新概念试题赏析
例析中考新概念试题
例析中考新概念试题宁波市惠贞书院王盛裕一、试题概述所谓新概念试题是指即时定义新概念、新公式、新运算、新法则、新方法，这些都是同学们从未接触过的，要求同学们在解题时能够运用已掌握的知识和方法理解“新定义”，做到“化生为熟”，现学现用，其目的是考查同学们的阅读理解能力、接受能力、应变能力和创新能力，培养同学们自主学习、主动探究的数学品质，在一定程度上促进教学方法和学习方法的转变.新概念试题是历年各地中考数学试题中的一朵奇葩，以其清雅、新颖的风格彰显出新课标中“由知识立意向能力立意”过渡的要求，是同学们“可持续发展”理念的具体体现，同时也警示我们的初中数学教学改变过去单一的教法和学法，重视同学们的数学阅读能力、数学迁移能力，以及运用数学方法解决实际问题和应用能力上要有进一步的突破.纵观近几年全国各地中考数学试题,新概念试题通常占试题总数的10％左右，而同学们解答这类试题的正确率却并不理想，另外此类试题重视数学学习潜能的综合考查，且命题中常引入初中数学教学中未曾见过的新概念，而这些新概念往往有着不可低估的作用.基于这些原因，对新概念试题进行深层次、多方位的研究，并在毕业复习中对同学们有意加强这方面的训练，就显得尤为重要.二、试题例析新概念试题要求同学们对给定的内容进行分析、研究、开发，然后加以运用。
解决这类问题的关键是读懂题意，确定探索方向，然后运用归纳与类比的方法寻找合理的解题思路．简而言之，同学们必须具备“给什么，用什么，怎么用”的能力． 1． 定义“概念”例1 （2009年山东）“上升数”是一个数中右边数字比左边数字大的自然数（如，34，568，2469等）任取一个两位数，是上升数的概率是解：最小的两位数是10，最大的两位数是99，一共有90个两位数，而在10～19中，“上升数”有8个，在20～29中，“上升数”有7个，在30～39中，“上升数”有6个；…；在90～99中，“上升数”有0个．因此在10～99中“上升数”共有8+7+6+5+4+3+2+1=36个．所以任取一个两位数，是上升数的概率为P=529036=．点评：这是一道边缘性的新概念试题，“上升数”是一种全新的、特殊的概念，要同学们在全面、准确地理解这种新概念含义的基础上，运用这种特殊概念去创造性地思考并解决问题；另此题也不同于以往中考单纯考查概率的知识点，使试题得到巧妙的创新． 2．定义“运算”例 2 （2009年定西）在实数范围内定义运算“⊕”，其法则为：22a b a b⊕=-，求方程（4⊕3）⊕24x =的解．解：∵ 22a b a b ⊕=- ， ∴ 2222(43)(43)77x x x x ⊕⊕=-⊕=⊕=-．∴22724x-=． ∴ 225x =．∴ 5x =±．点评：将一个一元二次方程定义于新运算中，比直接给出一元二次方程求解要有新意，给人耳目一新之感正所谓化腐朽为神奇． 3．定义“公式”例3（2009年益阳市）阅读材料：如图，过△ABC 的三个顶点分别作出与水平线垂直的三条直线，外侧两条直线之间的距离叫△ABC 的“水平宽”(a )，中间的这条直线在△ABC 内部线段的长度叫△ABC 的“铅垂高(h )”.我们可得出一种计算三角形面积的新方法：ahS ABC 21=∆，即三角形面积等于水平宽与铅垂高乘积的一半.解答下列问题：如图2，抛物线顶点坐标为点C (1,4),交x 轴于点A (3,0)，交y 轴于点B .（1）求抛物线和直线AB 的解析式；（2）点P 是抛物线(在第一象限内)上的一个动点，连结PA ，PB ，当P 点运动到顶点C 时，求△CAB 的铅垂高CD 及CAB S ∆；（3）是否存在一点P ，使S △PAB =89S △CAB ，若存在，求出P 点的坐标；若不存在，请说明理由. 解：(1)设抛物线的解析式为：xC Oy ABD114)1(21+-=x a y 1分把A （3,0）代入解析式求得1-=a所以324)1(221++-=+--=x x x y ··············································3分 设直线AB 的解析式为：b kx y +=2 由3221++-=x x y 求得B 点的坐标为)3,0( ····································4分把)0,3(A ，)3,0(B 代入bkx y +=2中解得：3,1=-=b k所以32+-=x y ···············································································6分(2)因为C 点坐标为(１,4) 所以当x ＝１时，y 1＝4，y 2＝2所以CD ＝4-2＝2 ··········································································8分32321=⨯⨯=∆CAB S (平方单位) (10)分(3)假设存在符合条件的点P ，设P 点的横坐标为x ，△PAB 的铅垂高为h ，则xx x x x y y h 3)3()32(2221+-=+--++-=-=································ 12分由S △PAB =89S △CAB 得：389)3(3212⨯=+-⨯⨯x x化简得：091242=+-x x解得，23=x将23=x代入3221++-=x x y 中，解得P 点坐标为)415,23(································································ 14分点评：本题给出了一个直角坐标系中求一般三角形的面积计算公式，并要求现学现用，总体来说本题难度不大． 4定义“点”例4（2009年台州）定义：到凸四边形一组对边距离相等，到另一组对边距离也相等的点叫凸四边形的准内点．．．．如图1，P H P J=，P I P G=，则点P 就是四边形ABCD 的准内点．（1）如图2，AFD ∠与DEC ∠的角平分线,FP EP 相交于点P ．求证：点P 是四边形ABCD 的准内点．（2）分别画出图3平行四边形和图4梯形的准内点．（作图工具不限，不写作法，但要有必要的说明） （3）判断下列命题的真假，在括号内填“真”或“假”． ①任意凸四边形一定存在准内点．（ ）②任意凸四边形一定只有一个准内点．（ ）③若P 是任意凸四边形ABCD 的准内点，则PD PC PB PA +=+ 或PD PB PC PA +=+．( )解：（1）如图2，过点P 作AD PJ CD PI BC PH AB PG ⊥⊥⊥⊥,,,，∵EP 平分DEC ∠， ∴PHPJ=．……………3分图1B JI HGD CA P图2图4FEDC B A P G HJI图2 FE CB A PG HJI同理PIPG =．…………………………………1分∴P 是四边形ABCD 的准内点．…………………1分 （2）…………………………………………………………………4分 平行四边形对角线BD AC ,的交点1P 就是准内点，如图3（1）. 或者取平行四边形两对边中点连线的交点1P 就是准内点，如图3（2）； 梯形两腰夹角的平分线与梯形中位线的交点2P 就是准内点． 如图4.（3）真；真；假．……………………………………………………………………3分点评：本题要求同学们对“准内点”定义进行准确的理解，并能用新定义进行作图、证明，考了同学们的操作能力和演绎推理能力，题型有证明、作图和填空，知识点有角平分线的性质、中心对称、梯形中位线的性质，具有较强的综合性． 5．定义“线”例5（茂名市2009）已知：如图，直线l ：13y x b =+，经过点104M ⎛⎫⎪⎝⎭，，一组抛物线的顶点112233(1)(2)(3)()n n B y B y B y B n y ，，，，，，，，（n 为正整数）依次是直线l 上的点，这组抛物线与x 轴正半轴的交点依次是：11223311(0)(0)(0)(0)n n A x A x A x A x ++ ，，，，，，，，（n为正整数），设101x dd =<<（）．（1）求b 的值；（2分）图3（1）图4图3（2）B BDD BF（2）求经过点112A B A 、、的抛物线的解析式（用含d 的代数式表示）（4分）（3）定义：若抛物线的顶点与x 轴的两个交点构成的三角形是直角三角形，则这种抛物线就称为：“美丽抛物线”．探究：当01dd <<（）的大小变化时，这组抛物线中是否存在美丽抛物线？若存在，请你求出相应的d 的值． （4分）解：（1）∵104M⎛⎫⎪⎝⎭，在13y x b =+上，∴11043b=⨯+，∴14b =． ··········· 2分（2）由（1）得：1134y x =+， ∵11(1)B y ，在l 上，∴当1x =时，111713412y =⨯+=，∴17112B ⎛⎫⎪⎝⎭，． ··································· 3 分∴设抛物线表达式为：27(1)(0)12y a x a =-+≠， ··························· 4分又∵1x d =， ∴1(0)A d ，，∴270(1)12a d =-+，∴2712(1)a d =--， ··· 5 分∴经过点112A B A 、、的抛物线的解析式为：2277(1)12(1)12y x d =--+-．6 分（3）存在美丽抛物线． ································································ 7 分 由抛物线的对称性可知，所构成的直角三角形必是以抛物线顶点为直角顶点的等腰直角三角形，∴此等腰直角三角形斜边上的高等于斜边的一半，又∵01d<<，∴等腰直角三角形斜边的长小于2，∴等腰直角三角形斜边上的高必小于1，即抛物线的顶点的纵坐标必小于 1． ∵当1x =时，111713412y=⨯+=<当2x =时，21111213412y =⨯+=<当3x =时，3111311344y =⨯+=>∴美丽抛物线的顶点只有12B B 、． ··················································· 8分①若1B 为顶点，由17112B ⎛⎫⎪⎝⎭，，则7511212d=-=； ······························· 9分②若2B 为顶点，由211212B ⎛⎫⎪⎝⎭，，则11111211212d ⎡⎤⎛⎫=---=⎪⎢⎥⎝⎭⎣⎦，综上所述，d 的值为512或1112时，存在美丽抛物线． ···················· 10分点评：本题是一次函数和二次函数的综合题，在解题时，首先利用抛物线的对称性，确定直角三角形必是以抛物线顶点为直角顶点的等腰直角三角形，再利用直角三角形斜边上的中线性质和等腰三角形的三线合一的性质，有一定的难度．例6（2007年连云港市）如图1，点C 将线段A B 分成两．部分，如果A C B C A BA C=，那么称点C 为线段A B 的黄金分割点．某研究小组在进行课题学习时，由黄金分割点联想到“黄金分割线”，类似地给出“黄金分割线”的定义：直线l 将一个面积为S 的图形分成两部分，这两部分的面积分别为1S ，2S ，如果121S S SS =，那么称直线l 为该图形的黄金分割线．