2模四
浙江省杭州市第二中学2024学年高考英语四模试卷(含解析)
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浙江省杭州市第二中学2024学年高考英语四模试卷注意事项1.考生要认真填写考场号和座位序号。
2.试题所有答案必须填涂或书写在答题卡上,在试卷上作答无效。
第一部分必须用2B 铅笔作答;第二部分必须用黑色字迹的签字笔作答。
3.考试结束后,考生须将试卷和答题卡放在桌面上,待监考员收回。
第一部分(共20小题,每小题1.5分,满分30分)1.—Did you have difficulty finding Ann'house?—Not really.She___us clear directions and we were able to find it.easily?A.was to give B.had givenC.was giving D.would give2.We went right round to the west coast by sea instead of driving across continent。
A.the;the B./ ;the C.the;/ D./ ;/3.American singer Taylor Swift, 21, ________ big at the 2011 Academy of Country Music Awards in the US on April 3rd. A.stood B.gave C.scored D.made4.The Chinese people are hopeful for ________ 2019 will bring for their families and the country.A.how B.whichC.what D.that5.School children must be taught how to deal with dangerous ________.A.states B.conditionsC.situations D.positions6.Many writers are drawn to building a world, _____ readers are somewhat familiar with but also feel distant from our normal lives.A.it B.one C.that D.the one7.I believed him to be honest but his actions showed that he had ________.A.the top dog B.the feet of clayC.his cup of tea D.the apple of his eye8.—Going to watch the Women’s Volleyball Match on Wednesday?—________! Will you go with me?A.Y ou bet B.Y ou got meC.Y ou there D.Y ou know better9.-My computer doesn't work!-Robert is a computer expert. How I wish he______ with me.A.came B.had comeC.is coming D.has come10.Julia has got a pretty _ deal—she was laid off just for being late once!A.rough B.toughC.illegal D.mean11.— Could you turn the TV down a little bit?— ________. Is it disturbing you?A.Take it easy. B.I’m sorry. C.Not a bit D.It depends12.James Smith and his girlfriend went to Chenyi Square to celebrate the New Y ear, never _________.A.returned B.to returnC.returning D.having returned13.He was elected______ president of the company, and _____news came ,in fact, as ______surprise.A.a; the ;X B.X; the ; a C.a; X; the D.the; the; a14.—I say, Harry. What did you say to the laid-off worker just now?—Nothing. I to myself.A.had only talked B.am only talking C.have just talked D.was just talking15.I was expecting a present from her, so I was disappointed I didn’t receive ______.A.it B.one C.that D.the one16.Y ou will have to stay at home all day ______ you finish all your homework.A.if B.unless C.whether D.because17.Wolf Warrior 2, which ________ the “Award for Best Visual Effects” at the Beijing Film Festival, indicates China's film industry has come of age.A.wins B.wonC.has won D.had won18.No matter how carefully you plan your finances, no one can _______ when the unexpected will happen.A.prove B.implyC.demand D.predict19.—Didn’t you go fishing with your friends last Sunday?—No. I ______ to the nursing home as usual.A.went B.go C.have gone D.had gone20.Class Two, our class became the Basketball Champion of our school.A.Beating B.to beat C.Beaten by D.Having beaten第二部分阅读理解(满分40分)阅读下列短文,从每题所给的A、B、C、D四个选项中,选出最佳选项。
2025届西藏自治区拉萨市拉萨那曲第二高级中学高考英语四模试卷含解析
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2025届西藏自治区拉萨市拉萨那曲第二高级中学高考英语四模试卷注意事项:1.答卷前,考生务必将自己的姓名、准考证号填写在答题卡上。
2.回答选择题时,选出每小题答案后,用铅笔把答题卡上对应题目的答案标号涂黑,如需改动,用橡皮擦干净后,再选涂其它答案标号。
回答非选择题时,将答案写在答题卡上,写在本试卷上无效。
3.考试结束后,将本试卷和答题卡一并交回。
第一部分(共20小题,每小题1.5分,满分30分)1.Our company is seeking for a manager, especially ________ with creativity and imagination.A.the one B.eachC.one D.that2.you can learn to appreciate the challenges in life, you will find inner strength.A.When B.WhileC.Before D.Unless3.Hot the night air was,we slept deeply because we were so tired after the long journey.A.although B.while C.as D.however4.In Australia, many road signs are now both in English and Chinese, ______ it easier for Chinese tourists to travel. A.making B.made C.make D.makes5.I would persuade her to make room for you ______it be necessary.A.could B.mightC.should D.would6.—Oh, my God! What’s wrong with you?—I was going the normal speed limit when a truck appeared in front of me ________ and I didn't have time to stop. A.between the lines B.around the clockC.out of the blue D.over the moon7.The draft regulation on the online protection of minors, ________ for public opinions by the cyberspace authorities, has drawn wide public concern.A.releasing B.having releasedC.to release D.released8.-- Mom, I’ m going to the graduation dance tonight but I don’ t think I look attractive enough.—Oh, darling, don’ t worry. _______A.They don’t know what beauty is. B.Nobody will care about it.C.Y ou look perfect the way you are. D.Impossible is nothing,9.He asked ______ for the computer.A.did I pay how muchB.I paid how muchC.how much did I payD.how much I paid10.The maple trees turn a brilliant red in autumn, adding another to the colors in the harvest season. A.theme B.versionC.category D.dimension11.He had a great dearie to have a home of his own, ______ he had always lived with his grandmother.A.or B.and C.so D.for12.—I felt it very difficult to carry on the work all by myself.—I could have helped you, but you _____me to.A.hadn’t asked B.didn’t ask C.haven’t asked D.don’t ask13.My friend warned me ______ going to the East Coast because it was crowded with tourists.A.by B.against C.on D.for14.The art historians tried to figure out how the temple __________ when built around 15 B.C.A.might look B.might have looked C.must look D.must have looked15.---Do you think Peter is a good partner?--- Not really! There are some things that are not easy to ________ , and his laziness is one.A.put aside B.put up withC.think of D.get along with16.The palace is heavily guarded, because inside its walls ________.A.where sit the European leaders B.the European leaders there sitC.sit the European leaders D.that the European leaders sit17.—Do you know our town at all?—Surely, this is the third time I ________ here.A.came B.come C.have come D.am coming18.If you sleep less than seven hours, you are three times more to catch a cold.A.possible B.certainly C.probable D.likely19.---But for your timely warning, we into great trouble.---Well, you know we’re friends.A.would get B.must have got C.would have got D.can’t have got20.He would be in better health now _______ with too much work when young.A.had he not burdened himself B.if he was not burdenedC.were he not burdened D.had he not been burdened himself第二部分阅读理解(满分40分)阅读下列短文,从每题所给的A、B、C、D四个选项中,选出最佳选项。
2024年吉林省长春市二道区长春五十二中赫行实验学校中考四模数学试题
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2024年吉林省长春市二道区长春五十二中赫行实验学校中考四模数学试题一、单选题1.下列几何体中,其主视图和俯视图完全相同的是( )A .B .C .D . 2.计算-5+3的结果是( )A .2B .-2C .8D .-83.2022年6月4日我国发布了世界首幅月球全月地质图,其比例尺为1:2500000,该地质图上1cm 的距离在月球上的实际距离为( )A .52510cm ⨯B .62.510cm ⨯C .72.510cm ⨯D .70.2510cm ⨯ 4.《九章算术》是中国古代重要的数学著作,其中“方程术”记载:今有甲乙二人持钱不知其数.甲得乙半而钱五十,乙得甲太半而亦钱五十,问甲、乙持钱各几何?其大意为:甲、乙两人各有若干钱,如果甲得到乙所有钱的一半,那么甲共有50钱;如果乙得到甲所有钱的三分之二,那么乙也共有50钱.问甲、乙两人各有多少钱?设甲、乙分别有x 、y 钱,可列方程组为( )A .2503502x y x y +=⎧⎪⎨+=⎪⎩B .3502250x y x y ⎧+=⎪⎨⎪+=⎩C .15022503x y x y ⎧+=⎪⎪⎨⎪+=⎪⎩D .25031502x y x y ⎧+=⎪⎪⎨⎪+=⎪⎩ 5.如图,放风筝的人与风筝的水平距离AB 是90米,若拉紧的风筝线与水平线的夹角32CAB ∠=︒,则放出的线AC 的长度为( )A .90cos32︒米B .90cos32︒米C .90sin32︒米D .90sin 32︒米 6.如图,BC 为O e 的直径,AC 为O e 的切线,连结AB 交O e 于点D ,连结OD,若50DOC ∠=︒,则A ∠的大小为( )A .75︒B .65︒C .60︒D .50︒7.如图,在ABC V 中,72BAC =︒∠,AB AC =,根据尺规作图痕迹,下列结论不正确的是( )A .AD BD =B .90B BDE ∠+∠=︒C .AE CD = D .36BDE ∠=︒8.如图,平面直角坐标系中,线段AB 的两个端点坐标分别为()2,1A 、()2,5B ,点P 在线段AB 上,将线段PB 绕点P 顺时针旋转90︒得到线段PQ ,若点Q 在反比例函数k y x=的图象上,则k 的最大值为( )A .252B .494C .12D .10二、填空题9.分解因式:24m -=.10.若关于x 的一元二次方程220x x c ++=有两个相等的实数根,则实数c 的值为. 11.不等式35x +<的解集是.12.如图,已知,164,233AB CD ︒︒∠=∠=∥,则B ∠的度数为.13.将等腰直角三角板与量角器按如图所示的方式摆放,使三角板的锐角顶点与量角器的中心O 重合,且两条边分别与量角器边缘所在的弧交于A 、B 两点,若5OA =厘米,则»AB 的长度为厘米.(结果保留π)14.在平面直角坐标系中,抛物线()22y a x h =--(a 、h 为常数)与直线y m =(m 为常数)相交于A 、B 两点,若抛物线上有且只有一点C 到x 轴的距离与A 、B 两点到x 轴的距离相等,且ABC V 的面积为4,则a 的值为.三、解答题15.先化简,再求值:()()()331a a a a +-++,其中9a =.16.现有三张不透明卡片,其正面均印有南朝时期的瓷器图案.其中两张卡片的正面图案为“青瓷莲花尊”,第三张卡片的正面图案为“青瓷刻花单柄壶”,卡片除正面图案不同外,其余均相同.将这三张卡片背面向上洗匀,从中随机抽取一张,记录图案后放回.重新洗匀后再从中随机抽取一张,请用画树状图(或列表)的方法,求两次抽出卡片上的图案都是“青瓷刻花单柄壶”的概率.(图案为“青瓷莲花尊”的两张卡片分别记为1A 、2A ,图案为“青瓷刻花单柄壶”的卡片记为B )17.某校为增强学生体质,提倡学生参与体育运动,举办“阳光体育节”活动,九年级甲、乙两名同学在跳绳比赛中,甲同学跳480个的时间与乙同学跳450个所用时间相同.已知甲同学平均每分钟比乙同学多跳10个,问乙同学平均每分钟跳多少个?18.图①、图②、图③均是66⨯的正方形网格,每个小正方形的边长均为1,其顶点称为格点,ABC V 、FGH V 、PQR V 的顶点均在格点上,只用无刻度的直尺,在给定的网格中,按下列要求作图,保留作图痕迹.(1)图①中,点D 为边BC 的中点且在格点上,在边AC 上确定一点E ,连接DE ,使得DE AB ∥;(2)图②中,点I 为边GH 上一点且在格点上,在边FH 上确定一点J ,连接IJ ,使得IJ FG ∥;(3)图③中,点M 为边QR 上一点且在格点上,在边PR 上确定一点N ,连接MN ,使得MN PQ ∥.19.如图,在ABCD Y 中,AC BC ⊥,E 为CD 上一点,且12CE DE =,过点E 作EF AD ⊥于点F ,延长FE 交BC 的延长线于点G .(1)求证:四边形ACGF 是矩形;(2)连结BE ,若13AD AB =,则tan EBC ∠的值为______. 20.2022年是我国5G 牌照发放三周年,某活动小组收集了2011年至2020年的移动电话用户数量的数据,并根据数据制作了相应的统计图.(1)从2011年到2020年,我国移动电话用户数量最多的是______年,移动电话用户数量的中位数是______千万户;(2)从2018年到2019年,我国移动电话用户数量增长了______千万户;(3)从2011年到2020年,我国移动电话用户数量年增长率持续上升的阶段是______;(填序号)①2011年至2015年;②2015年至2018年;③2018年至2020年.(4)从2018年到2019年,我国移动电话用户数量年增长率下降,但移动电话用户数量却在增加,请说明理由.21.小明和小亮兄弟两人一起去上学,家到学校的路程为1500米,两人先一起匀速走了10分钟后,小明发现有重要物品遗落在家,立即匀速跑步回家,取到物品后立即以返回家的速度跑回学校(取物品的时间忽略不计),恰好与步行的小亮同时到达学校,两人距家的路程y(米)与两人离家的时间x(分)之间的函数关系如图所示.a______,b=______;(1)=(2)求小明返回家后,再次返回学校时y与x之间的函数关系式;(3)直接写出两人相距600米时x的值.22.【教材呈现】如图是数学教材华师版九年级上册第80页的部分内容.的中点,结合图①写出证明过程;【结论应用】如图①,设ADB α∠=,CBD β∠=,当点M 、P 、N 三点共线时,α、β满足的数量关系为______;【拓展延伸】如图②,在Rt ABC △中,D 、E 分别为AC 、BC 上的点,3AD BE ==,连结DE ,M 、N 分别为DE 、AB 上的点,连结MN ,若12DM AN ME NB ==,则MN 的值为______. 23.如图,在菱形ABCD 中,10AB =,16AC =,点E 为边AD 的中点,动点P 从点D 出发,沿折线DC CB -以每秒1个单位长度的速度向终点B 运动.连结PE ,作点D 关于直线PE 的对称点D ¢,连结ED '、PD ',设点P 的运动时间为t 秒.(1) DB =______;(2)用含t 的代数式表示线段CP 的长;(3)当点D ¢落在边AB 上时,求PBD '△的面积;(4)当线段ED '与AC 平行或垂直时,直接写出t 的值.24.在平面直角坐标系中,抛物线2y x bx c =++(b 、c 为常数)的对称轴为直线1x =,与y 轴交于点()0,1A -,点B 、C 在抛物线上,其横坐标分别为m ,2m +.(1)求该抛物线对应的函数表达式;(2)若0m >,当点A 、B 的纵坐标之差为1时,求点B 的坐标;(3)该抛物线在点B 、C 之间的部分(包括B 、C 两点)记作图象M ,设图象M 上的点的纵坐标为0y ,当021y -≤≤时,求m 的值;(4)过点B 作直线l y ⊥轴,将该抛物线在点B 右侧的部分沿直线l 翻折,得到的图象与该抛物线在点B 及点B 左侧的图象组成一个新图象记作图象N .当直线2y m =-与图象N 有三个公共点时,直接写出m 的取值范围.。
