浙江省台州市书生中学2017-2018学年九年级9月起始考数学试题

适用年级:初三
试卷号:161824

试卷类型:开学考试
试卷考试时间:2017/9/13

1.单选题(共7题)

1.
>1,则关于的方程的根的情况是(   )
A.有一正根和一负根B.有两个正根C.有两个负根D.没有实数根
2.
用配方法解方程x2-2x-3=0时,配方后所得的方程为(   )
A.B.C.D.
3.
某果园2014年水果产量为100吨,2016年水果产量为144吨,求该果园水果产量的年平均增长率。设该果园水果产量的年平均增长率为,则根据题意可列方程为(  )
A.B.C.D.
4.
下列与函数图象形状不相同的函数是( )
A.B.C.D.
5.
把抛物线 向右平移1个单位,再向上平移3个单位,得到抛物线的解析式为(    )
A.B.
C.D.
6.
如图,在△ABC中,∠CAB=70°,将△ABC绕点A逆时针旋转到△AB′C′的位置,使得CC′∥AB,则∠BAB′的度数是(  )
A.70°B.35°C.40°D.50°
7.
某果园2011年水果产量为100吨,2013年水果产量为144吨,求该果园水果产量的年平均增长率.设该果园水果产量的年平均增长率为x,则根据题意可列方程为()
A.144(1﹣x)2=100B.100(1﹣x)2=144C.144(1+x)2=100D.100(1+x)2=144

2.选择题(共2题)

8.

阅读理解

    A man had a little dog, and he liked it a lot. He would pat (拍) its head, put it on his knee and talk to it. Then he would give it some food from his own plate.

    A donkey (驴子) looked in through the window and saw the man and the dog.

    " Why doesn't he choose me as his pet?" said the donkey. "It is not fair. I work hard, and the dog only shakes its tail, barks and jumps onto the master's (主人) knee. It is not fair. "

    Then the donkey said to himself, "If I do what the dog does, the master may choose me as

his pet. "

    So the donkey ran into the room. He brayed (嘶叫) at the top of his voice. He shook his tail so hard that he knocked over a jar on the table. Then he tried to jump onto the master's knee.

    The master thought the donkey was maniacal , and he shouted, "Help ! Help ! "

    Some men came running in with sticks in their hands and they beat the donkey until he ran out of the house.

"I only did what the dog did, " said the donkey, "and yet they still regard the dog as their pet and they beat me with sticks. It is not fair. "

根据短文内容,选择最佳答案,并将其标号填涂在答题卡相应位置。

9.

阅读理解

    A man had a little dog, and he liked it a lot. He would pat (拍) its head, put it on his knee and talk to it. Then he would give it some food from his own plate.

    A donkey (驴子) looked in through the window and saw the man and the dog.

    " Why doesn't he choose me as his pet?" said the donkey. "It is not fair. I work hard, and the dog only shakes its tail, barks and jumps onto the master's (主人) knee. It is not fair. "

    Then the donkey said to himself, "If I do what the dog does, the master may choose me as

his pet. "

    So the donkey ran into the room. He brayed (嘶叫) at the top of his voice. He shook his tail so hard that he knocked over a jar on the table. Then he tried to jump onto the master's knee.

    The master thought the donkey was maniacal , and he shouted, "Help ! Help ! "

    Some men came running in with sticks in their hands and they beat the donkey until he ran out of the house.

"I only did what the dog did, " said the donkey, "and yet they still regard the dog as their pet and they beat me with sticks. It is not fair. "

根据短文内容,选择最佳答案,并将其标号填涂在答题卡相应位置。

3.填空题(共4题)

10.
___.
11.
关于x 的一元二次方程(a﹣1)x2﹣2x+3="0" 有实数根,则整数a 的最大值是_____________.
12.
已知,当_______时,函数值随x的增大而减小.
13.
已知二次函数的部分图象如图所示,则一元二次方程的解为:_____.

4.解答题(共5题)

14.
一个两位数,其个位上的数与十位上的数的和等于6,而个位与十位上的数的积等于这两位数的三分之一,求这个两位数.
15.
已知m是方程的一个实数根,求代数式的值.
16.
解方程:(1) (2)
17.
关于x的方程
(1)求证:无论k为何值,方程总有实数根;
(2)设 是该方程的两个根,记,S的值能为2吗?若能求出此时k的值.
18.
如图1,已知:已知:等边△ABC,点D是边BC上一点(点D不与点B、点C重合),求证:BD+DC>AD.
下面的证法供你参考:
把△ACD绕点A顺时针旋转60°得到△ABE,连接ED,则有△ACD≌△ABE,DC=EB,∵AD=AE,∠DAE=60°,
∴△ADE是等边三角形,∴AD=DE.在△DBE中,BD+EB>DE,即:BD+DC>AD
实践探索:
(1)请你仿照上面的思路,探索解决下面的问题:
如图3,点D是等腰直角三角形△ABC边上的点(点D不与B、C重合).求证:BD+DC>AD.
(2)如果点D运动到等腰直角三角形△ABC外或内时,BD、DC和AD之间又存在怎样的数量关系?直接写出结论.
创新应用:
(3)已知:如图4,等腰△ABC中,AB=AC,且∠BAC=α(α为钝角),D是等腰△ABC外一点,且∠BDC+∠BAC=180°,BD、DC与AD之间存在怎样的数量关系?写出你的猜想,并证明.
试卷分析
  • 【1】题量占比

    单选题:(7道)

    选择题:(2道)

    填空题:(4道)

    解答题:(5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:2

    5星难题:0

    6星难题:10

    7星难题:0

    8星难题:2

    9星难题:2