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2020年初中中考重难点易错100题集锦714392

2020年初中中考重难点易错100题集锦714392
2020年初中中考重难点易错100题集锦714392

中考数学模拟试卷及答案解析

学校:__________

题号 一 二 三 总分 得分

注意事项:

1.答题前填写好自己的姓名、班级、考号等信息 评卷人 得分

一、选择题

1.当x 为任意实数时,下列分式一定有意义的是( ) A .

2x

B .2

1x C .

1||

x D .

21

1

x + 2.数轴上A 、B 两点分别是-8. 2,3

65,则A 、B 两点间的距离为( )

A .4

145

B .2

145

C .-1.6

D .1.6

3.如图,a ∥b ,若∠1=120°,则∠2 的度数是( ) A .l20°

B .70°

C .60°

D . 50

4.下列因式分解正确的是( ) A .222()m n m n +=+? B .2222()a b ab b a ++=+ C .222()m n m n -=-

D .2222()a ab b a b +-=-

5.用平方差公式计算2(1)(1)(1)x x x -++的结果正确的是( ) A .4(1)x -

B .41x +

C .41x -

D .4(1)x +

6.计算结果等于10

a 的式子是( ) A .5

2

a a ?

B .55

a a +

C .52

()a

D .20

2a

a ÷

7.下列分式中是最简分式的是( )

A .1

22

+x x B .x

24

C .1

12--x x

D .1

1--x x

8.已知方程组42ax by ax by -=??

+=?的解为2

1

x y =??=?,则2a-3b 的值为( )

A .4

B .6

C .-6

D .-4

9.鲁老师乘车从学校到省城去参加会议,学校距省城200千米,车行驶的平均速度为80千米/时.x 小时后鲁老师距省城y 千米,则y 与x 之间的函数关系式为( ) A .80200y x =- B .80200y x =-- C .80200y x =+

D .80200y x =-+

10.下列计算中,正确的是( ) A .9338(4)2x x x ÷= B .23234(4)0a b a b ÷= C .2m 2m a a a ÷=

D .221

2()4c 2

ab c ab ÷-=-

11.两个完全相间的长方体的长,宽,高分别是5 cm ,4 cm ,3 cm ,把它们叠放在一起组成一个新长方体,在这些新长方体中,表面积最大的是( ) A .188cm 2

B .176cm 2

C .164cm 2

D .158 cm 2

12.如图所示,已知∠1=∠2,AD=CB ,AC ,BD 相交于点0,MN 经过点O ,则图中全等三角形的对数为( ) A .4对

B .5对

C .6对

D .7对

13.如图,已知0A=OC ,OB=OD ,那么根据“SAS ”能直接判定三角形全等的对数为( ) A .1对

B .2对

C .3对

D .4对

14.如图,0A ⊥OC ,OB ⊥OD ,且∠BOC=α,则∠AOD 为( ) A .180°-2α

B .180°-α

C .90°+12

α

D .2α-90°

15.如图,将长方形ABCD 沿AE 折叠,使点D 落在BC 边上的点F .若∠BAF=60°,则∠DAE= ( ) A .150

B .30°

C . 45°

D .60°

16.下列图形能比较大小的是 ( ) A .直线与线段

B .直线与射线

C .两条线段

D .射线与线段

17.资料表明,发展中国家的国民生产总值占全世界生产总值之和的22%,发达国家占78%.要用扇形统计图表示这些数据,则各个扇形圆心角的度数之差为( ) A .56°

B .200°

C . 201.6°

D . 202°

18.下列各式中,正确的是( ) A .164=

B .164

C 3273-=-

D 2(4)4-=-

19.小红妈妈的 2 万元存款到期了,按规定她可以得到 2 的利息,但同时必须向国家缴 纳 20% 的利息所得税,则小红妈妈缴税的金额是( ) A .80 元

B .60 元

C .40 元

D .20 元

20.下列图案是几种名车的标志,在这几个图案中,是轴对称图形的有( ) A .1个

B .2个

C .3个

D .4个

21.如图,在矩形ABCD 中,对角线AC 、BD 相交于点O ,若OA =2,则BD 的长为 . ( )

