2015年全国重点高中提前招生考试全真试卷
全国重点高中提前招生考试全真试卷(二)评讲
3.(黄冈中学理科实验班自主招生)用大小为F的两个力将100块重为G的 砖头夹住,如图2-2所示。设所有接触面间的动摩擦因数均为μ,则第27 号和28号砖块之间的摩擦力为 ( A ) A.23G B.27G C.28G D.2μ P
【解析]先整体分析,将100块砖作为一个整体可得:砖1的左侧面和砖块 100的右侧面所受摩擦力大小相等,均为50G,方向均为竖直向上。然后 将砖块1-27号砖作为一个小的整体隔离出来,则它们受三个力的作用, 重力27G、砖块对它们的向上的摩擦力50 G、砖块28对它们的摩擦力。 物体在三个力作用下处于平衡状态.因此,第27块砖和第28块砖之间的摩 擦力为50G-27G=23G.故答案应选A项。
4.(黄冈中学自主招生)如图2-3所示,平面镜M正以120度每秒的速度绕 垂直于纸面的轴O匀速转动,AB为一段圆心在O点的圆弧形屏幕,其所对 圆心角∠AOB=60°,有一束来自频闪光源的平行光束通过狭缝S射向平 面镜M上的O点,已知光源每秒闪动12次,则屏幕AB上1s内最多可能出现 的光斑次数为 ( B ) A.1次 B.3次 C.6次 D.12次
7.(马鞍山一中自主招生)如图2-5所示,A、B是两个完全相同的匀质长方 形木块,长为L,叠放在一起,放在水平桌面上,端面都与桌边平行。A 放在B上,右端有3L/8伸出B外,为保证两木块都不翻倒,木块B伸出桌边 的长度不能超过 ( B )
【解析】应用整体法考虑、根据平衡条件得出若 两长方形木块不翻倒且B伸出最长时,应满足整 体的重心应恰好在桌子的边缘。将两个长方形木 块看做一个整体,则其总长度为L+3L/8=11L/8, 根据平衡条件看出,为了保持两长方形木块都不 翻倒,整体的重心应恰好在桌子边缘,所以整体 重心与A右边缘距离为11L/8×1/2=11L/16.由图可 知B边缘到桌子边缘的距离为 X=11L/16-3L/8=5L/16。故选B。
2015提前招生选拔考试科学试卷
2015提前招生选拔考试科学试卷一、选择题:(每题只有一个正确的选项)(40分)姓名班级1.现有密度分别为ρ1和ρ2的两种液体,且ρ1<ρ2 。
在甲杯中盛满这两种液体,两种液体的质量各占一半;在乙杯中也盛满这两种液体,两种液体的体积各占一半。
假设两种液体之间不发生混合现象,甲、乙两个杯子也完全相同,则(B)A.甲杯内液体的质量大B.乙杯内液体的质量大C.两杯内液体的质量一样大D.无法确定2.杠杆OA的B点挂着重物G,A端用细绳挂在圆弧EF上,此时OA恰成水平,且A点与圆弧形架EF的圆心重合。
当绳AM的M端从E点缓慢滑到F点的过程中,绳对A点拉力的大小将:( D )A、逐渐变大B、逐渐变小C、先变大再变小D、先变小再变大3. 小明在听讲座时,想把银幕上用投影仪投影的彩色幻灯片图像用照相机拍摄下来。
由于会场比较暗,他使用了闪光灯。
这样拍出来的照片:(C)A.色彩鲜艳,比不用闪光灯清楚多了B.色彩被“闪”掉了,拍到的仅有黑色的字和线条C.反而看不清投影到银幕上的图像,倒是把银幕上的一些污渍拍了出来D.与不用闪光灯时效果一样,因为拍摄的是银幕上的像,而不是实际的景物4.如图所示,一点光源位于凸透镜的主轴上,凸透镜位置固定。
当点光源位于A点时,它的像在B点;当点光源位子B点时,它的像在C点。
则凸透镜位于( A )A.A的左侧 B.A、B之间C.B、C之间 D.C的右侧5.在图9所示的电路中,当滑动变阻器的滑片P移动时,导致电压表V2读数变大,则下列关于其它电表读数变化情况的说法中,正确的是( A )(A)V1、A读数均变大(B)V3、V读数均变大(C)V、A读数均变大(D)V3、V1读数均变大6.溶液的密度随固体溶质溶解的增多而增大,某溶质的饱和溶液还能继续溶解一定质量的其他溶质,如图,一个悬挂在弹簧秤上的物体浸没在Ba(OH)2饱和溶液中,在恒温条件下,加入一些下列物质,能使弹簧秤读数变小的是(物体不与溶液发生化学反应)(D)A.H2O B.H2SO4溶液C.Ba(OH)2晶体D.BaCl2晶体7.将ag块状碳酸钙跟足量盐酸反应,反应物损失的质量随时间的变化曲线如图中的实线所示,在相同的条件下,将bg (a >b )粉末状碳酸钙与同浓度的盐酸反应,则相应的曲线(图中虚线所示)正确的是( C )8.将稀盐酸分别慢慢滴入装有Na 2CO 3溶液和NaHCO 3溶液的两试管中,会发现:装有NaHCO 3溶液的试管中很快产生气泡,而装有Na 2CO 3溶液的试管中开始没有气泡产生,但随着滴入稀盐酸的量增加时,才会产生气泡。
2015年全国重点高中重点班招生考试训练卷及答案和详解1
2015年全国重点高中重点班招生考试训练卷11.如图所示,在一粗糙水平面上有两个质量分别为m1和m2的木块1和2,中间用一原长为L,劲度系数为k的轻弹簧连接起来,木块与地面间的滑动摩擦因数均为μ.现用一水平力向右拉木块A、kwhB、kg*m2/s2C、kg*m/sD、N*m3.电灯悬挂于两墙之间,如图所示,使接点A上移,但保持O点位置不变,则A点上移过程中,绳OA的拉力()所受阻力与速度成正比,则汽车的运动情况是( )A、先加速,后减速最后静止B、先匀加速,后减速C、先加速,后减速直至匀速D、加速度逐渐减小直至为零6、小明晚上在阳台上发现远处在燃放连珠礼花,礼花绽放时间间隔均匀,闪光之后1秒有一声爆响.利用手表.在某次看见闪光开始计时.听到最后一声爆响停止计时,历时10s,共有3次闪光,4次爆响,由此他提出了礼花燃放地点到直状,木板上再放一重物,用手压重物,使弹簧再缩短些,然后放手,最后重物8、如图所示,两木块的质量分别为m1和m2,两轻质弹簧的劲度系数分别为k1和k2,上面木块压在上面的弹簧上(但不拴接),整个系统处于平衡状态.现缓慢向上提上面的木块,直到它刚离开上面弹簧.在这过程中下面木块移动的距离为。
9、在温度均匀的液体中,一个小气泡由液体的底层缓慢地升到液面,上升过程中气泡的体积不断增大,则气泡在浮起的过程中(填“吸热”“放热”或“既不吸热也不放热”)10、如图,物体A和B质量均为m,分别与轻绳连接跨过定滑轮(不计绳与滑轮之间的摩擦).当用水平变力F拉物体B沿水平方向向右做匀速直线运动时,物体A做(填“匀速”或“变速”);物体A的速度(填“大于”、“小于”或“等于”)物体B的速度。
11、如图所示的容器中,A、B各有一个可以自由移动的轻活塞,活塞截面积分别为SA 和SB,活塞下是水,上为空气,大气压恒为P,A、B底部由带有阀门K的管道相连,整个装置与外界无热交换.开始A中水面比B中高h,打开阀门,使A中的水逐渐流向B中,最后达到平衡,在这个过程中,大气压对水做功为,水的内能增加为。
(九)全国重点高中提前招生考试全真卷
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全国重点高中提前招生考试全真试卷
全国重点高中提前招生考试全真试卷(八)总分:100分考试时间:90分钟姓名:一、选择题(每小题4分,共40分)1.(2015年黄冈市市重点中学自主招生试题)伽利略创造的把实验、假设和逻辑推理相结合的科学方法,有力地促进了人类科学认识的发展。
利用如图8-1所示的装置做如下实验:小球从左侧斜面上的O点由静止释放后沿斜面向下运动,并沿右侧斜面上升。
斜面上先后铺垫三种粗糙程度逐渐降低的材时,小右侧斜面上升到的最高位置依次为1、2、3。
根据三次实验结果的对比,可以得到的最直接的结论是()A.如果斜面光滑,小球将上升到与O点等高的位置B.如果小球不受力,它将一直保持匀速运动或静止状态C.如果小球受到力的作用.它的运动状态将发生改变D.小球受到的力一定时,质量越大,它的速度越小2.(2015年黄冈市重点中学自主招生试题)如图是健身用的“跑步机”示意图。
质量为m的健身者踩在与水平面成a角的静止皮带上,用力向后蹬皮带,可使皮带以速度v匀速向后运动。
若皮带在运动过程中受到脚的摩擦力为f,则在运动的过程中,下列说法中正确的是()A.f是皮带运动的阻力B.人对皮带不做功C.人对皮带要做功,其做功的功率为fvD人的重力与皮带对人的支持力是一对平衡力3.(2014年华中师大一附中高中招生试题)实验室常用的弹簧秤如图8-3所示,弹簧的一端与连接有挂钩的拉杆相连,另一端固定在外壳上的O点,外壳上固定一个圆环,外壳和圆环的重为G,拉杆和挂钩的重为G0,弹簧质量忽略不计。
现将该弹簧秤在图甲所示的位置凋零后不动,再以如图乙和图丙的两种方式固定在地面上,并分别用图样的力F0(F0>G+G0)竖直向上拉弹簧秤,则稳定后弹簧秤的读数分别为()A.乙图读数为F0-G,丙数读数为F0-G0B.乙图读数为F0-G0,丙数读数为F0-GC乙图读数为F0-G0,丙数读数为F0-2GD.乙图读数为F0-G,丙数读数为F0-2G4(2012年蚌埠二中自自主招生试题)如图8-4所示,一个木块A放在长木板B上,弹簧秤一端接A,另一端固定在墙壁上,长木板B放在水平地面上,在恒力F作用下,长木版B以速度v匀速运动,水平弹簧秤的示数为T,下列关于摩擦力的说法正确的是()A木块受到的摩擦力大小等于FB.长木板受到的摩擦力大小等于TC.若长木板以2v的速度运动时,长木板受到的摩擦力大小等于2FD.若用2F的力作用在长木板上,木块受到的摩擦力大小仍等于T5(2016华中师大一附中高中招生试题)在学习物理过程中,某同学有以下观点:○1作为载体的电磁波,频率越高,相同时间内可传输的信息越多;○2光纤通信所说的激光,在光导纤维中通过折射传播;○3太阳能、核能都属于可再生能源;○4北导航系统进行定位和导航都是利用电磁波工作的;○5物体的温度越高,所含热量越多,内能一定大;○6内能同的两物体之间可能会发生热传递;○7可见光与无线电波在真空中的传播度大小相等;○8动圈式话筒的原理是电磁感现象,电线感应是把机械能转化为电能你认为其中说法正确的是()A. ○1○3○6○7B. ○1○2○4○6○8C. ○1○3○4○5D. ○2○5○7○86.(2014年华中师大一附中高中招生)如图8-5甲所的电路中,电源电压不变,小灯泡的额定电压为2.5V,滑动变阻器的最大阻值R0为定值电阻R0的3倍。
2015年重点高中自主招生提前班考试物理试题及解析
2015年重点高中自主招生提前班考试物理试题及解析2015年重点高中自主招生提前班考试物理试题及解析一、选择题(每题4分,共40分)1.一辆汽车由西向东匀速行驶,车上的乘客看到窗外的雨是竖直下落的。
那么在地面上的人看来,雨滴的下落方向是()。
A.竖直下落B.斜向东下落C.斜向西下落D.斜向南或斜向北下落解析:汽车由西向东匀速行驶,车上的乘客看到窗外的雨是竖直下落的,这说明雨滴和车相对静止,即和车运动的速度和方向相同。
因此,车相对于地球是由西向东匀速行驶,所以雨滴也是斜向东下落。
故选B。
2.小刚家中的几盏电灯突然全部熄灭了,检查保险丝发现并未烧断,用测电笔测试各处电路时,氖管都发光。
他对故障作了下列四种判断,其中正确的是()。
A.灯泡全部都烧坏B.进户零线断路C.室内线路发生短路D.进户火线断路解析:电灯突然全部熄灭,检查保险丝发现并未烧断,说明电路中的电流不会很强,因此电路不可能发生短路现象,也不可能几盏灯泡全部都烧坏。
如果用测电笔测试各处电路时,氖管都发光,说明该电路进户火线不可能断路。
由此可以判断是进户零线断路,使得几盏灯所在电路没有形成闭合回路,即使得电路中没有电流而出现几盏灯全部熄灭。
故选B。
3.小强在蚌埠将一根质量分布均匀的条形磁铁用一条线悬挂起来,使它平衡并呈水平状态,悬线系住磁体位置应在()。
A.磁体重心处B.磁体的某磁极处C.磁体重心的北侧D.磁体重心的南侧解析:如图,条形磁体的上端是N极,向下微倾,要使质地均匀的条形磁体水平平衡,悬线系在重心的北侧。
故选C。
4.小光在听讲座时,想把银幕上用投影仪投影的彩色幻灯片图象用照相机拍摄下来,由于会场比较暗,他使用了闪光灯,这样拍出来的照片()。
A.反而看不清投影到银幕上的图象,倒是把银幕上的一些污渍拍出来了B.色彩鲜艳,比不用闪光灯清楚多了C.色彩被“闪”掉了,拍到的仅有黑色的字和线条D.与不用闪光灯时效果一样,因为拍摄的是银幕上的像,而不是实际的景物解析:闪光灯的光照射到物体上,可以使物体表面的亮度增大,但闪光灯照射到银幕上以后,只能增加银幕的亮度,而不能增加图象的亮度。
2015年全国重点高中重点班招生考试训练卷及答案和详解3
2015年全国重点高中重点班招生考试训练卷3一、选择题:(3分×12=36分)1、下列说法错误的是()A、夏天,我们要喝冰凉的饮料,往往会在饮料中加上几个冰块,这是因为不仅冰块温度低,而且冰块熔化成水时吸热B、人们在高温天气里大汗淋漓,是人体自我保护的生理现象,汗液蒸发吸热使体温不致升得太高C、我国北方冬季树枝上出现的雾凇是凝华现象D、在运输食品时,为了防止食品腐烂变质,可以用干冰的熔化来吸热降温2、在凸透镜主轴上的一物点P,物距大于焦距,如果沿直径对称切除透镜很小一部分,如图所示,再把上、下半截透镜向原主轴位置合拢,则下列说法中正确的是()A、在透镜中间部分没有切除时,如果一只小飞虫恰好落在透镜上的A点,不会在光屏上留下小飞虫的影子B、在透镜中间部分没有切除时,如果P点向透镜不断靠近,则所成的像一直变大C、A、B合拢后,所成像情况与没切除前相同,只是亮度变低D、A、B合拢后,无论怎样移动光屏,在光屏上都不能成像3、如图,一个圆台形的筒子,下用一重力忽略不计薄片贴住,浸入水中后,薄片不会下落,如果筒中注入100g水,恰能使它脱落,则下列情况哪种能使薄片下落()A、在薄片中央轻放100g砝码B、慢慢注入100g酒精C、慢慢注入100g水银D、上述三种做法都不行4、如图所示情景是一种游戏,叫做蹦极.游戏者将一根有弹性的绳子一端系在身上,另一端固定在高处,从高处跳下.图中a点是弹性绳自然下垂时绳下端的位置,c点是游戏者所到达的最低点.对于游戏者离开跳台至最低点的过程,下列说法正确的是()A、游戏者从a到c动能逐渐减小B、游戏者从a到c受到的合力方向向下C、游戏者从a到c受到的合力先减小后增大D、游戏者到达c点时处于平衡状态5.如图所示,表面粗糙的传送带静止时,物块由皮带顶端A从静止开始滑到皮带底端B 用的时间是t,则()A、当皮带逆时针运动时,物块由A滑到B的时间一定大于tB、当皮带逆时针运动时,物块由A滑到B的时间一定等于tC、当皮带顺时针运动时,物块由A滑到B的时间一定等于tD、当皮带顺时针运动时,物块由A滑到B的时间一定大于t6.小明游览一座古寺时发现里面有一个变音钟,随着钟下燃烧的香火越旺,敲出的声音越高亢原因的可能是()A、香火使钟周围的空气温度升高,传声效果越来越好B、任何物体温度升高时,振动发出的声音音调都会变高C、香火使振动的振幅加大,使声音响度变大D 、香火使钟温度升高.材料的微观结构发生变化,钟振动频率改变7.在如图所示的电路中,当电键S 闭合后,电压表有示数,调节可变电阻R 的阻值,电压表的示数增大了△U.