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weiye.wang 2022-12-08 22:44:24 +08:00
parent f9e037620c
commit 7b823586b1
5 changed files with 484 additions and 39 deletions
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8
工具/寻找阶段末尾空闲题号.ipynb
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@ -9,7 +9,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"首个空闲id: 12117 , 直至 020000\n",
"首个空闲id: 12138 , 直至 020000\n",
"首个空闲id: 20227 , 直至 030000\n",
"首个空闲id: 30496 , 直至 999999\n"
]
@ -45,7 +45,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.9.7 ('base')",
"display_name": "Python 3.8.8 ('base')",
"language": "python",
"name": "python3"
},
@ -59,12 +59,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
"version": "3.8.8"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
}
}
},

14
工具/添加题目到数据库.ipynb
View File

@ -7,10 +7,10 @@
"outputs": [],
"source": [
"#修改起始id,出处,文件名\n",
"starting_id = 12117\n",
"origin = \"2021届杨浦区一模\"\n",
"filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目5.tex\"\n",
"editor = \"20221206\\t王伟叶\""
"starting_id = 12138\n",
"origin = \"2011年春季高考\"\n",
"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n",
"editor = \"20221208\\t王伟叶\""
]
},
{
@ -101,7 +101,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.9.7 ('base')",
"display_name": "Python 3.8.8 ('base')",
"language": "python",
"name": "python3"
},
@ -115,12 +115,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
"version": "3.8.8"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
}
}
},

50
工具/识别题库中尚未标注的题目类型.ipynb
View File

@ -9,27 +9,29 @@
"name": "stdout",
"output_type": "stream",
"text": [
"012117 填空题\n",
"012118 填空题\n",
"012119 填空题\n",
"012120 填空题\n",
"012121 填空题\n",
"012122 填空题\n",
"012123 填空题\n",
"012124 填空题\n",
"012125 填空题\n",
"012126 填空题\n",
"012127 填空题\n",
"012128 填空题\n",
"012129 选择题\n",
"012130 选择题\n",
"012131 选择题\n",
"012132 选择题\n",
"012133 解答题\n",
"012134 解答题\n",
"012135 解答题\n",
"012136 解答题\n",
"012137 解答题\n"
"012138 填空题\n",
"012139 填空题\n",
"012140 填空题\n",
"012141 填空题\n",
"012142 填空题\n",
"012143 填空题\n",
"012144 填空题\n",
"012145 填空题\n",
"012146 填空题\n",
"012147 填空题\n",
"012148 填空题\n",
"012149 填空题\n",
"012150 填空题\n",
"012151 填空题\n",
"012152 选择题\n",
"012153 选择题\n",
"012154 选择题\n",
"012155 选择题\n",
"012156 解答题\n",
"012157 解答题\n",
"012158 解答题\n",
"012159 解答题\n",
"012160 解答题\n"
]
}
],
@ -71,7 +73,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.9.7 ('base')",
"display_name": "Python 3.8.8 ('base')",
"language": "python",
"name": "python3"
},
@ -85,12 +87,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
"version": "3.8.8"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
}
}
},

14
文本处理工具/剪贴板文本整理_word文件.ipynb
View File

@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
@ -464,6 +464,12 @@
"#以下是为\\log_瘦身\n",
"modified_data = re.sub(r\"log[\\s]+_\",r\"log_\",modified_data)\n",
"\n",
"#以下是mathpix之后的空格去除\n",
"for i in range(3):\n",
" modified_data = re.sub(r\"([\\u4e00-\\u9fa5])( )([\\u4e00-\\u9fa5])\",lambda x:x.group(1)+x.group(3),modified_data)\n",
" modified_data = re.sub(r\"\\$ \",\"$\",modified_data)\n",
" modified_data = re.sub(r\" \\$\",\"$\",modified_data)\n",
"\n",
"setCopy(modified_data)\n",
"\n",
"with open(\"临时文件/outputfile.txt\",\"w\",encoding = \"utf8\") as f:\n",
@ -480,7 +486,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.9.7 ('base')",
"display_name": "Python 3.8.8 ('base')",
"language": "python",
"name": "python3"
},
@ -494,12 +500,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
"version": "3.8.8"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
}
}
},

