diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index ba4dfb5d..e5578b83 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -2,54 +2,70 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 14511\n", - "raworigin = \"2023届黄浦区一模试题\"\n", + "starting_id = 40001\n", + "raworigin = \"\"\n", "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", - "editor = \"20230217\\t王伟叶\"\n", - "indexed = True\n" + "editor = \"20230218\\t王伟叶\"\n", + "indexed = False\n" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "添加题号014511, 来源: 2023届黄浦区一模试题试题1\n", - "添加题号014512, 来源: 2023届黄浦区一模试题试题2\n", - "添加题号014513, 来源: 2023届黄浦区一模试题试题3\n", - "添加题号014514, 来源: 2023届黄浦区一模试题试题4\n", - "添加题号014515, 来源: 2023届黄浦区一模试题试题5\n", - "添加题号014516, 来源: 2023届黄浦区一模试题试题6\n", - "添加题号014517, 来源: 2023届黄浦区一模试题试题7\n", - "添加题号014518, 来源: 2023届黄浦区一模试题试题8\n", - "添加题号014519, 来源: 2023届黄浦区一模试题试题9\n", - "添加题号014520, 来源: 2023届黄浦区一模试题试题10\n", - "添加题号014521, 来源: 2023届黄浦区一模试题试题11\n", - "添加题号014522, 来源: 2023届黄浦区一模试题试题12\n", - "添加题号014523, 来源: 2023届黄浦区一模试题试题13\n", - "添加题号014524, 来源: 2023届黄浦区一模试题试题14\n", - "添加题号014525, 来源: 2023届黄浦区一模试题试题15\n", - "添加题号014526, 来源: 2023届黄浦区一模试题试题16\n", - "添加题号014527, 来源: 2023届黄浦区一模试题试题17\n", - "添加题号014528, 来源: 2023届黄浦区一模试题试题18\n", - "添加题号014529, 来源: 2023届黄浦区一模试题试题19\n", - "添加题号014530, 来源: 2023届黄浦区一模试题试题20\n", - "添加题号014531, 来源: 2023届黄浦区一模试题试题21\n" + "添加题号040001, 来源: 2024届高二下学期周末卷01\n", + "添加题号040002, 来源: 2024届高二下学期周末卷01\n", + "添加题号040003, 来源: 2024届高二下学期周末卷01\n", + "添加题号040004, 来源: 2024届高二下学期周末卷01\n", + "添加题号040005, 来源: 2024届高二下学期周末卷01\n", + "添加题号040006, 来源: 2024届高二下学期周末卷01\n", + "添加题号040007, 来源: 2024届高二下学期周末卷01\n", + "添加题号040008, 来源: 2024届高二下学期周末卷01\n", + "添加题号040009, 来源: 2024届高二下学期周末卷01\n", + "添加题号040010, 来源: 2024届高二下学期周末卷01\n", + "添加题号040011, 来源: 2024届高二下学期周末卷01\n", + "添加题号040012, 来源: 2024届高二下学期周末卷01\n", + "添加题号040013, 来源: 2024届高二下学期周末卷01\n", + "添加题号040014, 来源: 2024届高二下学期周末卷01\n", + "添加题号040015, 来源: 2024届高二下学期周末卷01\n", + "添加题号040016, 来源: 2024届高二下学期周末卷01\n", + "添加题号040017, 来源: 2024届高二下学期周末卷01\n", + "添加题号040018, 来源: 2025届高一下学期周末卷01\n", + "添加题号040019, 来源: 2025届高一下学期周末卷01\n", + "添加题号040020, 来源: 2025届高一下学期周末卷01\n", + "添加题号040021, 来源: 2025届高一下学期周末卷01\n", + "添加题号040022, 来源: 2025届高一下学期周末卷01\n", + "添加题号040023, 来源: 2025届高一下学期周末卷01\n", + "添加题号040024, 来源: 2025届高一下学期周末卷01\n", + "添加题号040025, 来源: 2025届高一下学期周末卷01\n", + "添加题号040026, 来源: 2025届高一下学期周末卷01\n", + "添加题号040027, 来源: 2025届高一下学期周末卷01\n", + "添加题号040028, 来源: 2025届高一下学期周末卷01\n", + "添加题号040029, 来源: 2025届高一下学期周末卷01\n", + "添加题号040030, 来源: 2025届高一下学期周末卷01\n", + "添加题号040031, 来源: 2025届高一下学期周末卷01\n", + "添加题号040032, 来源: 2025届高一下学期周末卷01\n", + "添加题号040033, 来源: 2025届高一下学期周末卷01\n", + "添加题号040034, 来源: 2025届高一下学期周末卷01\n", + "添加题号040035, 来源: 2025届高一下学期周末卷01\n", + "添加题号040036, 来源: 2025届高一下学期周末卷01\n" ] } ], "source": [ "import os,re,json\n", "\n", + "\n", "#从enumerate环境的字符串生成题目列表\n", "def GenerateProblemListFromString(data):\n", " try:\n", @@ -64,12 +80,13 @@ " for p in ProblemList_raw:\n", " startpos = data.index(p)\n", " tempdata = data[:startpos]\n", - " suflist = re.findall(r\"\\n\\%[\\dA-Za-z]+\",tempdata)\n", + " suflist = re.findall(r\"\\n(\\%[\\S]+)\\n\",tempdata)\n", " if len(suflist) > 0:\n", " suffix = suflist[-1].replace(\"%\",\"\").strip()\n", " else:\n", " suffix = \"\"\n", - " ProblemsList.append((p,suffix))\n", + " p_strip = re.sub(r\"\\n(\\%[\\S]+)$\",\"\",p).strip()\n", + " ProblemsList.append((p_strip,suffix))\n", " return ProblemsList\n", "\n", "# 创建新的空题目\n", @@ -136,26 +153,6 @@ " print(\"题号有重复, 请检查.\\n\"*5)" ] }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "''" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "suffix" - ] - }, { "cell_type": "code", "execution_count": null, diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index a9618b48..9f5620a5 100644 --- a/工具/讲义生成.ipynb +++ b/工具/讲义生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -15,9 +15,9 @@ "题块 2 处理完毕.\n", "正在处理题块 3 .\n", "题块 3 处理完毕.\n", - "开始编译教师版本pdf文件: 临时文件/高三下学期周末卷03_教师_20230217.tex\n", + "开始编译教师版本pdf文件: 临时文件/高三下学期周末卷04_教师_20230217.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/高三下学期周末卷03_学生_20230217.tex\n", + "开始编译学生版本pdf文件: 临时文件/高三下学期周末卷04_学生_20230217.tex\n", "0\n" ] } @@ -35,7 +35,7 @@ "\"\"\"---设置题块编号---\"\"\"\n", "\n", "problems = [\n", - "\"12697:12708\",\"12709:12712\",\"12713:12717\"\n", + "\"14511:14522\",\"14523:14526\",\"14527:14531\"\n", "]\n", "\n", "\"\"\"---设置结束---\"\"\"\n", @@ -49,7 +49,7 @@ "elif paper_type == 2:\n", " enumi_mode = 1 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n", " template_file = \"模板文件/测验周末卷模板.txt\" #设置模板文件名\n", - " exec_list = [(\"标题替换\",\"高三下学期周末卷03\")] #设置讲义标题\n", + " exec_list = [(\"标题替换\",\"高三下学期周末卷04\")] #设置讲义标题\n", " destination_file = \"临时文件/\"+exec_list[0][1] # 设置输出文件名\n", "elif paper_type == 3:\n", " enumi_mode = 0 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n", @@ -204,7 +204,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -223,7 +223,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 89cc8703..770fe03d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -54335,7 +54335,7 @@ }, "001963": { "id": "001963", - "content": "%2-**\n已知向量$\\overrightarrow{a}=(1,2,3)$, $\\overrightarrow{b}=(3,0,-1)$, $\\overrightarrow{c}=(-\\dfrac{1}{5},1,-\\dfrac{3}{5})$, 下述结论\\\\ \n(1) $|\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}|=|\\overrightarrow{a}-\\overrightarrow{b}-\\overrightarrow{c}|$; (2) $(\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c})^2=\\overrightarrow{a}^2+\\overrightarrow{b}^2+\\overrightarrow{c}^2$;\\\\ \n(3) $(\\overrightarrow{a}\\cdot\\overrightarrow{b})\\overrightarrow{c}=(\\overrightarrow{b}\\cdot \\overrightarrow{c})\\overrightarrow{a}$; (4) $(\\overrightarrow{a}+\\overrightarrow{b})\\cdot \\overrightarrow{c}=\\overrightarrow{a}\\cdot (\\overrightarrow{b}-\\overrightarrow{c})$\\\\ \n中, 