From 10019b753c7bda295df1f332d7ec1905e6af3b77 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Wed, 10 Apr 2024 19:39:51 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A5=E9=AB=98=E4=B8=89=E8=B0=83?= =?UTF-8?q?=E7=A0=94=E5=8D=B7=E6=96=B0=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 | 370 ++++++++++++++++++++++++++++++- 2 files changed, 370 insertions(+), 3 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 68049a02..ff1f3be1 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 @@ -487,3 +487,6 @@ 20240410-185350 高三测验卷04 032200:032201,040446,032202:032215,004285,015098,032216:032217 +20240410-193931 高三调研卷01 +011693:011694,012722,032218:032220,003659,032221:032222,011725,032223:032233 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index de87d775..c34bc21f 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -332040,7 +332040,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "032219" + ], "remark": "", "space": "4em", "unrelated": [] @@ -378970,7 +378972,9 @@ "20221212\t王伟叶" ], "same": [], - "related": [], + "related": [ + "032218" + ], "remark": "", "space": "", "unrelated": [] @@ -732709,7 +732713,9 @@ "edit": [ "20240131\t毛培菁" ], - "same": [], + "same": [ + "032223" + ], "related": [], "remark": "", "space": "", @@ -813985,6 +813991,364 @@ "space": "4em", "unrelated": [] }, + "032218": { + "id": "032218", + "content": "函数 $y=3 \\cos x-4 \\sin x$ 的最大值为 \\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [ + "012357" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "032219": { + "id": "032219", + "content": "$(x-1)^7$ 的二项式展开式中,系数最大的项为 \\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [ + "010881" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "032220": { + "id": "032220", + "content": "若 $f(x)$ 满足 $\\displaystyle\\lim _{h \\rightarrow 0}\\dfrac{f(2)-f(2+h)}{h}=1$, 则曲线 $y=f(x)$ 在点 $(2, f(2))$ 处切线的倾斜角为 \\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032221": { + "id": "032221", + "content": "若直线 $x+2 y+5=0$ 经过双曲线 $\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$ 的一个焦点, 且与该双曲线的一条渐近线平行,则该双曲线的方程为 \\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032222": { + "id": "032222", + "content": "设 $x$、$y \\in \\mathbf{R}$, 若 $1,5, x, y$ 的平均数为 4 , 则这四个数的中位数的取值范围是 \\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032223": { + "id": "032223", + "content": "$A$、$B$、$C$ 三位好友进行乒乓球循环赛, $A$、$B$ 先进行一局决胜负,负者下, 由 $C$ 挑战 $A$ 、 $B$ 的胜者, 继续进行一局决胜负,负者下,胜者下一局再接受第三人的挑战, 依此进行. 假设三人水平接近,任意两人的对决获胜的概率都是 0.5 且不受体力影响,已知三人共比赛了 3 局,那么这 3 局中三人各胜一局的概率为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [ + "024314" + ], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032224": { + "id": "032224", + "content": "如图,平面内一条长度为 $d$ 的线段 $AB$ 恰好能通过直角拐角,拐角点 $P$ 到 $O x$ 所在直线的距离为 $1 \\mathrm{m}$, 到 $O y$ 所在直线的距离为 $2 m$, 若 $AB$ 恰好过 $P$ 点才能通过拐角, 则 $d$ 的值约为\\blank{50}$\\mathrm{m}$. (结果精确到 $0.01 \\mathrm{m}$)\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (5,0) node [below] {$x$} coordinate (x);\n\\draw (2,1) node [above right] {$P$} coordinate (P);\n\\draw (0,3.5) node [left] {$y$} coordinate (y);\n\\draw (x)--(O)--(y)(x)++(0,1) --(P)--++(0,2.5);\n\\draw [ultra thick] (0.5,0.3) node [left] {$B$} coordinate (B)--++ ({2*sqrt(5)},0) node [right] {$A$} coordinate (A);\n\\end{tikzpicture}\n\\hspace{4em}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (5,0) node [below] {$x$} coordinate (x);\n\\draw (2,1) node [above right] {$P$} coordinate (P);\n\\draw (0,3.5) node [left] {$y$} coordinate (y);\n\\draw (x)--(O)--(y)(x)++(0,1) --(P)--++(0,2.5);\n\\draw [ultra thick] (0,2) node [left] {$B$} coordinate (B)-- (4,0) node [below] {$A$} coordinate (A);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032225": { + "id": "032225", + "content": "若正数 $m$、$n$、$a$ 均不为 1 , 则下列不等式中与``$m>n$''等价的是\\bracket{20}.\n\\fourch{$\\log _a m>\\log _a n$}{$\\log _m a>\\log _n a$}{$m^a>n^a$}{$a^m>a^n$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032226": { + "id": "032226", + "content": "已知函数 $y=f(x)$, $x \\in \\mathbf{R}$ 为奇函数, 当 $x \\geq 0$ 时, $f(x)=2 x^3+2^x-1$, 当 $x<0$ 时, $f(x)$ 的表达式为\\bracket{20}.\n\\fourch{$2 x^3+2^x-1$}{$2 x^3-2^{-x}+1$}{$-2 x^3+2^{-x}-1$}{$-2 x^3-2^x+1$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032227": { + "id": "032227", + "content": "有下列几何对象: \\textcircled{1} 长度为 $1.7 \\mathrm{cm}$ 的短棍(粗细忽略不计); \\textcircled{2} 面积为 $1.1 \\mathrm{cm}^2$ 的正方形纸片\n(厚度忽略不计,不可折叠); \\textcircled{3} 体积为 $0.3 \\mathrm{cm}^3$ 的正四面体木块. 关于上述几何对象能否单独完全装入一个棱长为 $1 \\mathrm{cm}$ 的正方体盘子(壁厚度忽略不计),正确的结论是\\bracket{20}.\n\\fourch{仅\\textcircled{1}\\textcircled{2}能}{仅\\textcircled{2}\\textcircled{3}能}{仅\\textcircled{1} \\textcircled{3}能}{\\textcircled{1}\\textcircled{2}\\textcircled{3}均能}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032228": { + "id": "032228", + "content": "对于命题: \\textcircled{1}存在 $\\sin \\theta$、$\\cos \\theta$、$\\tan \\theta$ 的某个排列, 使得对任意 $\\theta \\in(0, \\dfrac{\\pi}{2})$, 这三个数均不能成等比数列;\\textcircled{2} 对 $\\sin \\theta$、$\\cos \\theta$、$\\tan \\theta$ 的任意排列, 均存在相应的 $\\theta \\in(0, \\dfrac{\\pi}{2})$, 使得这三个数成等差数列. 下列判断正确的是\\bracket{20}.\n\\twoch{\\textcircled{1}和\\textcircled{2}均为真命题}{\\textcircled{1}和\\textcircled{2}均为假命题}{\\textcircled{1} 为真命题. \\textcircled{2} 为假命题}{\\textcircled{1} 为假命题, \\textcircled{2} 为真命题}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032229": { + "id": "032229", + "content": "如图, 在正四棱锥 $P-ABCD$ 中, 点 $E$ 为 $PC$ 的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw ({-sqrt(2)},0,{sqrt(2)}) node [left] {$A$} coordinate (A);\n\\draw (A) ++ ({2*sqrt(2)},0,0) node [right] {$B$} coordinate (B);\n\\draw (B) ++ (0,0,{-2*sqrt(2)}) node [right] {$C$} coordinate (C);\n\\draw (C) ++ ({-2*sqrt(2)},0,0) node [below] {$D$} coordinate (D);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\draw ($(P)!0.5!