1 . 如图,在正方体
中,
分别是棱
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fb21db4957fd92575d2675fb9089f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bbb48ff80e7a2e8788d5df078d5eb3.png)
A.![]() ![]() |
B.直线![]() |
C.过![]() ![]() |
D.过![]() ![]() |
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2 . 已知函数
,
(1)讨论
的单调性;
(2)若
存在两个零点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求a的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2ee3664a4cd7fd377b23485fd14c83.png)
(1)讨论
![](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/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求a的取值范围;
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9d26d79e6a09476dc5a0d372c24867.png)
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3 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45f1d8728779d4e4b0534a5c1721602.png)
A.函数![]() ![]() ![]() |
B.函数![]() |
C.函数![]() ![]() |
D.函数![]() |
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4 . 甲、乙、丙三人相互做传球训练,第1次由甲将球传出,每次传球时,传球者都等可能地将球传给另外两个人中的任何一人,则第3次传球后球在乙手中的概率为________ ,第n次传球后球在乙手中的概率为________ .
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5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d8fb0f2f65778f8f3e8f9509e77740.png)
(1)讨论
的单调性;
(2)当
时,若
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d8fb0f2f65778f8f3e8f9509e77740.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de35b2de0ac0a538b91b43bf6cbf3452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 对于函数
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728f2cc68f8ca8ef2faa681785798259.png)
A.函数![]() ![]() |
B.![]() |
C.若方程![]() ![]() |
D.对任意正实数![]() ![]() ![]() ![]() |
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7 . 两条动直线
和
分别与抛物线
相交于不同于原点的A,B两点,当
的垂心恰是C的焦点时,
.
(1)求p;
(2)若
,弦
中点为P,点
关于直线
的对称点N在抛物线C上,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766bc42b7ead98238a339bb4dc42bb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87f8af9ce5d927e6f422de42ead6ffb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c965530523e606200248f2dd720eb5c.png)
(1)求p;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771a2abef658aab00d81a85ac26d9128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8547f2b4e89b0ae1445bda02d46f0668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
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8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
求曲线
在点
处的切线方程.
(2)若
证明:
在
上单调递增.
(3)当
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20439836def79ea69d967d95e81320a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87676cc3ca413d9ba64fab2cd45c909c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec994bb92d9945a4369f1215d859ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . 已知函数
,
,
为
的零点,且
恒成立,
在区间
上有最小值无最大值,则
的取值可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a1b51fc74390c262bc0bcaeb20369c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a9f8b43d3ad32c17ccb97202586dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd977e4aaa4634f65c4733e8f6814e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b2b096238bd6eac8cd1ab2c4348fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.7 | B.3 | C.5 | D.11 |
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解题方法
10 . 已知椭圆
的左、右焦点分别为
,
,点A,B在C上,且满足
,
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888465c45bb120ff2aa979006c87eb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79e4292aade9d5ed1d7b40e7e766740.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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