，此时管道的长度为；19．（2017•闵行区校级模拟）若函数y=f（x）对定义域的每一个值x1，在其定义域均存在唯一的x2，满足f（x1）f（x2）=1，则称该函数为“依赖函数”．（1）判断，y=2x是否为“依赖函数”；（2）若函数y=a+sinx（a＞1），为依赖函数，求a的值，并给出证明．【解答】解：（1）函数，由f（x1）f（x2）=1，得=1，即x12x22=1，对应的x1、x2不唯一，所以，x﹣2不是“依赖函数”；对于函数y=2x，由f（x1）f（x2）=1，得2=1，得x1+x2=0，所以x2=﹣x1，可得定义域内的每一个值x1，都存在唯一的值x2满足条件，故函数y=2x是“依赖函数”．（2）当时，函数y=a+sinx（a＞1）为增函数，且函数关于（0，a）对称，若函数y=a+sinx（a＞1），为依赖函数，则只需要函数的最大值和最小值满足f（x1）f（x2）=1即可，则函数的最大值为a+1，最小值为a﹣1，则由（a+1）（a﹣1）=1得a2﹣1=1，得a2=2，得a=．20．（2017•闵行区校级模拟）已知椭圆（a＞b＞0）长轴的两顶点为A、B，左右焦点分别为F1、F2，焦距为2c且a=2c，过F1且垂直于x轴的直线被椭圆C截得的线段长为3．（1）求椭圆C的方程；（2）在双曲线上取点Q（异于顶点），直线OQ与椭圆C交于点P，若直线AP、BP、AQ、BQ的斜率分别为k1、k2、k3、k4，试证明：k1+k2+k3+k4为定值；（3）在椭圆C外的抛物线K：y2=4x上取一点E，若EF1、EF2的斜率分别为、，求的取值范围．【解答】解：（1）由题意a=2c，椭圆的通径丨AB丨==3，a2=b2+c2，则a=2，b=，c=1，∴椭圆的标准方程：；（2）由（1）可知：A（﹣2，0），B（2，0），F1（﹣1，0），F2（1，0），设P（x1，y1），则，则x12﹣4=﹣，k1+k2=+===﹣，设Q（x2，y2），则，则x12﹣4=，则k3+k4=+===，又与共线，∴x1=λx2，y1=λy2，∴=，k1+k2+k3+k4=（﹣+）=0；（3）设E（，y），由，解得：，由E在椭圆C外的抛物线K：y2=4x上一点，则y2＞，则EF1的斜率=，（y2＞且y≠﹣2），EF2的斜率=，（y2＞且y≠2）则=×==，（y2＞且y≠±2）则=，（y2＞且y≠±2）令t=y2，（t＞且t≠4，）设f（t）==﹣，（t＞且t≠4，），求导f′（t）=+＞0∴f（t）在（，4），（4，+∞）上单调递增，∴f（t）的取值范围（﹣，0）∪（0，+∞）∴的取值范围．21．（2014•卢湾区校级模拟）设T n为数列{a n}的前n项的积，即T n=a1•a2…•a n．（1）若T n=n2，求数列{a n}的通项公式；（2）若数列{a n}满足T n=（1﹣a n）（n∈N*），证明数列{}为等差数列，并求{a n}的通项公式；（3）数列{a n}共有100项，且满足以下条件：①a1•a2…•a100=2；②a1•a2…•a k+a k+1•a k+2…a100=k+2（1≤k≤99，k∈N*）．（Ⅰ）求a5的值；（Ⅱ）试问符合条件的数列共有多少个？为什么？【解答】解：（1）当n=1时，a1=T1=1；当n≥2时，a n==，∴a n=…（4分）（2）当n=1时，a1=T1=（1﹣a1），所以a1=，当n≥2时，2T n=1﹣a n=1﹣，所以﹣=2，数列{}为等差数列…（8分）=3+2（n﹣1）=2n+1，T n=，a n=1﹣2T n=…（10分）（3）（Ⅰ）由a1•a2…•a100=2，a1•a2…•a4+a5•a6…a100=6；可得T4=3±，由a1•a2…•a100=2，a1•a2…a5+a6•a7…a100=7，可得T5=，所以a5==或a5=．…（13分）（Ⅱ）a1+a2…•a100=3，所以a1=1或2T k是方程x2﹣（k+2）x+2=0的一个实根（△＞0），当数列前k（2≤k≤98）项确定后，其前k项积T k确定，由T k+1可得到两个a k+1所以符合条件的数列共有299个．…（18分）参与本试卷答题和审题的老师有：刘老师；caoqz；qiss；zlzhan；lcb001；陈高数；沂蒙松；742048；lincy；zhczcb；左杰；maths；铭灏2016；liu老师（排名不分先后）菁优网2017年6月18日。

