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中考专题复习-中考常见陷阱题(含答案)

中考专题复习-中考常见陷阱题(含答案)
中考专题复习-中考常见陷阱题(含答案)

中考常见陷阱题

【知识要点】 1 陷阱题的概念

所谓陷阱,就是学生平时解题中容易出错的一些问题,也是学生解题的薄弱环节。目前,陷阱题没有统一的定义。也有这样的观点:陷阱题通常也叫“圈套题”,是指学生在解题时容易“上当受骗”的题目。“陷阱题”与常规题不同,它具有较大的迷惑性,较好的隐蔽性。根据这些观点可以对陷阱题下这样的定义:能矫正学生知识掌握不准确考虑问题不全面的数学习题,称为数学陷阱题。 2 数学陷阱题的分类 a 、性质硬套型陷阱题

这类问题往往很容易一看题目就得到结论,但结论可能不止一个,而忽略其背后所隐含的题意而导致错误答案的出现。 b 、概念干扰型陷阱题

就是题目中没有出现概念性的东西,但解题过程却必须注意题目中隐含的定义来排除答案。学生往往忽略这些隐含条件而多出错误的答案。 c 、思维定势型的陷阱题

思维定势是指人们在长期的思维过程中所形成的一种固定的思维模式。它是一把双刃剑,如果运用得当,它可以帮助考生将考题内容与以前所学知识迅速联系起来,并在短时间内调集解决问题所需的相关知识进行分析、推理,并很快得出正确的结论;但若运用不当,它便会误导考生掉入命题人所预设的陷阱,得出错误的结论。 【历年考卷形势分析及中考预测】

在中考数学命题中,命题者为了考查同学们对所掌握知识的灵活运用情况,常常设置种种“陷阱”。同学们解题时如果审题不严、思考不周全,就会误入陷阱。

陷阱题是历年来中考的必考内容,因题目设计灵活,考察面(主要考察学生基本概念,常见数学思想)广而备受命题者的青睐,从简单的选择填空到较为复杂的中考压轴题甚至竞赛中的压轴题,出题范围极为广泛,对于学生的数学知识综合运用能力考察较多。纵观近6年广州市的中考试题,考点主要集中在考察学生基本概念及分类讨论的数学思想。 【考点精析】

考点1. 因对数学概念的认识模糊而掉入陷阱。 例1.当x =________时,分式

2

22---x x x 的值为零。

例2.方程

11

212=--+x x x 的解为( ) A .x =1 B . x =-1 C . x =1或-1 D .无解 【举一反三】 1. .函数1

1

2

-+=

x x y 的自变量x 的取值范围是_______________. 2.方程2)2(2-=-x x x 的解是___________.

3. .若二次根式9a a b +和a b +8是同类二次根式,则ab 的值是____________。

考点2. 因忽略题目的隐含条件而掉入陷阱

例3. 已知关于x 的一元二次方程(k +4)x 2+3x +k 2+3k -4=0的一个根为0,求k 的值。

例4.已知:关于x 的一元二次方程01422

=+++x k kx 有两个不相等的实数根,求k 的

取值范围。

【举一反三】

1.先化简代数式1

24)111(222+--÷--x x x x ,然后再任选一个你喜欢的x 的值代入求值。

2.某等腰三角形的两条边长分别是3cm 和6cm ,则它的周长是( ) A .9cm B .12cm C .15cm D .12cm 或15cm

3. .若一元二次方程x ax a 240--=的两实数根的和为432a -,则两根之积为( )。

A .-4

B .34或-

C .3

D .-34或

4. .已知()()x x x x x x x x x x

-+-=----?? ???÷+-+21201346

32

2

,求的值。

考点3. 因几何图形的形状或位置的多样性而掉入陷阱。

例5.如图,在梯形ABCD中,AD∥BC,∠A=900,AB=7,AD=2,BC=3,问:在线段AB上是否存在点P,使得以P、A、D为顶点的三角形和以P、B、C为顶点的三角形相似?如不存在,请说明理由;若存在,求出PA的长。

例6.在平面直角坐标系中,点A坐标为(1,1),在x轴上是否存在点p,使△AOP为等腰三角形?若存在,请直接写出P点的坐标;若不存在,请说明理由。

【举一反三】

1.相交两圆公共弦长16cm,其半径长分别为10cm和17cm,则两圆圆心距为__________。

2. 园内有一弦,其长度等于园的半径,则这条弦所对的圆周角的度数为_________.

