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【附20套中考模拟试题】陕西省西安市鄠邑区2019-2020学年中考数学模拟试卷含解析

【附20套中考模拟试题】陕西省西安市鄠邑区2019-2020学年中考数学模拟试卷含解析
【附20套中考模拟试题】陕西省西安市鄠邑区2019-2020学年中考数学模拟试卷含解析

陕西省西安市鄠邑区2019-2020学年中考数学模拟试卷

一、选择题(本大题共12个小题,每小题4分,共48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.小手盖住的点的坐标可能为( )

A .()5,2

B .()3,4-

C .()6,3-

D .()4,6--

2.一次函数1y kx b =+与2y x a =+的图象如图所示,给出下列结论:①k 0<;②0a >;③当3x <时,12y y <.其中正确的有( )

A .0个

B .1个

C .2个

D .3个

3.如图,在矩形ABCD 中,O 为AC 中点,EF 过O 点且EF ⊥AC 分别交DC 于F ,交AB 于点E ,点G 是AE 中点且∠AOG=30°,则下列结论正确的个数为( )DC=3OG ;(2)OG= 12BC ;(3)△OGE 是等边三角形;(4)16

AOE ABCD S S ?=矩形.

A .1

B .2

C .3

D .4

4.如图,在同一平面直角坐标系中,一次函数y 1=kx+b (k 、b 是常数,且k≠0)与反比例函数y 2=c x (c 是常数,且c≠0)的图象相交于A (﹣3,﹣2),B (2,3)两点,则不等式y 1>y 2的解集是( )

A.﹣3<x<2 B.x<﹣3或x>2 C.﹣3<x<0或x>2 D.0<x<2

5.已知△ABC,D是AC上一点,尺规在AB上确定一点E,使△ADE∽△ABC,则符合要求的作图痕迹是()

A.B.

C.D.

6.若2<2

a <3,则a的值可以是()

A.﹣7 B.16

3

C.

13

2

D.12

7.已知关于x的一元二次方程x2+mx+n=0的两个实数根分别为x1=2,x2=4,则m+n的值是()A.﹣10 B.10 C.﹣6 D.2

8.已知:如图,AD是△ABC的角平分线,且AB:AC=3:2,则△ABD与△ACD的面积之比为()

A.3:2 B.9:4 C.2:3 D.4:9

9.随着“中国诗词大会”节目的热播,《唐诗宋词精选》一书也随之热销.如果一次性购买10本以上,超过10本的那部分书的价格将打折,并依此得到付款金额y(单位:元)与一次性购买该书的数量x(单位:本)之间的函数关系如图所示,则下列结论错误的是()

A .一次性购买数量不超过10本时,销售价格为20元/本

B .a =520

C .一次性购买10本以上时,超过10本的那部分书的价格打八折

D .一次性购买20本比分两次购买且每次购买10本少花80元

10.如图,AD ,CE 分别是△ABC 的中线和角平分线.若AB=AC ,∠CAD=20°,则∠ACE 的度数是( )

A .20°

B .35°

C .40°

D .70°

11.如果数据x 1,x 2,…,x n 的方差是3,则另一组数据2x 1,2x 2,…,2x n 的方差是( ) A .3 B .6 C .12 D .5

12.如图,直角坐标平面内有一点(2,4)P ,那么OP 与x 轴正半轴的夹角α的余切值为( )

A .2

B .12

C .5

D .5

二、填空题:(本大题共6个小题,每小题4分,共24分.) 13.如图所示,点C 在反比例函数k y (x 0)x

=>的图象上,过点C 的直线与x 轴、y 轴分别交于点A 、B ,且AB BC =,已知AOB V 的面积为1,则k 的值为______.

14.如图,⊙O 的半径为2,AB 为⊙O 的直径,P 为AB 延长线上一点,过点P 作⊙O 的切线,切点为C .若

PC=23,则BC的长为______.

15.如图,10块相同的长方形墙砖拼成一个长方形,设长方形墙砖的长为x厘米,则依题意列方程为

_________.

16.如果一个扇形的弧长等于它的半径,那么此扇形成为“等边扇形”.则半径为2的“等边扇形”的面积为.

17.不等式组

20

1

2

x

x

x

-≤

?

?

?-

<

??

的最大整数解是__________.

18.已知二次函数y=ax2+bx(a≠0)的最小值是﹣3,若关于x的一元二次方程ax2+bx+c=0有实数根,则c的最大值是_____.

三、解答题:(本大题共9个小题,共78分,解答应写出文字说明、证明过程或演算步骤.