上海市七宝中学2017届高三5月月考英语试题 Word版含答

第I卷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. See a film with the man B. Offer the man some helpC. Listen to some great musicD. Say thanks to the man.2. A. At 1:00 pm B. At 3:00 pm C. At 4:00 pm D. At 5:00 pm3. A. On his way B. In a restaurant C. At home D. On a train4. A. A gay stole his clothes B. He found his clothes uglyC. Someone said he was uglyD. The clothes in the supermarket are ugly5. A. Ask for something cheaper B. Buy the vase she really likesC. Protect herself from being hurtD. Bargain with the shop assistant6. A. 147 pounds B. 150 pounds C. 153 pounds D. 163 pounds7. A. To get a haircut B. To attend a party C. To do some shopping D. To drive her home8. A. Use a computer in the lab B. Take a chemistry courseC. Help him revise his reportD. Get her computer repaired9. A. It spoke highly of the mayor B. It misinterpreted the mayor’s speechC. It made the mayor’s view clearerD. It carried the mayor’s speech accurately10. A. Germany B. France C. West Africa D. SpainSection BDirections: In Section B, you will hear several longer conversation(s) and short passage(s), and you will be asked several questions on each of the conversation(s)and short passage(s). Theconversation(s)and the passage(s)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. He was Mrs. Beach’s neighborB. He used to work at Ms. Beach’s bookstoreC. He has followed Ms. Beach’s way of doing businessD. He came from Britain12. A. She died B. The Germans made her give it upC. Her business went from bad to worseD. She decided to start a new business13. A. In 1951 B. In 1962 C. In 1964 D. In 1919Questions 14 through 16 are based on the following passage.14. A. 0.1 cm B. 1cm C. 0.01 mm D. 0.1mm15. A. There was a hole in it B. It got hurt by something hardC. It went off Bill Beaver’s eyeD. It sometimes didn’t work well16. A. It was made by handB. It was made by a special robotC. There was some blood during the operationD. The doctors didn’t take part during the opersationQuestions 17 through 20 are based on the following conversation.17. A. It couldn’t be doneB. It couldn’t be doneC. It was very difficultD. It was boring18. A. He didn’t like physical educationB. He had so little physical energyC. He was unable to sit still in classD. He can’t use skateboard at school19. A. He had a different schoolB. He let students plan P. E. classes on their ownC. He was kind to every studentD. He showed some techniques during classes20. A. It was robot-like with new tricksB. He was more professionalC. He created it by himselfD. It is smoother than others’II. Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.I have often though it would be a blessing(21)_________each human being were stricken blind and deaf for a few days at some time during his early adult life. Darkness would make him more appreciative of sight; silence would teach him the joys of sound.Now and then I have tested my seeing friends to discover what they see. Recently I was visited by a very good friend who had just returned from a long walk in the woods, and I asked her what she had observed. “Nothing in particular,” she replied. I (22)_______be suspicious if I had not been accustomed to such responses, for long ago I became convened that (23)____seeing see little.How was it possible, I asked myself, (24)__________(walk)for an hour through the woods and see nothing worthy of note? I who cannot see find hundreds of things to interest me(25)_______mere touch. I feel the delight of a flower, and something of the miracle of nature is revealed to me. Occasionally, if I am very fortunate, I place my hand gently in a small tree and feel the happy tremble of a bird in full song. I am delighted to have cool waters of a river (26)_________(rush)through my open fingers.To me the feast of seasons is a thrilling and unending drama, the action of (27)_________streams through my fingertips. At times my heart cries out, (28)________(thrill)to see al these things. If I can get so much pleasure by mere touch, how much more beauty must be revealed by sight? Yet, those who, have eyes apparently, see little. The view of color and action that fill the world(29)___________(take) for granted.It is human, perhaps, to appreciate little that which we have and to long for that which we have not, (30)________it is a great pity that in the world of light the gift of sight is used only as mere convenience rather than as a means of adding fullness to life.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.By now, how the immune system is affected by stress has been discovered. In one study, ___31___500 couples, those who showed very unfriendly behavior during a 30-minute discussion about marriage problems had lower immune functioning for 24-hour period following the experiment than people who showed less ___32___behavior. It is not just stress that can do damage. One researcher though that if the same cold virus was put under two different noses, the person who is depressed or anxious would be more likely to develop the cold. How can stress and related emotions contribute to poor health?These feelings can cause the __33___of substances that damage or weaken our immure cells. Negative emotion can also cause our bodies to produce fewer substances that __34___help fight off disease. If stress, depression, anger and other negative feelings can make you more likely to get sick, can the ___35____be true? Will you have a stronger immune__36___and greater health if you are happier, less stressed? Experts believe that the answer is yes. There are studies showing that by __-37___certain mind-body techniques that help reduce stress and improve outlook, cancer patients can live longer. And cancer patients aren’t the only ones who can benefit. Research has found that when patients with chronic pain use ____38___therapies and other techniques to deal with discomfort, they reduced their visits to the doctors by 36%. Relaxation produces better health through deep rhythmic breathing, muscle loosening and a slower heart rate. When some of the pressure is taken out of the body, they entire immune system will ___39___much better. Relaxation decreases blood pressure and heart rate. That is important because a body that is ___40___under pressure will exhaust.III. Reading Comprehension Section ADirections: For each blank in the following passage there are four words or phrases marked A, B,C and D. Fill in each blank with the word or phrase that best fits the context.Why do people go to university? There is a popular notion that a college education is something to be endured in order to become __41___to obtain certain kinds of jobs or to go to graduate school. This is not what we are trying to do at Harvard, nor would we wish to have many students here who took such a(n)___42___view of a college career. There are several goals we aim to reach in our undergraduate program.The most obvious one is to give knowledge—fairly___43___knowldege in one field and a more general knowledge of a variety of other subject areas which you may choose according to your interest. But if acquiring knowledge is a self-evident part of a college education, it is __44___the most important. Remarkably few of the facts you learn here will remain in your___45___for many years, and some of those that do will even be proved ___46___by new knowledge.__47___, we can instill(灌输)certain attitudes of mind-a willingness to accept uncertainly and the lack of definite truths; independence of mind, and a respect for facts and for the uncomfortable conclusions which facts sometimes lead to.In addition to these ___48___qualities, a college education should try to lay a foundation for the creative use of ___49___time. Some of this capacity can be stimulated in the classroom—in courses in the humanities and the arts. Yet, at least as much __50___will occur outside the lecture hall---on athletic fields, in music rooms, student theaters, concert hails, and so forth.These are some of the __51___of a liberal college education as I see them. I cannot resist concluding with a few private thoughts about our new careers at Harvard.To begin with, I hope that we will think__52___about what we want to accomplish here. It would be __53___for you to set your sights on some limited goal, such as getting good grades or merely getting into one or another graduate school.Second, I hope that you will give some thought to what you can do for others during your stay here. There are many problems waiting for your help, and many people who could __14___your efforts.My final bit of advice. Whatever else we do, let us remember not to take ourselves too seriously. However great our problems may seem, however urgent our complaints, they are overshadowed(黯然失色)by the __55__of countless other people on our planet.41. A. fascinated B. qualified C. determined D. required42. A. optimistic B. strong C. narrow D. sensitive43. A. concentrated B. expanded C. informed D. illustrated44. A. by far B. far from C. free from D. without doubt45. A. memory B. position C. evaluation D. foundation46. A. useful B. essential C. false D. common47. A. Besides B. However C. Therefore D. Somehow48. A. physical B. inborn C. emotional D. intellectual49. A. business B. study C. experiment D. leisure50. A. appreciation B. stimulation C. participation D. exposure51. A. benefits B. aims C. problems D. achievements52. A. broadly B. honestly C. freely D. continually53. A. fantastic B. magic C. tragic D. basic54. A. suffer from B. profit from C. reflect on D. complain about55. A. inspiration B. difference C. ambitions D. difficultiesSection BDirections: Read the following three passages. Each passage is followed by several questions orunfinished 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 read.(A)The Tide Rises, the Tide FallsBy Henry Wadsworth LongfellowThe tide rises, the tide falls,Along the sea — sands damp and brownThe traveler hastens toward the town,And the tide rises, the tide falls.Darkness settles on roofs and walls,But the sea, the sea in the darkness calls;The little waves, with their soft, white hands,Efface the footprints in the sands,And the tide rises, the tide falls.The morning breaks; the steeds in their stallsStamp and neigh, as the hostler calls;The day returns, but never moreReturns the traveler to the shore,And the tide rises, the tide falls.56. What is the figurative meaning (寓意)of the title “The Tide Rises, the Tide Falls” indicate?A. the change of the oceanB. the sequence of human historyC. the coming and going of travelersD. the eternity of the natural world57. In stanza 1, which line is parallel to “The morning breaks: the steeds in their stalls”?A. The tide rises, the tide fallsB. The twilight darkens, the curlew callsC. Alone the sea-sands damp and brownD. The traveler hastens toward the town58. In stanza 2, the word “Efface” in line 4 is the closest to _________in meaning.A. drawB. engraveC. eraseD. impress59. In stanza 3, “The day returns, but nevermore; Returns the traveler to the shore”, the poet possibly means ________.A. Time hustles; people bustleB. The traveler comes to the town just onceC. People will die while time goes onD. If time had feelings, people would stay(B)Predicti ng the future is always risky. But it’s probably safe to say that at least a few historians will one day speak of the 20th century as America’s “Disney ear”. Today, it’s certainly difficult to think of any other single thing that represents modern America as powerfully as the company that created Mickey Mouse. Globally, brands like Coca-Cola and McDonald's may be more widely known, but neither concludes 20th-century America in quite the same way as Disney.The reasons for Disney's success are quite a lot, but ultimately the credit belongs to one person - the man who created the cartoon and built the company from nothing, Walt Disney. Ironically, he could not draw particularly well. But he was a genius in other aspects. In business, his greatest skills were his insight and his management ability. After setting himself up in Hollywood, he single-handedly pioneered the concepts of branding and merchandising -- something his company still does brilliantly today.But what really distinguished Disney was his ability to identify with his audiences. Disney always made sure that his films championed the "little guy", and made him feel proud to be American. This he achieved by creating characters that reflected the hopes and fears of ordinary people. Some celebrated American achievements---He achieved this by creating characters that reflected the hopes and fears of ordinary people. Some Mickey Mouse, was “inspired by Charles Lindbergh’s flight across the Atlantic. Others, like the There Little Pigs and Snow White and the Seven Dwarves, showed how, through hard wok and helping one’s fellow man or Americans could survive social and economic crises like the Great Depression.Disney's other great virtue was the fact that his company -- unlike other big corporations--- had a human face. His Hollywood studio -- the public heard -- operated just like a democracy, where everyone was on first name terms and had a say in how things should be run. He was alsoregarded as a great patriot because not only did his cartoons praise America, but, during World War II, his studios made training films for American soldiers.The reality, of course, was less idyllic. As the public would later learn, Disney's patriotism had an unpleasant side. After a strike by cartoonists in 1941, he became convinced that Hollywood had been infiltrated by Communists . He agreed to work for the FB1 as a mole, identifying and spying on colleagues whom he suspected were subversives.But, apart from his affiliations with the FBI, Disney was more or less the genuine article. A new book, The Magic Kingdom: Walt Disney and the American Way of Life, by Steven Watts, confirms that he was very definitely on the side of ordinary Americans—in the 30s and 40s he voted for Franklin Roosevelt, believing he was a champion of the workers. Also, Disney was not an apologist for the FBI, as some have suggested. In fact, he was always suspicious of large, bureaucratic organizations, as is evidenced in films like That Darned Cat, in which he portrayed FB1 agents as bungling incompetents.By the time he died in 1966, Walt Disney was as icon like Thomas Edison and the Wright Brothers. To business people and filmmakers, he was a role model; to the public at large, he was "Uncle Walt" -- the man who had entertained them all their lives, the man who represented them all their lives, the man who represented all that was good about America.60. Walt Disney is believed to possess the following abilities EXCEPT______________.A . painting B. creativity C. management D. merchandising61. According to the passage, what was the pleasant side of Disney’s patriotism?A. He sided with ordinary Americans in his filmsB. He supported Arnorlca’s was efforts in his own wayC. He had doubts about large, bureaucratic organizationsD. He voted for Franklin Roosevelt in the 30s and 40s62. In the sixth paragraph the sentence “Disney was more or lets the genuine artic l e” means that _________.A. Disney was a creative and capable personB. Disney once agreed to work for the FB1C. Disney ran his company in a democratic wayD. Disney was sympathetic with ordinary people(C)For most thinkers since the Greek philosophers, it was self-evident that there is something called human nature, something that constitutes the essence of man. There were various views about what constitutes it, but there was agreement that such an essence exists---that is to say, that there is something by virtue of which man is man. Thus man was defined as a rational being, as a social animal, an animal that can make tools, or a symbol-making animal.More recently, this traditional view has begun to be questioned. One reason for this change was the increasing emphasis given to the historical approach to man. An examination of the history of humanity suggested that man in our time is so different from man in previous times that it seemed unrealistic to assume that men in every age have had in common something that can be called “human nature.” The historical approach was reinforced, particularly in the United States, by studies in the field of cultural anthropology (人类学). The study of primitive peoples has discovered such a diversity of customs, values, feelings, and thoughts that many anthropologists arrived at the concept that man is born as a blank sheet of paper on which each culture writes its text. Another factor contributing to the tendency to deny the assumption of a fixed human nature was that the concept has so often been abused as a shield behind which the most inhuman acts are committed. In the name of human nature, for example, Aristotle and most thinkers up to the eighteenth century defended slavery. Or in order to prove the rationality and necessity of the capitalist form of society, scholars have tried to make a case for acquisitiveness, competitiveness, and selfishness as natural human characters. Popularly, one refers cynically to “human nature” in accepting the inevitability of such undesirable human behavior as greed, murder, cheating and lying.Another reason for skepticism about the concept of human nature probably lies in the influence of evolutionary thinking. Once man came to be seen as developing in the process of evolution, the idea of a substance which is contained in his essence seemed untenable. Yet I believe it is precisely from an evolutionary standpoint that we can expect new insight into the problem of the nature of man.63. Most philosophers believed that human nature ________.A. is the quality distinguishing man from other animalsB. consists of competitiveness and selfishnessC. is something partly innate and partly acquiredD. consists of rationality and undesirable behavior64. The traditional view of “human nature” was strongly challenged by ________.A. the emergence of the evolutionary theoryB. the historical approach to manC. new insight into human behaviorD. the philosophical analysis of slavery65. The author mentioned Aristotle, a great ancient thinker, in order to ________.A. emphasize that he contributed a lot to defining the concept of “human nature”B. show that the concept of “human nature” was used to justify social evilsC. prove that he had a profound influence on the concept of “human nature”D. support the idea that some human characters are inherited.66. According to the passage, anthropologists believe that human beings ________.A. have some characters in commonB. are born with diverse culturesC. are born without a fixed natureD. change their characters as they grow upSection CDirections: Complete the following passage by using the sentences given below. Each sentence can be used only once. Note that there are two more sentences than you need.1) In a few years you will be able to order a transcript of your entire genetic code for less than $1,000. ____67____Two different university laboratories have developed test that will reveal the entirety of a baby’s genetic code using just a blood sample from the mother plus a drop of saliva(唾液)from the father.2) Prenatal(出生前的) whole-genome sequencing will provide volumes of information beyond the currently available tests exclusively for genetic disorders such as Down’s syndrome or Tay-Saches disease. The three billion units of code furnished in the new tests will also dwarf(使……相形见的) the relative trickle(零散)of information provided by consumer gene-testing services such as 23andMe, which currently look only at perhaps about one million locations in the genome.3)____68____Without careful panning, the new prenatal genetics might rob a child of the chance to make decisions best left until adulthood---whether or not to learn, for instance, if a mutation(突变)predicts the inevitability of Huntington’s disease 20 years hence.4)_____69_____. Similar laissez0faire(放住)action to prenatal whole-genome testing could portend(预示)tragedy.5)Ultimately certain agency will need to develop a comprehensive policy on prenatal whole genome testing. Bioethics scholars wrote an analysis last summer that calls on the medical community to develop a guide to the most relevant genomic data for future parents. ___70___Without access to a much higher level of refined expertise, the secrets of our offspring’s genetic code will continue to remain an unnerving cipher---or worse.IV. Summary WritingDirections: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.Rocks Tell TimeEarth’s surface is constantly changing, and its rocks are evidence of past geologic events. The age of rocks can be determined in various ways. By using relative-dating principles and noting the position of layers within a rock, it is also possible to reconstruct the sequence(顺序)of geologic events that have occurred at a site.One way scientists do this is by using the principle of uniformitarianism, which states that the processes affecting the earth today are the same ones that affected it in the past. For example, at an active volcano, today, lava can be observed to cool and form layers of basalt(玄武岩). Therefore, any time one sees layers of basalt, it can be assumed that they likely formed from lava cooling after a volcanic eruption.Second, the principle of original horizontality states that most sedimentary(由沉淀物所生成的)rock is deposited in a horizontal position, which means they form layers. The principle of superposition can be used to interpret the relative ages of these layers: In a sequence of undisturbed sedimentary layers or lava flows, the oldest layers are at the bottom. These principles allow scientists to determine the relative age of a rock compared with another rock. They can also compare the ages of rock layers in different areas. This type of comparison has enabled them to create a list of earth’s rock layers from youngest to oldest, called a geologic column.Another way to test a rock’s age is by using radioactivity. Radioactive parts of elements in rocks decay into other elements at a constant pace called a half-life. By comparing the amount of the originai element with the amount present today, scientists can come up with an absolute age for a rock. These ages are compiled into a history of earth. Long stretches of time on earth are called eras. Earth’s rock history includes the Paleozoic, Mesozoic, and Cenozoic eras.The scientists who interpret the stories told by rocks are called structural geologists and stratigraphers(地层学家). Structural geologists carefully observe and interpret layer of rock. They study the way in which the earth’s crust is deformed by mountain-building processes. They also study clues at the earth’s surface that reveal the underlying structure and geologic history of an area. Stratigaphers compare vertical sequences of rock layers form different areas to piece together the geologic history of a region.71._____________________________第II卷V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets. 72．在我看来，中国人是世界上最喜欢谈论国内外大事的民族。

