1 . 如图1,在平面直角坐标系中,点O为坐标原点,直线
交x轴正半轴于点A,交y轴负半轴于点B,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/16/edd30ac2-e26f-43ce-bbeb-fc3f2c6403d3.png?resizew=553)
(1)求k的值;
(2)如图2,P为y轴正半轴上一点,过点P作PD⊥AB于点D,交线段OA于点E,设点P的纵坐标为t,线段AD的长d,求d与t的函数解析式;
(3)如图3,在(2)的条件下,
,点H在线段OP上,连接AH,
,点G为第一象限内直线AP上方一点,连接PG、AG,
,点F为第二象限内一点,连接OF、FH、FG,若
,
,
,
,求点F的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb5a7ee17f537ae1043626601887e25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bc235df1d3cf1b65050cd1907590cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/16/edd30ac2-e26f-43ce-bbeb-fc3f2c6403d3.png?resizew=553)
(1)求k的值;
(2)如图2,P为y轴正半轴上一点,过点P作PD⊥AB于点D,交线段OA于点E,设点P的纵坐标为t,线段AD的长d,求d与t的函数解析式;
(3)如图3,在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b351f1e84de1b9383bc8704d2923228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd13063ddb712c28ee39883aef69c977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116b1fca18740683eacdda79a6bd70ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ae3a1c6ff9b1cc5af59ca553902dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e46f538d5403168a4ec0ebe662117b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b386e717c5cbdeb76986dec2db5ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13329652c07eb99724e57ea24bfb693.png)
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2 . 我市在创建全国文明城市过程中,决定购买A,B两种树苗对某路段道路进行绿化改造,已知购买A种树苗8棵,B种树苗3棵,需要950元;若购买A种树苗5棵,B种树苗6棵,则需要800元.
(1)求购买A,B两种树苗每棵各需多少元?
(2)考虑到绿化效果和资金周转,购进A种树苗不能少于52棵,且用于购买这两种树苗的资金不能超过7650元,若购进这两种树苗共100棵,则有哪几种购买方案?
(3)某包工队承包种植任务,若种好一棵A种树苗可获工钱30元,种好一棵B种树苗可获工钱20元,在第(2)问的各种购买方案中,种好这100棵树苗,哪一种购买方案所付的种植工钱最少?最少工钱是多少元?
(1)求购买A,B两种树苗每棵各需多少元?
(2)考虑到绿化效果和资金周转,购进A种树苗不能少于52棵,且用于购买这两种树苗的资金不能超过7650元,若购进这两种树苗共100棵,则有哪几种购买方案?
(3)某包工队承包种植任务,若种好一棵A种树苗可获工钱30元,种好一棵B种树苗可获工钱20元,在第(2)问的各种购买方案中,种好这100棵树苗,哪一种购买方案所付的种植工钱最少?最少工钱是多少元?
您最近一年使用:0次
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3 . 如图,在四边形
中,
,
与
互余,在线段
上取点
,
(点
在
之间),使
.当点
从点
匀速运动到点
时,点
恰好从点
匀速运动到点
.记
,
,已知
,当
为
中点时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/c8512158-2bd2-4465-bb79-0259ff85757e.png?resizew=493)
(1)判断
与
的位置关系,并说明理由.
(2)求
,
的长.
(3)若
,
分别平分
,
,并交线段
,
于点
,
(点
,
不重合).连接
并延长交
于点
,如图2所示,若
,当
时,通过计算比较
与
的大小关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853e81b1b9606ad25244ff82c8292df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23dc2d2dd56fcc67698c45a6e0e48f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb65bee4fb8c2cbdd36e318cd652f928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5329d64b07929c924ce26249a3a1eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/acc290b44635265137fdf13146b6a6d9.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/a0aecccf3a16590827a53ddacf606ce3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa1187495c7a6b82683982bd69a5a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750f123e07bd77acf1c82287b8d3c1fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7167b7285f35cf724430b63a7e0c7c51.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/c8512158-2bd2-4465-bb79-0259ff85757e.png?resizew=493)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4f63da042e57db1b4562dac4a29db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5f43e543266b9446fd1c5858ffb239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
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4 . 从甲地到乙地,先是一段上坡路,然后是一段平路,小冲骑车从甲地出发,到达乙地后休息一段时间,然后原路返回甲地.假设小冲骑车在上坡、平路、下坡时分别保持匀速前进,已知小冲骑车上坡的速度比平路上的速度每小时少5km,下坡的速度比在平路上的速度每小时多5km,设小冲出发xh后,到达离乙地ykm的地方,图中的折线ABCDEF表示y与x之间的函数关系.
![](https://img.xkw.com/dksih/QBM/2022/8/13/3043610943193088/3043777848532992/STEM/ca4c5e1d02e54643be2e0690acfd0835.png?resizew=235)
(1)求小冲在平路上骑车的平均速度以及他在乙地的休息时间;
(2)分别求线段AB、EF所对应的函数关系式;
(3)从甲地到乙地经过丙地,如果小冲两次经过丙地的时间间隔为0.85h,求丙地与甲地之间的路程.
![](https://img.xkw.com/dksih/QBM/2022/8/13/3043610943193088/3043777848532992/STEM/ca4c5e1d02e54643be2e0690acfd0835.png?resizew=235)
(1)求小冲在平路上骑车的平均速度以及他在乙地的休息时间;
(2)分别求线段AB、EF所对应的函数关系式;
(3)从甲地到乙地经过丙地,如果小冲两次经过丙地的时间间隔为0.85h,求丙地与甲地之间的路程.
