From 79b5ec4afca61b8512e21419dc83d96462919661 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sat, 6 Jan 2024 21:21:02 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A52025=E5=B1=8A=E5=91=A8?= =?UTF-8?q?=E6=9C=AB=E5=8D=B709=E8=A1=A5=E5=85=85=E9=A2=98=E7=9B=AE?= =?UTF-8?q?=E5=B9=B6=E5=BD=95=E5=85=A5related?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 283 +++++++++++++++++++++++++++++++++++++++++- 1 file changed, 279 insertions(+), 4 deletions(-) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index bd31fb5c..c0900807 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -14445,7 +14445,9 @@ "20220624\t朱敏慧, 王伟叶" ], "same": [], - "related": [], + "related": [ + "023233" + ], "remark": "", "space": "", "unrelated": [] @@ -117357,7 +117359,9 @@ "20220701\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023227" + ], "remark": "", "space": "", "unrelated": [] @@ -259514,7 +259518,8 @@ "same": [], "related": [ "009254", - "009255" + "009255", + "023229" ], "remark": "", "space": "4em", @@ -417173,7 +417178,9 @@ "20230413\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023235" + ], "remark": "", "space": "", "unrelated": [] @@ -621867,6 +621874,274 @@ "space": "4em", "unrelated": [] }, + "023224": { + "id": "023224", + "content": "若 $m$ 是小于 $10$ 的正整数, 则 $(15-m)(16-m) \\cdots(20-m)$ 等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023225": { + "id": "023225", + "content": "若把``hello''这个单词的五个字母随机排序, 可以组成\\blank{50}个不同的单词.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023226": { + "id": "023226", + "content": "现有 $4$ 种不同颜色, 要对如图所示的四个部分进行着色, 要求有公共边界的两部分不能用同一种颜色, 则不同的着色方法共有\\blank{50}种.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw (0,0) rectangle (3,3);\n\\draw (0,1) -- (3,1) (0,2) -- (3,2) (1.5,1) -- (1.5,2);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023227": { + "id": "023227", + "content": "三个人踢毽子, 互相传递, 每人每次只能踢一下, 从甲开始踢, 经过 $4$ 次传递后, 毽子又被踢回给甲, 则不同的传递方式共有\\blank{50}种.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [ + "003812" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023228": { + "id": "023228", + "content": "$\\{1,2\\}\\subset A \\subset\\{1,2,3,4,5\\}$, 且集合 $A$ 中恰有 $4$ 个元素, 则这样的集合 $A$ 共有\\blank{50}个.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023229": { + "id": "023229", + "content": "由 $0$、$1$、$2$、$3$、$4$、$5$ 这 6 个数字共可以组成\\blank{50}个没有重复数字的四位偶数.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [ + "009269" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023230": { + "id": "023230", + "content": "罗马数字是欧洲在阿拉伯数字传入之前使用的一种数码, 它的产生标志着一种古代文明的进步. 罗马数字的表示法如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}\n\\hline 数字 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\\\n\\hline 形式 & I & II & III & IV & V & VI & VII & VIII & IX \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n其中``I\"需要 $1$ 根火柴,``$V$ \"与``$X$ \"需要 $2$ 根火柴, 若为 $0$, 则用空位表示. (如 $123$ 表示为\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw (0,0) rectangle (3,1);\n\\draw (1,0) -- (1,1) (2,0) -- (2,1);\n\\draw (0.5,0.5) node {I} (1.5,0.5) node {II} (2.5,0.5) node {III};\n\\end{tikzpicture}, $405$表示为\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw (0,0) rectangle (3,1);\n\\draw (1,0) -- (1,1) (2,0) -- (2,1);\n\\draw (0.5,0.5) node {IV} (2.5,0.5) node {V};\n\\end{tikzpicture})如果把$6$根火柴以适当的方式全部放入下面的表格中, 那么可以表示的不同的三位数的个数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023231": { + "id": "023231", + "content": "对于自然数 $n$ 作竖式运算 $n+(n+1)+(n+2)$ 时不进位, 那么称 $n$ 是``良数''. 如``32 \"是``良数'', 由于计算 $32+33+34$ 时不进位, ``23''不是``良数'', 由于 $23+24+25$ 时要进位, 那么小于 $1000$ 的``良数''有\\blank{50}个.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023232": { + "id": "023232", + "content": "设无穷等比数列 $\\{a_n\\}$ 的公比为 $q$, 首项 $a_1>0$, 若 $\\displaystyle\\lim _{n \\to \\infty}(a_2+a_3+\\cdots+a_n)>2 a_1$, 则公比 $q$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023233": { + "id": "023233", + "content": "已知数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n=2^n-a$($a \\neq 1$), 则此数列的通项公式 $a_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [ + "000408" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023234": { + "id": "023234", + "content": "设数列 $\\{a_n\\}$ 是等差数列, $a_5=6$.\\\\\n(1) 当 $a_3=3$ 时, 请在数列 $\\{a_n\\}$ 中找到一项 $a_m$, 使得 $a_3, a_5, a_m$ 成等比数列.\\\\\n(2) 当 $a_3=2$ 时, 若 $k_1, k_2, \\cdots, k_n$($n \\in \\mathbf{N}$ 且 $n \\geq 1$) 满足 $5a_{n+1}$, 求实数 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [ + "015089" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023236": { + "id": "023236", + "content": "已知数列 $\\{a_n\\}$ 是首项 $a_1=\\dfrac{1}{4}$, 公比 $q=\\dfrac{1}{4}$ 的等比数列, 设 $b_n+2=3 \\log _{\\frac{1}{4}}a_n $($n \\in \\mathbf{N}$ 且 $n \\geq 1$), 数列 $\\{c_n\\}$ 满足 $c_n=a_n b_n$.\\\\\n(1) 证明: 数列 $\\{b_n\\}$ 是等差数列.\\\\\n(2) 求数列 $\\{c_n\\}$ 的前 $n$ 项和 $S_n$.\\\\\n(3) 若 $c_n \\leq \\dfrac{1}{4}m^2+m-1$ 对一切正整数 $n$ 恒成立, 求实数 $m$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "25届周末卷补充题目", + "edit": [ + "20240106\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0