则( )A 、可变电阻R 被调到较小的阻值B 、电阻R 2两端的电压减小,减小量等于△UC 、通过电阻R 2的电流减小,减小量小于△U/R 2D 、通过电阻R 2的电流减小,减小量等于△U/R 18.如图所示为乒乓球在水平地面上弹跳时产生的轨迹的一部分,该图表明( )A 、在图中乒乓球的弹跳方向为自右向左B 、乒乓球弹跳时机械能守恒C 、乒乓球某次弹起过程,弹起瞬间动能大于此过程最高点时的重力势能D 、乒乓球运动过程中重力势能一直减小9.如图所示,a 、b 、c 为三个物块,M 、N 为两个轻质弹簧,R 为跨过光滑定滑轮的轻绳,它们连接如图并处于静止状态.下列判断中,正确的是( )A 、有可能N 处于压缩状态而M 处于不伸不缩状态B 、有可能N 处于压缩状态而M 处于拉伸状态C 、有可能N 处于不伸不缩状态而M 处于拉伸状态D 、有可能N 处于拉伸状态而M 处于不伸不缩状态10.“蜻蜓点水”是常见的自然现象,蜻蜓点水后在平静的水面上会出现波纹.某同学在研究蜻蜓运动的过程中获得了一张蜻蜓点水的俯视照片,照片反映了蜻蜓连续三次点水后某瞬间的水面波纹.如果蜻蜒飞行的速度恰好与水波的传播速度相等,不考虑蜻蜓每次点水所用的时间,在下列四幅图中,与照片相吻合的是( )11、压敏电阻的阻值随所受压力的增大而减小,右位同学利用压敏电阻设计了判断小车运动状态的装置,其工作原理如图(a )所示,将压敏电阻和一块挡板固定在绝缘小车上,中间放置一个绝缘重球.小车向右做直线运动过程中,电流表示数如图(b )所示,下列判断正确的是( )A 、从t 1到t 2时间内,小车做匀速直线运动B 、从t 1到t 2时间内,小车做匀加速直线运动C 、从t 2到t 3时间内,小车做匀速直线运动D 、从t 2到t 3时间内,小车做匀加速直线运动12.如图所示,一闭合金属圆环用绝缘细绳挂于O 点,将圆环拉离平衡位置并释放,圆环摆动过程中经过匀强磁场区域,则(空气阻力不计)( )A 、圆环向右穿过磁场后,可以摆至原高度B 、在进入和离开磁场时,圆环中均有感应电流C 、圆环进入磁场后离平衡位置越近速度越大,感应电流也越大D 、圆环最终将静止在平衡位置二.非选择题:(13-23题每空2分,24、25题每题12分,共64分)A B CD13、“蜗轮增压”是目前在各种汽油机和柴油机中采用的一项节能、提高热机功率的技术.它是利用热机排出的废气带动蜗轮旋转,先将新鲜空气压缩后再送入内燃机的进气口.这样做的好处是(填“增大”或“减小”)排出废气所带走的能量,(填“提高”或“降低”)内燃机的效率.14、如图所示,粗细均匀的蜡烛长l1,它底部粘有一质量为m的小铁块.现将它直立于水中,它的上端距水面h.如果将蜡烛点燃,假定蜡烛燃烧时油不流下来,且每分钟烧去蜡烛的长为△l,则从点燃蜡烛时开始计时,经时间蜡烛熄灭(设蜡烛的密度为ρ,水的密度为ρ1,铁的密度为ρ2).15.如图,xOy平面内有一以原点O为圆心、半径为R的圆,动点P在圆周上由A点开始沿顺时针方向速度大小始终为v的圆周运动,A为圆与x轴的交点,经过一段时间后,P 点恰好又通过A点,则这段时间为.16.如图所示,甲、乙两人同时从A地出发.其中,甲沿直线AB朝正北方向匀速运动,乙沿直线AC朝正东方向匀速运动.甲运动的速度是乙的2倍,经过3分钟,甲到达B地后,立即改变运动方向并保持速度大小不变,马上沿直线向C地运动,恰好在C地与乙相遇.则乙从A地运动到C地的时间为分钟.17.一段粗细均匀的电阻丝电阻值为16Ω,将它围成一个封闭的圆圈,如图所示,则A、B两点间的电阻为Ω.18.螺旋常和杠杆连接在一起使用,达到省力的目的,那么使用螺旋时如何省力的呢?下面以举重螺旋(千斤顶)为例进行分析.下图为举重螺旋的结构示意图,设螺距为h,螺旋手柄末端到螺旋轴线的距离为L,当螺旋旋转一周时,重物被升高一个螺距.若这个螺旋的机械效率为η,用它将重力为G的物体举起,需要作用在手柄上的动力F为.19.如图中薄片组成45°直角三角形,按接法M、N间电阻为R,则按接法P、Q间电阻是.20.一种简易“千斤顶”,如图所示,一竖直放置的轻杆由于限制套管P的作用只能在竖直方向上运动.若支杆上放一质量为M=100kg的物体,支杆的下端通过一与杆固定连接的小轮放在倾角为θ=37°斜面体上,并将斜面体放在光滑水平面上,现沿水平方向对斜面体施以推力F,为了能将重物顶起F最小为。
2015年全国重点高中提前招生考试全真试卷
2015年全国重点高中提前招生考试全真试卷文科综合----英语部分(测评时间:45分钟满分:75分)一.单项选择(共15题,每小题1分,满分15分)从A,B,C,D四个选项中,选出可以填入空白处的最佳选项)1. ---Why didn’t Cindy play the violin at the concert last night.---She said her hand hurt, but that was only a(n)___.I saw her play tennis last night.(2014河北省重点高中自主招生试题)A. matterB. expressionC. resultD. excuse2. Her ___face suggested she____ high grades in the exams.A. exciting; achievedB. excited; achievedC. exciting: achieveD. excited: achieve3. ---Do you want David or Brown to do it ?-----_______is fit for the job, I’m afraid.(2015年黄冈中学理科实验班预录试题)A. EitherB. BothC. NoneD. Neither4. ----Do you know why he didn’t ____a word when he _____?------Because he was too nervous.A. speak ; speaksB. say; spokeC. say ; was spokenD. speak; is spoken5.---Dad, must we wait until the light becomes green?----Yes, I’m afraid we ______.That’s the traffic rule.(2014年温州高中自主招生模拟试题)A. mustB. mayC. have toD. need6.----I think it’s much more fascinating to do volunteer work than study indoors.-----__________________.(2014年华中师大一附中自主招生试题)A. You can’t say so.B. It doesn’t matter.C. I can’t agree more.D. It’s foolish to say so.7.Diaoyu Island are made up of a group of islands, _______China since ancient times.A. belong toB. belonged toC. are belonged toD. belonging to8.It will be two hours _______she can go out and enjoy the fresh air since she has a lot of housework to do .A. thatB. beforeC. untilD. since9. To get a better grade, you should _____ the notes again before the test.A. go overB. get overC. turn overD. take over10. The scientists got as _____as they could to the wild animals so as to watch them______.A. closely; closeB. close; closeC. close; closelyD. closely; closely11.We know that a smile is usually a sign ______people feel friendly and happy, but ______we don’t know who the new person is?A. that ; what ifB. when ;whatC. when; how aboutD. if ;how12.------Isn’t Amy helpful to us all?-----__________.She always encourages us.A. No ; she isB. Yes; she isn’tC. No; she isn’tD. Yes; she is13. Many a student _____it hard to find an acceptable job after graduation in modern scientific society.A. find B . finds C. found D. have found14. Please make my excuse at tomorrow’s meeting----I’ve got too much work_____.A. to do to comeB. doing comingC. to do comingD. doing to come15.----Do you mind my building the house out of recycling materials, darling?------_________.I’d like a grand house to live in.A. Not at all.B. Go aheadC. You’d better not.D. Of course not二. 完型填空( 共20小题,每小题1分,满分20分)阅读下面短文,然后在各题所给的四个选项中选出一个最佳答案I was tired and hungry after a long day of work.When I walked into the living-room , my 12-year-old son looked _16____ at me and said , “ I love you.” I didn’t know what to say.__17___several seconds all I could do was to stand there and __18____ down at him. My first thought was that he must need __19____ with his homework or he was trying to __20____ me for some news. Finally I asked,” What was that all about?”“Nothing,” he said. “ My teacher said we should ___21___ our parents that we love them and see what they say. It’s __22_____”The next day I called his teacher to find out more about this “experiment”and how the other parents had _23_____.“Most of the fathers had the _24____ reacting as you did,” the teacher said.” When I first __25____we try this, I asked the children what they thought their parents would say. Some of them thought their parents would have heart trouble. The ___26____ is,”the teacher explained, “feeling loved is an important part of __27_____.It is something all people__28_____. What I’m trying to tell the children is that it’s too __29____we don’t all express those feelings. A boy should be __30_____ to tell his dad h loves him.The teacher , a middle-aged man , understands how __31___ it is for some of us to say the things that would be good for us to say.When my son came to me that evening, I held on to him for ___32____ second .And just before he pulled away ,I said in my deepest , most manly voice, “Hey, I love you ,too.”I don’t know if __33___ that made either of us healthier, but it did feel pretty good. Maybe next time one of my children said “I love you”, it would not take me a whole ___34___ to think of the right __35____.三.阅读理解。
2015年普通高等学校招生全国统一考试全国卷1(答案)