2024年甘肃省兰州市安宁区西北师大二附中中考数学四模试卷+答案解析
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2024年甘肃省兰州市安宁区西北师大二附中中考数学四模试卷一、选择题:本题共12小题,每小题3分,共36分。
在每小题给出的选项中,只有一项是符合题目要求的。
1.的相反数是()A.2B.C.D.2.把多项式分解因式得()A.B.C.D.3.用配方法解方程时,配方后正确的是()A.B.C.D.4.如图,直线,,,则的度数是()A. B. C. D.5.如图,在平面直角坐标系中,矩形OABC 的顶点O 在坐标原点,边OA 在x 轴上,OC 在y 轴上,如果矩形与矩形OABC 关于点O 位似,且矩形的面积等于矩形OABC 面积的,那么点的坐标是()A. B.C.或D.或6.大自然中有许多小动物都是“小数学家”,如图1,蜜蜂的蜂巢结构非常精巧、实用而且节省材料,多名学者通过观测研究发现:蜂巢巢房的横截面大都是正六边形.如图2,一个巢房的横截面为正六边形ABCDEF ,若对角线AD 的长约为8mm ,则正六边形ABCDEF 的边长为()A.2mmB.C.D.4mm7.如图,一条公路公路的宽度忽略不计的转弯处是一段圆弧,点O是这段弧所在圆的圆心,半径,圆心角,则这段弯路的长度为()A.B.C.D.8.《九章算术》是中国传统数学重要的著作,奠定了中国传统数学的基本框架.其中《盈不足》卷记载了一道有趣的数学问题:“今有共买物,人出八,赢三;人出七,不足四.问人数、物价各几何?”译文:“今有人合伙购物,每人出8钱,会多出3钱;每人出7钱,又差4钱.问人数、物价各多少?”设人数为x人,物价为y钱,根据题意,下面所列方程组正确的是()A.B.C.D.9.不透明布袋中装有除颜色外没有其他区别的1个红球和2个白球,搅匀后从中摸出一个球,放回搅匀,再摸出一个球,两次都摸出白球的概率是()A. B. C. D.10.如图1,汉代初期的《淮南万毕术》是中国古代有关物理、化学的重要文献,书中记载了我国古代学者在科学领域做过的一些探索及成就.其中所记载的“取大镜高悬,置水盆于其下,则见四邻矣”,是古人利用光的反射定律改变光路的方法,即“反射光线与入射光线、法线在同一平面上;反射光线和入射光线位于法线的两侧;反射角等于入射角”.为了探清一口深井的底部情况,运用此原理,如图在井口放置一面平面镜可改变光路,当太阳光线AB与地面CD所成夹角时,要使太阳光线经反射后刚好垂直于地面射入深井底部,则需要调整平面镜EF与地面的夹角()A. B. C. D.11.如图,在中,,,,以点B为圆心,BC长为半径画弧,与AB交于点D,再分别以A、D为圆心,大于的长为半径画弧,两弧交于点M、N,作直线MN,分别交AC、AB于点E、F,则AE的长度为()A.B.3C.D.12.如图,等边、等边的边长分别为3和开始时点A与点D重合,DE在AB上,DF在AC上,沿AB向右平移,当点D到达点B时停止.在此过程中,设、重合部分的面积为y,移动的距离为x,则y与x的函数图象大致为()A. B.C. D.二、填空题:本题共4小题,每小题3分,共12分。
2023年辽宁省高三第二次全省统考暨朝阳市第一高级中学高三四模考试历史试题
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2023年辽宁省普通高等学校招生选择性考试模拟试题(二)历史注意事项:1.答卷前,考生务必将自己的姓名、考生号等填写在答题卡和试卷指定位置。
2.回答选择题时,选出每小题答案后,用铅笔把答题卡上对应题目的答案标号涂黑。
如需改动,用橡皮擦干净后,再选涂其他答案标号。
回答非选择题时,将答案写在答题卡上。
写在本试卷上无效。
3.考试结束后,将本试卷和答题卡一并交回。
一、选择题:本题共16小题,每小题3分,共48分。
在每小题给出的四个选项中,只有一项符合题目要求。
1.据研究,在可辨认的甲骨文中,卜黍之辞100多条,黍字出现300多次,卜稷之辞30多条,稷字出现40多次。
古文献也多次提到黍稷,如《尚书·盘庚》:“惰农自安······不服田亩,越其罔有黍稷。
”《尚书·酒诰》:“其艺黍稷,奔走事厥考厥长”。
这反映了当时A.劳动人民的实践活动C.耕作技术的重大飞跃B.土地经营的基本方式D.劳动效率的逐步提高2.图1是秦汉王朝的人员结构。
这可以说明当时A.民众对王朝的认同C.协作制衡的运行机制3.隋文帝时期、唐朝的贞观年间与开元天宝年间,政治比较清明,社会比较安定,百姓负担较轻,但逃户与隐丁漏口现象都非常严重。
这一现象主要是由于D.地主土地所有制发展4.五代时期,慕葬壁画中表现贵族生活的列戟、仪仗、出行、马球、升仙、礼佛等图像渐趋减少,反映日常生活的画面逐渐增多。
这一变化反映了A.厚葬之风的衰落C.社会阶层的变动D.思想文化的多元5.明代中后期,司礼监、内阁、六科对应的权力分别是代行批红权、票拟权、封驳权。
批红之权属于皇帝本人,往往授权司礼监秉笔太监,但不由内阁票拟而中旨径出,六科是可以封驳的。
这体现出A.权力制衡关系的构建C.政府行政效率的提高B.君主专制进一步加强D.宦官专权的局面出现6.下表是对《红楼梦》的相关记述。
这反映了《红楼梦》A.危及专制统治政权C.普及到社会各个阶层B.成为一种社会风尚D.直接取材于现实生活7.据统计,19世纪中后期存在华商附股的外资企业共62家,涉及航运、保险、银行、货栈、房地产、铁路等多个行业,实收资本达万两。
2024年黑龙江省富锦市第二中学中考模拟四模数学试题
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2024年黑龙江省富锦市第二中学中考模拟四模数学试题一、单选题1.下列运算中,正确的是( )A .623a a a ÷=B .246a a a -=⋅C .()333ab a b =D .()426a a = 2.在以下绿色食品、回收、节能、节水四个标志中,是轴对称图形的是( ) A . B . C . D . 3.如图所示是由若干个相同的小立方体搭成的几何体的俯视图和左视图,则小立方体的个数不可能是( )A .5个B .6个C .7个D .8个4.一组大于1的正整数5,7,3,m ,7,6的中位数是5.5;唯一的众数是7,则这组数据的平均数是( )A .163B .316C .5或163D .5或112 5.有一个人患了流行性感冒,经过两轮传染后,共有196人患流行性感冒,则每轮传染中平均一人传染的人数是( )A .14B .13C .12D .116.已知关于x 的分式方程311m x x +--=1的解是非负数,则m 的取值范围是( ) A .m >2 B .m≥2 C .m≥2且m≠3 D .m >2且m≠3 7.周末,小明的妈妈让他到药店购买口罩和酒精湿巾,已知口罩每包3元,酒精湿巾每包2元,共用了30元钱(两种物品都买),小明的购买方案共有( )A .3种B .4种C .5种D .6种8.如图,点A 在函数2(0)y x x =>的图像上,点B 在函数3(0)y x x=>的图像上,且AB x ∥轴,BC y ∥轴于点C ,则四边形ABCO 的面积为( )A .1B .2C .3D .49.如图,菱形ABCD 的边长为24,对角线AC BD 、交于点O ,且AC AB =,E F ,分别是AB 和OD 的中点,EF 的延长线交CD 于点G ,则FG 的长是( )A .B .6CD .10.如图,正方形ABCD 中,G 是AD 边的延长线上一点,以CG 为对角线作正方形CFGE ,GE 的延长线交对角线AC 于点H ,连接BE DF ,,延长FG CD ,交于点M .下列结论:①BE AC ⊥;②AHG AGF ∠=∠;③AD DG +;④22CF CH AC =⋅.其中结论正确的序号有( )A .①②③B .①②④C .②③④D .①③④二、填空题11.据报道,发射“天宫一号”的“长征二号”火箭的起飞质量约为493500kg ,数字493500用科学记数法表示为 .12.函数y 中,自变量x 的取值范围是. 13.如图在四边形ABCD 中,AB CD ∥,AC 平分DAB ∠,要使四边形ABCD 为菱形可添加一个条件为.(只写出一个即可)14.一个不透明的口袋中装有标号为1、2、3的三个小球,这些小球除标号外完全相同,随机摸出1个小球,然后把小球重新放回口袋并摇匀,再随机摸出1个小球,那么两次摸出小球上的数字之和是奇数的概率是.15.关于x 的一元一次不等式组20345x a x ->⎧⎨-<⎩有解,则a 的取值范围是. 16.如图,已知O e 上三点A ,B ,C ,半径1OC =,30ABC ∠=︒,切线P A 交OC 延长线于点P ,则PA 的长为.17.底面直径为6的圆锥,母线长为9,则圆锥侧面展开图圆心角的度数为.18.如图,正方形ABCD 的边长为2,点E 是平面内动点,AE BE ,将BE 绕点E 顺时针旋转90︒得FE ,连接AF ,CF ,当AF 最大时,CF 的长为.19.在矩形ABCD 中,对角线AC BD ,相交于点O ,60AOB ∠=︒,2AB =,M 是直线BD 上的一个动点,当AMC V 为直角三角形时,CM 的长为.20.如图,A 是y 轴正半轴上的一点,且OA 的长度为1,以线段OA 为边作正方形得对角线1OC ,再以1OC 为边,作第二个正方形2OC ,再以2OC 为边作正方形对角线3OC ,再以3OC 为边作正方形对角线4OC ……以此类推,得正方形对角线2023OC ,则点2023C 的坐标是.三、解答题21.先化简,再求值:2246911a a a a a ++⎛⎫+÷ ⎪--⎝⎭,其中2cos601a =︒+. 22.如图,在平面直角坐标系中,已知ABC V 的三个顶点坐标分别是(2,1)A -,(1,2)B -,(3,3)C -.(1)将ABC V 向上平移5个点位长度,在向左平移4个点位长度,得到111A B C △,请画出111A B C △,并写出点1A 的坐标;(2)请画出ABC V 关于x 轴对称的222A B C V ,并写出点2A 的坐标;(3)将ABC V 绕着原点O 顺时针旋转90︒,得到333A B C △,求线段AC 在旋转过程中扫过的面积(结果保留π).23.如图,抛物线交x 轴于A ,B 两点,于y 轴交于点D ,C 是抛物线的顶点,已知点(3,0)B ,(1,4)-C .(1)求此抛物线的解析式;(2)连接AD ,P 是抛物线上一点,且点P 在直线BD 上方(与点A 不重合).若PBD ABD S S =V V ,求出点P 的坐标.24.某校计划开展以弘扬“文化自信”为主题的系列才艺展示活动,要求每位学生从绘画、合唱、朗诵、书法中自主选择其中一项参加活动为此,学校从全体学生中随机抽取了部分学生进行问卷调查,根据统计的数据,绘制了如下图所示的条形统计图和扇形统计图(部分信息未给出).请你根据图中所提供的信息,完成下列问题:(1)该校此次调查共抽取了__________名学生;(2)在扇形统计图中,“书法”部分所对应的圆心角的度数为__________.(3)请补全条形统计图(画图后标注相应的数据);(4)若该校共有2000名学生,请根据此次调查结果,估计该校参加朗诵的学生人数.,,三地,甲车从A地出发匀速行驶到C地,停留1小25.在一条笔直的公路上依次有A B C时后掉头(掉头时间忽略不计)按原路原速到达B地,同时乙车从B地出发匀速行驶到C 地.在两车行驶的过程中,甲、乙两车距B地的距离y(单位:千米)与甲车行驶时间x(单位:小时)之间的函数图像如图所示,请结合图像解决下列问题:(1)乙车的速度为________千米/时,B地与C地之间的距离为________千米;(2)求甲车从C地返回到B地过程中y与x的函数解析式,并直接写出自变量x的取值范围;(3)在两车行驶过程中,甲车行驶多长时间甲、乙两车距B地的距离相等?请直接写出答案.26.某手机经销商计划同时购进一批甲、乙两种型号手机,若购进2部甲型号手机和1部乙型号手机,共需要资金8400元;若购进3部甲型号手机和2部乙型号手机,共需要资金13800元.(1)求甲、乙型号手机每部进价各为多少元?(2)该店计划购进甲乙两种型号的手机销售,预计用不多于5.52万元且不少于5.28万元的资金购进这两种手机共20台,请问有几种进货方案?(3)若甲型号手机的售价为4500元,乙型号手机的售价为4200元,为了促销,无论采取哪种进货方案,公司决定每售出一台乙型号手机,返还顾客相同现金a元,而甲型号手机售价不变,要使(2)中所有方案获利相同,求a的值.27.如图,在平面直角坐标系中,矩形OABC的边OC在x上,OA在y轴上,,OA OC的长>),O D A C⊥于点E,交AB于点D.动点P从点分别是27120-+=的两个根(OC OAx x-向点C运动,到点C停止,过点P作OD的平A出发,以每秒一个单位长度的速度AB BC△的面积为s.行线,交AC于点M,令ACP(1)求点B的坐标;(2)求s关于t的函数解析式,并写出自变量t的取值范围;(3)在直线AC上是否存在点M,使A D M△是等腰三角形?若存在,请直接写出点M的坐标;若不存在,请说明理由.。
2020年辽宁省朝阳市重点高中高考数学四模试卷2 (含答案解析)
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2020年辽宁省朝阳市重点高中高考数学四模试卷2一、选择题(本大题共12小题,共60.0分) 1.2+i 1−i=( )A. 1+3i 2B.3+i 2C.3−i 2D.−1+3i 22. 已知集合A ={x|x 2=4},B ={x|ax =1},若B ⊆A ,则实数a 的值组成的集合为( )A. {−12,12}B. {−12,12,0}C. {−2,2}D. {−2,2,0}3. 若x =π4,x =3π4是函数f(x)=sinωx(ω>0)两个相邻的对称轴,则ω=( )A. 2B. 32 C. 1D. 12 4. 圆x 2+y 2−4x −4y +7=0上的动点P 到直线x +y =0的最小距离为( )A. 1B. √2C. 2√2D. 2√2−1 5. 等比数列{a n }中,a 2a 3a 4=1,a 6a 7a 8=64,,则a 5=( )A. 2B. −2C. ±2D. 46. 四人登珠穆朗玛峰,仅有一人登到峰顶,当他们被问到谁登到山顶时,甲说:“丙或丁登到峰顶”;乙说:“丙登到峰顶”;丙说:“甲和乙都没有登到峰顶”;丁说:“乙登到峰顶”,假设这四人只有两个人说的对,那么登到峰顶的是( )A. 甲B. 乙C. 丙D. 丁7. 已知m ,n 是直线,α,β是平面,以下命题正确的是( )A. 若α⊥β,α∩β=m ,n ⊥m ,则n ⊥α或n ⊥βB. 若α//β,m ⊄α,n//m ,则n//βC. 若m 上有两个点到α的距离相等,则m//αD. 若α∩β=m ,n//m ;且n ⊄α,n ⊄β,则n//α且n//β8. 已知[x ]表示不超过实数x 的最大整数,如[1.8]=1,[−1.2]=−2;x 0是函数f (x )=lnx −2x 的零点,则[x 0]等于( )A. 2B. 1C. 0D. −29. 某班级有一个学生A 在操场上绕圆形跑道逆时针方向匀速跑步,每52秒跑一圈,在学生A 开始跑步时,在教室内有一个学生B 往操场看了一次,以后每50秒往操场上看一次,则该学生B “感觉”到学生A 的运动是( )A. 逆时针方向匀速前跑B. 顺时针方向匀速前跑C. 顺时针方向匀速后退D. 静止不动10. 已知点P 是△ABC 所在平面内一点,且PB ⃗⃗⃗⃗⃗ =AB⃗⃗⃗⃗⃗⃗ +AC ⃗⃗⃗⃗⃗ 2,BC ⃗⃗⃗⃗⃗ =λAP⃗⃗⃗⃗⃗ ,则λ=( ) A. −2 B. −1 C. 1 D. 211.设双曲线C:x2a2−y2b2=1(a>0,b>0)的左,右焦点分别为F1,F2,直线x=a与C的渐近线的一个交点记为P,若|PF2|,|PF1|,|FF2|成等比数列,则C的离心率为() A. 4−√3 B. 2+√3 C. 4−√5 D. 2+√512.已知函数f(x)=ax +xlnx,g(x)=x3−x2−5,若对任意的x1,x2∈[12,2],都有f(x1)−g(x2)≥2成立,则a的取值范围是()A. (0,+∞)B. [1,+∞)C. (−∞,0)D. (−∞,−1]二、填空题(本大题共4小题,共20.0分)13.若f(x)是周期为2的奇函数,当0≤x≤1时,f(x)=2x(1−x),则f(2017.5)=______ .14.设(x−1)4(x+2)8=a0x12+a1x11+⋯+a n x+a12,则a2+a4+⋯+a12=______ .15.在△ABC中,内角A,B,C所对的边分别为a,b,c,已知(a+b−c)(a+b+c)=3ab,且c=4,则△ABC面积的最大值为_________.16.三棱锥P−ABC中,已知PA⊥底面ABC,∠BAC=60°,PA=43,AB=AC=2,若三棱锥的所有顶点都在同一个球面上,则该球的体积为______.三、解答题(本大题共7小题,共84.0分)17.(本题12分)已知等差数列{an }满足: a1+a2+a3=−3, a1⋅a2⋅a3=8.(1)求等差数列{an}的通项公式.(2)若a2,a3,a1成等比数列,求数列{|a n|}的前n项和.18.从某校随机抽取部分男生进行身体素质测试,获得掷实心球的成绩数据,整理得到数据分组及频率分布表,成绩在11.0米(精确到0.1米)以上(含)的男生为“优秀生”.(Ⅱ)从参加测试男生的成绩中,根据表中分组情况,按分层抽样的方法抽取10名男生的成绩作为一个样本,再从该样本中任选2名男生的成绩,求至少选出1名男生的成绩不低于13.0米的概率;(Ⅲ)若将这次测试的频率作为概率,从该校全体男生中随机抽取3人,记X表示3人中“优秀生”的人数,求X的分布列及数学期望.19.已知椭圆C:x2a2+y2b2=1(a>b>0)的离心率为√32,且经过点(0,1).(Ⅰ)求椭圆C的标准方程;(Ⅱ)已知直线l:y=kx+m(k≠0)与椭圆C相交于A,B两点,若以AB为直径的圆过椭圆C 的右顶点.求证:直线l过定点,并求出该定点的坐标.20. 如图,在四棱锥P −ABCD 中,已知PA ⊥平面ABCD 且四边形ABCD 为直角梯形,∠ABC =∠BAD =π2,PA =AD =2,AB =BC =1.(1)求平面PAB 与平面PCD 所成二面角的余弦值;(2)Q 是线段BP 上的动点,当直线CQ 与DP 所成的角最小时,求线段BQ 的长.21. 已知函数f(x)=alnx −x +1.(Ⅰ)若a =1时,求f(x)的单调区间和极值;(Ⅱ)当0<a ≤e +1e 时,若函数g(x)=f(x)+1x −1有两个极值点x 1,x 2(x 1<x 2),求g(x 2)−g(x 1)的最大值.22. 在平面直角坐标系xOy 中,曲线C 的参数方程为{x =1+costy =√3+sint (t 为参数).(Ⅰ)以坐标原点为极点,x 轴正半轴为极轴建立极坐标系,求曲线C 的极坐标方程; (Ⅱ)若射线θ=α与C 有两个不同的交点M 、N ,求证|OM|+|ON|的取值范围.23.选修4—5:不等式选讲已知函数f(x)=|x−2|+|2x+4|.(1)解不等式f(x)≥−3x+4;(2)若函数f(x)的最小值为a,m+n=a(m>0,n>0),求2020m+1008+2020n+1008的最小值.-------- 答案与解析 --------1.答案:A解析:解:2+i1−i =(2+i)(1+i)(1−i)(1+i)=2+3i+i22=12+32i.故选:A.直接利用复数代数形式的乘除运算化简得答案.本题考查复数代数形式的乘除运算,是基础的计算题.2.答案:B解析:【分析】本题主要考查了集合与集合的关系,属于基础题.由B={x|ax=1}且B⊆A可得集合B可能为⌀,{−2},{2},由此求解即可.【解答】解:x2=4,x=±2,由B={x|ax=1}且B⊆A,∴集合B可能为⌀,{−2},{2}①当a=0,B=⌀,适合条件,②若B={−2},则必有−2a=1,解得a=−12,③若B={2},则必有2a=1,解得a=12,综上所述,实数a的值组成的集合为.{−12,12,0}故选B.3.答案:A解析:【分析】本题考查三角函数的图象和性质,属于基础题.根据f(x)=sinωx(ω>0)两个相邻的对称轴之间的距离为半个周期,可得出周期T的值,从而可求解ω.【解答】解:由题意,∵x=π4,x=3π4是函数f(x)=sinωx(ω>0)两个相邻的对称轴,,解得T=π,故.故选A.4.答案:D解析:【分析】本题考查直线与圆位置关系的应用,考查点到直线距离公式的应用,是基础题.化圆的方程为标准方程,求出圆心坐标与半径,再求出圆心到直线的距离,则答案可求.解析:解:圆x2+y2−4x−4y+7=0化为(x−2)2+(y−2)2=1,圆心坐标为(2,2),半径为1.=2√2.圆心到直线x+y=0的距离d=√2∴圆x2+y2−4x−4y+7=0上的动点P到直线x+y=0的最小距离为2√2−1.故选:D.5.答案:A解析:【分析】本题考查了等比数列的通项公式与性质,考查了推理能力与计算能力,属于基础题.设等比数列{a n}的公比为q,由a2a3a4=1,a6a7a8=64,可得(q4)3=64,解得q2.又(a 1q 2)3=1,解得a1.利用通项公式即可得出.【解答】解:设等比数列{an}的公比为q,∵a2a3a4=1,a6a7a8=64,∴(q4)3=64,解得q2=2..又(a1q2)3=1,解得a1= 12×22=2.则a5= 1 2故选A.6.答案:D解析:【分析】本题考查了合情推理的应用,属于基础题.先假设甲、乙、丙、丁中的其中一个登上峰顶,然后再逐个去判断四个人的说法,最后看是否满足题意,不满足排除.【解答】解:如果登到峰顶的是甲,则四人说的都错了,与题设矛盾,故不是甲;如果登到峰顶的是乙,则只有丁说的是对的,与题设矛盾,故不是乙;如果登到峰顶的是丙,则甲,乙,丙说的是对的,与题设矛盾,故不是丙;如果登到峰顶的是丁,则甲,丙说的是对的,与题设相符,故是丁.