（1）研究小组猜想：在A B C △中，若点D 为A B 边上的黄金分割点（如图2），则直线C D 是A B C △的黄金分割线．你认为对吗？为什么？ （2）请你说明：三角形的中线是否也是该三角形的黄金分割线？ （3）研究小组在进一步探究中发现：过点C 任作一条直线交A B 于点E，再过点D 作直线D F C E ∥，交A C 于点F ，连接E F （如图3），则直线E F 也是A B C △的黄金分割线． 请你说明理由．（4）如图4，点E 是平行四边形ABCD 的边A B 的黄金分割点，过点E作EF AD ∥，交D C 于点F ，显然直线E F 是平行四边形ABCD 的黄金分割线．请你画一条平行四边形ABCD 的黄金分割线，使它不经过平行四边形ABCD 各边黄金分割点．解：（1）直线C D 是A B C △的黄金分割线．理由如下： 设A B C △的边A B 上的高为h ．12A D C S A D h=⨯△，12B D CSB D h=⨯△，12A B CSA B h =⨯△，所以，AD C ABCS AD S AB=△△，BD C AD CS BD S AD=△△． ································· 2分又因为点D 为边A B 的黄金分割点，所以有A DB D A BA D=．因此A Ｃ Ｂ图1AD B图2CA DB 图3CF E E图4（第27题图）ADC BDC ABCADCS S S S =△△△△．所以，直线C D 是A B C △的黄金分割线． ······················· 4分 （2）因为三角形的中线将三角形分成面积相等的两部分，此时1212ss s ==，即121s s ss ≠，所以三角形的中线不可能是该三角形的黄金分割线． ··························································································· 6分（3）因为D F C E ∥，所以∆和EDF ∆的公共边DF 边上的高也相等， 所以有EDFS SCDF∆=∆所以AEFACD S S ∆∆=． ······················································ 7分同理CEDCEF S S ∆∆=所以CEF BCE CED BCE BDC S S S S S S 四边形=+=+=∆∆∆∆∆．又因为ADC BDC ABCADCS S S S =△△△△，所以BEFC AEF ABCAEFS S S S =四边形△△△． ·············· 9分因此，直线E F 也是A B C △的黄金分割线． ·················10分 （4）画法不惟一，现提供两种画法；························12分 画法一：如答图，取E F 的中点G ，再过点G 作一条直线分别交A B ，D C 于M ，N 点，则直线M N 就是平行四边形ABCD 的黄金分割线．画法二：如答图，在D F 上取一点N ，连接E N ，再过点F 作F M N E∥交A B 于点M ，连接M N ，则直线M N 就是平行四边形ABCD 的黄金分割线．点评：第（1）小题是利用黄金分割点和黄金分割线的定义完成证明；第（2）小题较简单，用定义说明不满足即可；第（3）小题是利用两条平行直线距离处处相等和面积的等积变形来处理；问题（4）有点发散，但我们用类比的数学思想方法应不难得到一种黄金分割线． 6．定义“形”例 7（2008年衢州市）如图，四边形ABCD 中，AB=AD ，CB=CD ，但AD ≠CD ，我们称这样的四边形为“半菱形”．小明说“‘半菱形’的面积等于两条对角线乘积的一半”，他的说法正确吗？请你判断并证明你的结论． 解：正确证明如下：方法一：设AC ，BD 交于O ，∵AB=AD ，BC=DC ，AC=AC ， ∴△ABC ≌△AD Ｃ， ∴∠BAC=∠DAC AB=AD ，∴AO ⊥BDAOBD 21S ABD ⋅=∆，COBD 21SBCD⋅=∆COBD 21AO BD 21S S S BCD ABD ABCD⋅+⋅=+=∴∆∆四边形ACBD 21)CO AO (BD 21⋅=+=方法二：∵AB=AD ， ∴点A 在线段BD 的中垂线上E A ME A MABCDO又∵CB=CD ，∴点C 与在线段BD 的中垂线上， ∴AC 所在的直线是线段BD 的中垂线，即BD ⊥AC ； 设AC ，BD 交于O ，∵AOBD 21SABD⋅=∆，COBD 21SBCD⋅=∆COBD 21AO BD 21S S S BCD ABD ABCD⋅+⋅=+=∴∆∆四边形ACBD 21)CO AO (BD 21⋅=+=点评：对某些满足一定条件的几何图形给以特定的名词，是几何图形类型的新概念命题．这类问题要求同学们能够灵活运用已掌握的几何知识，解决题中设置的新问题此题就是要求同学们以现有的知识水平，应用现有的数学思想方法，在一个全新的情境中思考问题，探求问题的最终答案，进一步培养同学们思考问题和解决问题的能力．其实本题的面积公式可以作更进一步的推广，只要是对角线垂直的四边形，它的面积就是对角线乘积的一半． 例8（2010年北京市顺义区中考二模数学试题压轴题）我们给出如下定义：有一组相邻内角相等的四边形叫做等邻角四边形．请解答下列问题：（1）写出一个你所学过的特殊四边形中是等邻角四边形的图形的名称；（2）如图1，在A B C △中，AB=AC ，点D 在BC 上，且CD=CA ，点E 、F 分别为BC 、AD 的中点，连接EF 并延长交AB 于点G ．求证：四边形AGEC 是等邻角四边形；（3）如图2，若点D 在A B C △的内部，（2）中的其他条件不变，EF与CD 交于点H ．图中是否存在等邻角四边形，若存在，指出是哪个四边形，不必证明；若不存在，请说明理由．解：（1）矩形，等腰梯形； （2）如图所示，连结AE ，CF ， ∵AB=AC ，E 是BC 的中点， ∴AE ⊥BC ，又F 是AD 中点，∴EF=AF=DF∴∠FED=∠FDE而CD=CA ∴∠FDE=∠CAD ∴∠FED=∠FDE=∠CAD 而AB=AC ∴∠B=∠ACB∴180°-∠B-∠FED=180°-∠ACD -∠FDE 即∠BGE=∠CAD ∴∠BGE=∠CAD=∠FED ∴∠AGE=∠CEG故四边形AGEC 是等邻角四边形图2图1H GFDE CBA GFE DCBA GFEDCBA（3）四边形AGHC是等邻角四边形点评：2010年北京市顺义区中考二模数学试题保持了06、07年北京市中考压轴题的风格，06年是等对角线四边形，07年是等对边四边形，好在第（2）小题的证明不是很难，第（3）小题仍是猜想而言，有兴趣的同学可以证明。
新概念命题赏析
新概念命题赏析武汉市黄陂区横店中学陈浩近年来的中考，竞赛中，屡屡涌现出一种新型试题?──新概念问题，它们立意考查学生阅读、分析、仿练、归纳、内化等综合能力，在解决它们过程中又可产生了许多新方法、新观念，增强了学生创新意识．试题新颖别致，颇具魅力，成为中考、竞赛试题中的一朵朵奇葩，现采撷几束予以赏析．一、定义一种新数【例1】（XX年浙江舟山市中考试题）日常生活中，“老人”是一个模糊的概念，有人想用“老人系数”来表示一个人的老年化程度，其中一个人的“老人系数”计算方法如下表：人的年龄x（岁）x≤6060＜x＜80x≥80该人的“老人系数”1武汉市黄陂区横店中学陈浩近年来的中考，竞赛中，屡屡涌现出一种新型试题?──新概念问题，它们立意考查学生阅读、分析、仿练、归纳、内化等综合能力，在解决它们过程中又可产生了许多新方法、新观念，增强了学生创新意识．试题新颖别致，颇具魅力，成为中考、竞赛试题中的一朵朵奇葩，现采撷几束予以赏析．一、定义一种新数【例1】（XX年浙江舟山市中考试题）日常生活中，“老人”是一个模糊的概念，有人想用“老人系数”来表示一个人的老年化程度，其中一个人的“老人系数”计算方法如下表：人的年龄x（岁）x≤6060＜x＜80x≥80该人的“老人系数”1武汉市黄陂区横店中学陈浩近年来的中考，竞赛中，屡屡涌现出一种新型试题?──新概念问题，它们立意考查学生阅读、分析、仿练、归纳、内化等综合能力，在解决它们过程中又可产生了许多新方法、新观念，增强了学生创新意识．试题新颖别致，颇具魅力，成为中考、竞赛试题中的一朵朵奇葩，现采撷几束予以赏析．一、定义一种新数【例1】（XX年浙江舟山市中考试题）日常生活中，“老人”是一个模糊的概念，有人想用“老人系数”来表示一个人的老年化程度，其中一个人的“老人系数”计算方法如下表：人的年龄x（岁）x≤6060＜x＜80x≥80该人的“老人系数”1。
新概念英语第二册语法解析及练习题
新概念英语第二册语法解析及练习题新概念英语第二册语法解析及练习题：过去将来进行时过去将来进行时：should / would be + 现在分词表示从过去的某个时间到未来的某个时间正在进行的动作。
. He asked me what I should be doing when he came the next day.练习：1. Tomorrow, I ________ the book all morning.A. am readingB. will be readingC. will readD. have read2. -"Can you attend the meeting tonight?" -"No,________ the manager aboutsomething urgent."A. I seeB. I'll have seenC. I'll be seeingD. I can see3. Of the millions who saw Haley's et in 1986, how many people ________long enough to see it return in the twenty-first century?A. will they liveB. they will be livingC. will liveD. living4. He told us that he ________ visiting Japan by this time next year.A. will beB. would beC. wasD. is5. It ________ when you wake up tomorrow morning.A. is snowingB. will snowC. will be snowingD. snows答案：1. B2. C3. C4. B5. C新概念英语第二册语法解析及练习题：过去完成进行时过去完成进行时:had been + 现在分词表示一直持续到过去某个时间的动作。
新概念英语第二册阅读理解题型及其解题技巧
英语阅读理解的常见题型及其解题技巧如下：1. 细节题：细节题是针对文章的某个细节而设置的试题。
解答这类试题时，一个常用的方法就是运用定位法，即根据题干或选项中的线索词从原文中找到相关的句子，与选项进行比较从而确定答案。
要注意一些常见的同义转换。
