陕西省西安市长安区2020年第一次中考模拟考试数学试题

陕西省西安市长安区2020年第一次中考模拟考试数学试题
陕西省西安市长安区2020年第一次中考模拟考试数学试题

陕西省西安市长安区2020年第一次中考模拟考

试数学试题

考生须知:

1.本试卷满分为120分,考试时间为120分钟。

2.答题前,考生先将自己的”姓名”、“考号”、“考场"、”座位号”在答题卡上填写清楚,将“条形码”准确粘贴在条形码区域内。

3.保持卡面整洁,不要折叠、不要弄脏、不要弄皱,不准使用涂改液、修正带、刮纸刀。

第Ⅰ卷 选择题(共30分)

一、选择题(每小3分,共计30分。每小超都给出A,B,C,D 四个选项,其中只有一个是正确的。) 1.2020

1的倒数是( ) A .2020 B .﹣2020 C .﹣20201 D .﹣2020

2.据统计,截止2020初,西安市实际居住人口约2000000人,2000000这个数用科学记数法表示为( )

A .2×105

B .2×105

C .2×106

D .2×107 3.若反比例函数y=的图象位于第一、三象限,则a 的取值范围是( )

A .a >0

B .a >3

C .a >

D .a <

4.如果关于x 的一元二次方程2x 2

﹣x+k=0有两个不相等的实数根,那么k 的取值范围是( )

A .k >

B .k <

C .k ≥﹣

D .k ≤﹣

5.如图,AB=DB ,∠1=∠2,请问添加下面哪个条件能判断△ABC ≌△DBE 的有( ) ∠ACB=∠DE B ∠A=∠D AC=DE

BC=BE

A.1个 B.2个 C.3个 D.4个

6.不透明袋子中有3个红球和2个白球,这些球除颜色外无其他差别,从袋中随机取出1个球,是红球的概率是()

A.B.C.D.

7.如图是用五个相同的立方块搭成的几何体,其主视图是()

A. B. C. D.

8.在一次函数y=(2m﹣1)x+1中,y的值随着x值的增大而减小,则它的图象不经过()A.第一象限B.第二象限C.第三象限D.第四象限

9.正方形ABCD内接于⊙O,若⊙O的半径是,则正方形的边长是()

A.1 B.2 C.D.

10.如图,已知点A为反比例函数y=(x<0)的图象上一点,过点A作AB⊥y轴,垂足为B,若△OAB的面积为3,则k的值为()

A.3B.﹣3C.6D.﹣6

第Ⅱ卷非选择题(共90分)

二、填空题(本大共6小题,每小题3分,满分18分)

11.分解因式:a3﹣4a= .

12.计算= .

13.如图在平面直角坐标系中,过格点A,B,C作一圆弧,圆心坐标是.

14.如图,将Rt△ABC绕直角顶点A顺时针旋转90°,得到△AB′C′,连结BB′,若∠1=20°,则∠C的度数是.

15.已知抛物线y=ax2+6x(a为实数)和直线y=x,当0<x<3时,抛物线位于直线上方,当x >3时,抛物线位于直线下方,则a的值为.

16.如图,六边形ABCDEF的六个内角都等于120°,若AB=BC=CD=3cm,DE=2cm,则这个六边形的周长等于cm.

三、解答题(共7小题,计72分)

17.(本题8分)

计算:4cos30°﹣计算:+()0+?sin45°﹣(π﹣2019)0.

18.(本题8分) 解不等式组:

19.(本题10分)

如图,在△ABC 中,6AB =,5AC BC ==,点D 为线段AB 的中点,过点D 作

DF ⊥AC ,交线段AC 与点F ,延长FD 交CB 的延长线于点E .

(1)求DF 的长;

(2)求tan ∠E 的值.

20.(本题10分)

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,并将结果绘制成图1的条形统计图和图2扇形统计图,但均不完整.请你根据统计图解答下列问题:

(1)求参加比赛的学生共有多少名?并补全图1的条形统计图.

(2)在图2扇形统计图中,m的值为,表示“D等级”的扇形的圆心角为度;

(3)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.(本题12分)

为落实“绿水青山就是金山银山”的发展理念,某县政府部门决定,招标一工程队负责完成一座水库的土方施工任务.该工程队有A,B两种型号的挖掘机,已知1台A型和2台B型挖掘机同时施工1小时共挖土80立方米,2台A型和3台B型挖掘机同时施工1小时共挖土140立方米.每台A型挖掘机一个小时的施工费用是350元,每台B型挖掘机一个小时的施工费用是200元.(1)分别求每台A型,B型挖掘机一小时各挖土多少立方米?

(2)若A型和B型挖掘机共10台同时施工4小时,至少完成1360立方米的挖土量,且总费用不超过14000元.问施工时有哪几种调配方案?且指出哪种调配方案的施工费用最低,最低费用多少元?

22.如图,在△ABC中,AB=AC,⊙O是△ABC的外接圆,连结OA、OB、OC,延长BO与AC 交于点D,与⊙O交于点F,延长BA到点G,使得∠BGF=∠GBC,连接FG.

(1)求证:FG是⊙O的切线;

(2)若⊙O的半径为4.

①当OD=3,求AD的长度;

②当△OCD是直角三角形时,求△ABC的面积.

23.如图所示,在平面直角坐标系中,抛物线y=ax2+bx+c(a≠0)的顶点坐标为C(3,6),并与y轴交于点B(0,3),点A是对称轴与x轴的交点.

(1)求抛物线的解析式;

(2)如图①所示,P是抛物线上的一个动点,且位于第一象限,连接BP,AP,求△ABP的面积的最大值;

(3)如图②所示,在对称轴AC的右侧作∠ACD=30°交抛物线于点D,求出D点的坐标;并探究:在y轴上是否存在点Q,使∠CQD=60°?若存在,求点Q的坐标;若不存在,请说明理

由.

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