辽宁省实验中学2020-2021学年度上学期期中阶段测试(教师版)
2019-2020学年辽宁省实验中学高二(上)期中数学试卷 试题及答案
2019-2020学年辽宁省实验中学高二（上）期中数学试卷一、单项选择题（每题只有一个正确选项，将正确选项涂在答题卡相应位置，每题正确得5分，错误不得分，共10题，满分50分） 1．数列1，3，7，15，⋯⋯的通项可以是( ) A ．21n -B ．21n -C ．21n -D ．21n n -+2．点(3,2)A -，(3,2)B ，直线10ax y --=与线段AB 相交，则实数a 的取值范围是( ) A ．4132a-剟 B ．1a …或1a -… C ．11a -剟D ．43a …或12a …3．若直线1:260l ax y ++=与直线22:(1)10l x a y a +-+-=平行，则(a = ) A ．2或1-B ．2C ．1-D ．以上都不对4．以双曲线22:13y C x -=的右焦点为圆心，且与双曲线C 的渐近线相切的圆的方程是( ) A ．22(2)3x y -+= B ．22(2)3x y ++=C ．22(2)1x y -+=D ．22(1)1x y ++=5．若圆22240x y x y m +-++=截直线30x y --=所得弦长为6，则实数m 的值为( ) A ．1-B ．2-C ．4-D ．31-6．若直线1:30(0)l x y m m ++=>与直线2:2630l x y +-=，则(m = ) A ．7B ．172C ．14D ．177．已知椭圆22:134x y C +=的上焦点为F ，直线10x y +-=和10x y ++=与椭圆分别相交于点A 、B 、C 、D ，则||||||||(AF BF CF DF +++= ) A．B．C ．4D ．88．数列{}n a ，{}n b 满足11111,2,n n n nb a b a a n N b +++==-==∈，则数列{}n a b 的前n 项和为( )A ．14(41)3n --B ．4(41)3n -C ．11(41)3n --D ．1(41)3n -9．美学四大构件是：史诗、音乐、造型（绘画、建筑等）和数学．素描是学习绘画的必要一步，它包括了明暗素描和结构素描，而学习几何体结构素描是学习素描最重要的一步．某同学在画“切面圆柱体”（用与圆柱底面不平行的平面去截圆柱，底面与截面之间的部分叫做切面圆柱体）的过程中，发现“切面”是一个椭圆，若“切面”所在平面与底面成60︒角，则该椭圆的离心率为( )A ．12B C D ．1310．已知点P ，Q 分别在直线1:20l x y ++=与直线2:10l x y +-=上，且1PQ l ⊥，点(3,3)A --，31(,)22B ，则||||||AP PQ QB ++的最小值为( )A B +C D ．二、多项选择题（每题至少有两个正确选项，将所有正确选项涂在答题卡相应位置，每题5分，全部正确得5分，选项不全得2分，若有错误选项得0分，共2题，满分10分） 11．已知数列{}n a 为等差数列，11a =，且2a ，4a ，8a 是一个等比数列中的相邻三项，记(0,1)n a n n b a q q =≠，则{}n b 的前n 项和可以是( )A ．nB ．nqC ．12(1)n n nq nq nq q q ++---D ．2112(1)n n n q nq nq q q ++++---12．在平面直角坐标系中，有两个圆22211:(2)C x y r ++=和22222:(2)C x y r -+=，其中1r ，2r 为正常数，满足124r r +<或12||4r r ->，一个动圆P 与两圆都相切，则动圆圆心的轨迹方程可以是( ) A ．两个椭圆B ．两个双曲线C ．一个双曲线和一条直线D ．一个椭圆和一个双曲线三、填空题（将正确答案填在答题卡相应位置，每题5分，共20分） 13．实轴长为12，离心率为2，焦点在x 轴上的双曲线的标准方程为 ．14．在数列{}n a 中，已知11a =，25a =，且*21()n n n a a a n N ++=-∈，则2020a = ． 15．已知直线1:350l x y +-=，2:310l kx y -+=．若1l ，2l 与两坐标轴围成的四边形有一个外接圆，则k = ．16．已知数列{}n a 中，11a =，1(2,)n n a a n n n N --=∈…，设12321111n n n n nb a a a a +++=+++⋯+，若对任意的正整数n ，当[1m ∈，2]时，不等式213n m mt b -+>恒成立，则实数t 的取值范围是 ．四、解答题（将解题步骤，必要的文字说明和计算结果写在答题卡相应位置，共70分） 17．已知数列{}n a 是递增的等比数列，且149a a +=，238a a =． （1）求数列{}n a 的通项公式； （2）设n S 为数列{}n a 的前n 项和，11n n n n a b S S ++=，求数列{}n b 的前n 项和n T ． 18．如图，DP y ⊥轴，点M 在DP 的延长线上，且||3||DM DP =．当点P 在圆221x y +=上运动时，（1）求点M 的轨迹方程．（2）过点1(1,)3Q 作直线l 与点M 的轨迹相交于A 、B 两点，使点Q 被弦AB 平分，求直线l的方程．19．黄河被称为我国的母亲河，它的得名据说来自于河水的颜色，黄河因携带大量泥沙所以河水呈现黄色，黄河的水源来自青海高原，上游的1000公里的河水是非常清澈的．只是中游流经黄土高原，又有太多携带有大量泥沙的河流汇入才造成黄河的河水逐渐变得浑浊．在刘家峡水库附近，清澈的黄河和携带大量泥沙的洮河汇合，在两条河流的交汇处，水的颜色一清一浊，互不交融，泾渭分明，形成了一条奇特的水中分界线，设黄河和洮河在汛期的水流量均为32000/m s ，黄河水的含沙量为32/kg m ，洮河水的含沙量为320/kg m ，假设从交汇处开始沿岸设有若干个观测点，两股河水在流经相邻的观测点的过程中，其混合效果相当于两股河水在1秒内交换31000m 的水量，即从洮河流入黄河31000m 的水混合后，又从黄河流入31000m 的水到洮河再混合．（1）求经过第二个观测点时，两股河水的含沙量；（2）从第几个观测点开始，两股河水的含沙量之差小于30.01/kg m ？（不考虑泥沙沉淀）20．已知椭圆22221(0)x y a b a b +=>>的左、右焦点为别为1F 、2F ，且过点和．（1）求椭圆的标准方程；（2）如图，点A 为椭圆上一位于x 轴上方的动点，2AF 的延长线与椭圆交于点B ，AO 的延长线与椭圆交于点C ，求ABC ∆面积的最大值，并写出取到最大值时直线BC 的方程．21．已知椭圆2222:1(0)x y C a b a b +=>>的左、右焦点1F ，2F ，M 是椭圆上任意一点，若以坐标原点为圆心，椭圆短轴长为直径的圆恰好经过椭圆的焦点，且△12MF F 的周长为4+． （1）求椭圆C 的方程；（2）设直线:(0)l y kx m k =+≠是圆224:3O x y +=的切线，l 与椭圆C 交与不同的两点Q ，R ，证明：QOR ∠的大小为定值．22．规定：在桌面上，用母球击打目标球，使目标球运动，球的位置是指球心的位置，我们说球A 是指该球的球心点A ．两球碰撞后，目标球在两球的球心所确定的直线上运动，目标球的运动方向是指目标球被母球击打时，母球球心所指向目标球球心的方向．所有的球都简化为平面上半径为1的圆，且母球与目标球有公共点时，目标球就开始运动，在桌面上建立平面直角坐标系，解决下列问题：（1）如图，设母球A 的位置为(0,0)，目标球B 的位置为(4,0)，要使目标球B 向(8,4)C -处运动，求母球A 球心运动的直线方程；（2）如图，若母球A的位置为(0,2)-，目标球B的位置为(4,0)，能否让母球A击打目标B 球后，使目标B球向(8,4)-处运动？（3）若A的位置为(0,)a时，使得母球A击打目标球B时，目标球(4,0)B运动方向可以碰到目标球11(8,)2-，求a的最小值（只需要写出结果即可）2019-2020学年辽宁省实验中学高二（上）期中数学试卷参考答案与试题解析一、单项选择题（每题只有一个正确选项，将正确选项涂在答题卡相应位置，每题正确得5分，错误不得分，共10题，满分50分） 1．数列1，3，7，15，⋯⋯的通项可以是( ) A ．21n -B ．21n -C ．21n -D ．21n n -+【解答】解：依题意，1112a +=，所以1121a =-，2212a +=，所以2221a =-， 3312a +=，所以3321a =-，⋯⋯故数列1，3，7，15，⋯⋯的通项可以是21n -， 故选：C ．2．点(3,2)A -，(3,2)B ，直线10ax y --=与线段AB 相交，则实数a 的取值范围是( ) A ．4132a-剟 B ．1a …或1a -… C ．11a -剟D ．43a …或12a …【解答】解：由直线10ax y --=的方程，判断恒过(0,1)P -， 如下图示：1PA K =-，1PB K =，结合图象可得：实数a 的取值范围是：1a -…或1a …． 故选：B ．3．若直线1:260l ax y ++=与直线22:(1)10l x a y a +-+-=平行，则(a = )A ．2或1-B ．2C ．1-D ．以上都不对【解答】解：直线1:260l ax y ++=与直线22:(1)10l x a y a +-+-=平行， (1)210a a ∴--⨯=，解得2a =，或1a =-当2a =时，两直线重合． 故选：C ．4．以双曲线22:13y C x -=的右焦点为圆心，且与双曲线C 的渐近线相切的圆的方程是( )A ．22(2)3x y -+=B ．22(2)3x y ++=C ．22(2)1x y -+=D ．22(1)1x y ++=【解答】解：根据题意，双曲线22:13y C x -=，其焦点在x 轴上，且1a =，b =， 则2c =，则双曲线的右焦点坐标为(2,0)，渐近线方程为y =0y ±=，则右焦点到渐近线的距离d ==则要求圆的圆心为(2,0)，半径r =， 则要求圆的方程为22(2)3x y -+=， 故选：A ．5．若圆22240x y x y m +-++=截直线30x y --=所得弦长为6，则实数m 的值为( ) A ．1-B ．2-C ．4-D ．31-【解答】解：由圆22240x y x y m +-++= 即22(1)(2)5x y m -++=-， ∴圆心为(1,2)-，∴圆心在直线30x y --=上， ∴此圆直径为6，则半径为3，253m ∴-=，4m ∴=-故实数m 的值为4-． 故选：C ．6．若直线1:30(0)l x y m m ++=>与直线2:2630l x y +-=，则(m = ) A ．7B ．172C ．14D ．17【解答】解：直线1:30(0)l x y m m ++=>，即2620x y m ++=， 它与直线2:2630l x y +-=，∴=，求得172m =， 故选：B ．7．已知椭圆22:134x y C +=的上焦点为F ，直线10x y +-=和10x y ++=与椭圆分别相交于点A 、B 、C 、D ，则||||||||(AF BF CF DF +++= ) A．B．C ．4D ．8【解答】解：如图：两条平行直线分别经过椭圆的两个焦点，连接1AF ，FD ．由椭圆的对称性可知，四边形1AFDF （其中1F 是椭圆的下焦点）为平行四边形，所以1AF FD =，同理1BF CF =．所以1148AF BF CF DF AF BF BF AF a +++=+++==． 故选：D ．8．数列{}n a ，{}n b 满足11111,2,n n n nb a b a a n N b +++==-==∈，则数列{}n a b 的前n 项和为( )A ．14(41)3n --B ．4(41)3n -C ．11(41)3n --D ．1(41)3n -【解答】解：数列{}n a ，{}n b 满足11111,2,n n n nba b a a n N b +++==-==∈，则数列{}n a 为等差数列，数列{}n b 为等比数列． 故21n a n =-，12n n b -=， 所以22124n n n a b --==，所以1411144(41)413n n n n S --=++⋯+==--， 故选：D ．9．美学四大构件是：史诗、音乐、造型（绘画、建筑等）和数学．素描是学习绘画的必要一步，它包括了明暗素描和结构素描，而学习几何体结构素描是学习素描最重要的一步．某同学在画“切面圆柱体”（用与圆柱底面不平行的平面去截圆柱，底面与截面之间的部分叫做切面圆柱体）的过程中，发现“切面”是一个椭圆，若“切面”所在平面与底面成60︒角，则该椭圆的离心率为( )A ．12B C D ．13【解答】解：椭圆的长轴为2a ，短轴的长为2b ，“切面”是一个椭圆，若“切面”所在平面与底面成60︒角，可得2cos602ba=︒，即2a b =，所以c e a ===． 故选：C ．10．已知点P ，Q 分别在直线1:20l x y ++=与直线2:10l x y +-=上，且1PQ l ⊥，点(3,3)A --，31(,)22B ，则||||||AP PQ QB ++的最小值为( )A B +C D ．【解答】解：由平行线距离公式得：||PQ ==，设(,2)P a a --，则3(2Q a +，1)2a --， 所以2232|||((3AP PQ QB +++，设点(,)M a a ，(1,3)C -，(1,0)D -，如下图：则有：||||||MC MD CD =+=…（即当D 、M 、C 三点共线时等号成立），综上，||||||AP PQ QB ++． 故选：B ．二、多项选择题（每题至少有两个正确选项，将所有正确选项涂在答题卡相应位置，每题5分，全部正确得5分，选项不全得2分，若有错误选项得0分，共2题，满分10分） 11．已知数列{}n a 为等差数列，11a =，且2a ，4a ，8a 是一个等比数列中的相邻三项，记(0,1)n a n n b a q q =≠，则{}n b 的前n 项和可以是( )A ．nB ．nqC ．12(1)n n nq nq nq q q ++---D ．2112(1)n n n q nq nq q q ++++---【解答】解：设等差数列{}n a 的公差为d ，又11a =，且2a ，4a ，8a 是一个等比数列中的相邻三项∴2428a a a =，即2111(3)()(7)a d a d a d +=++，化简得：(1)0d d -=，所以0d =或1， 故1n a =或n a n =，所以n b q =或n n b n q =，设{}n b 的前n 项和为n S ， ①当n b q =时，n S nq =； ②当n n b n q =时，23123n n S q q q n q =⨯+⨯+⨯+⋯⋯+⨯（1）， 2341123n n qS q q q n q +=⨯+⨯+⨯+⋯⋯+⨯（2），（1）-（2）得：2311(1)(1)1n nn n n q q q S q q q q n q n q q++--=+++⋯⋯+-⨯=-⨯-，所以121122(1)(1)1(1)n n n n n n q q n q q nq nq q S q q q ++++-⨯+--=-=---， 故选：BD ．12．在平面直角坐标系中，有两个圆22211:(2)C x y r ++=和22222:(2)C x y r -+=，其中1r ，2r 为正常数，满足124r r +<或12||4r r ->，一个动圆P 与两圆都相切，则动圆圆心的轨迹方程可以是( ) A ．两个椭圆B ．两个双曲线C ．一个双曲线和一条直线D ．一个椭圆和一个双曲线【解答】解：根据题意圆1(2,0)C -，半径1r ，圆2(2,0)C ，半径2r ，所以124C C =，设圆P 的半径为r ，（1）当124r r +<，即两圆外离时，动圆P 可能与两圆均内切或均外切或一个内切一个外切，①均内切时11||PC r r =-，22||PC r r =-，此时1212||||||||PC PC r r -=-， 当12r r ≠时，此时P 点的轨迹是以1C ，2C 为焦点的双曲线， 当12r r =时，此时点P 在1C ，2C 的垂直平分线上．②均外切时11||PC r r =+，22||PC r r =+，此时1212||||||||PC PC r r -=-． 此时P 点的轨迹是与①相同．③与一个内切与一个外切时，不妨设与圆1C 内切，与圆2C 外切， 11||PC r r =-，22||PC r r =+，2112||||PC PC r r -=+与圆2C 内切，与圆1C 外切时，同理得，1212||||PC PC r r -=+ 此时点P 的轨迹是以1C ，2C 为焦点的双曲线，与①中双曲线不一样．（2）当124r r +>，两圆相交，动圆P 可能与两圆均内切或均外切或一个内切一个外切， ④均内切时轨迹和①相同． ⑤均外切时轨迹和①相同⑥与一个内切另一个外切时，不妨设与圆1C 内切，与圆2C 外切， 11||PC r r =-，22||PC r r =+，1212||||PC PC r r +=+此时点P 的轨迹是以1C ，2C 为焦点的椭圆．