1 . “杨辉三角”是二项式系数在三角形中的一种几何排列.从第1行开始,第n行从左到右的数字之和记为
,如
,
,…,
的前n项和记为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7df0430db8db9fc354ffdd038fb432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c996a43ff8843aec0be0a9d0ac0e9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.在“杨辉三角”第10行中,从左到右第8个数字是120 |
B.![]() |
C.在“杨辉三角”中,从第2行开始到第n行,每一行从左到右的第3个数字之和为![]() |
D.![]() ![]() |
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解题方法
2 . 下列说法正确的是( )
A.已知复数![]() ![]() ![]() ![]() ![]() |
B.已知![]() ![]() ![]() |
C.有两个面互相平行,其余各面都是平行四边形的多面体是棱柱 |
D.![]() |
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解题方法
3 . 已知
的内角
,
,
的对边分别为
,
,
,且
.
(1)求
;
(2)若
的面积为
.
①已知
为
的中点,求
的最小值;
②求内角
的平分线
的最大值.
![](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/3df022d820aeb54fdd2a9746a36a243f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c181f86de3c96a7ef7a1a04c3a438f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de0e448610eac96bdd5f864f873e575d.png)
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
②求内角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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4 . 甲、乙、丙、丁四人相互做传球训练,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三个人中的任何一个人.则4次传球的不同方法总数为_________ (用数字作答);4次传球后球在甲手中的概率为_________ .
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5 . 已知
中,角
所对的边分别为
的面积记为
,若
,则( )
![](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/718b5b48053888ab3b234b8cb56a0fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d6dae531265e6d528cbf1346e41aca.png)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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解题方法
6 . 在
中,角
的对边分别为
,且
.
(1)求角
的大小;
(2)若边
,边
的中点为
,求中线
长的最大值.
![](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/d3fe37837e273544aa6b4be3ec860de3.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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解题方法
7 . 已知定圆
,动圆P过点
,且和圆
相切.
(1)求动圆圆心P的轨迹E的方程;
(2)设P是第一象限内轨迹E上的一点,
的延长线分别交轨迹E于点
.若
分别为
,
的内切圆的半径,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdc28de4b46c7a176ba6858a856a918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(1)求动圆圆心P的轨迹E的方程;
(2)设P是第一象限内轨迹E上的一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357e0872d9e98d662a780e7686de86ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8543261a8e351eb95cdfebb001a3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7733784336d1592cfe38e6a629140ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01d20fc53563351369c9bcb1360c410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd3d19b0c8b544d52b897ca30990b4.png)
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8 . 已知向量
,函数
.
(1)当
时,求
的单调递增区间;
(2)将
的图象向左平移
个单位长度后,所得图象对应的函数为
,若关于
的方程
在
上恰有两个不相等的实根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2500c8a420649ae5b6f370766e2f9d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737fead0e09a10e7f24977a70644d1a6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d75408bc3e0a180edd4960d1a3e2330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5c07fdcc3b6ce18e72bc873c624f1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
9 . 在
中,角
的对边分别为
.已知
,且
.
(1)求
;
(2)若
为边
的中点,求
的长.
![](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/c4361dd161a1a76fc21d64405686f7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb432a741c08243d6c2aa3f72fa18b03.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](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/03902478df1a55bc99703210bccab910.png)
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解题方法
10 . 已知数列
是首项是1,公比为
的等比数列,数列
的通项公式是
.设双曲线
的离心率为
且
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
________ 时,
最大.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c22c96b4d06bc3172cbeb08f4e8c4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb9cfdb0458c13bd70d68248c9d8524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baeb2eb229c4a6a90cb1db2cfaf43177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f567549e66b339299dbf8369ab5812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de43b581704cf3fbd2984340919672f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f567549e66b339299dbf8369ab5812.png)
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