2025届上海市闵行区七宝中学高三下学期第五次调研考试数学试题含解析

2025届上海市闵行区七宝中学高三下学期第五次调研考试数学试题考生请注意：1．答题前请将考场、试室号、座位号、考生号、姓名写在试卷密封线内，不得在试卷上作任何标记。

2．第一部分选择题每小题选出答案后，需将答案写在试卷指定的括号内，第二部分非选择题答案写在试卷题目指定的位置上。

3．考生必须保证答题卡的整洁。

考试结束后，请将本试卷和答题卡一并交回。

一、选择题：本题共12小题，每小题5分，共60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．已知,a b ∈R ，3(21)ai b a i +=--，则|3|a bi +=（） A ．10B ．23C ．3D ．42．已知点A 是抛物线24x y =的对称轴与准线的交点，点F 为抛物线的焦点，点P 在抛物线上且满足PA m PF =，若m 取得最大值时，点P 恰好在以,A F 为焦点的椭圆上，则椭圆的离心率为（）A ．31-B ．21-C ．512- D ．212- 3．已知复数168i z =-，2i z =-，则12z z =（） A ．86i -B ．86i +C ．86i -+D ．86i --4．如图，设P 为ABC ∆内一点，且1134AP AB AC =+，则ABP ∆与ABC ∆的面积之比为A ．14 B ．13 C ．23D ．165．若各项均为正数的等比数列{}n a 满足31232a a a =+，则公比q =（） A ．1B ．2C ．3D ．46．执行如图所示的程序框图，若输入ln10a =，lg b e =，则输出的值为（）A ．0B ．1C ．2lg eD ．2lg107．已知定义在R 上的偶函数()f x 满足()()11f x f x +=-，当[]0,1x ∈时，()1f x x =-+，函数()1x g x e --=（13x -≤≤），则函数()f x 与函数()g x 的图象的所有交点的横坐标之和为（） A ．2B ．4C ．5D ．68．定义在R 上的偶函数()f x 满足()()11f x f x +=-()()0≠f x ，且在区间()20172018,上单调递减，已知,αβ是锐角三角形的两个内角，则()()sin cos f f βα,的大小关系是（） A ．()()sin cos βα<f f B ．()()sin cos βα>f f C ．()()sin =cos βαf fD ．以上情况均有可能9．已知函数()ln xf x x =，()xg x xe -=.若存在()10,x ∈+∞，2x R ∈使得()()()120f x g x k k ==<成立，则221k x ex ⎛⎫ ⎪⎝⎭的最大值为（） A ．2e B ．eC ．24eD ．21e10． “tan 2θ=”是“4tan 23θ=-”的（） A ．充分不必要条件 B ．必要不充分条件 C ．充要条件 D ．既不充分又不必要条件11．函数3()cos ln ||f x x x x x =+在[,0)(0,]ππ-的图象大致为（）A ．B ．C ．D ．12．已知ABC ∆为等腰直角三角形，2A π=，22BC =M 为ABC ∆所在平面内一点，且1142CM CB CA =+，则MB MA ⋅=（） A ．224B ．72-C ．52-D ．12-二、填空题：本题共4小题，每小题5分，共20分。

2017届上海市闵行区七宝中学高三下学期开学数学试卷(解析版)