19.(6分)甲乙两名同学做摸球游戏,他们把三个分别标有1,2,3的大小和形状完全相同的小球放在一个不透明的口袋中.求从袋中随机摸出一球,标号是1的概率;从袋中随机摸出一球后放回,摇匀后再随机摸出一球,若两次摸出的球的标号之和为偶数时,则甲胜;若两次摸出的球的标号之和为奇数时,则乙胜;试分析这个游戏是否公平?请说明理由.

20.(6分)如图,△ABC中,CD是边AB上的高,且

AD CD

CD BD

=.

求证:△ACD∽△CBD;求∠ACB的大小.

21.(6分)计算:|﹣2|﹣8﹣(2﹣π)0+2cos45°.解方程:

3

3

x

x-

=1﹣

1

3x

-

22.(8分)顶点为D的抛物线y=﹣x2+bx+c交x轴于A、B(3,0),交y轴于点C,直线y=﹣x+m经过点C,交x轴于E(4,0).

求出抛物线的解析式;如图1,点M为线

段BD上不与B、D重合的一个动点,过点M作x轴的垂线,垂足为N,设点M的横坐标为x,四边形OCMN的面积为S,求S与x之间的函数关系式,并求S的最大值;点P为x轴的正半轴上一个动点,

过P作x轴的垂线,交直线y=﹣3

4

x+m于G,交抛物线于H,连接CH,将△CGH沿CH翻折,若点

G的对应点F恰好落在y轴上时,请直接写出点P的坐标.

23.(8分)在一个不透明的盒子中装有大小和形状相同的3个红球和2个白球,把它们充分搅匀.“从中任意抽取1个球不是红球就是白球”是事件,“从中任意抽取1个球是黑球”是事件;从中任意抽取1个球恰好是红球的概率是;学校决定在甲、乙两名同学中选取一名作为学生代表发言,制定如下规则:从盒子中任取两个球,若两球同色,则选甲;若两球异色,则选乙.你认为这个规则公平吗?请用列表法或画树状图法加以说明.

24.(10分)如图,点是线段的中点,,.求证:.

25.(10分)在如图的正方形网格中,每一个小正方形的边长为1;格点三角形ABC(顶点是网格线交点的三角形)的顶点A、C的坐标分别是(-4,6)、(-1,4);请在图中的网格平面内建立平面直角坐标系;请画出△ABC关于x轴对称的△A1B1C1;请在y轴上求作一点P,使△PB1C的周长最小,并直接写出点P的坐标.

26.(12分)某校为了解本校学生每周参加课外辅导班的情况,随机调査了部分学生一周内参加课外辅导

班的学科数,并将调查结果绘制成如图1、图2所示的两幅不完整统计图(其中A:0个学科,B:1个学科,C:2个学科,D:3个学科,E:4个学科或以上),请根据统计图中的信息,解答下列问题:

请将图2的统计

图补充完整;根据本次调查的数据,每周参加课外辅导班的学科数的众数是个学科;若该校共有2000名学生,根据以上调查结果估计该校全体学生一周内参加课外辅导班在3个学科(含3个学科)以上的学生共有人.

27.(12分)科技改变生活,手机导航极大方便了人们的出行,如图,小明一家自驾到古镇C游玩,到达A地后,导航显示车辆应沿北偏西55°方向行驶4千米至B地,再沿北偏东35°方向行驶一段距离到达古

(参考数据:tan55°≈1.4,镇C,小明发现古镇C恰好在A地的正北方向,求B、C两地的距离(结果保留整数)

tan35°≈0.7,sin55°≈0.8)

参考答案

一、选择题(本大题共12个小题,每小题4分,共48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.B

【解析】

【分析】

根据题意,小手盖住的点在第四象限,结合第四象限点的坐标特点,分析选项可得答案.

【详解】

根据图示,小手盖住的点在第四象限,第四象限的点坐标特点是:横正纵负;

分析选项可得只有B符合.

故选:B.

【点睛】

此题考查点的坐标,解题的关键是记住各象限内点的坐标的符号,进而对号入座,四个象限的符号特点分别是:第一象限(+,+);第二象限(?,+);第三象限(?,?);第四象限(+,?).

2.B

【解析】

【分析】

仔细观察图象,①k的正负看函数图象从左向右成何趋势即可;②a,b看y2=x+a,y1=kx+b与y轴的交点坐标;③看两函数图象的交点横坐标;④以两条直线的交点为分界,哪个函数图象在上面,则哪个函数值大.

【详解】

①∵y1=kx+b的图象从左向右呈下降趋势,

∴k<0正确;

②∵y2=x+a,与y轴的交点在负半轴上,

∴a<0,故②错误;

③当x<3时,y1>y2错误;

故正确的判断是①.

故选B.

【点睛】

本题考查一次函数性质的应用.正确理解一次函数的解析式:y=kx+b (k≠0)y随x的变化趋势:当k>0时,y随x的增大而增大;当k<0时,y随x的增大而减小.

