名校
解题方法
1 . 过抛物线
的焦点
作斜率为
的直线与抛物线相交于
、
两点,线段
的中点为
,垂直平分线与
轴相交于点
,则
与
的面积的比值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea87072d1ccedbc0491f781952e75e87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb41d09d7904d27e717b6e65cd80e81.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知直线
与圆
相交于
、
两点,
为坐标原点,若
,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0c4f7de0a94be0e0c6c0e2b68ad4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6fe733fa7d47b52730025b9cb6beb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 直线
的倾斜角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知集合
,则下列关系中:①
;②
;③
;④
;表述正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd62246d6a30ec24d1d4e145ae23b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca05074e5a317ae45d073962bdf74dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ab2c726fbefda0c51e1ac1ae0863f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1988827754496c230551741068c18458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b750b578d454a36906fcfef3ae98a51a.png)
A.1 | B.2 | C.3 | D.4 |
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5 . 已知向量
,
,则向量
在向量
方向上的投影为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f89d9cd2d59f0d0366e64469ad376b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3bb7ccb422f0c02385a5adcd1606c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
A.-1 | B.![]() | C.![]() | D.1 |
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6 . 函数
的最小正周期为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c2ab525feef0108f2a5a8636a4dbdd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 如图,网格纸上每个小正方形的边长均为1,粗线是某棱锥的三视图,则此棱锥的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/4119b2af-9010-4ed9-a7e7-4b25518fe71a.png?resizew=140)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/4119b2af-9010-4ed9-a7e7-4b25518fe71a.png?resizew=140)
A.![]() | B.![]() | C.![]() | D.1 |
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8 . 已知变量
,
的一组统计数据如下表所示,并据此计算得
关于
的线性回归方程为
,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f5bfebf2799ceda7f075da39ed3853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![]() | 0 | 1 | 2 | 3 |
![]() | 1 | 2 | ![]() | 3 |
A.2 | B.3 | C.4 | D.5 |
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9 . 在直角坐标系
中,以原点为极点、
轴正半轴为极轴建立极坐标系,圆
的极坐标方程为
,直线
的参数方程为
(
为参数).
(1)求圆
的直角坐标方程;
(2)设圆
与直线
相交于
、
两点,若点
的直角坐标为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4171a30d75286a3e4a1a91f31eba3c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117e7d3709ea8021150ea1530dc79f34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70ffe1cf724813ad2f65c9f28d8305e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a430c41f782c5c12f68a49c5d0cb1ee2.png)
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解题方法
10 . 从某中学高三年级随机选取4名男生,统计他们的身高
(单位:
)和体重
(单位:
),得到数据如下表:
(1)根据表中数据建立体重
关于身高
的回归方程(系数精确到0.01);
(2)利用(1)的回归方程,分析这4名男生的体重关于身高的变化趋势,并预测一位身高为
的男生的体重.
附:回归方程
的斜率和截距的最小二乘法公式分别为:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97153bc3d02dfb38ee046487a8037a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a541551402a5fadca4831fe902e95c61.png)
编号 | 1 | 2 | 3 | 4 |
身高![]() | 165 | 170 | 175 | 178 |
体重![]() | 60 | 64 | 70 | 74 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(2)利用(1)的回归方程,分析这4名男生的体重关于身高的变化趋势,并预测一位身高为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13171166927f43800e8678b40b52b456.png)
附:回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83c20a7ecf4b1ac7c1a6c92cf7c4276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9894237e194195ac44486a04fc940de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054e02d1144ef213108d1a61b8ff6439.png)
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