2016-2017学年上海市闵行区七宝中学高三（下）开学数学试卷一.填空题1．不等式的解集是．2．已知直线l 1： x ﹣y +2=0，l 2：3x +y ﹣5=0，则直线l 1与l 2的夹角是．3．函数f （x ）=的最大值是．4．i 为虚数单位，z=对应的点在第二象限，则θ是第象限的角．5．已知一组数据4.7，4.8，5.1，5.4，5.5，则该组数据的方差是． 6．从二项式（1+x ）11的展开式中取一项，系数为奇数的概率是．7．命题“对任意，tanx ＜m 恒成立”是假命题，则实数m 取值范围是．8．函数f （x ）=log a （x 2﹣4x +3）（a ＞0，a ≠1）在x ∈[m ，+∞）上存在反函数，则m 的取值范围是．9．若平面向量满足，，则的取值范围为．10．已知数列{a n }，a 1=1，，n ∈N *，则= ．11．已知函数f （x ）=x +（a ＞0），若对任意的m 、n 、，长为f （m ）、f （n ）、f（p ）的三条线段均可以构成三角形，则正实数a 的取值范围是．12．已知数列{a n }满足：对任意的n ∈N *均有a n +1=ka n +2k ﹣2，其中k 为不等于0与1的常数，若a i ∈{﹣272，﹣32，﹣2，8，88，888}，i=2、3、4、5，则满足条件的a 1所有可能值的和为．二.选择题13．已知实数m 、n ，则“mn ＞0”是“方程mx 2+ny 2=1代表的曲线是椭圆”的（） A ．充分非必要条件 B ．必要非充分条件 C ．充要条件D ．既非充分也非必要条件14．将半径为R 的半圆形铁皮制作成一个无盖圆锥形容器（不计损耗），则其容积为（）A ．B ．C ．D ．15．已知数列{a n }通项公式为a n =，其前m 项和为，则双曲线=1的渐近线方程是（）A．y=±x B．y=±x C．y=±x D．y=±x16．已知等比数列{a n}的前n项和为S n，则下列一定成立的是（）A．若a3＞0，则a2016＞0 B．若a4＞0，则a2017＞0C．若a3＞0，则S2017＞0 D．若a4＞0，则S2016＞0三.解答题17．如图，用一平面去截球O，所得截面面积为16π，球心O到截面的距离为3，O1为截面小圆圆心，AB为截面小圆的直径；（1）计算球O的表面积和体积；（2）若C是截面小圆上一点，∠ABC=30°，M、N分别是线段AO1和OO1的中点，求异面直线AC与MN所成的角；（结果用反三角表示）18．△ABC中，角A、B、C所对边分别为a、b、c，cosA=，tan，c=21；（1）求sinC的值；（2）求△ABC的面积．19．已知函数f（x）=x2﹣4x+a+3，a∈R；（1）若函数y=f（x）在[﹣1，1]上存在零点，求a的取值范围；（2）设函数g（x）=bx+5﹣2b，b∈R，当a=3时，若对任意的x1∈[1，4]，总存在x2∈[1，4]，使得g（x1）=f（x2），求b的取值范围．20．已知抛物线Γ：y2=2px上一点M（3，m）到焦点的距离为4，动直线y=kx（k≠0）交抛物线Γ于坐标原点O和点A，交抛物线Γ的准线于点B，若动点P满足，动点P的轨迹C的方程为F（x，y）=0；（1）求出抛物线Γ的标准方程；（2）求动点P的轨迹方程F（x，y）=0；（不用指明范围）（3）以下给出曲线C的四个方面的性质，请你选择其中的三个方面进行研究：①对称性；②图形范围；③渐近线；④y＞0时，写出由F（x，y）=0确定的函数y=f（x）的单调区间，不需证明．21．已知无穷数列{a n}，满足a n+2=|a n+1﹣a n|，n∈N*；（1）若a1=1，a2=2，求数列前10项和；（2）若a1=1，a2=x，x∈Z，且数列{a n}前2017项中有100项是0，求x的可能值；（3）求证：在数列{a n}中，存在k∈N*，使得0≤a k＜1．2016-2017学年上海市闵行区七宝中学高三（下）开学数学试卷参考答案与试题解析一.填空题1．不等式的解集是{x|0＜x＜1} ．【考点】其他不等式的解法．【分析】将不等式＞1移项后通分，即可求得不等式的解集．【解答】解：∵＞1，∴﹣1=＞0，∴＞0，∴0＜x＜1．∴不等式的解集为{x|0＜x＜1}．故答案为：{x|0＜x＜1}．2．已知直线l1：x﹣y+2=0，l2：3x+y﹣5=0，则直线l1与l2的夹角是．【考点】两直线的夹角与到角问题．【分析】先根据直线的斜率求出直线的倾斜角，再利用两条直线的倾斜角的大小求出这两条直线的夹角．【解答】解：因为直线l1的斜率为，故倾斜角为60°，直线l2的斜率为﹣，倾斜角为120°，故两直线的夹角为60°，即两直线的夹角为，故答案为．3．函数f（x）=的最大值是5．【考点】三角函数的最值．【分析】f（x）==3sinx+4cosx=5sin（x+θ），即可得出结论．【解答】解：f（x）==3sinx+4cosx=5sin（x+θ），∴函数f（x）=的最大值是5，故答案为5．4．i为虚数单位，z=对应的点在第二象限，则θ是第一、三象限的角．【考点】复数的代数表示法及其几何意义．【分析】利用共轭复数的意义可得z==c os2θ+isin2θ对应的点在第二象限，可得cos2θ＜0，sin2θ＞0，解出θ即可得出结论．【解答】解：z===cos2θ+isin2θ对应的点在第二象限，∴cos2θ＜0，sin2θ＞0，∴＜2θ＜2kπ+π，k∈Z．解得kπ+＜θ＜kπ+，k∈Z．k=2n（n∈Z）时，2nπ+＜θ＜2nπ+，θ为第一象限角．k=2n﹣1（n∈Z）时，2nπ﹣＜θ＜2nπ﹣，θ为第三象限角．综上可得：θ是第一、三象限的角．故答案为：一、三．5．已知一组数据4.7，4.8，5.1，5.4，5.5，则该组数据的方差是0.1．【考点】极差、方差与标准差．【分析】先求出数据4.7，4.8，5.1，5.4，5.5的平均数，由此能求出该组数据的方差．【解答】解：∵数据4.7，4.8，5.1，5.4，5.5的平均数为：=（4.7+4.8+5.1+5.4+5.5）=5.1，∴该组数据的方差：S2= [（4.7﹣5.1）2+（4.8﹣5.1）2+（5.1﹣5.1）2+（5.4﹣5.1）2+（5.5﹣5.1）2]=0.1．故答案为：0.1．6．从二项式（1+x）11的展开式中取一项，系数为奇数的概率是．【考点】二项式系数的性质．=x r，（r=0，1，2，…，11）．其中r=0，1，【分析】二项式（1+x）11的展开式中通项公式T r+12，3，8，9，10，11，为奇数．即可得出．=x r，（r=0，1，2，…，11）．【解答】解：二项式（1+x）11的展开式中通项公式T r+1其中r=0，1，2，3，8，9，10，11，为奇数．∴系数为奇数的概率==．故答案为：．7．命题“对任意，tanx＜m恒成立”是假命题，则实数m取值范围是（﹣∞，1] ．【考点】命题的真假判断与应用．【分析】由x的范围求出tanx的范围，再由tanx＜m恒成立求出m的范围，结合补集思想求得命题“对任意，tanx＜m恒成立”是假命题的m的取值范围．【解答】解：当时，tanx∈[0，1]，若tanx＜m恒成立，则m＞1．∵命题“对任意，tanx＜m恒成立”是假命题，∴m≤1．∴实数m取值范围是（﹣∞，1]．故答案为：（﹣∞，1]．8．函数f（x）=log a（x2﹣4x+3）（a＞0，a≠1）在x∈[m，+∞）上存在反函数，则m的取值范围是（3，+∞）．【考点】反函数．【分析】由反函数性质得函数f（x）=log a（x2﹣4x+3）（a＞0，a≠1）在x∈[m，+∞）单调，由此能求出m的取值范围．【解答】解：∵函数f（x）=log a（x2﹣4x+3）（a＞0，a≠1）在x∈[m，+∞）上存在反函数，∴函数f（x）=log a（x2﹣4x+3）（a＞0，a≠1）在x∈[m，+∞）单调，∵函数的定义域为（﹣∞，1）∪（3，+∞），y=x2﹣4x+3的对称轴为x=2，∴m ∈（3，+∞），故答案为：（3，+∞）．9．若平面向量满足，，则的取值范围为 [2，6] ．【考点】平面向量数量积的运算；向量的模．【分析】利用≤4||+，及≥﹣4||，求出||的取值范围．【解答】解：设的夹角为θ，∵=2•2•||cosθ+≤4||+，∴||≥2 或||≤﹣6（舍去）．又∵=2•2||cosθ+≥﹣4||，∴6≥||≥﹣2．综上，6≥||≥2，故答案为：[2，6]．10．已知数列{a n }，a 1=1，，n ∈N *，则=．【考点】数列的求和；极限及其运算．【分析】先根据数列关系式得到a 1+（a 2+a 3）+（a 4+a 5）+…+（a 2n ﹣2+a 2n ﹣1）=1+++…+，再根据等比数列的求和公式计算，最后求极限．【解答】解：∵，n ∈N ，∴a 1+（a 2+a 3）+（a 4+a 5）+…+（a 2n ﹣2+a 2n ﹣1）， =1+++…+，=1+，=1+﹣， =﹣，∴=（﹣）=，故答案为：11．已知函数f （x ）=x +（a ＞0），若对任意的m 、n 、，长为f （m ）、f （n ）、f（p ）的三条线段均可以构成三角形，则正实数a 的取值范围是（，）∪[1，）．【考点】函数的最值及其几何意义．【分析】求出f （x ）的导数，讨论当≥1即a ≥1时；当≤＜1且f （）≤f （1）即≤a ≤时；当≤＜1且f （）＞f （1）即＜a ＜1时；当＜，即0＜a ＜时．由单调性可得最小值和最大值，由题意可得最小值的2倍大于最大值，解不等式即可得到所求a 的范围．【解答】解：函数f （x ）=x +（a ＞0）的导数为f′（x ）=1﹣，当x ＞时，f′（x ）＞0，f （x ）递增；当x ＜时，f′（x ）＜0，f （x ）递减．当≥1即a ≥1时，[，1]为减区间，即有f （x ）的最大值为+3a ；最小值为1+a ．由题意可得只要满足2（1+a ）＞+3a ，解得1≤a ＜；当≤＜1且f （）≤f （1）即≤a ≤时，[，]为减区间，（，1）为增区间，即有f （x ）的最大值为1+a ；最小值为2．由题意可得只要满足1+a ＞4，解得0＜a ＜7﹣4，不成立；当≤＜1且f （）＞f （1）即＜a ＜1时，[，]为减区间，（，1）为增区间，即有f （x ）的最大值为+3a ；最小值为2．由题意可得只要满足+3a ＞4，解得0＜a ＜，不成立；当＜，即0＜a ＜时，[，1]为增区间，即有f （x ）的最小值为+3a ；最大值为1+a ．由题意可得只要满足2（+3a ）＞1+a ，解得＜a ＜．综上可得，a 的取值范围是（，）∪[1，）．故答案为：（，）∪[1，）．12．已知数列{a n }满足：对任意的n ∈N *均有a n +1=ka n +2k ﹣2，其中k 为不等于0与1的常数，若a i∈{﹣272，﹣32，﹣2，8，88，888}，i=2、3、4、5，则满足条件的a1所有可能值的和为．【考点】数列递推式．