名校
1 . 如图,抛物线
与x轴交于A、B两点,点A在点B的左边,与y轴交于点C,点A的坐标为(-2,0),
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/37d989a1-5f4a-43fa-921e-71a81a0e81e7.png?resizew=352)
(1)如图1,求抛物线的解析式;
(2)如图1,点D在直线BC下方的抛物线上运动(不含端点B、C),连接DC、DB,当四边形ABDC面积最大时,求出面积最大值和点D的坐标;
(3)如图2,将(1)中的抛物线向右平移,当它恰好经过原点时,设原抛物线与平移后的抛物线交于点E,连接BE.点M为原抛物线对称轴上一点,N为平面内一点,以B、E、M、N为顶点的四边形是菱形时,直接写出点N的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8352b2e643a7ce605334f1b0e572bfb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604ca48def96501f98571083e0181911.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/37d989a1-5f4a-43fa-921e-71a81a0e81e7.png?resizew=352)
(1)如图1,求抛物线的解析式;
(2)如图1,点D在直线BC下方的抛物线上运动(不含端点B、C),连接DC、DB,当四边形ABDC面积最大时,求出面积最大值和点D的坐标;
(3)如图2,将(1)中的抛物线向右平移,当它恰好经过原点时,设原抛物线与平移后的抛物线交于点E,连接BE.点M为原抛物线对称轴上一点,N为平面内一点,以B、E、M、N为顶点的四边形是菱形时,直接写出点N的坐标.
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2021-10-17更新
|
89次组卷
|
2卷引用:云南省大理市大理白族自治州民族中学2023-2024学年高一上学期开学数学试题
2 . 如图,在
中,
是
边上一点,以
为圆心,
为半径的圆与
相交于点
,连接
,且
.
![](https://img.xkw.com/dksih/QBM/2023/10/20/3350159630295040/3353837973987328/STEM/b6509deeb75545998d31c068a0fec7ad.png?resizew=190)
(1)求证:
是
的切线;
(2)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050026625966eb9fbb2aa68c7d5508a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffc2a946e72f26a8af584d8ead3a396.png)
![](https://img.xkw.com/dksih/QBM/2023/10/20/3350159630295040/3353837973987328/STEM/b6509deeb75545998d31c068a0fec7ad.png?resizew=190)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5831e128bb6d0a0c229582098a382020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
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3 . 如图,已知点A是x轴正半轴上一点,点B在反比例函数
的图象上,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03517310ea1e913f709753592ac65ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f933696496281d59aba4e87f16aa18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/3/52c8fc92-2a25-4ddd-9d54-f1896c38894c.png?resizew=109)
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名校
4 . 函数
中自变量
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e575925106069560a5f218df5ce0051.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
5 . 若双曲线y=
上任意一点P到两坐标轴的距离分别为d1,d2,则
=( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf35027e76f8ea593f82023973d4aba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a1f2f816a51069ca88b1665053c53e.png)
A.![]() | B.1 | C.2 | D.3 |
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名校
6 . 如图,已知点P是等边三角形ABC外接圆上任一点(异于B,C),求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/e1fc91ef-5870-449a-96c9-bc303cc58804.png?resizew=130)
(1) PA=PB+PC;
(2)若PA交BC于D,则
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/e1fc91ef-5870-449a-96c9-bc303cc58804.png?resizew=130)
(1) PA=PB+PC;
(2)若PA交BC于D,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb656e8e9277d9ffc12306cc5ca6ebd.png)
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名校
7 . 为保证中小学生每天锻炼一小时,某校开展了形式多样的体育活动项目,小明对某班同学参加锻炼的情况进行了统计,并绘制了下面的统计图(1)和图(2),则扇形统计图(2)中表示“足球”项目扇形的圆心角的度数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/1/454ad148-6835-4ac3-bf94-1fa0e590d7fb.png?resizew=415)
A.45° | B.60° | C.72° | D.108° |
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8 . 如图,在
中,
,以
为直径的
与
交于点
,点
是
的中点,连接
,
.
(1)求证:
是
的切线;
(2)若
,
,求
的长;
(3)在(2)的条件下,点
是
上一动点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/27/a9f701a1-6500-44fb-8749-a45b587e7f41.png?resizew=145)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583effa35880ba5704dfc4ae4e48a6fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(3)在(2)的条件下,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13ec9a812274ad0839f20ba17348687.png)
您最近一年使用:0次
9 . 关于三角函数有如下的公式:
……①
……②
(
)……③
利用这些公式可以将一些不是特殊角的三角函数转化为特殊角的三角函数来求值,如:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b234533c85e120f7dd9ff97b93c897.png)
根据上面的知识,你可以选择适当的公式解决下面实际问题:如图所示,直升机在一建筑物
上方
点处测得建筑物顶端
点的俯角
为
,底端
点的俯角
为
,此时直升机与建筑物
的水平距离
为42米,求建筑物
的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/befe5d12d0fe4c28a0a4fbafaa9db499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4b723500500ef61059ddad360f0200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570b1b76ebbfd021053f2428b69d6892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0498edee33a5fe35a7df4c08143816a8.png)
利用这些公式可以将一些不是特殊角的三角函数转化为特殊角的三角函数来求值,如:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b234533c85e120f7dd9ff97b93c897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e680e139402b2a810c3d7bc9872ce25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a4c9b697e3df2b5469b71d3b5e47a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/f0e2468e-ebd1-48e2-8f7d-bb41af47c82d.png?resizew=123)
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10 . 如图:图象①②③均是以
为圆心,1个单位长度为半径的扇形,将图形①②③分别沿东北,正南,西北方向同时平移,每次移动一个单位长度,第一次移动后图形①②③的圆心依次为
,第二次移动后图形①②③的圆心依次为
…,依此规律,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a995d5cf8617eac873100b8522d03f0a.png)
______ 个单位长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56448a74c1b8430c425d79d626764f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bceaa8a53fa787b9c83eb7801d4e986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a995d5cf8617eac873100b8522d03f0a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/b1825933-b9c1-4109-8edf-c13eb86819f7.png?resizew=170)
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