2015年普通高等学校招生全国统一考试(课标全国卷Ⅰ)一、选择题 1.A 由已知1+z 1-z=i,可得z=i -1i+1=(i -1)2(i+1)(i -1)=-2i-2=i,∴|z|=|i|=1,故选A.2.D 原式=sin 20°cos 10°+cos 20°sin 10°=sin(20°+10°)=sin 30°=12,故选D. 3.C 根据特称命题的否定为全称命题,知¬p:∀n∈N,n 2≤2n,故选C.4.A 该同学通过测试的概率P=C 32×0.62×0.4+0.63=0.432+0.216=0.648,故选A.5.A 若MF 1⃗⃗⃗⃗⃗⃗⃗⃗ ·MF 2⃗⃗⃗⃗⃗⃗⃗⃗ =0,则点M 在以原点为圆心,半焦距c=√3为半径的圆上,则{x 02+y 02=3,x 022-y 02=1,解得y 02=13.可知:MF 1⃗⃗⃗⃗⃗⃗⃗⃗ ·MF 2⃗⃗⃗⃗⃗⃗⃗⃗ <0⇒点M 在圆x 2+y 2=3的内部⇒y 02<13⇒y 0∈(-√33,√33).故选A.6.B 设圆锥底面的半径为R 尺,由14×2πR=8得R=16π,从而米堆的体积V=14×13πR 2×5=3203π(立方尺),因此堆放的米约有3203×1.62π≈22(斛).故选B.7.A AD ⃗⃗⃗⃗⃗ =AB ⃗⃗⃗⃗⃗ +BD ⃗⃗⃗⃗⃗⃗ =AB ⃗⃗⃗⃗⃗ +BC ⃗⃗⃗⃗⃗ +CD ⃗⃗⃗⃗⃗ =AB ⃗⃗⃗⃗⃗ +43BC ⃗⃗⃗⃗⃗ =AB ⃗⃗⃗⃗⃗ +43(AC ⃗⃗⃗⃗⃗ -AB ⃗⃗⃗⃗⃗ )=-13AB ⃗⃗⃗⃗⃗ +43AC ⃗⃗⃗⃗⃗ .故选A. 8.D 由题图可知T 2=54-14=1,所以T=2.结合题图可知,在[-34,54](f(x)的一个周期)内,函数f(x)的单调递减区间为(-14,34).由f(x)是以2为周期的周期函数可知,f(x)的单调递减区间为(2k -14,2k +34),k∈Z,故选D.9.C 第一次循环:S=1-12=12,m=14,n=1,S>t;第二次循环:S=12-14=14,m=18,n=2,S>t;第三次循环:S=14-18=18,m=116,n=3,S>t;第四次循环:S=18-116=116,m=132,n=4,S>t;第五次循环:S=116-132=132,m=164,n=5,S>t;第六次循环:S=132-164=164,m=1128,n=6,S>t;第七次循环:S=164-1128=1128,m=1256,n=7,此时不满足S>t,结束循环,输出n=7,故选C.10.C (x 2+x+y)5=[(x 2+x)+y]5的展开式中只有C 52(x 2+x)3y 2中含x 5y 2,易知x 5y 2的系数为C 52C 31=30,故选C.11.B 由已知可知,该几何体的直观图如图所示,其表面积为2πr 2+πr 2+4r 2+2πr 2=5πr 2+4r 2.由5πr 2+4r 2=16+20π,得r=2.故选B.12.D 由f(x0)<0,即e x0(2x0-1)-a(x0-1)<0得e x0(2x0-1)<a(x0-1). 当x0=1时,得e<0,显然不成立,所以x0≠1.若x0>1,则a>e x0(2x0-1)x0-1.令g(x)=e x(2x-1)x-1,则g'(x)=2xe x(x-32)(x-1)2.当x∈(1,32)时,g'(x)<0,g(x)为减函数,当x∈(32,+∞)时,g'(x)>0,g(x)为增函数,要满足题意,则x0=2,此时需满足g(2)<a≤g(3),得3e2<a≤52e3,与a<1矛盾,所以x0<1.因为x0<1,所以a<e x0(2x0-1)x0-1.易知,当x∈(-∞,0)时,g'(x)>0,g(x)为增函数,当x∈(0,1)时,g'(x)<0,g(x)为减函数,要满足题意,则x0=0,此时需满足g(-1)≤a<g(0),得32e≤a<1(满足a<1).故选D.评析本题主要考查导数的应用及分类讨论思想,分离参变量是解决本题的关键,本题综合性较强,属难题.二、填空题13.答案 1解析由已知得f(-x)=f(x),即-xln(√a+x2-x)=xln(x+√a+x2),则ln(x+√a+x2)+ln(√a+x2-x)=0,∴ln[(√a+x2)2-x2]=0,得ln a=0,∴a=1.14.答案(x-32)2+y2=254解析 由已知得该圆经过椭圆的三个顶点A(4,0)、B(0,2)、C(0,-2).易知线段AB 的垂直平分线的方程为2x-y-3=0.令y=0,得x=32,所以圆心坐标为(32,0),则半径r=4-32=52.故该圆的标准方程为(x -32)2+y 2=254.评析 本题考查圆和椭圆的方程,求出圆心坐标是解题关键. 15.答案 3解析 由约束条件画出可行域,如图.yx的几何意义是可行域内的点(x,y)与原点O 连线的斜率,所以yx 的最大值即为直线OA 的斜率,又由{x -1=0,x +y -4=0得点A 的坐标为(1,3),则(yx )max =k OA =3.16.答案 (√6-√2,√6+√2)解析 依题意作出四边形ABCD,连结BD.令BD=x,AB=y,∠CDB=α,∠CBD=β.在△BCD 中,由正弦定理得2sinα=xsin75°.由题意可知,∠ADC=135°,则∠ADB=135°-α.在△ABD 中,由正弦定理得xsin75°=ysin (135°-α).所以ysin (135°-α)=2sinα,即y=2sin (135°-α)sinα=2sin [90°-(α-45°)]sinα=2cos (α-45°)sinα=√2(cosα+sinα)sinα.因为0°<β<75°,α+β+75°=180°,所以30°<α<105°, 当α=90°时,易得y=√2; 当α≠90°时,y=√2(cosα+sinα)sinα=√2(1tanα+1),又tan 30°=√33,tan 105°=tan(60°+45°)=tan60°+tan45°1-tan60°tan45°=-2-√3, 结合正切函数的性质知,1tanα∈(√3-2,√3),且1tanα≠0,所以y=√2(1tanα+1)∈(√6-√2,√2)∪(√2,√6+√2). 综上所述:y∈(√6-√2,√6+√2).评析 本题考查了三角函数和解三角形.利用函数的思想方法是求解关键,属偏难题. 三、解答题17.解析 (Ⅰ)由a n 2+2a n =4S n +3,可知a n+12+2a n+1=4S n+1+3. 可得a n+12-a n 2+2(a n+1-a n )=4a n+1,即 2(a n+1+a n )=a n+12-a n 2=(a n+1+a n )(a n+1-a n ).由于a n >0,可得a n+1-a n =2.又a 12+2a 1=4a 1+3,解得a 1=-1(舍去)或a 1=3.所以{a n }是首项为3,公差为2的等差数列,通项公式为a n =2n+1.(6分) (Ⅱ)由a n =2n+1可知 b n =1an a n+1=1(2n+1)(2n+3)=12(12n+1-12n+3).设数列{b n }的前n 项和为T n ,则 T n =b 1+b 2+…+b n=12[(13-15)+(15-17)+…+(12n+1-12n+3)] =n3(2n+3).(12分)18.解析 (Ⅰ)连结BD.设BD∩AC=G,连结EG,FG,EF. 在菱形ABCD 中,不妨设GB=1.由∠ABC=120°,可得AG=GC=√3.由BE⊥平面ABCD,AB=BC,可知AE=EC.又AE⊥EC,所以EG=√3,且EG⊥AC. 在Rt△EBG 中,可得BE=√2,故DF=√22. 在Rt△FDG 中,可得FG=√62.在直角梯形BDFE 中,由BD=2,BE=√2,DF=√22,可得EF=3√22. 从而EG 2+FG 2=EF 2,所以EG⊥FG. 又AC∩FG=G,可得EG⊥平面AFC.因为EG ⊂平面AEC,所以平面AEC⊥平面AFC.(6分)(Ⅱ)如图,以G 为坐标原点,分别以GB ⃗⃗⃗⃗⃗ ,GC ⃗⃗⃗⃗⃗ 的方向为x 轴,y 轴正方向,|GB ⃗⃗⃗⃗⃗ |为单位长,建立空间直角坐标系G-xyz.由(Ⅰ)可得A(0,-√3,0),E(1,0,√2),F (-1,0,√22),C(0,√3,0),所以AE ⃗⃗⃗⃗⃗ =(1,√3,√2),CF ⃗⃗⃗⃗⃗ =(-1,-√3,√22).(10分) 故cos<AE⃗⃗⃗⃗⃗ ,CF ⃗⃗⃗⃗⃗ >=AE ⃗⃗⃗⃗⃗ ·CF ⃗⃗⃗⃗⃗ |AE ⃗⃗⃗⃗⃗ ||CF ⃗⃗⃗⃗⃗ |=-√33. 所以直线AE 与直线CF 所成角的余弦值为√33.(12分)评析 本题考查了线面垂直的判定和性质、面面垂直的判定、异面直线所成的角.建立适当的空间直角坐标系,利用空间向量的有关公式是求解的关键.证明“EG⊥平面AFC”是解题的难点.本题属中等难度题.19.解析 (Ⅰ)由散点图可以判断,y=c+d √x 适宜作为年销售量y 关于年宣传费x 的回归方程类型.(2分)(Ⅱ)令w=√x ,先建立y 关于w 的线性回归方程.由于 d ^=∑i=18(w i -w )(y i -y )∑i=18(w i -w )2=108.81.6=68,c ^=y -d ^w =563-68×6.8=100.6,所以y 关于w 的线性回归方程为y ^=100.6+68w,因此y 关于x 的回归方程为y ^=100.6+68√x .(6分)(Ⅲ)(i)由(Ⅱ)知,当x=49时,年销售量y 的预报值 y ^=100.6+68√49=576.6,年利润z 的预报值z ^=576.6×0.2-49=66.32.(9分) (ii)根据(Ⅱ)的结果知,年利润z 的预报值 z ^=0.2(100.6+68√x )-x=-x+13.6√x +20.12. 所以当√x =13.62=6.8,即x=46.24时,z ^取得最大值.故年宣传费为46.24千元时,年利润的预报值最大.(12分)20.解析 (Ⅰ)由题设可得M(2√a ,a),N(-2√a ,a)或M(-2√a ,a),N(2√a ,a).又y'=x2,故y=x 24在x=2√a 处的导数值为√a ,C 在点(2√a ,a)处的切线方程为y-a=√a (x-2√a ),即√a x-y-a=0.y=x 24在x=-2√a 处的导数值为-√a ,C 在点(-2√a ,a)处的切线方程为y-a=-√a (x+2√a ),即√a x+y+a=0.故所求切线方程为√a x-y-a=0和√a x+y+a=0.(5分) (Ⅱ)存在符合题意的点,证明如下:设P(0,b)为符合题意的点,M(x 1,y 1),N(x 2,y 2),直线PM,PN 的斜率分别为k 1,k 2. 将y=kx+a 代入C 的方程得x 2-4kx-4a=0. 故x 1+x 2=4k,x 1x 2=-4a. 从而k 1+k 2=y 1-b x 1+y 2-b x 2=2kx 1x 2+(a -b )(x 1+x 2)x 1x 2=k (a+b )a.当b=-a 时,有k 1+k 2=0,则直线PM 的倾斜角与直线PN 的倾斜角互补,故∠OPM=∠OPN,所以点P(0,-a)符合题意.(12分)21.解析 (Ⅰ)设曲线y=f(x)与x 轴相切于点(x 0,0),则f(x 0)=0,f '(x 0)=0,即{x 03+ax 0+14=0,3x 02+a =0.解得x 0=12,a=-34.因此,当a=-34时,x 轴为曲线y=f(x)的切线.(5分)(Ⅱ)当x∈(1,+∞)时,g(x)=-ln x<0,从而h(x)=min{f(x),g(x)}≤g(x)<0,故h(x)在(1,+∞)无零点.当x=1时,若a≥-54,则f(1)=a+54≥0,h(1)=min{f(1),g(1)}=g(1)=0,故x=1是h(x)的零点;若a<-54,则f(1)<0,h(1)=min{f(1),g(1)}=f(1)<0,故x=1不是h(x)的零点.当x∈(0,1)时,g(x)=-ln x>0,所以只需考虑f(x)在(0,1)的零点个数. (i)若a≤-3或a≥0,则f '(x)=3x 2+a 在(0,1)无零点,故f(x)在(0,1)单调.而f(0)=14,f(1)=a+54,所以当a≤-3时, f(x)在(0,1)有一个零点;当a≥0时,f(x)在(0,1)没有零点.(ii)若-3<a<0,则f(x)在(0,√-a 3)单调递减,在(√-a 3,1)单调递增,故在(0,1)中,当x=√-a 3时,f(x)取得最小值,最小值为f (√-a 3)=2a 3√-a 3+14. ①若f (√-a3)>0,即-34<a<0,f(x)在(0,1)无零点;②若f (√-a3)=0,即a=-34,则f(x)在(0,1)有唯一零点;③若f (√-a 3)<0,即-3<a<-34,由于f(0)=14,f(1)=a+54,所以当-54<a<-34时,f(x)在(0,1)有两个零点;当-3<a≤-54时,f(x)在(0,1)有一个零点.(10分)综上,当a>-34或a<-54时,h(x)有一个零点;当a=-34或a=-54时,h(x)有两个零点;当-54<a<-34时,h(x)有三个零点.(12分)22.解析 (Ⅰ)连结AE,由已知得,AE⊥BC,AC⊥AB.在Rt△AEC 中,由已知得,DE=DC,故∠DEC=∠DCE. 连结OE,则∠OBE=∠OEB.又∠ACB+∠ABC=90°,所以∠DEC+∠OEB=90°,故∠OED=90°,DE 是☉O 的切线.(5分) (Ⅱ)设CE=1,AE=x,由已知得AB=2√3,BE=2由射影定理可得,AE 2=CE·BE,所以x 2=√12-x 2,即x 4+x 2-12=0.可得x=√3,所以∠ACB=60°.(10分)23.解析 (Ⅰ)因为x=ρcos θ,y=ρsin θ,所以C 1的极坐标方程为ρcos θ=-2,C 2的极坐标方程为ρ2-2ρcos θ-4ρsin θ+4=0.(5分)(Ⅱ)将θ=π4代入ρ2-2ρcos θ-4ρsin θ+4=0,得ρ2-3√2ρ+4=0,解得ρ1=2√2,ρ2=√2,故ρ1-ρ2=√2,即|MN|=√2.由于C 2的半径为1,所以△C 2MN 的面积为12.(10分) 24.解析 (Ⅰ)当a=1时,f(x)>1化为|x+1|-2|x-1|-1>0. 当x≤-1时,不等式化为x-4>0,无解;当-1<x<1时,不等式化为3x-2>0,解得23<x<1;当x≥1时,不等式化为-x+2>0,解得1≤x<2.所以f(x)>1的解集为{x|23<x<2}.(5分)(Ⅱ)由题设可得,f(x)={x-1-2a,x<-1,3x+1-2a,-1≤x≤a, -x+1+2a,x>a.所以函数f(x)的图象与x轴围成的三角形的三个顶点分别为A(2a-13,0),B(2a+1,0),C(a,a+1),△ABC的面积为23(a+1)2.由题设得23(a+1)2>6,故a>2.所以a的取值范围为(2,+∞).(10分)。
2015年普通高等学校招生全国统一考试全国卷1(正文)
