From 9d0b127e5a1c52b2e5a4834f0fa3ae00e32b1368 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Fri, 2 Jun 2023 21:46:24 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A5=E4=BA=A4=E5=A4=A7=E9=99=84?= =?UTF-8?q?=E4=B8=AD=E4=B8=89=E6=A8=A1=E8=AF=95=E9=A2=98=E5=8F=8A=E7=AD=94?= =?UTF-8?q?=E6=A1=88?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/批量收录题目.py | 2 +- 工具/文本文件/metadata.txt | 149 ++++--------- 题库0.3/Problems.json | 420 +++++++++++++++++++++++++++++++++++++ 3 files changed, 464 insertions(+), 107 deletions(-) diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py index 96e6541b..9728a4a2 100644 --- a/工具/批量收录题目.py +++ b/工具/批量收录题目.py @@ -1,5 +1,5 @@ #修改起始id,出处,文件名 -starting_id = 17444 +starting_id = 17465 raworigin = "" filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex" editor = "20230602\t王伟叶" diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index ce489d14..ea1b1d2d 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,126 +1,63 @@ -usages -000573 -p20230529 2023届高三03班 0.690 +ans +17465 +$\{-1,1\}$ +17466 +$\dfrac{\sqrt{2}}{2}$ -000618 -p20230518 2023届高三11班 0.952 -p20230518 2023届高三12班 1.000 -p20230518 2023届高三01班 0.900 -p20230518 2023届高三06班 0.974 -p20230518 2023届高三09班 0.967 +17467 +$(-\infty,-3]\cup (1,+\infty)$ +17468 +$-\dfrac{1}{8}$ -000622 -p20230518 2023届高三11班 0.619 -p20230518 2023届高三12班 0.739 -p20230518 2023届高三01班 0.900 -p20230518 2023届高三06班 0.921 -p20230518 2023届高三09班 0.767 +17469 +$\pi$ +17470 +$x=4$ -000625 -p20230518 2023届高三11班 0.429 -p20230518 2023届高三12班 0.565 -p20230518 2023届高三01班 0.933 -p20230518 2023届高三06班 0.921 -p20230518 2023届高三09班 0.467 +17471 +$28$ +17472 +$8.5$ -000616 -p20230518 2023届高三12班 1.000 -p20230518 2023届高三06班 0.947 +17473 +$(-3,+\infty)$ +17474 +$95.5$ -000617 -p20230518 2023届高三12班 1.000 -p20230518 2023届高三06班 1.000 -p20230518 2023届高三09班 1.000 +17475 +$(-4,0)cup \{2\sqrt{2}-2\}$ +17476 +$1518.5$ -000624 -p20230518 2023届高三12班 0.870 -p20230518 2023届高三09班 0.967 +17477 +A +17478 +D -013307 -p20230519 2023届高三11班 0.636 -p20230519 2023届高三12班 0.773 -p20230519 2023届高三08班 0.645 -p20230519 2023届高三09班 0.821 +17479 +B +17480 +B -000637 -p20230519 2023届高三11班 0.905 -p20230519 2023届高三08班 0.923 -p20230519 2023届高三09班 0.929 +17481 +(1) $a_n=n$, $b_n=2^{n-1}$; (2) 证明略 +17482 +(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\sqrt{3}}{3}$ -030154 -p20230519 2023届高三11班 0.286 -p20230519 2023届高三12班 0.208 -p20230519 2023届高三09班 0.286 - - -000636 -p20230519 2023届高三12班 0.958 -p20230519 2023届高三01班 1.000 -p20230519 2023届高三06班 0.975 -p20230519 2023届高三09班 0.964 - - -000654 -p20230526 2023届高三11班 0.316 -p20230526 2023届高三12班 0.524 -p20230526 2023届高三01班 0.846 -p20230526 2023届高三06班 0.707 -p20230526 2023届高三08班 0.667 -p20230526 2023届高三09班 0.611 - - -000655 -p20230526 2023届高三11班 0.474 -p20230526 2023届高三12班 0.476 -p20230526 2023届高三08班 0.333 -p20230526 2023届高三09班 0.500 - - -030162 -p20230526 2023届高三12班 0.857 -p20230526 2023届高三08班 1.000 -p20230526 2023届高三09班 0.833 - - -000669 -p20230526 2023届高三12班 0.737 -p20230526 2023届高三01班 1.000 -p20230526 2023届高三06班 0.949 -p20230526 2023届高三09班 0.870 - - -000672 -p20230526 2023届高三12班 0.684 -p20230526 2023届高三09班 0.826 - - -000673 -p20230526 2023届高三12班 0.368 -p20230526 2023届高三01班 0.750 -p20230526 2023届高三06班 0.692 -p20230526 2023届高三09班 0.522 - - -000675 -p20230526 2023届高三12班 0.526 -p20230526 2023届高三01班 0.750 -p20230526 2023届高三06班 0.744 -p20230526 2023届高三09班 0.478 - - -000685 -p20230530 2023届高三12班 0.857 -p20230530 2023届高三01班 1.000 -p20230530 2023届高三06班 0.925 -p20230530 2023届高三08班 0.897 +17483 +(1) $y=27\times (\dfrac{4}{3})^x$, $x\ge 0$; (2) $9$分钟 +17484 +(1) $6$; (2) $-4$; (3) $(2,0)$或$(-\dfrac{2}{7},-\dfrac{12}{7})$ +17485 +(1) 证明略; (2) $\dfrac{\mathrm{e}}{2}$; (3) $(-\dfrac{27}{\mathrm{e}^3},0)\cup (0,+\infty)$ diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 9ace1ac4..278c4a74 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -451298,6 +451298,426 @@ "space": "4em", "unrelated": [] }, + "017465": { + "id": "017465", + "content": "已知集合$A=\\{x \\| x | \\leq 1\\}, B=\\{-1,1,3,5\\}$, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\{-1,1\\}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题1", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017466": { + "id": "017466", + "content": "复数$z=\\dfrac{1-2 \\mathrm{i}}{3+\\mathrm{i}}$的模为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac{\\sqrt{2}}{2}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题2", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017467": { + "id": "017467", + "content": "不等式$\\dfrac{x+3}{x-1} \\geq 0$的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$(-\\infty,-3]\\cup (1,+\\infty)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题3", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017468": { + "id": "017468", + "content": "已知幂函数$y=f(x)$的图像过点$(\\dfrac{1}{2}, 8)$, 则$f(-2)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$-\\dfrac{1}{8}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题4", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017469": { + "id": "017469", + "content": "已知函数$f(x)=\\sin 2 x+2 \\sqrt{3} \\cos ^2 x$, 则函数$f(x)$的最小正周期是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\pi$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题5", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017470": { + "id": "017470", + "content": "由函数的观点, 不等式$2^x+\\log _4 x=17$的解是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$x=4$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题6", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017471": { + "id": "017471", + "content": "$(\\dfrac{1}{x}-\\sqrt{x})^8$的展开式中含$x$项的系数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$28$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题7", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017472": { + "id": "017472", + "content": "某单位为了解该单位党员开展学习党史知识活动情况, 随机抽取了部分党员, 对他们一周的党史学习时间进行了统计, 统计数据如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline 党史学习时间(小时) & 7 & 8 & 9 & 10 & 11 \\\\\n\\hline 党员人数 & 6 & 10 & 9 & 8 & 7 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n则该单位党员一周学习党史时间的第$40$百分位数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$8.5$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题8", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017473": { + "id": "017473", + "content": "若存在实数$a$, 使得$x=1$是方程$(x+a)^2=3 x+b$的解, 但不是方程$x+a=\\sqrt{3 x+b}$的解, 则实数$b$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$(-3,+\\infty)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题9", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017474": { + "id": "017474", + "content": "若随机变量$X \\sim N(105,19^2)$, $Y \\sim N(100,9^2)$, 若$P(X \\leq A)=P(Y \\leq A)$, 那么实数$A$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$95.5$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题10", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017475": { + "id": "017475", + "content": "已知曲线$C_1: |y|=x+2$与曲线$C_2: (x-a)^2+y^2=4$恰有两个公共点, 则实数$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$(-4,0)cup \\{2\\sqrt{2}-2\\}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题11", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017476": { + "id": "017476", + "content": "函数$y=f(x)$是最小正周期为$4$的偶函数, 且在$x \\in[-2,0]$时, $f(x)=2 x+1$, 若存在$x_1$、$x_2$、$\\cdots$、$x_n$满足$0 \\leq x_1=latex]\n\\draw [->] (-1.4,0) -- (1.4,0) node [below] {$x$};\n\\draw [->] (0,-0.6) -- (0,0.6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1.4] plot (\\x,{pow(\\x-0.2,3)-\\x+0.2});\n\\end{tikzpicture}\n\\end{center}\n\\fourch{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.4,0) -- (1.4,0) node [below] {$x$};\n\\draw [->] (0,-0.6) -- (0,0.6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1.4] plot (\\x,{-(\\x+1)*(\\x-1.3)*(\\x+0.5)*(\\x-0.2)/1.5});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.4,0) -- (1.4,0) node [below] {$x$};\n\\draw [->] (0,-0.6) -- (0,0.6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1.4] plot (\\x,{(\\x+1)*(\\x-1.3)*(\\x+0.5)*(\\x-0.2)/1.5});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.4,0) -- (1.4,0) node [below] {$x$};\n\\draw [->] (0,-0.6) -- (0,0.6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1.4] plot (\\x,{-2.5*(0.05 + 0.192*\\x - 0.44* \\x*\\x - 0.2*pow(\\x,3)+ pow(\\x,4)/4)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.4,0) -- (1.4,0) node [below] {$x$};\n\\draw [->] (0,-0.6) -- (0,0.6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1.4] plot (\\x,{2.5*(0.15 + 0.192*\\x - 0.44* \\x*\\x - 0.2*pow(\\x,3)+ pow(\\x,4)/4)});\n\\end{tikzpicture}}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "D", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题14", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017479": { + "id": "017479", + "content": "已知函数$f(x)=a x^2+|x+a+1|$为偶函数, 则不等式$f(x)>0$的解集为\\bracket{20}.\n\\fourch{$\\varnothing$}{$(-1,0) \\cup(0,1)$}{$(-1,1)$}{$(-\\infty,-1) \\cup(1,+\\infty)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "B", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题15", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017480": { + "id": "017480", + "content": "已知$n \\in \\mathbf{N}$, $n\\ge 1$, 集合$A=\\{\\sin (\\dfrac{k \\pi}{n}) | k \\in \\mathbf{N},\\ 0 \\leq k \\leq n\\}$, 若集合$A$恰有$8$个子集, 则$n$的可能值有\\bracket{20}个.\n\\fourch{$1$}{$2$}{$3$}{$4$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "B", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题16", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "017481": { + "id": "017481", + "content": "已知$\\{a_n\\}$为等差数列, $\\{b_n\\}$为等比数列, $a_1=b_1=1$, $a_5=5(a_4-a_3)$, $b_5=4(b_4-b_3)$.