+2=k（a n+2），再对a1=﹣2与a1≠﹣2讨论，特别是a1≠﹣2时对【分析】依题意，可得a n+1公比k分|k|＞1与|k|＜1，即可求得a1所有可能值，从而可得答案．=ka n+2k﹣2，【解答】解：∵a n+1+2=k（a n+2），∴a n+1∴①若a1=﹣2，则a1+1+2=k（a1+2）=0，a2=﹣2，同理可得，a3=a4=a5=﹣2，即a1=﹣2复合题意；②若a1≠﹣2，k为不等于0与1的常数，则数列{a n+2}是以k为公比的等比数列，∵a i∈{﹣272，﹣32，﹣2，8，88，888}，i=2，3，4，5，a n+2可以取﹣270，﹣30，10，90，∴若公比|k|＞1，则k=﹣3，由a2+2=10=﹣3（a1+2）得：a1=﹣；若公比|k|＜1，则k=﹣，由a2+2=﹣270=﹣（a1+2）得：a1=808．综上所述，满足条件的a1所有可能值为﹣2，﹣，808．∴a1所有可能值的和为：﹣2=．故答案为：．二.选择题13．已知实数m、n，则“mn＞0”是“方程mx2+ny2=1代表的曲线是椭圆”的（）A．充分非必要条件 B．必要非充分条件C．充要条件D．既非充分也非必要条件【考点】必要条件、充分条件与充要条件的判断．【分析】先根据mn＞0看能否得出方程mx2+ny2=1的曲线是椭圆；这里可以利用举出特值的方法来验证，再看方程mx2+ny2=1的曲线是椭圆，根据椭圆的方程的定义，可以得出mn＞0，即可得到结论．【解答】解：当mn＞0时，方程mx2+ny2=1的曲线不一定是椭圆，例如：当m=n=1时，方程mx2+ny2=1的曲线不是椭圆而是圆；或者是m，n都是负数，曲线表示的也不是椭圆；故前者不是后者的充分条件；当方程mx2+ny2=1的曲线是椭圆时，应有m，n都大于0，且两个量不相等，得到mn＞0；由上可得：“mn＞0”是“方程mx2+ny2=1的曲线是椭圆”的必要不充分条件．故选B．14．将半径为R的半圆形铁皮制作成一个无盖圆锥形容器（不计损耗），则其容积为（）A．B．C．D．【考点】棱柱、棱锥、棱台的体积．【分析】推导出设这个盖圆锥形底面半径r=，母线长l=R，高h==，由此能求出这个无盖圆锥形容器（不计损耗）的容积．【解答】解：将半径为R的半圆形铁皮制作成一个无盖圆锥形容器，设这个盖圆锥形底面半径为r，则πR=2πr，解得r=，这个盖圆锥形母线长l=R，∴这个盖圆锥形的高h==，∴这个无盖圆锥形容器（不计损耗）的容积：V====．故选：A．15．已知数列{a n}通项公式为a n=，其前m项和为，则双曲线=1的渐近线方程是（）A．y=±x B．y=±x C．y=±x D．y=±x【考点】双曲线的简单性质．【分析】利用数列求和，推出m，然后求解双曲线的渐近线方程．【解答】解：数列{a n}通项公式为a n=，其前m项和为，可得1﹣=，即1﹣=．解得m=9．双曲线=1的渐近线方程：y=±x．故选：C．16．已知等比数列{a n}的前n项和为S n，则下列一定成立的是（）A．若a3＞0，则a2016＞0 B．若a4＞0，则a2017＞0C．若a3＞0，则S2017＞0 D．若a4＞0，则S2016＞0【考点】等比数列的通项公式．【分析】设等比数列{a n}的公比为q，利用通项公式与求和公式即可判断出结论．【解答】解：设等比数列{a n}的公比为q，若a3＞0，则＞0，则a1＞0．∴S2017=＞0．a2016=与0的大小关系不确定．若a4＞0，则＞0，则a1与q同号，则a2017=，S2016=与0的大小关系不确定．故选：C．三.解答题17．如图，用一平面去截球O，所得截面面积为16π，球心O到截面的距离为3，O1为截面小圆圆心，AB为截面小圆的直径；（1）计算球O的表面积和体积；（2）若C是截面小圆上一点，∠ABC=30°，M、N分别是线段AO1和OO1的中点，求异面直线AC与MN所成的角；（结果用反三角表示）【考点】球的体积和表面积．【分析】（1）求出小圆的半径，然后利用球心到该截面的距离为3cm，小圆的半径，通过勾股定理求出球的半径，即可求出球的表面积．（2）由MN∥OA得，∠OAC为异面直线AC与MN所成的角（或补角），连接OC，然后利用余弦定理求出此角的余弦值，最后利用反三角表示出此角即可．【解答】解：（1）连接OA，由题意得，截面小圆半径为4，在Rt△OAO1中，O1A=4，OO1=3，由勾股定理知，AO=5，∴球O的表面积为：4π•25=100π（2）由MN∥OA得，∠OAC为异面直线AC与MN所成的角（或补角）．在Rt△ABC中，AB=8，∠ABC=30°，则AC=4，连接OC，在△OAC中，OA=OC=5，由余弦定理知：cos∠OAC===，∴∠OAC=，∴异面直线AC与MN所成的角为．18．△ABC中，角A、B、C所对边分别为a、b、c，cosA=，tan，c=21；（1）求sinC的值；（2）求△ABC的面积．【考点】两角和与差的正切函数；三角函数中的恒等变换应用．【分析】（1）先根据弦切之间的关系对tan进行化简，再由二倍角公式可得到sinB 的值，结合cosA的值可判断B为锐角，进而由sinC=sin（A+B）根据两角和与差的正弦公式和（1）中的sinB，sinA，cosB，cosA的值可求得sinC的值．（2）再由正弦定理可求得a的值，最后根据三角形的面积公式可求得答案．【解答】解：（1）由tan==，得sinB=，∵cosA=，∴sinA=＞sinB，∴B为锐角，可得cosB=，∴sinC=sin（A+B）=sinAcosB+cosAsinB=×+×=．（2）∵c=21，∴a===20，=acsinB=×20×21×=126．∴S△ABC19．已知函数f（x）=x2﹣4x+a+3，a∈R；（1）若函数y=f（x）在[﹣1，1]上存在零点，求a的取值范围；（2）设函数g（x）=bx+5﹣2b，b∈R，当a=3时，若对任意的x1∈[1，4]，总存在x2∈[1，4]，使得g（x1）=f（x2），求b的取值范围．【考点】二次函数的性质；函数的最值及其几何意义．【分析】（1）根据f（x）在[﹣1，1]上单调递减且存在零点可得f（﹣1）f（1）≤0，从而解出a的范围；（2）对b进行讨论，判断g（x）的单调性，分别求出f（x），g（x）在[1，4]上的值域，令g（x）的值域为f（x）的值域的子集列出不等式组得出b的范围．【解答】解：（1）∵f（x）=x2﹣4x+a+3的函数图象开口向上，对称轴为x=2，∴f（x）在[﹣1，1]上是减函数，∵函数y=f（x）在[﹣1，1]上存在零点，∴f（﹣1）f（1）≤0，即a（8+a）≤0，解得：﹣8≤a≤0．（2）a=3时，f（x）=x2﹣4x+6，∴f（x）在[1，2]上单调递减，在[2，4]上单调递增，∴f（x）在[2，4]上的最小值为f（2）=2，最大值为f（4）=6．即f（x）在[2，4]上的值域为[2，6]．设g（x）在[1，4]上的值域为M，∵对任意的x1∈[1，4]，总存在x2∈[1，4]，使得g（x1）=f（x2），∴M⊆[2，6]．当b=0时，g（x）=5，即M={5}，符合题意，当b＞0时，g（x）=bx+5﹣2b在[1，4]上是增函数，∴M=[5﹣b，5+2b]，∴，解得0＜b≤．当b＜0时，g（x）=bx+5﹣2b在[1，4]上是减函数，∴M=[5+2b，5﹣b]，∴，解得﹣1≤b＜0．综上，b的取值范围是．20．已知抛物线Γ：y2=2px上一点M（3，m）到焦点的距离为4，动直线y=kx（k≠0）交抛物线Γ于坐标原点O和点A，交抛物线Γ的准线于点B，若动点P满足，动点P的轨迹C的方程为F（x，y）=0；（1）求出抛物线Γ的标准方程；（2）求动点P的轨迹方程F（x，y）=0；（不用指明范围）（3）以下给出曲线C的四个方面的性质，请你选择其中的三个方面进行研究：①对称性；②图形范围；③渐近线；④y＞0时，写出由F（x，y）=0确定的函数y=f（x）的单调区间，不需证明．【考点】直线与抛物线的位置关系；抛物线的标准方程．【分析】（1）利用抛物线的定义，可得抛物线Γ的标准方程；（2）求出A，B的坐标，利用动点P满足，求出动点P的轨迹C的方程；（3）根据方程，可得结论．【解答】解：（1）由题意，3+=4，∴p=2，∴抛物线Γ的标准方程为y2=4x；（2）设P（x，y），则y=kx，与抛物线方程联立，可得x=，y=，即A（，），与x=﹣1联立，可得B（﹣1，﹣k），∵，∴（x，y）=（+1， +k），∴x=+1，y=+k，消去k可得；（3）由，可得①关于x轴对称；②x∈（1，+∞），y∈（﹣∞，﹣4]∪[4，+∞）；③渐近线x=1；④在（1，2]上递减，在[2，+∞）上递增．21．已知无穷数列{a n}，满足a n+2=|a n+1﹣a n|，n∈N*；（1）若a1=1，a2=2，求数列前10项和；（2）若a1=1，a2=x，x∈Z，且数列{a n}前2017项中有100项是0，求x的可能值；（3）求证：在数列{a n}中，存在k∈N*，使得0≤a k＜1．【考点】数列递推式；数列的求和．【分析】（1）由条件分别计算前10项，即可得到所求和；（2）讨论x=1，2，3，…，计算得到数列进入循环，求得数列中0的个数，即可得到所求值；（3）运用反证法证明，结合条件及无穷数列的概念，即可得证．【解答】解：（1）数列{a n}，满足a n+2=|a n+1﹣a n|，n∈N*；a1=1，a2=2，则a3=1，a4=1，a5=0，a6=1，a7=1，a8=0，a9=a10=1．∴数列前10项和S10=1+2+6=9．（2）当x=1时，数列数列{a n}的各项为1，1，0，1，1，0，1，1，0，1，1，0…所以在前2017项中恰好含有672项为0；当x=2时，数列数列{a n}的各项为1，2，1，1，0，1，1，0，1，1，0…所以在前2017项中恰好含有671项为0；当x=3时，数列数列{a n}的各项为1，3，2，1，1，0，1，1，0，1，1，0…所以在前2017项中恰好含有671项为0；当x=4时，数列数列{a n}的各项为1，4，3，1，2，1，1，0，1，1，0，…所以在前2017项中恰好含有670项；当x=5时，数列数列{a n}的各项为1，5，4，1，3，2，1，1，0，1，1，0…所以在前2017项中恰好含有670项为0；…由上面可以得到当x=1144或x=1145时，在前2017项中恰好含有100项为0；当x=﹣1141或x=﹣1140时，在前2017项中恰好含有100项为0；（3）证明：假设数列{a n}中不存在a k（k∈N*），使得0≤a k＜1，则a k＜0或a k≥1（k=1，2，3，…）．由无穷数列{a n}，满足a n+2=|a n+1﹣a n|，n∈N*，可得a k≥1，由于无穷数列{a n}，对于给定的a1，a2，总可以相减后得到0，故假设不成立．在数列{a n}中，存在k∈N*，使得0≤a k＜1．2017年5月8日。

