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1 . 如图,过抛物线
的右焦点
的直线
交抛物线于点A,B,交其准线于点C,若
,且
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/ee3b03a4-2fc0-4177-b459-e60bfac65b24.png?resizew=144)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc8b65205560c499912ac833ef68119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c3f0f11d9bbe85bc4463ed8b8078a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58acf95344d6e5759cb2e05a6e61a151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/ee3b03a4-2fc0-4177-b459-e60bfac65b24.png?resizew=144)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 已知函数
.
(1)若
,求证:
在区间
是增函数;
(2)设
,若对任意的
,恒有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0145c6588620a7301f14698c8837a93e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52767cb407873a34008a70a6f5111266.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6e28dbfcdd6fb66b9ff759be044287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09408ffff3b1e7a0fafbc8fafd229b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9157ac76812effa31cff2d83bd300f75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3 . 函数
的图像大致为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4472216c5c08e8d29c2cbc9d5866100e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 在平面四边形
中,
,
,
,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb4952fb4df340736bd8b9a10373946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ceeb6ac7f248397e846f5b61fac6c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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5 . 已知各项均为正数的数列
的前
项和为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976350c923047d4ac547d42d66efd057.png)
,
.
(1)证明数列
为等差数列,并求
的通项公式;
(2)设
,数列
的前
项和记为
,证明:
.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976350c923047d4ac547d42d66efd057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed6b09d94b70d7d47602cfed41339c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429c1cc35267f0cffd1f0f036772759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a790c41cca405e0e31ea0a7114d31.png)
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6 . 已知函数
.
(1)解不等式
;
(2)设函数
的最小值为t,实数
满足
,且
.
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e42491e1a3b262360e42c0b1f39d13.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/335c6cb34ba1ae8efc3c9711d38b0c55.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1863f07aaa3d1060a60732b9d59e8c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a27cac3985e9613d24e42949558f0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e99853dddd205a4d75ace309731ab7.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b0f9616f5561636d3a46ec1f849308.png)
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7 . 已知数列
满足
,且
.记数列
的前
项和为
,若对一切的
,都有
恒成立,则实数
能取到的最大整数是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d379316dbb3a43e30f166865e0b2b9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411a62ce67f3136311d6c8cb7f19fb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 .
中,
,
,
为线段
上一点,且满足
.
(1)求
的值;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b6bef27de230acad352f25e954f4e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca82c4bb227bc23d70f258159934889.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c19c2cd5febf438abfc98c5cee065cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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9 . 已知椭圆
的左右焦点分别为
点.
为椭圆上的一动点,
面积的最大值为
.过点
的直线
被椭圆截得的线段为
,当
轴时,
.
(1)求椭圆
的方程;
(2)椭圆
上任取两点A,B,以
,
为邻边作平行四边形
.若
,则
是否为定值?若是,求出定值;如不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d07f601bec284ecba716638f4c57b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bafd46edac43544a564c59b1868e3a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ff410a277986fc6045c1cb36f89e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165a501b2e6a3acc46212e59a166c053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40708a3a8ef35e870584af345d0c03ac.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab5d83deeb175ee80d83f0d9c658950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe63c3d7205f2a7e3c9ab47904c668f6.png)
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3卷引用:重庆市合川实验中学2021届高三上学期期中数学(理)试题
重庆市合川实验中学2021届高三上学期期中数学(理)试题重庆市西南大学附属中学校2019-2020学年高三第四次月考数学(理)试题(已下线)大题专练训练30:圆锥曲线(探索性问题2)-2021届高三数学二轮复习
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10 . 在中国足球超级联赛某一季的收官阶段中,广州恒大淘宝、北京中赫国安、上海上港、山东鲁能泰山分别积分59分、58分、56分、50分,四家俱乐部都有机会夺冠.A,B,C三个球迷依据四支球队之前比赛中的表现,结合自己的判断,对本次联赛的冠军进行如下猜测:
猜测冠军是北京中赫国安或山东鲁能泰山;
猜测冠军一定不是上海上港和山东鲁能泰山;
猜测冠军是广州恒大淘宝或北京中赫国安.联赛结束后,发现A,B,C三人中只有一人的猜测是正确的,则冠军是()
![](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)
A.广州恒大淘宝 | B.北京中赫国安 | C.上海上港 | D.山东鲁能泰山 |
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