全一卷
1.已知
,
,
满足
,
,则
( ).
![](http://static.xuejinqu.com/qimg/f7e/f7ebe3f1509f13bb46fb292fc2a3f596.png)
![](http://static.xuejinqu.com/qimg/86f/86f5f26c3dbfc59dccdb7a4238dd40a6.png)
![](http://static.xuejinqu.com/qimg/53b/53bd245fb966a4fa3542021690fc67d7.png)
![](http://static.xuejinqu.com/qimg/f04/f0468a8b3ded2e11834b63f24e4458e3.png)
![](http://static.xuejinqu.com/qimg/633/633bc1ed01639f87f8e9e99687b7d838.png)
![](http://static.xuejinqu.com/qimg/362/362ff428d4c939a8d1545cc627cb44a5.png)
A.0 | B.3 | C.6 | D.9 |
2.若抛物线
与
轴只有一个公共点,且过点
,
,则
( )
![](http://static.xuejinqu.com/qimg/3df/3df44e24416177fef2ccd5639cfe03a2.png)
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/c1c/c1c1d699922aa5e835c6897e678c9dcf.png)
![](http://static.xuejinqu.com/qimg/a48/a4854b4eef539205f7b15e4c7183c437.png)
![](http://static.xuejinqu.com/qimg/e65/e65a4d42f4173a1fd9e36d06559a8810.png)
A.![]() | B.![]() | C.![]() | D.![]() |
3.矩形
中,
,
,
、
分别为矩形外的两点,
,
,则
( )
![](//static.xuejinqu.com/qimg/e84/e8438553d101878f0b49fdc9130912e6.png)
![](http://static.xuejinqu.com/qimg/56a/56a783b8c5d7d71cfbda642b979070b0.png)
![](http://static.xuejinqu.com/qimg/72b/72b58db8781558b24ba5df9c82a41fd7.png)
![](http://static.xuejinqu.com/qimg/a01/a01760e7f5b71304987d849882f4baa2.png)
![](http://static.xuejinqu.com/qimg/00e/00ec78cc7c5ca95d140f4a5d92fd938e.png)
![](http://static.xuejinqu.com/qimg/19a/19a3526b4c50c7a971af5e0128614d80.png)
![](http://static.xuejinqu.com/qimg/3ec/3ec8e4526af4f646dbe4e2921d53fbed.png)
![](http://static.xuejinqu.com/qimg/dbb/dbb8759f51386101e8154a47419ffc6d.png)
![](http://static.xuejinqu.com/qimg/e1d/e1de7907582a3e53aa1f9887a23dd601.png)
![](http://static.xuejinqu.com/qimg/e84/e8438553d101878f0b49fdc9130912e6.png)
A.![]() | B.15 | C.![]() | D.![]() |
4.已知
为坐标原点,位于第一象限的点
在反比例函数
的图象上,位于第二象限的点
在反比例函数
的图象上,且
,则
的值为( )
![](http://static.xuejinqu.com/qimg/878/8782c97902a9f447b53fed3ac5e0bc64.png)
![](http://static.xuejinqu.com/qimg/cb6/cb6933706dda0f995597792b3203bbbd.png)
![](http://static.xuejinqu.com/qimg/c39/c39c9535e0e1b5299aec90487def898d.png)
![](http://static.xuejinqu.com/qimg/71b/71b289743dc47a31da8442646887d30f.png)
![](http://static.xuejinqu.com/qimg/6df/6df2168c8864f95cdec03523b4b6f28d.png)
![](http://static.xuejinqu.com/qimg/0a5/0a52a00c63c3e354f81b2b62e57d2a38.png)
![](http://static.xuejinqu.com/qimg/670/670c4b405715ec39e1a12a181d14b073.png)
A.![]() | B.![]() | C.1 | D.2 |
5.已知实数
,
满足关系式
,则
的最小值为( )
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/ae3/ae3d592441dc4632c35d8b7efe75dba7.png)
![](http://static.xuejinqu.com/qimg/94f/94fdc4b3b3a330759d604c20e6b4ac4e.png)
![](http://static.xuejinqu.com/qimg/7ae/7ae1279867bc8cfec01af6e3215398f6.png)
A.![]() | B.![]() | C.1 | D.![]() |
6.设
是小于100的正整数且使
是15的倍数,则符合条件的所有正整数
的和是( )
![](http://static.xuejinqu.com/qimg/4f2/4f24e0a828b5192b36176d7c6a5f5aa9.png)
![](http://static.xuejinqu.com/qimg/bc9/bc9b4ac2ee5a6a28cc390fcd6bb1664f.png)
