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1 . 传说古希腊毕达哥拉斯学派的数学家用沙粒和小石子来研究数他们根据沙粒或小石子所排列的形状把数分成许多类,下图中第一组的1,3,6,10称为三角形数,第二组的1,5,12,22称为五边形数,则三角形数的第7项为___________ ,五边形数的第n项为___________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/232d818c-663b-421e-b90e-15b50e94d206.png?resizew=440)
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解题方法
2 . 已知函数
是定义在R上的奇函数,若当
时,有
,则当
时,函数
的解析式为______________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbe8e0c5f83900d2d0d8c0160ede5a9.png)
______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a652e73ce3ca5dee3d7bee5159d36c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbe8e0c5f83900d2d0d8c0160ede5a9.png)
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3 . 一个总体的容量为60,其中的个体编号为00,01,02,…,59.现需从中抽取一个容量为7的样本,请从随机数表的倒数第5行(下表为随机数表的最后5行)第11~12列的18开始,依次向下,到最后一行后向右,直到取足样本,则第一个入样的号码是______ ,最后一个入样的号码是______ .
95 33 95 22 00 18 74 72 00 18 46 40 62 98 80 54 97 20 56 95
38 79 58 69 32 81 76 80 26 92 15 74 80 08 32 16 46 70 50 80
82 80 84 25 39 90 84 60 79 80 67 72 16 42 79 71 59 73 05 50
24 36 59 87 38 82 07 53 89 35 08 22 23 71 77 91 01 93 20 49
96 35 23 79 18 05 98 90 07 35 82 96 59 26 94 66 39 67 98 60
95 33 95 22 00 18 74 72 00 18 46 40 62 98 80 54 97 20 56 95
38 79 58 69 32 81 76 80 26 92 15 74 80 08 32 16 46 70 50 80
82 80 84 25 39 90 84 60 79 80 67 72 16 42 79 71 59 73 05 50
24 36 59 87 38 82 07 53 89 35 08 22 23 71 77 91 01 93 20 49
96 35 23 79 18 05 98 90 07 35 82 96 59 26 94 66 39 67 98 60
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2022-08-08更新
|
122次组卷
|
2卷引用:宁夏银川市三沙源上游学校2023届高三上学期开学检测数学(理)试题
名校
4 . 已知直线
,则圆
截直线
所得的弦长的最小值是________ ;直线
与曲线
有两个公共点,则实数
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9d987264d2068cb9472e975dd33c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3880d0e73ec5a29eeca36d45a6bc237b.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/f4beb424850f2cdd3d688bd760ce0684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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5 . 第十四届国际数学教育大会(简称ICME-14)于2021年7月在上海举办,会徽的主题图案(如图)有着丰富的数学元素,展现了中国古代数学的灿烂文明,其右下方的“卦”是用中国古代的计数符号写出的八进制数字3745.八进制有0~7共8个数字,基数为8,加法运算时逢八进一,减法运算时借一当八.八进制数字3745换算成十进制是
,表示
的举办年份.设正整数
,其中
,
.记
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609f311e834b30e41f2a7ba60a9abefd.png)
_______ ;当
时,用含
的代数式表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae5ae56a0293f54c977dee4aaa60368.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350373daed1dbb9e132068795f1b30d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9366665f8db1c83cfe90a522b319368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8517d550a4711c816791378c6a44595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd628117f1dcc07642a46e989805a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acecfd7044968e807684834687105cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c5569209bfd915710696e703a8e1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0587aff6fa0c179d2de29d72e580db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609f311e834b30e41f2a7ba60a9abefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6315b1d874b89d3162ce28c120a41bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae5ae56a0293f54c977dee4aaa60368.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/059adad0-36c7-4a64-940b-2e43f542bb82.png?resizew=174)
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2022-05-05更新
|
918次组卷
|
3卷引用:宁夏石嘴山市第三中学2022届高三第四次模拟数学(理)试题
6 . 已知
,
,
,
成等比数列,且
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
___________
(填“>”或“<”);![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
___________
(填“>”或“<”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ef75182a222ac4c9ab10395ce8bc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8141d87fb02b08c88b0c9f27f839a7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
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解题方法
7 .
,
,
,
四点均在同一球面上,
,
是边长为
的等边三角形,则
面积的最大值为__________ ,四面体
体积最大时球的表面积为___________ .
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86c589939053ce21ce0a67cf40054a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2022-04-11更新
|
1964次组卷
|
3卷引用:宁夏石嘴山市2022届高三适应性测试数学(理)试题
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解题方法
8 . 若在数列的每相邻两项之间插入此两项的积,形成新的数列,再把所得数列按照同样的方法不断构造出新的数列.现对数列1,2进行构造,第一次得到数列1,2,2;第二次得到数列1,2,2,4,2;依次构造,第
次得到的数列的所有项的积记为
,令
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d022a7a5a83884e8bc72aadcce297d.png)
___________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc321599521a98661ed719cc82ca87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f6000421c5370e4b89f23be199f388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d022a7a5a83884e8bc72aadcce297d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
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2022-04-10更新
|
981次组卷
|
3卷引用:宁夏回族自治区银川一中2023届高三上学期第一次月考数学(理)试题
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9 . 等差数列
满足:
,且它的前
项和
有最大值,则
取最大值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
_____ ;
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ee0f9d3d9828fbf7a19a7866b24139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49763402b2f2023f0ba64c37924267d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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解题方法
10 . 已知抛物线
的焦点为
,过焦点的直线
与抛物线交于
两点,则
的最小值为_________ ,此时直线
的斜率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3b5f2c868caddba2f4d94e5da0f242c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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