真命题有\\blank{50}.", + "content": "已知向量$\\overrightarrow{a}=(1,2,3)$, $\\overrightarrow{b}=(3,0,-1)$, $\\overrightarrow{c}=(-\\dfrac{1}{5},1,-\\dfrac{3}{5})$, 下述结论\\\\ \n(1) $|\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}|=|\\overrightarrow{a}-\\overrightarrow{b}-\\overrightarrow{c}|$; (2) $(\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c})^2=\\overrightarrow{a}^2+\\overrightarrow{b}^2+\\overrightarrow{c}^2$;\\\\ \n(3) $(\\overrightarrow{a}\\cdot\\overrightarrow{b})\\overrightarrow{c}=(\\overrightarrow{b}\\cdot \\overrightarrow{c})\\overrightarrow{a}$; (4) $(\\overrightarrow{a}+\\overrightarrow{b})\\cdot \\overrightarrow{c}=\\overrightarrow{a}\\cdot (\\overrightarrow{b}-\\overrightarrow{c})$\\\\ \n中, 真命题有\\blank{50}.", "objs": [ "K0627005X" ], @@ -54490,7 +54490,7 @@ }, "001968": { "id": "001968", - "content": "%1-**\n已知空间四点$A(1,-2,1)$, $B(2,-1,2)$, $C(3,2,-1)$, $D(1,1,-1)$, 有一点$E$, 使$\\overrightarrow{DE}\\perp \\overrightarrow\n{AB}$, $\\overrightarrow{DE}\\perp \\overrightarrow{AC}$, 且$|\\overrightarrow{DE}|=\\sqrt{14}$同时成立. 则$E$点的坐标为\\blank{50}.", + "content": "已知空间四点$A(1,-2,1)$, $B(2,-1,2)$, $C(3,2,-1)$, $D(1,1,-1)$, 有一点$E$, 使$\\overrightarrow{DE}\\perp \\overrightarrow\n{AB}$, $\\overrightarrow{DE}\\perp \\overrightarrow{AC}$, 且$|\\overrightarrow{DE}|=\\sqrt{14}$同时成立. 则$E$点的坐标为\\blank{50}.", "objs": [ "K0627006X" ], @@ -63718,7 +63718,7 @@ }, "002290": { "id": "002290", - "content": "圆$x^2+y^2-2x=3$与直线$y=ax+1$的交点个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{随$a$的不同而改变}%2 C", + "content": "圆$x^2+y^2-2x=3$与直线$y=ax+1$的交点个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{随$a$的不同而改变}", "objs": [ "K0711001X" ], @@ -349803,7 +349803,7 @@ }, "014416": { "id": "014416", - "content": "如图, 在三棱锥$D-ABC$中, 平而$ACD \\perp$平面$ABC$, $AD \\perp AC$, $AB \\perp BC$, $E$、$F$分别为棱$BC$, $CD$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (3,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,2.5,0) node [left] {$D$} coordinate (D);\n\\draw ({1.5+1.5*cos(80)},0,{1.5*sin(80)}) node [below] {$B$} coordinate (B);\n\\draw ($(B)!0.5!(C)$) node [below right] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(D)$) node [above] {$F$} coordinate (F);\n\\draw (D)--(A)--(B)--(C)--cycle(B)--(D)(E)--(F);\n\\draw [dashed] (A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: 直线$EF\\parallel$平面$ABD$;\\\\\n(2) 求证: 直线$BC \\perp$平面$ABD$;\\\\\n(3) 若直线$CD$与平面$ABC$所成的角的大小为$45^{\\circ}$, 直线$CD$与平面$ABD$所成角的大小为$30^{\\circ}$, 求二面角$B-AD-C$的大小.\n%15", + "content": "如图, 在三棱锥$D-ABC$中, 平而$ACD \\perp$平面$ABC$, $AD \\perp AC$, $AB \\perp BC$, $E$、$F$分别为棱$BC$, $CD$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (3,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,2.5,0) node [left] {$D$} coordinate (D);\n\\draw ({1.5+1.5*cos(80)},0,{1.5*sin(80)}) node [below] {$B$} coordinate (B);\n\\draw ($(B)!0.5!