解题方法
1 . 已知指数函数
,且
的图象过点
,
.
(1)若
,求
的取值范围;
(2)判断
在
上的单调性;
(3)设
,试比较
的大小,并将它们按从小到大的顺序排起来.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cae47ad50ac506ced900f0a5156c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf960e02c72a12e97c86091b8a8f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ef72191a9ac3bd5a325395a72bdc2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1d195c6dcc117e03c8703273120401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d94bd43003dbb6412d6fe38c89abd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c5fe8a9ad42e52a8a40242865c6752.png)
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名校
2 . 有三个含30°角的直角三角形,它们的大小互不相同,但均有一条长为a的边.这三个三角形按照从大到小的顺序,求其面积比.
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3 . 已知
,
,那么M,N,P,Q之间的大小顺序是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d27c3b25ffaf77645e44b04ba3dc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6cc9721a2649221bd246eb06baf240d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
4 .
满足:
都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc2af33d9e2ad677b2120235f799d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9962d7d23d4245e4aa5186329a62775.png)
,则
的大小顺序为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6b13c45d8cc2f9c82ac6882a46013b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc2af33d9e2ad677b2120235f799d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9962d7d23d4245e4aa5186329a62775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e452d2787d833493c850090409bec5bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f24eb470b2ebc7a9b1f84b59d38059.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 三个关于
的方程:
,
,
,已知常数
,若
分别是按上顺序对应三个方程的正根,则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a3bbd5ce0c21f6487d53bed654941de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5feb770f58c76d5ebe8f67ea5a73a82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1ebfe1e74a47dea957b45177a30780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2227c388ff1295daf4e49846f8d920a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
A.![]() |
B.![]() |
C.![]() |
D.不能确定![]() |
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解题方法
6 . 如图,试用直观的方法比较以
为边长的正方形的面积与四个长为
、宽为
的矩形面积之和的大小,把这种大小关系用不等式表示出来,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6f19b84484b5480ea2100165abfd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
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解题方法
7 . 已知直角梯形
,
,
,
,扇形圆心角
,
,如图,将
,
以及扇形
的面积分别记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
的表达式,并指出其大小关系(不需证明);
(2)用
表示梯形
的面积
;并证明:
;
(3)设
,
,试用代数计算比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36572a10fcb483a9abb63a5039e09ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201339005285d682fbc2cf65fbabddd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fec41d46ca97d3e900ef1db5a1f002c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc4a85bbf152031dc8ebd182e44ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be31dfad4f16cf1f2158b3011e3b68b9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e8d7d33749979b7d7acc17532d86b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7787a01998f68ccc931c00ccb475f6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ba6b6ee00c4b2763cb3fa59caa69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bf4af3d4543cada4b52871ac9dfb1a.png)
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2023-07-09更新
|
608次组卷
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6卷引用:上海市复旦大学附属中学2022-2023学年高一下学期期末数学试题
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