上海市七宝中学高三上学期5月质量检测英语试卷精编版

上海市七宝中学2015年高三第二学期英语5月质量检测卷出卷人：沈鹏审卷人：竹娉娉I. Listening Comprehension (30’)Section A (10’)Directions: 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. In a library. B. In a hotel. C. In a classroom. D. In a bookstore2. A. She thinks the man needs a vacation.B. She thinks the man should be preparing for his tests.C. She thinks the man doesn’t need to worry about his exams.D. She is not interested in surfing.3. A. She may fail the exam. B. She shouldn’t have worried.C. She should work harder.D. She needn’t take any more courses.4. A. Scholarship. B. Major. C. Hobby. D. Travelling.5. A. Thoughtful. B. Humorous. C. Careless. D. Helpful.6. A. A rent increase. B. A bargain. C. A salary cut. D. A vacation trip.7. A. By car. B. By bus. C. On foot. D. By train.8. A. Only one person can come. B. There have been few responses.C. Almost everyone can come.D. They’re waiting for Tina’s response.9. A. He has no interest in wild life protection.B. He is sorry to fail in the examination.C. He can’t join the group since he is about to graduate.D. He’s already busy with the Student Union issue.10. A. Because she is all wet. B. Because she is tried out.C. Because she walked a long distance.D. Because she left something in the school.Section B (12’)Directions: In Section B, you will hear two short passages, and you will be asked three questions on each passage. The passage 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. Functions of Facial Expressions. B. Types of Printed Words.C. Means of Communication.D. Importance of Language.12. A. It was the first invention of mankind.B. It is a must for man’s survival.C. It makes other inventions possible.D. It helps people to know the modern world.13. A. Man would have to use signals only.B. The modern world couldn’t function well.C. Man would keep on inventing things.D. Man wouldn’t be able to live with his fellow beings.Questions 14 through 16 are based on the following passage.14. A. The design of the laboratory. B. The laboratory experiment.C. The workbook for the laboratory course.D. A piece of equipment in the laboratory.15. A. Homework must be handed in on time.B. A great deal of equipment is available.C. The students must follow all instructions exactly.D. The students can make choices about the lab work.16. A. The activities take less time.B. The activities are to be done in class.C. Few instructions are given for the activities.D. Students are not required to do the activates.Section C (8’)Directions:In Section C, you will hear two longer conversations. The conversation will be read twice. After you hear the conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Blanks 21 through 24 are based on the following conversation.II. Grammar (16’)Directions:After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.As a big fan of Manchester United, it is always hard for me to believe that Man Utd should finish seventh in the final Premier League table(英超联赛积分榜) last season. To be frank, that result [25]_______ never be more disappointing and frustrating for me. If there is someone who is [26]________ (blame) for this, it must be the Manager David Moyes.So at the end of last season, everyone knew that it was only a matter of time before he [27]________ (dismiss) and to [28]________ Man Utd should hand the task of getting the team back on track became a matter of concern.When the news came on the night of Wednesday 16 July [29]________ Louis van Gaal was appointed the new Manager of Man Utd, I knew he could be the one to restore the Red Devils to their former glories, [30]________ some claims that this decision was even more risky since Louis is [31]________ (familiar) with the league compared with Man Utd’s ill-fated former Manager David Moyes, who at least has worked in the league for years. “ Experienced [32]________ Louis van Gaal is,” Gary Neville, currently [33]________ occasional sports columnist for the Daily Mail (每日邮报), wrote in his column, “it is apparently unlikely for this new comer to win the title this year.” And some of the concerns were right, especially when Louis [34]________ admitted that it would take 2 [35]________ 3 months to get fully acquainted with the Premier League. Thus, Man Utd’s failure to stay on top of the Premier League table before Christmas, [36]________ used to be a rare case, didn’t come as a surprise to me.But in the last two months, things have changed. Man Utd has gained six successive victories against different rivals [37]________ (include) its noisy neighbor—Manchester City, [38]________ ________ which the team has now climbed from rock bottom to No. 3 in the table.With only 5 matches [39]________ (leave) and Man Utd temporarily ranking No. 3 (last season No. 7) at the league table, now everyone can agree on one thing that [40]________ ________ ________ this season ends eventually, the decision to replace David Moyes with Louis van Gaal in the last summer was a right one.III. Vocabulary (10’)Directions:Complete the following passage by using the words in the box. Each word can only be used once. Do note that there is one word more than you need.My Reflection on Johnnie To’s Running on Karma(大隻佬) Recently I have seen the film Running on Karma again, a controversial film that has long been taken as a courageous attempt of Johnnie To’s and also a significant [41]________ from his other works. Those [42]________ plots which used to limit my understanding of the film now start to make sense. It just feels as if I were [43]________ with an old acquaintance whom I once misunderstood.If there is one line that can represent what To really wants to [44]________ to his audience, itmust be the saying that all but one’s karma(佛教用语：业) can be cast away, which [45]________ appears in the film.As the theme’s finishing touch, not only does the above saying reveal some [46]________ thoughts hidden in the film, but it also throws a light on To’s [47]________ of responsibility. Karma means “act or deed.” What was sown before is now reaped. But as sowing also takes place in the present, it [48]________ involves responsibility towards the future. Since nothing can be done to alter the past, what one should be concerned about is not yesterday’s cause, but how to sow his or her karma today—which will [49]________ fruit tomorrow.To put it in another way, the idea of the film is that no matter what one has done, once it has been done, it just becomes water under the bridge. So what truly matters is to [50]________ the responsibility for the future, since that is something one can make a difference to.IV. Cloze (15’)Directions:For each blank in the following passage there are four words marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Many theories concerning the causes of juvenile delinquency (crimes committed by young people) focus either on the individual or on society as the major contributing influence. Theories centering on the individual suggest that children [51]_______ criminal behavior because they were not sufficiently [52]________ for previous misbehaviors or that they have learned criminal behavior through interaction with others. Theories focusing on the role of society suggest that children commit crimes in [53]________ to their failure to rise above their socioeconomic status or as a rejection of middle-class values.Most theories of juvenile delinquency have focused on children from disadvantaged families, [54]________ the fact that children from wealthy homes also commit crimes. The latter may commit crimes for lack of adequate control from parents. All [55]________, however, are uncertain or unimproved and are of course challenged with criticism.Changes in the social structure may indirectly [56]________ juvenile crime rates. For example, changes in the economy that [57]________ to fewer job opportunities for youth and rising unemployment [58]________ make gainful employment increasingly difficult to obtain. This results in dissatisfaction among youths and may in [59]________ lead more youths into criminal behavior.Families have also experienced [60]________ these years. More families consist of one parent households or two working parents; [61]________, children are likely to have less supervision at home than was common in the traditional family [62]________. This lack of parental supervision is thought to be an influence on juvenile crime rates. Other noticeable [63]________ of offensive acts include unfavorable experience or failure in school, the [64]________ availability of drugs and alcohol, and the growing phenomenon of child abuse and child neglect. All these conditions tend to increase the [65]________ of a child committing a criminal act, although a direct cause and effect relationship has not yet been established.51. A. refer to B. know about C. engage in D. learn of52. A. punished B. forgiven C. forgotten D. excused53. A. return B. contact C. reference D. response54. A. considering B. ignoring C. highlighting D. believing55. A. values B. misbehaviors C. criminals D. theories56. A. affect B. reduce C. prevent D. reflect57. A. point B. lead C. come D. add58. A. in general B. on average C. by contrast D. at last59. A. case B. short C. turn D. essence60. A. failure B. miseries C. development D. changes61. A. contrarily B. consequently C. similarly D. occasionally62. A. education B. concept C. structure D. economy63. A. suggestions B. causes C. ideas D. reports64. A. increased B. restricted C. reasonable D. popular65. A. knowledge B. aspect C. strength D. probabilityV. Reading Comprehension (2*16)Section A (2’*12)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)Pride and Prejudice for the Modern WomanLet us imagine how Pride and Prejudice, Jane Austen’s most fa mous work, might be updated, 200 years on.Austen’s popularity is rooted in her intelligence. But today she would certainly have had a very different life, as would her character s. Here’s my own suggestion.It is a truth finally and universally acknowledged that a single woman with brains deserves to have equal opportunities to men, however disadvantaged she may feel by sexism.“My dear husband,”said his hopeful wife one day, “have you heard that the local store, standing empty for so long, is taken over b y a bright young businesswoman?”Her dull and indifferent husband replied that he had not. “But it is, it is,” she replied excitedly. Mr. Dull-Husband made no reply.“Don’t you want to know her plans?” she cried with some impatience.“Well, clearly you think it matters to your silly little head... so I’d better listen.”“Well, my dear, the rumour is that she has already set up a string of successful businesses in northern England, though how a woman can know anything about that is beyond me. She will move in herself next month.“What is her name?”“Bingley.”“Is she married or single?”“What a question! And none of your business.” But her coming will be a fine thing for our five boys. “How so? H ow can it possibly affect them?”“My dear love; those lazy boys need something to wake them up. There are bound to be jobs going.”“Is that her point in settling here? Surely as a woman she has sim ply taken a fancy to the place.”“Nonsense, my love, how little you’ve noticed the world has changed. She’s got a first-rate degree and some sort of business qualification, I’m told. She surely needs one of our boys! Perhapsyou might give her a call.”“Me? No. Perhaps you can take an interest. You still have your looks, after all. She may even offer you a job.”“Oh, that’s not likely. These new chances belong to the younger generation. But now you mention it, I think I’ll go along all the same.”And Mrs. Bennet went along. That was 10 years ago. She is now managing director of a FTSE(英国富时指数)-listed company.... It would remain the case, of course, that Mrs. Bennet would be one of very few women on the company board, that her salary would be lower than her male colleagues, her bonus of a more “female”dimension and her lifespan among the city’s business leaders shorter than theirs. Still, she’d no doubt have enjoyed Davos(达沃斯论坛)—and might even have hobnobbed (攀谈) with influential figures.66. Which of the following is TRUE according to the passage?A. Austen was born 200 years age.B. Austen rewrote Pride and Prejudice.C. Austen’s success lies in her wisdom.D. Austen’s updated work gains popularity.67. The underlined part in the passage suggests that Mrs. Bennet ________.A. had mixed feelings of admiration and surprise about BingleyB. felt kind of worried and doubtful about BingleyC. was extremely anxious to meet BingleyD. had a great curiosity about Bingley68. In the eyes of Mrs. Bennet, Bingley surely needed one of their boys to ________.A. get married toB. work for herC. help her move inD. take over her store69. What does the writer intend to tell us?A. Women with brains can also be as successful as men.B. Women have to pay a high price for success.C. A judgment must be made free from prejudice.D. Sex discrimination still exists nowadays.(B)Shanghai is filled with interesting museums, and they will educate, intrigue and delight children with exhibitions of animation characters, insects and chopsticks, to name a few. Here are some lesser-known, non-art museum scattered around the city.Animation MuseumChildren will love this museum covering the world history of cartoons and animations. The first floor covers history, from China’s shadow puppets to Disney’s characters. The main hall is filled with posters and life-sized statues. Short animation is screened.In a second-floor studio, children can dub(配音) voices for favorite characters.Tel: 5895-7998Address: 69 Zhangjiang Rd, Pudoing New AreaOpening hours: 10am-5pm, closed on MondaysAdmission: 30 yuanBrush and Ink MuseumThe one-room museum covers the history of ink, inkstones and brushes. It explains how to make ink and features stories about Shanghai and its calligraphers. Brushes and inkstones are displayed, each with an English audio explanation.Tel: 5169-8918Address: 2/F, 429 Fujiang Rd, Huangpu DistrictOpening hours: 9:30am-5:30pm, dailyAdmission: FreeChopsticks MuseumThis is one of the city’s smallest museums. It’s the personal exhibition of Lan Xiang, who has collected 2,000 pairs of chopsticks from around Asia. Lan, 81, lives upstairs. The prized pair is a gilded silver set from the Tang Dynasty (AD 618-907).Tel: 5671-7528Address: 191 Duolun Rd, Hongkou DistrictOpening hours: Call in advanceAdmission: FreeInsect MuseumThe museum contains more than a million specimens(标本) of insects from around the world, many rare and beautiful, some extinct. The museum was founded in 1868 and once called the British Museum in Asia. Today it’s in a modern building.Tel: 5492-4191Address: 300 Fenglin Rd, Xuhui DistrictOpening hours: 9am-4pmAdmission: 15 yuan for adults (18+), 10 yuan for childrenPostal MuseumThis is a wonderful free museum with a beautiful Baroque clock tower, rooftop garden and glassed-in courtyard. The 1924 landmark building was the original Shanghai Postal Museum and explains the history of the postal service in China. It’s filled with interesting exhibits, concession-period post marks, clay seals and postage stamps.Tel: 6393-6666 ext. 1280Address: 250 Suzhou Rd, Hongkou DistrictOpening hours: Wednesday, Thursdays, Saturdays and Sundays, 9am-5pm70. Children can do the following in the Animation Museum EXCEPT ________.A. making shadow puppetsB. dubbing in the studioC. learning the history of cartoonsD. watching the short animation71. What do the Chopsticks Museum and the Postal Museum have in common?A. They are closed on Mondays.B. They are private museums.C. They offer excellent views.D. They are admission free.72. If a 40-year-old man takes three of his nephews (aged 4, 13 and 19) to the Insect Museum, heneeds to pay ________ for admission fees.A. 60 yuanB. 50 yuanC. 45 yuanD. 40 yuan73. An American who is fond of learning some traditional Chinese culture but knows little Chinese isadvised to dial ________.A. 5492-4191B. 5895-7998C. 5671-7528D. 5169-8918(C)Just five one-hundredths of an inch thick, light golden in color and with a perfect “saddle curl,”the Lay’s potato chip(乐事薯片) seems an unlikely weapon for global domination. But its maker, Frito-Lay, thinks otherwise. “Potato chips are a snack food for the world,” said Salman Amin, the company’s head of global marketing. Amin believes there is no corner of the world that can resist the charms of a Frito-Lay potato chip.Frito-Lay is the biggest snack maker in America owned by PepsiCo(百事公司) and accounts for over half of the parent company’s $3 billion annual profits. But the U.S. snack food market is largely saturated(饱和), and to grow the company has to look overseas.Its strategy rests on two beliefs: first a global product offers economies of scale with which local brands cannot compete. And second, consumers in the 21st century are drawn to “global” as a concept. “Global” does not mean products that are consciously identified as American, but ones that consumers—especially young people—see as part of a modern, innovative world in which people are linked across cultures by shared beliefs and tastes. Potato chips are an American invention, but most Chinese, for instance, do not know that Frito-Lay is an American company. Instead, Riskey, the company’s research and development head, would hope they associate the brand with the new world of global communications and business.With brand perception a crucial factor, Riskey ordered a redesign of the Frito-Lay logo. The logo, along with the company’s long-held marketing image of the “irresistibility” of its chips, would help facilitate the company’ global expansion.The executives acknowledge that they try to swing national eating habits to a food created in America, but they deny that amounts to economic imperialism. Rather, they see Frito-Lay as spreading the benefits of free enterprise across the world. “We’re making products in those countries, we’re adapting them to the tastes of those countries, building business and employing people and changing lives,” said Steve Reinemund, PepsiCo’s chief executive.74. It is the belief of Frito-Lay’s head of global marketing that ________.A. Potato chips can hardly be used as a weapon to dominate the world marketB. Their company must find new ways to promote domestic salesC. The light golden color enhances the charm of their company’s potato chipsD. People over the world enjoy eating their company’s potato chips75. One of the assumptions on which Frito-Lay bases its development strategy is that ________.A. consumers worldwide today are attracted by global brandsB. local brands cannot compete successfully with American brandsC. products suiting Chinese consumers’ needs bring more profitsD. products identified as American will have promising market value76. Why did Riskey have the Frito-Lay logo redesigned?A. To suit changing tastes of young consumers.B. To promote the company’s strategy of globalization.C. To change the company’s long-held marketing image.D. To compete with other American chip producers.77. Frito-Lay’s executives claim that the promoting of American food in the international market________.A. won’t affect the eating habits of the local peopleB. will lead to economic imperialismC. will be in the interest of the local peopleD. won’t spoil the taste of their potato chipsSection B (2’*4)Directions: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Oscar-winning director Ang Lee’s new epic Life of Pi reveals the relationship between a teenage Indian boy and a Bengal tiger. But in reality, the predators(肉食性动物) are under increasing threat from humans. Animal rights group PETA is hoping to use the popularity of the film to focus people’s attention on the real life of Bengal tigers.With the rising demand for tiger parts from East Asia, illegal hunting remains a tremendous danger for the remaining cat population. Back in 1947, there were 40,000 tigers in India, but the number is experiencing a sharp decline to 1,707 despite campaigns to protect the animal.Rising man-animal conflict is also one of the leading causes of decline in tiger numbers. In one of numerous reported attacks on the endangered big cats, villagers near the Bangladesh-India border, armed with sticks and boat oars, set upon the animal suspected to have attacked a local fisherman and beat it to death earlier this month. So far this year, 58 tigers deaths have been reported in the country.“The first instinct when a tiger is spotted is to just kill it,” grieved Gurmeet Sapal, a wildlife filmmaker. “The feeling of fear and revenge is so strong that is shuts out any other emotion.” What we don’t realize is that the tiger never attacks humans until it is forced to.”India has been struggling to stop tiger’s decline in the face of the loss of habitat as well that encourages the animals to leave the forest for food. “The tiger’s rapidly exhausted prey base causes the predator to go all out to get its food. Consequently, livestock and human beings become easy prey, which leads inevitably to conflicts,” says a wildlife conservationist.Filmmakers Sapal says it is only normal for people to think of the tiger as a dangerous animal, but its image as a human killer bears some injustice. “Tigers never kill for sport nor store meat. They kill their prey only in case of hunger.”(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)78. PETA hopes Life of Pi can _____________________________________________________.79. Why did villagers beat the tiger to death?80. The main reasons for the decline in tiger numbers are ____________________________ and__________________________.81. When will tigers attack and kill people according to the article?VI. Translation (3’+4’+5’+5’+5’ = 22’)Directions: Translate the following sentences into English, using the words given in the brackets.1. 公司明确表示只有精通计算机技能的人才能申请这个职位。

