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1．计算：1﹣（+2）+3﹣（+4）+5﹣（+6）…+2015﹣（+2016）= ．

2．已知a 、b 、c 的位置如图：则化简|﹣a|﹣|c ﹣b|﹣|a ﹣c|= ．

3．有理数a 、b 在数轴上的位置如图所示

化简：|a+2|﹣|a|+|b ﹣1|+|a+b|可得到 ．

4．在数轴上，点P 表示的数是a ，点P′表示的数是，我们称点P′是点P 的“相关点”，已知数轴上A 1的相关点为A 2，点A 2的相关点为A 3，点A 3的相关点为A 4…，这样依次得到点A 1、A 2、A 3、A 4，…，A n ．若点A 1在数轴表示的数是，则点A 2016在数轴上表示的数是 ．

5．如果x 、y 都是不为0的有理数，则代数式

的最大值是 ．

6．|x+2|+|x ﹣2|+|x ﹣1|的最小值是 ．

7．当式子|x+1|+|x ﹣2|取最小值时，相应的x 的取值范围是 ，最小值是 ．

8．如图，方格表中的格子填上了数，每一行每一列及两条对角线中所填数的和均相等，则x 的值 ．

9．先观察：1﹣=×，1﹣=×，1﹣=×，… （1）探究规律填空：1﹣

=

× ； （2）计算：（1﹣

）?（1﹣

）?（1﹣）…（1﹣） 10．阅读下列各式：（a?b）2=a 2b 2，（a?b）3=a 3b 3，（a?b）4=a 4b 4

…

回答下列三个问题：

（1）验证：（2×）100= ，2100×（）100= ；

（2）通过上述验证，归纳得出：（a?b）n= ；（abc）n= ．

（3）请应用上述性质计算：（﹣0.125）2017×22016×42015．

11．数轴上的点M对应的数是2，一只蚂蚁从点M出发沿着数轴以每秒2个单位的速度向左或向右爬行，当它到达数轴上的点N后，立即返回到原点，共用6秒．

（1）蚂蚁爬行的路程是多少？

（2）点N对应的数是多少？

（3）点M和点N之间的距离是多少？

12．我们已经学习过“乘方”和“开方”运算，下面给同学们介绍一种新的运算，即对数运算．

定义：如果a b=N（a＞0，a≠1，N＞0），则b叫做以a为底N的对数，记作log a N=b．

例如：因为53=125，所以log5125=3；因为112=121，所以log11121=2．

（1）填空：log66= ，log381= ．

（2）如果log2（m﹣2）=3，求m的值．

13．在抗洪抢险中，解放军战士的冲锋舟加满油沿东西方向的河流抢救灾民，早晨从A地

出发，晚上到达B 地，约定向东为正方向，当天的航行路程记录如下（单位：千米）：14，﹣9，+8，﹣7，13，﹣6，+12，﹣5．

（1）请你帮忙确定B地位于A地的什么方向，距离A地多少千米？

（2）若冲锋舟每千米耗油0.5升，油箱容量为28升，求冲锋舟当天救灾过程中至少还需补充多少升油？

（3）救灾过程中，冲锋舟离出发点A最远处有多远？

14．已知：数轴上点A表示的数是8，点B表示的数是﹣4．动点P从点A出发，以每秒6个单位长度的速度沿数轴向左运动，动点Q从点B出发，以每秒4个单位长度的速度沿数轴向左运动．P，Q两点同时出发．

（1）经过多长时间，点P位于点Q左侧2个单位长度？

（2）在点P运动的过程中，若点M是AP的中点，点N是BP的中点，求线段MN的长度．

15．已知数轴上的点A和点B之间的距离为32个单位长度，点A在原点的左边，距离原点5个单位长度，点B在原点的右边．

（1）点A所对应的数是，点B对应的数是；

（2）若已知在数轴上的点E从点A出发向左运动，速度为每秒2个单位长度，同时点F 从点B出发向左运动，速度为每秒4个单位长度，在点C处点F追上了点E，求点C对应的数．

16．如图，点A、B都在数轴上，且AB=6

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九年级英语培优试题 一、单项选择题（30×0.5分＝15分） ( )1. —Is your father a Party member? —Yes, he the Party three years ago. He Party member for 3 years. A. has joined, has been B. joined, has been C. joined, took part in D. took part in, was ( )2. —Do you feel like to the cinema with me? —No, I’d like my lessons at home. A. going, to do B. to go, to do C. to go, doing D. going, doing ( )3. —You in Harbin, didn’t you? —Yes, but I in Wuhan now. A. used to live, used to live B. are used to living, used to live C. used to live, am used to living D. are used to living, am used to living ( )4. —Do you speak English or French? —I don’t speak of them. A. none B. both C. neither D. either ( )5. —Your desk needs . —I’ll have it tomorrow. A. repair, repaired B. repairing, repaired C. repair, repairing D. to repair, repaired ( )6. —Mr Green is very strict his students and strict his teaching work. —What a good teacher! A. with ,in B. in ,with C. in, in D. with, on ( )7. —What would you do if you cut yourself ? —If it’s a deep cut, I should see a doctor. A. by mistake B. in a hurry C. by accident D. with great care ( )8. —Do you like that picture on display? —It’s wonderful. I’ve never seen picture before. A. a so fine B. so beautiful C. such a nice D. a such pretty ( )9. —The sports shoes must be Linda’s. —No, they be, for they are too small for her. A. mustn’t B. can’t C. may not D. needn’t ( )10. Jim three years learning Chinese before he came to China. A. cost B. paid C. took D. spent ( )11. —The students in our class each an English dictionary. —That’s not true. Jim as well as Tom no dictionaries. A. has, has B. have , has C. has, have D. have, have ( )12. —You’ve got a new dress, too. —Yes. Mine is , but not so as yours. A. better, cheap B. more better, expensive C. better, more expensive D. good, cheaper ( )13. —I’d like to go , because it’s too cold here in winter. —You’d better go to Kunming, for it’s never too cold or too hot all the year round. A. warm somewhere B. somewhere peaceful C. somewhere warm D. peaceful somewhere ( )14. —How are you getting on with your study? —, thank you. A. Not at all. B. Quite well C. Never mind D. Very nice ( )15. —It is impolite to those people who are in trouble. —I agree with you.