22. 已知β为锐角,且tan β=3.387 ,则β等于( ) A .73033′

B . 73027′

C . 16027′

D . 16021′

23.如图,ABCD 是平行四边形,则图中与DEF △相似的三角形共有( )

A .1个

B .2个

C .3个

D .4个

24.某学习小组在讨论“变化的鱼”,知道大鱼与小鱼是位似图形,如图所示,则小鱼上的点 (a ,b )对应大鱼上的点( )

A . ( -2a , -2b )

B .(-a, -2b )

C .(-2b, -2a )

D . (-2a, -b )

25.在一张由复印机复印出来的纸上,一个多边形的一条边由原来的1 crn 变成了 4 cm ,那么这次复印的多边形的面积变为原来的( ) A . 不变

B .2 倍

C .4 倍

D . 16 倍

26.已知等腰△ABC 的两边为 3 和 5,等腰△A ′B ′C ′的两边为 9 和 15,那么这两个三 角形( ) A . 相似 B .不相似 C .不一定相似

D . 以上答案都不对

27.下列命题中为真命题的是( ) A .三点确定一个圆 B .度数相等的弧相等

C .圆周角是直角的角所对的弦是直径

D .相等的圆心角所对的弧相等,所对的弦也相等

28.将抛物线2

2y x =-平移,得到2

23y x =--的图象,正确的方法是( )

A . 向上平移 3 个单位

B .向下平移3个单位

C . 向上平移2 个单位

D . 向下平移 2 个单位 29.如图所示的长方体的三视图是( )

A .三个正方形

B .三个一样大的长方形

C .三个大小不_样的长方形但其中可能有两个大小一样

D .两个正方形和一个长方形

30. 已知反比例函数y =k

x (k<0)的图象上有两点A (x 1,y 1),B (x 2,y 2),且

x 1

B .负数

C .非正数

D .不能确定

31. 如图,AB 是⊙O 的直径,弦 AC 、BD 相交于点P ,

CD

AB

等于( )

A .sin ∠BPC

B .cos ∠BPC

C .tan ∠BPC

D .cot ∠BPC

32.有两块同样大小且含60°角的三角板,把它们相等的边拼在一起(两块三角板不重叠),可以拼出的四边形的个数( ) A .1

B .2

C .3

D .4

33.若方程2

0ax bx c ++=(0a ≠)中,a ,b ,c 满足0a b c ++=,0a b c -+=,则方程的根是( ) A .1,0

B . -1,0

C .1, -1

D . 无法确定

34.如图所示,在口ABCD 中,EF ∥BC ,GH ∥AB ,EF ,GH 相交于点0,则图中平行四边形共有 ( ) A .7个

B .8个

C .9个

D .l0个

35.已知等腰三角形的腰长为3 3,则此等腰三角形的面积为( )

A .

338

2

B .

339

4

C .

33

2

D .

33

4

36.下列各式中不是二次根式的是( ) A .12+x

B .4-

C .0

D .

()2b a -

37.下列各点在抛物线2

3y x =上的是( ) A .(-1,-3)

B .(一1,3)

C .(-2,6)

D .( 1

3

,1)

38.把长为 6个单位长度的木条的左端放在数轴上表示-10 和-11 的两点之间,则木条的右端会落在( ) A . -4~3之间

B . -6~5之间

C .-5~4之间

D .-7~6之间

39.将一个有80个数据的样本经统计分成6组,如果某一组的频率为0.15,那么该组的频数为 ( )

A .12

B .1.8

C .13.34

D .2

40.在同一平面内,用两个边长为a 的等边三角形纸片(纸片不能裁剪)可以拼成的四边形是( ) A .矩形

B .菱形

C .正方形

D .梯形

41.沿着虚线将矩形剪成两部分,既能拼成三角形又能拼成梯形的是( )

A .

B .

C .

D .