与圆2C 内切，与圆1C 外切时，同理得1212|||PC PC r r +=+， 此时点P 的轨迹是以1C ，2C 为焦点的椭圆． 故选：BCD ．三、填空题（将正确答案填在答题卡相应位置，每题5分，共20分）13．实轴长为12，离心率为2，焦点在x 轴上的双曲线的标准方程为2136108y -= ． 【解答】解：根据题意，要求双曲线的实轴长为12，则212a =，即6a =， 又由其离心率2e =，即2ce a==，则有12c =，则b ==，又由双曲线的焦点在x 轴上，则其标准方程为：22136108x y -=； 故答案为：22136108x y -=． 14．在数列{}n a 中，已知11a =，25a =，且*21()n n n a a a n N ++=-∈，则2020a = 1- ． 【解答】解：法一：令1n =，则321514a a a =-=-=； 令2n =，则432451a a a =-=-=-；令3n =，则543145a a a =-=--=-；令4n =，则6545(1)4a a a =-=---=-； 令5n =，则7654(5)1a a a =-=---=； 令6n =，则8761(4)5a a a =-=--=； ∴数列{}n a 为周期为6的周期数列，20203366441a a a ⨯+∴===-．法二：*21()n n n a a a n N ++=-∈①， 321n n n a a a +++=-②，①+②得32121n n n n n n a a a a a a ++++++=-+-， 3n n a a +∴=-，63n n n a a a ++∴=-=，{}n a 周期为6， 2020336644a a a ⨯+∴==，∴由11a =，25a =，得34a =，41a =-．15．已知直线1:350l x y +-=，2:310l kx y -+=．若1l ，2l 与两坐标轴围成的四边形有一个外接圆，则k = 1± ．【解答】解：由题意知，1l ，2l 与两坐标轴围成的四边形有一组对角互补．由于直线1:350l x y +-=是一条斜率等于13-的固定直线，直线2:310l kx y -+=经过定点(0,1)A ，当直线2l 的斜率大于零时，应有12l l ⊥，3∴1()13k ⨯-=-，解得1k =．当直线2l 的斜率小于零时，如图所示：设直线1l 与y 轴的交点为B ，与x 轴的交点为C ，2l与x 轴的交点为D ，要使四边形ABCD 是圆内接四边形，应有ABC ∠与ADC ∠互补，即tan tan ABC ADC ∠=-∠． 再由1tan(90)3BC ABC K ︒+∠==-，可得tan 3ABC ∠=，tan 33AD ADC K k ∴∠=-==，解得1k =-．综上可得，1k =或1k =-， 故答案为：1±．16．已知数列{}n a 中，11a =，1(2,)n n a a n n n N --=∈…，设12321111n n n n nb a a a a +++=+++⋯+，若对任意的正整数n ，当[1m ∈，2]时，不等式213n m mt b -+>恒成立，则实数t 的取值范围是 (,1)-∞ ．【解答】解：11a =，1(2,)n n a a n n n N --=∈…，当2n …时，1n n a a n --=，121n n a a n ---=-，⋯，212a a -=， 并项相加，得：1(1)32n a a n n -=+-+⋯++， 1123(1)2n a n n n ∴=+++⋯+=+， 又当1n =时，111(11)12a =⨯⨯+=也满足上式， ∴数列{}n a 的通项公式为1(1)2n a n n =+， 12321111n n n n nb a a a a +++∴=+++⋯+222(1)(2)(2)(3)2(21)n n n n n n =++⋯++++++1111112()1223221n n n n n n =-+-+⋯+-+++++211222()112123123n n n n n n n=-==++++++， 令1()2(1)f x x x x =+…，则21()2f x x'=-，当1x …时，()0f x '>恒成立， ()f x ∴在[1x ∈，)+∞上是增函数，故当1x =时，()min f x f =（1）3=，即当1n =时，1()3n max b =，对任意的正整数n ，当[1m ∈，2]时，不等式213n m mt b -+>恒成立， 则须使211()33n max m mt b -+>=， 即20m mt ->对[1m ∀∈，2]恒成立，即t m <的最小值， 可得得1t <，∴实数t 的取值范围为(,1)-∞，故答案为：(,1)-∞．四、解答题（将解题步骤，必要的文字说明和计算结果写在答题卡相应位置，共70分） 17．已知数列{}n a 是递增的等比数列，且149a a +=，238a a =． （1）求数列{}n a 的通项公式； （2）设n S 为数列{}n a 的前n 项和，11n n n n a b S S ++=，求数列{}n b 的前n 项和n T ． 【解答】解：（1）数列{}n a 是递增的等比数列，且149a a +=，238a a =． 149a a ∴+=，14238a a a a ==．解得11a =，48a =或18a =，41a =（舍)， 解得2q =，即数列{}n a 的通项公式12n n a -=；（2）1(1)211n n n a q S q -==--， 1111111n n n n n n n n n n a S S b S S S S S S +++++-∴===-， ∴数列{}n b 的前n 项和11223111111111111121n n n n n T S S S S S S S S +++=-+-+⋯+-=-=--．18．如图，DP y ⊥轴，点M 在DP 的延长线上，且||3||DM DP =．当点P 在圆221x y +=上运动时，（1）求点M 的轨迹方程．（2）过点1(1,)3Q 作直线l 与点M 的轨迹相交于A 、B 两点，使点Q 被弦AB 平分，求直线l的方程．【解答】解：（1）设(,)M x y ，0(P x ，0)y ，则(0,)D y ，0y y =，0||||DP x =，||||DM x =， ||3||DM DP =，03x x ∴= 003x x y y =⎧⎨=⎩， ∴003x x y y⎧=⎪⎨⎪=⎩① P 在圆221x y +=上，∴2201x y +=， 把①代入可得：2219x y +=．||3||DM DP =，||0DP ∴≠，0x ∴≠， ∴221(0)9x y x +=≠． （2）设1(A x ，1)y ，2(B x ，2)y ．代入可得：221119x y +=，222219x y +=，相减可得：12121212()()()()09x x x x y y y y +-++-=．又122x x +=，1223y y +=．∴22093l k +=，可得：13l k =-． ∴直线l 的方程为：11(1)33y x -=--，化为：320x y +-=． 19．黄河被称为我国的母亲河，它的得名据说来自于河水的颜色，黄河因携带大量泥沙所以河水呈现黄色，黄河的水源来自青海高原，上游的1000公里的河水是非常清澈的．只是中游流经黄土高原，又有太多携带有大量泥沙的河流汇入才造成黄河的河水逐渐变得浑浊．在刘家峡水库附近，清澈的黄河和携带大量泥沙的洮河汇合，在两条河流的交汇处，水的颜色一清一浊，互不交融，泾渭分明，形成了一条奇特的水中分界线，设黄河和洮河在汛期的水流量均为32000/m s ，黄河水的含沙量为32/kg m ，洮河水的含沙量为320/kg m ，假设从交汇处开始沿岸设有若干个观测点，两股河水在流经相邻的观测点的过程中，其混合效果相当于两股河水在1秒内交换31000m 的水量，即从洮河流入黄河31000m 的水混合后，又从黄河流入31000m 的水到洮河再混合．（1）求经过第二个观测点时，两股河水的含沙量；（2）从第几个观测点开始，两股河水的含沙量之差小于30.01/kg m ？（不考虑泥沙沉淀）【解答】解：（1）在第二个观测点时，洮河流入黄河31000m 的水混合后， 黄河的含沙量为：3220002010008/3000kg m ⨯+⨯=，又从黄河流入31000m 的水到洮河再混合后，洮河的含沙量为38100020100014/2000kg m ⨯+⨯=．（2）设在第n 个观测点时黄河的含沙量为n a ，洮河的含沙量为n b ， 由题意有12a =，120b =，且110002*********n n n nn b a a b a +++==， 1110001000220003n n n nn b a a b b ++++==， 所以111()3n n n n b a b a ++-=-，1118b a -=，所以1118()3n n n b a --=⨯，根据题意，有1118()0.013n -⨯<，即131800n ->，解得7n >，所以从第8个观测点开始．20．已知椭圆22221(0)x y a b a b +=>>的左、右焦点为别为1F 、2F ，且过点和．（1）求椭圆的标准方程；（2）如图，点A 为椭圆上一位于x 轴上方的动点，2AF 的延长线与椭圆交于点B ，AO 的延长线与椭圆交于点C ，求ABC ∆面积的最大值，并写出取到最大值时直线BC 的方程．【解答】解：（1）将两点代入椭圆方程，有2222111213124a b ab ⎧+=⎪⎪⎨⎪+=⎪⎩解得2221a b ⎧=⎨=⎩，所以椭圆的标准方程为2212x y +=．（2）因为A 在x 轴上方，可知2AF 斜率不为0，故可以设2AF 的方程为1x ty =+，22221(2)21021x y t y ty x ty ⎧+=⎪⇒++-=⎨⎪=+⎩， 得1221222212t y y t y y t -⎧+=⎪⎪+⎨-⎪=⎪+⎩，所以12||||AB y y =-= 设原点到直线2AF 的距离为d，则d =所以2ABC OAB S S ∆∆= 12||2AB d =⨯⨯⨯==，ABC ∆．在0t =时取到等号成立，此时AB 的方程为：1x =，可得，A，(1,B，(1,C -，此时BC的方程为：y = 21．已知椭圆2222:1(0)x y C a b a b +=>>的左、右焦点1F ，2F ，M 是椭圆上任意一点，若以坐标原点为圆心，椭圆短轴长为直径的圆恰好经过椭圆的焦点，且△12MF F的周长为4+． （1）求椭圆C 的方程；（2）设直线:(0)l y kx m k =+≠是圆224:3O x y +=的切线，l 与椭圆C 交与不同的两点Q ，R ，证明：QOR ∠的大小为定值．【解答】解：（1）由椭圆的定义可知周长为224a c +=+ 焦点在圆上，所以b c =，222c a b =-，解得2,a b c ===所以椭圆方程为22142x y +=． （2=，即22344m k =+， 联立22222(12)4240142y kx m k x kmx m x y =+⎧⎪⇒+++-=⎨+=⎪⎩， 由韦达定理可得21221222412412m x x k kmx x k ⎧-=⎪⎪+⎨-⎪+=⎪+⎩，1212()()y y kx m kx m ∴=++221212()()k x x km x x m =+++222222222222444121212m k k k m m k m k k k --=-+=+++，∴22121224()()12m k y y kx m kx m k -=++=+， ∴2212122344021m k OP OQ x x y y k --=+==+， ∴2ROQ π∠=为定值．22．规定：在桌面上，用母球击打目标球，使目标球运动，球的位置是指球心的位置，我们说球A 是指该球的球心点A ．两球碰撞后，目标球在两球的球心所确定的直线上运动，目标球的运动方向是指目标球被母球击打时，母球球心所指向目标球球心的方向．所有的球都简化为平面上半径为1的圆，且母球与目标球有公共点时，目标球就开始运动，在桌面上建立平面直角坐标系，解决下列问题：（1）如图，设母球A 的位置为(0,0)，目标球B 的位置为(4,0)，要使目标球B 向(8,4)C -处运动，求母球A 球心运动的直线方程；（2）如图，若母球A 的位置为(0,2)-，目标球B 的位置为(4,0)，能否让母球A 击打目标B 球后，使目标B 球向(8,4)-处运动？（3）若A 的位置为(0,)a 时，使得母球A 击打目标球B 时，目标球(4,0)B 运动方向可以碰到目标球11(8,)2-，求a 的最小值（只需要写出结果即可）【解答】解：（1）点(4,0)B 与点(8,4)C -的直线方程为：40x y +-=，依题意，知A ，B 两球碰撞时，球A 的球心在直线40x y +-=上，且在第一象限， 此时||2AB =，设A ，B 两球碰撞时球A 的球心坐标为(,)a b ，则有：4020,0a b a b +-=⎧=>>⎪⎩，解得：4a =b =，即：A ，B 两球碰撞时球A的球心坐标为(4A '， 所以，母球A运动的直线方程为：y ==（2）(0,2)A -，(4A '-，要使B 沿着40x y +-=的方向移动，则AA '的斜率小于等于1，而1AA k '==>， 故不可能让母球A 击打目标球B 球后，使目标球B 向(8,4)-运动；（3）得a 最小为2-．。
辽宁省实验中学2024-2025学年高三上学期期中考试物理试题(含答案)
辽宁省实验中学2024-2025学年度上学期期中阶段测试高三年级物理试卷考试时间75分钟试题满分100分命题人：高三物理组校对人：高三物理组一、选择题（1-7题单选题每题4分。
8-10题为多选题每题6分，漏选得3分、错选不得分。
共计46分）1.对于日常生活中的一些现象，下列说法正确的是（）A.运动员在110m栏比赛过程中的平均速率比平均速度大B.研究行驶的复兴号列车的运动时，列车一定可以看成质点C.高速行驶的轿车紧急刹车，刹车时间越短，轿车惯性越大D.作用力和反作用力是等大反向的一对力，作用效果可以相互抵消2.商场自动感应门如图，人走进时两扇门从静止开始同时向左右平移，两扇门移动距离均为2m，若门完全打开时速度恰好为0，且门加速和减速时的加速度大小均为0.5m/s2，则：为使门能最快打开，其最高运行速度至少应设置为（）A.2m/sB.1.5m/sC.1m/sD.0.5m/s3.如图所示，一根轻绳a一端固定于竖直墙上的A点，另一端绕过动滑轮P悬挂一重物B，其中P与A之间的绳子处于水平状态：另一根轻绳b一端与动滑轮P的轴相连，绕过光滑的定滑轮Q后在其端点O施加一水平向左的拉力F，使整个系统处于平衡状态。
滑轮均为光滑、轻质，且大小可以忽略。
已知轻绳b 与竖直方向夹角为θ。
现拉住绳子的端点O使其向左缓缓移动一小段距离，则（）A.拉力F增大，角θ增大B.拉力F减小，角θ减小C.轻绳a对滑轮P的作用力减小D.轻绳b对滑轮Q的作用力增大4.游乐园的夜晚身披彩灯的摩天轮格外醒目。
若摩天轮绕中间的固定轴匀速转动，则以下说法正确的是（）A.因为角速度为恒量，所以在相同的时间内，乘客的速度变化量相同B.乘客在最低点时，他的动量变化率为零C.当乘客位于摩天轮的最高点时他对座椅的压力最小D.乘客在与转轴等高的位置时，他的加速度就是重力加速度5.某行星的两卫星A 、B 绕以该行星为焦点的椭圆轨道运行，A 、B 受到该行星的引力随时间的变化如图所示，其中，卫星A 、B 与行星的距离分别为r A 、r B ，假设卫星A 、B 只受到行星的引力。
2020-2021学年度高一上学期期中考试化学试卷及答案（含五套题）
2020-2021学年度⾼⼀上学期期中考试化学试卷及答案（含五套题）10 / 102020－2021学年度⾼⼀上学期期末考试化学试题题号⼀⼆三总分得分（满分：100分时间：100分钟）可能需要的相对原⼦质量数据H: 1 , C ：12， O ：16，Na ：23，S ：32，Cl ：35.5，Al ：27，Cu: 64, Ba:137 Fe ：56 Mg ：24 Cr:52 K:39 N:14 Si:28⼀、选择题：本⼤题共16⼩题，每⼩题3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.对于易燃、易爆、有毒的化学物质，往往会在其包装上⾯贴上危险警告标签。
