20-21高一·江苏·课后作业
1 . 下表是某地一年中10d(天)的白昼时间.
(1)以日期在365d(天)中的位置序号为横坐标,白昼时间为纵坐标,描出这些数据的散点图;
(2)选用一个三角函数来近似描述白昼时间与日期序号之间的函数关系;
(3)用(2)中的函数模型估计该地7月8日的白昼时间.
日期 | 1月1日 | 2月28日 | 3月21日 | 4月27日 | 5月6日 |
白昼时间/h | 5.59 | 10.23 | 12.38 | 16.39 | 7.26 |
日期 | 6月21日 | 8月14日 | 9月23日 | 10月25日 | 11月21日 |
白昼时间/h | 19.40 | 16.34 | 12.01 | 8.48 | 6.13 |
(2)选用一个三角函数来近似描述白昼时间与日期序号之间的函数关系;
(3)用(2)中的函数模型估计该地7月8日的白昼时间.
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解题方法
2 . 以下四个命题中错误的序号为__________ .
①已知
三内角A,B,C的对边分别为a,b,c,且
,若角A的平分线交BC于D点,且
,则
的最小值为4
②在平行四边形
中,
,
,若点
,
满足
,
,则
的值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
③设O是
的外心,且满足
,则
.
④在矩形ABCD中,AB=
,BC=2,点E为BC的中点,点F在边CD上,若
=
,则
的值是
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58296d4772a7cd31792f6a54e31e18f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ffbcd82b98a9ae69aa4ee28bb49a907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
②在平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1203f93e3696820124f310b51903d6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e0e0a61bc7aedebcb4a10b423d21e9.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/173118fd038ef312ae3d8dd947f4cd3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b0b73bae90597775a1a9219fdeb1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc724b92355546b4da634b485d042f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
③设O是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ff9d4fdd0d176042505b7aac016852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda3f418a8b01b6d0ab3ed0135fb84a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706e774dfd32305229cf4e06b36eecc0.png)
④在矩形ABCD中,AB=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad28b5f1101403620ddbdbe536a620ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f651a0f32c32d43a5e629e6e3fd479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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3 . 下列说法中,所有正确的命题序号为( )
①在同一坐标系中,函数
与函数
的图象关于
轴对称;
②函数
(
且
)的图象经过顶点
;
③函数
的最大值为1;
④任取
,都有
.
①在同一坐标系中,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996a92bcfc7fb20171fa1768d5ffddb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa80ae0b0eab1f14cccf872500f0843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2e1bb3e70e20280047d9b6c546dd16.png)
④任取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf7a904df8f22e3f1e26a4116eb7913.png)
A.①②③④ | B.② | C.①② | D.①②③ |
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2021-10-24更新
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3卷引用:吉林省长春市实验中学2021-2022学年高一上学期第一次阶段考试数学试题
名校
4 . 如图,已知⊙
、⊙
的半径分别为
、
,⊙
经过点
,且两圆相交于点A、B,C为⊙
上的点,连接AC交⊙
于点D,再连接BC、BD、
、
、
有如下四个结论:①
, ②
, ③AD=DC, ④BC=DC,其中正确结论的序号为______________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee51552e3c12bc27cf8ab1777bf191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6973bc602348065901b58bb1b4e6bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28677c8dd8bb83b996d1d9e4fc6ef21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45143c362aa4cdb71c347561f2455593.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/19/35a53867-c1bb-48ef-8fd9-15fd595702cc.png?resizew=187)
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5 . 复数
满足
,①
;②
;③复数
的虚部为
;④
是方程
在复数范围内的一个解.则以上四个结论中正确序号为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5bf0ee9e45490fb6503cc88f58d9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145e6e8cb3f167d16cdeabd3bd17ca12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369d595329752492349210d55544d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/396df1e2e35bf3040082cbb783314e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467354a996bf765789a18542f1beb008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fc19c302085de8a90e2827c32f15e7.png)
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2卷引用:天津市西青区2020-2021学年高一下学期期末数学试题
20-21高一·江苏·课后作业
6 . 判断下列表述是否正确:
(1)
; (2)
;
(3)
; (4)
;
(5)
; (6)
;
(7)
; (8)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec538184bd8d3c44daa125ff84cc742b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e16c585bf84d772b03e64c33d5c224.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffa77ed1678e5c275f8cb9b8c649124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1e46247fa97d0f98dfe75663bc72f1.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf82d0306f6f5ce7b8aa3c8b4059e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c596440b19b651cc3f63581c84510e6.png)
(7)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06978f01170060df1da59a8c5d213fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f721cc481254f8592c91e9273e7620ef.png)
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20-21高一·全国·课后作业
7 . 给出下列说法:
①若直线a∥直线b,a⊂平面α,b⊂平面β,则α∥β;
②若α∥β,直线a与α相交,则a与β相交;
③若l⊂α,m⊂α,且l∥β,m∥β,则α∥β;
④若直线a∥平面β,直线b∥平面α,且α∥β,则a∥b.
其中说法错误的序号是_____.
①若直线a∥直线b,a⊂平面α,b⊂平面β,则α∥β;
②若α∥β,直线a与α相交,则a与β相交;
③若l⊂α,m⊂α,且l∥β,m∥β,则α∥β;
④若直线a∥平面β,直线b∥平面α,且α∥β,则a∥b.
其中说法错误的序号是_____.
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解题方法
8 . 下列说法中不正确的是______ (只需填写序号)
①设集合
,则
;
②若集合
,
,则
;
③在集合A到
的映射中,对于集合
中的任何一个元素
,在集合A中都有唯一的一个元素
与之对应;
④函数
的单调减区间是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d028846b8614318fbf90387d13c75b5.png)
⑤设集合
,
,若
,则
①设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cec1a82f40122b306b15aa29da2f8c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a88caacdbf71fca44d1ca412c68fa66.png)
②若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5361ed288fa23f3b5d16cbc09d3293d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f808f81b6ea9da53d51c549be04f4267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
③在集合A到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c9320d009a17deba67f208c7d8be8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d028846b8614318fbf90387d13c75b5.png)
⑤设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a569ad6f0b7c49d11d7e167bb0527ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa7b8acbc8b0027cbe9e3986ad1d859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
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9 . 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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10 . 某同学在解答题目:“化简并求值
,其中
”时:解答过程是:
;
(1)请判断他的解答是否正确;如果不正确,请写出正确的解答过程.
(2)设
(n为正整数),考查所求式子的结构特征:
①先化简通项公式
;
②求出与S最接近的整数是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f52f02bd7958e99d7662b815571ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88e026f5e5a7782144513c691259159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a8c00f7789b2dd683659fe639f7db7.png)
(1)请判断他的解答是否正确;如果不正确,请写出正确的解答过程.
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e0c644272e0903a5c415a70b6bab4c.png)
①先化简通项公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b86c2c47a753faa1508b7eaac99132.png)
②求出与S最接近的整数是多少?
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