故选D.7.答案:D解析:【分析】本题考查命题真假的判断,是中档题,解题时要注意空间思维能力的培养.利用空间中线线、线面、面面间的位置关系判断求解即可.【解答】解:在A中,α⊥β,α∩β=m,n⊥m,则n与α可能相交不垂直,故A错误;B中α//β,m⊄α,n//m,则n与β可能相交,故B不正确;C中m上有两个点到α的距离相等,当直线与平面相交时,交点的两侧等距的两点到平面的距离相等,故C不正确;D中若α∩β=m,n//m;且n⊄α,n⊄β,则n//α且n//β,满足直线与平面平行的判断定理,故D正确;故选:D.8.答案:A解析:∵f(x)=lnx−2x,则函数f(x)在(0,+∞)上单调递增,∴f(1)=ln1−2=−2<0,f(2)=ln2−1<0,f(3)=ln3−23>0,∴f(2)f(3)<0,∴函数f(x)=lnx−2x在区间(2,3)内存在唯一的零点∵x0是函数f(x)=lnx−2x的零点,∴2<x0<3,[x0]=2.9.答案:C解析:解:设操场周长为C,则学生B每隔50秒看一次,学生A 都与上一次的位置相距C26,且在上一次立足点的后面,据此判断得该学生B “感觉”到学生A 的运动是顺时针方向匀速后退的. 故选:C .设操场周长为C ,则学生B 每隔50秒看一次,学生A 都与上一次的位置相距C26,且在上一次立足点的后面,由此能求出结果.本题考查推理能力,考查进行简单的合情推理,考查学生分析解决问题的能力,正确解题的关键是读懂题意.10.答案:A解析:解:根据题意画出图形,如图所示; 以AB 、AC 为邻边作平行四边形ABDC , 连接AD ,交BC 于点O ,则AO ⃗⃗⃗⃗⃗ =12AD⃗⃗⃗⃗⃗⃗ =AB⃗⃗⃗⃗⃗⃗ +AC ⃗⃗⃗⃗⃗ 2, 又PB ⃗⃗⃗⃗⃗ =AB ⃗⃗⃗⃗⃗⃗ +AC ⃗⃗⃗⃗⃗ 2,∴AO ⃗⃗⃗⃗⃗ =PB ⃗⃗⃗⃗⃗ ,∴四边形APBO 是平行四边形; ∴AP ⃗⃗⃗⃗⃗ =OB⃗⃗⃗⃗⃗⃗ , 且OB ⃗⃗⃗⃗⃗⃗ =−12BC ⃗⃗⃗⃗⃗ ,BC ⃗⃗⃗⃗⃗ =λAP ⃗⃗⃗⃗⃗ , ∴λ=−2. 故选:A .根据题意画出图形,结合图形,利用平面向量的线性运算法则即可求出λ的值. 本题考查了平面向量的线性表示与运算问题,是基础题.11.答案:D解析:解:双曲线C :x 2a 2−y 2b 2=1(a >0,b >0)的左,右焦点分别为F 1(−c,0),F 2(c,0),直线x =a 与C 的渐近线bx −ay =0的一个交点P(a,b), 若|PF 2|,|PF 1|,|F 1F 2|成等比数列, 可得|PF 1|2=|PF 2|⋅|F 1F 2|,即为(a +c)2+b 2=√(a −c)2+b 2⋅2c , 由b 2=c 2−a 2,化为2c 2+2ac =√2c 2−2ac ⋅2c , 可得(c +a)2=2c 2−2ac ,化为c 2−4ac −a 2=0, 由e =ca ,可得e 2−4e −1=0, 解得e =2+√5(负值舍去), 故选:D .设出双曲线的焦点和渐近线方程,可得P 的坐标,再由等比数列中项性质,结合两点的距离公式和a ,b ,c 的关系,解方程可得所求离心率.本题考查双曲线的性质,主要是渐近线方程和离心率的求法,考查等比数列中项性质,以及方程思想和运算能力,属于中档题.12.答案:B解析: 【分析】本题主要考查不等式恒成立问题,属于难题.构造函数利用参数分离法结合函数单调性和导数之间的关系转化为求函数的最值是解决本题的关键.根据不等式恒成立,利用参数分类法进行转化为a ≥x −x 2lnx 在12≤x ≤2上恒成立,构造函数ℎ(x)=x −x 2lnx ,求函数的导数,利用函数单调性和 导数之间的关系求出函数的最值即可. 【解答】解:函数g(x)的导数g′(x)=3x 2−2x =x(3x −2),∴函数g(x)在[12,23]上递减,则[23,2]上递增, g(12)=18−14−5=−418,g(2)=8−4−5=−1,则g(x)在[12,2]上最大值为−1, 若对任意的 x 1,x 2∈[12,2],都有f(x 1)−g(x 2)≥2成立,即当12≤x ≤2时,f(x)−(−1)≥2恒成立,则f(x)≥1恒成立,即ax +xlnx ≥1恒成立, 即a ≥x −x 2lnx 在12≤x ≤2上恒成立,令ℎ(x)=x −x 2lnx ,则ℎ′(x)=1−2xlnx −x ,ℎ′′(x)=−3−2lnx , 当在12≤x ≤2时,ℎ′′(x)=−3−2lnx <0, 即ℎ′(x)=1−2xlnx −x 在12≤x ≤2上单调递减, 由于ℎ′(1)=0,∴当12≤x ≤1时,ℎ′(x)>0,当1≤x ≤2时,ℎ′(x)<0, ∴ℎ(x)≤ℎ(1)=1,∴a ≥1. 故选B .13.答案:−12解析:解:∵当0≤x≤1时,f(x)=2x(1−x),∴f(0.5)=1,2由f(x)是奇函数,,可得:f(−0.5)=−f(0.5)=−12由f(x)是周期为2的周期函数,,可得:f(2017.5)=f(−0.5)=−12.故答案为:−12根据已知中函数的周期性和奇偶性,可得f(2017.5)=f(−0.5)=−f(0.5),进而得到答案.本题考查函数的周期性,函数的奇偶性,函数求值,难度基础.14.答案:7解析:【分析】分别令x=1与x=−1即可求得a0+a2+a4+⋯+a12的值,而a0=1,从而可得答案.本题考查二项式定理的应用,考查二项式系数的性质,突出赋值法的应用,属于中档题.【解答】解:∵(x−1)4(x+2)8=a0x12+a1x11+⋯+a11x+a12,∴当x=1时,a0+a1+a2+⋯+a12=0,①当x=−1时,a0−a1+a2−⋯−a11+a12=16,②①+②得:2(a0+a2+a4+⋯+a12)=16,∴a0+a2+a4+⋯+a12=8;又含x12项的系数为1,即a0=1,∴a2+a4+⋯+a12=7.故答案为:7.15.答案:4√3解析:【分析】本题考查余弦定理、三角形面积公式和基本不等式,属于中档题.由余弦定理得∠C =60°,由基本不等式得ab ≤16,再由三角形面积公式即可得出结果. 【解答】解:∵(a +b −c )(a +b +c )=3ab , ∴a 2+b 2−c 2=ab , ∴cosC =a 2+b 2−c 22ab=ab 2ab =12,∵0°<C <180°, ∴∠C =60°, ∵a 2+b 2−c 2=ab ,∴16=a 2+b 2−ab ≥2ab −ab =ab , 即ab ≤16,当且仅当a =b =4时等号成立,∴△ABC 的面积S =12absinC =√34ab ≤√34×16=4√3,故答案为4√3.16.答案:256π81解析:【分析】本题考查球的体积的求法,解题时要认真审题,注意空间思维能力的培养,是中档题. 由题意求解底面ABC 外接圆的半径r ,利用球心到三个顶点距离相等求解球的半径R 可得结论. 【解答】解:由题意∠BAC =60°,AB =AC =2,可得△ABC 是等边三角形,可得外接圆的半径r =√3, ∵PA ⊥底面ABC ,PA =43, ∴球心与圆心的距离为23.该球的半径为R =√(23)2+r 2=43,该球的体积V =43πR 3=256π81,故答案为256π81.17.答案:解:(Ⅰ)设等差数列{a n }的公差为d ,则a 2=a 1+d ,a 3=a 1+2d ,由题意得{3a 1+3d =−3a 1(a 1+d )(a 1+2d )=8 解得{a 1=2d =−3或{a 1=−4d =3,所以由等差数列通项公式可得a n =2−3(n −1)=−3n +5,或a n =−4+3(n −1)=3n −7.故a n =−3n +5,或a n =3n −7.(Ⅱ)当a n =−3n +5时,a 2,a 3,a 1,分别为−1,−4,2,不成等比数列; 当a n =3n −7时,a 2,a 3,a 1,分别为−1,2,−4,成等比数列,满足条件; 故|a n |={−3n +7,n =1,23n −7,n ≥3记数列{|a n |}的前n 项和为S n ; 当n =1时,S 1=|a 1|=4; 当n =2时,S 2=|a 1|+|a 2|=5;当n ≥3时,S n =S 2+|a 3|+⋯+|a n |=5×(3×3−7)+(3×4−7)+⋯+(3n −7)=5+(n−2)[2+(3n−7)]2=32n 2−112n +10,当n =2时,满足此式;故综上,S n ={4 ,(n =1)32n 2−112n +10,(n ≥2).解析:本题考查等差数列的通项公式和求和公式的运用,考查等比数列中项的性质,考查方程思想和化简整理的运算能力,属于基础题.(1)设等差数列{a n }的公差为d ,运用等差数列的通项公式和性质,求得首项和公差,即可得到所求通项公式;(2)运用等比数列中项性质可得a 3=2,a 1=−4,a 2=−1,进而得到a n +7=3n ,运用等差数列的求和公式即可得到所求和.18.答案:解:(Ⅰ)第6小组的频率为1−(0.10+0.10+0.20+0.40)=0.10,∵第6小组的频数为10, ∴总人数为100.10=100(人).∴第5、6组的学生均为“优秀生”,人数为(0.40+0.10)×100=50(人). 即“优秀生”的人数为50.(Ⅱ) 根据分层抽样,在各组抽取的人数分别1人,1人,1人,2人,4人,1人. 其中成绩不低于13.0米的有1人.设事件A 为“至少1名男生成绩不低于13.0米”,则P(A)=C 91C 11C 102=15.∴选出的2名男生的成绩中至少有1名男生的成绩不低于13.0米的概率为15 (Ⅲ)从该校全体男生中任选一人,这个人是“优秀生”的概率为50100=12. 由题意知X 的可能取值为0,1,2,3.P(X =0)=C 30(12)0(12)3=18, P(X =1)=C 31(12)2(12)=38, P(X =2)=C 32(12)2(12)=38,P(X =3)=C 33(12)3(12)0=18.所求分布列为:∴EX =0×8+1×8+2×8+3×18=32解析:(Ⅰ)由频率分布直方图先求出第6小组的频率,由第6小组的频率为10,能求出总人数,由此能求出“优秀生”的人数.(Ⅱ)根据分层抽样,在各组抽取的人数分别1人,1人,1人,2人,4人,1人.其中成绩不低于13.0米的有1人.设事件A 为“至少1名男生成绩不低于13.0米”,利用排列组合知识能求出至少选出1名男生的成绩不低于13.0米的概率.(Ⅲ)从该校全体男生中任选一人,这个人是“优秀生”的概率为50100=12.由题意知X 的可能取值为0,1,2,3.分另求出相应的概率,由此能求出X 的分布列及数学期望.本题考查频率分布直方图、概率、离散型随机变量分布列及数学期望等基础知识,考查推理论证能力、运算求解能力,考查化归与转化思想、函数与方程思想,是中档题.19.答案:解:(Ⅰ)∵点(0,1)在椭圆上,∴b 2=1,即b =1.∵e =c a=√32,∴a 2−1a 2=34,解得a =2.∴椭圆的标准方程为x 24+y 2=1;(Ⅱ)设A(x 1,y 1),B(x 2,y 2),由{y =kx +mx 24+y 2=1,得(1+4k 2)x 2+8mkx +4(m 2−1)=0, △=64m 2k 2−16(1+4k 2)(m 2−1)>0,即1+4k 2−m 2>0. x 1+x 2=−8km1+4k 2,x 1x 2=4(m 2−1)1+4k 2.y 1⋅y 2=(kx 1+m)⋅(kx 2+m)=k 2x 1x 2+mk(x 1+x 2)+m 2=m 2−4k 21+4k 2.∵以AB 为直径的圆过椭圆的右顶点D(2,0),∴AD ⊥BD , ∴AD ⃗⃗⃗⃗⃗⃗ ⋅BD⃗⃗⃗⃗⃗⃗ =0, ∵AD ⃗⃗⃗⃗⃗⃗ =(2−x 1,−y 1),BD ⃗⃗⃗⃗⃗⃗ =(2−x 2,−y 2), ∴x 1x 2−2(x 1+x 2)+4+y 1y 2=0,即4(m 2−1)1+4k 2+16mk1+4k 2+4+m 2−4k 21+4k 2=0,即5m 2+16mk +12k 2=0,解得:m 1=−2k,m 2=−6k5,且满足1+4k 2−m 2>0. 当m =−2k 时,l :y =k(x −2),直线过定点(2,0),与已知矛盾; 当m =−6k5时,l :y =k(x −65),直线过定点(65,0).综上可知,直线l 过定点,定点坐标为(65,0).解析:(Ⅰ)由已知求得b ,结合离心率及隐含条件求得a ,则椭圆方程可求;(Ⅱ)联立直线方程和椭圆方程,化为关于x 的一元二次方程,利用根与系数的关系求得两点横纵坐标的乘积,再由向量数量积为0求得m 与k 的关系,分类求出直线方程可得直线l 过定点的坐标. 本题考查椭圆标准方程的求法,考查椭圆的简单性质,训练了直线与椭圆位置关系的应用,属中档题.20.答案:解:以{AB ⃗⃗⃗⃗⃗ ,AD ⃗⃗⃗⃗⃗⃗ ,AP ⃗⃗⃗⃗⃗ }为正交基底建立空间直角坐标系A −xyz ,其中B(1,0,0),C(1,1,0),D(0,2,0),P(0,0,2).(1)因为AD ⊥平面PAB ,所以AD ⃗⃗⃗⃗⃗⃗ 是平面PAB 的一个法向量,AD ⃗⃗⃗⃗⃗⃗ =(0,2,0). 因为PC⃗⃗⃗⃗⃗ =(1,1,−2),PD ⃗⃗⃗⃗⃗ =(0,2,−2). 设平面PCD 的一个法向量为m ⃗⃗⃗ =(x,y,z),则m ⃗⃗⃗ ⋅PC ⃗⃗⃗⃗⃗ =0,m ⃗⃗⃗ ⋅PD ⃗⃗⃗⃗⃗ =0,即{x +y −2z =0,2y −2z =0.令y =1,得x =1,z =1,所以m⃗⃗⃗ =(1,1,1)为平面PCD 的一个法向量, cos⟨AD ⃗⃗⃗⃗⃗⃗ ,m ⃗⃗⃗ ⟩=AD ⃗⃗⃗⃗⃗⃗⋅m ⃗⃗⃗ |AD ⃗⃗⃗⃗⃗⃗ ||m ⃗⃗⃗ |=√33. 所以平面PAB 与平面PCD 所成二面角的余弦值为√33.(2)因为BP ⃗⃗⃗⃗⃗ =(−1,0,2),设BQ ⃗⃗⃗⃗⃗⃗ =λBP ⃗⃗⃗⃗⃗ =(−λ,0,2λ)(0≤λ≤1),又CB ⃗⃗⃗⃗⃗ =(0,−1,0),则CQ ⃗⃗⃗⃗⃗ =CB⃗⃗⃗⃗⃗ + BQ ⃗⃗⃗⃗⃗⃗ =(−λ,−1,2λ),又DP ⃗⃗⃗⃗⃗ =(0,−2,2),从而cos⟨CQ ⃗⃗⃗⃗⃗ ,DP ⃗⃗⃗⃗⃗ ⟩=CQ ⃗⃗⃗⃗⃗ ⋅DP ⃗⃗⃗⃗⃗⃗|CQ ⃗⃗⃗⃗⃗ |⋅|DP ⃗⃗⃗⃗⃗⃗ |=√10λ2+2. 设1+2λ=t ,t ∈[1,3],则cos 2⟨CQ⃗⃗⃗⃗⃗ ⋅DP ⃗⃗⃗⃗⃗ ⟩=2t 25t 2−10t+9=29(1t −59)2+209≤910,当且仅当t =95,即λ=25时,|cos⟨CQ ⃗⃗⃗⃗⃗ ⋅DP ⃗⃗⃗⃗⃗ ⟩|的最大值为3√1010. 因为y =cos x 在(0,π2)上是减函数,此时直线CQ 与DP 所成角取得最小值, 又因为BP =√12+22=√5,所以BQ =25BP =2√55.解析:【分析】本题考查求二面角的三角函数值,考查用空间向量解决问题的能力,注意解题方法的积累,属于中档题.以A 为坐标原点,以AB 、AD 、AP 所在直线分别为x 、y 、z 轴建系A −xyz . (1)所求值即为平面PAB 的一个法向量与平面PCD 的法向量的夹角的余弦值的绝对值,计算即可; (2)利用换元法可得cos2<CQ ⃗⃗⃗⃗⃗ ,DP ⃗⃗⃗⃗⃗ >≤910,结合函数y =cosx 在(0,π2)上的单调性,计算即得结论. 21.答案:解:(Ⅰ)a =1时,f(x)=lnx −x +1,f′(x)=1x −1=1−x x,(x >0)令f′(x)>0,解得:0<x <1, 令f′(x)<0,解得:x >1, 故f(x)在(0,1)递增,在(1,+∞)递减, 故f(x)极小值=f(1)=0,无极大值.(Ⅱ)g(x)=f(x)+1x −1=alnx −x +1x ,(x >0) 则g′(x)=ax −1−1x2=−x 2+ax−1x 2,由已知,可得g′(x)=0,即方程−x 2+ax −1=0有2个不相等的实数根x 1,x 2(x 1<x 2),则{x 1+x 2=a x 1x 2=a △>0,解得x 1=1x 2,a =x 2+1x 2,a >2,其中0<x 1<1<x 2,而g(x 2)−g(x 1)=alnx 2−x 2+1x 2−alnx 1+x 1−1x 1=alnx 2x 1+(x 1−x 2)+(1x 2−1x 1) =(x 2+1x 2)lnx 22+1x 2−x 2+1x 2+x 2 =2[(1x 2+x 2)lnx 2+1x 2−x 2],由2<a ≤e +1e ,得2<x 2+1x 2≤e +1e ,又x 2>1,∴1<x 2≤e ,设t(x)=2(x +1x )lnx +2x −2x ,1<x ≤e , 则1−2x >0,lnx >0,∴t′(x)>0, ∴t(x)在(1,e]单调递增,∴当x =e 时,t(x)取得最大值,最大值为t(e)=4e .解析:(Ⅰ)求出函数的导数,解关于导函数的不等式,求出函数的单调区间和极值即可;(Ⅱ)g(x)=alnx −x +1x ,求出函数的导数,由此利用导数性质能求出当x =e 时,t(x)取得最大值.本题考查函数的单调性的讨论,考查实数的取值范围、函数最大值的求法,考查导数性质、构造法等基础知识,考查运算求解能力和思维能力,考查函数与方程思想,属于难题.22.答案:解:(Ⅰ)曲线C 的直角坐标方程为(x −1)2+(y −√3)2=1,即x 2+y 2−2x −2√3y +3=0,又x 2+y 2=ρ2,x =ρcosθ,y =ρ=sinθ,所以曲线C 的极坐标方程为ρ2−2(cosθ+√3sinθ)ρ+3=0.(Ⅱ)联立射线θ=α与曲线C ,得ρ2−2(cosα+√3sinα)ρ+3=0,设M(ρ1,α),N(ρ2,α), |OM|+|ON|=ρ1+ρ2=2(cosα+√3sinα)=4sin(α+π6), 又圆心C(1,√3)的极坐标为(2,π3),所以α的取值范围是π6<α<π2, 所以π3<α+π6<2π3,√32<sin(α+π6)≤1,2√3<4sin(α+π6)≤4, 所以|OM|+|ON|的取值范围为(2√3,4].解析:(Ⅰ)先消去参数得曲线C 的直角坐标方程再利用互化公式可得曲线C 的极坐标方程; (Ⅱ)利用极径的几何意义以及三角函数的性质可得. 本题考查了简单曲线的极坐标方程,属中档题.23.答案:解:(1)∵f(x)=|x −2|+|2x +4|,∴f(x)={−3x −2,x <−2x +6,−2≤x ≤23x +2,x >2,当x <−2时,不等式f(x)≥−3x +4,即为−3x −2≥−3x +4,即−2≥4,此时无解; 当−2≤x ≤2时,不等式f(x)≥−3x +4,即为x +6≥−3x +4,x ≥−12,∴−12≤x ≤2; 当x >2时,不等式f(x)≥−3x +4,即3x +2≥−3x +4,x ≥13,∴x >2. 综上所述,不等式f(x)≥−3x +4的解集为{x|x ≥−12}. (2)由(1)可知f(x)的最小值为4, ∴a =4, ∴m +n =a =4,∴2020m +1008+2020n +1008=m +1008+n +1008m +1008+m +1008+n +1008n +1008=2+n +1008m +1008+m +1008n +1008 ≥2+2√n+1008m+1008·m+1008n+1008=4.当且仅当m =n =2时等号成立.解析:本题考查绝对值不等式求解及利用基本不等式求最值.(1)对x分类去绝对值求解不等式即可;(2)求出f(x)的最小值,利用基本不等式求出最值即可.。
2024学年上海第二初级中学中考语文四模试卷含解析
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2024学年上海第二初级中学中考语文四模试卷注意事项:1.答卷前,考生务必将自己的姓名、准考证号填写在答题卡上。
2.回答选择题时,选出每小题答案后,用铅笔把答题卡上对应题目的答案标号涂黑,如需改动,用橡皮擦干净后,再选涂其它答案标号。
回答非选择题时,将答案写在答题卡上,写在本试卷上无效。
3.考试结束后,将本试卷和答题卡一并交回。
一、积累与运用1.下列各句中划线字的字音有误的一项是( )A.那朵红莲,被那繁密(mì)的雨点,打得左右攲(qī)斜。
在无遮蔽的天空之下,我不敢下台阶去,也无法可想。
B.这是达卡多拉游泳运动场的八千名观众一齐翘(qiào)首而望、屏息敛声的一刹(shà)那。
C.鸟儿将巢安在繁花嫩(nèn)叶当中,高兴起来了,呼朋引伴地卖弄清脆的喉咙,唱出宛转的曲子,跟轻风流水应和(hè)着。
D.只听咯(kā)吧一声,一丈青大娘折断了一棵茶碗口粗细的河柳,带着呼呼风声挥舞起来,把这几个纤(qiàn)夫扫下河去,就像正月十五煮元宵,纷纷落水。
2.下列关于名著的表述,不正确...的一项是()A.《三国演义》中曾温酒斩华雄、千里走单骑、刮骨疗毒,被后人尊为“武圣”的是关羽。
B.《简·爱》中的女主人公富有激情和反抗精神,有着对更高精神境界的追求。
C.《老人与海》中的小男孩儿从老人那里学到了捕鱼的本领和自尊自强的精神。
D.《草房子》中细马经历家境败落,在被迫辍学后,随父亲远走放鸭。
3.下列句子没有语病....、句意明确的一项是()A.马航MH370失踪后,许多中国大陆的游客纷纷取消去马来西亚旅游的预约。
B.在学习过程中,我们应该注意培养自己解决、分析、观察问题的能力。
C.通过在扬州钟书阁举办的《人间送小温》首发式,使更多年读者深入了解汪曾祺。
D.“天鲲号”不仅身躯庞大,而且拥有国际领先的智能集成控制系统。
4.下列词语中没有错别字的一项是()A.驻扎剃须刀按图索骥不容质疑B.坐标洽谈会包罗万象恻隐之心C.宣泄满堂采德高望重等闲之辈D.踊跃路由器逢场做戏甘拜下风5.选出下列文学常识表述有误的...一项()A.《诗经》是我国最早的一部诗歌总集,收录了从东周到春秋时期的诗歌305篇,这些诗歌分为“风”“雅”“颂”三部分。
广西壮族自治区南宁市第二中学2024届中考四模英语试题含答案
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广西壮族自治区南宁市第二中学2024届中考四模英语试题含答案注意事项1.考生要认真填写考场号和座位序号。
2.试题所有答案必须填涂或书写在答题卡上,在试卷上作答无效。
第一部分必须用2B 铅笔作答;第二部分必须用黑色字迹的签字笔作答。
3.考试结束后,考生须将试卷和答题卡放在桌面上,待监考员收回。