下列物质贴错了包装标签的是( ) A. 浓硫酸B. 汽油C. 酒精D. 氯化钾2.完成下列实验所选择的装置或仪器（夹持装置已略去）正确的是A. AB. BC. CD. D3.我国古代四⼤发明之⼀的⿊⽕药是由硫磺粉、硝酸钾和⽊炭粉按⼀定⽐例混合⽽成的，爆炸的反应为：S+2KNO 3+3C K 2S+N 2↑+3CO 2↑，下列说法中正确的是（） A. 该反应中的还原剂为KNO 3B. 该反应中C 被还原C. 若消耗32g S ，该反应转移电⼦数为2 N AD. 若⽣成标准状况下⽓体22.4L ，则有0.75 mol 物质被还原 4.阿伏加德罗常数的值为N A ，下列说法中正确的是（） A. 5NH 4NO 32HNO 3＋4N 2↑＋9H 2O 反应中，⽣成28 g N 2，转移的电⼦数⽬为3.75N AB. 常温常压下，ag 某⽓体含分⼦数为b ，则cg 该⽓体的体积为22.4bc aN ALC. 2mol/L 的CaCl 2溶液中Cl -的数⽬为4N AD. 46g NO 2和N 2O 4的混合⽓体中含有的氧原⼦个数为3N A 5.下列说法正确的是( )A. 摩尔是⼀种国际基本物理量B. 氧⽓的摩尔质量为32gC. H 2的⽓体摩尔体积约为22.4LD. 1mol H 2O 约含有6.02×1023个⽔分⼦6.氧化还原反应与四种基本反应类型的关系如下所⽰,则下列化学反应属于阴影部分的是( )此卷只装订不密封班级姓名准考证号考场号座位号10 / 10A. Cl 2+2KBrBr 2+2KClB. 2NaHCO 3Na 2CO 3+H 2O+CO 2↑C. 4NO 2+O 2+2H 2O=4HNO 3D. 2Na 2O 2+2CO 2=2Na 2CO 3+O 2 7.下列说法正确的个数有①盐卤点⾖腐、江河⼊海⼝处“三⾓洲”的形成、⾼压直流电除烟尘均与胶体的性质有关②通电时，溶液中的溶质粒⼦分别向两极移动，胶体中的分散质粒⼦向某⼀极移动③氢氧化铁胶体能稳定存在的主要原因是胶体粒⼦做布朗运动④做氢氧化铁胶体电泳实验时，阴极周围红褐⾊加深，说明氢氧化铁胶体带正电⑤向FeCl 3溶液中滴加NaOH 溶液，可制得Fe(OH)3胶体⑥1mol FeCl 3完全与⽔反应⽣成氢氧化铁胶体粒⼦数约为N A 个⑦淀粉溶液和蛋⽩质溶液是溶液，不可能是胶体 A. 1个 B. 2个 C. 3个 D. 4个8.下列各组离⼦中，能在溶液中⼤量共存的是（） A. Na +、Cu 2+、Cl ﹣、OH ﹣ B. H +、Ca 2+、HCO 3﹣、NO 3﹣ C. Fe 2+、H +、SO 42﹣、NO 3﹣ D. Na +、CO 32﹣、OH ﹣、K + 9.下列离⼦⽅程式正确的是( ) A. 往NaHSO 4溶液中加Ba(OH)2溶液⾄恰好中和:Ba 2++2OH -+2H ++SO 42-=BaSO 4↓+2H 2O B. 碳酸钙与盐酸反应:2H ++CO 32-=CO 2↑+H 2OC. 铁与稀盐酸反应:2Fe+6H +=2Fe 3++3H 2↑D. 往Ba(OH)2溶液中加少量硫酸溶液:Ba 2++OH -+H ++SO 42-=BaSO 4↓+H 2O10.下列溶液中，溶质的物质的量浓度不是1 mol ·L －1的是（） A. 10g NaOH 固体溶解在⽔中配成250mL 溶液 B. 将80g SO 3溶于⽔并配成1L 的溶液C. 将0.5mol ·L －1的NaNO 3溶液100mL 加热蒸发掉50g ⽔的溶液D. 标况下，将22.4L 氯化氢⽓体溶于⽔配成1L 溶液11.今有⼀种固体化合物X ，X 本⾝不导电，但熔化状态或溶于⽔中能够电离，下列关于该化合物X 的说法中正确的是 A. X ⼀定是电解质 B. X 可能为⾮电解质 C. X 只能是盐类 D. X 可以是任意化合物12.将SO 2通⼊⾜量Fe 2(SO 4)3溶液中,完全反应后再加⼊K 2CrO 4溶液,发⽣的两个化学反应为SO 2+2Fe 3++2H 2O=SO 42-+2Fe 2++W ①, Cr 2O 72-+a Fe 2++b H +Cr 3++Fe 3++H 2O ②,下列有关说法正确的是A. 还原性:Cr 3+>SO 2B. 配平后⽅程式②中,a=6,b=7C. Cr 2O 72-能将Na 2SO 3氧化成Na 2SO 4D. ⽅程式①中W 为OH - 13.200 mL 0.3 mol/L 的K 2SO 4溶液和100 mL 0.2 mol/L 的Fe 2(SO 4)3溶液混合后(不考虑混合后溶液体积的变化)，溶液中SO 42-的物质的量浓度为A. 0.3 mol/LB. 0.4 mol/LC. 0.45 mol/LD. 0.5 mol/L 14.下列离⼦⽅程式的书写中，正确的是A. H 2SO 4与Ba （OH ）2溶液反应: Ba 2＋+ OH － + H ＋⼗SO 42－= BaSO 4↓ + H 2O10 / 10B. 碳酸钙中加⼊盐酸 : CO 32- + 2H + = CO 2↑ + H 2OC. 将氢氧化铁放⼊盐酸中: Fe （OH ）3 + 3H + = Fe 3+ + 3H 2OD. 氧化铜与稀硫酸反应: 2H + + O 2—= H 2O15.物质的量浓度为0.05 mol ·L -1的⾦属氯化物(RCl x ) 溶液20 mL ，恰好与20 mL 0.15 mol ·L -1的AgNO 3溶液完全反应。
2024-2025学年辽宁省实验中学高三上学期期中考试英语试题(含听力)
2024-2025学年辽宁省实验中学高三上学期期中考试英语试题(含听力）1. Which language can Robert speak well?A．Russian. B．German. C．French.2. What are the speakers probably talking about?A．A tour. B．A movie. C．A friend.3. What is the time now?A．About 10:05. B．About 10:10. C．About 10:15.4. Where is the woman?A．On a flight. B．In China. C．At home.5. What does the man own?A．The flat. B．The car. C．The furniture.听下面一段较长对话，回答以下小题。
6. What does the woman say about buying the car?A．She doesn’t like the car.B．The price is not reasonable.C．She doesn’t have enough money.7. Why does the man want to talk with the manager?A．To get the price down another $500.B．To get the price down another $1,000.C．To get the price down another $2,000.听下面一段较长对话，回答以下小题。
8. What will the speakers probably do in the morning?B．Go to the local beach. C．Eat in the restaurant.A．Go to the amusementpark.9. Where is the Natural History Museum?A．Near the beach. B．Next to the restaurant. C．By the amusement park.10. What does the woman think of watching the sun go down?A．It’s relaxing.B．It’s wonderful.C．It’s impossible.听下面一段较长对话，回答以下小题。
辽宁省实验中学2024-2025学年高二上学期期中考试英语试题(含答案,含听力原文无音频)
辽宁省实验中学2024-2025学年度上学期期中阶段测试考试时间：120分钟试题满分：150分第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. Who might the man be?A. A journalist.B. A student.C. A teacher.2. What will the speakers do?A. Go to the airport.B. Go to the theater.C. Go to a bookstore.3. What does the woman need help with?A. Preparing the materials.B. Picking up a client.C. Translating a file.4. What did the man do last night?A. He stayed up late to watch the game.B. He attended to Alice all night long.C. He worked deep into the night.5. How does the woman feel?A. Hot.B. Thirsty.C. Hungry.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料，回答第6、7题。
6. What are the speakers probably doing?A. Checking the “done” list.B. Confirming the flight.C. Booking a ticket.7. Where will the wedding be held?A. In Dallas.B. In New York.C. In Los Angeles.听第7段材料，回答第8至10题。
2024年辽宁省东北育才、实验中学、大连八中、鞍山一中等物理高三第一学期期中学业水平测试试题含解析
2024年辽宁省东北育才、实验中学、大连八中、鞍山一中等物理高三第一学期期中学业水平测试试题请考生注意：1．请用2B铅笔将选择题答案涂填在答题纸相应位置上，请用0．5毫米及以上黑色字迹的钢笔或签字笔将主观题的答案写在答题纸相应的答题区内。
写在试题卷、草稿纸上均无效。
2．答题前，认真阅读答题纸上的《注意事项》，按规定答题。
一、单项选择题：本题共6小题，每小题4分，共24分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1、如图所示，质量为m的小滑块静止在半径为R的半球体上，它与半球体间的动摩擦因数为μ，它与球心连线跟水平地面的夹角为θ，则小滑块（）．A．所受摩擦力大小为mg cos θB．所受摩擦力大小为mg sin θC．所受摩擦力大小为μmg sin θD．对半球体的压力大小为mg cos θ2、回旋加速器工作原理示意图如图所示，磁感应强度为B的匀强磁场与盒面垂直，两盒间的狭缝很小，粒子穿过的时间可忽略，它们接在电压为U、频率为f的交流电源上．若H）在加速器中被加速，下列说法正确的是A处粒子源产生的质子（11A．若只增大交流电压U，则质子获得的最大动能增大B．若只增大交流电压U，不改变质子在回旋加速器中的运行时间C．若磁感应强度B增大，交流电源频率f必须适当增大才能正常工作D ．不改变磁感应强度B 和交流电源频率f ，该回旋加速器也能用于加速α粒子（42He ）3、跳水运动员从10m 高的跳台上腾空跃起，先向上运动一段距离达到最高点后，再自由下落进入水池，不计空气阻力，关于运动员在空中的上升过程和下落过程，以下说法正确的有（）A ．上升过程处于超重状态，下落过程处于失重状态B ．上升过程处于失重状态，下落过程处于超重状态C ．上升过程和下落过程均处于超重状态D ．上升过程和下落过程均处于完全失重状态4、双星系统由两颗绕着它们中心连线上的某点旋转的恒星组成．假设两颗恒星质量相等，理论计算它们绕连线中点做圆周运动，理论周期与实际观测周期有出入，且=(1)1T n n T >理论观测，科学家推测，在以两星球中心连线为直径的球体空间中均匀分布着暗物质，设两星球中心连线长度为L ，两星球质量均为m ，据此推测，暗物质的质量为（ ）A ．(n -1)mB ．(2n -1)mC ．14n m -D ．28n m - 5、如图所示，斜面上放有两个完全相同的物体a 、b ，两物体间用一根细线连接，在细线的中点加一与斜面垂直的拉力F ，使两物体均处于静止状态．则下列说法正确的是( )A ．a 、b 两物体的受力个数一定相同B ．a 、b 两物体对斜面的压力不一定相同C ．a 、b 两物体受到的摩擦力大小可能不相等D ．当逐渐增大拉力F 时，物体b 先开始滑动6、我国ETC （电子不停车收费系统）已实现全国联网，大大缩短了车辆通过收费站的时间．一辆汽车以20 m/s 的速度驶向高速收费口，到达自动收费装置前开始做匀减速直线运动，经4 s 的时间速度减为5 m/s 且收费完成，司机立即加速，产生的加速度大小为2.5 m/s 2，假设汽车可视为质点．则下列说法正确的是（ ）A ．汽车开始减速时距离自动收费装置110 mB ．汽车加速4 s 后速度恢复到20 m/sC ．汽车从开始减速到速度恢复到20 m/s 通过的总路程为125 mD ．汽车由于通过自动收费装置耽误的时间为4 s二、多项选择题：本题共4小题，每小题5分，共20分。
辽宁省沈阳市辽宁省实验中学2024-2025学年高二上学期期中考试数学试卷(含解析)
辽宁省实验中学2024-2025学年高二上学期期中阶段测试数学试卷考试时间：120分钟试题满分：150分一.选择题：本题共8小题，每小题5分，共40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．不选、多选、错选均不得分．1．已知正方体的棱长为1，则直线与所成角的正弦值为（ ）A ．0B ．CD2．在空间直角坐标系中，已知，若共面，则的值为（ ）A ．B ．0C ．1D ．23的倾斜角为（ ）A ．B ．C ．D ．4．圆和圆的公切线有（ ）A ．1条B ．2条C ．3条D ．4条5．已知且，则的最大值为（ ）A ．1BCD ．56．若椭圆（ ）A ．1B ．4C ．1或4D ．以上都不对7．已知是椭圆的两个焦点，过且与椭圆长轴垂直的直线交椭圆于两点，若是正三角形，则这个椭圆的离心率是（ ）AB CD8．曲线所围成图形的面积为（ ）A ．2B ．C ．4D．二.选择题：本题共3小题，每小题6分，共18分．在每小题给出的四个选项中，有多项符合题目要求，全部选对的得6分，部分选对的得部分分，有选错的得0分．9．已知且，则的值可能是（ ）1111ABCD A B C D -1A D AC 12Oxyz (1,1,0),(0,1,1),(2,1,)a b c z === ,,a b cz 1-340y ++=150︒120︒60︒30︒222410x y x y ++-+=224210x y x y +--+=,x y ∈R 221x y +=43x y -2212x y m +=m =12,F F 1F AB 2ABF △21||x y y -=-3π2,,x y z ∈R 2221x y z ++=222(1)(1)(2)x y z -+-+-A ．1B ．2C ．3D ．410．在空间直角坐标系Oxyz 中，已知，点，点，且P ，O 不重合，P ，A 不重合，则（ ）A ．若，则x ，y ，z 满足：B ．若，则x ，y ，z 满足：C ．若，则x ，y ，z 满足：D ．若，则x ，y ，z 满足：11．现有圆锥顶点为，底面所在平面为，母线PM 与底面直径MN 的长度都是2.点是PM 的中点，平面经过点与所成二面角（锐角）为.已知平面与该圆锥侧面的交线是某椭圆（或其一部分），则该椭圆长轴的长可能是（ ）AB ．1C ．D ．2三、填空题：本题共3小题，每小题5分，共15分．12．直线经过点垂直，则直线的方程是 .13．已知点，点B ，C 是直线与圆的交点，则经过点A ，B ，C 的圆的方程是 ．14．已知点在椭圆上，点，则的取值范围是 .四.解答题：本题共5小题，共7分．解答应写出文字说明，证明过程或演算步骤．15．已知椭圆的长轴端点是和(1)求椭圆的方程；(2)若点在椭圆上，求点到点的距离的取值范围.16．如图，正四棱锥中，，侧棱与底面所成的角为.(1)求侧面与底面所成的二面角（锐角）的余弦值；(2)在线段上是否存在一点，使得？若存在，确定点的位置；若不存在说明理由.(1,1,1)n =(1,0,0)A (,,)P x y z ||1AP =2221x y z ++=AP n ⊥1x y z ++=//AP n1x y z-==,45OP n ︒〈〉=2224440x y z xy yz zx ++---=P αA βA α30︒β32l P 50y -+=l (5,0)A 1x =225x y +=M 22:1169x y C +=(3,0)(3,0)P Q -、||||MP MQ +C (A -B C P C P (0,1)M P ABCD -AB =PA ABCD 60o PAB ABCD PB E AE PC ⊥E17．如图，在三棱柱中，点是棱AC 的中点.侧面底面ABC ，底面ABC 是等边三角形，.(1)求证：平面ABC ；(2)求平面与平面所成锐二面角平面角的余弦值.18．已知点与点关于直线对称.(1)求点的坐标m ，n （用表示）；(2)若点在曲线所在曲线的方程.19．在平面直角坐标系中，已知点，点的轨迹为.