河南省周口市西华县2017-2018学年八年级上学期期末考试数学试题

适用年级:初二
试卷号:190809

试卷类型:期末
试卷考试时间:2018/2/12

1.单选题(共9题)

1.
观察下列图形,则第n个图形中三角形的个数是
A.2n-1B.C.4n+1D.4n-1
2.
计算正确的是(   )
A.B.C.D.
3.
下列各式变式正确的个数是(   )
①()(b-a)=b2-a2
②()( 
③(a+b)2=(a-b)2+4ab
④(a+b)2+(a-b)2=2a2+2b2
A.1B.2C.3D.4
4.
分式可变形为( )
A.B.C.D.
5.
有意义的条件是(   )
A.B.C.D.
6.
点A(a + 1,a)关于x轴对称的点在第一象限,则a的取值范围是(   )
A.-1< a < 0B.C.D.
7.
若一个三角形两边长分别是3、7,则第三边长可能是(   )
A.4B.8C.10D.11
8.
如图,△ABC是等边三角形,AD是角平分线,△ADE也是等边三角形,下列结论:①ADBC.②EFFD.③BEBD.④ACAE.其中正确的个数是()

A. 1    B. 2    C. 3    D. 4
9.
如图,直线l外有不重合的两点A、B.在直线l上求一点C,使得的长度最短,作法为:①作点B关于直线l的对称点B'.②连接AB'交直线l于点C,则点C即为所求.在解决这个问题时,没有用到的知识点是(  )
A.线段的垂直平分线性质     B.两点之间线段最短
B.三角形两边之和大于第三边C.角平分线的性质

2.选择题(共1题)

10.

根据短文理解选择正确答案。

      Everyone needs friends. Friends bring us happiness and hope in our lives. But the ability to make friends changes from person to person. To some people, making friends is easy, and to others it's very difficult.

      Making friends is a skill, and the first thing is to know how to get on with others.

      If you have trouble in making friends, maybe I can tell you how to do it.

      ★Realize your own good points. You have skills and talents(才能) that others will like.

      ★ Believe that you are a good person and have something nice to share with others.

      ★ Be humourous. Learn to laugh at yourself and your weakness. Remember to smile at others.

      ★ Respect(尊敬) others. Everyone has his own idea. Learn how to listen to others’ ideas without trying to make them accept(接受) yours.

      ★ Be kind. If you are kind to others, they will usually be kind to you. There are hundreds of little things you can do to show your kindness. Open the door for someone. Wave to a friend and so on.

      ★  Don't complain(抱怨). Learn to accept what you can't change, and work hard to change what you can. No one is willing to hear your complaints all the time.

      ★ Never give up. Even if you are faced with some closed-minded people, never give up. And try to find someone who will understand you.

3.填空题(共5题)

11.
计算:_________________.
12.
观察下列各式的规律:
(a﹣b)(a+b)=a2﹣b2
(a﹣b)(a2+ab+b2)=a3﹣b3
(a﹣b)(a3+a2b+ab2+b3)=a4﹣b4

可得到(a﹣b)(a2016+a2015b+…+ab2015+b2016)=____.
13.
分式的值为0,则____________.
14.
如图,在△ABC中,点P、Q分别是BC、AC边上的点,PSAC,PRAB,若AQPQ,PRPS,则下列结论:①ASAR;②QP∥AR;③△BRP ≌△CPS;④S四边形ARPQ=.其中正确的结论有____________(填序号).
15.
如图,△ABC中,ABAC,AB的垂直平分线DE交AC于D,交AB于E,且BD平分∠ABC,则∠BDC=___________度.

4.解答题(共7题)

16.
已知4x=3y,求代数式的值.
17.
分解因式:① -a4+16;②6xy2-9x2y-y3
18.
(10分) 铭润超市用5000元购进一批新品种的苹果进行试销,由于销售状况良好,超市又调拨11000元资金购进该品种苹果,但这次的进货价比试销时每千克多了0.5元,购进苹果数量是试销时的2倍.
(1)试销时该品种苹果的进货价是每千克多少元?
(2)如果超市将该品种苹果按每千克7元的定价出售,当大部分苹果售出后,余下的400千克按定价的七折(“七折”即定价的70%)售完,那么超市在这两次苹果销售中共盈利多少元?
19.
如图(1)四边形ABCD中,已知∠ABC+∠ADC=180°,ABADDAAB,点ECD的延长线上,∠BAC=∠DAE
(1)求证:△ABC≌△ADE
(2)求证:CA平分∠BCD
(3)如图(2),设AF是△ABCBC边上的高,求证:EC=2AF
20.
如图,AD,AE分别是△ABC的高和角平分线.
(1)已知∠B=30°,∠C=60°,求∠DAE的度数;
(2)设∠B=x,∠C=y(x<y).请直接写出∠DAE的度数 .(用含x,y的代数式表示)
21.
已知△ABN和△ACM位置如图所示,AB=AC,AD=AE,∠1=∠2.
(1)试说明:BD=CE;
(2)试说明:∠M=∠N.
22.
如图,已知△ABC是边长为3cm的等边三角形,动点P、Q同时从A、B两点出发,分别沿AB、BC方向匀速移动,它们的速度都是1 cm/s,当点P到达点B时,P、Q两点停止运动,设点P的运动时间为t(s),则(1)BP cm,BQ  cm.(用含t的代数式表示)
(2)当t为何值时,△PBQ是直角三角形?
试卷分析
  • 【1】题量占比

    单选题:(9道)

    选择题:(1道)

    填空题:(5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:0

    5星难题:0

    6星难题:18

    7星难题:0

    8星难题:3

    9星难题:0