Ⅰ. 单项选择1、The place was so beautiful that her husband could not stop _____ photos. He took two hundred photos that day ! A.to show B.showing C.taking D.to take2、The popular restaurant is always crowded with people. You need to make a booking in advance.A.order food B.pay the bill C.arrive there D.make a reservation3、-- ____ people are there in your family, Jack?--Four. They are my father, my mother, my sister and I.A.How much B.How many C.How long D.How often4、visitors came to take photos of Hongyadong during the vacation.A.Thousand B.Thousand of C.Thousands D.Thousands of5、— Cindy never eats the food that ______ and often pours it away.—But it’s really wastefull to do so.A.stays B.keeps C.remains D.leaves6、—Do you know how to spell ______word “strength” in English?—Yes. It begins with ______“s”.A.The; a B.the; an C.a; the D.the ; the7、The little pet dog was so lovely. It ________ the heart of the lady.A.offered B.held C.expected D.won8、— ---Must I finish my homework now?----No, you _________. You ________ do it this evening.A.mustn’t; can B.needn’t; may C.c an’t; must D.needn’t; must to9、You won't succeed _____ you work hardA.if B.because C.unless D.so that10、Every day, _______ people wait to watch the raising of the national flag at Tian’anmen Square.A.thousands B.two thousands C.thousand of D.thousands ofⅡ. 完形填空11、One small thing changes(改变) Sonia. She always thinks of the boy, but 1 doesn't she help him?The boy wants to buy a book, but he can't because he has 2 money. He is not happy. He looks at the money in Sonia's hand. He can buy the 3 with it. But Sonia goes away. Sonia doesn’t know his idea, Then she comes back home. She 4 it to her brother David. David says,"" Why not give him money? He needs 5 ,and you canhelp him.Sonia 6 to that shop to look for that boy, but time never waits for(等待) her.On that day, Sonia 7 a lesson. Many people are like Sonia. We can help people a little sometimes, but we8 want to wait for big chances (机会). Big chances don t come at any time. But we 9 small ones every day.Sonia waits for 10 chances at first, but now she changes a lot. She also helps people with small things. 1.A.how B.why C.what2.A.some B.no C.much3.A.money B.food C.book4.A.brings B.sees C.says5.A.me B.us C.it6.A.wants B.has C.goes7.A.gets B.teaches C.likes8.A.don’ t B.always C.never9.A.have B.buy C.know10.A.good B.small C.bigⅢ. 语法填空12、Tu Youyou is a Chinese pharmaceutical chemist(药学家) and educator. She is best known for discovering artemisinin(青蒿素) which 1.(use) to treat malaria(疟疾) and has saved 2.(million) of lives. She won the Nobel Prize in Medicine in October 2015. She is the 3.(one) Chinese woman to win this prize.Tu was born in Ningbo, Zhejiang Province, China 4.December 30th, 1930. From 1951 to 1955, she attended Peking University Medical School. Later, Tu was trained for two and a half 5.(year) in traditional Chinese medicine. Now she is the Chief Scientist in the Academy(研究院) of Chinese Medicine in Beijing.Tu has some health problems as a result of working poor conditions for 6.long time. But she is still doing research. When Tu finally received Nobel Prize for her achievements, she said the success 7.(belong) to her team, which did research in those poor conditions. And she thinks artemisinin is a gift from China and from 8.(tradition) Chinese medicine to the world, to the millions and millions of people, 9.(especial) poor children, all over the world who have malaria.Tu Youyou is already 87 years old, 10.she says she won’t stop studying or working.Ⅳ. 阅读理解A13、Babies born after 2017 may never need to take a driving lesson because of the development of self-driving cars. Some scientists say that self-driving or driverless cars(无人驾驶汽车)may hit the road within 15 years, and it ispossible that driving may become unnecessary, or more relaxing and enjoyable.Companies like Google, Baidu, Apple and Alibaba are working on driverless cars. But, if the tests are successful, these electric self-driving cars could be put into use very soon. This kind of cars may change the way we live in the future. All you have to do is typing in your address!According to Baidu, the driverless technology has the following four advantages. Firstly, driverless cars are actually safer. In China, there are mom than 500 deaths caused by accidents. With driverless cars, the number will decrease by 100 times. Secondly, driverless cars are more efficient(有效的)than manned cars. Thirdly, driverless cars follow the traffic rules. Therefore, traffic controlling will be easier. At last, the cost of transportation will be reduced as the labor cost becomes less.There are many different technologies needed to make a successful self-driving car. The most difficult technologies of all, environmental perception(感知),behavior prediction, planning control, HD mapping, and exact GPS. 1.According to some scientists, driverless cars may make driving become _____________.A.necessary B.difficult C.boring D.enjoyable2.The third paragraph mainly talks about the ___________ of driverless cars.A.instructions B.standards C.advantages D.theories3.What can we learn from the passage?A.Driverless cars may not follow the traffic rules.B.The technologies for driverless cars haven't yet well developed.C.The communication between the car and a man is perfect.D.Driverless cars will have more accidents than man-controlled cats.B14、It was summertime. Donna walked into the classroom. “ Good afternoon, everybody !” That was a joke Donna told every day. Usually the class started with only two or three students in the classroom, and then the other students came as the minutes went by.Donna knew that the students didn’t like studying English. The head teacher had told her the reason. The students thought English was confusing.Donna waited until all the students were sitting in their seats. She smiled a nd said, “ Okay, well. Let’s get started. Please turn to Page 36. Today we’re studying participles as adjectives(分词作形容词). Students often feel confused when they learn about the present and past participles, so we need to practice a lot. Today, we’re just going to practice using present p articiples as adjectives.” Donna looked at all the blank faces around the classroom. Then she wrote two sentences on the blackboard.“ The present participle tells us what kind of emotion the subject(主语)is causing. For example, when we say‘grammar is boring’, we mean that the subject—grammar —causes an emotion of boredom. If we say, ‘The movie is interesting’, we are saying that the movie causes an emotion of interest. Any questions so far ? Is anyone confused ? ”The classroom was quiet. Donna knew it would take some time for everyone to understand what she was talking about. After a while, Donna got a little excited because she saw looks of understanding on some of the students’ faces. 1.When did the story take place ?A.On a spring morning. B.On a winter afternoon.C.On a summer afternoon. D.On an autumn evening.2.How did Donna explain the usage of present participles as adjectives ?A.By telling a story. B.By asking questions.C.By giving examples. D.By showing a movie.3.Why was the classroom quiet ?A.Because the students were afraid of Donna.B.Because Donna asked the students to be quiet.C.Because the students were doing their homework.D.Because the students didn’t understand what Donna was saying.4.From the passage, we can learn that Donna was a____ .A.teacher B.host C.writer D.reporteC15、Mr. and Mrs. Smith have just opened a small restaurant. In order to attract customers, they put a notice in front of the restaurant, which s aid: “Meals on the house for three days.”A foreign student who didn’t know much English passed by the restaurant on the second day. It was lunchtime and he felt hungry. “Well, here is a restaurant. I’m going to have something to eat,” he said.He saw the notice when he walked towards the restaurant. “American people are really strange. They even eat dinners on the hous e! But how can I get onto the top of the house?” he asked himself. He looked around and found a ladder(梯子) against a tree nearby. He was very glad. But as he reached the top, he heard someone shouting at him, “Hey, what are you doing up there?”Mr. Smith w as looking at him angrily. Beside him was a policeman. “Doesn’t your notice say …Meals on the house for three days’? Is it just a joke?” the foreign student answered. On hearing this, both Mr. Smith and the policeman burst into laughter. Do you know the m eaning of “on the house”?1.The Smiths have __________.A.opened a restaurant B.built a houseC.climbed onto the top D.been policemen2.Why do Mr. and Mrs. Smith put up the notice?A.Because they wanted to attract policemenB.Because they wanted people to eat on the roofC.Because they wanted to attract more customersD.Because they liked to play jokes3.The student walked past the restaurant ___________.A.when the Smiths started their businessB.when the Smiths put on the noticeC.when the policeman came to the restaurantD.when it was time to have lunch4.The student _________, so Mr. Smith shouted at him.A.was very hungry B.knew little about EnglishC.climbed onto the top of the house D.took away the ladder5.