(1)求的方程；(2)已知点，设点M ，N 在上，点M ，N 与点不重合，且直线MN 不与轴垂直，记分别为直线AM ，AN 的斜率.（ⅰ）对于给定的数值入（且，若，证明：直线MN 经过定点；（ⅱ）记（ⅰ）中的定点为Q ，求点的轨迹方程.111ABC A B C -O 11AA C C ⊥11,AB AA A B AC =⊥1A O ⊥11AA B B 11CC B B (,)P m n ()00,Q x y :l y =P 00,x y (,)P m n y (,)Q x y 12(1,0),(2,0)F F P P C C (1,1)A C A x 12,k k λR λ∈1)λ≠12k k λ=Q答案1．D解析：在正方体中，可得，，所以四边形是平行四边形，所以，所以是异面直线直线与所成的角，又易得是等边三角形，所以，所以与故选：D.2．A解析：由空间向量共面定理可得存在实数，使得，即，所以，解得.故选：A 3．A得故直线的斜率为，所以倾斜角为．故选：A ．4．B1111ABCD A B C D -11A B AB CD ∥∥11A B AB CD ==11A B CD 11A D B C P 1B CA ∠1A D AC 1B CA V 160B CA =∠︒1sin B CA ∠1A D AC ,x y a xb yc =+()()()1,1,00,,2,,x x y y yz =+1210y x y x yz=⎧⎪=+⎨⎪=+⎩12121x y z ⎧=⎪⎪⎪=⎨⎪=-⎪⎪⎩340y ++=43y =-)0,180︒⎡⎣150︒解析：由题意得，圆，即以为圆心，为半径的圆，圆，即以为圆心，为半径的圆，则故，因此两圆相交，则有2条公切线.故选：B.5．D解析：令，则，其中，因为，则，所以的最大值为.故选：D 6．C解析：当焦点在轴上时，；当焦点在轴上时，.故选：C 7．A解析：是正三角形，，故选：.8．A 解析：()()222222410122x y x y x y ++-+=⇔++-=()11,2C -12r =()()222224210212x y x y x y +--+=⇔-+-=()22,1C =22r =12C C ==12022224C C =-<<+=[]cos ,sin ,0,2x y θθθπ==∈()434sin 3cos 5sin x y θθθϕ-=-=-3tan 4ϕ=()[]sin 1,1θϕ-∈-()[]5sin 5,5θϕ-∈-43x y -5x e =1m =y e ==4m =2ABF V 212|||AF F F ∴==1212||2||,||||2AF AF AF AF a ∴==+==e ∴A由可得，即，所以，又，即，当且时，则方程为，即，所以，当且时，则方程为，即，当时，则，所以方程为，即，画出如图所示图像，其中弓形与弓形相等，由割补法可知，围成图形的面积为.故选：A 9．CD解析：因，则表示以原点为球心，半径为1的球表面上的点.则表示到距离的平方.类比点到圆上距离的范围，可得，，则 ，.故，则只有CD 满足条件.故选：CD 10．BCD解析：A 由题，，因，则A 错误；B 因，则，故B 正确；C 因，则，故C 正确；21x y y -=-10y -≥1y ≤11y -≤≤22221x y y x y y x x =-+≥-+==11x -≤≤[]0,1∈y 20x y -≥21x y y -+=21x =1x =±[]0,1∈y 20x y -<21y x y -+=212x y +=[)1,0y ∈-20x y ->21x y y --=212x y -=AB CD 212⨯=2221x y z ++=(),,x y z 222(1)(1)(2)x y z -+-+-(),,x y z ()1,1,2)2222(1)(1)(2)17x y z -+-+-≤=+)2222(1)(1)(2)17x y z -+-+-≥+=-1.414 1.732≈≈ 2.449≈711.898+≈7 2.102-≈22222(1)(1(1)2)x y z <-+-<-+()1,,AP x y z =- ()2222221112AP x y z x y z x =⇒-++=⇒++= AP n ⊥101AP n x y z x y z ⋅=-++=⇒++= //AP n 11111x y zx y z -==⇒-==D 因，则.即，故D 正确.故选：BCD.11．ABC解析：如上图，做出过点的轴截面，由已知条件可知，平面与轴截面相交得到的线段最短为，最长为，当平面与圆锥面所截得的椭圆的长轴落在平面内时，长轴长或.根据已知的几何关系可以计算出当与圆锥所截得的椭圆的长轴不在图中所作的轴截面内时，长轴长度满足：.对于A对于B，长轴长度可以为；对于C；对于D 选项，.故选：ABC 12．的斜率为所以的方程为：，即.故答案为：13．,45OP n ︒〈〉=()()22221cos ,23x y z OP n x y z ++〈〉==⇒=++ ()()2222222324440x y z x y z x y z xy yz zx ++=++⇒++---=A PMN β1AA AM βPMN 12a AA =2a AM =1AA =AM =βPMN 12AA a AM <<1<<132<322>240x -=50y -+=l l )1y x =-40x -=40x -=2250x y x -=+解析：因点B ，C 是直线与圆的交点，则设过B ，C 的圆的方程为：，代入，则，则过过点A ，B ，C 的圆的方程是：.故答案为：14．解析：由椭圆与椭圆有相同的短轴，由椭圆与椭圆有相同的长轴，又椭圆与椭圆有相同的焦点，即点，由椭圆方程可知椭圆在椭圆上及其内部，椭圆在椭圆上及其内部，当点在上时，因椭圆方程可知椭圆在椭圆上及其内部，所以，当点在短轴的端点时取等号，当点在上时，，因椭圆方程可知椭圆在椭圆上及其内部，所以，当点在长轴的端点时取等号，所以的取值范围是.故答案为：.1x =225x y +=()22510x y x λ+-+-=(5,0)A 255405λλ-+=⇒=-()2222551050x y x x y x +---=⇔+-=2250x y x -=+22:1169x y C +=221:1189x y C +=22:1169x y C +=222:1167x y C +=222:1167x y C +=221:1189x y C +=12(3,0),(3,0)F F -(3,0)(3,0)P Q -、22:1169x y C +=221:1189x y C +=222:1167x y C +=22:1169x y C +=P 221:1189x y C +=12||||2PF PF a +==22:1169x y C +=221:1189x y C +=12||||||||MP MQ PF PF +≤+=P P 222:1167x y C +=12||||28PF PF a +==222:1167x y C +=22:1169x y C +=12||||||||8MP MQ PF PF +≥+=P ||||MP MQ +15．(1)(2)解析：（1）由题意得：，解得：.故椭圆的方程为：（2）设是椭圆上的任意一点，所以，所以..故点到点的距离的取值范围是.16．(2)在线段上存在点，点满足，使得.解析：（1）设为底面的中心，以点为原点，分别为轴，轴，轴正方向，建立空间直角坐标系，如图所示．由题意知，.设，其中，则，向量是平面的法向量.22182x y +=-222a c a a b c ⎧=⎪⎪=⎨⎪=+⎪⎩a b ⎧=⎪⎨=⎪⎩C 22182x y +=(,)P x y 2284x y =-PM ==[y ∈1||PM ≤≤P (0,1)M -PB E E 13BE BP =AE PC ⊥O ABCD O ,,OB OC OPx y z (0,1,0),(1,0,0),(0,1,0)A B C -(0,0,)P h 0h >(0,1,)AP h =1(0,0,1)n = ABCD由题意得，，解得设平面的法向量为.因为，，所以，即，令，则，则.则故侧面与底面（2）由（1）知，，设，则.因为，若，则.即，解得，故在线段上存在点，点满足，使得17．(1)证明见解析(2)解析：（1）连结OB .在中，，所以，且.又因为，所以平面.从而．又因为平面平面ABC，A C 是平面与平面ABC 的交线，111cos ,cos30AP n AP n AP n ⋅==⋅h =PAB ()2222,,n x y z =(AP = (1,1,0)AB =2200AP n AB n ⎧⋅=⎪⎨⋅=⎪⎩ 222200y x y ⎧=⎪⎨+=⎪⎩21y =221x z =-⎧⎪⎨=⎪⎩21,1,n ⎛=- ⎝ 12cos n n ⋅==PAB ABCD (1,1,0)AB =(BP =- BE BP λ=(()(1,1,0)1AE AB BE λλ=+=+-=- (0,CP =-AE PC ⊥()(10,0AE CP λ⋅=-⋅-= 130λ-+=13λ=PB E E 13BE BP =.AE PC ⊥35ABC V ,BA BC AO OC ==BO AC ⊥BO AC 1A B AC ⊥AC ⊥1A BO 1AC AO ⊥11AA C C ⊥11AA C C所以平面ABC（2）在中，，所以.设.以点为原点，分别为轴轴轴正方向，建立空间直角坐标系Oxyz ，如图所示．有，，.设平面的法向量为，平面的法向量为.由题意得：.则取平面的法向量为，平面的法向量为.则.故平面与平面所成锐二面角平面角的余弦值是18．(1)(2).1AO ⊥1AA O 1190,2A OA AA AO ︒∠==1A O AC =2AC =O 1,,OB OC OA x y z (0,1,0),(0,1,0)A B C -11,0)A AB CB ==- 11AA BB == 11AA B B ()1111,,n x y z = 11CC B B ()2222,,n x y z = 111112221112220000AA n y BB n y AB n y CB n y ⎧⎧⋅==⋅=+=⎪⎪⎨⎨⋅=+=⋅=-=⎪⎪⎩⎩，11AA B B 1(1,n = 11CC B B 21)n =- 13cos 5n ⋅ 11AA B B 11CC B B 35m n ⎧=⎪⎪⎨⎪=⎪⎩22162x y -=解析：（1）依题意，，解得（2）依题意，整理得：（其中），所以点所在曲线的方程为.19．(1)(2)（ⅰ）证明见解析，（ⅱ）点的轨迹方程为直线（除去点）解析：（1）设，整理得，所以的方程为.（2）设直线MN 的方程为：，其中.点M ，N 满足：所以满足：，即.从而.（ⅰ）证明：因为，所以，整理得，其中（即直线MN 不经过点）.所以直线MN 的方程为：，且直线MN 不经过点.所以直线MN 过定点 .000022y n x m y n x m -⎧=⎪-⎪⎨++⎪⎪⎩m n ⎧=⎪⎪⎨⎪=⎪⎩m n n ⎧=⎪⎪⎪⎪=⎨⎪⎪=⎪⎪⎩=2200162x y -=000x ≠(,)Q x y 22162x y -=222x y +=Q y x =-(1,1)-(),P x y =222x y +=C 222x y +=y kx m =+1k m +≠222x y y kx m⎧+=⎨=+⎩,M N x x 22()2x kx m ++=()2221220k x kmx m +++-=22222,11M N M N km m x x x x k k -+=-=++()()()()()()()()2222222222222111211111122111111111M N M N M N N M M N M N M N M N m km k km k m m kx m kx m k x x km k x x m m y y k m k k m km x x x x x x x x k m k k -⎛⎫⋅+--+-+ ⎪+-+-+-++-+---+++⎝⎭⋅====-------++++++++11k m k m λ-+-=++1(1)1m k λλ+=+-10k m ++≠(1,1)-111(1)111y kx k k x λλλλλλ+++⎛⎫=++=++ ⎪---⎝⎭(1,1)-11,11λλλλ++⎛⎫- ⎪--⎝⎭（ⅱ）解：由得（其中）,所以点的轨迹方程为直线（除去点）.1,11.1Q Q x y λλλλ+⎧=-⎪⎪-⎨+⎪=⎪-⎩Q Q y x =-1Q x ≠Q y x =-(1,1)-。
2023-2024学年辽宁省沈阳实验学校初中教育集团九年级上学期期中物理试题
2023-2024学年辽宁省沈阳实验学校初中教育集团九年级上学期期中物理试题1.以下生活中常见的物理量，你认为比较符合实际的是（）A．家庭冰箱的电流约0.1AB．常见的家用汽车的热机效率可达90%C．手机电池电压约为220VD．一般分子的直径只有百亿分之几米2.小明按图甲所示的电路进行实验，当闭合开关用电器正常工作时，电压表V1和V2的指针位置完全一样，如图乙所示，则R1、R2两端的电压为分别为A． 1.2V 6V B． 1.4V 5.2V C． 4.8V 1.2V D． 1.4V 3.8V3.甲、乙两灯串联接入电路中，发现甲灯较亮，乙灯较暗，下列说法正确的是（）A．电流先经过甲灯，所以甲灯亮B．通过甲灯中的电流大，所以甲灯亮C．甲灯的电阻小，所以通过甲灯中的电流大D．通过甲、乙两灯的电流一样大4.图甲有两个相同的验电器A和B，A带正电，B不带电，A的金属箔张角变小，B的金属箔明显张开（）A．若用橡胶棒连接A、B的金属球，也能出现相同现象B．验电器A带正电是因为得到了正电荷C．此时瞬间电流的方向是从验电器B到验电器AD．验电器B金属箔张开是因为缺少了电子5.某学习小组用装满盐水的气球连接在如图所示的电路中。
当用手向相反的方向拉扯连接气球的导线（盐水与导线充分接触且气球不破裂）时，下面说法正确的是（）A．小灯泡变得更暗B．电压表与电流表示数的比值变小C．电流表的示数变大D．无论怎样拉动，电压表的示数不变6.甲、乙两地相距40km，在甲、乙两地之间沿直线架设了两条输电线，已知所用的输电线每千米的电阻为0.4Ω，为确定短路位置，检修员在甲地利用电压表、电流表、定值电阻和电源接成如图所示电路进行测量。
当电压表的示数为4V，则短路位置离乙地的距离为（）A．10km B．15km C．25km D．50km7.规格相同的甲、乙两容器装了相同质量的水，用不同的电加热器加热，忽略散热，下列说法正确的是（）A．加热相同的时间，甲杯水升温比乙杯的多B．加热相同的时间，两杯水吸收的热量相同C．吸收相同的热量，甲杯水升温比乙杯的多D．甲杯水加热4min与乙杯水加热7min吸收的热量相同8.下列四个图中，电阻R0的阻值已知，电源电压未知且保持不变，以下四个图中能测出R x阻值的是( )A．B．C．D．9.如图所示，电源电压恒定，关于电路说法正确的是（）A．若灯L 1被短路，闭合S、S 1后，则灯L 1不亮，灯 L 2亮B．先闭合开关S，当再闭合开关 S 1时，电流表甲的示数变大，电流表乙的示数不变C．先闭合开关S，当再闭合开关 S 1时，电流表甲的示数不变，电流表乙的示数变小D．闭合开关S、S 1后，若拧去灯泡L 1，电流表甲的示数变小，电流表乙的示数不变10.在图中的圆圈内是电流表或电压表，开关S闭合后两灯均能发光，各表均有示数。
九年级化学上册第一学期期中综合测试卷(人教辽宁版 2024年秋)
九年级化学上册第一学期期中综合测试卷（人教辽宁版2024年秋）可能用到的相对原子质量：H－1C－12O－16第一部分选择题(共10分)(本部分共包括10道小题，每小题1分。
下列每小题只有一个最符合题目要求的选项)题序12345678910答案1．中华文化博大精深。
下列过程中只涉及物理变化的是()A．甲骨刻字B．烧制陶瓷C．粮食酿酒D．火药爆炸2．规范化学实验操作是实验成败的关键。
下列实验操作正确的是()A．点燃酒精灯B．取用固体粉末C．加热液体D．量取液体3．下列情况一般不会造成空气污染的是()A．汽车排出的尾气B．燃烧产生的烟雾C．植物光合作用放出的气体D．工业生产产生的烟尘4．大气平流层中的臭氧(O3)能吸收大部分紫外线，保护地球生物，臭氧属于() A．纯净物B．混合物C．氧化物D．化合物5．物质的用途主要是由其性质决定的。
下列物质的用途主要与其化学性质相关的是()A．液氮作医疗冷冻剂B．高粱常用于酿制白酒C．氢气用于充探空气球D．干冰可用作人工降雨6．下列实验现象的描述正确的是()A．氢气在空气中燃烧，发出淡蓝色火焰B．红磷在空气中燃烧，产生大量白烟雾C．蜡烛在空气中燃烧，生成CO2和H2OD．木炭在空气中燃烧，生成黑色固体7．对下列现象解释不合理的是()A．一滴水里有1．67×1027个水分子，说明分子体积小B．变瘪的乒乓球放在热水中鼓起，是由于分子的体积变大C．湿衣服在阳光下比在阴凉处干得快，是由于温度升高，分子运动速率加快D．H2O2与H2O组成元素相同但化学性质不同，是因为构成它们的分子种类不同8．2023年10月31日，神舟十六号载人飞船返回舱成功着陆，返回舱的“避火衣”是由钛合金等材料制成的。