考点4. 因忽略变量的取值范围而掉入陷阱。

例7.如图,在平面直角坐标系中,四边形ABCD 为矩形,点A 、B 的坐标分别为(6,1)、(6,3),C 、D 在y 轴上,点M 从点A 出发,以每秒3个单位的速度沿AD 向终点D 运动,点N 从点C 同时出发,以每秒1个单位的速度沿CB 向终点B 运动,当一个点到达终点时,另一个点也同时停止运动。过点M 作MP ⊥AD ,交BD 于P ,连接NP ,两动点同时运动了t 秒。当运动了t 秒时,△NPB 的面积为S ,求S 与t 的函数关系式,并求S 的最大值。

【举一反三】

1.在△ABC 中,∠B =900,AB =6 cm ,BC =7 cm ,点P 从点A 开始沿AB 边向点B 以1 cm /s 的速度移动,点Q 从点B 开始沿BC 边向点C 以2 cm /s 的速度移动。如果点P 、Q 同时从A 、B 两点出发,经过几秒钟后,△PBQ 的面积等于8 cm 2?

考点5. 因思维定势而掉入陷阱。

例8.直角三角形的两条边长分别为6和8,那么这个三角形的外接圆半径等于_________。

【举一反三】

1.若关于x 函数1)3(2

+--=x a ax y 的图像与x 轴有唯一公共点,则a =__________.

考点6. 因审题不细致而掉入陷阱。

例17.某商场销售一批名牌衬衫,平均每天可售出20件,每件盈利40元,如扩大销售量增加盈利,尽快减少库存,商场决定要取适当的降价措施。经调查发现,如果每件衬衫降低1元,商场平均每天可多售出2件。如果商场平均每天要盈利1200元,每件衬衫应降价多少元?

【举一反三】

1. .已知圆O 的半径为R ,则此圆中36°的圆周角所含的弧长是_______________。

常见陷阱题锦集

一、容易漏解的题目

1.一个数的绝对值是5,则这个数是_________;__________数的绝对值是它本身.(5±,非负数)

2._________的倒数是它本身;_________的立方是它本身.(1±,1±和0)

3.关于x 的不等式40x a -≤的正整数解是1和2;则a 的取值范围是_________.(412a ≤<) 4.不等式组213,.x x a ->??>?

的解集是2x >,则a 的取值范围是_________.(2a ≤)

5.若()

2

211a a a +--=,则a =_________.(2-,2,1-,0)

6.当m 为何值时,函数21(3)45m y m x x +=++-是一个一次函数.(0m =或3m =-) 7.若一个三角形的三边都是方程212320x x -+=的解,则此三角形的周长是_________.(12,24或20)

8.若实数a 、b 满足221a a =+,221b b =+,则a b +=________.(2,2± 9.在平面上任意画四个点,那么这四个点一共可以确定_______条直线.

10.已知线段AB =7cm ,在直线AB 上画线段BC =3cm ,则线段AC =_____.(4cm 或10cm ) 11.一个角的两边和另一个角的两边互相垂直,且其中一个角是另一个角的两倍少30?,求这两个角的度数.(30?,30?或70?,110?)

12.三条直线公路相互交叉成一个三角形,现在要建一个货物中转站,要求它到三条公路的距离相等,则可供选择的地址有_______处?(4)

13.等腰三角形一腰上的高与腰长之比为1:2,则该三角形的顶角为_____.(30?或150?) 14.等腰三角形的腰长为a ,一腰上的高与另一腰的夹角为30?,则此等腰三角形底边上的

高为_______.(

2

a

15.矩形ABCD 的对角线交于点O .一条边长为1,OAB △是正三角形,则这个矩形的周长

为______.(2+2 16.梯形ABCD 中,AD BC ∥,90A ∠=?,AB =7cm ,BC =3cm ,试在AB 边上确定P 的位置,使得以P 、A 、D 为顶点的三角形与以P 、B 、C 为顶点的三角形相似.(AP =1cm ,6cm 或

