如图,一个点从数轴上的原点开始,先向左移动
到达A点,再向右移动
到达B点,然后再向右移动
到达C点,数轴上一个单位长度表示
.
![](https://img.xkw.com/dksih/QBM/2022/11/14/3109432796438528/3110770115239936/STEM/fbe43c7ee3e84ea1bd1147edfd2e67d3.png?resizew=384)
(1)请你在数轴上标出A、B、C三点的位置,并写出A、B、C三点分别表示的数;
(2)把点A到点C的距离记为AC,则
___________
,
___________
;
(3)若点A沿数轴以每秒
匀速向右运动,经过多少秒使
?
(4)若点A以每秒
的速度匀速向左移动,同时点B、点C分别以每秒
、
的速度匀速向右移动.设移动时间为t秒,试用含t的代数式表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9938aea41f03701b233dee15809f2126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02eb1e5fe467f2731c059ebf9ef1a4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://img.xkw.com/dksih/QBM/2022/11/14/3109432796438528/3110770115239936/STEM/fbe43c7ee3e84ea1bd1147edfd2e67d3.png?resizew=384)
(1)请你在数轴上标出A、B、C三点的位置,并写出A、B、C三点分别表示的数;
(2)把点A到点C的距离记为AC,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
(3)若点A沿数轴以每秒
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818309e7b9a67c54ab1530fdb4b0edc0.png)
(4)若点A以每秒
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78d0ab561d0c9bb9099772c596af8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976260cbf5e30856d4fd37a4b0a671a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d2e56af0d14a3a401ac6824d9c748b4.png)
更新时间:2022-11-16 11:00:54
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【推荐1】观察下列每对数在数轴上的对应点间的距离
与
,
与
.并回答下列各题:
(1)你能发现:
与
在数轴上的对应点间的距离可以表示为:
;
与
在数轴上的对应点间的距离可以表示为:
;根据以上规律,则
与
在数轴上的对应点的距离是 .
(2)若数轴上的点
表示的数是
,点
表示的数是
,则
与
两点间的距离可以表示为 .
(3)结合数轴思考,
的最小值为多少?
(4)满足
,求
的值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/20/3af20308-d26a-4d0d-830e-51978ff50b3b.png?resizew=381)
(1)你能发现:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd529494cfd2a4700e84c13b25db0f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846b357b9e63a3627aca880cd0a40b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
(2)若数轴上的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)结合数轴思考,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13cf6f34ceecab7d47400dd3d0e247c.png)
(4)满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ce110b52b8ee0f943a481e7619830b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a960e7bc045efb3966d50791f26f0248.png)
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【推荐2】如图,已知A,
为数轴上的两个点,点A表示的数是
,点
表示的数是10.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/26/47749d4d-cbed-41b2-a0ef-d98acb7ab8e1.png?resizew=291)
(1)线段
的中点
对应的数为__________;
(2)若点
在数轴上,且
,求
的长;
(3)若一只蚂蚁从点A出发,在数轴上每秒向右前进3个单位长度;同时一只毛毛虫从点
出发,在数轴上每秒向右前进1个单位长度,它们在点
处相遇,求点
对应的数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f86b86a6ccdf2c077d195db7bc380ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/26/47749d4d-cbed-41b2-a0ef-d98acb7ab8e1.png?resizew=291)
(1)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9463fa05ba2b239f90c8acb5a0d7654c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)若一只蚂蚁从点A出发,在数轴上每秒向右前进3个单位长度;同时一只毛毛虫从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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【推荐3】在数轴上,点A表示的数为a,点B表示的数为b,且a、b满足
,其中O为原点,如图:
![](https://img.xkw.com/dksih/QBM/2021/11/10/2848153065676800/2853358854258688/STEM/e6c5df42-470f-44f7-a44c-5e30c9eaa7f5.png)
(1)直接写出:
_____,
______,A,B两点之间的距离为______.
(2)在数轴上有一动点M,若点M到点A的距离是点M到点B的距离的2倍,求点M对应的数.
(3)在数轴上有一动点P,动点P从点A出发第一次向左运动1个单位长度;然后在此位置进行第二次运动,向右运动2个单位长度;然后在此位置进行第三次运动,向左运动3个单位长度……;按照如此规律不断地进行左右运动,当运动到2021次时,求此时点P所对应的有理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba216a17aad624726505e5bca1e5ee8.png)
![](https://img.xkw.com/dksih/QBM/2021/11/10/2848153065676800/2853358854258688/STEM/e6c5df42-470f-44f7-a44c-5e30c9eaa7f5.png)
(1)直接写出:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)在数轴上有一动点M,若点M到点A的距离是点M到点B的距离的2倍,求点M对应的数.
(3)在数轴上有一动点P,动点P从点A出发第一次向左运动1个单位长度;然后在此位置进行第二次运动,向右运动2个单位长度;然后在此位置进行第三次运动,向左运动3个单位长度……;按照如此规律不断地进行左右运动,当运动到2021次时,求此时点P所对应的有理数.
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【推荐1】已知数轴上A,B两点表示的数分别为a,b,且a,b满足
.点P沿数轴从A出发以3个单位长度/秒的速度向右匀速运动.