如图是钛元素在元素周期表中的相关信息，下列说法错误的是()(第8题)A．钛属于金属元素B．钛元素符号为TiC．钛的原子序数为22D．钛的相对原子质量是47．87g9．绿茶中的单宁酸具有抑制血压上升、清热解毒、抗癌等功效，其化学式为C76H52O46。
辽宁省沈阳市2024高三英语上学期期中考试试题
辽宁省试验中学2024-2025学年度上学期期中阶段测试高三英语试卷考试时间：120分钟试题满分：150分第一部分：听力（共两节，满分30分）第一节（共5小题；每题1. 5分，满分7. 5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What do you learn from the conversation?A. John Smith isn't in right now.B. John Smith can't come to the phone.C. The caller dialed the wrong number.2. What happens to the cup?A. It is missing.B. It is broken.C. It is somewhere in the room.3. When was the fire put out?A. At 2 o'clock.B. At 5 o'clock.C. At 3 o'clock.4. Which word can be used to describe the man?A. Poor.B. Greedy.C. Forgetful5. To whom is the man closer?A. His mum.B. His dad.C. Both.其次节（共15小题；每题1. 5分，满分22. 5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
辽宁省实验中学2024-2025学年高一上学期期中考试生物试题(含答案)
辽宁省实验中学2024-2025学年度上学期期中阶段测试高一生物学试卷考试时间75分钟试题满分100分命题人、校对人：高二生物组一、单选题（本题共15小题，每小题2分，共30分。
每小题只有一个选项符合题目要求）1．近日，科学家发现了一种被称作GFAJ-1的独特细菌，这种细菌能利用剧毒化合物砒霜中的砷来代替磷元素构筑生命分子，进行一些关键的生化反应，根据上述材料进行预测，下列说法正确的是（）A．GFAJ-1与新冠病毒最本质的区别是其没有以核膜为界限的细胞核B．GFAJ-1是原核生物，以RNA为遗传物质C．砷元素可能存在于GFAJ-1的细胞膜、核酸和糖类中D．GFAJ-1的发现拓宽了人类对地球极端环境研究的思路2．如图是构成细胞的某些化合物的元素组成情况，下列对甲、乙、丙所表示的物质及其所能表现的生理功能推测错误的是（）A．甲可能是叶绿素，能吸收光能进行光合作用B．乙可能是血红素，具有运输氧的作用C．丙可能是核酸，是遗传信息的携带者D．若植物培养液中缺微量元素Mg，将导致叶片发黄3．关于下图所示过程的叙述，错误的是（）A．DNA中的乙与RNA中的乙不相同B．DNA中的丙与RNA中的丙不完全相同C．DNA和RNA都是由丁相互连接形成的D．物质乙有2种，物质丙有4种，物质丁有8种4．俗话说“霜降摘柿子，立冬打软枣”。
霜降之前的柿子硬邦邦的，又苦又涩，难以下口，霜降后的柿子颜色红似火，尝起来甜腻可口。
有关分析错误的是（）A．与柿子苦涩相关的物质可能存在于液泡中B．“甜腻可口”的原因是细胞内多糖、二糖和单糖等分子含量都增多C．霜降后植物细胞内结合水比例增大，有利于增强抗寒能力D．植物细胞可以通过胞间连丝进行物质交换和信息交流5．正常细胞中普遍存在一种特殊的蛋白质分子伴侣，它从多个方面参与维持蛋白质的稳态，而本身不参与组成终产物，某分子伴侣X的作用机理如图所示。
下列说法正确的是（）A．分子伴侣只存在于真核生物中，不存在于原核生物中B．因加热导致变性的蛋白质的活性可能被伴侣蛋白恢复C．分子伴侣X既能识别正常蛋白质，也能识别异常蛋白质D．分子伴侣X发挥作用的场所可能是细胞内的核糖体6．下列关于细胞的结构和功能的叙述，正确的是（）A．细胞骨架由磷脂分子构成，对细胞起支撑、保护等作用B．一个动物细胞中有一个中心粒，高等植物细胞中没有中心粒C．能够产生囊泡的细胞器包括内质网和高尔基体D．细胞核和细胞质之间的物质交换都要通过核孔来进行7．下图中野生型是分泌正常的酵母菌，甲、乙型突变体是部分细胞器膜结构异常，分泌过程出现障碍的酵母菌，下列说法正确的是（）A．野生型酵母菌的分泌蛋白在游离核糖体中合成B．野生型酵母菌分泌蛋白质的过程依赖于细胞膜的结构特点C．甲型突变体的光面内质网因功能障碍积累大量无活性的蛋白质D．乙型突变体的高尔基体因功能障碍导致其膜面积减小8．如图所示为细胞核结构模式图，下列叙述正确的是（）A．①是内质网，在生物膜系统中面积最大B．物质通过⑤出入细胞核时无选择透过性C．细胞核中的DNA和RNA主要分布于④D．破坏③会影响蛋白质的合成，因为③是合成蛋白质的场所9．钙调蛋白是真核细胞中的Ca2+感受器，每个钙调蛋白分子有4个结合钙离子的区域。
辽宁省实验中学2024-2025学年高一上学期期中考试英语试题
辽宁省实验中学2024-2025学年高一上学期期中考试英语试题一、阅读理解1．Which of the following is TRUE about George Clooney?A．He has been trained in wilderness survival.B．He may not be able to help you survive.C．He does not think Roseane is beautiful.D．He is the choice of most South A frican women.2．From the survey we know ______.A．Lin Xi from China has no love for his family membersB．Julia from Jordan has a violent temper when she is not satisfied with her partnerC．MP3 player on average is of secondary importance in the choice of the respondentsD．most Frenchmen would like to take a dog for company when they go for an adventure 3．The survey results are analyzed in terms of the respondents’ ______.A．race, nationality and sex B．marriage, age and raceC．age, sex and marriage D．sex, age and nationalityAs I sat on my sofa, I recalled the joy I had experienced back in my glory days, winning National Championships and representing the United States at the World Championships. I thought of all of the friends I had made in the sport.It had been a decade since I entered a competition. Strangely, tears began to roll down my cheeks. Then, for the first time in many years, I wept openly. I tried to calm myself and walked to the bathroom to wash my face. It was there that I took a good, long, hard look at myself in the mirror.I was no longer that marathon runner. I was a middle-aged man to sit behind the desk in my office for the day and had grown content in my life and appeared comfortable with the increase in the size of my waistline.When I took a serious look at myself, I knew it was time to change. I lacked discipline (自制力) and had no readily identifiable goals. Strange quiet came over me. I was going to transform my life. It was time to reinvent myself, to become all that I could imagine. I asked myself one more question, “What are you willing to do to make this dream a reality?” The answer was a very simple one, “Whatever it takes! ”The first few days, I was filled with enthusiasm and it was easy to stay on track. I prepared myself mentally for the difficult days. As the days went by, my newly discovered disciplinedeveloped into more discipline. I vowed (发誓) to remain true to my restricted diet of 1,200 calories per day. I was running for an hour every morning and lifting weights for another hour three or four days per week. Weight began to reduce. I lost about three pounds every week. This was feeling good. I was gaining momentum and strength as each day passed. There was no doubt in my mind that I would get down to my desired weight.4．What can we learn about the author from paragraph 3?A．He used to be a lawyer.B．He was totally out of shape.C．He was no longer fit to work out.D．He had something wrong with his waist. 5．What was the author actually doing in the bathroom?A．He was reflecting upon himself.B．He was doing thorough cleaning.C．He was wiping tears off his face.D．He was dressing up in front of the mirror. 6．Which can replace the underlined word “momentum” in the last paragraph?A．weight B．motivation C．experience D．knowledge 7．How does the author mainly develop the text?A．By telling a funny story.B．By employing dialogues.C．By describing mental activities.D．By showing possible results.As summer gives way to autumn, many of us long for warmth and sunlight. It is common for some of us to feel upset when the days get shorter. People call this phenomenon autumn sadness.While autumn sadness is a common seasonal feeling we have as sunlight comes in shorter supply, for some people, it takes on a more serious form known as seasonal affective disorder, or SAD．SAD, a form of depression (抑郁症), mostly starts in late autumn or early winter and goes away in spring and summer. People who have SAD typically oversleep, overeat, and lose interest in activities they once enjoyed. Generally, almost all people suffering from SAD feel sad, helpless, and even desperate.The exact cause of SAD is not yet completely understood, but several factors have been linked to its development. Johns Hopkins University suggests that reduced exposure (接触) to natural light during the autumn and winter months may disrupt the body’s internal clock and thehormones (荷尔蒙) produced, such as melatonin (褪黑素) and serotonin (血清素), which are related to sleep and emotions, respectively. This disruption can lead to depression.Addressing SAD often requires medical help. Light therapy is a common and effective treatment. Patients are advised to expose themselves to sunlight or man-made light that imitates natural sunlight. Light therapy can help regulate patients’ hormones and get their lives back on track.Moreover, living a healthier life, such as maintaining a regular sleep schedule, taking part in regular physical activity, and having a balanced diet, can help manage SAD．But it’s also important that people seek help from a medical professional to determine the most suitable treatment plan for their specific needs.It is worth noticing that, according to the National Institute of Mental Health of the US, in most cases, SAD begins in young adulthood. So, while embracing (接受) knowledge in books and classes, don’t forget to embrace the sunlight outdoors and get energy from nature!8．