2. 推理题：推理题是指从文章中找出相关信息，并运用这些信息进行逻辑推理，得出正确答案的试题。
解答这类试题时，需要细心阅读文章，理解作者的意图和思路，并注意文章中的关键词和句子。
3. 主旨大意题：主旨大意题主要测试学生对文章主旨大意的理解能力。
解答这类试题时，可以运用串线法，即抓首段和其余各段的第一句话，把其意思连接成一个整体。
要特别注意总结性的提示词和转折词，以及中心句。
4. 词义句意猜测题：词义句意猜测题是指根据上下文推测某个单词或句子的意思。
解答这类试题时，需要运用上下文信息进行推测，同时也可以运用语法知识和常识进行判断。
5. 结构顺序题：结构顺序题主要测试学生对文章结构和顺序的理解能力。
解答这类试题时，需要细心阅读文章，理解文章的结构和顺序，并运用逻辑思维进行分析和判断。
6. 指代题：指代题主要测试学生理解代词和名词短语在句子中的指代关系。
解答这类试题时，可以根据上下文的语境进行推断，或者利用指代词的特点进行判断。
7. 推理引申题：推理引申题主要测试学生根据文章内容进行逻辑推理和引申，得出结论的能力。
解答这类试题时，需要仔细阅读文章，把握作者的观点和态度，并根据文章内容进行合理的推理。
8. 观点态度题：观点态度题主要测试学生理解作者对某个问题的看法和态度。
解答这类试题时，需要通过阅读文章的关键信息，如作者的观点、态度、语气等，来推断作者的立场和观点。
9. 综合题型：综合题型是指将多种题型进行组合，要求学生根据文章内容进行综合判断和解答的试题。
解答这类试题时，需要灵活运用所学的解题技巧，结合文章的语境进行综合分析和判断。
针对不同题型，我们可以采取以下策略来提高解题效率和准确率：1. 先看题目，再读文章：通过阅读题目，了解试题的要求，带着问题去阅读文章，提高阅读的针对性。
新概念2册测试题分值与解析.doc
综合能力尚可，可从三册建立新的语言认知和建设。
新概念III（上）
91-100分
综合能力很强哦~~不要松懈，英语学习前途不可限量^_^
新概念III（下）
（二）词汇部分评析（2.5分每题，满分25分）
1.水平鉴定
总分
水平鉴定
推荐课程
0-10分
词汇量偏少，不利于英语的学习哦，须知单词是一切的基石哦！
新概念Ⅱ（上）
11-20分
词汇量较少，需要在单词部分再加把劲啊！
新概念Ⅱ（上）
21-25分
词汇量不错哦，相信在日后的新概念学习中会有更大的收获。
新概念Ⅱ（下）
2.典型错误
题号
考点及说明
第一题
对形容词和副词掌握的能力。
如果这个空格学生填错了，那么说明该学生需要继续加强词性的区分和用法。
第五题
对被动语态和动词不定式的掌握。（一）总分评析（满分1源自0分）总分水平鉴定
推荐课程
0-10分
语法词汇能力基本为零,须从基础打起。
新概念I（上）
11-20分
对英语有一定认知，但基础仍不扎实，须打实基础。
新概念I（下）
21-60分
理解能力不理想，须多多加强。
新概念Ⅱ（上）
60-80分
理解能力水平居中，好好努力，有很大的进步空间。
新概念Ⅱ（下）
1.水平鉴定
总分
水平鉴定
推荐课程
0-15分
理解能力较差，须多多加强。
新概念Ⅱ（上）
16-40分
理解能力水平居中，好好努力，有很大的进步空间。
新概念Ⅱ（上）
41-50分
综合能力很强哦~~不要松懈，英语学习前途不可限量^_^
新概念英语第二册试题和答案解析
WORD 格式 .整理版标准试卷专业本科年级班姓名学号题号一二三四五总分得分Part I Vocabulary and Structure (30%)Directions: There are 30 incomplete sentences in this part. For each sentence there are four choices marked A), B), C) and D). Choose the ONE that best completes the sentence.1.He made a big decision. He ______.A .thought about it B. made up his mind C. changed his mind D. made a wish2.He didn ’twrite a single card. So he __________.A wrote only one B. Didn ’twrite even oneC.wrote just oneD. wrote all the cards except one3.On the last day he made a big decision. It was the ______ day of his holiday.A final Bend C. latest D bottom4.The waiter lent him a book. He _______ a book from the waiter.A lentB borrowedC tookD stole5.Tim is in Australia. How long _______ there?A is heB has he beenC has heD was he6.Mr. Scott can ’tget a telephone. Telephones are hard to_______A. takeB. ReceiveC. obtainD. find7.He has sent requests for spare parts. He has _____ spare parts.A. askedB. asked forC. beggedD. pleased8.He has visited a great number of different places. He has not stayed in_______ place.A. the onlyB. a similarC. the sameD. alike9.He has just one to Alice Springs. He has never______ there before.A. wentB. beingC. beenD. was10.Mr. Tim can not get a telephone for his garage. _______he has just bought twelvepigeons.A. That ’s soB. That ’s whyC. BecauseD. For11. What ’s the distance from Pinhurst to Silbury? How ____ is Pinhurst ____ Silbury?优质 .参考 .资料A.long ago... tillB. long... awayC. Away... tillD.far...from12.Urgent messages are important, so they must be sent ____ .A. quicklyB. slowlyC.by handD. largely13.Mr. Button ’s telephone service is private. It is ____ .A. generalB. spareC. secretD. his own14.She gave____A. to him a mealB. a meal for himC. him to a mealD. a meal to him15.Everyone knows him. ____ know him.A. The allB. EachC. EveryD. All they16.You can have a meal ____ .A. only in the morningB. at any timeC. only at middayD.only in the evening17.All the housed in our ____ are the same age and size.A. streetB. wayC. roadD. route18.Joe ’ s garden is the best in the town. It_____ them’s allthe. bestA. in B of C. for D by19._____, it is an important book.A. By the wayB. On the wayC. In the wayD. In a way20.What ‘ s it _____ A? clavichord.A. told B said C called D spoken21.The family have had he clavichord _____ many years.A. since B for C from D by22.______I was looking for it, the inn-keeper came in.A. BecauseB. WhileC. ButD. Even if23.They are not allowed to watch TV _____ the week.A. on B .at C.during D. for24.____ does he call? Once a month.A. How seldomB.How longC. How soonD. How often25.The detective were _____ a valuable parcel of diamonds.A. expectingB. waitingC. expecting forD. expecting to26.Someone had filled the parcel with stones and sand. It was _____ stones and sand.A. full withB. full ofC. full byD. full in27.Two men took the box off the plane. They _____ .A. took off itB. it took offC. took offD. took it off28.The thieves wanted to _____ the diamonds.A. robB. stealC. take fromD. take to优质 .参考 .资料29.Joe wins every time. He always _____ Bill Frith.A. winsB. beatsC. gainsD. earns30.Mary ’s garden is interesting. She is _____ in gardening.A. interestingB. interestC. interestinglyD. interestedPart II Translation (20%)Directions: Translate the following phrases into Chinese or English.31. 到现在为止36.it ’s none of your business.32.