真题
解题方法
1 . 已知函数
.
(1)若
,则
的定义域是___________ ;
(2)若
在区间
上是减函数,则实数a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43b312904eaaed95921a2121468b36a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf87d9d48c3de0a5e9f1a70e51a0bef.png)
您最近一年使用:0次
真题
2 . 设
,点
是函数
与
的图象的一个公共点,两函数的图象在点P处有相同的切线.
(1)用t表示a,b,c;
(2)若函数
在
上单调递减,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b119d0cf10a948cdc53c1066af0b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfab448603e05838ec794f8fdb64d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9e36cc9698be9553fbc21d12563941.png)
(1)用t表示a,b,c;
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df49341b57eb107f416a014903ce25a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881fe2df23c5a0fe1d1fecbe9ffa55fb.png)
您最近一年使用:0次
2022-11-09更新
|
405次组卷
|
2卷引用:2005年普通高等学校招生考试数学(文)试题(湖南卷)
真题
解题方法
3 . 已知
是曲线
上的点,
,
是数列
的前
项和,且满足
,
,
.
(1)证明:数列
是常数数列;
(2)确定
的取值集合
,使
时,数列
是单调递增数列;
(3)证明:当
时,直线
的斜率随
单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fcfca2a223425da57d1f24c98640dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e71b147dbef10ba4a9443348167b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ec0b97655e6bd7004df04457c493ac.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951ae3104708a981076f51389885a499.png)
(2)确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582ad43edf388c096e7704d92340bf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582ad43edf388c096e7704d92340bf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91491440dcb994a89107c0e92134ec78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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真题
解题方法
4 . 如图,某地为了开发旅游资源,欲修建一条连接风景点P和居民区O的公路,点P所在的山坡面与山脚所在水平面
所成的二面角为
,且
,点P到平面
的距离
.沿山脚原有一段笔直的公路AB可供利用,从点O到山脚修路的造价为a万元
,原有公路改建费用为
万元
,当山坡上公路长度为
时,其造价为
万元,已知
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/e6de8ea8-1f69-4f8f-a111-bf2bb2c3adc3.png?resizew=345)
(1)在AB上求一点D,使沿折线PDAO修建公路的总造价最小;
(2)对于(1)中得到的点D,在DA上求一点E,使沿折线PDEO修建公路的总造价最小;
(3)在AB上是否存在两个不同的点
,使沿折线
修建公路的总造价小于(2)中得到的最小总造价,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f5d1218c4f7d9263da333a4edf06af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0503736d21c5e5432d933990cf511c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e689190fd5a655655c264d4b134ba00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98024ce2e23a5e81b2bcdd7c96ccef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576833b76e9cad3b523f87132308df99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98024ce2e23a5e81b2bcdd7c96ccef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6db945cfc09c3a78843068acc18fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48dc9c56c4d2ed0d3529460ef2cf8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ac747fa7e033b09ab20370fd27d5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e4c39ba72d14560e283ad7f75353a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5881bc21725be10ac0151c445393b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d645ac2b7ccb0f0d290c05dc5d328d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/e6de8ea8-1f69-4f8f-a111-bf2bb2c3adc3.png?resizew=345)
(1)在AB上求一点D,使沿折线PDAO修建公路的总造价最小;
(2)对于(1)中得到的点D,在DA上求一点E,使沿折线PDEO修建公路的总造价最小;
(3)在AB上是否存在两个不同的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c18dea2399109b0d0e1c23e31f227bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6003623c3413d3e2a3c1e41049fa31b2.png)
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解题方法
5 . 已知
,抛物线
,且
的公共弦
过椭圆
的右焦点.
