From 875e8314dbeb3bc8c76f4b1731f345b2901adc61 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 15:14:43 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A=E8=AF=95=E5=8D=B703=E6=96=B0?= =?UTF-8?q?=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 292 ++++++++++++++++++++++++++++++- 2 files changed, 293 insertions(+), 2 deletions(-) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index fe3e30c6..e55e8e05 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -217,3 +217,6 @@ 20240125-150948 024171:024172,000737,024173,013397,024174:024183 +20240125-151424 +024184:024196,009093,024197 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 9c3b2862..823d35b2 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -205401,7 +205401,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024191" + ], "remark": "", "space": "4em", "unrelated": [] @@ -493904,7 +493906,9 @@ "20230705\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024184" + ], "remark": "", "space": "4em", "unrelated": [] @@ -650645,6 +650649,290 @@ "space": "4em", "unrelated": [] }, + "024184": { + "id": "024184", + "content": "若角 $\\alpha$ 的终边经过点 $P(2,-3)$, 则角 $\\alpha$ 的余弦值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "018330" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024185": { + "id": "024185", + "content": "已知 $\\mathrm{i}$ 为虚数单位, 若复数 $z=\\dfrac{\\mathrm{i}}{\\sqrt{2}+\\mathrm{i}}$, 则 $z \\cdot \\overline{z}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024186": { + "id": "024186", + "content": "化简: $\\dfrac{\\sin (2 \\pi-\\alpha) \\tan (\\pi+\\alpha) \\tan (-\\alpha-\\dfrac{\\pi}{2})}{\\cos (\\pi-\\alpha) \\tan (3 \\pi-\\alpha)}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024187": { + "id": "024187", + "content": "若函数 $f(x)=\\sin (k x+\\dfrac{\\pi}{5})$ 的最小正周期为 $\\dfrac{2 \\pi}{3}$, 则实数 $k=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024188": { + "id": "024188", + "content": "已知向量 $\\overrightarrow{a}$、$\\overrightarrow{b}$ 满足 $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|=2$, 且向量 $\\overrightarrow{a}$、$\\overrightarrow{b}$ 的夹角为 $\\dfrac{\\pi}{4}$, 若 $\\overrightarrow{a}-\\lambda \\overrightarrow{b}$ 与 $\\overrightarrow{b}$ 垂直, 则实数 $\\lambda$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024189": { + "id": "024189", + "content": "设 $\\theta \\in(0, \\dfrac{\\pi}{2})$. 若关于 $x$ 的方程 $(\\sin \\theta+\\cos \\theta)^2=2^x+2^{-x}$ 有解, 则 $\\dfrac{1}{\\sin \\theta}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024190": { + "id": "024190", + "content": "锐角 $\\triangle ABC$ 中, 若 $\\tan C=2$, 则 $\\dfrac{\\sin A}{\\sin B}$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024191": { + "id": "024191", + "content": "计算: $1+2 \\mathrm{i}+3 \\mathrm{i}^2+4 \\mathrm{i}^3+5 \\mathrm{i}^4+\\cdots+2021 \\mathrm{i}^{2020}+2022 \\mathrm{i}^{2021}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "007097" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024192": { + "id": "024192", + "content": "已知 $\\triangle ABC$ 是边长为 $2 \\sqrt{3}$ 的正三角形, $PQ$ 为 $\\triangle ABC$ 外接圆 $O$ 的一条直径, 若 $M$ 为 $\\triangle ABC$ 边上的动点, 则 $\\overrightarrow{PM}\\cdot \\overrightarrow{MQ}$ 的最大值是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024193": { + "id": "024193", + "content": "下列命题中, 正确的是\\bracket{20}.