2015年普通高等学校招生全国统一考试(课标全国卷Ⅰ)理 数本卷满分150分,考试时间120分钟.第Ⅰ卷(选择题,共60分)一、选择题:本大题共12小题,每小题5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.设复数z 满足1+z 1-z=i,则|z|=( )A.1B.√2C.√3D.22.sin20°cos10°-cos160°sin10°=( ) A.-√32B.√32C.-12D.123.设命题p:∃n∈N,n 2>2n,则¬p 为( ) A.∀n∈N,n 2>2nB.∃n∈N,n 2≤2nC.∀n∈N,n 2≤2nD.∃n∈N,n 2=2n4.投篮测试中,每人投3次,至少投中2次才能通过测试.已知某同学每次投篮投中的概率为0.6,且各次投篮是否投中相互独立,则该同学通过测试的概率为( ) A.0.648B.0.432C.0.36D.0.3125.已知M(x 0,y 0)是双曲线C:x 22-y 2=1上的一点,F 1,F 2是C 的两个焦点.若MF 1⃗⃗⃗⃗⃗⃗⃗⃗ ·MF 2⃗⃗⃗⃗⃗⃗⃗⃗ <0,则y 0的取值范围是( ) A.(-√33,√33) B.(-√36,√36) C.(-2√23,2√23) D.(-2√33,2√33) 6.《九章算术》是我国古代内容极为丰富的数学名著,书中有如下问题:“今有委米依垣内角,下周八尺,高五尺.问:积及为米几何?”其意思为:“在屋内墙角处堆放米(如图,米堆为一个圆锥的四分之一),米堆底部的弧长为8尺,米堆的高为5尺,问米堆的体积和堆放的米各为多少?”已知1斛米的体积约为1.62立方尺,圆周率约为3,估算出堆放的米约有( )A.14斛B.22斛C.36斛D.66斛7.设D 为△ABC 所在平面内一点,BC⃗⃗⃗⃗⃗ =3CD ⃗⃗⃗⃗⃗ ,则( )A.AD ⃗⃗⃗⃗⃗ =-13AB⃗⃗⃗⃗⃗ +43AC ⃗⃗⃗⃗⃗ B.AD ⃗⃗⃗⃗⃗ =13AB⃗⃗⃗⃗⃗ -43AC ⃗⃗⃗⃗⃗ C.AD ⃗⃗⃗⃗⃗ =43AB⃗⃗⃗⃗⃗ +13AC ⃗⃗⃗⃗⃗D.AD⃗⃗⃗⃗⃗ =43AB ⃗⃗⃗⃗⃗ -13AC ⃗⃗⃗⃗⃗ 8.函数f(x)=cos(ωx+φ)的部分图象如图所示,则f(x)的单调递减区间为( )A.(kπ-14,kπ+34),k∈ZB.(2kπ-14,2kπ+34),k∈ZC.(k -14,k +34),k∈ZD.(2k -14,2k +34),k∈Z 9.执行下面的程序框图,如果输入的t=0.01,则输出的n=( )A.5B.6C.7D.810.(x 2+x+y)5的展开式中,x 5y 2的系数为( ) A.10B.20C.30D.6011.圆柱被一个平面截去一部分后与半球(半径为r)组成一个几何体,该几何体三视图中的正视图和俯视图如图所示.若该几何体的表面积为16+20π,则r=( )A.1B.2C.4D.812.设函数f(x)=e x(2x-1)-ax+a,其中a<1,若存在唯一的整数x 0使得f(x 0)<0,则a 的取值范围是( ) A.[-32e,1) B.[-32e ,34)C.[32e ,34) D.[32e,1)第Ⅱ卷(非选择题,共90分)本卷包括必考题和选考题两部分.第13题~第21题为必考题,每个试题考生都必须作答.第22题~第24题为选考题,考生根据要求作答. 二、填空题:本大题共4小题,每小题5分.13.若函数f(x)=xln(x+√a +x 2)为偶函数,则a= .14.一个圆经过椭圆x 216+y 24=1的三个顶点,且圆心在x 轴的正半轴上,则该圆的标准方程为 .15.若x,y 满足约束条件{x -1≥0,x -y ≤0,x +y -4≤0,则yx 的最大值为 .16.在平面四边形ABCD 中,∠A=∠B=∠C=75°,BC=2,则AB 的取值范围是 .三、解答题:解答应写出文字说明,证明过程或演算步骤. 17.(本小题满分12分)S n 为数列{a n }的前n 项和.已知a n >0,a n 2+2a n =4S n +3.(Ⅰ)求{a n }的通项公式; (Ⅱ)设b n =1a n a n+1,求数列{b n }的前n 项和.18.(本小题满分12分)如图,四边形ABCD 为菱形,∠ABC=120°,E,F 是平面ABCD 同一侧的两点,BE⊥平面ABCD,DF⊥平面ABCD,BE=2DF,AE⊥EC. (Ⅰ)证明:平面AEC⊥平面AFC;(Ⅱ)求直线AE 与直线CF 所成角的余弦值.19.(本小题满分12分)某公司为确定下一年度投入某种产品的宣传费,需了解年宣传费x(单位:千元)对年销售量y(单位:t)和年利润z(单位:千元)的影响.对近8年的年宣传费x i 和年销售量y i (i=1,2,…,8)数据作了初步处理,得到下面的散点图及一些统计量的值.x y w ∑i=18(x i -x )2∑i=18(w i -w )2∑i=18(x i -x )(y i -y ) ∑i=18(w i -w )(y i -y )46.65636.8289.81.61469 108.8表中w i =√x i ,w =18∑i=18w i .(Ⅰ)根据散点图判断,y=a+bx 与y=c+d √x 哪一个适宜作为年销售量y 关于年宣传费x 的回归方程类型?(给出判断即可,不必说明理由)(Ⅱ)根据(Ⅰ)的判断结果及表中数据,建立y 关于x 的回归方程;(Ⅲ)已知这种产品的年利润z 与x,y 的关系为z=0.2y-x.根据(Ⅱ)的结果回答下列问题: (i)年宣传费x=49时,年销售量及年利润的预报值是多少? (ii)年宣传费x 为何值时,年利润的预报值最大?附:对于一组数据(u 1,v 1),(u 2,v 2),…,(u n ,v n ),其回归直线v=α+βu 的斜率和截距的最小二乘估计分别为β^=∑i=1n(u i -u )(v i -v )∑i=1n(u i -u )2,α^=v -β^u .20.(本小题满分12分)在直角坐标系xOy 中,曲线C:y=x 24与直线l:y=kx+a(a>0)交于M,N 两点. (Ⅰ)当k=0时,分别求C 在点M 和N 处的切线方程;(Ⅱ)y 轴上是否存在点P,使得当k 变动时,总有∠OPM=∠OPN?说明理由.21.(本小题满分12分)已知函数f(x)=x 3+ax+14,g(x)=-lnx.(Ⅰ)当a 为何值时,x 轴为曲线y=f(x)的切线?(Ⅱ)用min{m,n}表示m,n 中的最小值,设函数h(x)=min{f(x),g(x)}(x>0),讨论h(x)零点的个数.请考生在第22、23、24题中任选一题作答,如果多做,则按所做的第一题计分.22.(本小题满分10分)选修4—1:几何证明选讲如图,AB是☉O的直径,AC是☉O的切线,BC交☉O于点E.(Ⅰ)若D为AC的中点,证明:DE是☉O的切线;(Ⅱ)若OA=√3CE,求∠ACB的大小.23.(本小题满分10分)选修4—4:坐标系与参数方程在直角坐标系xOy中,直线C1:x=-2,圆C2:(x-1)2+(y-2)2=1,以坐标原点为极点,x轴的正半轴为极轴建立极坐标系.(Ⅰ)求C1,C2的极坐标方程;(ρ∈R),设C2与C3的交点为M,N,求△C2MN的面积. (Ⅱ)若直线C3的极坐标方程为θ=π424.(本小题满分10分)选修4—5:不等式选讲已知函数f(x)=|x+1|-2|x-a|,a>0.(Ⅰ)当a=1时,求不等式f(x)>1的解集;(Ⅱ)若f(x)的图象与x轴围成的三角形面积大于6,求a的取值范围.。
全国重点高中提前招生考试全真卷5
全国重点高中提前招生考试全真卷(五)1.在互联网上用百度搜索“中央电视台每周质量报告”时,搜索到的下列被曝光的事件中,一定涉及化学变化的是()A.用毛发水、酱色、水、盐等兑制成“假酱油”B.用工业石蜡等涂抹在瓜子表面给瓜子“美容”C.用硫磺燃烧法熏蒸粉丝D.用淀粉、蔗糖、奶香精等掺和成“假奶粉”2.在物质混合、反应等过程中,存在着“1+1≠2”的有趣现象,通常情况下,下列各种物质混合或反应过程中,符合“1+1≠2”的是()A.1ml酒精与1ml水混合后的总体积B.1g碳与1g氧气反应后生成物的质量C.1g氢氧化钠溶液和1g硫酸溶液混合后溶液的质量D.1g饱和硝酸铵溶液中加入1g硝酸铵后所得溶液的质量3.氯碱工业是化学工业的基础,某化工厂电解饱和食盐水前,先要除去粗盐中Ca2+、Mg2+、SO42-及泥沙,可将粗盐溶于水,然后进行下列五项操作,其中正确的操作顺序是()①过滤②加过量的NaOH溶液③加适量盐酸④加过量Na2CO3溶液⑤加过量BaCl2溶液.A. ①④②⑤③B. ④①②⑤③C. ②④⑤①③D. ⑤②④①③4.往硝酸银和硝酸铜的混合液中加入一定量的铁粉,充分反应后过滤,向滤渣中加入稀盐酸,没气泡产生.根据上述现象,你得出的结论的是()A.滤渣中一定有铁粉B.滤渣中一定有铜粉C.滤液中一定有Fe2+D.滤液中一定有Ag+、Cu2+5.将一定量的丙醇(C3H8O)和氧气置于一个密闭的容器中引燃并充分反应,测得反应前后下列判断正确的是()A.表中a的值是3.8 B.X可能是炭黑C.X可能含有氢元素D.若起始时氧气的质量是14.4g,则无X生成A. CH4、NH3B. HCl 、CO 、H2C. HCl 、COD. HCl CO CO28.六硅酸镁可表示为aMgO·6SiO2·bH2O。
确定六硅酸镁组成的方法是:取10.6g六硅酸镁,充分加热失水后,得到固体8.8g;另取相同质量的六硅酸镁加入足量盐酸,充分反应后,经处理得SiO2固体7.2g.下列说法正确得是()A.a=2 B.a=3 C.b=5 D.b=7C.可能是一种分子和一种原子D.可能是两种不同的离子12.小明同学在总结酸、碱、盐之间的相互反应关系时发现,选用适当物质既可实现右图中所示的所有反应。
2015年普通高等学校招生全国统一考试(答案)
2015年普通高等学校招生全国统一考试(课标全国卷Ⅰ)一、选择题1.D 由已知得A={2,5,8,11,14,17,…},又B={6,8,10,12,14},所以A∩B={8,14}.故选D.2.A 根据题意得=(3,1),∴=-=(-4,-3)-(3,1)=(-7,-4).故选A.3.C 由已知得z=+1=2-i,故选C.4.C 从1,2,3,4,5中任取3个不同的数有10种取法:(1,2,3),(1,2,4),(1,2,5),(1,3,4),(1,3,5),(1,4,5),(2,3,4),(2,3,5),(2,4,5),(3,4,5),其中能构成一组勾股数的有1种:(3,4,5),故所求事件的概率P=,故选C.5.B 抛物线C:y2=8x的焦点坐标为(2,0),准线方程为x=-2.从而椭圆E的半焦距c=2.可设椭圆E的方程为+=1(a>b>0),因为离心率e==,所以a=4,所以b2=a2-c2=12.由题意知|AB|==2×=6.故选B.评析本题考查了椭圆、抛物线的方程和性质,运算失误容易造成失分.6.B 设圆锥底面的半径为R尺,由×2πR=8得R=,从而米堆的体积V=×πR2×5=(立方尺),因此堆放的米约有≈22(斛).故选B.7.B 由S8=4S4得8a1+×1=4×,解得a1=,∴a10=a1+9d=,故选B.评析本题主要考查等差数列的前n项和,计算准确是解题关键,属容易题.8.D 由题图可知=-=1,所以T=2,ω=π,又由题图知f =0,即+φ=+2kπ,k∈Z,得φ=+2kπ,k∈Z,此时f(x)=cos=cos,k∈Z,由2kπ<πx+<2kπ+π,k∈Z,得2k-<x<2k+,k∈Z,所以f(x)的单调递减区间为,k∈Z,故选D.9.C S=1-=,m=,n=1;S=-=,m=,n=2;S=-=,m=,n=3;S=-=,m=,n=4;S=-=,m=,n=5;S=-=,m=,n=6;S=-=,m=,n=7,此时不满足S>t,结束循环,输出n为7,故选C.10.A 当a≤1时,f(a)=2a-1-2=-3,即2a-1=-1,不成立,舍去;当a>1时,f(a)=-log2(a+1)=-3,即log2(a+1)=3,得a+1=23=8,∴a=7,此时f(6-a)=f(-1)=2-2-2=-.故选A.评析本题主要考查分段函数,指数与对数的运算,考查分类讨论的思想,属中等难度题.11.B 由已知条件可知,该几何体由圆柱的一半和半球组成,其表面积为2πr2+πr2+4r2+2πr2=5πr2+4r2.由5πr2+4r2=16+20π得r=2.故选B.12.C 在y=f(x)的图象上任取一点P(x0,y0),则P(x0,y0)关于直线y=-x对称的点为P'(-y0,-x0),所以P'必在y=2x+a的图象上,即-x0=,所以-y0+a=log2(-x0),所以y0=a-log2(-x0),所以f(x)=a-log2(-x),又f(-2)+f(-4)=1,所以2a-log22-log24=1,所以2a-1-2=1,解得a=2,故选C.二、填空题13.答案 6解析由已知得{an}为等比数列,公比q=2,由首项a1=2,S n=126得=126,解得2n+1=128,∴n=6.评析本题主要考查等比数列的定义及前n项和公式,属容易题,注意运算要准确哦!14.答案 1解析由题意可得f '(x)=3ax2+1,∴f '(1)=3a+1,又f(1)=a+2,∴f(x)=ax3+x+1的图象在点(1,f(1))处的切线方程为y-(a+2)=(3a+1)(x-1),又此切线过点(2,7),∴7-(a+2)=(3a+1)(2-1),解得a=1.15.答案 4解析由线性约束条件画出可行域,如图.解方程组得即A点坐标为(1,1).当动直线3x+y-z=0经过点A(1,1)时,z取得最大值,z max=3×1+1=4.16.答案12解析由已知得双曲线的右焦点F(3,0).设双曲线的左焦点为F',则F'(-3,0).由双曲线的定义及已知得|PF|=2a+|PF'|=2+|PF'|.△APF的周长最小,即|PA|+|PF|最小.|PA|+|PF|=|PA|+2+|PF'|≥|AF'|+2=17,即当A、P、F'三点共线时,△APF的周长最小.设P点坐标为(x0,y0),y0>0,由得+6y0-96=0,所以y0=2或y0=-8(舍去).所以当△APF的周长最小时,该三角形的面积S=×6×6-×6×2=12.三、解答题17.解析(Ⅰ)由题设及正弦定理可得b2=2ac.又a=b,可得b=2c,a=2c.由余弦定理可得cos B==.(6分)(Ⅱ)由(Ⅰ)知b2=2ac.因为B=90°,由勾股定理得a2+c2=b2.故a2+c2=2ac,得c=a=.所以△ABC的面积为1.(12分)评析本题考查了正弦定理、余弦定理;考查了解三角形的基本方法,属容易题.18.解析(Ⅰ)因为四边形ABCD为菱形,所以AC⊥BD.因为BE⊥平面ABCD,所以AC⊥BE.故AC⊥平面BED.又AC⊂平面AEC,所以平面AEC⊥平面BED.(5分)(Ⅱ)设AB=x,在菱形ABCD中,由∠ABC=120°,可得AG=GC=x,GB=GD=.因为AE⊥EC,所以在Rt△AEC中,可得EG=x.由BE⊥平面ABCD,知△EBG为直角三角形,可得BE=x.由已知得,三棱锥E-ACD的体积V E-ACD=×AC·GD·BE=x3=.故x=2.(9分)从而可得AE=EC=ED=.所以△EAC的面积为3,△EAD的面积与△ECD的面积均为.故三棱锥E-ACD的侧面积为3+2.(12分)19.解析(Ⅰ)由散点图可以判断,y=c+d适宜作为年销售量y关于年宣传费x的回归方程类型.(2分)(Ⅱ)令w=,先建立y关于w的线性回归方程.由于===68,=-=563-68×6.8=100.6,所以y关于w的线性回归方程为=100.6+68w,因此y关于x的回归方程为=100.6+68.