1 . 规定:
表示不大于
的最大整数.
表示不小于
的最小整数,
表示最接近
的整数(
,
为整数),例如:
,
,
,则下列说法正确的是______ .(写出所有正确说法的序号)
①当
时,
;
②当
时,
;
③方程
的解为
;
④当
时,函数
的图像与正比例函数
的图像有两个交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c2719fc8914037d61e5bac0e1c5980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efe124c3e4a990276cfd12d6e6ecce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2885c5aea049f79db1faa99f1c40ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d54a0e82778f606d95a486835ac9f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618dd2aa80e1defb90ffbb5608a22799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3296a94b5421bf78627de2130d27b4.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc6d451543676efed0aaa864b953f0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fafc35c5b505364926a2be4569ff54.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6561e832adb14d1bc6f0858081642a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe8776a5e467bc6c363b97c8d6b0440.png)
③方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9943f6f6f70592cf3617bb14204172b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82bb2030f782a73d448466c38700e57f.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b88e53e6ca674b4cb92ba78dddf989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82c8c08709916bb2ff112bd1d5978ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23afc43a8c5b8cfe6bf2a1caed920c01.png)
您最近一年使用:0次
名校
2 . 如图所示,正方形
的面积是4,点
在反比例函数
的图像上,若点
是该反比例函数图像上异于点
的任意一点,过点
分别作
轴、
轴的垂线,垂足为
,
,从矩形
的面积中减去其与正方形
重合部分的面积,记剩余部分的面积为
.则当
(
为常数,且
)时,点
的坐标是______ .(用含
的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82cd05cbc975c37968421b35dda479e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef60c8de5d0ede9d879695fc86ff8a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8ae60020dbd83456c25428054b4f34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9059219044592024f63637984f86be30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/0169be9d-72b8-4804-babe-f34e01713633.png?resizew=151)
您最近一年使用:0次
名校
3 . 如图所示的八个点
,
,
,
,
,
,
,
处各写一个数,分别是
,
,
,
,
,
,
,
,已知每个点处所写的数等于与这个点有线段相连的三个点处的数的平均数,则代数式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58847e42ef00c5dc852d12c5ac42b570.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276509f01529d982ab21e479a4619268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58847e42ef00c5dc852d12c5ac42b570.png)
![](https://img.xkw.com/dksih/QBM/2022/7/9/3018993180073984/3020168932491264/STEM/a3675e470d274d5fbbbb136f22b18da1.png?resizew=135)
您最近一年使用:0次
名校
4 . 某中学每年都要举行秋季运动会,为了进一步科学地指导学生提高运动成绩,某体育老师在学校的秋季运动会上根据一名同学1500m跑的测试情况绘成下图,图中
是一条折线段,图形反映的是这名同学跑步的时间与距离的关系,由图可知下列说法错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/15/ff5aec1a-5d62-4465-a342-600c45e6589f.png?resizew=194)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/15/ff5aec1a-5d62-4465-a342-600c45e6589f.png?resizew=194)
A.这名同学跑完1500m用了6分钟,最后一分钟跑了300m |
B.这名同学的速度越来越快 |
C.这名同学第3到第5分钟的速度最慢 |
D.这名同学第2、第3分钟的速度是一样的 |
您最近一年使用:0次
2022-07-11更新
|
151次组卷
|
2卷引用:北京一零一中学2020-2021学年高一新生入学摸底测试数学试题
名校
5 . 有两种糖块,A种糖块18元/kg,B种糖块24元/kg,超市计划把A,B两种糖块按照
的比例混合出售,则合理的价格应为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d65e051e943ab28fa57aee2fb57994.png)
A.18元/kg | B.24元/kg | C.21元/kg | D.22元/kg |
您最近一年使用:0次
2021-11-22更新
|
160次组卷
|
4卷引用:内蒙古阿拉善盟第一中学2020-2021学年高二上学期开学考试理科数学试题
名校
6 . 已知:如图,正方形
中,
,
相交于点O,E,F分别为边
上的动点(点E,F不与线段
的端点重合),且
,连接
.在点E,F运动的过程中,有下列四个说法:①
是等腰直角三角形;②
面积的最小值是
;④至少存在一个
,使得
的周长是
;④四边形
的面积是1.其中正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833303298727936/2839663310209024/STEM/2da247401fa84b86b314003fe24d4e6a.png?resizew=158)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f805768a5ffaf8bdfa4bc3b680aafdc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a84cd6b65892b2548afa72a9504f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc869125145c0139d92490a41bd3918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc869125145c0139d92490a41bd3918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e5a933a2a0ff3a28009cc989293ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e5a933a2a0ff3a28009cc989293ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab46ea0cba2d06283fae3d864a2329e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e689223dbda856ab0898b0010ffb86a.png)
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833303298727936/2839663310209024/STEM/2da247401fa84b86b314003fe24d4e6a.png?resizew=158)
A.① | B.② | C.③ | D.④ |
您最近一年使用:0次
7 . 小明同学做了下面四道计算题:①
;②
;③
;④
,其中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ad3ebc312524c860b0779cd7c3bf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4868a11b424f3cd99e20db5a83d5519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e50f64670ec5f23c05a6b5b34964cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d63a341fae95c017e2cf4565dbb37bf.png)
A.① | B.② | C.③ | D.④ |
您最近一年使用:0次
名校
8 . 如图,
,且
,E、F是
上两点,
,若
,,则
的长为( )
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833303298727936/2839663310094336/STEM/679c9963ea09484c8abee9bf5da6abff.png?resizew=180)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c220eadc312101e2fb89dfe920f7b30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a319599e5897029e5545a1f4d38b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0609ee19804728a2b9dc9e5e5ea83185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833303298727936/2839663310094336/STEM/679c9963ea09484c8abee9bf5da6abff.png?resizew=180)
A.7 | B.6 | C.5 | D.4 |
您最近一年使用:0次
名校
9 . 如图,二次函数
的图象y与轴交于点
,与
轴负半轴交于B,与正半轴交于点
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/db655efe-cf6b-422c-b56f-4e512a7f7dcf.png?resizew=165)
(1)求该二次函数解析式.