上海市七宝中学2023届高三5月第一次模拟练习数学试题(2)

一、单选题二、多选题1. 若，且，则是（）A ．第一象限角B ．第二象限角C ．第三象限角D ．第四象限角2. 某冷饮店的日销售额(单位：元)与当天的最高气温(单位：℃，)的关系式为，则该冷饮店的日销售额的最大值约为（）A ．907元B ．910元C ．915元D ．920元3. 已知双曲线的一条渐近线与直线垂直，则的焦点坐标为（）A．B．C．D．4. 被1000除的余数是（）A．B．C ．1D ．9015. 已知,是空间两条不同的直线，是空间两个不同的平面，下列命题为真命题的是（）A ．若，，则B ．若，，，则C ．若，则D ．若，，，则6. 某单位有男职工60人，女职工40人，其中男职工平均年龄为35岁，方差为6，女职工平均年龄为30岁，方差是1，则该单位全体职工的平均年龄和方差分别是（）A ．32.5，3.5B ．33，7C ．33，10D ．32.5，47.展开式中，含的项的系数为（）A ．15B ．20C ．60D ．3608. 已知函数是定义在上的偶函数，若对于任意，不等式恒成立，则不等式的解集为（）A．B．C．D．9. 已知函数，的部分图象如图所示，则（）A．B．将的图象向右平移个单位，得到的图象C ．，都有D ．若方程在上有两个不相等的实数根，则实数10. 下列物体中，能够被整体放入棱长为1（单位：）的正方体容器（容器壁厚度忽略不计）内的有（）A ．表面积为的球体上海市七宝中学2023届高三5月第一次模拟练习数学试题(2)上海市七宝中学2023届高三5月第一次模拟练习数学试题(2)三、填空题四、解答题B．体积为的正四面体C ．体积为的圆柱体D ．底面直径为，高为的圆锥11. 关于的展开式，下列结论正确的是（）A．的展开式中不含字母x的项为B．的展开式中不含字母x的项为C．的展开式中不含字母y的项为D．的展开式中不含字母y的项为12. 已知直线x ＝my －1经过椭圆C ：的一个焦点F ，且与C 交于不同的两点A ，B ，椭圆C 的离心率为，则下列结论正确的有（）A ．椭圆C的短轴长为B．弦的最小值为3C ．存在实数m ，使得以AB为直径的圆恰好过点D ．若，则13.已知等差数列的前项和记为，若．，则______；______．14. 已知函数在处的切线方程为，则______.15. 若直线为函数的一个对称轴，则常数的一个取值为________．16. 已知函数f （x ）＝ln x ＋ax 2－x .(1)若a ＝－1，求函数f （x ）的极值；(2)设f ′（x ）为f （x ）的导函数，若x 1，x 2是函数f ′（x ）的两个不相等的零点，求证：f （x 1）＋f （x 2）<x 1＋x 2－5.17. 的内角A ，B ，C 的对边分别是a ，b ，c ．已．(1)求A ；(2)D 为的中点，，垂足为E ，，垂足为F ．若，求面积的最大值．18. 已知双曲线E：（，）一个顶点为，直线l过点交双曲线右支于M ，N两点，记，，的面积分别为S ，，.当l 与x 轴垂直时，的值为.(1)求双曲线E 的标准方程；(2)若l 交y 轴于点P，，，求证：为定值；(3)在（2）的条件下，若，当时，求实数m 的取值范围.19.已知函数，其中.(1)若的图象在处的切线过点，求a 的值；(2)证明：，，其中e 的值约为2.718，它是自然对数的底数；(3)当时，求证：有3个零点，且3个零点之积为定值.20. 已知椭圆的左、右焦点分别为、，点是椭圆上的点，离心率为.(1)求椭圆的方程；(2)点在椭圆上上，若点与点关于原点对称，连接，并延长与椭圆的另一个交点为，连接，求面积的最大值.21. 已知椭圆E：的离心率为，四个顶点围成的四边形面积为4．(1)求椭圆E的方程；(2)过点作直线l与椭圆E交于A，B两点，与x轴交于点Q，若，求证：为定值．。