3.C

【解析】

∵EF⊥AC,点G是AE中点,

∴OG=AG=GE=1

2 AE,

∵∠AOG=30°,

∴∠OAG=∠AOG=30°,

∠GOE=90°-∠AOG=90°-30°=60°,

∴△OGE是等边三角形,故(3)正确;

设AE=2a,则OE=OG=a,

由勾股定理得,,∵O为AC中点,

∴,

∴BC=12,

在Rt △ABC 中,由勾股定理得,, ∵四边形ABCD 是矩形,

∴CD=AB=3a ,

∴DC=3OG ,故(1)正确;

∵OG=a ,12BC=2

a , ∴OG≠12

BC ,故(2)错误;

∵S △AOE =12=2

2

S ABCD 2,

∴S △AOE =16

S ABCD ,故(4)正确; 综上所述,结论正确是(1)(3)(4)共3个,

故选C .

【点睛】本题考查了矩形的性质,等边三角形的判定、勾股定理的应用等,正确地识图,结合已知找到有用的条件是解答本题的关键.

4.C

【解析】

【分析】一次函数y 1=kx+b 落在与反比例函数y 2=c x

图象上方的部分对应的自变量的取值范围即为所求. 【详解】∵一次函数y 1=kx+b (k 、b 是常数,且k≠0)与反比例函数y 2=

c x (c 是常数,且c≠0)的图象相交于A (﹣3,﹣2),B (2,3)两点,

∴不等式y 1>y 2的解集是﹣3<x <0或x >2,

故选C .

【点睛】本题考查了反比例函数与一次函数的交点问题,利用数形结合是解题的关键.

5.A

【解析】

【分析】

以DA 为边、点D 为顶点在△ABC 内部作一个角等于∠B ,角的另一边与AB 的交点即为所求作的点.

【详解】

如图,点E即为所求作的点.故选:A.

【点睛】

本题主要考查作图-相似变换,根据相似三角形的判定明确过点D作一角等于∠B或∠C,并熟练掌握做一个角等于已知角的作法式解题的关键.

6.C

【解析】

【分析】

根据已知条件得到4<a-2<9,由此求得a的取值范围,易得符合条件的选项.

【详解】

a <3,

解:∵22

∴4<a-2<9,

∴6<a<1.

又a-2≥0,即a≥2.

∴a的取值范围是6<a<1.

观察选项,只有选项C符合题意.

故选C.

【点睛】

考查了估算无理数的大小,估算无理数大小要用夹逼法.

7.D

【解析】

【分析】

根据“一元二次方程x2+mx+n=0的两个实数根分别为x1=2,x2=4”,结合根与系数的关系,分别列出关于m和n的一元一次不等式,求出m和n的值,代入m+n即可得到答案.

【详解】

解:根据题意得:

x1+x2=﹣m=2+4,

解得:m=﹣6,

x1?x2=n=2×4,

解得:n=8,

m+n =﹣6+8=2,

故选D .

【点睛】

本题考查了根与系数的关系,正确掌握根与系数的关系是解决问题的关键.

8.A

【解析】

试题解析:过点D 作DE ⊥AB 于E ,DF ⊥AC 于F.

∵AD 为∠BAC 的平分线,

∴DE=DF ,又AB:AC=3:2,

11:():():3:222

ABD ACD S S AB DE AC DF AB AC ∴=??==V V , 故选A.

点睛:角平分线上的点到角两边的距离相等.

9.D

【解析】

【分析】

A 、根据单价=总价÷数量,即可求出一次性购买数量不超过10本时,销售单价,A 选项正确;C 、根据单价=总价÷数量结合前10本花费200元即可求出超过10本的那部分书的单价,用其÷前十本的单价即可

得出C 正确;B 、根据总价=200+超过10本的那部分书的数量×

16即可求出a 值,B 正确;D ,求出一次性购买20本书的总价,将其与400相减即可得出D 错误.此题得解.

【详解】

解:A 、∵200÷10=20(元/本),

∴一次性购买数量不超过10本时,销售价格为20元/本,A 选项正确;

C 、∵(840﹣200)÷(50﹣10)=16(元/本),16÷

20=0.8, ∴一次性购买10本以上时,超过10本的那部分书的价格打八折,C 选项正确;

B 、∵200+16×(30﹣10)=520(元),

∴a =520,B 选项正确;

D 、∵200×2﹣200﹣16×(20﹣10)=40(元),

∴一次性购买20本比分两次购买且每次购买10本少花40元,D 选项错误.

故选D .