我不能忍受37.a few words33.多么糟糕的一天!38. turn around34.脱下外套39.Dear me!35.许多（修饰复数可数名词）40. in the centre ofPart III Fill the blanks with prepositions( 介词 ) (10%)41.He went ___ America six months ago.42.He will go there _____ air.43._____ Wednesday evening, we went to the Town Hall.44._____ return for this, the bagger stood on his head and sang song.45.Please write an essay _____ English.Part IV Reading Comprehension (30%)Directions: There are 2 passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A), B) C) and D). You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single line through the center.Passage OneOne day a big rock （岩石） fell down from a mountain. The rock stopped in the middle of the road in a village. It was like a big ball. Some of the strongest men in the village tried to move the rock. But no matter how hard they tried, they couldn't move it away. They tried to push it; they tried to roll it and they tried to pull it with a rope, but nothing worked."Well" they agreed, "there's nothing we can do about it. We'll have to build another road. "At this time, a young boy of about 12 years old said, "Excuse me, sirs, but I thinkI can help you move the rock. ""You?" they shouted, "What are you talking about? All of us have just tried and we优质 .参考 .资料can't move it at all.” The men all laughed at the boy.The next morning some people came into the street. One of them shouted, "The rockis gone!" More people ran out into the street to see for themselves. It was true, and noone could see it anywhere."It is impossible, where has it gone?" they said. The boy stood out, saying "I did it last night. I dug a deep hole next to the rock and the rock rolled down into the hole by itself. Then I covered it with earth. "46.Where was the big rock from? ________A. a streetB. a mountainC. a hillD. a tree47.Why did the people in the village want to move the rock away? Because________ .A. it was in the middle of the roadB. it was on the mountainC. they didn't like the rockD. they wanted to build a road48.What did the people decide to do when they were not able to move the rock away?They decided to________A. find someone stronger to help themB. ask a little boy of 12 to help themC. build another roadD. break the rock49.Why did the people laugh at the boy? They thought that_____.____A the boy was too weak to move the rock awayB the boy was so strong that he could move the rockC.the boy was very helpfulD.it was easy for him to move the rock50.The next morning the people in the village found the rock _________A. disappearedB. was still thereC. was back on the mountain againD. was rolling down from the mountainPassage TwoSome ants（蚂蚁） make their homes under a stone. If the weather is warm, you may see many ants under the stone. If the weather is cold, many ants will be in their house under the ground.Most of the ants are workers. They are very busy. They look for food and take care of the young ants. Each family of ants has a queen ant （蚁后） . The queen ant doesn't work. She is important because she lays eggs. Those eggs will become baby ants.There are many kinds of ants in America. One kind of these is very strong. Peopleare afraid of it, and animals are afraid of it, too.These ants move in groups. They eat all the animals on their way. They can kill andeat elephants, and they can eat wooden houses. When the ants come near, people leave their homes. But people are sometimes glad after the ants pass through, because they will see no other insects or snakes.优质 .参考 .资料51. Where can you find ants on warm days? ________A. Under the ground.B. On the ground.C. Inside people's houses.D. Under a stone.52.Why is a queen ant more important than a worker ant? Because ___________A.a queen ant produces the youngB.a queen ant is stronger than all the other family membersC.a queen ant finds food for all the other family membersD.a queen ant does more work than all the other family members53.Where can you find many kinds of ants according to the passage? ________A. In America.B. In China.C. In Canada.D. In Britain.54. Why are people glad after the dangerous ants pass through? ________A. Because they are goneB. Because they are not dangerous anymoreC. Because there are no other insects or snakesD. Because the ants can be eaten55.Which of the following is true? ________A.People are not afraid of any kind of ant.B.Big animals are not afraid of any kind of ant.C.An elephant can kill and eat a kind of very strong ant.D.One kind of ants moves in groups.Passage ThreeTom Green spent his 114th birthday the other day and some reporters visited him to findout the secret of a long life.“ The secret of a long life is happiness,” Green said.“ If you are happy, you w long time.”“ Are you married?” a reporter asked.“ Yes,” Green answered.