42.成中心对称的图形的对称中心是 ( ) A .一条线段的中点

B .连结图形上任意两点的线段中点

C .连结两对称点的线段的中点

D .以上答案都不对 评卷人 得分

二、填空题

43.棱长是1cm 的小立方体共10块,组成如图所示的几何体,那么这个几何体的表面积是 cm 2.

44.如果节约 16 度电记作+16 度,那么浪费6度电记作 度. 45.-6 的倒数是 ,相反数是 ,绝对值是 . 46.71()4

的底数是 ,指数是 ,表示的意义是 .

47.如图,已知AB=AC=8 cm ,BE ⊥AC 于E ,CD ⊥AB 于D .若AD=5 cm ,则EC= cm .

48.(1)要反映某学生从 6岁到12岁每年一次体检时的视力情况,要用 统计图; (2)要反映某班40名学生所穿鞋的尺码,要用统计图 ;

(3)

要反映某市五个区的占地面积与全市总面积的对比情况,要用 统计图. 49.若∠1的对顶角是∠2,∠2的补角是∠

3,且∠3=54°,则∠l= .

50.已知A 、B 是数轴上的两点,它们分别表示有理数-2和x,若线段AB 的长是3,则x 的值是____ ____.

51.如图,OP 平分BOA ∠,PD OB ⊥于D ,PC OA ⊥于C ,写出你可以得到的结论 (至少写出3个). 52.已知22753y x x y -=+且y ≠0,则x y

= .

53.如图,△ABC ≌△CDA ,A 与C 对应,D 与B 对应,则∠1与 是对应角. 54.在1:1000000的地图上,A ,B 两地相距10cm ,则A ,B 两地的实际距离是_____千米.

55.小明和小红两名同学进行射击比赛,小红射击20次,命中目标l6次,小明射击l5次, 命中目标l0次, 命中率高一些.

56.如图,AD 是△ABC 的中线. 如果△ABC 的面积是18 cm 2,则△ADC 的面积是 cm 2.

57. 相反数等于本身的数是 .

58.随机抽取某城市一年(以365天计)中的30天的日平均气温状况统计如下: 那么该城市一年中日平均气温为26℃的约有 天.

59.如图,半径为5

的⊙P 与y 轴交于点

M (0,-4),N (0,-10),函数(0)k

y x x

=<的图像经过点P ,则k = . 解答题

60.如图,两个半圆中,小圆的圆心O '在大⊙O 的直径CD 上,长为4的弦AB 与直径

CD 平行且与小半圆相切,那么圆中阴影部分面积等于 .

61.在直角坐标系中,以点 P 为圆心,3 为半径的圆与直线x=-1相切,则点 P 的横坐标为 .

温度(℃) 10 14 18 22 26 30 32 天数

3

5

5

7

6

2

2

62.如图所示,CD 直角△ABC 斜边上的高线,且 AC = 10 cm ,若sin ∠ACD=3

5

,则CD= cm .

63.反比例函数x

m y 1

2--=

(m 为常数)的图像如图所示,则m 的取值范围是________. 64.有三个连续自然数,中间一个是x ,则它们的积是 .

65.某商店销售一种纪念品,已知成批购进时单价为 4 元,根据市场调查,销售量与销售单价在一段时间内满足如下关系:单价为10 元时销售量为 300 枚,而单价每降低 1元,就可多售出 5枚,那么当销售单价降低x 元(4

66.如图,∠1 = 120°,∠2= 60°,则直线 a 与b 的位置关系是 .

67.菱形的周长是8 cm ,高是1cm ,则菱形各角的度数为 , , , . 68.直线4y ax =-与直线3y bx =+交于x 轴上一点,则a

b

等于 . 69.若不等式组21

23

x a x b -

->?的解为22x -<<,则(1)(1)a b +-的值等于 .

70.如图,已知AB 是⊙0的直径,BD=OB ,∠CAB=30°,请根据已知条件和所给图形,写出三个正确结论.(除OA=OB=BD 外): ① ; ② ; ③ .