What do we know about SAD?A．It usually starts in early autumn.B．It can lead to long- term depression.C．Its main symptoms include feeling sad.D．It is most commonly found in older people. 9．According to Johns Hopkins University, what is a possible cause of SAD?A．An unbalanced diet.B．A lack of sunlight.C．An irregular sleep schedule.D．A lack of physical exercise.10．What do paragraphs 5 and 6 mainly talk about?A．How people can deal with SAD．B．What people with SAD have in common.C．Who people with SAD can turn to for help.D．Why medical help is needed for people with SAD．11．What can be inferred from the last paragraph?A．Young adults are the only group affected by SAD．B．Embracing nature’s sunlight is enough to prevent SAD．C．It’s important for young adults to take outdoor activities.D．It’s never too late to embrace the beauty that nature offers.At first, they sounded distant, as if they were around a phone in a prison. But as we chatted, they slowly started to sound more like themselves. They told me personal stories I’d never heard. I learned about the first time my dad got drunk. Mum talked about getting in trouble for staying out late. They gave me life advice and told me things about their childhoods, as well as my own. It was amazing. For a moment I forgot I wasn’t really talking to my parents at all, but to their digital copies.This Mum and Dad live inside an app on my phone as voice assistants created by the company HereAfter AI. The company’s goal is to let the living communicate with the dead. Technology like this, which lets you “talk” to people who have died, has been a mainstay of science fiction for decades. But now it’s becoming a reality, thanks to advances in AI and voice technology. I wanted to test out what it might be like.My real, flesh-and-blood parents are still alive and well; their virtual versions (虚拟版) were made just to help me understand the technology. But their digital copies offer a glimpse at a world where it’s possible to have conversations with loved ones long after they’re gone. From what I could know over a dozen conversations with my virtual parents, this really will make it easier to keep the people we loved close. It’s not hard to see the attraction. People might turn to digital copies for comfort, or to mark special occasions like anniversaries.But for some, this tech may be alarming or frightening. When I talked to friends about this article, some of them just went away. There’s a common, deeply held belief that we shouldn’t mess with death.But I’m only human, and that worry ends up being washed away by the even scarier possibility of losing the people I love. If technology might help me hang onto them, is it so wrong to try?12．Why did the writer chat with his virtual parents?A．To remember his late parents.B．To learn more about his parents.C．To see how the technology works.D．To find ways to improve the technology. 13．What can we learn about the technology mentioned?A．It allows users to live on an app.B．It leads users to lose their friends.C．It is invented by a science fiction writer.D．It offers a link between the dead and the living.14．What is the writer’s attitude towards the technology?A．Supportive.B．Unclear.C．Objective.D．Doubtful. 15．Which of the following is a suitable title for the text?A．Your can talk to your parents.B．Parents appear on your phone.C．AI means never having to say goodbye.D．A breakthrough in AI may benefit you.Are you an “I person” or an “E person”? 16 These two personality labels in particular are widely discussed online. They are part of a popular personality test called the Myers-Briggs Type Indicator, or MBTI. 17 All of the results have four letters, and there are 16 results in total. “I” and “E” refer to “introverted” and “extroverted”, respectively.Even if someone is typically quiet and shy, many online discussions suggest that an “I” person can still act outgoing at times. For example, when an introverted person is with a group of introverted friends, they might become more social like an “E” person.According to psychologists, this idea of temporarily switching personalities is called “masking”. 18 Human beings want to feel they belong, and they might become people-pleasers to do so.Using the MBTI result to identify and describe someone’s personality seems fun. 19 The MBTI personality test may show something you don’t know about yourself, and can even be a fun ice-breaker question when meeting new friends. And that’s all it is, for fun. Knowing someone’s MBTI result doesn’t mean you really know this person. 20A．How can you find the answer to the question?B．However, do not go too far or take it too seriously.C．That is hiding your true personality in specific situations.D．And those four letters of yours don’t define (定义) who you are.E．But no one personality type is best or better than another.F．Have you heard someone describe themselves as an INTJ or an ESTP?G．It is a self-report list to identify a person’s personality, strengths, and preferences.二、完形填空Our neighbors had a loud party last night. We weren’t 21 but this was one of those celebrations that I didn’t mind. They are a bunch of young, single guys and I would have felt out of place.What 22 me was the way they behaved. Ono of the young men came over 23 in the day to “warn” us of the upcoming event and said it would be over at about 11 p. m. That was the first step. Even more 24 was what they did next. “Here’s my 25 ”, offered our neighbor 26 “Text me if it’s too noisy.” That was a level of 27 I had never experienced in all my years of being a neighbor!And it really worked in their favor. My husband and I were so friendly that even when the event went past the 28 end time, even when the music reached high decibels(分贝), and even when we couldn’t get through to the phone number, we felt no 29 . We knew they would stop and 30 to it eventually.It takes such little effort to make people feel that they 31 and get people on your side. Everyone needs to 32 every now and then, especially in these uniquely tough times. But people who do it without disturbing others are few and far between. I hadn’t fully 33 my neighbors until this week. But now I see them in a new light and with greater 34 . They didn’t just bring the noise to the neighborhood; they showed us a good manner of 35 in life.21．A．located B．explored C．challenged D．invited 22．A．trapped B．impressed C．annoyed D．embarrassed 23．A．later B．closer C．earlier D．further 24．A．shocking B．frightening C．puzzling D．amazing 25．A．call number B．room number C．account number D．car number 26．A．anxiously B．politely C．regularly D．obviously 27．A．imagination B．consideration C．recognition D．organization 28．A．promised B．supplied C．designed D．compared 29．A．stress B．anxiety C．worry D．anger 30．A．respond B．adapt C．contribute D．stick 31．A．figure B．succeed C．matter D．access32．A．sleep B．maintain C．travel D．relax 33．A．noticed B．delivered C．explored D．proved 34．A．surrounding B．respect C．curiosity D．distance 35．A．strategy B．apology C．communication D．inspiration三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。
辽宁省实验中学2023-2024学年高二上学期期中数学试题(附解析版)
