山东省济宁市2018年中考全真模拟卷数学试卷

适用年级:初三
试卷号:621410

试卷类型:中考模拟
试卷考试时间:2018/7/8

1.单选题(共13题)

1.
的相反数是( )
A.B.C.D.
2.
的平方根是(   )
A.B.C.D.
3.
下列因式分解正确的是(  )
A.x2-6x+9=(x-3)2B.x 2-y2=(x-y)2C.x2-5x+6=(x-1)(x-6)D.6x2+2x=x(6x+2)
4.
如图,将边长为12 cm的正方形ABCD沿其对角线AC剪开,再把ABC沿着AD方向平移,得到△A′B′C′,若两个三角形重叠部分的面积为32 cm2,则它移动的距离AA′等于( )
A.4 cmB.8 cmC.6 cmD.4 cm或8 cm
5.
若关于x的方程的解为正数,则m的取值范围是(  )
A.m<4B.m>4C.m<4且m≠2D.m>0且m≠2
6.
规定如min(2,4)=2.按照上面的规定,方程的根是(   )
A.B.-1C.D.或-1
7.
若不等式组的解集是x<a-1,则实数a的取值范围是(   )
A.a≤-6B.a≤-5C.a≤-4D.a<-4
8.
如图,△ABC是边长为4cm的等边三角形,动点P从点A出发,以2cm/s的速度沿A→C→B运动,到达B点即停止运动,过点P作PD⊥AB于点D,设运动时间为x(s),△ADP的面积为y(cm2),则能够反映y与x之间函数关系的图象大致是(  )
A.B.C.D.
9.
如果代数式有意义,那么一次函数的大致图象是(   )
A.B.C.D.
10.
在平面直角坐标系中直线y=x+2与反比例函数的图像有唯一公共点,若直线y=x+m与反比例函数的图像有2个公共点,则m的取值范围是(  )
A.m>2B.-2<m<2
C.m<-2D.m>2或m<-2
11.
下列运算正确的是(  )
A.a2+a3=a5B.a2•a3=a6C.(a2)4 = a6D.a4÷a2=a2
12.
如图,下列四种标志中,既是轴对称图形又是中心对称图形的为(  )
A.B.C.D.
13.
某学校教研组对八年级360名学生就“分组合作学习”方式的支持程度进行了调查,随机抽取了若干名学生进行调查,并制作统计图如图所示,据此统计图估计该校八年级学生对“分组合作学习”方式非常喜欢和喜欢的人数约为(  )
A.216人B.324人C.288人D.252人

2.选择题(共1题)

14.阅读理解

    Here's an interesting fact: Every teenager American seems to have, at some point, appeared drunk or rude online. This generation didn't invent stupidity, of course; it's just the first to post the picture online the entire world to see. And that's the rub: Employers are getting clever at looking you up online. They look at what people post and wonder. Is that new salesperson, the one who made a strange face on collegehumor.com,likely to do the same at a conference?”

    Anything that you put online is public information. This should seem pretty obvious to the generation who grew up on these sites, right? But it's not. When it comes to the Net, young people tend to fell for two traps. One:“ Many of them believe it's truly private, and they'll determine who gets to sec what, and it will stop there.” Wrong! And two: “Their sense of what things will be like in the next stage of their life is not realistic.”

    So what do you do about that picture? Take it down! But what if it is now on other sites? After all, a friend can post your photo elsewhere, and from there, it can be posted on another site. This problem is so common that a new industry has appeared: identity management, which helps people remove embarrassing material.

    The new industry serves to remind us that we've got to be careful out there. Most of us have got drunk or done something we regret. But putting it online is another matter. And for some, it's even become an addiction, one with a nickname: Crackspace. Young or old, students and managers alike turn into exhibitions, putting every aspect of their lives on public display(展示).

    Yes, it can be great fun. But should those of us posting pictures of ourselves dancing in our underwear be given a good comment? In a forgiving, kindly environment, yes. But what about in a business environment? Well, you decide.

3.填空题(共6题)

15.
在函数y=中,自变量x的取值范围是___________.
16.
计算:=______.
17.
如果抛物线y=ax2﹣2ax+1经过点A(﹣1,7)、B(x,7),那么x=_____.
18.
如图,已知反比例函数的图象过Rt△ABO斜边OB的中点D,与直角边AB相交于点C,连接AD,OC.若△ABO的周长为,AD=2,则△ACO的面积为_________.
19.
如图,∠MON=30°,点A1,A2,A3,…在射线ON上,点B1,B2,B3,…在射线OM上,△A1B1A2,△A2B2A3,△A3B3A4…均为等边三角形.若OA1=1,则△AnBnAn+1的边长为_____.
20.
计算:__________.

4.解答题(共7题)

21.
先化简,再求值:(a﹣)÷(),其中a满足a2﹣3a+2=0.
22.
小明到服装店参加社会实践活动,服装店经理让小明帮助解决以下问题:
服装店准备购进甲乙两种服装,甲种每件进价80元,售价120元;乙种每件进价60元,售价90元.计划购进两种服装共100件,其中甲种服装不少于65件。
(1)若购进这100件服装的费用不得超过7500,则甲种服装最多购进多少件?
(2)在(1)的条件下,该服装店对甲种服装以每件优惠a(0<a<20)元的价格进行优惠促销活动,乙种服装价格不变,那么该服装店应如何调整进货方案才能获得最大利润?
23.
如图,已知抛物线(m>0)与x轴相交于点A,B,与y轴相交于点C,且点A在点B的左侧.
(1)若抛物线过点(2,2),求抛物线的解析式;
(2)在(1)的条件下,抛物线的对称轴上是否存在一点H,使AH+CH的值最小,若存在,求出点H的坐标;若不存在,请说明理由;
(3)在第四象限内,抛物线上是否存在点M,使得以点A,B,M为顶点的三角形与△ACB相似?若存在,求出m的值;若不存在,请说明理由.
24.
如图,点A(-2,n),B(1,-2)是一次函数y=kx+b的图象和反比例函数的图象的两个交点.

(1)求反比例函数和一次函数的解析式;
(2)若C是x轴上一动点,设t=CB-CA,求t的最大值,并求出此时点C的坐标.
25.
尺规作图,不写作法,保留作图痕迹.
如图:已知∠AOB和C、D两点,求作一点P,使PC=PD,且P到∠AOB两边的距离相等.
26.
在△ABC 中,D 是 BC 边的中点,E、F 分别在 AD 及其延长线上,CE∥BF,连接BE、C
A.
(1)求证:△BDF ≌△CDE;
(2)若 DE =BC,试判断四边形 BFCE 是怎样的四边形,并证明你的结论.
27.
青少年视力水平下降已引起全社会的广泛关注,为了解某市初中毕业年级5 000名学生的视力情况,我们从中抽取了一部分学生的视力作为样本进行数据处理,得到如下的不完整的频数分布表和频数分布直方图:
   
请根据以上图表信息回答下列问题:
(1)在频数分布表中,a=________,b=________;
(2)补全条形统计图;
(3)若视力在4.6以上(含4.6)均属正常,根据上述信息估计全区初中毕业生中视力正常的学生有多少?
试卷分析
  • 【1】题量占比

    单选题:(13道)

    选择题:(1道)

    填空题:(6道)

    解答题:(7道)

  • 【2】:难度分析

    1星难题:0

    2星难题:0

    3星难题:0

    4星难题:3

    5星难题:0

    6星难题:11

    7星难题:0

    8星难题:4

    9星难题:7