(6分)(Ⅲ)(i)由(Ⅱ)知,当x=49时,年销售量y的预报值=100.6+68=576.6,年利润z的预报值=576.6×0.2-49=66.32.(9分)(ii)根据(Ⅱ)的结果知,年利润z的预报值=0.2(100.6+68)-x=-x+13.6+20.12.所以当==6.8,即x=46.24时,取得最大值.故年宣传费为46.24千元时,年利润的预报值最大.(12分)评析本题主要考查变量间的相关关系及回归分析,正确求出回归直线方程是解题关键,考查学生的运算求解能力,属中等难度题.20.解析(Ⅰ)由题设,可知直线l的方程为y=kx+1.因为l与C交于两点,所以<1.解得<k<.所以k的取值范围为.(5分)(Ⅱ)设M(x1,y1),N(x2,y2).将y=kx+1代入方程(x-2)2+(y-3)2=1,整理得(1+k2)x2-4(1+k)x+7=0.所以x1+x2=,x1x2=.(7分)·=x1x2+y1y2=(1+k2)x1x2+k(x1+x2)+1=+8.由题设可得+8=12,解得k=1,所以l的方程为y=x+1.故圆心C在l上,所以|MN|=2.(12分)21.解析(Ⅰ)f(x)的定义域为(0,+∞), f '(x)=2e2x-(x>0).当a≤0时, f '(x)>0, f '(x)没有零点;当a>0时,因为y=e2x单调递增,y=-单调递增,所以f '(x)在(0,+∞)上单调递增.又f '(a)>0,当b满足0<b<且b<时, f '(b)<0,故当a>0时, f '(x)存在唯一零点. (6分)(Ⅱ)由(Ⅰ),可设f '(x)在(0,+∞)上的唯一零点为x0,当x∈(0,x0)时, f '(x)<0;当x∈(x0,+∞)时, f '(x)>0.故f(x)在(0,x0)上单调递减,在(x0,+∞)上单调递增,所以当x=x0时, f(x)取得最小值,最小值为f(x0).由于2-=0,所以f(x0)=+2ax0+aln≥2a+aln.故当a>0时, f(x)≥2a+aln.(12分)评析本题主要考查利用导数求函数零点及利用导数研究不等式,考查分类讨论思想,是综合性较强的题,属难题!22.解析(Ⅰ)连结AE,由已知得,AE⊥BC,AC⊥AB.在Rt△AEC中,由已知得,DE=DC,故∠DEC=∠DCE.连结OE,则∠OBE=∠OEB.又∠ACB+∠ABC=90°,所以∠DEC+∠OEB=90°,故∠OED=90°,DE是☉O的切线.(5分)(Ⅱ)设CE=1,AE=x,由已知得AB=2,BE=.由射影定理可得,AE2=CE·BE,所以x2=,即x4+x2-12=0.可得x=,所以∠ACB=60°.(10分)评析本题考查了直线与圆的位置关系;圆的切线问题是本题的难点,利用射影定理建立方程是求解的关键.23.解析(Ⅰ)因为x=ρcos θ,y=ρsin θ,所以C 1的极坐标方程为ρcos θ=-2,C2的极坐标方程为ρ2-2ρcos θ-4ρsin θ+4=0.(5分)(Ⅱ)将θ=代入ρ2-2ρcos θ-4ρsin θ+4=0,得ρ2-3ρ+4=0,解得ρ1=2,ρ2=.故ρ1-ρ2=,即|MN|=.由于C2的半径为1,所以△C2MN的面积为.(10分)评析本题考查了极坐标方程,通过极径求出线段的长是解题关键.24.解析(Ⅰ)当a=1时,f(x)>1化为|x+1|-2|x-1|-1>0.当x≤-1时,不等式化为x-4>0,无解;当-1<x<1时,不等式化为3x-2>0,解得<x<1;当x≥1时,不等式化为-x+2>0,解得1≤x<2.所以f(x)>1的解集为.(5分)(Ⅱ)由题设可得, f(x)=所以函数f(x)的图象与x轴围成的三角形的三个顶点分别为A,B(2a+1,0),C(a,a+1),△ABC的面积为(a+1)2.由题设得(a+1)2>6,故a>2.所以a的取值范围为(2,+∞).(10分)。
全国重点高中提前招生考试全真卷1
全国重点高中提前招生考试全真卷(一)3.课本中的图表、数据等可以提供很多信息.下面有关的说法正确的是()①根据相对分子质量可比较气体的密度大小②“酸、碱、盐的溶解性表”是判断复分解反应能否发生的依据之一③根据不同物质的溶解度曲线图,可确定混合溶液的分离方法④根据某元素的原子结构示意图可判断该元素原子核内中子的数目A.①②④B.①③④C.②③④D.①②③4.某水溶液中含有以下离子中的若干种:K+、Cl—、Zn2+、Ca2+、SO42—、CO32-,现取两份100mL 溶液进行如下实验:(1)第一份加入AgNO3溶液有沉淀产生.(2)第二份加足量BaCl2溶液后,得沉淀物6。
63g,经足量硝酸洗涤、干燥后,沉淀质量为4。
66g,在所得滤液中加入AgNO3溶液有沉淀产生。
根据上述实验,以下推测不正确的是()A. Cl—一定存在B。
SO42-和CO32—一定存在,且二者的个数比为2:1C. Zn2+和Ca2+一定不存在D。
100mL溶液中K+的质量不小于2。
34g5.等质量的下列固体物质分别与一定质量的稀盐酸(溶质质量分数相同)恰好完全反应,下列说法正确的是()A.金属Al和Mg比较,Mg反应速度快,但生成氢气的质量少B.Mg和MgO比较,Mg消耗的盐酸的质量少,反应后溶液中溶质的质量分数小C.碳酸钠与碳酸氢钠比较,碳酸氢钠反应速度快,反应的稀盐酸的质量少D.CuO与Cu(OH)2比较,反应后溶液中的溶质的质量相等,溶液质量也相等6.根据事物的某些相似性类推其他的相似性,并预测类似的可能性,是我们经常使用的一种思维方法。
以下类推结果与实际相符的是()①氧化物中都含有氧元素,含有氧元素的化合物都是氧化物;②同一种元素的粒子质子数相同;质子数相同的粒子一定属于同种元素;③氢氧化钠溶液中有OH-,能与酸反应,氢氧化钾溶液中也有OH-,也能与酸反应;④盐中含有金属离子和酸根离子,NH4NO3中没有金属离子,不属于盐类⑤收集比空气轻的气体可用向下排空气法,能用向下排空气法的气体一定比空气轻;A.②③⑤B.③⑤C.①③④D.②③④7.向100g质量分数为3.65%的盐酸中逐滴加入4%的氢氧化钠溶液,同时测定有关数据下列图象正确的是(横坐标为每次加入氢氧化钠溶液的量)()8.两个或多个同种含氧酸分子之间可以脱水形成相对分子质量更大的酸,如磷酸H3PO4可形成H4P2O7或H5P3O10等.下列物质不属于硫酸(H2SO4)脱水后形成的是()A.H2S2O7B.H2S3O10C.H2S2O8D.H2S4O139.常温下,取下列各固体1g,分别与9克水充分混合,形成溶液,其中溶质的质量分数最小的是( )A.Na2O B.SO3C.CaO D.CuSO4•5H2O11.下列说法或数据,正确的是()A.用10ml量筒量取了7。
全国重点高中提前招生考试全真试卷物理(15)
全国重点高中提前招生考试全真试卷(十五)一、选择题(每小题4分,共40分)1.当坐在野外的篝火旁时,我们看到篝火后面的物体是晃动的,原因是( )A.视觉错误,因为火焰在跳动B.火焰加热空气,使空气密度不均匀且不稳定C.火焰作为光源在抖动,所以经后面物体反射的光也在晃动D.火焰加热了另一边的物体,使它热胀冷缩,所以看到它在晃动2.如图15-1所示,两端开口的弯管,左管插入水银槽中,右管有一段高为h的水银,中间封有一段空气则下列说法错误的是()A.弯管左管内外水银面的高度差为hB若把弯管向上移动少许,则管内气体体积增大C.若把弯管向下移动少许,右管内的水银柱沿管壁上升D.若环境温度升高,右管内的水银柱沿管壁上升3.加图15—2所示,在竖直放置的穹形光滑支架上根不可伸长的轻绳能过光滑滑轮悬挂一重物G,其一端固定于支架的A点,另一端从穹形顶端B沿支架缓慢地向C点靠近,C点与A点等高,在此过程中绳子上的拉力( )A.先变小后变大B.先变大后不变 C.先变小后不变D.先变大后变小4.用电钻给建筑物钻孔时,钻头所受阻力与深正比,当钻头匀速钻进时,所做的功与深度h的关系,图15—3中的图象表示正确的是()5.如图15-4所示,滑动变阻器的滑片在某两点移动时,电流表的示数范围在1A至2A之间,电压表的示数范围在6V至9V之间则定值电阻R的阻值及电源电压分别是( ) A.3Ω 15V B.6Ω,15VC.3Ω,12VD.6Ω,12V6.P、Q是两个由同种材料制成的底面积均为正方形的柱状型导体板,导体图P的底面积大于导体Q的底面积,现将两导体按如图15—5所示串联接到电源上,下列说法中正确的是()A.若P、Q的体积相同,则P的电阻值等于Q的电阻值B.若P、Q的体积相同,则通过P的电流大于通过Q的电流图C.若P、Q的厚度相同,则P两端的电压等于Q两端的电压D.若P 、Q 的厚度相同,则P 的电功率大于Q 的电功率7.有四个完全相同的均匀正方体木块放在水平桌上,现将甲、乙、丙截去完全相同的两截面均为正方形的长方体(图15—6中阴影部分)后,它们对桌面的压强分别为P 甲、P 乙、P 丙、P 丁,则( )A.P 丁>P 甲=P 乙=P 丙B.P 乙>P 丙>P 丁>P 甲C.P 乙>P 丙=P 丁>P 甲D.P 乙>P 丁>P 丙>P 甲8.如果不慎在照相机镜头上粘上一个灰尘颗粒(如图15—7),那么拍的相片( )A.其上部将出现一个黑点B.其下部将出现一个黑点 C.其上部和下部皆无黑点D.其上部和下部各出现一个黑点9.在如图15-8所示的装置中,A,B 两物体的质量均为1kg,物体A 置于光滑的水平桌面上,与物体A 相连的细绳呈水平状态,不考虑滑轮的摩擦和动滑轮、细绳的质量剪断与物体A 右端相连的细绳,物体B 下降1m 时(A 和定滑轮的距离足够远),物体A 的速度大小为( ) A.1m/s B.2m/s C.3m/sD.4m/s10.用电阻丝加热某种物质得到如图15-9所示的熔化图象电阻丝的发热的功率为P,放出的热量有50%被该物质吸收,该物质的质量为m,则这种物质比热容的大小为(假设这种物质固态和液体的比热容相同)( )A.小于)温温1314(2)(t t m t t P --B.大于)(2)(1314温温t t m t t P -- C.等于)(2)(1314温温t t m t t P -- D.等于2232)(温mt t t P -二、填空题(每小题6分,共24分)11.如图15—10所示,在一根很细的尼龙丝下悬挂一个小磁针,磁针的上方固定一面小平面镜,在镜子的前方,与镜面在同一高度处,固定了一根与镜面平行的刻度尺和光源。
2015年全国重点高中重点班招生考试训练卷及答案和详解2
2015年全国重点高中重点班招生考试训练卷2一.选择题:1.如图,当A 、B 两点间接入10欧的电阻时,电流表的示数I 1为0.5安,若A 、B 间改接20欧的电阻时,则电流表的示数I 为( )A. 0.125AB.0.25AC.0.36AD.0.5A2.2.如图①所示,一个电压恒定的电源跟一个电阻R 串联后,给电路供电,如图②中直线OAC 为该电源的输出功率P 出随电流I 变化的图象,抛物线OBC 为该电阻R 的热功率P R 随电流变化的图象,若A 、B 对应的横坐标为2A .则下列说法不正确的是( )A. 电源电压为3V ,电阻为1ΩB. 线段AB 表示的功率为2WC. 电流为3A 时,外电路电阻为0.2ΩD. 电流为2A 时,外电路电阻为0.5Ω3.如图,高度为L 、横截面积为s 的物块浮在盛水的杯内,杯内水的高度恰好为L .已知杯子的截面积为2s ,水密度为ρ0,物块密度为ρ0,用外力将物块按入水底,则外力所做的功至少是( )A. ρ0gsL 2B. ρ0gsL 2C. ρ0gsL 2D.ρ0gsL 24.如图所示,两个相同的光滑弧形槽,一个为A 1B 1C 1凸形,一个为 A 2B 2C 2凹形,两个相同小球分别进入两弧形槽的速度都为v ,运动到槽的末端速度也都为v ,小球通过凸形槽的时间为t 1,通过凹形槽的时间为t 2,则 t 1,、t 2的关系为( )A. t 1=t 2B. t 1>t 2C. t 1<t 2D. 无法确定5.如图所示,光线AB 经过某凸透镜的一个焦点,B 点在薄透镜上.已知F是该透镜的另一个焦点.若使用圆规和刻度尺来确定透镜的位置,则还需知道的条件是( )A. 光线AB 经过的焦点位置B. 透镜光心的位置C. 光线AB 经透镜后的折射光线D. 不需要任何条件6.夜晚,人们仰望天空,有时能看到闪烁的人造地球卫星.地球赤道处有一观察者,在日落4小时后看到一颗人造地球卫星从赤道正上方高空中经过,设地球半径为R ,则这颗人造地球卫星距赤道地面的高度至少为( )A. R/2B. RC. 2RD. 4R7. 太阳从东边升起,西边落下,是地球上的自然现象,但在某些条件下,在纬度较高地区上空飞行的飞机上,旅客可以看到太阳从西边升起的奇妙现象.这些条件是( )A. 时间必须是在清晨,飞机正在由东向西飞行,飞机的速度必须较大B. 时间必须是在清晨,飞机正在由西向东飞行,飞机的速度必须较大C. 时间必须是在傍晚,飞机正在由东向西飞行,飞机的速度必须较大D. 时间必须是在傍晚,飞机正在由西向东飞行,飞机的速度不能太大8.如图所示,位于凸透镜主光轴上某发光点P 发出红、黄、绿三色复光,当用与主光轴相垂直的毛玻璃屏从透镜附近沿轴方向向远移动时,在屏上将依次看到( )A. 红、黄、绿亮点B. 红、绿、黄亮点C. 黄、红、绿亮点D. 绿、黄、红亮点9.如图所示,一平面镜垂直于凸透镜的主光轴,位于凸透镜的2倍焦距处,在平面镜和凸透镜之间有一发光棒,当发光棒来回移动的过程中,处于某一位置时,整个系统成像的情况中不可能出现的是( )A. 一个实像和两个虚像B. 一个实像和一个虚像C. 两个虚像,无实像D. 两个实像和一个虚像10. 如图,一个劈形物体ABC 置于固定的光滑斜面上,AB 面光滑且水平,在AB 面上放一个小物体,现将ABC 由静止开始释放,则小物块在碰到斜面之前的运动轨迹是( )A. 沿斜面直线下落B. 竖直下落C.弧形下落D.折线下落11.如图所示,地球由西向东自转,赤道上某高处有一竖直的避雷针,当带有正电的乌云经过避雷针的上方时,避雷针开始放电,则此时地磁场对避雷针作用力的方向为( )A. 向东B. 向南C. 向西D. 向北12.装有金属球的小容器A 漂浮在盛有水的圆柱形大容器B 的水面上,所受的浮力为F 1,如图.若把金属球从A 中拿出投入水中沉到B 的底部时,小容器A 所受的浮力大小为F 2,池底对金属球的支持力大小为N ,那么以下错误的是( )A. 金属球所受重力的大小为F 1﹣F 2B. 小容器所受重力的大小为F 2C. 小容器所受浮力减小了ND. 大容器底部受水的压力减小了N13.如图,物体a 、b 和c 叠放在水平桌面上,水平为F b =5N ,F c =10N ,分别作用于物体b 、c上,a 、b 和c 仍保持静止,以f 1、f 2和f 3分别表示a 与b 、b 与c 、c 与桌面的静摩擦力大小,则( )A. f 1=5N ,f 2=0,f 3=5NB. F f1=5N ,F f2=5N ,F f3=0C.f 1=0,f 2=5N ,f 3=5ND.f 1=0,f 2=10N ,f 3=5N二.