1 . 设命题
:方程
有两个不相等的实数根;命题
:
.
(1)若命题
为真命题,求实数
的取值范围;
(2)若命题
,
一真一假,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7a2b4d2e5087e251c9466672d09bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2be02ee5328f124ff1fe9a98a500b54.png)
(1)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
2 . 设p:实数x满足
,其中
;q:实数x满足
.
(1)若
,且p和q均为真,求实数x的取值范围;
(2)若q是p的充分条件,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258fe80c99905bd0c525aa703f2444e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d712e5dc451ae02ef4442ba59fb25a3a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)若q是p的充分条件,求实数a的取值范围.
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3 . 判断下列命题的真假:
(1)
是
的必要条件;
(2)
是
的充分条件;
(3)两个三角形的两组对应角分别相等是两个三角形相似的充要条件;
(4)
是
的充分而不必要条件.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/421a473589d5abdd504fdb110828611a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f7c54faca6eac8af5309942062058d.png)
(3)两个三角形的两组对应角分别相等是两个三角形相似的充要条件;
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78485f19aefc6110e03ece0207e391e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
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4 . 判断下列语句哪些是命题,是真命题还是假命题.
(1)
;
(2)等腰三角形两底角相等;
(3)若
,
是任意实数且
,则
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
(2)等腰三角形两底角相等;
(3)若
![](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/26f7c54faca6eac8af5309942062058d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
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5 . 判断下列命题的真假:
(1)
,
;
(2)
,
;
(3)
,
;
(4)
,
;
(5)设
,
,
是平面上不在同一直线上的三点,在平面上存在某个点
使得
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa139aad70ad1ac124affc3fe5d75c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb853af35191946081f0b78f5dfca4c2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871454d1a0c9e545c7a9cad1d8482ee9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/687e3cb51a6b0f7eee667097d49c5dec.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65256b8bdeba77547b692c2a16563bd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48796cc830526828ccedeaab0733da.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf3c7c2c4607a2a2c237dc995919e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48796cc830526828ccedeaab0733da.png)
(5)设
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30fc65a72853bd8ac1ad0828270d3baf.png)
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6 . 判断命题“如果直线l在x轴,y轴上的截距分别为a,b且
,则l的斜率是
”的真假.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
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7 . 把下列命题改写成“若p,则q”的形式,并判断命题的真假.
(1)偶数不能被2整除;
(2)当
时,
;
(3)两个相似三角形是全等三角形.
(1)偶数不能被2整除;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a5a5db1e8afe4818e92bff53ef908d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48adb8a59b5c02fad5eada1b35171cf3.png)
(3)两个相似三角形是全等三角形.
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解题方法
8 . 已知
,设命题
在
时恒成立;命题
关于x的不等式
的解集为
.若命题p与q恰有一个为真命题,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afb5ef7c5ce7b50ba3c9d850e4e5996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538193a4717d564c01145e82314c2d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f848b5674856d770d83ab775f31a3ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
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9 . 设命题
:方程
有两个不相等的正根;命题
:方程
无实根.若
与
中有且只有一个是真命题,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4ea5c1de4b41af90aa3c1d51144fa57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436d16e39334520bef4d3cffffc26cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
10 . 把下列命题改写成“若
则
”的形式,并判断它们的真假.
(1)能被6整除的整数一定能被3整除;
(2)二次函数的图像是一条抛物线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)能被6整除的整数一定能被3整除;
(2)二次函数的图像是一条抛物线.
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