(1)当
轴时,求m、p的值,并判断抛物线
的焦点是否在直线
上;
(2)是否存在m、p的值,使抛物线
的焦点恰在直线
上?若存在,求出符合条件的m、p的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6533a2123bcaa8c7dcd36d5e3f37700f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e2dbe7c46898216e14556c84ff13ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880248fa1259b2600a87f09a61287d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24624dffd30b66a5e4de57362b32b2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)是否存在m、p的值,使抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
真题
6 . 对1个单位质量的含污物体进行清洗,清洗前其清洁度(含污物体的清洁度定义为:
)为0.8,要求洗完后的清洁度是0.99.有两种方案可供选择,方案甲:一次清洗;方案乙:两次清洗.该物体初次清洗后受残留水等因素影响,其质量变
.设用
单位质量的水初次清洗后的清洁度是
,用
单位质量的水第二次清洗后的清洁度是
,其中
是该物体初次清洗后的清洁度.
(1)分别求出方案甲以及
时方案乙的用水量,并比较哪一种方案用水量较少;
(2)若采用方案乙,当
为某定值时,如何安排初次与第二次清洗的用水量,使总用水量最少?并讨论
取不同数值时对最少总用水量多少的影响.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24cbfb5088bc5fbc54c73c8394d6772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a986a2262323f03f172cd658c69be57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b19be06bc3ebcff404914d98c78f70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837baf1725801da9c015bb4a574c8bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94fe68b6bdbaeebe4069502daaa905af.png)
(1)分别求出方案甲以及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d8fc3c7232039b4ade32cfefb76ea4.png)
(2)若采用方案乙,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-11-09更新
|
338次组卷
|
2卷引用:2006年普通高等学校招生考试数学(理)试题(湖南卷)
真题
解题方法
7 . 已知函数
,数列
满足:
,
.证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52142482df6bbd431d300f011e3ccb12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4738119275a2f952503cd073b9bfec47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bce6187f3f11e0ceead8a645f5f9d32.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89948adf1e13b6abee5aa37fb5eaefb4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16496a925991d2be8befa69c6c32c1e5.png)
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真题
8 . 如图1,已知
是上.下底边长分别为2和6,高为
的等腰梯形,将它沿对称轴
折成直二面角,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/3d9c392e-b93d-4be9-9f17-297f8d70b851.png?resizew=414)
(1)证明:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/3d9c392e-b93d-4be9-9f17-297f8d70b851.png?resizew=414)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/400d97da3779f117510058b0526df75a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8faef5f821d00d9c69e65e0988fe1f.png)
您最近一年使用:0次
2022-11-09更新
|
480次组卷
|
2卷引用:2005年普通高等学校招生考试数学(文)试题(湖南卷)
真题
解题方法
9 . 如图,直线
与
相交于点P.直线
与x轴交于点
,过点
作x轴的垂线交直线
于点
,过点
作y轴的垂线交直线
于点
,过点
作x轴的垂线交直线
于点
,…,这样一直作下去,可得到一系列点
.点
的横坐标构成数列
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/81139a1a-9d54-45a6-a83d-58c99c0c95ba.png?resizew=243)
(1)证明:
;
(2)求数列
的通项公式;
(3)比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dabe36db0d20694a8018e4b5f6c1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/214891009bbb880eb8a2eb62a381dd29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2370d1a77fb948aceb4f262acf310f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13b6e735df4341ac62ed109ef48c9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/81139a1a-9d54-45a6-a83d-58c99c0c95ba.png?resizew=243)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d9e87ee26e0cf54e6cbbfdd5e3f621.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(3)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bdea933692674c9414a616f6bd7250a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea94e1f1ecec4a72ab2891d7e00eea31.png)
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真题
解题方法
10 . 如图,过抛物线
的对称轴上任一点
作直线与抛物线交于
,
两点,点
是点
关于原点的对称点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/9f139a8e-ff9b-4ce6-929d-75c5af1e7cef.png?resizew=184)
(1)设点
分有向线段
所成的比为
,证明:
;
(2)设直线
的方程是
,过
,
两点的圆
与抛物线在点
处有共同的切线,求圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c2eb6221ac5ff075bd2430b8d6c03f.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/9f139a8e-ff9b-4ce6-929d-75c5af1e7cef.png?resizew=184)
(1)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d810ea976b725e2e7bf864695be672.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76576264f7853ee62e989f1889425a20.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2022-11-09更新
|
550次组卷
|
3卷引用:2004 年普通高等学校招生考试数学(理)试题(湖南卷)