\\\\\n(1) 求$\\{a_n\\}$和$\\{b_n\\}$的通项公式;\\\\\n(2) 记$\\{a_n\\}$的前$n$项和为$S_n$, 求证: $S_n S_{n+2}=latex]\n\\draw (0,0,0) node [above right] {$D$} coordinate (D);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\draw (0,0,1) node [left] {$A$} coordinate (A);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (P)--(A)--(B)--(C)--cycle(P)--(B);\n\\draw [dashed] (A)--(D)--(C)(D)--(B)(D)--(P);\n\\end{tikzpicture}\n\\end{center}\n(1) 求异面直线$AB$与$PC$所成角的大小;\\\\\n(2) 求二面角$B-PC-D$的余弦值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $\\dfrac{\\pi}{4}$; (2) $\\dfrac{\\sqrt{3}}{3}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题18", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "017483": { + "id": "017483", + "content": "流行性感冒简称流感, 是流感病毒引起的急性呼吸道感染, 也是一种传染性强、传播速度快的疾病, 了解引起流感的某些细菌、病毒的生存条件、繁殖习性等对于预防流感的传播有极其重要的意义, 某科研团队在培养基中放入一定是某种细菌进行研究. 经过$2$分钟菌落的覆盖面积为$48 \\text{mm}^2$, 经过$3$分钟覆盖面积为$64 \\text{mm}^2$, 后期其蔓延速度越来越快; 菌落的覆盖面积$y$(单位: $\\text{mm}^2$) 与经过时间$x$(单位: $\\text{min}$) 的关系现有三个函数模型: \\textcircled{1} $y=k a^x$($k>0$, $a>1$); \\textcircled{2} $y=\\log _b x$($b>1$); \\textcircled{3} $y=p \\sqrt{x}+q$($p>0$)可供选择.\\\\\n(1) 选出你认为符合实际的函数模型, 说明理由, 并求出该模型的解析式;\\\\\n(2) 在理想状态下, 至少经过多少分钟培养基中菌落的覆盖面积能超过$300 \\text{mm}^2$?(结果保留到整数)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $y=27\\times (\\dfrac{4}{3})^x$, $x\\ge 0$; (2) $9$分钟", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题19", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "017484": { + "id": "017484", + "content": "在平面直角坐标系$x O y$中, 已知椭圆$E: \\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$的左、右焦点分别为$F_1$、$F_2$, 点$A$在椭圆$E$上且在第一象限内, $AF_2 \\perp F_1F_2$, 直线$AF_1$与椭圆$E$相交于另一点$B$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\path [name path = elli,draw] (0,0) ellipse (2 and {sqrt(3)});\n\\draw (-1,0) node [above left] {$F_1$} coordinate (F_1);\n\\draw (1,0) node [below] {$F_2$} coordinate (F_2);\n\\path [name path = AF2] (F_2) --++ (0,2);\n\\path [name intersections = {of = AF2 and elli, by = A}];\n\\draw (A) node [above] {$A$} --(F_2); \n\\path [name path = AB] (A) -- ($(F_1)!-0.5!(A)$);\n\\path [name intersections = {of = AB and elli, by = B}];\n\\draw (A)--(B) node [left] {$B$} -- (O) -- cycle;\n\\end{tikzpicture}\n\\end{center}\n(1) 求$\\triangle AF_1F_2$的周长;\\\\\n(2) 在$x$轴上任取一点$P$, 直线$AP$与椭圆$E$的右准线相交于点$Q$, 求$\\overrightarrow{OP} \\cdot \\overrightarrow{QP}$的最小值;\\\\\n(3)设点$M$在椭圆$E$上, 记$\\triangle OAB$与$\\triangle MAB$的面积分别为$S_1$、$S_2$, 若$S_2=3S_1$, 求点$M$的坐标.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $6$; (2) $-4$; (3) $(2,0)$或$(-\\dfrac{2}{7},-\\dfrac{12}{7})$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题20", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "017485": { + "id": "017485", + "content": "记$y=f'(x)$、$y=g'(x)$分别为函数$y=f(x)$、$y=g(x)$的导函数, 若存在$x_0 \\in \\mathbf{R}$, 满足$f(x_0)=g(x_0)$且$f'(x_0)=g'(x_0)$, 则称$x_0$为函数$f(x)$与$g(x)$的一个``$S$点''.\\\\\n(1) 证明: 函数$y=x$与$y=x^2+2 x-2$不存在``$S$点'';\\\\\n(2) 若函数$y=a x^2-1$与$y=\\ln x$存在``$S$点'', 求实数$a$的值;\\\\\n(3) 已知$f(x)=-x^2+a$, $g(x)=\\dfrac{b \\mathrm{e}^x}{x}$, 若存在实数$a>0$, 使函数$y=f(x)$与$y=g(x)$在区间$(0,+\\infty)$内存在``$S$点'', 求实数$b$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 证明略; (2) $\\dfrac{\\mathrm{e}}{2}$; (3) $(-\\dfrac{27}{\\mathrm{e}^3},0)\\cup (0,+\\infty)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届交大附中三模试题21", + "edit": [ + "20230602\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "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.",