填空题:14.三电阻值均为10Ω的电阻R 1、R 2、R 3串联后接在电压恒为U 的电路中,某同学误将一只电流表并联在电阻R 2两端,如图,发现电流表示数为1.5A ,据此可知电源电压U 为 V .15.古代起重的一种辘轳如图所示.轴的大半径为R=30cm ,小半径为 r=20cm ,摇把离轴中心为L=50cm .若不计摩擦,滑轮,辘轳的重力的影响,要提升一重为G=500N 的重物,则摇把上的力F 至少为 .16.如图所示,电源电压为6V ,滑动变阻器R’的最大阻值为30Ω,当滑动变阻器R’的滑片P 在最右端时,电压表的示数为1.5V ,则小灯泡L 的电阻是 Ω.当滑动变阻器的滑片P 移到a 点时,电压表的示数为U a ,滑动变阻器的功率为P a ;再移动滑片P 到b 点时,电压表的示数为Ub ,滑动变阻器的功率为Pb.若Ua:Ub,=2:3,Pa:Pb=8:9,则滑动变阻器的滑片p在a、b两点时连入电路的电阻变化了Ω(不计灯丝电阻随温度的变化).17.夜里,在海洋的同一条航线上,甲、乙两船分别以5米/秒和10米/秒的速度相向而行.当两船相隔一定距离时,两船上的驾驶员同时拉响了汽笛,驾驶员在听到对方的汽笛声后立刻开亮自己船上的探照灯.若两船驾驶员探照灯打开的时间正好相隔0.2秒,则表明拉响汽笛时两船之间相距米,甲船亮灯时距离乙船米;乙船亮灯时距离甲船米.(已知空气中声音的传播速度为340米/秒)18.如图所示,重3N的甲物体和重12N的乙物体通过细线绕过定滑轮与丙物体连在一起,丙放在倾角为30°的光滑斜面上,整个装置处于静止状态.现将斜面变成粗糙的斜面,乙物体重量变为20N,其余不变,整个装置处于静止状态.则此时丙物体受到的摩擦力大小为N.(不计绳重和滑轮处摩擦)三.实验题:19. 实际的电源都有一定的电阻,如干电池,我们需要用它的电压U和电阻r两个物理量来描述它.实际计算过程中,可以把它看成是由一个电压为U、电阻为0的理想电源与一个电阻值为r的电阻串联而成,如图甲所示.实验室有一电源,电源电压约为3V、电阻不到1Ω.为了测量该电源的电压和电阻,现有两个电阻R1=15Ω,R2=5Ω,一量程为0.3A的电流表,并设计了如下的两种测量电路:乙和丙.(1)请选择可行的测量电路,理由是;(2)简要叙述实验步骤:;(3)根据测量数据和已知量,得到电源电压U= ,电源内阻r= .20. 将满偏电流Ig=300μA、内阻未知的电流表G改装成电压表并进行校准.①利用如图所示的电路测量电流表G的内电阻(图中电源的电动势E=4V),先闭合S1,调节R,使电流表指针偏转到满度;再闭合S2,保持R不变,调节R′,使电流表指针偏转到满度的,读出此时R′的电阻值为450Ω,则电流表内电阻的测量值Rg= Ω.②将该表改装成量程为3V的电压表,需(填“串联”或“并联”)阻值为R= Ω的电阻.③把改装好的电压表与标准电压表进行对照校准,试在答卷中对应的虚线框中画出实验原理图.四、解答题:21. 某一用直流电动机提升重物的装置,如图所示,重物质量m=50kg,电源的电压为U=110V,不计电源内阻及各处摩擦,当电动机以v=0.90m/s的恒定速度向上提升重物时,电阻中的电流I=5A,由此可知电动机的线圈的电阻R为多少?参考答案与试题解析一.选择题1. C. 2.逐个选项分析排除.故选C. 3. A. 4. B5.解答:由题意知,B在凸透镜上,AB经过焦点,连接BF,并延长,还是经过焦点,以B为圆心,BF为半径作圆,交AB上为F′,F′就是凸透镜的另外一个焦点,连接F′F,则F′F就是主光轴,过B作F′F的垂线,交F′F于O点,O就是该凸透镜的中心位置,再以OB画凸透镜就可以了,故选D.6.解答:如图所示:地球在4小时内转过的角度为×4=60°,由此可知是直角三角形,所以可以求得高度h=R.故选B.7. 解:由于地球自西向东旋转,故我们看到太阳从东边升起,西边落下.如果飞机向西飞行的速度等于地球自转的速度,旅客相对于太阳就是静止的,此时旅客看到的现象是太阳既不升起也不落下,所以我们要看到太阳从西边升起,必需要求乘客相对于地球向西运动,且飞机由东向西飞行的速度大于地球自转的速度.故C正确.8.解答:凸透镜镜对不同颜色光的折射率不同.玻璃对绿光的折射率比红光大,所以在屏上将依次看到绿、黄、红亮点.故选D.9.分析:发光物体在平面镜中成虚像,通过凸透镜可以成实像、也可以成实像,可以分别将物体放在1f 内、焦点上、f和2f之间进行分析.故选C.10.将ABC由静止开始释放后,支持力将小于重力,合力方向竖直向下,故选B.11. A. 12. C. 13. C.二.填空题14.解答:由电路图知,电流表与电阻R2并联时,电阻R2被短路,电流表与电阻R1、R3串联接入电路,电流表测电路电流,此时电路I=1.5A,电源电压U=U1+U3=IR1+IR3=1.5A×10Ω+1.5A×10Ω=30V;故为:30.15.解答:由图知,由两段绳子承担物重,所以每段绳子上的力是F′=G=×500N=250N.而要使物体G上升,从右看,应使轮轴沿逆时针方向转动.作用在大轴上的力使其向顺时针运动,小轴上的力使其沿逆时针方向转动.根据杠杆的平衡条件:F′•R=F′•r+F•L代入数据得:250N×30cm=250N×20cm+F×50cm解得:F=50N16. R L=10Ω;滑动变阻器的滑片P在a、b两点时连入电路的电阻变化了10Ω.17.解答:(1)s=4830m;(2)此时两船之间的距离:s′=s﹣△s=4830m﹣207m=4623m;(3)此时两船之间的距离:s′=s﹣△s=4830m﹣210m=4620m.18. 8N.三.实验题:19.(1)请选择可行的测量电路丙,理由是若选择乙图电路中的电流会超过电流表的量程;(2)简要叙述实验步骤:①闭合开关S1、S2,读出电流表示数为I1;②闭合开关S1,断开开关S2读出电流表示数为I2;(3)根据测量数据和已知量,得到电源电压r= .20. 将满偏电流I g=300μA、内阻未知的电流表G改装成电压表并进行校准.①利用如图所示的电路测量电流表G的内电阻(图中电源的电动势E=4V),先闭合S1,调节R,使电流表指针偏转到满度;再闭合S2,保持R不变,调节R′,使电流表指针偏转到满度的,读出此时R′的电阻值为450Ω,则电流表内电阻的测量值R g= 150Ω.②将该表改装成量程为3V的电压表,需串(填“串联”或“并联”)阻值为R0= 9850Ω的电阻.③把改装好的电压表与标准电压表进行对照校准,试在答卷中对应的虚线框中画出实验原理图.四、解答题:21.解:电动机消耗的总能量一部分用于提升重物的机械能,一部分消耗在电动机线圈电阻发热上.根据能量守恒定律得: P电=P机+P热,其中P电=IU,P机=mgv,P热=I2R,所以有IU=mgv+I2R,代入解得 R==4Ω。
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2015年全国重点高中提前招生考试全真试卷文科综合----英语部分(测评时间:45分钟满分:75分)一.单项选择(共15题,每小题1分,满分15分)从A,B,C,D四个选项中,选出可以填入空白处的最佳选项)1. ---Why didn’t Cindy play the violin at the concert last night.---She said her hand hurt, but that was only a(n)___.I saw her play tennis last night.(2014河北省重点高中自主招生试题)A. matterB. expressionC. resultD. excuse2. Her ___face suggested she____ high grades in the exams.A. exciting; achievedB. excited; achievedC. exciting: achieveD. excited: achieve3. ---Do you want David or Brown to do it ?-----_______is fit for the job, I’m afraid.(2015年黄冈中学理科实验班预录试题)A. EitherB. BothC. NoneD. Neither4. ----Do you know why he didn’t ____a word when he _____?------Because he was too nervous.A. speak ; speaksB. say; spokeC. say ; was spokenD. speak; is spoken5.---Dad, must we wait until the light becomes green?----Yes, I’m afraid we ______.That’s the traffic rule.(2014年温州高中自主招生模拟试题)A. mustB. mayC. have toD. need6.----I think it’s much more fascinating to do volunteer work than study indoors.-----__________________.(2014年华中师大一附中自主招生试题)A. You can’t say so.B. It doesn’t matter.C. I can’t agree more.D. It’s foolish to say so.7.Diaoyu Island are made up of a group of islands, _______China since ancient times.A. belong toB. belonged toC. are belonged toD. belonging to8.It will be two hours _______she can go out and enjoy the fresh air since she has a lot of housework to do .A. thatB. beforeC. untilD. since9. To get a better grade, you should _____ the notes again before the test.A. go overB. get overC. turn overD. take over10. The scientists got as _____as they could to the wild animals so as to watch them______.A. closely; closeB. close; closeC. close; closelyD. closely; closely11.We know that a smile is usually a sign ______people feel friendly andhappy, but ______we don’t know who the new person is?A. that ; what ifB. when ;whatC. when; how aboutD. if ;how12.------Isn’t Amy helpful to us all?-----__________.She always encourages us.A. No ; she isB. Yes; she isn’tC. No; she isn’tD. Yes; she is13. Many a student _____it hard to find an acceptable job after graduation in modern scientific society.A. find B . finds C. found D. have found14. Please make my excuse at tomorrow’s meeting----I’ve got too much work_____.A. to do to comeB. doing comingC. to do comingD. doing to come15.----Do you mind my building the house out of recycling materials, darling?------_________.I’d like a grand house to live in.A. Not at all.B. Go aheadC. You’d better not.D. Of course not二. 完型填空( 共20小题,每小题1分,满分20分)阅读下面短文,然后在各题所给的四个选项中选出一个最佳答案I was tired and hungry after a long day of work.When I walked into the living-room , my 12-year-old son looked _16____ at me and said , “ I love you.” I didn’t know what to say.__17___several seconds all I could do was to stand there and __18____ down at him. My first thought was that he must need __19____ with his homework or he was trying to __20____ me for some news.Finally I asked,” What was that all about?”“Nothing,”he said. “My teacher said we should ___21___ our parents that we love them and see what they say. It’s __22_____”The next day I called his teacher to find out more about this “experiment” and how the other parents had _23_____. “Most of the fathers had the _24____ reacting as you did,” the teacher said.” When I first __25____we try this, I asked the children what they thought their parents would say. Some of them thought their parents would have heart trouble. The ___26____ is,”the teacher explained, “feeling loved is an important part of __27_____.It is something all people__28_____. What I’m trying to tell the children is that it’s too __29____we don’t all express those feelings. A boy should be __30_____ to tell his dad h loves him.The teacher , a middle-aged man , understands how __31___ it isfor some of us to say the things that would be good for us to say. When my son came to me that evening, I held on to him for ___32____ second .And just before he pulled away ,I said in my deepest , most manly voice, “Hey, I love you ,too.”I don’t know if __33___ that made either of us healthier, but it did feel pretty good. Maybe next time one of my children said “I love you”, it would not take me a whole ___34___ to think of the right __35____.三.阅读理解。