![](http://static.xuejinqu.com/qimg/4f2/4f24e0a828b5192b36176d7c6a5f5aa9.png)
A.285 | B.350 | C.540 | D.635 |
7.设实数
,
,
满足:
,
,则
( )
![](http://static.xuejinqu.com/qimg/f7e/f7ebe3f1509f13bb46fb292fc2a3f596.png)
![](http://static.xuejinqu.com/qimg/86f/86f5f26c3dbfc59dccdb7a4238dd40a6.png)
![](http://static.xuejinqu.com/qimg/53b/53bd245fb966a4fa3542021690fc67d7.png)
![](http://static.xuejinqu.com/qimg/f04/f0468a8b3ded2e11834b63f24e4458e3.png)
![](http://static.xuejinqu.com/qimg/633/633bc1ed01639f87f8e9e99687b7d838.png)
![](http://static.xuejinqu.com/qimg/362/362ff428d4c939a8d1545cc627cb44a5.png)
A.12 | B.9 | C.6 | D.3 |
8.已知实数
满足关系式
,则
的最大值为( )
![](http://static.xuejinqu.com/qimg/eb7/eb7ed7ca348a61f2c474ae108e0a4dc6.png)
![](http://static.xuejinqu.com/qimg/355/3556df12ca31ec06934af4f433e4c0a8.png)
![](http://static.xuejinqu.com/qimg/410/410e0d1dcf7630947f09e4742823a21a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
9.设
是小于100的正整数且使
是6的倍数,则符合条件的所有正整数
的和是( )
![](http://static.xuejinqu.com/qimg/4f2/4f24e0a828b5192b36176d7c6a5f5aa9.png)
![](http://static.xuejinqu.com/qimg/c6b/c6b5492f264793160529e2bc94b4842f.png)
![](http://static.xuejinqu.com/qimg/4f2/4f24e0a828b5192b36176d7c6a5f5aa9.png)
A.784 | B.850 | C.1536 | D.1634 |
10.设
,
是一元二次方程
的两根,则
的值为__________ .
![](http://static.xuejinqu.com/qimg/f7e/f7ebe3f1509f13bb46fb292fc2a3f596.png)
![](http://static.xuejinqu.com/qimg/86f/86f5f26c3dbfc59dccdb7a4238dd40a6.png)
![](http://static.xuejinqu.com/qimg/80b/80bc08827aaa2c1059594fab22e9bd5c.png)
![](http://static.xuejinqu.com/qimg/465/465edadd2e6653a6fc83559f53053dcf.png)
11.从三边长均为整数且周长为24的三角形中任取一个,它是直角三角形的概率为__________ .
12.已知锐角
的外心为
,
交
于
,
、
分别为
、
的外心,若
,
,则![](//static.xuejinqu.com/qimg/25a/25a143f3aea7887631fbbf3ffea72c3b.png)
__________ .
![](//static.xuejinqu.com/qimg/5d5/5d5f10dbecc4050429db969077a5767e.png)
![](http://static.xuejinqu.com/qimg/41e/41ebbb18b14a033a4840836554e3a205.png)
![](http://static.xuejinqu.com/qimg/878/8782c97902a9f447b53fed3ac5e0bc64.png)
![](http://static.xuejinqu.com/qimg/e28/e283e1f33808bcc6355ed3998ddb4177.png)
![](http://static.xuejinqu.com/qimg/9ad/9ad78c83588572af8248fbdc0552a2f2.png)
![](http://static.xuejinqu.com/qimg/83a/83a9bfa5a1c38fcfe9e7d88d7b39cdd7.png)
![](http://static.xuejinqu.com/qimg/00e/00ec78cc7c5ca95d140f4a5d92fd938e.png)
![](http://static.xuejinqu.com/qimg/19a/19a3526b4c50c7a971af5e0128614d80.png)
![](http://static.xuejinqu.com/qimg/ea9/ea95cc3a22babc87ea475ce82a9b7921.png)
![](http://static.xuejinqu.com/qimg/188/188aee85107710c67be2ba5bbf307c2b.png)
![](http://static.xuejinqu.com/qimg/718/71834f05b7ae7211eff279bce64f6846.png)
![](http://static.xuejinqu.com/qimg/a0b/a0bc5abde6f1f19241bcd30c94b1229c.png)
![](http://static.xuejinqu.com/qimg/25a/25a143f3aea7887631fbbf3ffea72c3b.png)
![](http://static.xuejinqu.com/qimg/5d5/5d5f10dbecc4050429db969077a5767e.png)
13.将数字1,2,3,…,34,35,36填在
的方格中,每个方格填一个数字,要求每行数字从左到右是从小到大的顺序,则第三列所填6个数字的和的最小值为______ .