上海市七宝中学2024-2025学年高三上学期开学考试数学试题

上海市七宝中学2024-2025学年高三上学期开学考试数学试题一、填空题1．函数tan 2y x =的最小正周期为．2．在复平面内，复数z 对应的点的坐标是(1,2)，则i z ⋅=.3．已知集合{}|1A x x =≤，{}|B x x a =≥，且A B ⋃=R ，则实数a 的取值范围是______________________ .4．某校老年、中年和青年教师的人数如表所示，采用分层抽样的方法调查教师的身体状况，在抽取的样本中，青年教师有32人，则该样本的老年教师人数为．5．已知(1,0),(5,5)a b ==r r ，则向量b r 在向量a r 方向上的投影向量的坐标为． 6．一圆锥的轴截面是边长为4cm 的等边三角形，则这个圆锥的体积是．7．在ABC V 中，sin :sin :sin 2:3:4A B C =，则ABC ∠=．（结果用反三角函数值表示） 8．若32(2)+2n n n x x ax bx cx +=++++…（*n N ∈且3n ≥），且:3:2,a b =则n =.9．对于正数a 、b ，称2a b +是a 、b 的算术平均值，a 、b 的几何平均值.设1x >，1y >，若ln x 、ln y 的算术平均值是1，则x e 、y e 的几何平均值（e 是自然对数的底）的最小值是.10．已知()f x 是以2为周期的偶函数，当[0,1]x ∈时，()f x (1,3)-内，关于x 的方程()()f x kx k k R =+∈有4个根，则k 的取值范围是 11．已知双曲线2222:1(0,0)x y C a b a b-=>>的左、右焦点分别为1F ，2F ，点M 在双曲线C 的右支上，12MF MF ⊥，若1MF 与C 的一条渐近线l 垂直，垂足为N ，且12NF ON -=，其中O 为坐标原点，则双曲线C 的标准方程为．12．已知()()()1111R 2a b a b c m m d n n m n ===⋅==--∈r r r r r r ，，，，，，，存在a b r r ，，对于任意的实数,m n ，不等式a c b d T -+-≥r r r u r ，则实数T 的取值范围为．二、单选题13．设a 、b 均为非零实数且a b >，则下列结论中正确的是（）A ．22a b -->B ．11a b -->C ．22a b >D ．33a b >14．已知事件A 与事件B 是互斥事件，则（）A ．()1P AB =IB ．()()()P A B P A P B ⋂=C ．()()1P A P B =-D ．()1P A B =U15．设正四棱柱1111ABCD A B C D -的底面边长为1，高为2，平面α经过顶点A ，且与棱1,,AB AD AA 所在直线所成的角都相等，则满足条件的平面α共有（）个．A ．1B ．2C ．3D ．416．已知{}n a 是等差数列，()sin n n b a =，存在正整数()8t t ≤，使得n t n b b +=，n ∈N ，1n ≥.若集合{}|,,1n S x x b n n ==∈≥N 中只含有4个元素，则t 的可能取值有（）个A ．2B ．3C ．4D ．5三、解答题17．如图，四棱锥P ABCD -的底面ABCD 是菱形，AC 与BD 交于点O ，OP ⊥底面ABCD ，点M 为PC 中点， 2AC =，1BD =，2OP =．(1)求异面直线AP 与BM 所成角；(2)求平面ABM 与平面P AC 所成锐二面角18．某企业2022年年初有资金5千万元，由于引进了先进生产设备，资金年平均增长率可达到50%，每年年底扣除下一年的消费基金1.5千万元后，剩余资金投入再生产.设从2022年的年底起，每年年底企业扣除消费基金后的剩余资金依次为1a ，2a ，3a ，…(1)写出1a ，2a ，3a ，并证明数列{}3n a -是等比数列；(2)至少到哪一年的年底，企业的剩余资金会超过21千万元？19．某校举办了“我爱古诗词”对抗赛，在每轮对抗赛中，高二年级胜高三年级的率为25，高一年级胜高三年级的概率为13，且每轮对抗赛的成绩互不影响. (1)若高二年级与高三年级进行4轮对抗赛，求高三年级在对抗赛中至少有3轮胜出的概率；(2)若高一年级与高三年级进行对抗，高一年级胜2轮就停止，否则开始新一轮对抗，但对抗不超过5轮，求对抗赛轮数X 的分布列与数学期望.20．已知椭圆2222:1x y a b Γ+=的右焦点为()1,0，且经过点()0,1A ，设O 为原点，直线:(1)l y kx t t =+≠±与椭圆Г交于两个不同点P ，Q ，(1)求椭圆Г的方程；(2)若直线AP 与x 轴交于点M ，直线AQ 与x 轴交于点N ，且2OM ON ⋅=，求证：直线l 经过定点；(3)若AP AQ ⊥，求APQ △面积的最大值，并求此时直线l 的方程．。

2017年七宝中学高二年级上学期期末考试数学试卷

2016-2017学年上海市闵行区七宝中学高二年级上学期期末考试数学试卷一、填空（每题4分，共48分）1、准线方程为10y +=的抛物线标准方程为 .【答案】24x y =【解析】由题意可知，准线方程为1y =-，开口向上，所以抛物线的标准方程为24x y =. 故答案为：24x y =.2、已知圆225x y +=和点()1,2A ，则过点A 圆的切线方程为 .【答案】250x y +-=【解析】由于点()1,2A 在圆225x y +=上，故过点A 且与圆相切的直线方程是250x y +-=.故答案为：250x y +-=.3、若椭圆221369x y +=的弦被点()4,2平分，则此弦所在直线的斜率为 . 【答案】12-【解析】设斜率为k ，则直线的方程为()24y k x -=-，即240kx y k -+-=，代入椭圆的方程化简得()()22221416326464200k x k k x k ++-+--=，所以21223216814k k x x k -+==+，解得12k =-. 故答案为：12-.4、参数方程2cos 2sin x y θθ=⎧⎨=+⎩（θ为参数，且R θ∈）化为普通方程是 . 【答案】23y x =-+【解析】由22sin cos 1θθ+=得221y x -+=，化简得23y x =-+，[]1,1x ∈-故答案为：23y x =-+，[]1,1x ∈-.5、已知椭圆()222104x y a a +=>与双曲线22193x y -=有相同的焦点，则a 的值为 . 【答案】4【解析】由题意得，2493,a -=-解得4a =±，0,4a a >∴=Q .故答案为：4.6、设1F 和2F 为双曲线22421x y -=的两个焦点，点P 在双曲线上，且满足1260F PF ∠=o ，则12F PF V 的面积是 .【答案】2【解析】由双曲线焦点三角形面积公式21cotcot 30222S b θ==︒=.7、已知抛物线24y x =的焦点F 和点()1,1A ，点P 为抛物线上的动点，则PA PF +取得最小值时点P 的坐标为 .【答案】1,14⎛⎫⎪⎝⎭【解析】过点P 作PB 垂直于准线，过点A 作AH 垂直于准线，PA PF PA PB AH +=+≤, 此时最小，点P 与点A 纵坐标相同，所以点P 为1,14⎛⎫⎪⎝⎭. 故答案为：1,14⎛⎫⎪⎝⎭.8、椭圆2211612x y +=上的点到直线2120x y --=的距离最大值为 .【答案】【解析】椭圆2211612x y +=的参数方程为4cos x y θθ=⎧⎪⎨=⎪⎩∴设点()4cos P θθ∴点P 到直线2120x y --=的距离d ==当cos 13πθ⎛⎫+=- ⎪⎝⎭时，d取得最大值，即max d ==.故答案为：9、双曲线22214x y b -=的左右焦点分别为12,F F ，P 为右支上一点，且1126,0PF PF PF =⋅=u u u r u u u r u u u u r ，则双曲线渐近线的夹角为 .【答案】2arctanπ-或2arctan 【解析】根据题意22PF =,由焦点三角形面积公式2121cot 4562S b PF PF =︒=⨯⨯=， ∴26b =，渐近线为y x =，夹角为π-或故答案为：2arctan 2π-或2arctan 3.10、已知定点()4,0P -和定圆22:8Q x y x +=，动圆M 与圆Q 外切，且经过点P ，求圆心M 的轨迹方程 .【答案】22=1412x y - 【解析】点M 到点P 的距离和点M 到点Q 的距离之差为常数4R =，则动点M 的轨迹是以P 、Q 为焦点，且24a =的双曲线，得2a =，4c =，所以轨迹方程为22=1412x y -.故答案为：22=1412x y -.11、设直线l 与抛物线24y x =相交于,A B 两点，与圆()()22250x y r r -+=>相切于点M ，且M 为线段AB 的中点，若这样的直线l 恰有4条，则r 的取值范围是 .【答案】()2,4【解析】设()()()112200,,,,,A x y B x y M x y ，则21122244y x y x ⎧=⎪⎨=⎪⎩两式相减，得()()()121212+4y y y y x x -=-，当l 的斜率不存在，即12x x =时，符合条件的直线l 必有两条，当l 的斜率k 存在，即12x x ≠时，有()()0121224y y y x x -=-，即02k y =当CM AB ⊥,得00052CM y y k x ==-，即03x =，因为点M 在抛物线内部，所以20412y x <=，又12x x ≠，所以120y y +≠，即20012y <<，因为点M 在圆上，所以()222005x y r -+=，即2204r y =+，所以2416r <<，即24r <<.故答案为：()2,4.12、已知直线1:310l mx y m --+=与2:310l x my m +--=相交于点P ，线段AB 是圆()()22:114C x y +++=的一条动弦，且AB =PA PB +u u u r u u u r的最小值是 .【答案】1【解析】12l l ⊥，1l 过定点()3,1，2l 过定点()1,3，P ∴轨迹为圆()()222+22x y --=，作垂线段CD AB ⊥,1CD =,+++22PA PB PC CA AC CB PC CD PD +==+=u u u r u u u r u u u r u u u r u u u r u u u r u u u r u u u r u u u r,结合图形可知，最小值为1.故答案为：1.二、选择题：（每题4分，共16分）13.当0ab <时，方程22ax ay b -=所表示的曲线是（）【A 】.焦点在x 轴的椭圆【B 】.焦点在x 轴的双曲线【C 】.焦点在y 轴上的椭圆【D 】.焦点在y 轴上的双曲线【答案】D【解析】原方程可变形为x 2b a -y 2b a=1,∵a ,b 异号，\ba <0，所以此方程表示的曲线为焦点在y 轴上的双曲线。

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