辽宁省实验中学2023-2024学年高二上学期期中数学试题．．．．,,PB PC 是从点P 出发的三条射线，每两条射线的夹角均为60︒，那么直线PC PAB 所成角的余弦值是（ ）．63B ．3322D ．12．设直线l 的方程为sin 20θ--=x y ，则直线的倾斜角α的范围是（ ）．[]0,πππ,⎡⎤⎢⎥7．圆心在直线x -y -4＝0上，且经过两圆x 2+y 2+6x -4＝0和x 2+y 2+6y -28＝0的交点的圆的方程为（ ）A ．x 2+y 2-x +7y -32＝0B ．x 2+y 2-x +7y -16＝0C ．x 2+y 2-4x +4y +9＝0D ．x 2+y 2-4x +4y -8＝08．设三棱锥V ABC -的底面是正三角形，侧棱长均相等，P 是棱VA 上的点（不含端点），记直线PB 与直线AC 所成角为α，直线PB 与平面ABC 所成角为β，二面角P AC B --的平面角为γ，则A ．,βγαγ<<B ．,βαβγ<<C ．,βαγα<<D ．,αβγβ<<二、多选题A ．AC 与1BD 的夹角为为2三、填空题四、未知(1)AC '的长；(2)直线AC '与CD '所成的角的余弦值.五、解答题六、未知20．在如图所示的试验装置中，两个正方形框架,ABCD ABEF 的边长都是2，且它们所在的两个半平面所成的角为120︒.活动弹子,M N 分别在正方形对角线AC 和BF 上移动，且AM FN x ==.(1)用x 表示出MN 的长度，并求出MN 的长的取值范围；(2)当MN 的长最小时，平面MNA 与平面MNB 所成角的余弦值.七、解答题21．在平面直角坐标系xOy 中，已知圆C 经过点()4,1M -，且与圆22:60+--+=D x y x y a 相切于点()1,2N .(1)求圆C 的方程；八、未知(1)求证：//EF平面PAB (2)在线段PD上是否存在一点存在，求出DMDP的值，若不存任，说明理由；(3)在平面PBC内是否存在点。
辽宁省实验中学2023-2024学年高一上学期11月期中考试英语试题
辽宁省实验中学2023-2024学年高一上学期11月期中考试英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解There is no doubt that books have the power to change how people think about the world and the universe around them. These 3 astronomy books have had a significant impact on the way humans think about our place and purpose in the universe:On the Heavens (about 350 BC) by AristalleAristotle proposed a geocentric (以地球为中心的) model of the universe in the book. This work is significant as a master work of the Aristotelian worldview, a school of philosophy that dominated (支配) intellectual thinking for almost 2000 years．Eventually，almost everything in it was proven incorrect, but On the Heavens, which is still in print, provides a fascinating view of astronomical evolution.The Revolutions of Heavenly Spheres (1543) by Nicolaus CopernicusIn this book, Copernicus argued that the Sun rather than the Earth lies in the center of the universe. The Earth moves as a planet around the Sun. The most important advantage offered by Copernicus was a vision of the universe as an integrated system, where all the planets move together in elegant harmony.The Mechanism of the Heavens (1831) by Mary SomervilleDifferent from his book Physical Geography, this book was embraced as an important contribution to the understanding of celestial motion (天体运动). It became extremely valuable to both astronomers and students and it was used as a textbook for more than half a century. The book went through many revisions, keeping pace with astronomical developments over time. It proves that given the opportunity, women could match the men in science step for step.1．What can we learn about the book On the Heavens?A．It is banned from printing.B．It mainly focuses on philosophy.C．It is used by many schools today.D．It has proven almost completely wrong.2．What do On the Heavens and The Revolutions of Heavenly Spheres have in common?A．They revealed the truth of the universe.B．They are master works of the same era.C．They explored the center of the universe.D．They regard the universe as an integrated system.3．Which book brings more motivation to women in science?A．On the Heavens.B．Physical Geography.C．The Mechanism of the Heavens.D．The Revolutions of Heavenly Spheres.I was sitting at my kitchen table the other day with a pen, notebook, calculator and a pile of bills. I was doing my monthly budget. There were bills for electric water, rent, insurance, the car payment, the phone bill, and the cable bill. Plus money needed to be set aside for food, gas, clothes and hopefully a little left over to save for those unexpected bills that always seemed to show up. When I was done, I shook my head, closed my eyes and thought of a time long ago when I would regularly get treasures.When I was a boy. we lived across the road from Camp Caesar. It held week long camps all through the summer and my grandma who I lovingly called “Nanny” worked in her big kitchen. I remember slipping there getting a smile, a hug, a kiss and a hot roll from Nanny. Then she would always take deep in her pockets and pull out a treasure, a shiny quarter. She would give it to me and I would run down the hill to either get an ice cold can of coke from the pop machine or I would head to the camp’s swimming pool where I could buy a warm cup of cherry coke for 15 cents and a tiny 10 cent bag of chips from a stand. I took my time because it was always a big decision. It was nice too feeling so rich for a few minutes.Looking back now I can see that the real treasure was not the quarter at all. It was the love with which Nanny gave it to me. I would have still visited her at work every day if I had never gotten a single quarter. It was her smile, hugs, and kisses that were priceless in my heart then and now.The old saying is true, “With your work you can make a living, but it is with your love that you make a life.” You can always welcome love into your heart, soul and mind. And you can always share your love with others. It is that one treasure that lasts forever. 4．According to Paragraph 1, what was the author trying to figure out?A．Where to get treasures.B．What food and supplies to buy.C．How to sort out these bills at hand.D．How to balance the money available.5．What does the underlined word “roll” in Paragraph 2 refer to?A．A sound.B．A greeting.C．A kind of act.D．A kind of bread. 6．Which of the following best describes Nanny?A．Affectionate.B．Helpful.C．Humorous.D．Selfless. 7．Why does the author mention the old saying in the last Paragraph?A．To change people’s heart and soul.B．To show what we should value in life.C．To explain work and love can make a life.D．To advise more love and sharing in childhood.Companies which sell liquids like drinks or shampoo depend on bottles made of plastic or glass for their packaging. But as customers have become more worried about the environment, many companies have begun working to develop paper bottles.Paper bottles have many advantages. They are easy to recycle and weigh less than glass or plastic bottles, meaning they’ll require less energy to produce and to move around.A company called Paboco has been working with many large companies to develop paper bottles. Clearly, one of the biggest challenges is keeping a paper bottle from leaking (渗漏). Therefore, many companies are lining their bottles with a thin sheet of plastic. Though this liner can be taken away and recycled, many recycling programs don’t have the right machines to deal with these liners.A Danish beer company called Carlsberg is working with Paboco on a paper bottle called the “Green Fiber Bottle”. In the future the company hopes to use a “bio-plastic” that will break down naturally over time. A company named Diageo has just announced the first paper bottle that’s completely plastic-free. Instead of a plastic liner, a non-plastic coating will be used on the inside of the bottles. This should make the bottle fully recyclable. Diageo says they’ll use the bottle with their whiskey in 2023.However, there’s still lots of testing to be done before paper bottles can replace glass or plastic bottles. Companies will need to see how long liquids can be stored in the bottles, and make sure the bottles don’t influence the taste. But with so many companies working towardthe same goal, it’s likely that we can expect to see paper bottles on store shelves in the near future.8．What forces many companies to develop paper bottles?A．The cost of making plastic or glass bottles.B．The customers’ caring about the environment.C．The energy needed to produce ordinary bottles.D．