“On the house” may mean that the meal _____________.A.is taken on the house B.is paid on the houseC.is made on the house D.is free for the customersD16、2018 is the Year of the Dog. Although dogs are seen as friends and part of the family today, China and Western countries have different cultural beliefs about dogs.In Chinese, some words about dogs have derogatory meaning, such as “Lead a dog’s life.” In English, however, the situation is different. People use “every dog has his day” to describe a period of good luck, “work like a dog” to describe a h ard worker and “a gay dog” to describe a happy person.The dog-human relationship goes right back to the beginnings of Western civilization. Perhaps the most moving example is from the 8th century BC, in Greek poet Homer’s The Odyssey. When Greek hero Odys seus finally returnshome after 20 years away at war, no one but his dog Argos recognizes him. The Argos is an old, sick dog, and is about to die; but he is overjoyed to see his owner again after so many years.In fact, people were close to dogs in away t hey weren’t close to cows, pigs or even horses. Farmers worked closely with dogs. But even after science came to agriculture and dogs lost their traditional roles, the relationship between men and dogs remained.Nowadays in the West, millions of people keep dogs as pets. They are at the heart of family life. People feed them, take them on holidays and look after them. In return, dogs are loyal in a way that friends sometimes aren’t. This loyalty is the origin of the English saying, “A dog is man’s best friend.”1.Which may be a saying about dogs in China?A.A gay dog. B.Lead a dog’s life.C.Work like a dog. D.Every dog has its day.2.The story of Odysseus and his dog is moving because .A.the dog will die in two years B.he is overjoyed to see his dog againC.only the dog recognizes him after the war D.he returns home after twenty years away at war3.What happened to dogs after science came to agriculture?A.Farmers worked closely with dogs. B.They still kept their traditional roles.C.People preferred pigs and horses to dogs. D.Men and dogs remained in good relationship.4.What can we know from the passage?A.All people keep dogs as pets in western countries. B.In fact, dogs may be more loyal than some friends. C.Argos was a great Greek hero in the 8th century BC.D.China and England have the same beliefs about dogs.E17、What are you going to do if you are in a burning house? How will you escape? Do you know how to save yourself? Please read the following passage.Escaping a fire is a serious matter.Knowing what to do during a fire can save yourself.It is important to know the ways you can use and to show them to everyone in the family, such as stairways (楼梯)and fire escapes, but not lifts.From the lower floors of the building, escaping through windows is possible, learn the best way of leaving through windows with the least chance of serious injury (伤害).The second floor windows are usually not very high from the ground.An average (普通的)person, hanging by the finger-tips will have a drop of about six feet to the ground.It is about the height of an average man.Of course, it is safer to jump a short way than to stay in a burning building.Windows are also useful when you are waiting for help.Be sure to keep the door closed, or smoke and fire may be drawn into the room.Keep your head low at the window to be sure you get fresh air rather than smoke that may haveleaked (渗入)into the room.On a second or third floor, the best windows for escaping are those which open onto a roof.From the roof a person can drop to the ground more safely, dropping onto stones might end in injury, bushes and grass can help to break a fall.1.From the beginning, we know that it is important to______.A.know the way to escape a fireB.put out a fire in a burning houseC.jump out of a burning houseD.keep the door closed2.It is possible to escape through the windows ______.A.if there are some stones on the groundB.if there is some grass on the groundC.if you live on a higher floorD.if you have a short enough rope3.Which of the following is RIGHT according to the information in the passage? ______A.Y ou can escape through lifts.B.Y ou can choose fire escapes.C.Y ou can’t escape through stairways.D.Keep your head high at the window to be sure you get fresh air.4.Keep the door closed so that ______ if the building is on fire.A.smoke and fire can’t be drawn into the roomB.you can call for helpC.you can get fresh airD.you can be sent first5.The best title for the passage is ______.A.Escaping through the windowsB.Saving yourself from a burning houseC.Knowing on fireD.Waiting for helpF18、HopperPrice: Free for Android and iOS systemThis app can predict(预测)when the price of the flight to your destinationwillbe the lowest, when they will change and the best time to buy a ticket for acertain day and place. Y ou can save money and book tickets quickly on thisapp.PackPointPrice: Free for Android and iOS systemThis app can provide a travel checklist for you and tell you what you needto pack according to the place you are going to, how long you are going tostay and why you are going there. So next time you won't feel sorry becauseof leaving something important at home.Dark SkyPrice: Free for Android, $3.99 for iOS system"Dark Sky" is in the list of the best apps for App Store in the year of 2015.It can tell you the weather when you get to your destination and predict theweather of the next hour and even the rest of the week with highaccuracy(准确度).TripAdvisorPrice: Free for Android and iOS systemTripAdvisor is your special guide to hotels, restaurants and attractionsworldwide. You can see millions of comments(评论),images and videos ofthe places you are going to visit. It can also tell you the place of interestnearby according to your location.1.The underlined word "destination" means in Chinese.A.出发地B.中途站C.目的地D.机场2.What can PackPoint help you to do?A.It can help you pack your luggage(行李)you need.B.It can help you find the place you want to go to.C.It can help you buy cheaper flight tickets.D.It can tell you the weather of the place you'll visit.3.According to the passage, which of the following is NOT TRUE?A.Dark Sky is good at predicting weather correctly.B.Users can't watch videos of sights on TripAdvisor.C.Packpoint can tell users what to take during a trip.D.Users can book tickets that you want on Hopper.Ⅴ.书面表达19、书面表达(本大题共10分)今年2月28日,前中央台记者柴静向多家视频网站免费奉献了大型空气污染深度调查记录——《穹顶之下》,该纪录片再度唤起了我们对环境问题的关注。
浙江省普通高中第二共同体2025届高考数学四模试卷含解析
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浙江省普通高中第二共同体2025届高考数学四模试卷注意事项1.考生要认真填写考场号和座位序号。
2.试题所有答案必须填涂或书写在答题卡上,在试卷上作答无效。
第一部分必须用2B 铅笔作答;第二部分必须用黑色字迹的签字笔作答。
3.考试结束后,考生须将试卷和答题卡放在桌面上,待监考员收回。
一、选择题:本题共12小题,每小题5分,共60分。
在每小题给出的四个选项中,只有一项是符合题目要求的。
1.设,则"是""的( )A .充分不必要条件B .必要不充分条件C .充要条件D .既不充分也不必要条件2.在空间直角坐标系O xyz -中,四面体OABC 各顶点坐标分别为:22(0,0,0),(0,0,2),3,0,0,0,3,033O A B C ⎛⎫⎛⎫⎪ ⎪⎝⎭⎝⎭.假设蚂蚁窝在O 点,一只蚂蚁从O 点出发,需要在AB ,AC 上分别任意选择一点留下信息,然后再返回O 点.那么完成这个工作所需要走的最短路径长度是( ) A .22B .1121-C .521+D .233.如图,平面四边形ACBD 中,AB BC ⊥,3AB =,2BC =,ABD △为等边三角形,现将ABD △沿AB 翻折,使点D 移动至点P ,且PB BC ⊥,则三棱锥P ABC -的外接球的表面积为( )A .8πB .6πC .4πD .8234.已知z 的共轭复数是z ,且12z z i =+-(i 为虚数单位),则复数z 在复平面内对应的点位于( ) A .第一象限 B .第二象限C .第三象限D .第四象限5.已知函数2()e (2)e xx f x t t x =+--(0t ≥),若函数()f x 在x ∈R 上有唯一零点,则t 的值为( )A .1B .12或0 C .1或0 D .2或06.已知实数,x y 满足线性约束条件1020x x y x y ≥⎧⎪+≥⎨⎪-+≥⎩,则1y x +的取值范围为( )A .(-2,-1]B .(-1,4]C .[-2,4)D .[0,4]7.下列说法正确的是( )A .命题“00x ∃≤,002sin x x ≤”的否定形式是“0x ∀>,2sin x x >”B .若平面α,β,γ,满足αγ⊥,βγ⊥则//αβC .随机变量ξ服从正态分布()21,N σ(0σ>),若(01)0.4P ξ<<=,则(0)0.8P ξ>= D .设x 是实数,“0x <”是“11x<”的充分不必要条件 8.正方体1111ABCD A B C D -,()1,2,,12i P i =是棱的中点,在任意两个中点的连线中,与平面11A C B 平行的直线有几条( )A .36B .21C .12D .69.下列命题中,真命题的个数为( ) ①命题“若1122a b <++,则a b >”的否命题; ②命题“若21x y +>,则0x >或0y >”;③命题“若2m =,则直线0x my -=与直线2410x y -+=平行”的逆命题. A .0B .1C .2D .310.已知双曲线()222:10y C x b b-=>的一条渐近线方程为2y x =,1F ,2F 分别是双曲线C 的左、右焦点,点P在双曲线C 上,且13PF =,则2PF =( ) A .9B .5C .2或9D .1或511.在直角梯形ABCD 中,0AB AD ⋅=,30B ∠=︒,23AB =2BC =,点E 为BC 上一点,且AE xAB y AD =+,当xy 的值最大时,||AE =( )A 5B .2C 30D .2312.已知等差数列{}n a 的公差为-2,前n 项和为n S ,若2a ,3a ,4a 为某三角形的三边长,且该三角形有一个内角为120︒,则n S 的最大值为( ) A .5B .11C .20D .25二、填空题:本题共4小题,每小题5分,共20分。
湖南长沙市湘一芙蓉二中学2024年中考四模英语试题含答案
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湖南长沙市湘一芙蓉二中学2024年中考四模英语试题含答案注意事项:1.答卷前,考生务必将自己的姓名、准考证号填写在答题卡上。
2.回答选择题时,选出每小题答案后,用铅笔把答题卡上对应题目的答案标号涂黑,如需改动,用橡皮擦干净后,再选涂其它答案标号。
回答非选择题时,将答案写在答题卡上,写在本试卷上无效。
3.考试结束后,将本试卷和答题卡一并交回。
Ⅰ. 单项选择1、—________ do you celebrate your father’s birthday?—We usually have a big meal and buy a nice gift for him.A.Why B.What C.Where D.How2、—Have you heard that there’s a big fire near your home last night?— Sure. Luckily, the firemen came quickly and ______ the fire.A.came out B.broke out C.put out D.cut out3、-- is the playground?----It’s about 7,000 square metres .A.How long B.How large C.How far D.How much4、I was very tired last night, ________ I went to sleep earlier.A.but B.or C.so D.for5、The music is fantastic and it is well worth __________.A.listening B.to listen to C.being listened D.listening to6、—Have you seen the movie Forever Young?—Yes. I__________ the movie with my friend last night.A.watch B.watched C.watches D.have watched7、--Today is Linda’s birthday. Have you bought her a gift?--Oh, my god! I __________ forgot her birthday.A.probably B.completely C.hardly8、---How can I get along well with others, Father?---Try to smile to others. You will find it _____ to make new friends than before.A.easy B.more easily C.easier D.easily9、-Have you improved your spoken English?-Not yet.I'll try my best______I am not good at it now.A.so B.although C.but D.until10、—Shall we go out for Chinese food or Western food?—I would rather _____ Chinese food. I think Chinese food looks nice and it tastes delicious.A./ B.have C.having D.to haveⅡ. 