1 . 教育局为了了解本区高中生参加户外运动的情况,从本区随机抽取了600名高中学生进行在线调查,收集了他们参加户外运动的时间(单位:小时)分配情况等数据,并将样本数据分成[0,2],(2,4],(4,6],(6,8],(8,10],(10,12],(12,14],(14,16],(16,18]九组,绘制成如图所示的频率分布直方图.
(2)以调查结果的频率估计概率,从该区所有高中学生中随机抽取10名学生,用“
”表示这10名学生中恰有k名学生户外运动时间在(10,12](单位:小时)内的概率,当
最大时求k的值.
(2)以调查结果的频率估计概率,从该区所有高中学生中随机抽取10名学生,用“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331b5fb443d7420238d50da3ca9f084d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331b5fb443d7420238d50da3ca9f084d.png)
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2 . 在
中,角
,
,
所对的边依次为
,
,
,已知
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/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/b4d5f963c3485870c100b3f09c9346dc.png)
A.![]() |
B.![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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解题方法
3 . 在
中,
,点
满足
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4486890c4ba79dc50593b864800a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12dcfb8f3fc0ac45d50782c3f248672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aaee7371c1e926fe02eddfde7ee33be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知可导函数
的定义域为
,其导函数
满足
,则不等式
的解集为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9414348d57c7fc77dcfa8f0744cb0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132e592f60387d2a5b275c147a8b93e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ed4df20edf6e1fc0b671af6614244.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 在
中,
分别为
的中点,
交
于点
.若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a644ab854c2bc4676a79bff6c91646f8.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af2f502e92e09d86ecbbf93777781e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1371fe98a65d8ebd840c8d98346b6d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a644ab854c2bc4676a79bff6c91646f8.png)
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6 . 已知数列
的前n项和为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
(1)证明:
是等比数列,并求出
的通项公式;
(2)已知
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0e184b6489ceb9fa3e3068bf91a855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d13e4dc9e1494ace25f8f1ca08e40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
7 . 已知
,
,且
,
为函数
的极小值点,则下列不等式可以成立的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8440725e1df5ca0990b572dd84127914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343dc2efff2e4a23640d96272d51c550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ef1121c52ff3041f061b4c85b48953.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
8 . 设已知函数
,
,在同一直角坐标系中,直线
分别与函数
和
的图象相交于A点和B点,则A点与B点的坐标距离的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d1c740261329c54a07d72174188d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d55b0b17a54c0c1a1ddbdc2fc7c944c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ff39dd1dfc9caf911ad0d11ba21d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
A.2 | B.![]() | C.3 | D.![]() |
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解题方法
9 . 记
的内角
的对边分别为
,若
,且
.
(1)求
及
;
(2)若点
在边
上,且
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff6de7e61d3d317e63da726f2940b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a329c64d1da0fa30cf0aa5d3dfbd3f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若点
![](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/a7b31f831da58e0cf708770d2c29fcef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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10 . 把函数
的图象向左平移
个单位长度,再把横坐标变为原来的
倍(纵坐标不变),得到函数
的图象,下列关于函数
的说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ec42b7c3781e77b869e1ea2445d958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
A.函数![]() ![]() |
B.函数![]() ![]() |
C.函数![]() |
D.函数![]() ![]() ![]() |
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