437
题库0.3/Problems.json
View File

@ -299605,6 +299605,443 @@
"remark": "",
"space": "12ex"
},
"012138": {
"id": "012138",
"content": "函数$y=\\lg(x-2)$的定义域是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题1",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012139": {
"id": "012139",
"content": "若集合$A=\\{x | x \\ge 1\\}$, $B=\\{x | x^2 \\le 4\\}$, 则 $A \\cap B=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题2",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012140": {
"id": "012140",
"content": "在 $\\triangle ABC$ 中, 若 $\\tan A=\\dfrac{\\sqrt 2}3$, 则 $\\sin A=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题3",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012141": {
"id": "012141",
"content": "若行列式$\\begin{vmatrix}2^x & 4 \\\\1 & 2\\end{vmatrix}=0$, 则 $x=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题4",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012142": {
"id": "012142",
"content": "若 $\\sin x=\\dfrac 13$, $x \\in[-\\dfrac{\\pi}2, \\dfrac{\\pi}2]$, 则 $x=$\\blank{50}(结果用反三角函数表示).",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题5",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012143": {
"id": "012143",
"content": "$(x+\\dfrac 1x)^6$ 的二项展开式的常数项为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题6",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012144": {
"id": "012144",
"content": "两条直线 $l_1: x-\\sqrt 3 y+2=0$ 与 $l_2: x-y+2=0$夹角的大小是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题7",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012145": {
"id": "012145",
"content": "若$S_n$为等比数列$\\{a_n\\}$的前$n$项和, $8 a_2+a_5=0$, 则 $\\dfrac{S_6}{S_3}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题8",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012146": {
"id": "012146",
"content": "若椭圆$C$的焦点和顶点分别是双曲线$\\dfrac{x^2}5-\\dfrac{y^2}4=1$的顶 点和焦点, 则椭圆$C$的方程是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题9",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012147": {
"id": "012147",
"content": "若点$O$和点$F$分别为椭圆$\\dfrac{x^2}2+y^2=1$的中心和左焦点, 点$P$为椭圆上的任意一点, 则$|OP|^2+|PF|^2$的最小值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题10",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012148": {
"id": "012148",
"content": "根据如图所示的程序框图, 输出结果$i=$\\blank{50}.(缺框图)",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题11",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012149": {
"id": "012149",
"content": "2011年上海春季高考有$8$所高校招生, 如果某$3$位同学恰好被其中$2$所高校录取, 那么录取方法的种数为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题12",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012150": {
"id": "012150",
"content": "有一种多面体的饰品, 其表面由$6$个正方形和$8$个正三角形组成(如图), $A B$与$CD$所成角的大小是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = {(215:0.5)}]\n\\def\\l{2}\n\\draw (0,0,0) coordinate (A);\n\\draw (A) ++ (\\l,0,0) coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) coordinate (C);\n\\draw (A) ++ (0,0,-\\l) coordinate (D);\n\\draw (A) ++ (0,\\l,0) coordinate (A1);\n\\draw (B) ++ (0,\\l,0) coordinate (B1);\n\\draw (C) ++ (0,\\l,0) coordinate (C1);\n\\draw (D) ++ (0,\\l,0) coordinate (D1);\n\\draw ($(A)!0.5!(B)$) coordinate (M);\n\\draw ($(B)!0.5!(C)$) coordinate (N) node [right] {$D$};\n\\draw ($(C)!0.5!(D)$) coordinate (P);\n\\draw ($(D)!0.5!(A)$) coordinate (Q);\n\\draw (M) ++ (0,\\l) coordinate (M1);\n\\draw (N) ++ (0,\\l) coordinate (N1);\n\\draw (P) ++ (0,\\l) coordinate (P1) node [above] {$B$};\n\\draw (Q) ++ (0,\\l) coordinate (Q1) node [above] {$A$};\n\\draw ($(A)!0.5!(A1)$) coordinate (A2);\n\\draw ($(B)!0.5!(B1)$) coordinate (B2);\n\\draw ($(C)!0.5!(C1)$) coordinate (C2) node [right] {$C$};\n\\draw ($(D)!0.5!(D1)$) coordinate (D2);\n\\draw (M) -- (A2) -- (Q) -- cycle (M) -- (B2) -- (N) -- cycle;\n\\draw (N) -- (C2) -- (N1) -- (B2);\n\\draw (N1) -- (M1) -- (Q1) -- (P1) -- cycle;\n\\draw (B2) -- (M1) -- (A2);\n\\draw (A2) -- (Q1);\n\\draw [dashed] (C2) -- (P1) -- (D2) -- (P) -- cycle;\n\\draw [dashed] (N) -- (P) -- (Q);\n\\draw [dashed] (Q) -- (D2) -- (Q1);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题13",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012151": {
"id": "012151",