完形填空11、When the Spring Festival falls, red flowers bloom(盛开) on the windows of my home. Of course, these are not 1 flowers. But in the cold of 2 , these wonderful flowers bring warmth to us. They are made of paper by my grandma, who is in her 3 with a few cuts, she 4 a piece of paper into a beautiful work of art.When my grandma was young, all the 5 thought she was clumsy(笨拙的). But 6 a cold winter night, she saw some beautiful red paper works of art on her new neighbor’s windows. She was so interested in it and decided to 7 from her neighbor. Tons of paper was wasted, and her fingers were cut many times. But she 8 practicing. It took 10 years 9 my grandma could make paper art skillfully(娴熟地). The red flowers, blooming like burning fire, light up her world. Now, everyone in the village respects her.My grandma's story has shown me 10 takes us time to realize one's dream.1.A.nice B.real C.full D.sweet2.A.spring B.summer C.autumn D.winter3.A.seventy B.seventieth C.seventies D.seventeen4.A.changes B.spreads C.places D.burns5.A.villagers B.parents C.students D.animals6.A.in B.on C.at D.among7.A.buy B.steal C.learn D.borrow8.A.ended up B.kept on C.put off D.thought about9.A.before B.after C.while D.since10.A.this B.after C.it D.oneⅢ. 语法填空12、In one’s life, one usually has little understanding of oneself. When you succeed, you may be very proud. When you 1., you may lose heart. If you don’t get a thorough understanding of yourself, you may miss lots of 2.(chance) in life.To get a thorough understanding of yourself is to know well 3.yourself. Y ou may know your strong points and weak 4.(one). You may hope for a wonderful future, but be sure not to expect too much because not all dreams can 5.(realize). You may be confident enough to meet challenges, but first you should know what to do.To get a thorough understanding of yourself, you should have a real sense of self-appreciation. Maybe you think you are not a tall tree 6.just small grass, as long as you get full confidence, you are sure to face any trouble.To get a thorough understanding of yourself also 7.to look after yourself. When you are angry, find a quiet place so that you won’t be hurt. When you are sad, tell your friends about it to 8.the mood into a good one. When you are tired, get a good sleep. If you don’t take good care of yourself, you won’t be able to stay away from 9.(ill).So if you get a thorough understanding of yourself, you 10.(get) a full control of yourself and find your life full of color.Ⅳ. 阅读理解A13、Welcome to our Toy Museum. We can tell you stories behind toys. Do you know who invented the Barbie Doll?How did your toys get their names? Let’s find out about some of the world’s favorite toys.The Barbie DollRuth Handler designed the The Barbie Doll in 1959. She named it after her daughter, Barbara, who gave Ruth the idea while playing with her friends. The first Barie Doll wore a black and white swimsuit, but these days she has many kinds of great clothes to choose from.Rubik’s CubeEmo Rubik invented his famous puzzle in 1974. It is a cube with nine small squares on each of its six sides. Every side has one color. Players mix up the small colored squares, and they try to put them back in place again. It certainly keeps people busy.ScrabbleIn 1931, Akfred M Butts invented a board game called Criss-Cross which was similar to acrossword puzzle. Butts couldn’t sell his game, but in 1948 James Brunot improved t he rules and design of the game and gave it a new name, Scrabble, which became a brand name. It is now one of the most popular games in the world.1.Which of the following was invented earliest?A.The Barbie Doll. B.Rubik’s Cube C.Scrabble D.Criss-Cross2.How did the Barbie Doll get its name?A.It was named after the inventor’s daughter.B.It was named according to its shape.C.It was named after a brand. D.It was from the inventor’s friends.3.What is a Rubik’s Cube like?A.It has six sides with different colors. B.It has nine squares with the same color.C.It has nine sides with mixed colors. D.It has six squares with mixed colors.4.Which of the following descriptions is NOT true?A.The Barbie Doll has more clothes now than when it was first invented.B.Y ou need to think hard about how to put the colored squares in place.C.Scrabble was made on the basis of Criss-Cross.D.The three toys were all made by an American.5.What can we learn from the reading?A.How we can play with the most popular toys. B.Where we can buy the wonderful toys.C.What the stories behind these fun toys are. D.Why these great toys are so popular.B14、What does success mean? I s it becoming famous, rich, coming up with an idea that changes people’s lives, or helping others and feeling happy?For example, there are many people who have a billion dollars. Are they successful? Why don’t they stop trying to make more because there will never be enough. They will never be happy enough.If all that you’re working for is money, you’ll do terrible things to get it. If all that you want is a successful business, you’ll cheat people to get it. If all that you wa nt is fame(名声), you’ll give up your dignity to achieve it.What’s the real success? For me, being rich or famous is not all to life. I might have a lot of readers now on Zen Habits, but I don't feel that’s what makes me a success. I’ve been a success even when I had no readers, because I was doing what I loved. Even when no one else would have called me a successful man, I loved writing, and I was happy. Success isn’t about achieving something in the future, but about doing something right now that you lov e.So forget about success, and just find joy and love right now, in this moment. That is a success you can achieve, without any method. Just go out and do it.1.Some people don’t stop making money because _____A.They want to change their lives.B.Making money can make them very happy.C.Money will never be enough for them.D.They want to become the richest men in the world.2.The writer felt happy when ____________.A.he had a lot of readers B.he made lots of moneyC.he began to write D.he gave up his job3.Which of the following is RIGHT?A.people who have a billion dollars must be very happy.B.Readers can read the writer’s articles on Zen Habits.C.Success is very important to the writer.D.The writer thinks if people want to own success, they should try many ways.4.What does the writer advise us to do?A.Find joy and love right now.B.Keep success in mind and try to get itC.Read the writer’s articles o n Zen Habits.D.Work hard to be rich or famous.5.This passage talks about_____________.A.being rich of famous B.starting a businessC.how to achieve success D.what real success isC15、The painter Craigie Aitchison was born in Scotland. He came to London intending(打算)to study law, but went to art school instead. There he found the traditional drawing classes diffcult, but still kept on painting.In his late twenties he was given money by the Italian government to study art and liked early Italian artists, which shows in some of his work. He loved the greens and browns of the Italian fields and the clear light there, and wanted to put this light into his paintings.This led him to paint colours thinly one on top of another from light to dark, but he insists he's never sure what the results will be. He says, "It's a secret-because I don't know myself. I don't start by painting yellow, knowing I'm going to put anything on top." Like most talented people, Aitchison makes it sound easy. "Anyone can do the colours-you can buy them. I simply notice what you put the colours next to."Unlike some artists, he never does drawings before he starts a painting, as he feels that if he did, he might get bored and not do the painting afterwards. Instead, Aitchison changes his paintings many times before they are finished. Thisexplains why his favourite models are people who don't ask to see their pictures while he's painting them. "If I feel they're worried and want to look at the painting, I can't do it."Since moving to London years ago, he has not felt part of the Scottish(苏格兰的)painting scene. He says he doesn't want to follow any tradition, but just paints the way he can. However, his work still influences young British painters.1.In the passage, the writer is trying to .A.describe particular works by Craigie AitchisonB.teach readers how to paint like Craigie AitchisonC.introduce the artist Craigie Aitchison to the readersD.explain how Craigie Aitchison has made money from painting2.What can the reader learn about Aitchison from the passage?A.He works in a different way from other artists.B.He often gets bored easily with his paintings.C.He found the drawing classes easy at art school.D.He was sure what his painting was like before drawing.3.Aitchison prefers models who don't .A.keep moving around while he's workingB.ask him about his strange method of workingC.worry about how long the work will takeD.feel worried to see the work as it's developing4.What might a visitor at an exhibition say about Aitchison's work?A.I love his recent painting of Scotland, which are very similar to a number of other Scottish painters.B.Y ou can still see the influence of his trip to Italy in some of these pictures.C.Y ou can tell he spent a lot of time drawing the picture before he started painting.D.I wonder if his law training helps him at all, especially in selling his work.D16、Some time ago I discovered that one of my chairs had a broken leg. I didn’t think there would be any difficulty in getting it repaired, as there are a lot of antique (古董) shops near my home. So I left home one morning carrying the chair with me. I went into the first shop expecting a friendly reception. I was quite wrong. The man wouldn’t even look at my chair.The second shop, though a little more polite, was just the same, and the third and the fourth. I realized that my approach must be wrong so I decided to try another way. I entered the fifth shop with a plan in my mind. I placed