14

5

cm )

17.已知线段AB =10cm ,端点A 、B 到直线l 的距离分别为6cm 和4cm ,则符合条件的直线有___条.(3条)

18.过直线l 外的两点A 、B ,且圆心在直线l 的上圆共有_____个.(0个、1个或无数个) 19.在Rt ABC △中,90C ∠=?,3AC =,5AB =,以C 为圆心,以r 为半径的圆,与斜边

AB 只有一个交点,求r 的取值范围.( 2.4r =或34r <≤)

20.直角坐标系中,已知(1,1)P ,在x 轴上找点A ,使AOP △为等腰三角形,这样的点P 共有多少个?(4个)

21.在同圆中,一条弦所对的圆周角的关系是______________.(相等或互补) 22.圆的半径为5cm ,两条平行弦的长分别为8cm 和6cm ,则两平行弦间的距离为 _______.(1cm 或7cm )

23.两同心圆半径分别为9和5,一个圆与这两个圆都相切,则这个圆的半径等于多少?(2或7)

24.一个圆和一个半径为5的圆相切,两圆的圆心距为3,则这个圆的半径为多少?(2或8)

25.PA 切⊙O 于点A ,AB 是⊙O 的弦,若⊙O 的半径为1,AB 则PA 的长为____.(1

26.PA 、PB 是⊙O 的切线,A 、B 是切点,80APB ∠=?,点C 是上异于A 、B 的任意一

点,那么ACB ∠= ________.(50?或130?)

27.在半径为1的⊙O 中,弦AB AC BAC ∠=________.(75?或15?) 二、容易多解的题

28.已知()()2

2222215x y x y +++=,则22x y +=_______.(3)

29.在函数y =

中,自变量的取值范围为_______.(1x ≥)

30.已知445x x -+=,则22x x -+=________)

31.当m 为何值时,关于x 的方程2(2)(21)0m x m x m ---+=有两个实数根.(1

4

m ≥-,

且2m ≠).

32.当m 为何值时,函数2

(1)350m m y m x x -=++-=是二次函数.(2) 33.若22022(43)x x x x --=-+,则x =?.(1-)

34.方程组22240,

3260.

x y x xy x y ?-=??-+++=??的实数解的组数是多少?(2)

35.关于x 的方程2210x k ++-=有实数解,求k 的取值范围.(1

13k -≤≤)

36.k 为何值时,关于x 的方程2(2)320x k x k -++-=的两根的平方和为23?(3k =-) 37.m 为何值时,关于x 的方程21202x m x m ?

?-++= ??

?的两根恰好是一个直角三角形的两个

锐角的余弦值?.(m = 38.若对于任何实数x ,分式21

4x x c

++总有意义,则c 的值应满足______.(4c >)

39.在ABC △中,90A ∠=?,作既是轴对称又是中心对称的四边形ADEF ,使D 、E 、F 分别在AB 、BC 、CA 上,这样的四边形能作出多少个?(1)

40.在⊙O 中,弦AB =8cm ,P 为弦AB 上一点,且AP =2cm ,则经过点P 的最短弦长为多

少?()

41.两枚硬币总是保持相接触,其中一个固定,另一个沿其周围滚动,当滚动的硬币沿固定

的硬币滚动一周,回到原来的位置,滚动的那个硬币自转的圈数为_______.(2) 三、容易误判的问题:

1.两条边和其中一组对边上的高对应相等的两个三角形全等。 2.两边及第三边上的高对应相等的两个三角形全等。 3.两角及其对边的和对应相等的两个三角形全等。 4.两边及其一边的对角对应相等的两个三角形全等。

沁园春·雪

北国风光, 千里冰封, 万里雪飘。

望长城内外,惟余莽莽;大河上下,顿失滔滔。

山舞银蛇,原驰蜡象,欲与天公试比高。

须晴日,看红装素裹,分外妖娆。江山如此多娇,引无数英雄竞折腰。惜秦皇汉武,略输文采;唐宗宋祖,稍逊风骚。

一代天骄,成吉思汗,只识弯弓射大雕。

俱往矣,数风流人物,还看今朝。

中考英语单选易错题(教师版)

