名校
1 . 甲乙两位同学求关于
的方程组
的解集
时,甲因看错了
,解得
;乙因看错了
,解得
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30800bcb030cf5ee97d0e21fbbe8c368.png)
___________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22d7c214d9685da7be80319ed80d8df.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7822f361618da0965955d7bc25c4b49c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46102fb6ed356e25bae44efe2139ee4.png)
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2 . 若
是方程组
的一组解,则代数式
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75da314a02f84e0e59884ca772da2c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14c450a5c56c661230a974cb29417e0.png)
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2023-11-02更新
|
182次组卷
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2卷引用:北京市人大附中2023-2024学年高一期中数学试题
3 . 甲、乙两位同学分别做下面这道题目:在平面直角坐标系中,动点
到
的距离比
到
轴的距离大
,求
的轨迹.甲同学的解法是:解:设
的坐标是
,则根据题意可知
,化简得
; ①当
时,方程可变为
;②这表示的是端点在原点、方向为
轴正方向的射线,且不包括原点; ③当
时,方程可变为
; ④这表示以
为焦点,以直线
为准线的抛物线;⑤所以
的轨迹为端点在原点、方向为
轴正方向的射线,且不包括原点和以
为焦点,以直线
为准线的抛物线. 乙同学的解法是:解:因为动点
到
的距离比
到
轴的距离大
. ①如图,过点
作
轴的垂线,垂足为
. 则
.设直线
与直线
的交点为
,则
; ②即动点
到直线
的距离比
到
轴的距离大
; ③所以动点
到
的距离与
到直线
的距离相等;④所以动点
的轨迹是以
为焦点,以直线
为准线的抛物线; ⑤甲、乙两位同学中解答错误的是________ (填“甲”或者“乙”),他的解答过程是从_____ 处开始出错的(请在横线上填写① 、②、③、④ 或⑤ ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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![](https://img.xkw.com/dksih/QBM/2020/1/9/2373416240177152/2374112457277440/STEM/78967d5dd05c4092a839695b53af67a5.png?resizew=140)
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名校
4 . 我国南北朝时期的数学家张丘建是世界数学史上解决不定方程的第一人,他在
张丘建算经
中给出一个解不定方程的百鸡问题,问题如下:鸡翁一,值钱五,鸡母一,值钱三,鸡雏三,值钱一
百钱买百鸡,问鸡翁母雏各几何?用代数方法表述为:设鸡翁、鸡母、鸡雏的数量分别为x,y,z,则鸡翁、鸡母、鸡雏的数量即为方程组
的解
其解题过程可用框图表示如图所示,则框图中正整数m的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a4bbcf2e9404da66210a33f9006bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080cd6e4fac19934612fb5907fc89e93.png)
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![](https://img.xkw.com/dksih/QBM/2019/3/26/2168983764451328/2170069115224064/STEM/f543efef393144f9a719402b4cec18ec.png?resizew=153)
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2018-05-14更新
|
338次组卷
|
2卷引用:【全国百强校】北京师大实验中学2019届高三3月份高考模拟文科数学试题
5 . 对于三次函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19951f3364fb04433feed743bc37975d.png)
,给出定义:设
是函数
的导数,
是
的导数,若方程
有实数解
,则称点
为函数
的“拐点”,同学经过探究发现:任何一个三次函数都有“拐点”;任何一个三次函数都有对称中心,且拐点就是对称中心,若
,请你根据这一发现,求:(1)函数
的对称中心为___________ ;(2)计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb8378ae701d9f5a5d66da3cf62c65d.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19951f3364fb04433feed743bc37975d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5bb89c3ad435f1ef59307b174105ed.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb8378ae701d9f5a5d66da3cf62c65d.png)
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2021-10-23更新
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658次组卷
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10卷引用:北京市第一六一中学2022届高三10月月考数学试题