\n\\onech{复数与它的共轭复数的差是纯虚数}{$z_1^2+z_2^2=0$ 是复数 $z_1=z_2=0$ 的充要条件}{复数 $Z$ 为纯虚数的必要非充分条件是 $Z+\\overline{Z}=0$}{任何两个复数都不可以比较大小}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024194": { + "id": "024194", + "content": "点 $O$ 在 $\\triangle ABC$ 所在平面内, 给出下列关系式:\\\\\n\\textcircled{1} $\\overrightarrow{OA}+\\overrightarrow{OB}+\\overrightarrow{OC}=\\overrightarrow{0}$;\\\\\n\\textcircled{2} $\\overrightarrow{OA}\\cdot \\overrightarrow{OB}=\\overrightarrow{OB}\\cdot \\overrightarrow{OC}=\\overrightarrow{OC}\\cdot \\overrightarrow{OA}$;\\\\\n\\textcircled{3} $\\overrightarrow{OA}\\cdot(\\dfrac{1}{|\\overrightarrow{AC}|}\\overrightarrow{AC}-\\dfrac{1}{|\\overrightarrow{AB}|}\\overrightarrow{AB})=\\overrightarrow{OB}\\cdot(\\dfrac{1}{|\\overrightarrow{BC}|}\\overrightarrow{BC}-\\dfrac{1}{|\\overrightarrow{BA}|}\\overrightarrow{BA})=0$;\\\\\n\\textcircled{4} $(\\overrightarrow{OA}+\\overrightarrow{OB}) \\cdot \\overrightarrow{AB}=(\\overrightarrow{OB}+\\overrightarrow{OC}) \\cdot \\overrightarrow{BC}=0$.\\\\\n则点 $O$ 依次为 $\\triangle ABC$ 的\\bracket{20}.\n\\twoch{内心、外心、重心、垂心}{重心、外心、内心、垂心}{重心、垂心、内心、外心}{外心、内心、垂心、重心}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024195": { + "id": "024195", + "content": "已知 $\\overrightarrow{OP}=(2,1)$, $\\overrightarrow{OA}=(1,7)$, $\\overrightarrow{OB}=(5,1)$, 设 $M$ 是直线 $OP$ 上一点 ($O$ 为坐标原点).\\\\\n(1) 求使 $\\overrightarrow{MA}\\cdot \\overrightarrow{MB}$ 取最小值时的 $\\overrightarrow{OM}$;\\\\\n(2) 对 (1) 中的点 $M$, 求 $\\angle AMB$ 的值 (结果用反三角函数值表示).", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024196": { + "id": "024196", + "content": "如图, 某快递小哥从 $A$ 地出发, 沿小路 $AB \\to BC$ 以平均时速 $20 \\mathrm{km}/ \\mathrm{h}$, 送快件到 $C$处, 已知 $BD=10 \\mathrm{km}$, $\\angle DCB=45^{\\circ}$, $\\angle CDB=30^{\\circ}, \\triangle ABD$ 是等腰三角形, $\\angle ABD=120^{\\circ}$.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (2,0) node [right] {$D$} coordinate (D);\n\\draw (-120:2) node [left] {$A$} coordinate (A);\n\\draw (105:{2/sin(45)*sin(30)}) node [left] {$C$} coordinate (C);\n\\draw (C)--(B)--(A)--(D)--cycle(B)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 试问, 快递小哥能否在 $50 \\mathrm{min}$ 内将快件送到 $C$ 处?\\\\\n(2) 快递小哥出发 $15 \\mathrm{min}$ 后, 快递公司发现快件有重大问题, 由于通信不畅, 公司只能派车沿大路 $AD arrow DC$ 追赶, 若汽车平均时速 $60 \\mathrm{km}/ \\mathrm{h}$, 问汽车能否先到达 $C$ 处?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024197": { + "id": "024197", + "content": "如图, 点 $P$ 在直径 $AB=1$ 的半圆上移动 (点 $P$ 不与 $A$、$B$ 重合), 过 $P$ 作圆的切线 $PT$, 且 $PT=1$, $\\angle PAB=\\alpha$. 过点 $B$ 作 $BC \\perp PT$ 于点 $C$.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 2.5]\n\\def\\t{110}\n\\def\\s{60}\n\\draw (\\t:0.5) node [above] {$A$} coordinate (A);\n\\draw ({\\t-180}:0.5) node [below] {$B$} coordinate (B);\n\\draw (\\s:0.5) node [above] {$P$} coordinate (P);\n\\draw (P) ++ ({\\s-90}:1) node [right] {$T$} coordinate (T);\n\\draw ($(P)!(B)!(T)$) node [above right] {$C$} coordinate (C);\n\\draw (A)--(B)--(T)--(P)--cycle(P)--(B)--(C);\n\\draw (B) arc ({\\t-180}:\\t:0.5);\n\\draw [dashed] (B) arc ({\\t+180}:\\t:0.5);\n\\draw pic [draw, \"$\\alpha$\", scale = 0.5, angle eccentricity = 1.8] {angle = B--A--P};\n\\end{tikzpicture}\n\\end{center}\n(1) 求三角形 $PAB$ 的面积 (用 $\\alpha$ 表示);\\\\\n(2) 当 $\\alpha$ 为何值时, 四边形 $ABTP$ 的面积最大?\\\\\n(3) 求 $PA+PB+PC$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "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