“ I married m when I was 102. If you are happily married, you will live better. But for（要不是）my thirdwife, I would have died years ago.”“ What about smoking and drinking?” another reporter asked.“ Yes, they are important,” Green said.“ Don’ t smoke at all and you will feel well. Drink two glasses ofwine a day and you will be healthy and happy.”56.Some reporters visited Green because________A. he did something peculiarB. he was a friend of themC. he had lived much longer than most peopleD. he had married three times57. Green thought that________ was the most important to life.A. his third wifeB. gladC. happinessD. smoking优质 .参考 .资料58. Green thought his third wife helped him to live________ years longer.A.12B.14C.16D.1859.The writer wants to tell us________A.drinking a great deal is good for our healthB.drinking within a limit is helpfulC. smoking and drinking are indispensable （不可缺少的） to good healthD.we should quit smoking or drinking.60. The best title for this passage is________A. Drinking and SmokingB. The Secret of a Long LifeC. Happiness in LifeD. Astonished ReportersPart V Writing (10%)Directions: For this part you are allowed thirty minutes to write a composition on the topic The Use of Computers in Schools . Your composition should be no less than 120 words and based on the outline (given in Chinese) below:1.学生越来越多地使用电脑的好处。
新概念英语第一册期末测试试题附答案解析22574
新概念英语第一册（1-144课）期末测试试卷新概念英语一测试题(1) 数词, 冠词, 介词, 动词时态变化, 比较级和最高级一写出复数1. radio2. knife3. glass4. shelf5. boss6. dress7. housewife8.postman9. leaf 10. church 11. mouth 12. family13. tie 14. tomato 15. piano 16. baby17. tooth 18. country 19. key 20 potato21. match 22. box 23. hour 24. hero二用冠词a, an, the 或 some , any 填空, 如果不需要,则用 / 代替.1. Alice is ____ air-hostess. Her father is ____ engineer and her mother is _____ housewife. They all play ______ tennis very well.2. He has ____ uncle and his uncle lives in ____ United Kindom. He first saw him in ____ autumn of 1978. 7. We need _____ ink, is there _____ left?3. It is better to tell ______ truth than to tell _______ lies.4. Will you have ______ more tea? There’s plenty in the pot.5. There is ___university near my home. Every Saturday evening,___ students hold ____ party. ___ are dancing, ____ are singing. They make a lot of noise.6. Get me ________ cigarettes, please. ______ kind will do.三用适当介词填空.1. Can you see the words written ________ the blackboard? (in, on, by, with)2. She is taking the children out _______ a walk. (in, on, for, by)3. You can choose the best one ________ them. (in, on, among, by)4. Jack broke the chocolate _______ several pieces. (in, on, with, into)5. There are two bridges ______ the river. ( in, on, with, into)6. There is a slogan(标语) _______ the wall. (on, in, over, above)7. He sits ________ his desk all day _______his head _______ his hands. He is deep in thought. (on, in, at, with)8. _______ the help _______ the teachers, the students have made great progress _______their study. (on, in, of, with)9. He will be back _______ a minute. ( on, in, for, by)10. The teacher is standing _______ the class. (on, before, to, in)11.Our train arrived_____Shanghai_____6:30______a foggy November day .(on, in, at, by)四用所给词的适当形式填空1. Tom ______ (be) ill last week, he ______ (be) much better now.2. Jimmy and his sister _______ (be) here several days ago.They ________ (leave) for Beijing yesterday.3. He ___________ (have ) a bath when the telephone ________(ring).4. While I __________ (cook ) the dinner, he ___________(read) the paper.5. He arrived just as I _____________ (answer) the phone.6. After I heard the news, I ___________ (hurry) to see him.7. We ____________ (be) disappointed if there is no snow for Christmas.8. You ____________ (lie)! Stop it, and tell the truth like a man.9. I _________ (be) hungry since five o’clock this morning.10.His hair is long; he ________ (have) a haircut tomorrow.11.A: _______ Mr. Smitch ________ (leave) for Beijing today or tomorrow?B: Oh, he ____ (go ) already. He _____ (take) the morning train yesterday.12. ________ the rain still _______ (fall), or _______ it _______(stop)?I want to go shopping today.13.No one _________ (watch) the television, so Father turned it off.14.He usually ______(get) up at 6 o’clock in the moring, but he ______(have) to get up very early yesterday morning, because he wanted to catch a train.15.This big car ________(drive) by a 19-year-old girl in trhe car race yesterday. 16. The boy____________ (not invite) to the party yet, but I think he will be invited soon.