北京市第一六一中学2022届高三10月月考数学试题江苏省淮安市高中校协作体2021-2022学年高三上学期期中联考数学试题(已下线)第1讲 函数的图象与性质(练 )-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)(已下线)考向08 函数的奇偶性、周期性与对称性(重点)(已下线)第24讲 章末检测四-备战2023年高考数学一轮复习考点帮(新高考专用)江苏省徐州市第七中学2022-2023学年高三上学期12月学情检测数学试题江苏省盐城市大丰区新丰中学2022-2023学年高二上学期期末数学试题(已下线)宁夏石嘴山市第三中学2023-2024学年高二上学期期末数学试题(已下线)期末考试押题卷一(考试范围:苏教版2019选择性必修第一册)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)江苏省南菁高级中学2023-2024学年高二下学期5月月考数学试题
解题方法
6 . 解决问题“求方程
的解”有以下思路:
可变为
,考虑函数
可知,
,且函数
在
上单调递减,所以原方程有唯一解
.类比上述解法,可得不等式
的解集是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c18c032d75893db45e61e6c4eb0d4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c18c032d75893db45e61e6c4eb0d4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cfb1e9557770560280b5248ae2d0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef18670761b20b08d0db1a5f0307e05.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2197c1c9e5e09713fe45dc1e73edf509.png)
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2024高三·北京·专题练习
7 . 已知函数
,则下列说法正确的有________ .
①函数
的值域为
;
②方程
有两个不等的实数解;
③不等式
的解集为
;
④关于
的方程
的解的个数可能为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4631d2c8bc7dfbc9646b98430556152a.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ca5e984d5e14b4be18a5ee99f80a4f.png)
②方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
③不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76eb0cc201c45f1abf7a3c0f21253811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3979b42d7d6cdb7a54d00ba41b92a0.png)
④关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ad7cd0c02bb7220641b9729bac2168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29376026a31f34b0b418c93d86785872.png)
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名校
解题方法
8 . 关于
的不等式
的解集中至多包含1个整数,写出满足条件的一个
的取值范围__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977e320287da8520ffdde26da8e0b86a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
9 . “求方程
的解”有如下解题思路:设
,则
在
上单调递减,且
,所以原方程有唯一解
,类比上述解题思路,不等式
的解集是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cfb1e9557770560280b5248ae2d0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570ae76599e821173f4a5905e54e41c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9da4fdfdddc259dcef9fdd4b826b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbada0ea09c57a2c3d3e2e5141d4645e.png)
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2018-03-04更新
|
247次组卷
|
5卷引用:北京市第四中学2018届高三第一次模拟考试(一模)仿真卷(A卷)文科数学试题
(已下线)北京市第四中学2018届高三第一次模拟考试(一模)仿真卷(A卷)文科数学试题湖北省沙市中学2018届高三1月月考数学(文)试题(已下线)2018年高考二轮复习测试专项【苏教版】专题九 算法 推理与证明 复数【全国百强校】黑龙江省大庆第一中学2017-2018学年高二下学期第三次阶段检测数学(理)试题2020届宁夏六盘山高级中学高三下学期第二次模拟考试数学(理)试题
名校
10 . 对于三次函数
,给出定义:设
是函数
的导数,
是函数
的导数,若方程
有实数解
,则称点
为函数
的“拐点”.某同学经过探究发现:任何一个三次函数都有“拐点”;任何一个三次函数都有对称中心,且“拐点”就是对称中心.给定函数
,请你根据上面的探究结果,解答以下问题:
①函数
的对称中心坐标为______ ;
②计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a9ce5fb3ebe45a01b8218947bc89f9.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f087ded8039eedaa8aa724b81ec393e9.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f087ded8039eedaa8aa724b81ec393e9.png)
②计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a9ce5fb3ebe45a01b8218947bc89f9.png)
您最近一年使用:0次
2019-12-02更新
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667次组卷
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3卷引用:北京市西城区北京师范大学第二附属中学2019-2020学年高三上学期期中数学试题