From e1ebd54f9139236243cc7f7799b13729e69fd2c7 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Sun, 4 Feb 2024 14:56:54 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A5=E9=AB=98=E4=BA=8C=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A11?= 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 | 248 +++++++++++++++++++++++++++++-- 2 files changed, 242 insertions(+), 9 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 d6f8945f..7ea7348f 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 @@ -349,3 +349,6 @@ 20240204-144112 高二寒假作业10 024538:024541,019480,024542:024543,040820,024544:024546,016469 +20240204-145635 高二寒假作业11 +024547,003392,023692,024548:024556 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 77dd2f08..72b86946 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -74725,7 +74725,8 @@ ], "same": [], "related": [ - "023690" + "023690", + "024548" ], "remark": "", "space": "", @@ -106829,7 +106830,9 @@ "20220701\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024553" + ], "remark": "", "space": "", "unrelated": [] @@ -299184,7 +299187,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024551" + ], "remark": "", "space": "4em", "unrelated": [] @@ -369195,7 +369200,9 @@ "20230118\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024555" + ], "remark": "", "space": "", "unrelated": [] @@ -543165,7 +543172,9 @@ "same": [ "020317" ], - "related": [], + "related": [ + "024548" + ], "remark": "", "space": "", "unrelated": [] @@ -546726,7 +546735,9 @@ "same": [ "020190" ], - "related": [], + "related": [ + "024548" + ], "remark": "", "space": "", "unrelated": [] @@ -645504,7 +645515,8 @@ ], "same": [], "related": [ - "002292" + "002292", + "024548" ], "remark": "", "space": "", @@ -664629,6 +664641,220 @@ "space": "4em", "unrelated": [] }, + "024547": { + "id": "024547", + "content": "如果原点在圆 $x^2+y^2+x+3 y-a=0$ 的外部, 则实数 $a$ 的取值范围是\\blank{50};", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "040908" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024548": { + "id": "024548", + "content": "若实数 $x, y$ 满足 $x^2+y^2-2 x+4 y=0$, 则 $x-y$ 的最大值为\\blank{50}, 最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "002292", + "023690", + "020190", + "020317" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024549": { + "id": "024549", + "content": "对于圆 $x^2+(y+1)^2=1$ 上的任意一点, 恒有 $x+y+m>0$, 则实数 $m$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024550": { + "id": "024550", + "content": "若 $A(a, a^2)$, $B(b, b^2)$($a \\neq b$) 两点的坐标满足方程 $a^2 \\sin \\theta+a \\cos \\theta=1$, $b^2 \\sin \\theta+b \\cos \\theta=1$, 圆 $C: x^2+y^2=1$, 则圆 $C$ 与直线 $AB$ 的位置关系是\\blank{50}(相交, 相切或者相离).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024551": { + "id": "024551", + "content": "过点 $A(1,4)$, 且与已知圆 $M: x^2+y^2-6 x-2 y+5=0$ 切于点 $B(1,2)$ 的圆 $C$ 的方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "010655" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024552": { + "id": "024552", + "content": "圆心在直线 $x-y-1=0$ 上, 与直线 $4 x+3 y+14=0$ 相切, 且截直线 $3 x+4 y+10=0$ 所得的弦长等于 6 的圆的方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024553": { + "id": "024553", + "content": "``$D^2=4F$''是``圆 $x^2+y^2+D x+E y+F=0$ 与 $x$ 轴相切''的\\bracket{20}.\n\\fourch{充分非必要条件}{必要非充分条件}{充要条件}{非充分非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "040918", + "003396" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024554": { + "id": "024554", + "content": "直线 $l$ 过点 $P(0,2)$, 且被圆 $x^2+y^2=4$ 所截得的线段长为 $2$, 那么直线 $l$ 的斜率为 \\bracket{20}.\n\\fourch{$\\sqrt{2}$ 或 $-\\sqrt{2}$}{$\\dfrac{\\sqrt{2}}{2}$ 或 $-\\dfrac{\\sqrt{2}}{2}$}{$\\sqrt{3}$ 或 $-\\sqrt{3}$}{$\\dfrac{\\sqrt{3}}{3}$ 或 $-\\dfrac{\\sqrt{3}}{3}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024555": { + "id": "024555", + "content": "若直线 $y=x+\\log _2 t$ 与曲线 $y=\\sqrt{4-x^2}$ 恰有一个公共点, 求实数 $t$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "013118" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024556": { + "id": "024556", + "content": "如图, 在平面直角坐标系中, 方程为 $x^2+y^2+D x+E y+F=0$ 的圆 $M$ 的内接四边形 $ABCD$的对角线 $AC$ 和 $BD$ 互相垂直, 且 $AC$ 和 $BD$ 分别在 $x$ 轴和 $y$ 轴上.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [name path = x,->] (-2,0) -- (2.5,0) node [below] {$x$};\n\\draw [name path = y,->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$} coordinate (O);\n\\draw [name path = circle] (0.5,0.9) circle (1.5) node [above] {$M$} coordinate (M);\n\\filldraw (M) circle (0.03);\n\\draw [name intersections = {of = circle and x, by = {A,C}}];\n\\draw (A) node [below left] {$A$};\n\\draw (C) node [below right] {$C$};\n\\draw [name intersections = {of = circle and y, by = {D,B}}];\n\\draw (B) node [below left] {$B$};\n\\draw (D) node [above left] {$D$};\n\\draw (A)--(B)--(C)--(D)--cycle;\n\\draw ($(C)!0.5!(D)$) node [above right] {$G$} coordinate (G);\n\\filldraw (G) circle (0.03);\n\\draw ($(A)!(O)!(B)$) node [below left] {$H$} coordinate (H);\n\\draw (O)--(H);\n\\filldraw (H) circle (0.03) (O) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $F<0$;\\\\\n(2) 若四边形 $ABCD$ 面积为 $8$, 对角线 $AC$ 长为 $2$, 且 $\\overrightarrow{AB}\\cdot \\overrightarrow{AD}=0$, 求 $D^2+E^2-4F$ 的值;\\\\\n(3) 设四边形 $ABCD$ 的一条边 $CD$ 的中点为 $G$, $OH \\perp AB$ 且垂足为 $H$. 试用平面解析几何的研究方法判断点 $O$、$G$、$H$ 是否共线, 并说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\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