五写出比较级和最高级1. good2. bad3. little4. beautiful5.many 6. small 7. fat 8.thin 9.pretty10. dirty(2) 介词, 情态动词, 形容词比较级, 反意疑问句六用适当介词填空1. The fur coat is not ____ fashion now.2. The boss is busy now. Can you wait ______ two o’clock in the afternoon?3. Have you seen the film “Murder on the orient Express” ______ a B.B.C. Television programme?4. The examiner asked the students to write their names ____ the top of paper.5. In many countries people can buy things ______ installments.6. Please turn ______the light, it’s dark now.7. When the boy got ______ the bus, he found that two policemen were walking towards him in the street.8. I took three books ______ me when I came out of the library.9. Last year I travelled ______ a very large and beautiful ship to Hong Kong.10.Have you made _____ your mind where to go during the summer vacation?11.When I am ______ work, don’t bother me.12.When Miss Jones came _________. She found the doctors and nurses standing by her bed.13.Mary went to open the door and looked out _______ the garden.14.This monkey belonged ______ an old man who was fond of monkeys.15.She spent two evenings _______ playing chess.16.I am looking forward _______ your visit here.17.He is sitting at the table covered _______ flowers.18.What’s ______ today’s news paper?19.They ran wildly crying ________help where no help could be.20.My little brother dreams _________ becoming a seaman.七选择正确的一项.1. You _____ take an umbrella, I am sure it won’t rain.(A.mustn’t, B. needn’t)2. You _____ cross the road w hen the lights are red. (A.mustn’t, B. needn’t)3. She has fallen asleep, she _____be very tired. (A. must, B. can)4. He has eaten a lot at lunch, he _____ be seriously ill. ( A. mustn’t,B. can’t)5. What’s the matter with you? You look pale, you ______ go to see the doctor. (A. must, B.need)6. You _____ do whatever you like at home, but you _____ keep the rules at school. ( A.must, B.can, C.need)7. The streets are so wet that it ___ rained last night.(A.must have,B.can have)8. She seems to know nothing about the accident. She _____ been here.(A.can’t have, B.mustn’t have)9. He is not at home, he ____ gone to the office. (A. can have, B.may have)10.The box is very heavy. I think there ______ some books in it.(A. may be, B. may have been)八用形容词的适当形式填空1. An elephant is __________(big) than a horse.2. This is the ___________ (helpful) servant we have ever emplyed.3. My elder sister is four years __________ (old) than I.4. A car can not run _______________ (fast) a train, but it can run _____ (fast) than a bicycle.5. Beijing is one of _____________(large) cities in our country.6. A: Are you busy now? B: No, I am not ___________ (busy) I was yesterday.7. To a European, Chinese is ________________ (difficult ) than French.8. The Yangtze River is the _________________(long) river in China.9. He studies ___________(hard) than I do, so that he often gets high marks. 九完成反意疑问句1. It isn’t snowing hard now, ______________?2. Tim is upstairs, ______________?3. You are not coming to the meeting tomorrow, ______________?4. You haven’t seen the film yet, ________________?5. The workers aren’t Dutch, _______________?7. He can play tennis very well, _________________?8. Mary studied very hard, _________________?9. Mr. Li couldn’t speak English very well, __________________?10.Mother has cooked the meal, ___________________?11.He will visit London next month, ______________?12.They won’t go to the park this afternoon, _________________?13.Peter hopes to wash the clothes himself, _________________?14.Mrs. Food was in Paris last spring, ______________?15.You have a sister, ______________?16.He had a good swim the day before yesterday, ________________?17.The man wants to go to Trafalgar Square, ______________?18.He was going to the dining-hall, _________________?19.You like stories, _______________?20.Harry may go abroad this year, _______________?21.Everyone likes her, _____________? /_________________?22.There is never a sports meeting hold in our school, _____________?23.She was unhappy just then, ______________?(3) 选择及改错十选择填空( ) 1. Father came ______ Sally was slipping on the floor.A. whileB. just asC. whenD. as( ) 2. I am a student, ______?A. isn’t IB. am IC. aren’t ID. don’t I( ) 3. Comrade Chang did quite well, he made very ______mistakes.A. a littleB. a fewC. littleD. few( ) 4. _____ the typewriter to the next room, and ____ the recorder here.A. Bring, takeB. Take, bringC. Carry, takeD. Bring, carry( ) 5. As you are ____ insistent person, I will go with you.A. soB. suchC. a soD. such an( ) 6. The men _____were all engineers.A. which I talkedB. to those I talkedC. those I talked toD. I talked to( ) 7. Your book is on the floor. ___________---A. Pick it up!B. Put up it!C. Pick it!D. Take up it!