(C)$) node [below right] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(D)$) node [above] {$F$} coordinate (F);\n\\draw (D)--(A)--(B)--(C)--cycle(B)--(D)(E)--(F);\n\\draw [dashed] (A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: 直线$EF\\parallel$平面$ABD$;\\\\\n(2) 求证: 直线$BC \\perp$平面$ABD$;\\\\\n(3) 若直线$CD$与平面$ABC$所成的角的大小为$45^{\\circ}$, 直线$CD$与平面$ABD$所成角的大小为$30^{\\circ}$, 求二面角$B-AD-C$的大小.", "objs": [], "tags": [], "genre": "解答题", @@ -350164,7 +350164,7 @@ }, "014435": { "id": "014435", - "content": "已知正四棱锥的侧棱长为$l$, 其各顶点都在同一球面上. 若该球的体积为$36 \\pi$, 且$3 \\leq l \\leq 3 \\sqrt{3}$, 求该正四棱锥体积的取值范围.\n%16", + "content": "已知正四棱锥的侧棱长为$l$, 其各顶点都在同一球面上. 若该球的体积为$36 \\pi$, 且$3 \\leq l \\leq 3 \\sqrt{3}$, 求该正四棱锥体积的取值范围.", "objs": [], "tags": [], "genre": "解答题", @@ -350544,7 +350544,7 @@ }, "014455": { "id": "014455", - "content": "如图, 在三棱柱$ABC-A_1B_1C_1$中, 底面$ABC$是以$AC$为斜边的等腰直角三角形, 侧面$AA_1C_1C$为菱形, 点$A_1$在底面上的投影为$AC$的中点$D$, 且$AB=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (1,{sqrt(3)},0) node [above] {$A_1$} coordinate (A_1);\n\\draw (A_1) ++ (2,0,0) node [above] {$C_1$} coordinate (C_1);\n\\draw (1,0,0) node [above right] {$D$} coordinate (D);\n\\draw ($(A_1)+(B)-(A)$) node [below right] {$B_1$} coordinate (B_1);\n\\draw ($(A_1)!0.4!(B_1)$) node [above right] {$E$} coordinate (E);\n\\draw (A)--(B)--(C)--(C_1)--(A_1)--cycle(A_1)--(B_1)--(C_1)(B_1)--(B);\n\\draw [dashed] (A_1)--(D)--(E)(A)--(C)(B)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $BD \\perp CC_1$;\\\\\n(2) 求点$C$到侧面$AA_1B_1B$的距离;\\\\\n(3) 在线段$A_1B_1$上是否存在点$E$, 使得直线$DE$与侧面$AA_1B_1B$所成角的正弦值为$\\dfrac{\\sqrt{6}}{7}$? 若存在, 请求出$A_1E$的长; 若不存在, 请说明理由.\n%19", + "content": "如图, 在三棱柱$ABC-A_1B_1C_1$中, 底面$ABC$是以$AC$为斜边的等腰直角三角形, 侧面$AA_1C_1C$为菱形, 点$A_1$在底面上的投影为$AC$的中点$D$, 且$AB=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (1,{sqrt(3)},0) node [above] {$A_1$} coordinate (A_1);\n\\draw (A_1) ++ (2,0,0) node [above] {$C_1$} coordinate (C_1);\n\\draw (1,0,0) node [above right] {$D$} coordinate (D);\n\\draw ($(A_1)+(B)-(A)$) node [below right] {$B_1$} coordinate (B_1);\n\\draw ($(A_1)!0.4!(B_1)$) node [above right] {$E$} coordinate (E);\n\\draw (A)--(B)--(C)--(C_1)--(A_1)--cycle(A_1)--(B_1)--(C_1)(B_1)--(B);\n\\draw [dashed] (A_1)--(D)--(E)(A)--(C)(B)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $BD \\perp CC_1$;\\\\\n(2) 求点$C$到侧面$AA_1B_1B$的距离;\\\\\n(3) 在线段$A_1B_1$上是否存在点$E$, 使得直线$DE$与侧面$AA_1B_1B$所成角的正弦值为$\\dfrac{\\sqrt{6}}{7}$? 若存在, 请求出$A_1E$的长; 若不存在, 请说明理由.", "objs": [], "tags": [], "genre": "解答题", @@ -350943,7 +350943,7 @@ }, "014476": { "id": "014476", - "content": "在平面直角坐标系$x O y$中, 已知椭圆$\\Gamma: \\dfrac{x^2}{2}+y^2=1$, 过右焦点$F$作两条互相垂直的弦$AB$、$CD$, 设$AB$、$CD$中点分别为$M$、$N$.\\\\\n(1) 证明: 直线$MN$必过定点, 并求出此定点坐标;\\\\\n(2) 若弦$AB$、$CD$的斜率均存在, 求$\\triangle FMN$面积的最大值.\n%20", + "content": "在平面直角坐标系$x O y$中, 已知椭圆$\\Gamma: \\dfrac{x^2}{2}+y^2=1$, 过右焦点$F$作两条互相垂直的弦$AB$、$CD$, 设$AB$、$CD$中点分别为$M$、$N$.