thechair on the floor and said to the shopkeeper, “Would you like to buy a chair? Twenty pounds,” I said. “OK. I’ll give you twenty pounds for it,” he said. “It’s got a slightly broken leg,” I added. “Yes, I saw that. It’s nothing,” the shopkeeper replied.Everything was going according to the plan and I was getting excited. “What will you do with it?” I asked. “Oh, it will be easy to sell after the repair is done.” “I’ll buy it,” I said. “What do you mean? You’ve just sold it to me,” the man asked in surpri se. “Yes, I know. But I’ve changed my mind. I am sorry. I’ll give you twenty-seven pounds for it.” “You must be crazy,” he said. Then, suddenly_________He shouted, “I know what you want. You want me to repair your chair.” “You’re right,” I said, “And what would you have said if I had walked in and asked you to repair my chair?” “I wouldn’t have agreed to do it. We don’t do repairs, not enough money in it and too much trouble. But I’ll repair this for you. Five pounds will be the cost,” the man answered. He was a very nice man and was greatly amused by the whole thing.1.What happened to the writer in the first shop?A.He broke his leg.B.His chair was repaired.C.He was refused impolitely.D.The shopkeeper bought his chair.2.What does the underlined phrase “the penny dropped” in the last paragraph mean?A.The shopkeeper changed his mind.B.The shopkeeper accepted the price.C.The shopkeeper decided to help the writer.D.The shopkeeper found out the writer’s purpose.3.How much did the writer pay the shopkeeper at last?A.5 pounds. B.7 pounds.C.20 pounds. D.27 pounds.4.From the passage, we can learn that the writer was__________.A.honest B.smartC.careful D.crazy5.Which of the following statements is true?A.The writer wanted to sell his chair for 20 pounds.B.It was very easy to repair the writer’s broken chair.C.The writer succeeded in getting his chair repaired at last.D.The man in the first shop thought the chair was too old to repair.E17、If you ask your parents: “Did you buy salt recently?” They might either say: “Yes, we bought more salt than usual”, or “No, we couldn’t find any in the market.”This is because of the recent craze(狂热) of salt buying in China. In big cities like Beijing, Shanghai and Shenzhen, salt almost sold out in only one night.After the big earthquake in Japan on March 11, there was a nuclear leak(核泄漏). And rumors(传言) about whether it will affect our daily life appeared: first, iodized(含碘的) salt can keep us from the dangers of radiation(辐射);second, there will be less sea-salt in the ocean because of the nuclear pollution.Both the government and experts said the rumors were not true, but people still bought as much salt as possible. Why? Many salt-buyers didn’t really care or know what experts or the government were s aying. That was the real reason behind the craze of salt buying.On March 20, the government said the salt market is back to normal. And most of China’s salt is from lakes, not the ocean.Now, many people want to return the salt they bought. “There is no r eason why those people should get their money back,” an article in Xinhua Daily Telegraph said. “They made the craze in the first place.”Perhaps people should learn a lesson from the salt: don’t believe everything youhear.1.The recent craze of salt buying in China happened because of ________.A.the earthquakeB.the rumorsC.the shortage(缺乏) of salt2.When did the rumors start?A.On March 11.B.After March 11.C.On March 20.3.According to the passage most of China’s salt is from ________.A.lakes B.the ocean C.rivers4.Which of the following statements is true according to the passage?A.People believed what the government and experts said first.B.People could return the salt and got back their money later.C.Salt almost sold out in only one night because of the rumors.5.The passage tells us that ________.A.we can’t believe everything we hearB.there must be a nuclear leak after an earthquakeC.only iodized salt can keep us from the dangers of radiationF18、Now many people like fast food. We all know that fast food is notverygood for our health. So more and more fast food restaurants are serving healthier food and you can make healthier choices. Here are some tips for ordering healthy food at fast food restaurants.◆Don't order the biggest size. The biggest size seems cheaper, but it is not good for your health. The biggest size has the most fat, sugar and so on. A smaller size is probably enough for you.◆Some drinks are full of sugar. So when you are thirsty, you should choose milk or water.◆Usually fried food is not the best choice. You should choose baked(烘烤的)food. It is healthier.◆Go for the kids menu, because the sizes of kids food are usually smaller. You can eat less.◆Today, more and more fast food restaurants are starting to serve healthier food. You can order the food with words like "healthy’’ or“light”on the menu.By making smart choices, eating at fast food restaurants can be not that bad.根据短文内容,选择最佳答案。
浙江省杭州市杭州第二中学2023-2024学年高考物理四模试卷含解析
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2024年高考物理模拟试卷注意事项:1.答卷前,考生务必将自己的姓名、准考证号填写在答题卡上。
2.回答选择题时,选出每小题答案后,用铅笔把答题卡上对应题目的答案标号涂黑,如需改动,用橡皮擦干净后,再选涂其它答案标号。
回答非选择题时,将答案写在答题卡上,写在本试卷上无效。
3.考试结束后,将本试卷和答题卡一并交回。
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、一列简谐横波沿x轴正向传播,波形如图所示,波速为10m/s。
下列说法正确的是()A.该波的振幅为0.5m,频率为2HzB.此时P点向y轴负方向运动C.再经0.9s,Q点有沿y轴正方向的最大加速度D.再经1.05s,质点P沿波传播方向迁移了10.5m2、14C测年法是利用14C衰变规律对古生物进行年代测定的方法.若以横坐标t表示时间,纵坐标m表示任意时刻14C 的质量,m0为t=0时14C的质量.下面四幅图中能正确反映14C衰变规律的是A.B.C.D.3、物理学重视逻辑,崇尚理性,其理论总是建立在对事实观察的基础上。
下列说法正确的是A.贝克勒尔发现天然放射现象,其中 射线来自原子最外层的电子B.密立根油滴实验表明核外电子的轨道是不连续的C.卢瑟福的a粒子散射实验发现电荷量子化的D.汤姆逊发现电子使人们认识到原子内部是有结构的4、在离地高h处,同时自由下落和竖直向上抛出各一个小球,其中竖直上抛的小球初速度大小为v,不计空气阻力,重力加速度为g ,两球落地的时间差为( )A .h vB .2h vC .2v gD .2222v v h h g g g g++- 5、如图所示,相距为L 的两条足够长的光滑平行不计电阻的金属导轨与水平面夹角为θ,处于方向垂直导轨平面向下且磁感应强度为B 的匀强磁场中。
将金属杆ab 垂直放在导轨上,杆ab 由静止释放下滑距离x 时速度为v 。
已知金属杆质量为m ,定值电阻以及金属杆的电阻均为R ,重力加速度为g ,导轨杆与导轨接触良好。
吉林省白山市2024届中考四模数学试题含解析
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吉林省白山市2024届中考四模数学试题注意事项:1.答题前,考生先将自己的姓名、准考证号填写清楚,将条形码准确粘贴在考生信息条形码粘贴区。
2.选择题必须使用2B铅笔填涂;非选择题必须使用0.5毫米黑色字迹的签字笔书写,字体工整、笔迹清楚。
3.请按照题号顺序在各题目的答题区域内作答,超出答题区域书写的答案无效;在草稿纸、试题卷上答题无效。
4.保持卡面清洁,不要折叠,不要弄破、弄皱,不准使用涂改液、修正带、刮纸刀。
一、选择题(每小题只有一个正确答案,每小题3分,满分30分)1.钟鼎文是我国古代的一种文字,是铸刻在殷周青铜器上的铭文,下列钟鼎文中,不是轴对称图形的是( ) A.B.C.D.2.如图所示,将含有30°角的三角板的直角顶点放在相互平行的两条直线其中一条上,若∠1=35°,则∠2的度数为()A.10°B.20°C.25°D.30°3.点M(1,2)关于y轴对称点的坐标为()A.(﹣1,2)B.(﹣1,﹣2)C.(1,﹣2)D.(2,﹣1)4.如图,在△ABC中,∠C=90°,AC=BC=3cm.动点P从点A出发,以2cm/s的速度沿AB方向运动到点B.动点Q同时从点A出发,以1cm/s的速度沿折线AC CB方向运动到点B.设△APQ的面积为y(cm2).运动时间为x(s),则下列图象能反映y与x之间关系的是()A.B.C.D.5.等腰三角形一边长等于5,一边长等于10,它的周长是( )A.20 B.25 C.20或25 D.156.如图,AB∥CD,E为CD上一点,射线EF经过点A,EC=EA.若∠CAE=30°,则∠BAF=()A.30°B.40°C.50°D.60°7.如图,在平面直角坐标系中,以O为圆心,适当长为半径画弧,交x轴于点M,交y轴于点N,再分别以点M、N为圆心,大于12MN的长为半径画弧,两弧在第二象限交于点P.若点P的坐标为(2a,b+1),则a与b的数量关系为()A.a=b B.2a+b=﹣1 C.2a﹣b=1 D.2a+b=18.如图,在平行四边形ABCD中,E是边CD上一点,将△ADE沿AE折叠至△AD′E处,AD′与CE交于点F,若∠B=52°,∠DAE=20°,则∠FED′的度数为()A.40°B.36°C.50°D.45°9.在Rt△ABC中,∠C=90°,如果AC=4,BC=3,那么∠A的正切值为()A.34B.43C.35D.4510.已知(AC BC)ABC ∆<,用尺规作图的方法在BC 上确定一点P ,使PA PC BC +=,则符合要求的作图痕迹是( )A .B .C .D .二、填空题(共7小题,每小题3分,满分21分)11.如图,已知点E 是菱形ABCD 的AD 边上的一点,连接BE 、CE ,M 、N 分别是BE 、CE 的中点,连接MN ,若∠A=60°,AB=4,则四边形BCNM 的面积为_____.12.如图,在平面直角坐标系中,已知抛物线y=x 2+bx+c 过A ,B ,C 三点,点A 的坐标是(3,0),点C 的坐标是(0,-3),动点P 在抛物线上. b =_________,c =_________,点B 的坐标为_____________;(直接填写结果)是否存在点P ,使得△ACP 是以AC 为直角边的直角三角形?若存在,求出所有符合条件的点P 的坐标;若不存在,说明理由;过动点P 作PE 垂直y 轴于点E ,交直线AC 于点D ,过点D 作x 轴的垂线.垂足为F ,连接EF ,当线段EF 的长度最短时,求出点P 的坐标.13.如图,已知抛物线和x 轴交于两点A 、B ,和y 轴交于点C ,已知A 、B 两点的横坐标分别为﹣1,4,△ABC 是直角三角形,∠ACB=90°,则此抛物线顶点的坐标为_____.14.已知⊙O1、⊙O2的半径分别为2和5,圆心距为d,若⊙O1与⊙O2相交,那么d的取值范围是_________.15.如图,AB是⊙O的直径,且经过弦CD的中点H,过CD延长线上一点E作⊙O的切线,切点为F.若∠ACF=65°,则∠E= .16.有一个正六面体,六个面上分别写有1~6这6个整数,投掷这个正六面体一次,向上一面的数字是2的倍数或3的倍数的概率是____.17.抛掷一枚均匀的硬币,前3次都正面朝上,第4次正面朝上的概率为________.三、解答题(共7小题,满分69分)18.(10分)如图,在Rt△ABC中,∠ACB=90°,CD 是斜边AB上的高(1)△ACD与△ABC相似吗?为什么?(2)AC2=AB•AD 成立吗?为什么?19.(5分)已知:如图,点A,F,C,D在同一直线上,AF=DC,AB∥DE,AB=DE,连接BC,BF,CE.求证:四边形BCEF是平行四边形.20.(8分)中华文明,源远流长;中华汉字,寓意深广.为了传承中华民族优秀传统文化,我市某中学举行“汉字听写”比赛,赛后整理参赛学生的成绩,将学生的成绩分为A,B,C,D四个等级,并将结果绘制成如图所示的条形统计图和扇形统计图,但均不完整.请你根据统计图解答下列问题:参加比赛的学生共有____名;在扇形统计图中,m的值为____,表示“D等级”的扇形的圆心角为____度;组委会决定从本次比赛获得A等级的学生中,选出2名去参加全市中学生“汉字听写”大赛.已知A等级学生中男生有1名,请用列表法或画树状图法求出所选2名学生恰好是一名男生和一名女生的概率.21.(10分)阅读下列材料,解答下列问题:材料1.把一个多项式化成几个整式的积的形式,这种变形叫做因式分解,也叫分解因式.如果把整式的乘法看成一个变形过程,那么多项式的因式分解就是它的逆过程.公式法(平方差公式、完全平方公式)是因式分解的一种基本方法.如对于二次三项式a2+2ab+b2,可以逆用乘法公式将它分解成(a+b)2的形式,我们称a2+2ab+b2为完全平方式.但是对于一般的二次三项式,就不能直接应用完全平方了,我们可以在二次三项式中先加上一项,使其配成完全平方式,再减去这项,使整个式子的值不变,于是有:x2+2ax﹣3a2=x2+2ax+a2﹣a2﹣3a2=(x+a)2﹣(2a)2=(x+3a)(x﹣a)材料2.因式分解:(x+y)2+2(x+y)+1解:将“x+y”看成一个整体,令x+y=A,则原式=A2+2A+1=(A+1)2再将“A”还原,得:原式=(x+y+1)2.上述解题用到的是“整体思想”,整体思想是数学解题中常见的一种思想方法,请你解答下列问题:(1)根据材料1,把c2﹣6c+8分解因式;(2)结合材料1和材料2完成下面小题:①分解因式:(a﹣b)2+2(a﹣b)+1;②分解因式:(m+n)(m+n﹣4)+3.22.(10分)如图,已知一次函数y1=kx+b(k≠0)的图象与反比例函数的图象交于A、B两点,与坐标轴交于M、N两点.且点A的横坐标和点B的纵坐标都是﹣1.求一次函数的解析式;求△AOB的面积;观察图象,直接写出y1>y1时x的取值范围.23.(12分)某初中学校组织400 位同学参加义务植树活动,每人植树的棵数在5至10之间,甲、乙两位同学分别调查了30位同学的植树情况,并将收集的数据进行了整理,绘制成统计表分别为表1和表2:表1:甲调查九年级30位同学植树情况统计表(单位:棵)每人植树情况7 8 9 10人数 3 6 15 6频率0.1 0.2 0.5 0.2表2:乙调查三个年级各10位同学植树情况统计表(单位:棵)每人植树情况 6 7 8 9 10人数 3 6 3 11 6频率0.1 0.2 0.1 0.4 0.2根据以上材料回答下列问题:(1)表1中30位同学植树情况的中位数是棵;(2)已知表2的最后两列中有一个错误的数据,这个错误的数据是,正确的数据应该是;(3)指出哪位同学所抽取的样本能更好反映此次植树活动情况,并用该样本估计本次活动400位同学一共植树多少棵?24.(14分)如图,在Rt△ABC中,∠ACB=90°,以AC为直径的⊙O与AB边交于点D,过点D作⊙O的切线.交BC于点E.求证:BE=EC填空:①若∠B=30°,3,则DE=______;②当∠B=______度时,以O,D,E,C为顶点的四边形是正方形.参考答案一、选择题(每小题只有一个正确答案,每小题3分,满分30分)1、A【解题分析】根据轴对称图形的概念求解.解:根据轴对称图形的概念可知:B,C,D是轴对称图形,A不是轴对称图形,故选A.“点睛”本题考查了轴对称图形的概念.轴对称图形的关键是寻找对称轴,图形两部分折叠后可重合.2、C【解题分析】分析:如图,延长AB交CF于E,∵∠ACB=90°,∠A=30°,∴∠ABC=60°.∵∠1=35°,∴∠AEC=∠ABC﹣∠1=25°.∵GH∥EF,∴∠2=∠AEC=25°.