( ) 8. There are only _____cigarettes in the box. I havetoo____ time to buy any today.A. a few, littleB. a little, fewC. a few, a littleD. a little, a few( ) 9. I would like to ___to your English teacher if he is not too busy now.A. askB. tellC. sayD. talk( ) 10. Harry hasn’t passed in the exam. ___Dick.A. So hasB. Neither hasC. Either hasD. Nor is( ) 11. “Don’t eat too ____ before going to bed” Mum said to me.A. manyB. muchC. fewD. lot( ) 12. Please don’t say anything that might ____ her feeli ngs.A. injureB. hurtC. woundD. damage( ) 13. The little boy____ his pencil everywhere, but hecouldn’t_____it.A. was looking for, findB. was looking after, findC. was finding, look atD. was finding, look after( ) 14. Li Yin is not _____ today. She is ill.A. goodB. wellC. betterD. best( ) 15. He has been in Shanghai ____ last month.A. forB. sinceC. afterD. before( ) 16. I hate this snow and frost. Shall we go to a country with a warmer_?A. climateB. weatherC. daysD. season( ) 17. That’s the place ______last year.A. which we visitedB. at which we visitedC. where we visited itD. in where we visited( ) 18. ____will you get to Xi’an? By plane.A. whenB. whereC. How D What( ) 19. She lets each of the boys _____ a bar of chocolate.A. hasB. havingC. to haveD. have( ) 20. You are not so wise ______he.A. asB. thanC. toD. over十一改错1. Mathematics are my favorite subject. ___________2. They have no any time to waste. ___________3. Have you ever gone to Hangzhou? ___________4. He asks me what shall we do after lunch. ___________5. I have done my homework yesteray. ___________6. A number of students is there. ___________7. Here are two books. Which one do yo like best? ___________8. It is old enough for the boy to go to school. ___________10.Between you and he, there is a difference. ___________11.They are talking each other. ___________新概念英语第一册期末测试卷答案II1.He must call the doctor.2.He is going to telephone him.3.He can go with her.4.He has a new car.5.He comes from America.6.He is American.7.He likes ice cream.8.He wants a newspaper.9.He was at school yesterday.10.He doesn’t live here.III1.There are some watches on the table.2.There are some knives near that tin.3.There are some policmen in the kitchen.4.There are some cups on the table.5.There are some letters on the shelf.6.There are some peaches on the desk.7.There are some passports on the shelf.8.There are some fishes in the cupboard.9.There are some trees in the garden.10.There are some boats on the river.IV1.a2.some3.some4.any5.a6.a7.some8.any9.some10.someV1.at2.on3.on4.from5.in6.at7.in8.in9.on10.atVI1.over2.under3.across4.along5.on6.in7.off8.between9.into10.out of VII1.making2.swimming3.shining4.shaving5.running6.sitting7.typing8.puttinging10.givingVIII1.Can he come now? / When can he come? / He cann’t come now.2.Is there a newspaper on the desk?/What is it on the desk?/There isn’ta newspaper on the desk.3.Does he want a new car?/What does he want?/He doesn’t want a new car.4.Is he going to come now?/When is he going to come?/He isn’t going to come now.5.Do they like ice cream?/What do they like?/They don’t like ice cream.6.Does he come from Germany?Where does he come from?/He does’t come frome Germany.7.Must they go home now?/When must they go home?/They mustn’t go home now.8.Does he feel ill?/How does he feel?/He doesn’t feel ill.9.Does he have a headache?/What does he have?/He doesn’t have a headache.10.Did he clean his shoes?/When did he clean his shoes?/He didn’t clean his shoes.。
新概念一结课测试题答案与解析
新概念一结课测试答案与解析一、单词解析1daughter2engineer3Italian4across5children6magazine7picture8clothes9favourite10empty二、单选解析1答案为B，考察人称和be动词的搭配。
口诀为“我用am，你用are，is用于他她它，复数名词全用are”。
2答案为B，考察形容词性物主代词。
我们的our；他们的their。
3答案为D，考察人称代词主格和宾格的用法。
口诀是：放句首，作主语，用主格；放动（介）后，作宾语，用宾格。
books为复数，所以宾格是them；Mary是女孩，所以宾格是her。
4答案为A，考察特殊疑问句。
“谁的”用whose表示；答语为“是Sally的”，要用名词所有格形式表示，即Sally’s。
5答案为C，考察一般疑问句的回答。
由第三句Sorry，sir（对不起先生），结合语境，得知要使用否定回答，即No,it isn’t.6答案为B，考察名词单数变复数。
以o结尾的名词一般情况下直接加s，某些特殊的单词要加es，口诀是：黑人（negro）英雄（hero）喜欢站在火山上（volcano）吃西红柿（tomato）和土豆（potato）。
7答案为C，考察情景对话。
Nice to meet you答语为Nice to meet you, too.8答案为B，考察人称代词主格和宾格用法。
动词和介词后用代词的宾格，she的宾格为her；I的宾格为me。
9答案为A，考察上下文理解。
根据下文“我是老师”可知，上文问的是职业。
询问职业有两种问法：What is your job？或者What are you？10答案为A，根据题意，我的妹妹不矮，所以是高的，即tall；long 表示长度，tall和high表示高度，所以主要还是区别tall和high。
形容人用tall；形容山峰建筑物用high或者tall。
11答案为C，考察some和any的区分。
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2014年中考“新概念”试题综述与赏析 上海市青浦区金泽中学 李雪峰
“新概念”试题，其设计新颖，构思独特，思维容量大，既能考查学生的阅读、分析、推理、概括等能力，又能考查学生知识迁移的能力和数学素养，同时还兼具了区分选拔的功能，因此越来越受到全国各地命题者的青睐，已经成为了近几年数学中考试题中的一道亮丽风景线。
因对“新概念”试题的研究及突破对教师的教学和学生都具有很高的价值。
下面笔者就2014年全国中考试题中出现的“新概念”试题进行综述，并精选几道试题作一赏析，以期为广大进行“新概念”试题研究的教师提供参考。
一、2014年中考“新概念”试题综述
通过对150余份2014年中考数学试卷的研究发现，2014年中考新概念试题大致分为以下8类，相关类型及题目出处见表1:
1、新定义点—梦之点
例1(2014年·湖南长沙)、在平面直角坐标系中，我们不妨把横坐标和纵坐标相等
的点叫“梦之点”，例如点（1,1），（-2，-2），，…都是“梦之点”，显然“梦之点”有无数个.
(1)若点P （2，m ）是反比例函数n y x
=（n 为常数，n ≠0）的图像上的“梦之点”，求这个反比例函数的解析式；
(2)函数31y kx s =+-（k,s 为常数）的图像上存在“梦之点”吗？若存在，请求出“梦之点”的坐标，若不存在，说明理由；
(3)若二次函数21y ax bx =++（a ,b 是常数，a ＞0）的图像上存在两个“梦之点”11(,)A x x 、22(,)B x x ，且满足-2＜1x ＜2，12x x -=2，令215748
t b b =-+，试求
t 的取值范围.