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5 . 已知椭圆
的中心在坐标原点
,焦点在
轴上,左、右焦点分别为
、
,离心率
,短轴长为2,.
(1)求椭圆
的标准方程;
(2)设过
且斜率不为零的直线
与椭圆
交于
、
两点,过
作直线
的垂线,垂足为
,证明:直线
恒过一定点,并求出该定点的坐标;
(3)过点
作另一直线
,与椭圆分别交于
、
两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ea9f5967c96e60f03f332fd792cd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e1ba8ef888dfe9a639dddd38d6d603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](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/17ae93479f71c86ffa37131326cfd993.png)
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2021-12-10更新
|
1117次组卷
|
3卷引用:2021年黑龙江省哈尔滨市第三中学校高二上学期期中数学试题
2021年黑龙江省哈尔滨市第三中学校高二上学期期中数学试题江西省赣州市赣县第三中学2021-2022学年高二12月月考数学(理)试题(已下线)易错点12 圆锥曲线-备战2022年高考数学考试易错题(新高考专用)
名校
解题方法
6 . 已知抛物线的顶点为原点,焦点F在x轴的正半轴,F到直线
的距离为
.点
为此抛物线上的一点,
.直线l与抛物线交于异于N的两点A,B,且
.
(1)求抛物线方程和N点坐标;
(2)求证:直线AB过定点,并求该定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0bac81568b8624599b4b9b39fbae2f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6c9ca0f54b6a84bb93d435933aae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715426331815c4e34ad97a8b66ab3ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97618ba661e223cae2b219835a93847.png)
(1)求抛物线方程和N点坐标;
(2)求证:直线AB过定点,并求该定点坐标.
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2021-12-08更新
|
6101次组卷
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7卷引用:黑龙江省哈尔滨市呼兰区第一中学校2021-2022学年高三上学期第二次校内检测数学(文)试题
黑龙江省哈尔滨市呼兰区第一中学校2021-2022学年高三上学期第二次校内检测数学(文)试题河北省深州市长江中学2021-2022学年高二上学期12月月考数学试题河南省开封市杞县高中2021-2022学年高二上学期第四次月考数学(理)试题江苏省无锡市天一中学2021-2022学年高二上学期期末数学试题(已下线)专题22 圆锥曲线中的定点、定值、定直线问题 微点1 圆锥曲线中的定点问题(已下线)专题11 解析几何2湖北省潜江市园林高级中学2022-2023学年高二上学期期中数学试题
7 . 已知圆
,圆
.
(1)证明圆A与圆B相交,并求圆A与圆B的公共弦所在直线的方程;
(2)已知点
,若直线PA,PC相交于点P,且它们的斜率之积为
,求动点P的轨迹方程并说明轨迹图形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f452837312ab84d303e5f7c65ed30201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6760e30d72ade9f912170a0a25d33bd.png)
(1)证明圆A与圆B相交,并求圆A与圆B的公共弦所在直线的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d36cf4115062073e8a0468bae7e8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
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2021-12-04更新
|
707次组卷
|
4卷引用:黑龙江省鸡西市密山市第一中学2021-2022学年高二上学期期中数学试题
名校
8 . 以平面直角坐标系的原点为极点,
轴正半轴为极轴,建立极坐标系,两种坐标系中取相同的长度单位,设点
的极坐标为
,直线
过点
且倾斜角为
,圆
的极坐标方程为
.
(1)写出点
的直角坐标,直线
的标准参数方程,并把圆
的方程化为直角坐标方程;
(2)设直线
与圆
交于
、
两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dfa01ada016e445e9d1f0af2da2013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87454bbb4935421bc1ba124d31f5600.png)
(1)写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/843363e1d63e1e4b8a6bde5825ef5a4f.png)
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9 . 已知函数
.
(1)判断函数
在其定义域上的单调性(不需要证明)﹔
(2)对任意的
,都有
,若存在
的两个取值
,使得
为常数),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bff5eeeb9414192fe13fe7fa5599864.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c995d957e9e95c66544e876318641d5c.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0044f2840ab023ee12a23f6d88dadf6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38a915d8585180f3731ece24e3cf995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1579867c6de8346ee8fb115b2fa0ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb561b71047c16ab4354be0e4653359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d52943e3995bdda062b3f7930265682.png)
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2021-11-07更新
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417次组卷
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4卷引用:黑龙江省大庆铁人中学2021-2022学年高一上学期期中数学试题
名校
解题方法
10 . 教育部《关于落实主体责任强化校园食品安全管理的指导意见》指出:非寄宿制中小学、幼儿园原则上不得在校内设置食品小卖部、超市,已经设置的,要逐步退出.为了了解学生对校内开设小卖部的意见,某校对65名住校生30天内在小卖部消费过的天数进行了统计,情况如下:
(1)用分层抽样的方法在消费天数不低于15天的住校生中选择6人进行意见调查,分别求其中消费天数在区间
,
,
内的人数;
(2)从(1)中选择的6人中任意抽取2人对取消校内小卖部给出具体意见,求这2人消费天数均在
内的概率.
天数 | |||||
人数 | 4 | 7 | 18 | 9 | 27 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fc432330eed6e6c51d7abc5e38dcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27582493e2169299738c4ebc1c8d171c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9ab835e5d5d0bb7bdde1cb9d81a5a2.png)
(2)从(1)中选择的6人中任意抽取2人对取消校内小卖部给出具体意见,求这2人消费天数均在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9ab835e5d5d0bb7bdde1cb9d81a5a2.png)
您最近一年使用:0次
2021-10-30更新
|
379次组卷
|
2卷引用:黑龙江省实验中学2021-2022学年高二上学期期中数学试题