故选C.3、A【解题分析】关于y轴对称的点的坐标特征是纵坐标不变,横坐标变为相反数.【题目详解】点M(1,2)关于y轴对称点的坐标为(-1,2)【题目点拨】本题考查关于坐标轴对称的点的坐标特征,牢记关于坐标轴对称的点的性质是解题的关键.4、D【解题分析】在△ABC中,∠C=90°,AC=BC=3cm,可得AB=32,∠A=∠B=45°,分当0<x≤3(点Q在AC上运动,点P在AB上运动)和当3≤x≤6时(点P与点B重合,点Q在CB上运动)两种情况求出y与x的函数关系式,再结合图象即可解答.【题目详解】在△ABC中,∠C=90°,AC=BC=3cm,可得AB=32,∠A=∠B=45°,当0<x≤3时,点Q在AC上运动,点P在AB上运动(如图1),由题意可得AP=2x,AQ=x,过点Q作QN⊥AB于点N,在等腰直角三角形AQN中,求得QN=22x,所以y=12AP QN⋅=21212=222x x x⨯⨯(0<x≤3),即当0<x≤3时,y随x的变化关系是二次函数关系,且当x=3时,y=4.5;当3≤x≤6时,点P与点B重合,点Q在CB上运动(如图2),由题意可得PQ=6-x,AP=32,过点Q作QN⊥BC于点N,在等腰直角三角形PQN中,求得QN=22(6-x),所以y=12AP QN⋅=12332(6)=9222x x⨯⨯--+(3≤x≤6),即当3≤x≤6时,y随x的变化关系是一次函数,且当x=6时,y=0.由此可得,只有选项D符合要求,故选D.【题目点拨】本题考查了动点函数图象,解决本题要正确分析动线运动过程,然后再正确计算其对应的函数解析式,由函数的解析式对应其图象,由此即可解答.5、B【解题分析】题目中没有明确腰和底,故要分情况讨论,再结合三角形的三边关系分析即可.【题目详解】+=,此时无法构成三角形;当5为腰时,三边长为5、5、10,而5510=++=当5为底时,三边长为5、10、10,此时可以构成三角形,它的周长5101025故选B.6、D【解题分析】解:∵EC=EA.∠CAE=30°,∴∠C=30°,∴∠AED=30°+30°=60°.∵AB∥CD,∴∠BAF=∠AED=60°.故选D.点睛:本题考查的是平行线的性质,熟知两直线平行,同位角相等是解答此题的关键.7、B【解题分析】试题分析:根据作图方法可得点P在第二象限角平分线上,则P点横纵坐标的和为0,即2a+b+1=0,∴2a+b=﹣1.故选B.8、B【解题分析】由平行四边形的性质得出∠D=∠B=52°,由折叠的性质得:∠D′=∠D=52°,∠EAD′=∠DAE=20°,由三角形的外角性质求出∠AEF=72°,与三角形内角和定理求出∠AED′=108°,即可得出∠FED′的大小.【题目详解】∵四边形ABCD是平行四边形,∴∠D=∠B=52°,由折叠的性质得:∠D′=∠D=52°,∠EAD′=∠DAE=20°,∴∠AEF=∠D+∠DAE=52°+20°=72°,∠AED′=180°﹣∠EAD′﹣∠D′=108°,∴∠FED′=108°﹣72°=36°.故选B.【题目点拨】本题考查了平行四边形的性质、折叠的性质、三角形的外角性质以及三角形内角和定理;熟练掌握平行四边形的性质和折叠的性质,求出∠AEF和∠AED′是解决问题的关键.9、A 【解题分析】根据锐角三角函数的定义求出即可. 【题目详解】解:在Rt △ABC 中,∠C=90°,AC=4,BC=3,∴ tanA=34BC AC =. 故选A. 【题目点拨】本题考查了锐角三角函数的定义,熟记锐角三角函数的定义内容是解题的关键. 10、D 【解题分析】试题分析:D 选项中作的是AB 的中垂线,∴PA=PB ,∵PB+PC=BC , ∴PA+PC=BC .故选D . 考点:作图—复杂作图.二、填空题(共7小题,每小题3分,满分21分) 11、33 【解题分析】如图,连接BD .首先证明△BCD 是等边三角形,推出S △EBC =S △DBC =34×42=43,再证明△EMN ∽△EBC ,可得EMN EBC S S ∆∆=(MN BC )2=14,推出S △EMN =3,由此即可解决问题. 【题目详解】 解:如图,连接BD .∵四边形ABCD 是菱形,∴AB=BC=CD=AD=4,∠A=∠BCD=60°,AD ∥BC , ∴△BCD 是等边三角形, ∴S △EBC =S △DBC 3423∵EM=MB ,EN=NC ,∴MN ∥BC ,MN=12BC , ∴△EMN ∽△EBC , ∴EMN EBC S S ∆∆=(MN BC )2=14, ∴S △EMN,∴S 阴故答案为【题目点拨】本题考查相似三角形的判定和性质、三角形的中位线定理、菱形的性质等知识,解题的关键是灵活运用所学知识解决问题,属于中考常考题型.12、(1)2-,3-,(-1,0);(2)存在P 的坐标是(14)-,或(-25),;(1)当EF 最短时,点P 的坐标是:,32-,32-) 【解题分析】(1)将点A 和点C 的坐标代入抛物线的解析式可求得b 、c 的值,然后令y =0可求得点B 的坐标;(2)分别过点C 和点A 作AC 的垂线,将抛物线与P 1,P 2两点先求得AC 的解析式,然后可求得P 1C 和P 2A 的解析式,最后再求得P 1C 和P 2A 与抛物线的交点坐标即可;(1)连接OD .先证明四边形OEDF 为矩形,从而得到OD =EF ,然后根据垂线段最短可求得点D 的纵坐标,从而得到点P 的纵坐标,然后由抛物线的解析式可求得点P 的坐标.【题目详解】解:(1)∵将点A 和点C 的坐标代入抛物线的解析式得:3930c b c =-⎧⎨++=⎩, 解得:b =﹣2,c =﹣1,∴抛物线的解析式为223y x x =--.∵令2230x x --=,解得:11x =-,23x =,∴点B 的坐标为(﹣1,0).故答案为﹣2;﹣1;(﹣1,0).(2)存在.理由:如图所示:①当∠ACP 1=90°.由(1)可知点A 的坐标为(1,0).设AC 的解析式为y =kx ﹣1.∵将点A 的坐标代入得1k ﹣1=0,解得k =1,∴直线AC 的解析式为y =x ﹣1,∴直线CP 1的解析式为y =﹣x ﹣1.∵将y =﹣x ﹣1与223y x x =--联立解得11x =,20x =(舍去),∴点P 1的坐标为(1,﹣4).②当∠P 2AC =90°时.设AP 2的解析式为y =﹣x +b .∵将x =1,y =0代入得:﹣1+b =0,解得b =1,∴直线AP 2的解析式为y =﹣x +1.∵将y =﹣x +1与223y x x =--联立解得1x =﹣2,2x =1(舍去),∴点P 2的坐标为(﹣2,5).综上所述,P 的坐标是(1,﹣4)或(﹣2,5).(1)如图2所示:连接OD .由题意可知,四边形OFDE 是矩形,则OD =EF .根据垂线段最短,可得当OD ⊥AC 时,OD 最短,即EF 最短. 由(1)可知,在Rt △AOC 中,∵OC =OA =1,OD ⊥AC ,∴D 是AC 的中点.又∵DF ∥OC ,∴DF =12OC =32, ∴点P 的纵坐标是32-, ∴23232x x --=-,解得:x 210±, ∴当EF 最短时,点P 的坐标是:210+,32-210-,32-). 13、(32 ,258) 【解题分析】连接AC ,根据题意易证△AOC ∽△COB ,则AO OC OC OB=,求得OC=2,即点C 的坐标为(0,2),可设抛物线解析式为y=a (x+1)(x ﹣4),然后将C 点坐标代入求解,最后将解析式化为顶点式即可.【题目详解】解:连接AC ,∵A 、B 两点的横坐标分别为﹣1,4,∴OA=1,OB=4,∵∠ACB=90°,∴∠CAB+∠ABC=90°,∵CO ⊥AB ,∴∠ABC+∠BCO=90°,∴∠CAB=∠BCO,又∵∠AOC=∠BOC=90°,∴△AOC∽△COB,∴AO OC OC OB,即1OC=4OC,解得OC=2,∴点C的坐标为(0,2),∵A、B两点的横坐标分别为﹣1,4,∴设抛物线解析式为y=a(x+1)(x﹣4),把点C的坐标代入得,a(0+1)(0﹣4)=2,解得a=﹣12,∴y=﹣12(x+1)(x﹣4)=﹣12(x2﹣3x﹣4)=﹣12(x﹣32)2+258,∴此抛物线顶点的坐标为(32,258).故答案为:(32,258).【题目点拨】本题主要考查相似三角形的判定与性质,抛物线的顶点式,解此题的关键在于熟练掌握其知识点,利用相似三角形的性质求得关键点的坐标.14、3<d<7【解题分析】若两圆的半径分别为R和r,且R≥r,圆心距为d:相交,则R-r<d<R+r,从而得到圆心距O1O2的取值范围.【题目详解】∵⊙O1和⊙O2的半径分别为2和5,且两圆的位置关系为相交,∴圆心距O1O2的取值范围为5-2<d<2+5,即3<d<7.故答案为:3<d<7.【题目点拨】本题考查的知识点是圆与圆的位置关系,解题的关键是熟练的掌握圆与圆的位置关系.15、50°.【解题分析】解:连接DF,连接AF交CE于G,∵EF为⊙O的切线,∴∠OFE=90°,∵AB为直径,H为CD的中点∴AB⊥CD,即∠BHE=90°,∵∠ACF=65°,∴∠AOF=130°,∴∠E=360°-∠BHE-∠OFE-∠AOF=50°,故答案为:50°.16、【解题分析】∵投掷这个正六面体一次,向上的一面有6种情况,向上一面的数字是2的倍数或3的倍数的有2、3、4、6共4种情况,∴其概率是=.【题目点拨】此题考查概率的求法:如果一个事件有n种可能,而且这些事件的可能性相同,其中事件A出现m种结果,那么事件A的概率P(A)=.17、1 2【解题分析】根据概率的计算方法求解即可.【题目详解】∵第4次抛掷一枚均匀的硬币时,正面和反面朝上的概率相等,∴第4次正面朝上的概率为1 2 .故答案为:1 2 .【题目点拨】此题考查了概率公式的计算方法,如果一个事件有n种可能,而且这些事件的可能性相同,其中事件A出现m种结果,那么事件A的概率P(A)=mn.三、解答题(共7小题,满分69分)18、(1)△ACD 与△ABC相似;(2)AC2=AB•AD成立.【解题分析】(1)求出∠ADC=∠ACB=90°,根据相似三角形的判定推出即可;(2)根据相似三角形的性质得出比例式,再进行变形即可.【题目详解】解:(1)△ACD 与△ABC相似,理由是:∵在Rt△ABC 中,∠ACB=90°,CD 是斜边AB上的高,∴∠ADC=∠ACB=90°,∵∠A=∠A,∴△ACD∽∠ABC;(2)AC2=AB•AD成立,理由是:∵△ACD∽∠ABC,∴=,∴AC2=AB•AD.【题目点拨】本题考查了相似三角形的性质和判定,能根据相似三角形的判定定理推出△ACD∽△ABC 是解此题的关键.19、证明见解析【解题分析】首先证明△ABC≌△DEF(ASA),进而得出BC=EF,BC∥EF,进而得出答案.【题目详解】∵AB∥DE,∴∠A=∠D,∵AF=CD,∴AC=DF,在△ABC和△DEF中,,∴△ABC≌△DEF,∴BC=EF,∠ACB=∠DFE,∴BC∥EF,∴四边形BCEF是平行四边形.【题目点拨】本题考查了全等三角形的判定与性质与平行四边形的判定,解题的关键是熟练的掌握全等三角形的判定与性质与平行四边形的判定.20、(1)20;(2)40,1;(3)23.【解题分析】试题分析:(1)根据等级为A的人数除以所占的百分比求出总人数;(2)根据D级的人数求得D等级扇形圆心角的度数和m的值;(3)列表得出所有等可能的情况数,找出一男一女的情况数,即可求出所求的概率.试题解析:解:(1)根据题意得:3÷15%=20(人),故答案为20;(2)C级所占的百分比为820×100%=40%,表示“D等级”的扇形的圆心角为420×360°=1°;故答案为40、1.(3)列表如下:所有等可能的结果有6种,其中恰好是一名男生和一名女生的情况有4种,则P恰好是一名男生和一名女生=46=23.21、(1)(c-4)(c-2);(2)①(a-b+1)2;②(m+n-1)(m+n-3).【解题分析】(1)根据材料1,可以对c2-6c+8分解因式;(2)①根据材料2的整体思想可以对(a-b)2+2(a-b)+1分解因式;②根据材料1和材料2可以对(m+n)(m+n-4)+3分解因式.【题目详解】(1)c2-6c+8=c2-6c+32-32+8=(c-3)2-1=(c-3+1)(c-3+1)=(c-4)(c-2);(2)①(a-b)2+2(a-b)+1设a-b=t,则原式=t2+2t+1=(t+1)2,则(a-b)2+2(a-b)+1=(a-b+1)2;②(m+n)(m+n-4)+3设m+n=t,则t(t-4)+3=t2-4t+3=t2-4t+22-22+3=(t-2)2-1=(t-2+1)(t-2-1)=(t-1)(t-3),则(m+n)(m+n-4)+3=(m+n-1)(m+n-3).【题目点拨】本题考查因式分解的应用,解题的关键是明确题意,可以根据材料中的例子对所求的式子进行因式分解.22、(1)y1=﹣x+1,(1)6;(3)x<﹣1或0<x<4【解题分析】试题分析:(1)先根据反比例函数解析式求得两个交点坐标,再根据待定系数法求得一次函数解析式;(1)将两条坐标轴作为△AOB的分割线,求得△AOB的面积;(3)根据两个函数图象交点的坐标,写出一次函数图象在反比例函数图象上方时所有点的横坐标的集合即可.试题解析:(1)设点A坐标为(﹣1,m),点B坐标为(n,﹣1)∵一次函数y1=kx+b(k≠0)的图象与反比例函数y1=﹣的图象交于A、B两点∴将A(﹣1,m)B(n,﹣1)代入反比例函数y1=﹣可得,m=4,n=4∴将A(﹣1,4)、B(4,﹣1)代入一次函数y1=kx+b,可得,解得∴一次函数的解析式为y1=﹣x+1;,(1)在一次函数y1=﹣x+1中,当x=0时,y=1,即N(0,1);当y=0时,x=1,即M(1,0)∴=×1×1+×1×1+×1×1=1+1+1=6;(3)根据图象可得,当y1>y1时,x的取值范围为:x<﹣1或0<x<4考点:1、一次函数,1、反比例函数,3、三角形的面积23、(1)9;(2)11,12;(3)3360棵【解题分析】(1)30位同学的植树量中第15个、16个数都是9,即可得到植树的中位数;(2)根据频率相加得1确定频率正确,计算频数即可确定错误的数据是11,正确的硬是12;(3)样本数据应体现机会均等由此得到乙同学所抽取的样本更好,再根据部分计算总体的公式即可得到答案. 【题目详解】(1)表1中30位同学植树情况的中位数是9棵,故答案为:9;(2)表2的最后两列中,错误的数据是11,正确的数据应该是30×0.4=12;故答案为:11,12;(3)乙同学所抽取的样本能更好反映此次植树活动情况,(3×6+6×7+3×8+12×9+6×10)÷30×400=3360(棵),答:本次活动400位同学一共植树3360棵.【题目点拨】此题考查统计的计算,掌握中位数的计算方法,部分的频数的计算方法,依据样本计算总体的方法是解题的关键.24、(1)见解析;(2)①3;②1.【解题分析】(1)证出EC为⊙O的切线;由切线长定理得出EC=ED,再求得EB=ED,即可得出结论;(2)①由含30°角的直角三角形的性质得出AB,由勾股定理求出BC,再由直角三角形斜边上的中线性质即可得出DE;②由等腰三角形的性质,得到∠ODA=∠A=1°,于是∠DOC=90°然后根据有一组邻边相等的矩形是正方形,即可得到结论.【题目详解】(1)证明:连接DO.∵∠ACB=90°,AC为直径,∴EC为⊙O的切线;又∵ED也为⊙O的切线,∴EC=ED,又∵∠EDO=90°,∴∠BDE+∠ADO=90°,∴∠BDE+∠A=90°又∵∠B+∠A=90°,∴∠BDE=∠B,∴BE=ED,∴BE=EC;(2)解:①∵∠ACB=90°,∠B=30°,3∴3∴22,AB AC∵AC为直径,∴∠BDC=∠ADC=90°,由(1)得:BE=EC,∴DE=12BC=3,故答案为3;②当∠B=1°时,四边形ODEC是正方形,理由如下:∵∠ACB=90°,∴∠A=1°,∵OA=OD,∴∠ADO=1°,∴∠AOD=90°,∴∠DOC=90°,∵∠ODE=90°,∴四边形DECO是矩形,∵OD=OC,∴矩形DECO是正方形.故答案为1.【题目点拨】本题考查了圆的切线性质、解直角三角形的知识、切线长定理等知识,解题的关键是学会添加常用辅助线,构造直角三角形解决问题,属于中考常考题型.。
四年级下册人教版2模课文翻译。
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四年级下册人教版2模课文翻译。
1.unit2教材第12页课文翻译Zoom:What time is it?祖姆:几点了?London,12 noon伦敦,中午十二点It's 12 o'clock.It's time for lunch.十二点钟了。
到吃午餐的时间了。
Beijing,8 p.m.北京,晚上八点It's time to watch TV.到看电视的时间了。
Cairo,2 p.m.开罗,下午两点It's 2 o'clock. Let's play football.两点钟了。
让我们踢足球八。
OK.好的。
2.unit2教材第13页课文翻译Sydney,10 p.m.悉尼,晚上十点It's 10 o'clock.It's time to go to bed.十点钟了。
到上床睡觉的时间了。
Brasilia,9 a.m.巴西利亚,上午九点Hurry up! It's time for school!快点儿!到上学的时间了!New York, 7 a.m.纽约,上午七点What time is it?几点了?It's 7 o'clock.Its time to get up.七点钟了。
到起床的时间了。
ARCTIC OCEAN北冰洋ATLANTIC OCEAN大西洋AFRICA非洲EUROPE欧洲ASIA亚洲OCEANIA大洋洲PACIFIC OCEAN太平洋NORTH AMERICA北美洲SOUTH AMERICA南美洲ANTARCTICA南极洲INDIAN OCEAN印度洋1.Let's talk部分翻译John:Hi! School is over.Let's go to the playground.约翰:嗨!放学了。
让我们去操场吧。
Wu Yifan:OK.吴一凡:好的。
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实验四 模拟运算电路
一、实验目的
1、深刻理解运算放大器的“虚短”、“虚断”的概念。
熟悉运放在信号放大和模拟运算方面的应用;
2、掌握反相比例运算电路、同相比例运算电路、加法和减法运算及单电源交流放大等电路的设计方法;
3、学会测试上述各运算电路的工作波形及电压传输特性。
二、实验仪器与器材
示波器、直流稳压源、函数发生器、交流毫伏表、模拟电路实验箱、万用表、µA741运算放大器等。
三、实验内容
用运算放大器µA741完成下面的设计题目。
µA741的外观和引脚图如图4-1。
本次实验中µA741的工作电压为±15V 。
引脚说明: 2――反相输入端; 3――同相输入端; 4――负电源; 6――输出端; 7――正电源;
1、设计反相放大器
设计一反相放大器,满足关系式V f A
=-10(原理图:书71页图2-4-1,已知Ω=10K R 1,其它电阻值自取)。
(1) 在输入接地的情况下,进行调零。
调零电路见图2-4-8。
(2) 输入直流信号i U 分别为0.5V 、0.2V 、-0.2V 、-0.5V ,用万用表测量对应于不同i U 的U o 值填入
表4-1,计算V f A
且与理论值比较。
1
2345
67
8
µ A 741U _
U +
-U C C
+U C C
U 图4-1 µA741外观和引脚图
(3)输入1KHz 的正弦信号,在输入不失真的情况下(建议i U =0.2V ),测量O U 、H f 、L f ,计算Vf A 及BW 。
(选做)
BW 测试方法:给入1KHz 的正弦信号,调节输入电压使得输出波形不失真(如i U =0.2V ),调整示波器的“W Div ”及其微调旋钮使显示的O U 波形高度正好为5格。
保持输入信号i U 大小不变(由交流毫伏表监视),分别将信号源频率向高频及低频调节,O U 波形的幅度将会随频率的变化而逐渐减小,当在频率的高端及低端波形幅度下降到最大幅度的0.7倍时,所对应的信号源的频率就是被测放大器的上限截止频率H f 及下限截止频率L f 。
2、设计加法器
设计一加法器,满足O i1i 2U (U U )=-+,原理图2-4-4,Ω===10K R R R F 21。
选取两组直流信号电压,测量相应的O U 值,填入表4-2中,并与理论值进行比较。
表4-2
3、设计减法器
设计一减法器,满足O i1i 2U 10(U U )=--,原理图2-4-5,Ω==Ω==100K R R ,10K R R F 321。
选取两组直流信号电压,测量相应的O U 值,填入表4-3中,并与理论值进行比较。
表4-3
4、设计单电源交流放大器(本科要求完成,杏林不作要求)
设计一个单电源交流放大器,要求V f A
=-4,原理图2-4-6,F R 为可调电阻,调节其值为40K Ω。
(1) 输入1KHz ,且i U =0.5V 的正弦信号,观察输入输出波形并记录波形(标出峰峰值或计算出有效值)。
(2) 测量输出电压有效值,验证是否满足V f A
=-4。
(3) 改变信号频率,测量H f 、L f ,并确定放大器的带宽BW 。
5、设计电路满足O i1i 2U 2U 3U =-+。
(选做)
(1)i1U 接入1KHz ,有效值1V 的方波信号,i 2U 接入5KHz ,有效值0.1V 的方波信号,用示波器观察输出电压O U 的波形,在同一个坐标系中记录输入输出波形图。
(2)将波形与理论波形比较。
五、预习要求
1、复习集成运放有关模拟运算应用方面的内容,弄清各电路的工作原理。
2、根据实验内容设计实验电路,并选择相应的器件参数。
3、写出每个实验的步骤、所用仪器,画出表格待填。
4、在预习报告中计算好有关内容的理论数据,便于在实测中进行比较。
5、回答所有思考题。
六、实验报告要求
1、写出所做实验电路的目的、仪器、原理、实验步骤,画出设计,并标注元件参数值。
2、整理实验数据,并在同一个坐标系中画出相应的输入、输出波形。
3、对实验数据进行分析,并与理论数据进行比较、分析。
4、回答所有思考题。
七、思考题
1、理想运算放大器具有哪些特点?
2、单电源运放用来放大交流信号时,电路结构上应满足哪些要求?若改用单一负电源供电,电路应作如何改动?
3、运放用作模拟运算电路时,“虚短”、“虚断”能永远满足吗?试问:在什么条件下“虚短”、“虚断”将不再存在?。