(B)$) node [right] {$E$} coordinate (E);\n\\draw (A)--(B)--(C)--(P)--cycle (P)--(B) (A)--(E);\n\\draw [dashed] (P)--(D) (A)--(D)--(C) ;\n\\end{tikzpicture}\n\\end{center}\n(1) 若 $F$ 为 $PD$ 的中点,判断直线 $AF$ 与 $BE$ 的位置关系,并说明理由:\\\\\n(2) 正四棱锥 $P-ABCD$ 的各棱长均为 2 ,求直线 $BE$ 与底面 $ABCD$ 所成角的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "032230": { + "id": "032230", + "content": "袋中有大小和质地均相同的 10 个球,其中 4 个黄球, 6 个白球, 从中随机地摸出 3 个球, 用 $X$表示其中黄球的个数.\\\\\n(1) 采用不放回摸球,求 $X$ 的分布; \\\\\n(2) 采用有放回摸球,求 $X$ 的分布、期望和方差.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "032231": { + "id": "032231", + "content": "如图,某公园有一三角形的花坛 $ABC$,已知围栏 $BC$ 长 5 米, $AC$ 长 7 米, $B=60^{\\circ}$,拟在该花坛中修建一条直围栏 $PQ$ (即线段 $PQ$, 点 $P$、$Q$ 分别在三角形的两边上), 以种植两种不同颜色的菊花供游客观赏,花坛设计者希望通过围栏实现两种菊花的种植面积相等且同一时刻花坛边游客近距离赏花的人数的最大值相等.\n试问:在 $\\triangle ABC$ 的边上是否存在 $P$、$Q$ 两点,使得线段 $PQ$ 既平分 $\\triangle ABC$ 的面积又平分其周长?若存在,求出所有满足要求的点 $P$、$Q$ 的位置(结果精确到 $0.1$ 米);若不存在,请说明理由.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.4]\n\\draw (0,0) node [below] {$A$} coordinate (A);\n\\draw (8,0) node [below] {$B$} coordinate (B);\n\\draw (B) ++ (120:5) node [above] {$C$} coordinate (C);\n\\draw ($(A)!0.4!(C)$) coordinate (P);\n\\draw ($(B)!0.5!(C)$) coordinate (Q);\n\\draw (P)--(Q)(A)--(B)--(C)--cycle;\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "032232": { + "id": "032232", + "content": "已知函数 $y=f(x)$, $x \\in D$ 满足:在定义域 $D$ 内存在实数 $t$, 使得 $f(t+1)=f(t)+f(1)$. 设集合 $M$ 是满足上述性质的函数 $y=f(x)$ 的全体.\\\\\n(1) 若 $f(x)=3 x+2$, 判断函数 $y=f(x)$ 是否属于集合 $M$, 并说明理由;\\\\\n(2) 设 $a>0$, $f(x)=\\lg \\dfrac{a}{x^2+2}$, 若函数 $y=f(x)$ 属于集合 $M$, 求 $a$ 的取值范围;\\\\\n(3) 设 $b \\in \\mathbf{R}$, $f(x)=2^x+b x^2$, 求证:对任意实数 $b$, 函数 $y=f(x)$ 均属于集合 $M$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "032233": { + "id": "032233", + "content": "如图, 设椭圆 $\\Gamma: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1(a>b>0), F_1$、$F_2$ 为 $\\Gamma$ 的左、右焦点,过点 $F_1$ 的直线 $l$ 与 $\\Gamma$ 交于 $A$、$B$ 两点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-3.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [name path = elli] (0,0) ellipse (3 and {3*sqrt(3)/2});\n\\filldraw (1.5,0) circle (0.05) node [below] {$F_2$} coordinate (F_2);\n\\filldraw (-1.5,0) circle (0.05) node [above] {$F_1$} coordinate (F_1);\n\\draw (100:3 and {3*sqrt(3)/2}) node [above] {$A$} coordinate (A);\n\\path [name path = AF1] (F_1)--($(A)!1.7!(F_1)$);\n\\draw [name intersections = {of = elli and AF1, by = B}];\n\\draw (B) node [below left] {$B$} -- (A)--(F_2)--cycle;\n\\end{tikzpicture}\n\\end{center}\n(1) 若椭圆 $\\Gamma$ 的离心率为 $\\dfrac{1}{2}, \\Delta F_1F_2A$ 的周长为 $6$, 求椭圆 $\\Gamma$ 的方程;\\\\\n(2) 求证: $\\dfrac{1}{|F_1A|}+\\dfrac{1}{|F_1B|}$ 为定值;\\\\\n(3) 是否存在直线 $l$, 使得 $\\triangle ABF_2$ 为等腰直角三角形? 若存在,求出 $\\Gamma$的离心率 $e$ 的值, 若不存在, 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": { + "来源": "自拟题目" + }, + "edit": [ + "20240410\t余利成" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "040001": { "id": "040001", "content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",