![](http://static.xuejinqu.com/qimg/b41/b416d596a444c67f49d8aa514c92f677.png)
14.三边长均为整数且周长为24的三角形的个数为__________ .
15.
、
两点在以
为直径的半圆周上,
平分
,
,
,则
的长为__________ .
![](//static.xuejinqu.com/qimg/21c/21ca488087c4608f8ba10fef0b73b05e.png)
![](http://static.xuejinqu.com/qimg/7f4/7f4ba58e204b9831a2d04610deeb3622.png)
![](http://static.xuejinqu.com/qimg/83a/83a9bfa5a1c38fcfe9e7d88d7b39cdd7.png)
![](http://static.xuejinqu.com/qimg/ef4/ef48d5225c41bc83e1fe326feacfa973.png)
![](http://static.xuejinqu.com/qimg/eb7/eb78d09521489c0947493bab21f20031.png)
![](http://static.xuejinqu.com/qimg/f8f/f8f9c98828301da502673dc42494f62d.png)
![](http://static.xuejinqu.com/qimg/940/940a56b6879be540ee342970864261bc.png)
![](http://static.xuejinqu.com/qimg/6e6/6e61a81c076b864fa3a6aea3a83ae527.png)
![](http://static.xuejinqu.com/qimg/343/34384d696a238aeb71b4cf989eca877d.png)
![](http://static.xuejinqu.com/qimg/21c/21ca488087c4608f8ba10fef0b73b05e.png)
16.在圆周上按序摆放和为15的五个互不相等的正整数
,
,
,
,
,使得
最小,则这个最小值为___________ .
![](http://static.xuejinqu.com/qimg/f7e/f7ebe3f1509f13bb46fb292fc2a3f596.png)
![](http://static.xuejinqu.com/qimg/86f/86f5f26c3dbfc59dccdb7a4238dd40a6.png)
![](http://static.xuejinqu.com/qimg/53b/53bd245fb966a4fa3542021690fc67d7.png)
![](http://static.xuejinqu.com/qimg/d87/d8743ca177991c91e5829c36b8dd31be.png)
![](http://static.xuejinqu.com/qimg/9b5/9b5f8a856cfe275556b837ebfb605dd0.png)
![](http://static.xuejinqu.com/qimg/ffc/ffc2e5c1ad41bf724bc33d3c2712cbe3.png)
17.关于
的方程
有且仅有一个实数根,求实数
的取值范围.
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/e6c/e6c1f32dfc1f1783f39dca1bdfa1ff26.png)
![](http://static.xuejinqu.com/qimg/164/16450be3be8aeed50b467ba6fd4dd895.png)
18.如图,圆内接四边形
的对角线
、
交于点
,且
,
.过点
作
,交
的延长线于点
,
的平分线分别交
、
于点
、
.
![](//static.xuejinqu.com/qimg/9e4/9e490715199e758bea776d9d1a6f637c.png)
(1)证明:
;
(2)如果
,证明:
.
![](http://static.xuejinqu.com/qimg/56a/56a783b8c5d7d71cfbda642b979070b0.png)
![](http://static.xuejinqu.com/qimg/343/34384d696a238aeb71b4cf989eca877d.png)
![](http://static.xuejinqu.com/qimg/bc6/bc6fc6d12fff9ded29cd899330f480da.png)
![](http://static.xuejinqu.com/qimg/00e/00ec78cc7c5ca95d140f4a5d92fd938e.png)
![](http://static.xuejinqu.com/qimg/33d/33d59297b31882582ed7f3ad9bc84b09.png)
![](http://static.xuejinqu.com/qimg/00b/00b6e559be03b13af2f3cefc5f5123f1.png)
![](http://static.xuejinqu.com/qimg/83a/83a9bfa5a1c38fcfe9e7d88d7b39cdd7.png)
![](http://static.xuejinqu.com/qimg/ba1/ba1d703e8caa26d237cdd3823c7b0766.png)
![](http://static.xuejinqu.com/qimg/cf2/cf2ecbb73805e7dec44cdab4c307f511.png)
![](http://static.xuejinqu.com/qimg/19a/19a3526b4c50c7a971af5e0128614d80.png)
![](http://static.xuejinqu.com/qimg/076/076b035b6d66cbb573c88e65d023a824.png)
![](http://static.xuejinqu.com/qimg/eb7/eb78d09521489c0947493bab21f20031.png)
![](http://static.xuejinqu.com/qimg/bc6/bc6fc6d12fff9ded29cd899330f480da.png)
![](http://static.xuejinqu.com/qimg/ca5/ca51e5f4f5942968ee7729490691a944.png)
![](http://static.xuejinqu.com/qimg/ba8/ba813027cee927a859bbe4ea78c8d588.png)
![](http://static.xuejinqu.com/qimg/9e4/9e490715199e758bea776d9d1a6f637c.png)
(1)证明:
![](http://static.xuejinqu.com/qimg/fbc/fbcc8fe1fa64efd4a5427d67170d0ed7.png)
(2)如果
![](http://static.xuejinqu.com/qimg/caf/caffa1f58a5fae83b23775de2124465d.png)
![](http://static.xuejinqu.com/qimg/409/40989c248ee57e1a4c2fbb3ccac019b8.png)
19.设正整数
,
满足:关于
的方程
至少有一个正整数解,证明:
.