71.某校男子足球队22名队员的年龄如下表所示,则这些队员的平均年龄为 岁(精确到1岁). 年龄(岁) 14 15 16 17 18 19 人数(人)

2

1

3

6

7

3

72.为了在平面上表示空间物体,人们常用数学上的“投影”方法,即把物体从不同的方向投射到平面上,然后通过这些平面的捉影图形去想像空间立体图形.这是人类征服空间所

表现出的伟大智慧 ! 如图是某一物体的三个方向的影像图. 它相当于光线从正面、侧面和上面照射时,该物体留下的影子. 那么这个几何体大约是.

73.在⊙O中,30°的圆心角所对的弧长与30°的圆周角所对的弧长之比是.

评卷人得分

三、解答题

74.某工厂有甲、乙两个相邻的长方体的水池,甲池的水均匀地流入乙池;如图,是甲、乙两个水池水的深度y(米)与水流动时间x(小时)的函数关系的图象.

(1)分别求两个水池水的深度y(米)与水流动时间x(小时)的函数关系式,并指出自变量x的取值范围;

(2)水流动几小时,两个水池的水的深度相同?

75.以给定的图形“○○、△△、二二”(两个圆、两个三角形、两条平行线段)为构件,尽可能多地构思出独特且有意义的图形,并写上一两句贴切诙谐的解说词.如图左框中是符合要求的一个图形,请在右框中画出与之不同的图形,比一比,看谁想得多.

76.某商场销售一批衬衫,进货价为每件40元,按每件50元出售,一个月内可售出500件.已知这种衬衫每件涨价l元,其销售量要减少10件.为在一个月内赚取8000元的利润且假定每件售价大于50元,售价应定为每件多少元?

77.据报道,我省农作物秸杆的资源巨大,但合理利用量十分有限,2006年的利用率只有30%,大部分秸杆被直接焚烧了,假定我省每年产出的农作物秸杆总量不变,且合理利用量的增长率相同,要使2008年的利用率提高到60%,求每年的增长率.(取2≈1.41)

78.用 3,0,0,2 这四个数字(每个数字至少用一次)共可写出几个不同的偶数?

79.计算:(23)(322)(32)

-+--- (精确到 0.01).

80.某中学为了了解该校学生的课余活动情况,从阅读、运动、娱乐、其他等四个方面调查了若干名学生的兴趣爱好,并将调查结果绘制了如下两幅不完整的统计图(图1,图2),请你根据统计图中提供的信息解答下列问题:

(1)在这次研究中,一共调查了多少名学生?

(2)“其他”在扇形统计图中所占的圆心角是多少度?

(3)补全条形统计图.

81.如图所示,在△ABC中,AD⊥BC,AE平分∠BAC,∠B=70°,∠C=34°,求∠DAE的大小.

82.用加减消元法解方程组.

(1)

28

37

x y

x y

+=

?

?

-=

?

;(2)

29

31

x y

x y

+=

?

?

-=-

?

;(3)

1

43

2

43

x y

x y

?

-=

??

?

?+=

??

83.计算:

(1)8x3÷(-2x)2-(3x2-x) (2)(5xy+3x2y)÷(-xy)-2x(6x-7)

84.某市为更有效地利用水资源,制定了用水标:准:如果一户三口之家.每月用水量不超过M立方米,按每立方米水 1.30元计算;如果超过M立方米,超过部分按每立方米水2.90元收费,其余仍按每立方米水 1.30元计算. 小红一家三人,1月份共用水 12立方米,支付水费22元.问该市制定的用水标准M为多少?小红一家超标使用了多少立方米的水?

85.如图,从山下到山上的一个小亭子修了138级台阶,每级台阶的高大约是24 cm,宽大约是32 cm,从山下到小亭子大约要走多远(精确至0.1 m)?

86.浙江省的民营企业在市场经济的运作下,迅速壮大起来.从下面一个企业提供的数据之中,我们就能感觉到中国经济迅猛发展的趋势:1997年产值110万,l999年产值200万,2001年产值500万,2002年产值900万,2003年产值1700万.请你设计一张统计表,简明地表达这一段文字的信息.

87.4(2)532

x a

+-=+的解小于31(23)

32

a a x

x

++

=的解,求a的取值范围.