"content": "为求解方程$x^5-1=0$的虚根, 可以把原方程变形为 $(x-1)(x^4+x^3+x^2+x+1)=0$, 再变形为$(x-1)(x^2+a x+1)(x^2+b x+1)=0$, 由此可得原方程的一个虚根为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题14",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012152": {
"id": "012152",
"content": "若向量$\\overrightarrow a=(2,0)$, $\\overrightarrow b=(1,1)$ , 则下列结论正确的是\\bracket{20}.\n\\fourch{$\\overrightarrow a \\cdot \\overrightarrow b=1$}{$|\\overrightarrow a|=|\\overrightarrow b|$}{$(\\overrightarrow a-\\overrightarrow b) \\perp \\overrightarrow b$}{$\\overrightarrow a \\parallel \\overrightarrow b$}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题15",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012153": {
"id": "012153",
"content": "函数 $f(x)=\\dfrac{4^x-1}{2^x}$ 的图像关于\\bracket{20}.\n\\fourch{原点对称}{直线$y=x$对称}{直线$y=-x$对称}{$y$轴对称}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题16",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012154": {
"id": "012154",
"content": "直线$l: y=k(x+\\dfrac 12)$与圆$C: x^2+y^2=1$的位置关系为\\bracket{20}.\n\\fourch{相交或相切}{相交或相离}{相切}{相交}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题17",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012155": {
"id": "012155",
"content": "若 $\\overrightarrow{a_1}$、$\\overrightarrow{a_2}$、$\\overrightarrow{a_3}$均为单位向量, 则$\\overrightarrow{a_1}=(\\dfrac{\\sqrt 3}3, \\dfrac{\\sqrt 6}3)$是$\\overrightarrow{a_1}+\\overrightarrow{a_2}+\\overrightarrow{a_3}=(\\sqrt 3, \\sqrt 6)$的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{既不充分又不必要条件}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题18",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012156": {
"id": "012156",
"content": "向量$\\overrightarrow a=(\\sin 2 x-1, \\cos x), \\overrightarrow b=(1,2 \\cos x)$, 设函数$f(x)=\\overrightarrow a \\cdot \\overrightarrow b$, 求函数$f(x)$的最小正周期及$x \\in[0, \\dfrac{\\pi}2]$时的最大值.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题19",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"012157": {
"id": "012157",
"content": "某甜品店制作一种蛋筒冰激凌, 上部分是半球形, 下半部分呈圆锥形(如图), 现把半径为$10\\text{cm}$ 的圆形蛋皮等分成$5$个扇形, 用一个蛋皮围成圆锥的侧面 (蛋皮厚度忽略不计), 求该蛋筒冰激凌的表面积和体积. (精确到$0.01$)\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\fill [gray!20] (0,{-2*sqrt(6)}) -- (1,0) arc (360:180:1 and 0.3) -- cycle;\n\\draw (0,{-2*sqrt(6)}) -- (1,0) (0,{-2*sqrt(6)}) -- (-1,0);\n\\draw (1,0) arc (360:180:1 and 0.3);\n\\draw [dashed] (1,0) arc (0:180:1 and 0.3);\n\\draw (1,0) arc (0:180:1);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题20",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"012158": {
"id": "012158",
"content": "已知抛物线 $F:x^2=4y$.\\\\\n(1) $\\triangle ABC$ 的三个顶点在抛物线 $F$ 上, 记$\\triangle ABC$的三边 $AB$、$BC$、$CA$所在直线的斜率分别为$k_{AB}$、$k_{BC}$、$k_{CA}$, 若点 $A$在坐标原点, 求 $k_{AB}-k_{BC}+k_{CA}$的值;\\\\\n(2) 请你给出一个以$P(2,1)$为顶点, 且其余各顶点均为抛物线$F$上的动点的多边形, 写出多边形各边所在直线的斜率之间的关系式, 并说明理由. 说明: 第(2)题将根据结论的一般性程度给与不同的评分.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题21",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"012159": {
"id": "012159",
"content": "定义域为 $\\mathbf{R}$, 且对任意实数 $x_1$、$x_2$都满足不等式$f(\\dfrac{x_1+x_2}2) \\le \\dfrac{f(x_1)+f(x_2)}2$的所有函数$f(x)$组成的集合记为$M$, 例如$f(x)=k x+b \\in M$.\\\\\n(1) 已知函数 $f(x)=\\begin{cases}x, & x \\ge 0,\\\\ \\dfrac 12 x & x<0,\\end{cases}$ 证明: $f(x) \\in M$;\\\\\n(2) 写出一个函数$f(x)$, 使得$f(x) \\not\\in M$, 并说明理由;\\\\\n(3) 写出一个函数$f(x) \\in M$, 使得数列极限$\\displaystyle\\lim_{n \\to \\infty} \\dfrac{f(n)}{n^2}=1$, $\\displaystyle\\lim_{n \\to \\infty} \\dfrac{f(-n)}{-n}=1$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题22",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"012160": {
"id": "012160",
"content": "对于给定首项$x_0>\\sqrt[3]a(a>0)$, 由递推式$x_{n+1}=\\dfrac 12(x_n+\\sqrt {\\dfrac a{x_n}})$($n \\in \\mathbf{N}$, $n\\ge 1$)得到数列$\\{x_n\\}$, 且对于任意的$n \\in \\mathbf{N}$, $n\\ge 1$, 都有 $x_n>\\sqrt[3]a$, 用数列$\\{x_n\\}$可以计算$\\sqrt[3]a$的近似值.\\\\\n(1) 取$x_0=5$, $a=100$, 计算 $x_1$、$x_2$、$x_3$的值(精确到$0.01$), 并且归纳出$x_n$、$x_{n+1}$的大小关系;\\\\\n(2) 当$n \\ge 1$时, 证明: $x_n-x_{n+1}<\\dfrac 12(x_{n-1}-x_n)$;\\\\\n(3) 当$x_0 \\in [5,10]$时, 用数列$\\{x_n\\}$计算$\\sqrt [3]{100}$的近似值, 要求满足$|x_n-x_{n+1}|<10^{-4}$, 请你估计$n$, 并说明理由.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2011年春季高考试题23",
"edit": [
"20221208\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"020001": {
"id": "020001",
"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",