(1)则
_______,
_______.
(2)若点P到点A的距离是点P到点B距离的2倍,求点P运动的时间.
(3)若点Q在点P运动3秒后,从点B出发以2个单位长度/秒的速度向左匀速运动,当P,Q两点相遇后,再同时都向右运动(速度不变),当其中一点先到达B点,则两点同时停止运动,试求在整个运动过程中,当P点运动时间为多少秒时,P,Q两点之间的距离为1?并求出此时Q点所对应的数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93422878a6fbade00c5f65465a147a3e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/91564729-5ccc-47e9-989f-e32015df1510.png?resizew=313)
(1)则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)若点P到点A的距离是点P到点B距离的2倍,求点P运动的时间.
(3)若点Q在点P运动3秒后,从点B出发以2个单位长度/秒的速度向左匀速运动,当P,Q两点相遇后,再同时都向右运动(速度不变),当其中一点先到达B点,则两点同时停止运动,试求在整个运动过程中,当P点运动时间为多少秒时,P,Q两点之间的距离为1?并求出此时Q点所对应的数.
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名校
【推荐2】如图将一条数轴在原点
,点
,点
,点
处各折一下,得到一条“折线数轴”.图中点
表示
,点
表示
,点
表示
,点
表示
,点
表示
,我们称点
和点
在数轴上相距
个长度单位.动点
从点
出发,以
单位/秒的速度沿着“折线数轴”的正方向运动,同时,动点
从点
出发,以
单位/秒的速度沿着数轴的负方向运动,两点上坡时速度均变为初始速度的一半,下坡时速度均变为初始速度的两倍,平地则保持初始速度不变.当点
运动至点
时则两点停止运动,设运动的时间为
秒.问:
(1)动点
从点
运动至
点需要 秒,此时点
对应的点是 .
(2)
,
两点在点
处相遇,求出相遇点
所对应的数是多少?
(3)求当
为何值时,
,
两点在数轴上相距的长度与
,
两点在数轴上相距的长度相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b9a5f1362c12e1ea8f6fc0d9d787ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e60fbe6820130fb20abc555a94b5ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbecbd7e92dcbe1766462fcf40066de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492b6d3883713fcaa8a4fdd87b87b480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/22/5547ecb7-fa8f-45c2-924c-f362708a2c83.png?resizew=307)
(1)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)求当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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【推荐2】观察下列式子:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57550ac22a0b1560bc4eaef835358b2.png)
将以上三个等式两边分别相加得:
.
(1)直接写出结果:
_______;
(2)请用上述方法计算(写出具体过程):
______;;
(3)直接写出计算结果:
_______;
(4)直接写出计算结果:
________;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57550ac22a0b1560bc4eaef835358b2.png)
将以上三个等式两边分别相加得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803b4243a314353ccc0e2b7ea67bafcb.png)
(1)直接写出结果:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf6d050dc074eee244f9cb55fee4f83.png)
(2)请用上述方法计算(写出具体过程):
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba6560bd44a94c96e47c284ef4f4642.png)
(3)直接写出计算结果:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b298465ea2a572cff61d54631f0f0a.png)
(4)直接写出计算结果:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccfb1cead7afe80dc8dabc253984079.png)
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【推荐1】某农户2020年承包荒山若干亩,投资7800元改造后,种果树2000棵.今年水果总产量为36000千克,此水果在市场上每千克售
元,在果园每千克售
元(
).若该农户将水果拉到市场出售平均每天出售1000千克,需8人帮忙,每人每天付工资100元,农用车运费及其他各项税费平均每天300元.
(1)当
,
时,农户在水果市场或在果园中出售完全部水果的总收入分别是多少元?
(2)用
,
分别表示农户在水果市场或在果园中这两种方式出售完全部水果的纯收入?(纯收入
总收入
总支出)
(3)若
,
且
是整数,若两种出售水果方式都在相同的时间内售完全部水果,试讨论当
为何值时,选择哪种出售方式较好.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5556dd86322752a457b3a6ba979c80.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b700fa9aeb1016aa71f76e4b6bb212e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c06bbdd405ddef80942a282021f2357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f53a8137ab0278532569367562429b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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【推荐2】已知x=m与x=n分别是关于x的方程ax+b=0(a≠0)与cx+d=0(c≠0)的解.
(1)若关于x的方程ax+b=0(a≠0)的解与方程6x-7=4x-5的解相同,求m的值;
(2)当n=1时,求代数式3c2+cd+2c-2(
cd
c2-d)的值;
(3)若|m-n|
,则称关于x的方程ax+b=0(a≠0)与cx+d=0(c≠0)为“差半点方程”.试判断关于x的方程4042x
9×2020﹣2020t+x,与4040x+4=8×2021﹣2020t﹣x,是否为“差半点方程”,并说明理由.
(1)若关于x的方程ax+b=0(a≠0)的解与方程6x-7=4x-5的解相同,求m的值;
(2)当n=1时,求代数式3c2+cd+2c-2(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05a452a777d62f530e3de76e03d9f2e.png)
(3)若|m-n|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50a39604477d1d9326eb455cda2e838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79a91dcd4b762e440af9a1586f16ee6.png)
您最近一年使用:0次