1

15

a>-

88.如图所示,Rt△ABC 中,∠C= 90°, AC= 3 , tanA =4

3

,⊙C 的半径为 2.4. 求证:⊙C与AB 相切.

89.某商店对一周内甲、乙两种计算器每天销售情况统计如下(单位:个):

品种\星期一二三四五六日

甲3443455

乙4334356(1)求出本周内甲、乙两种计算器平均每天各销售多少个?(2)甲、乙两种计算器哪个销售更稳定一些?请你说明理由.

90.阅读下列解题过程,再回答问题:

解方程:(2)(3)6

x x

-+=.

解:26

x-=,36

x+=,得

18

x=,

23

x=.

请你判断上述解题过程是否正确?.

若不正确,请写出正确的解题过程.

91.如图,在四边形ABCD 中,AD∥BC,BE⊥AC,DF⊥AC,E,F分别为垂足,且∠CDF=∠ABE,试说明四边形BEDF是平行四边形.

92.长36cm的铝丝能否将其剪成相等的两段,用其中一段弯成一个长方形,另一段弯成一个底边为8cm的等腰三角形,且使长方形面积与等腰三角形面积相等,若能,求出长方形的边长,若不能,说明理由.

93.为配合新课程的实施,某市举行了“应用与创新”知识竞赛,共有1万名学生参加了这次竞赛(满分100分,得分全为整数).为了解本次竞赛成绩情况,从中随机抽取了部分学生的竞赛成绩,进行统计,整理见下表:

组别分组频数频率

149.5~59.5600.12

259.5~69.51200.24

369.5~79.51800.36

479.5~89.5130c

589.5~99.5b0.02

合计a 1.00

解答下列问题:

(1)在这个问题中,总体是,样本容量a=;

(2)第四小组的频率c=;

(3)被抽取的学生成绩的中位数落在第几小组内?

(4)若成绩在90分以上(含90分)的学生获一等奖,请你估计全市获一等奖的人数.

94.某广告公司设计一幅周长为12m的矩形广告牌,广告设计费为每平方米1000元,设矩形-边长为x(m) ,面积为S(m2).请你设计一个方案,使获得的设计费最多,并求出这个费用.

95.如图,一条公路的转弯处是一段圆弧CD,点O是CD所在圆的圆心,E为CD的中点,OE 交 CD 于点F.已知CD=600 m,EF=90m,求这段弯路的半径.

96.已知△ABC,作△ABC 的外接圆 (不写作法,保留作图痕迹).

97.如图,△ADE∽△ABC,写出相等的对应角和对应边成比例的比例式.

98.小颖和小红两位同学在学习“概率”时,做投掷骰子(质地均匀的正方体)实验,他们共做了60次实验,实验的结果如下:

朝上的点数123456

出现的次数79682010

(1)计算“3点朝上”的频率和“5点朝上”的频率.

(2)小颖说:“根据实验,一次实验中出现5点朝上的概率最大”;小红说:“如果投掷600次,那么出现6点朝上的次数正好是100次.”小颖和小红的说法正确吗?为什么?(3)小颖和小红各投掷一枚骰子,用列表或画树状图的方法求出两枚骰子朝上的点数之和为3的倍数的概率.

99.已对某篮球运动员进行 3 分球投篮测试结果如下表:

投篮次数 n1050100150200

命中次数 m4256590120

命中频率0.4

(1)计算表中投篮 50 次、100 次、150 次、200次的相应的命中频率;

(2)这个运动员投篮一次命中的概率约是多少?

100.从甲、乙、丙三个厂家生产的同一种产品中,各抽出8件产品,对其使用寿命进行跟

踪调查,结果如下(单位:年):

甲:3,4,5,6,8,8,8,10;

乙:4,6,6,6,8,9,12,13;

丙:3,3,4,7,9,10,11,12.

三家在广告中都称该种产品的使用寿命是8年,请根据调查结果判断厂家在广告中分别运用了平均数、众数、中位数的的哪一种集中趋势的特征数.