【点睛】

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2018 年陕西省中考数学试卷 一、选择题:(本大题共 10 题,每题 3 分,满分 30 分) 1.-的倒数是 A. B.- C. D.- 2.如图,是一个几何体的表面展开图,则该几何体是 A. 正方体 B. 长方体 C. 三棱柱 D. 四棱锥 3.如图,若 l1∥l2, l 3∥ l4,则图中与∠ 1 互补的角有 A. 1个 B. 2 个 C. 3 个 D. 4 个 4. 如图,在矩形ABCD中, A( -2, 0), B(0,1) .若正比例函数y= kx 的图像经过点C,则k 的取值为 A.- B. C.-2 D.2 5.下列计算正确的是 A. a2·a2= 2a4 B. ( - a2)3=- a6 C. 3a2-6a2= 3a2 D. ( a-2)2=a2-4 6.如图,在△ABC 中,AC= 8,∠ ABC= 60°,∠ C= 45°, AD ⊥ BC,垂足为 D ,∠ABC 的平分线交 AD 于点E,则 AE 的长为 A. B.2 C. D.3 7.若直线 l1经过点 (0, 4),l 2经过 (3, 2),且 l1与 l 2关于 x 轴对称,则 l 1与 l2的交点坐标为 A. ( - 2,0) B. (2, 0) C. (- 6,0) D. (6 , 0)

8.如图,在菱形 ABCD 中,点 E、 F、 G、H 分别是边 AB、 BC、 CD 和 DA 的中点,连接 EF、 FG 、 GH 和HE .若 EH = 2EF,则下列结论正确的是 A. AB=EF B. AB= 2EF C. AB=EF D. AB=EF 9.如图,△ABC 是⊙ O 的内接三角形, AB= AC,∠ BCA= 65°,作 CD ∥AB,并与○O 相交于点 D,连接 BD,则∠ DBC 的大小为 A. 15° B. 35° C. 25° D. 45° 10.对于抛物线 y= ax2+ (2a- 1)x+ a- 3,当 x= 1 时, y> 0,则这条抛物线的顶点一定在 A. 第一象限 B. 第二象限 C. 第三象限 D. 第四象限 二、填空题:(本大题共 4 题,每题 3 分,满分 12 分) 11.比较大小: 3_________( 填<, >或= ). 12.如图,在正五边形 ABCDE 中, AC 与 BE 相交于点 F,则AFE 的度数为 ________ 13.若一个反比例函数的图象经过点A(m, m)和 B(2m,- 1),则这个反比例函数的表达式为______ 14.点 O 是平行四边形 ABCD 的对称中心, AD >AB,E、 F 分别是 AB 边上的点,且 EF= AB; G、 H 分别是 BC 边上的点,且 GH= BC;若 S1,S2分别表示 ? EOF 和 ? GOH 的面积,则 S1,S2之间的等量关系是 ______________ 三、解答题(共11小题,计 78 分.解答应写出过程) 15.计算:(-) ×(-)+ |-1|+(5-2π) 16.化简:

初三英语中考模拟试题(一)(附答案)

初三英语中考模拟试题 (一) I .词汇(15分) A. 根据所给汉语意思,完成句子(5分) 1.1 was ____ (惊奇的)to see that he was badly hurt in the accident. 2」don ' t like eating apples ____ (和)oranges. 3. “ Help yourselves to some bananas.” Mother said to the ___ (孩子). 4. What is the ___ (天气)like today? 5. There are ___ (百)of people in the hall. B. 用所给单词的适当形式填空(10分) 1. The TV play is so ___ (in terest) that I want to see it aga in. 2. Look! How ___ (happy) the childre n are dancing! 3. Ma ny __ (travel) have visited the Great Wall of Chi na. 4. The room next to mine is always___ (no ise). 5. D on't ope n your books.Please keep them ___ (close). 6. The dicti onary is very ___ (help) to my study. 7. Mr.Read lear ns Chin ese as his ___ (two) Ian guage. 8.ln our class about two _____ (three) of the stude nts are boys. 9. ________________________ E nglish is spoke n by the (large) nu mber of people in the world. 10.1 hear Tom is good at ____ (surf). n .选择(15分) I. Which of the following sig ns is often found in a doctor ' s waiting room ? 2. M eimei is not here.She ___ A.is goi ng C.has gone 3. ______ —is your school? —It's about ten minu tes' walk. to the school library. B.will go D.has bee n A.How soon C.How ofte n B.How long D.How far 4. L i n Tao jumped A.higher C.highest 5. This box is heavy A.too; to C.too; that 6.lf I _____free next Su nday, I A.will be; will go C.am; go than Bill at the sports meeti ng. B.high D.the highest I can't carry it. B.so; that D.very; that ___ to the farm with you. B.am; will go D.will be; go G

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