(20小题,每小题2分,满分40分。
)A.Mr. Read was born in a small village which is surrounded(环绕)with high mountains.He has few fields and he can't get enough food for his family.He's often worried about it.So he works harder and harder and tries his best to get more money.One afternoon,Mr. Read went out to look for some grass for his cows.It was very hot and he had to have a swim .Suddenly he saw something sparkling(闪闪发光)in the water.He swam there and found it was some gold in the sand.He was so happy that he hardly forgot he was in the river.He ran home and asked his son to help him to get all the gold out of the water.The next morninghe sent his son to sell it in the markets.But the young man was afraid to do it.He had to go to the town himself.He didn't pay any attention to the traffic lights when he crossed the street.A car hit him down and he was hurt .He was sent to hospital at once.The doctors looked him over and had an operation on him .Two months later he felt much better.The doctors were satisfied with the operation and said ,“You'll .We're sure you can write with your right hand when you leave hospital.”“It's really a miracle(奇迹)!”shouted Mr Read,“I could neither read nor write before!”36.The Reads have little food because _________ .A.they live in a small villageB.They’re too lazy to workC.they have few fieldsD.Nobody would help them to get money37.Mr. Read ran home to _________ .A.ask for help B.make his family happy C.change the wet clothes D.send the gold back38.In Chinese the phrase “be fully recovered”means__________ .A.完全覆盖B.全部找回C.恢复疲劳D.恢复健康39. What the doctor said meant that ______________ .A. he did a very successful operationB. the farmer was lucky enough to write after the operationC. the accident helped the farmer to writeD. he taught the farmer to write while he was staying in hospitalBEarly one morning, more than a hundred years ago, an American inventor called Elias Howe finally fell asleep. He had been working all night on the design of a sewing machine but he had run into a very difficult problem: It seemed impossible to get the thread to run smoothly around the needle. Though he was tired, Howe slept badly. He turned and turned. Then he had a dream. He dreamt that he had been caught by terrible savages whose king wanted to kill him and eat him unless he could build a perfect sewing machine. When he tried to do so, Howe ran into the same problem as before. The thread kept getting caught around the needle. The king flew into the cage and ordered his soldiers to kill Howe. They came up towards him with their spears raised. But suddenly the inventor noticed something. There was a hole in the tip of each spear. The inventor awoke from the dream, realizing that he had just found the answer to the problem. Instead of trying to get the thread to run around the needle, he should make it run through a small hole in the center of the needle. This was thesimple idea that finally made Howe design and build the first really practiced sewing machine.Elias Howe was not the only one in finding the answer to his problem in this way.Thomas Edison, the inventor of the electric light, said his best ideas came into him in dreams. So did the great physicist Albert Einstein. Charlotte Bronte also drew in her dreams in writing Jane Eyre.To know the value of dreams, you have to understand what happens when you are asleep. Even then, a part of your mind is still working. This unconscious(无意识的), but still active part understands your experiences and goes to work on the problems you have had during the day. It stores all sorts of information that you may have forgotten or never have really noticed. It is only when you fall asleep that this part of the brain can send messages to the part you use when you are awake. However, the unconscious part acts in a special way. It uses strange images which the conscious part may not understand at first. This is why dreams are sometimes called “secret messages to ourselves”. ( ) 40. According to the passage, Elias Howe was________.A. the first person we know of who solved problems in his sleepB. much more hard-working than other inventorsC. the first person to design a sewing machine that really workedD. the only person at the time who knew the value of dreams ( ) 41.The problem Howe was trying to solve was________.A. what kind of thread to useB. how to design a needle which would not breakC. where to put the needleD. how to prevent the thread from getting caught around the needle( ) 42.Thomas Edison is spoken of because________.A. he also tried to invent a sewing machineB. he got some of his ideas from dreamsC. he was one of Howe’s best friendsD. he also had difficulty in falling asleep( ) 43. Dreams are sometimes called “secret messages to ourselves” because___.A. strange images are used to communicate ideasB. images which have no meaning are usedC. we can never understand the real meaningD. only specially trained people can understand themCSoon computers and other machines will be able to remember you by looking at your eyes! The program works because everyone’seyes are different. So in the future you won’t have to remember a number when you want to use a machine or take money out of a bank. You’ll just have to look at the machine and it will be able to tell who you are.The eye-recognition (眼睛识别)program is already being tested in shops and banks in the USA, Britain, Spain, Italy and Turkey. Soon this technology (技术)However, scientists are also working on other systems(系统). Machines will soon be able to know you from the shape of your face or hand or even your smell! We already have machines that can tell who you are from your voice or the mark made by your finger.Eye-recognition is better than other kinds because your eyes don’t change as you get older, or get dirty like hands or fingers, and even twins have different eyes. So the eye-recognition program can be up to 94% correct, depending on how good the technology is. Some programs may only be right 51% of the time. In Britain, it was found that 91% of people who had tried it said that they liked the idea of eye-recognition.In the future your computer will be looking you in the eye. So smile!