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1 . 在
中,
是
外一动点,满足
,设
,则下列结论正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/c7b0f670-66c4-4872-afbe-6e518519b4e0.png?resizew=127)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cb0c151c65b03e17996dbc13c29000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a8cb4c14a70137ab4ebc08e1e40568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4a41cf2b61cb7dd54ba549a549694b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/c7b0f670-66c4-4872-afbe-6e518519b4e0.png?resizew=127)
A.![]() |
B.设四边形![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
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2 . 龟、兔进行600米赛跑,赛跑的路程s(米)与时间t(分钟)的关系如图所示(兔子睡觉前后速度保持不变),根据图像信息,下列说法正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/c6ea60ef-2990-46ed-a8ba-9a754fa2437e.png?resizew=247)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/c6ea60ef-2990-46ed-a8ba-9a754fa2437e.png?resizew=247)
A.赛跑中,兔子共睡了40分钟 |
B.兔子在整个赛跑过程中的平均速度是10米/分钟 |
C.兔子到达终点时,乌龟已经到达了8分钟 |
D.兔子刚醒来时,乌龟已经领先了300米 |
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3 . 在第36届全国中学生物理竞赛决赛中,华师一物理竞赛团队有5位同学获金牌,并全部进入国家集训队.五位同学猜谁是第一名,A说:是B,B说:是D,C说:是A,D说:B说错了,E说:不是我,教练说:你们中只有一人说对了,那么第一名是( )
A.B | B.C | C.D | D.E |
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4 . 在
中,
是
中点,
是射线
上的一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/81a83048-546d-475e-8ec7-7ac6de245317.png?resizew=369)
(1)如图1,连接
并延长交
于点
,求
的值;
(2)如图2,
交
于点
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/81a83048-546d-475e-8ec7-7ac6de245317.png?resizew=369)
(1)如图1,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00e7e28f754e518812e746b9be245da.png)
(2)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa73b8b8f7a9ed8d505b81eb7b3f521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856ddcafb0a8610ed9a95eff0f41e6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d4d78dce0cf121e288749e58b1924d.png)
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5 . 已知拋物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/0f7bcae5-04cf-4256-9f00-948fcfa8cd38.png?resizew=467)
(1)设
为直线
在第一象限图象上的一动点,过
作
轴,垂足为
,将
沿
翻折,得到
(如图1所示),若点
恰好在抛物线上,求点
的坐标;
(2)设
为抛物线在第一象限图象上的两个动点,过
分别作
轴的垂线,垂足分别为
(如图2所示),记
的面积为
,梯形
的面积为
,若
,求直线
的解析式.
(参考公式:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/0f7bcae5-04cf-4256-9f00-948fcfa8cd38.png?resizew=467)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3a3db6d96518255f96ad7fc1ac98f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a51268fce97426487c3338d6ec3d571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02c6f05016c03cbf6f92d8807afb2d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6222def769e5be98070bb27702b5bf4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704cc8677a1e4777607cdecdcea80747.png)
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6 . 关于
的方程
有两个不相等的实数根,以这两个根作为等腰
的底边长和腰长,这样的等腰三角形有且仅有一个.
(1)求
的取值范围;
(2)当
取最大值时,求该等腰三角形外接圆半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64cba0c6d78a4f35cb9924d259531372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b980a6a0f8fd5a957034a5291207bbe7.png)
(2)若关于
的方程
没有实数根,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b980a6a0f8fd5a957034a5291207bbe7.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa18a8752b6023da8fdf4a418f249ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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8 . 若关于
的一元二次方程
有两个不相等的实数根
,且
.
(1)下列说法正确的有__________ .(将正确选项的序号填在横线上)
①若
,则
,
②
,
③若
,则
,
④若
,则
.
(2)某数学兴趣小组为了增加此题的趣味性,将题目改成:若关于
的方程
有两个不相等的实数根
,且
,其中
均为整数,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b800b7d6a688abf8a3018c133cec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5ffa21fddc7c55d35f13435792b2d4.png)
(1)下列说法正确的有
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/badd7f3edb52106b897fe62c9e9ada2e.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d57bdb85ad21a427ebc3126fab41ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c56b1ee18c6809b339d980671b4d09a.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a066bbbcf164565325c66d9e5f500d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1adacd10539c74b82fc1e6e88ea6f6.png)
(2)某数学兴趣小组为了增加此题的趣味性,将题目改成:若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9c0dce1f975d1203a1bff7580a892d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097f28b6443848c98413364953c37ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . 如图,
两点在双曲线
上,
两点在双曲线
上,若
轴,且
,则
的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114947179bed8c2c86ac078e2f8497f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2311a0e8fe086ac4bfa89b75417da00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db27d050c1f126c5b94b2e3b22a14f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cd2fd2fbb51a162b1054b531daaa9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b417db3873f3e6d0e9cd235a4ef685a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/221ac969-cb33-47cb-bbd6-b6a29bd9c582.png?resizew=160)
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解题方法
10 . 已知二次函数
(
为常数)的对称轴为
,其图像如图所示,则下列选项正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/e66d49f8-48d8-468e-9b1f-14e47e3ac33d.png?resizew=205)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c73794bb66dac68091c906b0d56e758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/e66d49f8-48d8-468e-9b1f-14e47e3ac33d.png?resizew=205)
A.![]() |
B.当![]() ![]() |
C.关于![]() ![]() ![]() ![]() |
D.若关于![]() ![]() ![]() ![]() ![]() |
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2023-03-20更新
|
1666次组卷
|
12卷引用:湖北省武汉市华中师范大学第一附属中学2021年高中自主招生考试数学试题
湖北省武汉市华中师范大学第一附属中学2021年高中自主招生考试数学试题(已下线)高一上学期第一次月考数学试卷(提高篇)-举一反三系列(已下线)2.3 二次函数与一元二次方程、不等式(AB分层训练)-【冲刺满分】(已下线)专题2.7 一元二次函数、方程和不等式全章综合测试卷(提高篇)-举一反三系列福建省宁德第一中学2023-2024学年高一上学期入学考试数学试题重庆市西南大学附属中学校2023-2024学年高一上学期9月定时检测(一)数学试题福建省厦门第一中学2023-2024学年高一上学期第一次适应性练习数学试题湖南省株洲市南方中学2023-2024学年高一上学期10月月考数学试题广东省四校(珠海市实验中学、东莞市第六高级中学、河源高级中学、中山市实验中学)2023-2024学年高一上学期10月联考数学试题湖南省邵阳市2023-2024学年高一上学期拔尖创新人才早期培养竞赛(初赛)数学试题(已下线)第二章 函数的概念与性质 第四节 二次函数(B素养提升卷)(已下线)一次函数与二次函数