The difficulty in shaping the plastic or glass bottles.9．Why are plastic liners used inside the bottles?A．To make them easy to recycle.B．To make bottles reusable.C．To prevent liquid from escaping.D．To lower the production cost. 10．What can we infer about the making of paper bottles?A．Non-plastic coatings may be hard to recycle.B．Paper bottles can’t go without a plastic liner.C．There’s still a long way to go to reach the goal.D．Not all paper bottles are better than glass bottles.11．What can be the best title for the text?A．Traditional Bottles or Paper BottlesB．Companies Work to Develop Paper BottlesC．Paper Bottles Are Getting Increasingly PopularD．Advantages and Disadvantages of Paper BottlesAre you patient? Do you have attention to detail, free time and access to a computer? Well, then a scientist might welcome your help. Researchers in the UK say it’s becoming important to count on common people to help them with their projects. They need people to examine data and submit their observations online.British teenagers Sasha and Matthew are taking part in a study of penguins (企鹅) from the comfort of their homes. The pair look at pictures and tag (加标签于) photos identifying adults, chicks and eggs. Every click of their mouse is helping to build up a detailed picture of penguin colonies (群). They, and thousands of others, are helping scientists to understand why some colonies are growing and others are decreasing. Within the first four hours of Penguin Watch going live, “citizen scientists” marked more images than the research team did in five years.Dr. Tom Hart, Penguin Watch Coordinator at Oxford University, says, “When you go beyond what a scientist can analyse to what a mass audience can do, then it increases beyond what any other project could do.”The British Science Association says families are helping out with careful research. It made a difference to the Planet Hunters Project, which ran for five years. V olunteers looked at dots which showed how the brightness of a star changed at different points in its solar system.According to Dr. Robert Simpson from Oxford University, who took part in the project, the volunteers discovered planets and these are now in published papers. He says with pride, “We can go and look at these planets with other telescopes and we know they exist because of those helpers.”But how do scientists guard their research against accidental or deliberate mistakes in observation? Dr. Simpson isn’t worried. “We get lots of people looking at the same things, ”he says. The researcher warns that people who are mistakenly clicking on the site are very obvious and can be identified very quickly. So, there’s no fooling the scientists.And to make sure things go well, the Penguin Watch paper will go through a peer review before being published. After that, every “citizen scientist” will be credited. 12．According to the passage, who will be suitable to help the scientists?A．An engineer who works in a company.B．A university student who likes science.C．A businessman who invests in a new project.D．A careful teenager who uses the computer smoothly.13．What is a volunteer required to do?A．Publish his observation data by himself.B．Observe pictures and record his observation.C．Discuss his observation with other volunteers.D．Take his report to the scientist and correct mistakes.14．How could scientists avoid mistakes in observation?A．By working with volunteers.B．By using their own data.C．By identifying pictures and photos.D．By going through a peer review. 15．What’s Dr. Simpson’s attitude towards the volunteers’ observation?A．Objective B．Supportive.C．Negative.D．Doubtful.二、七选五If you can’t get your hands off your cellphone, you have unknowingly become a slave to this device. Being addicted to a cellphone can be potentially harmful. Here are some reasons why you should use your cellphone less.16 Very often you forget the world outside your cellphone. Just leave the phone at home, take a walk, and get to know what you really want in life. Discover what sparks your interest and pursue it with all your heart.You should focus more on personal interactions in real life. Can you hug your dad and feel his strength through the phone? Can you kiss your mom goodnight over the phone?17 Cellphones just snatch these precious things away from you.Your grades will go up. Leave your phone behind when going to school. Once you get home, don’t lie on the bed and text your friends. 18 Your grades will improve.You need to give your mind a break. Constantly chatting on the phone puts too much pressure on your brain, which does great harm to both your physical and mental health.19You need to keep away from anxiety. Research has shown that people who use cellphones all day long are more anxious and restless. 20 When they don’t get what they want, they will become depressed. Therefore, keep the phone away to keep anxiety at bay.A．Get through your homework first.B．You should develop your true interests.C．You should continuously learn new things.D．These are small gestures that play a big role in life.E．With their growing popularity, your laziness will grow, too.F．They seem to look for recognition and acceptance through the device.G．So make your mind rest so that you can think and function well the next day.三、完形填空What is intelligence anyway? When I was in the army I received an intelligence test thatI had an auto-repair (汽车维修) man once, who, on these intelligence tests, could not possibly have scored more than 80. Yet, when anything went wrong with my car I hurried to him — and he always 22 it.Well, then, suppose my auto-repair man 23 questions for some intelligence tests. By every one of them I’d prove myself a 24 . In a world where I have to work with my 25 I’d do poorly.Consider my auto-repair man again. He had a habit of telling jokes. One time he said, “Doc, a deaf-and-dumb (聋哑) man 26 some nails. Having entered a store, he put two fingers together on the counter and made 27 movements with the other hand. The clerk brought him a hammer. He 28 his head and pointed to the two fingers he was hammering. The clerk 29 him some nails. He picked out the right size and left. Well, Doc, the 30 man who came in was blind. He wanted scissors. 31 do you suppose he asked for them?” I lifted my right hand and made scissoring movements with my first two fingers. He burst out laughing and said, “Why, you fool,” he used his 32 and asked for them. I’ve been 33 that on all my customers today, but I knew 34 I’d catch you. “Why is that?” I asked. “Because you are so goddamned educated, Doc. I knew you couldn’t be very 35 .”And I have an uneasy feeling he had something there21．A．average B．total C．exam D．number 22．A．fixed B．checked C．drove D．crashed 23．A．answered B．encountered C．designed D．braved 24．A．teacher B．partner C．winner D．fool 25．A．brains B．effort C．hands D．attention 26．A．bought B．tested C．found D．needed 27．A．cutting B．hammering C．waving D．circling 28．A．nodded B．raised C．shook D．turned 29．A．brought B．packed C．sent D．sought 30．A．clever B．other C．right D．next 31．A．What B．How C．Who D．Which 32．A．imagination B．information C．voice D．hand 33．A．trying B．examining C．practising D．proving 34．A．for sure B．at once C．in fact D．above all35．A．clear B．silly C．slow D．smart四、用单词的适当形式完成短文五、其他应用文46．假如你是李华，是校英语报的记者。