【参考答案】***试卷处理标记,请不要删除

一、选择题

1.D

2.A

3.C

4.B

5.C

6.C

7.A

8.B

9.D

10.D

11.C

12.C

13.B

14.B

15.A

16.C

17.C

18.C

19.A

20.C

21.4

22.A

23.B

24.A

25.D

26.C

27.C

28.B

29.C

30.D

31.B

32.D

33.C

34.C

35.B

36.B

37.B

38.C

39.A

40.B

41.D

42.C

二、填空题

43.36

44.-6

45.

1

6

-,6,6

46.

1

4

-,7,7 个(

1

4

-)相乘

47.3

48.(1)折线;(多)条形;(3)扇形

49.126° 50.-5和1 51.略 52.17

4-

53.∠3 54.100 55.小红 56.9 57.0 58.73 59.28 60.2π 61.-4 或 2 62.8 63.2

1-

65.300 + 5x ,(6)(3005)y x x =-+ 66.a ∥b

67.30°,l50°,30°,l50°

68.43

-

69.-14

70.CD 是⊙0的切线;∠D=30°;AC=CD 71.17

72.一个倒立圆锥 73.2:1

三、解答题

74.(1)甲(:432+-=x y (0≤x ≤6),乙:23

1

+=x y (0≤x ≤6);(2)2小时.

75.

76.60 元或 80 元

77.解:设我省每年产出的农作物秸杆总量为a ,合理利用量的增长率是x ,由题意得: 30%a (1+x )2=60%a ,即(1+x )2=2

∴x 1≈0.41,x 2≈-2.41(不合题意舍去),∴x ≈0.41 即我省每年秸秆合理利用量的增长率约为41% . 78.5 个 79.-1. 73

80.解 (1) 20÷20%=100 (人) (2)“娱乐”人数=100×40%=40(人) “其他”人数=100-30-20-40=10 (人) “其他”在扇形统计图中所占的圆心角=360°×10

100

=36° (3) 略 81.18°

82. (1)32x y =??=?;(2)14x y =??=?;(3)6

3

2

x y =??

?=??

83.(1)3x -3x 2 ,(2)-12x 2+11x -5 84.M= 8m 3, 超标4m 3 85.55.2 m 86.略

87.115

a >-

88.作 CD ⊥AB 于D ,由 AC=3,4

tan 3

A =,可求得 BC=4,22345A

B + 34

2.45

CD r ?=

==,∴⊙C 与 AB 相切.

89.(1)4个,4个;(2)甲方差为

74,乙方差为7

8

,∴甲销售更稳定. 90.错误,正确答案为14x =-,23x =,

91.方法不唯一,如:先证四边形ABCD 为□,再证 //DF BE 92.解:设矩形的长为xcm ,则宽为(9-x )cm

由题意得(9-x )x =1

2 ×3×8,解得x 1=9+3

3 2 ,x 2=9-33 2 答:矩形的边长为9+33 2 cm 和9-33 2

cm . 93.(1)1万名学生这次竞赛成绩的全体,500;(2)0.26;(3)3;(4)200 94.S =-x 2+6x ,边长为3m 的正方形面积最大,最大面积为9m 2,最多设计费为9000元.

95.连结 OC ,∵OE ⊥CD ,∴.CF=

1

2

CD=300m ,OF=OE-EF . 设弯路的半径为R(m),∴则OF = (R 一90) m ,

∴222OC CF OF =+,即222300(90)R R =+-,R=545. ∴这段弯路的半径为 545m .

96.作图略.

97.∠EAD 与∠CAB ,∠AED 与∠C ,∠ADE 与∠E 是对应角; 对应边的比例式是

AD AE DE

AB AC BC

-=

98.解:(1)“3点朝上”出现的频率是

61

6010

=; “5点朝上”出现的频率是201603

=; (2)小颖的说法是错误的.这是因为,“5点朝上”的频率最大并不能说明“5点朝上”这一事件发生的频率最大.只有当实验的次数足够大时,该事件发生的频率稳定在事件发生的概率附近.小红的判断是错误的,因为事件发生具有随机性,故“6点朝上”的次数不

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