( ) 44. How does the eye-recognition program work?A. You write your number.B. You show your ID card.C. You look at the machine.D. You say your name.( ) 45. Why can the program be up to 94% correct?A. Because eyes never change.B. Because hands or fingers can get dirty.C. Because people like the idea of the program.D. Because the program is widely used around the world.( ) 46. Which of the following is true?A. The program is being tested in Japan.B. Machines with other systems can also tell who you are.C. 91% of people like the idea of the program.D. Computers can remember you by looking at your clothes. ( ) 47. What does the underlined phrase “take the place of” in paragraph 2 mean?A. 拿走B. 取代C. 发生D. 安置DThe greatest recent changes have been in the lives of women. During the twentieth century there was an unusual shortening of the time of a woman’s life spent in caring for children. A woman marrying at the end of the 19th century would probably have been in her middle twenties, and would be likely to have seven or eightchildren, of whom four or five lived till they were five years old. By the time the youngest was fifteen, the mother would have been in her early fifties and would expect to live a further twenty years, during which custom, chance and health made it unusual for her to get paid work. Today women marry younger and have fewer children. Usually a woman’s youngest child will be fifteen when she is forty-five and is likely to take paid work until retirement at sixty. Even while she has the care of children, her work is lightened by household appliances and convenience foods.This important change in women’s way of life has only recently begun to have its full effect on women’s economic position. Even a few years ago most girls left school at the first opportunity and most of them took a full-time job. However, when they married, they usually left work at once and never returned to it. Today the school-leaving age is sixteen, many girls stay at school after that age, and though women tend to marry younger, more married women stay at work at least until shortly before their first child is born. Many more after wads, return to full or part-time work. Such changes have led to a new relationship in marriage, with both husband and wife accepting a great share of the duties and satisfaction of family life, and with both husband and wife sharing more equally in providing the money and running thehome, according to the abilities and interest of each of them. ( ) 48.We are told that in an average family about 1890________.A. many children died before they were fiveB. the youngest child would be fifteenC. seven of eight children lived to be more than fiveD. four or five children died when they were five( ) 49. When she was over fifty, the late 19th century mother________.A. would expect to work until she diedB. was usually expected to take up paid employmentC. would be healthy enough to take up paid employmentD. was unlikely to find a job even if she is now likely( ) 50. Many girls, the passage says, are now likely to ________.A. marry so that they can get a jobB. leave school as soon as they canC. give up their jobs for good after they are marriedD. continue working until they are going to have a baby( ) 51. According to the passage, it is now quite usual for women to ________.A. stay at home after leaving schoolB. marry men younger than themselvesC. start working again later in lifeD. marry while still at schoolEWINTER break! Two whole weeks without homework -two whole weeks of heaven. Two weeks to relax. I imagined myself getting plenty of sleep. I planned on reading "The Giver", which I hadn't had time to read.But soon I noticed something: I couldn't sleep. It would be 12:30 am and I would be trying to fall asleep. I would begin thinking that I haven't done anything today!This happened the next night, and the night after. During the day, when I had free time, I would be pacing (踱步) around the room moaning (抱怨) that I had nothing to do! I was eating when I wasn't hungry. I was playing a computer game even though it was boring.The truth, I concluded(总结), is that relaxation doesn't mean doing nothing. Relaxation means doing something enjoyable. I planned to swim at the local high school. I set up a practice schedule of an hour and a half per day. I decided to read two books that my friend had recommended (推荐) to me. I planned to do a little community(社区) service work, volunteering to help at the nearby old people's home for two hours every day. After doing those things, writing e-mails to my friends, watching DVDsand sleeping 12 hours a day, my days are full. And I'm truly enjoying myself relaxing.Of course, some of my earlier wishes have come true. Being free from schoolwork has taken a load off my mind, helped me to get in perspective (洞察力) and brought me back in touch with my family and myself. Getting so much sleep has done wonders for my state of mind.After each past winter break, I haven't been able to say what I did, how I used my time. This winter break will be different. I am relaxing by working.( ) 52. According to the passage, the writer had his/her vacation .A. for a monthB. for one weekC. for two weeksD. for six weeks ( ) 53. What was the writer's problem after a few days?A. He had no books to read.B. He couldn't fall asleep at night.C. He played too many computer games.D. He was always hungry.( ) 54. What did the writer do at first during his/her winter vacation?A. He/She paced around the room.B. He/She moaned and ate.C. He/She played a computer game.D. All the above.( ) 55. What does relaxation mean to the writer finally?A. Doing nothing at all.B. Getting 15 hours of sleep every day.C. Filling the days with fun things.D. Reading books all day long.。