解析：（1）4y x
=
； （2）由题意得：“梦之点”应该在直线y x =上，所以当y x =时，由31
y kx s =+-得，(13)1k x s -=-（）：①当13
k =且s=1时，x 有无数个解，此时的“梦之点”存在，有无数个；此时的“梦之点”存在，坐标为（113s k --，113s k
--）； （3）由21y a x b x y x ⎧=++⎨=⎩得：2(1)10ax b x +-+=，则12,x x 为此方程的两个不等实根，则121211, b x x x x a a -+=⋅=；由12x x -=2，得221214()4b x x a a
-⎛⎫-=-= ⎪⎝⎭，所以22b b -2(21)2a =+-，22157612(21)4848
t b b a ∴=-+=++；又因为122x -<<，且122x x -=，所以244x -<<，1288x x -<⋅<；故188a -<<，又1108, 8
a a ∴<<>即时，0,a > 当a =18时，t =176，本题最后得：当a ＞18时， 176
t >. 2、新定义图形—准蝶形
例2（2014年·南昌市）、如图1，抛物线2(0)y ax bx c a =++>的顶点为M ，直线y =m 与x 轴平行，且与抛物线交于点A ，B ，若三角形AMB 为等腰直角三角形，我们把抛物线上A 、B 两点之间的部分与线段AB 围成的图形称为该抛物线对应的准蝶形，线段AB 称为碟宽，顶点M 称为碟顶，点M 到线段AB 的距离称为碟高.
（1）抛物线212
y x =对应的碟宽为____；抛物线24y x =对应的碟宽为_____；抛物线2y ax =（a >0）对应的碟宽为____；抛物线2(2)3(0)y a x a =-+>对应的碟宽____；
（2）若抛物线254(0)3
y ax ax a =--
>对应的碟宽为6，且在x 轴上，求a 的值；
（3）将抛物线2(0)n n n n n y a x b x c a =++>的对应准蝶形记为F n （n=1,2,3，…），定义F 1，F 2，…，F n 为相似准蝶形，相应的碟宽之比即为相似比。
若F n 与F n-1的相
似比为12
，且F n 的碟顶是F n-1的碟宽的中点，现在将（2）中求得的抛物线记为y 1，其对应的准蝶形记为F 1.
①求抛物线y 2的表达式；
② 若F 1的碟高为h 1,F 2的碟高为h 2，…，F n 的碟高为h n ，则h n =_______；F n 的碟宽右端点横坐标为 ；F 1，F 2，…，F n 的碟宽右端点是否在一条直线上？若是，直接写出改直线的表达式；若不是，请说明理由.
解：（1）4、12 、2a 、2a
. （2）∵254(0)3y ax ax a =--
>可得， ∴2a
=6，解得，a =13 ；∴y ＝13(x -2)2-3． (3) ①∵F 1的碟宽︰F 2的碟宽=2:1， ∴
12222:1a a =:，∵113a =，∴223a =； ∵211233
y x =--（）的碟宽AB 在x 轴上（A 在B 左边）， ∴A （-1，0），B （5，0），∴F 2的碟顶坐标为（2，0）， ∴22223
y x =-（）； ②∵n F 的准碟形为等腰直角三角形，∴n F 的碟宽为2n h ， ∵12122
n n h h -=，∴23112311111()()...()2222n n n n n h h h h h ----=====. ∵1h =3，∴112
n n h -=（）·3. ∵n h ∥1n h -，且都过1n F -的碟宽中点，
∴1231n n h h h h h -⋯，，，，，都在同一条直线上，
∵1h 在直线x =2上，
∴1231n n h h h h h -⋯，，，，，都在直线x =2上，
∴n F 的碟宽右端点横坐标为2+112
n -（）·3. F 1，F 2，…，F n 的的碟宽右端点在一条直线上，直线为5y x =+．
点评：
本题给出了准碟形的有关概念，阅读量大，文字多，要求考生能理解新
概念背后的所蕴含的数学知识与本质意义；考查学生对新定义和新知识的学习、模仿和应用能力．题目中主要涉及特殊直角三角形，二次函数解析式与图象性质，多点共线证明等知识，综合难度较高，学生对题意要清晰的理解比较困难。
3.新定义函数——有界函数
例3（2014年·北京市） 对某一个函数给出如下定义：若存在实数M >0，对于任意的函数值y ，都满足-M ≤y ≤M ，则称这个函数是有界函数．在所有满足条件的M 中，其最小值称为这个函数的边界值．例如，下图中的函数是有界函数，其边界值是1．
（1）分别判断函数1 (0)y x x
=> 和y = x + 1（- 4 < x ≤ 2）是不是有界函数？若是有界函数，求边界值；
（2）若函数
1 (,)y x a x b b a =-+≤≤>的边界值
是2，且这个函数的最大值也是2，求b 的取值范围；
（3）将函数2(1
,0)y x x m m =-≤≤≥的图象向下平移m 个单位，得到的函数的边界值是t ，当m 在什么范围时，满足3
14t ≤≤？
三、几点思考
新概念试题实质上是原有认识结构与新知识之间的迁移，解决此类问题的关键是读懂题意，理解“新定义”，确定探索方向，然后运用类比与归纳的方法寻找合理的解题思路，为了让学生能行之有效地突破的解决此类问题，笔者提出以下思考和建议。
1、鼓励学生自主探索，培养自学的能力，加强学习策略的指导
“新概念”试题需要学生自己阅读新知，再运用相关的知识去解决问题，这种思维的路径折射出的是学生自主学习的能力和主动探索的品质，这种能力和品质需要教师在平常的课堂教学中，自觉践行新课程的理念，坚持“先学后教”的原则，同时不断加强对学生学习策略的指导。
2、关注“过程与方法”维度，切实提升学生分析与综合、归纳与概括的能力
时下课堂教学中还存在“轻两头烧中段”的现象，忽视知识的形成和发展过程，仅关注知识的结果和运用，从上述例题中可以看出，“新概念”试题虽然知识新颖，但问题的解决仍然是运用学生已有的知识和经验，这种求解的过程实质上就是探索知识的发生、形成和运用的过程，这警示我们三维目标不可轻视“过程与方法”维度，学生创造性的思维和求解能力，是孕育在长期的学习探索的实
践过程中。
3、重视“基本思想”的领悟和“基本活动经验”的积累
课标提出“四基”，重视基础知识和基本技能是我们教学的传统，但基本思想和基本活动经验还未能引起足够的重视，数学思想是探索和研究数学的基础，是解决数学问题的主线；数学活动是伴随学生相应的数学知识学习而设计的观察、试验、猜想、验证、推理与交流、抽象概括、问题反思与建构等，上述例题的解析均蕴含着数学思想，需要设计解决问题的策略、过程和程序，“思想”需要领悟，经验需要积累，我们应在教学中引起关注和重视。