解题方法
1 . 某工厂共有200名工人,将他们随机分成两组,每组100人,规定每个工人都生产同样的1000个零件,根据工人完成生产任务的工作时间(单位:
)绘制了如下频数分布表:
甲车间
乙车间
(1)若认定完成生产任务的工作时间小于80分钟的工人为操作能手,分别求从甲、乙两个车间中任选一个工人,该工人为操作能手的概率;
(2)分别计算甲、乙两个车间中100位工人完成生产任务的平均工作时间,并判断哪个车间的效率比较高?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e008ee8b0dc593ce21d8d4c87afef1c.png)
甲车间
工作时间区间 | ![]() | ![]() | ![]() | ![]() |
频数 | 15 | 45 | 35 | 5 |
工作时间区间 | ![]() | ![]() | ![]() | ![]() |
频数 | 18 | 43 | 36 | 3 |
(2)分别计算甲、乙两个车间中100位工人完成生产任务的平均工作时间,并判断哪个车间的效率比较高?
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2 . 如图,点
在
外,
为
中点,
在
上,且
,连接
并延长交
于点
,则
能否成立?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a122e25cf4eb9f03ffe5ec823bfc31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f834e8d16a6e26a65ff2ed5809823f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc960c33db841e63ab5983f7a5a847bd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/427d79ea-94e7-4032-9151-d2015cbd61e2.png?resizew=131)
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3 .
可以表示为数轴上1右边的点
(1)
可以在平面直角坐标系中表示为__________;
(2)在坐标系中用阴影表示满足
的点;
(3)
与上述阴影部分围成的封闭图形(不含边界)中包含2个整点(横纵坐标均为整数的点)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecedde061163f1e524308688204e9ef9.png)
(2)在坐标系中用阴影表示满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1be1f7713bf93673b52fef8d8cae01.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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4 . (1)已知
为
中点,过点
作
于
,交
于点
,求
.
(2)已知
,过点
作
于
,交
于点
,求
.
(3)在(2)的条件下,
为常数,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c4c49765e33742b4204d6904dc3a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/5378a3867bf1a7386b1330aa8b36f0a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/1e748517-2524-4763-aeb1-30d7a2bd7e1d.png?resizew=155)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df89cefacfd826262825276a739ca4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/5378a3867bf1a7386b1330aa8b36f0a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/7e2e9fd4-ce48-414d-8682-dee6f813a104.png?resizew=154)
(3)在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f03cab451843012fd80fa6cc698c648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe857997fa13837880f520673db7809.png)
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5 . 已知
是圆
的切线,
是直径,
是弧
的中点,
是直线
与
的交点
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/6442f898-647e-4b07-bfd5-6b3db2686872.png?resizew=163)
(1)
,求
;
(2)
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/f52a58fbaf4fea03567e88a9f0f6e37e.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/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/6442f898-647e-4b07-bfd5-6b3db2686872.png?resizew=163)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9639896487e6cf18e8fd02d2a7ed2087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d9d43e562dd78eeb55b5ed675b6f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b020e3977f31139a1153a1c1d23dc7.png)
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6 . 如图,
为
的外接圆,
为
边上的高.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c8162e02-5e95-46fc-bd52-fb046a22dbe8.png?resizew=159)
(1)请写出
与
半径
的关系;
(2)如果作
的角平分线交
于
,那么
是否是
的角平分线?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c8162e02-5e95-46fc-bd52-fb046a22dbe8.png?resizew=159)
(1)请写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831f65020b4b53186e44d5312d063e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)如果作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a037c23a11c7783b1b44988c21634f.png)
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7 . 二次函数
与
交于
两点且
在
的右侧,交
的对称轴于点
;
(1)当
__________时,
重合;
(2)当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353b27715b12c8020985cee29deffdbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836b419464e4734e99af06c2fb104716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/353b27715b12c8020985cee29deffdbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf989b692c5d2880cbd7e18c8149904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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解题方法
8 . 如图,在平面直角坐标系
中,过
上的点
作切线
,
分别与直线
,
交于点
,圆
与
轴交于点
.
(1)若
点坐标是
,求直线
的方程;
(2)若
是圆
上的动点,证明:两条动直线
的交点
总在同一个椭圆
上,并求出椭圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a327470311e876d8489eeb8c66435dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da322ac8867e8a47c6588601078abf18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf2917e77945b30da7be9b48b0b317a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9454e7762d6924d4a9e5dcf31fb6bc74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf639890f27a42e1383cc6cfa14117a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/d55806ac-c399-4b9c-b012-1d4e5c5bbf3a.png?resizew=180)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cceff0e7d103475c3ba9a2712f373185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7040823265da65a030f0c81f3ae7ddd0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37254351125380127823c0fd7d95458d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7040823265da65a030f0c81f3ae7ddd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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2024-02-23更新
|
91次组卷
|
2卷引用:中原名校2022年高三上学期第一次精英联赛文科数学试题
9 . 如图所示,在
中,点
在
边上,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/a5b4a0d2-1629-4d90-99fb-a6479cb11e05.png?resizew=488)
(1)若
.
①如图1,若
,
,过
作
于点
,直接写出
的值为 ;
②如图2,若
,求
的值.
(2)如图3,已知
为
的角平分线,
,
,直接写出线段
的长度.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/a5b4a0d2-1629-4d90-99fb-a6479cb11e05.png?resizew=488)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092f6c8e7e90d46c1ee0457f17daeb4a.png)
①如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629be4a6de577f13c9b0a524e7a5e383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b62ce0cbffa4758c7a0e6fb7ca4d24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c06aa28f4e4ee00cdf3c8e7847225ed.png)
②如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7e75d7342e6f087370d09181b17a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120223970943dc87c216b0860e502254.png)
(2)如图3,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e50f0d02d0bd51ae361d276ed9dea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d035c3a7a6126dabbba817cf0506a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
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10 . 当前,奥密克戎变异毒株传播速度快、隐匿性强、感染风险高.为进一步巩固疫情防控成果,自2022年5月23日起,7月4日止,在石家庄市开展每周一次城乡居民全员核酸检测筛查.燕都融媒体记者探访石家庄三处核酸检测点,观察到现场居民对新的管理措施反应较平静,已做好常态化检测准备,同时希望检测网点分布更均衡,获取检测结果更及时,以便大家在做好疫情防控的同时,尽量不影响日常工作与生活.在早6点到7点时间段,记者从所有参加检测的居民中分别抽取100人的年龄进行统计分析(抽取的居民年龄均在区间[16,40]内),经统计得出年龄频率分布直方图.回答下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/ed9c0ea6-03b8-45b5-92d3-fc48f206471c.png?resizew=257)
(1)利用频率分布直方图,估计参加检测居民的平均年龄(同一组中的数据用该组区间的中点值为代表);
(2)用分层抽样方法在年龄区间为
和
周岁的居民中抽取
人,再从这
人中随机抽取
人,这
人年龄恰好都在区间
内的概率.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/ed9c0ea6-03b8-45b5-92d3-fc48f206471c.png?resizew=257)
(1)利用频率分布直方图,估计参加检测居民的平均年龄(同一组中的数据用该组区间的中点值为代表);
(2)用分层抽样方法在年龄区间为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680f01ad2ce4ee1ee9d9d31f552b3eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17759991493ed6511b508073aefcca25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17759991493ed6511b508073aefcca25.png)
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