九年级单项选择专练 C1. --- ____ do you study for a test? --- I study by listening to tapes. A. What B. Which C. How D. Where B2. I _____ really quiet. Now I’m very outgoing. A. use to be B. used to be C. use to D. used to A3. Ann ____ to choose her own clothes, but she isn’t allowed to get her ear pierced穿耳洞yet. A. is allowed B. allow C. allowed D. is allowing D4. ---What ___ you do if you had a million dollars? --- I’d give it to charity. A. will B. did C. were D. Would ①提出将来会发生的事:主句:主语+would/should/might/could+动词原形 从句:if+should+动词原形/were to+动词原形 eg. If he should go to Harvard University, he would make full use of his time. 如果他要上哈佛大学的话,他就会充分利用他的时间了。 ②提出现在的条件:主句:主语+would/should/might/could+动词原形 从句:if+动词过去式 eg. If he studied at this school, he would know the enviornment around the school very much. 如果他在这所学校学习的话,他会很了解周边环境。 ③提出过去的未发生的条件:主句:主语+would/should/might/could have+动词过去分词 从句:if+had+动词过去分词 A5. --- Have you ever ____ another country? ---- Yes, I have. A. been to B. gone to C. be to D. went to B6. --- _____ would you like to go ? --- I’d like to go somewhere warm. A. Which B. where C. What D. How B7. He looks sad. Let’s ____ . A. to cheer him up B. cheer him up C. to cheer up him D. cheer up him C8. ----Jack,you look tired today. What’s wrong?

初中数学中考命题规律及32个陷阱

初中数学中考命题规律及32个陷阱 面对中考,今天给同学们推送一份礼物,让我们看看中 考数学卷中的一些套路——命题老师最爱的32个陷阱,这也是大部分同学容易犯错丢分的知识点,请大家对照这些知 识点将相关内容再过一遍!相信看过这些后,你即将要面对 的中考数学题将不再有“陷阱”,这样的题目就像没了牙齿的老虎。大家要在心理上轻视它,在态度上要重视它! 一、数学式 陷阱1:在较复杂的运算中,因不注意运算顺序或者不 合理使用运算律,致使运算出现错误。常见陷阱是在实数的 运算中符号层层相扣。 陷阱2:要求随机或者在某个范围内代入求值时,注意 所代值必须要使式子有意义,常见陷阱是候选值里有一个会 使分母为零。 陷阱3:注意分式运算中的通分不要与分式方程计算中 的去分母混淆。 陷阱4:非负数的性质:若几个非负数的和为0,则每个式子都为0;常见非负数有:绝对值,非负数的算术平方根,完全平方式。 陷阱5:五个基本数的混合运算:0指数,基本三角函数,绝对值,负指数,二次根式的化简,这些需牢记。

陷阱6:科学计数法中,精确度和有效数字的概念要清 楚。 二、方程(组)与不等式(组) 陷阱1:运用等式性质解方程时,切记等式两边不能直 接约去含有未知数的公因式,必须要考虑约去的含有未知数 的公因式为零的情形。 陷阱2:常在考查不等式的题目时候埋设关于性质3的陷阱,许多人因忘记改变符号的方向而导致结果出错。 陷阱3:关于一元二次方程中求某参数的取值范围的题 目中,埋设二次项系数包含参数这一陷阱,易忽视二次项系 数不为0导致出错。 陷阱4:解分式方程时,首要步骤是去分母,分数相当 于括号,易忘记最后对根的检验,导致运算结果出错。 陷阱5:关于一元一次不等式组有解无解的条件,易忽 视相等的情况;利用函数图象求不等式的解集和方程的解 时,注意端点处的取值。 三、函数 陷阱1:关于函数自变量的取值范围埋设陷阱。注意: ①分母≠0,二次根式的被开方数≥0,0指数幂的底数≠0; ②实际问题中许多自变量的取值不能为负数。 陷阱2:根据一次函数的性质(或者实际问题、动点问 题等)判断函数的图象出错,一次函数图象性质与k、b之

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