![](http://static.xuejinqu.com/qimg/164/16450be3be8aeed50b467ba6fd4dd895.png)
![](http://static.xuejinqu.com/qimg/4f2/4f24e0a828b5192b36176d7c6a5f5aa9.png)
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/651/651edbac163a1a4746c465b82e9abf92.png)
![](http://static.xuejinqu.com/qimg/32b/32b35cb69c41f55ce27b03ce0359eb2f.png)
20.若正数
,
满足
,求
的最小值.
![](http://static.xuejinqu.com/qimg/f7e/f7ebe3f1509f13bb46fb292fc2a3f596.png)
![](http://static.xuejinqu.com/qimg/86f/86f5f26c3dbfc59dccdb7a4238dd40a6.png)
![](http://static.xuejinqu.com/qimg/921/921f53a88c1493c03b282f000747c3ab.png)
![](http://static.xuejinqu.com/qimg/47c/47c6dce78fb94acbfcd8a36881632a54.png)
21.如图,圆内接四边形
的对角线
、
交于点
,且
,
.过点
作
,交
的延长线于点
,
的平分线分别交
、
于点
、
.
![](//static.xuejinqu.com/qimg/dba/dba131cac1bceaced8b067b3c00366bd.png)
(1)证明:
;
(2)如果
,证明:
.
![](http://static.xuejinqu.com/qimg/56a/56a783b8c5d7d71cfbda642b979070b0.png)
![](http://static.xuejinqu.com/qimg/343/34384d696a238aeb71b4cf989eca877d.png)
![](http://static.xuejinqu.com/qimg/bc6/bc6fc6d12fff9ded29cd899330f480da.png)
![](http://static.xuejinqu.com/qimg/00e/00ec78cc7c5ca95d140f4a5d92fd938e.png)
![](http://static.xuejinqu.com/qimg/33d/33d59297b31882582ed7f3ad9bc84b09.png)
![](http://static.xuejinqu.com/qimg/c06/c065327aebf44e486ff912d375dad96e.png)
![](http://static.xuejinqu.com/qimg/83a/83a9bfa5a1c38fcfe9e7d88d7b39cdd7.png)
![](http://static.xuejinqu.com/qimg/ba1/ba1d703e8caa26d237cdd3823c7b0766.png)
![](http://static.xuejinqu.com/qimg/cf2/cf2ecbb73805e7dec44cdab4c307f511.png)
![](http://static.xuejinqu.com/qimg/19a/19a3526b4c50c7a971af5e0128614d80.png)
![](http://static.xuejinqu.com/qimg/076/076b035b6d66cbb573c88e65d023a824.png)
![](http://static.xuejinqu.com/qimg/eb7/eb78d09521489c0947493bab21f20031.png)
![](http://static.xuejinqu.com/qimg/bc6/bc6fc6d12fff9ded29cd899330f480da.png)
![](http://static.xuejinqu.com/qimg/ca5/ca51e5f4f5942968ee7729490691a944.png)
![](http://static.xuejinqu.com/qimg/ba8/ba813027cee927a859bbe4ea78c8d588.png)
![](http://static.xuejinqu.com/qimg/dba/dba131cac1bceaced8b067b3c00366bd.png)
(1)证明:
![](http://static.xuejinqu.com/qimg/fbc/fbcc8fe1fa64efd4a5427d67170d0ed7.png)
(2)如果
![](http://static.xuejinqu.com/qimg/409/40989c248ee57e1a4c2fbb3ccac019b8.png)
![](http://static.xuejinqu.com/qimg/6a8/6a850c7850c3b05bc00d332de07bc2d8.png)
22.若关于
的方程
至少有一个正整数根,求满足条件的正整数
的值.
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/384/3844e4b738e0908269b027049efdb706.png)
![](http://static.xuejinqu.com/qimg/93c/93c0a0677a1a991b4911061811aa1f77.png)