名校
解题方法
1 . 在
中,
,
为
边上的中线,点
在
边上,设
.
(1)当
时,求
的值;
(2)若
为
的角平分线,且点
也在
边上,求
的值;
(3)在(2)的条件下,若
,求
为何值时,
最短?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8520a21b909d04f763d0f61dd74bc158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](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/8a775cd2e88d786d495ae2cb262a2b0f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9680bd6f250acb8b568510419b59d3e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](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/82f4f8e27f307a8a998a3335ba7d1bb4.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441b642fc2d954a5117710a053a21a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2024-06-13更新
|
407次组卷
|
2卷引用:四川省成都市成飞中学2023-2024学年高一下学期5月月考数学试题
名校
解题方法
2 . 如图所示,红星高级中学要在一块扇形空地上修建一个矩形花园,矩形
的四个顶点均在边界上,扇形
的半径
,
,
,
,
分别交
于
,
.
时,求边
的长;
(2)当矩形
的面积
取最大值时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e6feccb6113e9aa32fdd4dc169e95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a56dba4e984e1c7bfc20dd2340e929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90c780dac29ff8b7df5881d3b33abab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d5a52b8d415fcbf4f22187ecde4b41c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)当矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa9c3aaf46da69f39fc5328a70daf5c.png)
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3 . 在平面直角坐标系
中,定义向量
为函数
的有序相伴向量.
(1)设
为函数
的有序相伴向量,求实数
的值;
(2)若
的有序相伴向量为
,若函数
,
与直线
有且仅有四个不同的交点,求实数
的取值范围;
(3)将(1)中所得函数
的图象向左平移
得到函数
.已知
,
,请问在函数
图象上是否存在一点
,使得
成立.若存在,求出
点的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0945d4c70ece41de53a8c910a45607a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651055fdc939ef20d1e92e82e6b32f36.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf624e31f9cdf697fcafa55d7f0d5cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9616f809e87cdd1adc5e623008a3af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557c1a8dbeeb137f8e8631058df5e1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6135c9808e151ef160d8b9e833434b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b604c6522119e77c1cb16b91532a2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead6a3dbd03539ef5e0807be57bb1e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)将(1)中所得函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb486a2e713246204f62cd6f19b5ef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772d1b3c6d3a815b9d6b78cf9480338e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc52054fdb9b146bbc9fda376f7a2874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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4 . 边长为4的正方形
的中心为
,以
为圆心的单位圆
上有两动点
满足
.若点
为正方形
边
上的一个动点.
的值;
(2)求
的最小值;
(3)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ffe69ab39492e018a51e21b52dd0fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5fccb2d96700ef42e1524ade155d2e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751d11a71e1fdf02c4a990220ca4e67d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4525ccf4dc75d7c56d87a8a686624a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd950ec83d93596468e3aff0bb91e0e9.png)
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名校
解题方法
5 . 如图,正方形
的边长为
分别为边
上的点,则以下错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850a0ec73c3fba08a6764a7bc2209c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630754333e7043c573d0ecdb64cf1246.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.![]() ![]() |
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6 . 在
中,内角
的对边分别为
,且
.
(1)求
.
(2)若
,点
是边
上的两个动点,当
时,求
面积的取值范围.
(3)若点
是直线
上的两个动点,记
.若
恒成立,求
的值.
![](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/38e316ce37a4e6964f2872471ba6035d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1113ce8ff2b2113a466e8cdaf05dff89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2264aa0d66a9542095586afb611c048d.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9709ce2ca2e90912412c50332f6778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8975e2f0098642933c12ac5a8ba932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2024-04-16更新
|
1249次组卷
|
7卷引用:四川省渠县中学2023-2024学年高一下学期半期考试数学试题
名校
7 . 下面四个结论正确的是( )
A.点![]() ![]() ![]() ![]() ![]() |
B.若对平面中任意一点![]() ![]() |
C.在![]() ![]() ![]() |
D.如图,扇形的半径为1,圆心角![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
8 . 已知函数
的定义域为
,
,
,且
在区间
上单调递减.
(1)求证:
;
(2)求
的值;
(3)当
时,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c7798e8266916b8501e3837194407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707f481ce3097ef1da3af9964bd36bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da1ddf59efd582614505be50e813af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6bfefa5b41faae17987876d570685d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5980a054af3e565d5d0511b14695aaf1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e861f148f57d5bcdd82cd1fec3d594.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a3d8f7ee39ac3245c840a40f8af63d.png)
您最近一年使用:0次
2024-01-24更新
|
364次组卷
|
2卷引用:四川省泸州市泸县第四中学2023-2024学年高一下学期开学考试数学试题
9 . 关于
的一元二次方程
的两个实数根分别为
,且
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d436744147a2f3454b111c3b4951a74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.![]() ![]() |
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解题方法
10 . 已知函数
(
)有最大值为2,且相邻的两条对称轴的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
的解析式,并求其对称轴方程;
(2)将
向右平移
个单位,再将横坐标伸长为原来的
倍,再将纵坐标扩大为原来的25倍,再将其向上平移60个单位,得到
,则可以用函数
模型来模拟某摩天轮的座舱距离地面高度H随时间t(单位:分钟)变化的情况.已知该摩天轮有24个座舱,游客在座舱转到离地面最近的位置进仓,若甲、乙已经坐在a,b两个座舱里,且a,b中间隔了3个座舱,如图所示,在运行一周的过程中,求两人距离地面高度差h关于时间t的函数解析式,并求最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0912273ca8068fe8bba670c8a1258a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4441ad594b4f1ecf4ddfa411f10327c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb17843c51402a1f7cd9b07542597b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3b61f06b89016d84dac97e1939792b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667c4923ac23ec536f06edc10fb0160d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ad8d8a8a678a8cdea5961968d256c8.png)
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2024-01-18更新
|
541次组卷
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3卷引用: 四川省成都市武侯高级中学2023-2024学年高一下学期第一次月考数学试题