(2)若N是线段
上一动点,作
,交
于点E,连结
,当
面积最大时,求点N的坐标.
(3)若点P为x轴上方的抛物线上的一个动点,连接
,设所得
的面积为S.问:是否存在一个S的值,使得相应的点P有且只有2个?若有,求出这个S的值,并求此时点P的横坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6337d68cd5653767e3a1889b8b2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c84818cfbd9a885081cb4e3294eabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51775ad7d2e925dfbc4c9fa3ba4ee0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/db655efe-cf6b-422c-b56f-4e512a7f7dcf.png?resizew=165)
(1)求该二次函数解析式.
(2)若N是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525c52bb66fb415cfc0a2ed0780b5e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0702bd0b088224b2aedcc925f313d93f.png)
(3)若点P为x轴上方的抛物线上的一个动点,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735fff085611587ad30bf2849e546a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
您最近一年使用:0次
名校
10 . 《见微知著》谈到:从一个简单的经典问题出发,从特殊到一般,由简单到复杂:从部分到整体,由低维到高维,知识与方法上的类比是探索发展的重要途径,是思想阀门发现新问题、新结论的重要方法.
阅读材料一:利用整体思想解题,运用代数式的恒等变形,使不少依照常规思路难以解决的问题找到简便解决方法,常用的途径有:(1)整体观察;(2)整体设元;(3)整体代入;(4)整体求和等.
例如,
,求证:
.
证明:原式
.
波利亚在《怎样解题》中指出:“当你找到第一个藤菇或作出第一个发现后,再四处看看,他们总是成群生长”类似问题,我们有更多的式子满足以上特征.
阅读材料二:基本不等式
,当且仅当
时等号成立,它是解决最值问题的有力工具.
例如:在
的条件下,当x为何值时,
有最小值,最小值是多少?
解:∵
,∴
,即
,∴
,
当且仅当
,即
时,
有最小值,最小值为2.
请根据阅读材料解答下列问题
(1)已知如
,求下列各式的值:
①
___________.
②
___________.
(2)若
,解方程
.
(3)若正数a、b满足
,求
的最小值.
阅读材料一:利用整体思想解题,运用代数式的恒等变形,使不少依照常规思路难以解决的问题找到简便解决方法,常用的途径有:(1)整体观察;(2)整体设元;(3)整体代入;(4)整体求和等.
例如,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2764ccd2cfe6de0c53dce98e45b120.png)
证明:原式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87898da3367d13667477a10c9cc47ac2.png)
波利亚在《怎样解题》中指出:“当你找到第一个藤菇或作出第一个发现后,再四处看看,他们总是成群生长”类似问题,我们有更多的式子满足以上特征.
阅读材料二:基本不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28514741f365301978e922fdca0fcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
例如:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f40c24c64bbb0645fcf585f4e66872.png)
解:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c42b50f6f9e56ea5f222b0a40cb4a3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91bb4a7110c19cd10cb915e55438314b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d32ba3941cef6b1d549f050f0d314e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63af71b9e6f71cd26e6e97541154cd8c.png)
当且仅当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6a593ef3641dbd11e324dbe78b4dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f40c24c64bbb0645fcf585f4e66872.png)
请根据阅读材料解答下列问题
(1)已知如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0dd92f322200ecabfb74ffd7cf3f4a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af71e37295978173629004816b65791a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9093a255130a938a4d84595c0c56ce.png)
(3)若正数a、b满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab1cbf887eca130c254f6e0cf3fdb2f.png)
您最近一年使用:0次
2021-10-29更新
|
532次组卷
|
3卷引用:江苏省南通中学2020-2021学年高一上学期开学考试数学试题
江苏省南通中学2020-2021学年高一上学期开学考试数学试题江西省南昌市第二中学2023-2024学年高一上学期月考数学试题(一)(已下线)第二章 等式与不等式(压轴题专练)-速记·巧练(沪教版2020必修第一册)