\\\\\n(1) 证明: 直线$MN$必过定点, 并求出此定点坐标;\\\\\n(2) 若弦$AB$、$CD$的斜率均存在, 求$\\triangle FMN$面积的最大值.", "objs": [], "tags": [], "genre": "解答题", @@ -351285,7 +351285,7 @@ }, "014494": { "id": "014494", - "content": "设直线$x-3 y+m=0$($m \\neq 0$)与双曲线$\\dfrac{x^2}{4}-\\dfrac{y^2}{b}=1$($b>0$)的两条渐近线分别交于$A$、$B$两点. 若点$P(m, 0)$满足$|PA|=|PB|$, 则实数$b$的值是\\blank{50}.\n%21", + "content": "设直线$x-3 y+m=0$($m \\neq 0$)与双曲线$\\dfrac{x^2}{4}-\\dfrac{y^2}{b}=1$($b>0$)的两条渐近线分别交于$A$、$B$两点. 若点$P(m, 0)$满足$|PA|=|PB|$, 则实数$b$的值是\\blank{50}.", "objs": [], "tags": [], "genre": "填空题", @@ -428262,5 +428262,689 @@ ], "remark": "", "space": "" + }, + "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}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040002": { + "id": "040002", + "content": "将参数方程$\\begin{cases}x=1+2 \\cos \\theta, \\\\ y=2 \\sin \\theta\\end{cases}$($\\theta$为参数)化为普通方程, 所得方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040003": { + "id": "040003", + "content": "下列参数($t$为参数)方程中, 与$x^2-y=0$表示同一曲线的是\\bracket{20}.\n\\fourch{$\\begin{cases}x=t^2, \\\\ y=t\\end{cases}$}{$\\begin{cases}x=\\sqrt{|t|}, \\\\ y=t\\end{cases}$}{$\\begin{cases}x=\\sin t, \\\\ y=\\sin ^2 t\\end{cases}$}{$\\begin{cases}x=\\tan t, \\\\ y=\\dfrac{1-\\cos 2 t}{1+\\cos 2 t}\\end{cases}$}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040004": { + "id": "040004", + "content": "参数方程$\\begin{cases}x=t+\\dfrac{1}{t}, \\\\ y=t-\\dfrac{1}{t}\\end{cases}$表示的曲线是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040005": { + "id": "040005", + "content": "曲线$\\begin{cases}x=1+2 \\cos ^2 \\theta, \\\\ y=\\sqrt{2} \\sin \\theta\\end{cases}$($\\theta$为参数, $\\theta \\in \\mathbf{R}$)与直线$y=x$的交点坐标是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040006": { + "id": "040006", + "content": "将参数方程$\\begin{cases}x=\\sin \\theta+\\cos \\theta, \\\\ y=\\sin \\theta-\\cos \\theta,\\end{cases}$ $\\theta \\in[\\dfrac{3 \\pi}{4}, \\dfrac{5 \\pi}{4}]$($\\theta$为参数)化为普通方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040007": { + "id": "040007", + "content": "经过点$P(2,1)$, 且倾斜角为$\\dfrac{2 \\pi}{3}$的直线$l$的参数方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040008": { + "id": "040008", + "content": "已知直线$l$的参数方程为: $\\begin{cases}x=1+\\dfrac{1}{2} t, \\\\ y=2-\\dfrac{\\sqrt{3}}{2} t\\end{cases}$($t$为参数), 则直线$l$的倾斜角的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040009": { + "id": "040009", + "content": "已知$A(3,1), F$是抛物线$y^2=4 x$的焦点, $P$是抛物线上的一个动点, 则$\\triangle APF$周长的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040010": { + "id": "040010", + "content": "已知长度为$7$的线段$AB$的两个端点在抛物线$x^2=4 y$上运动, 则线段$AB$的中点$G$到$x$轴的距离的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040011": { + "id": "040011", + "content": "过抛物线$C: y^2=4 x$的焦点$F$的直线交$C$于$A$、$B$两点, 过$A$、$B$两点分别作$C$的准线的垂线, 垂足为$A_1$、$B_1$, 以线段$A_1B_1$为直径的圆$E$过点$M(-2,3)$, 则圆$E$的方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040012": { + "id": "040012", + "content": "在平面直角坐标系$x O y$中, $O$为坐标原点, 定点$A(-2,3)$, 动点$B$在曲线$x^2+4 y^2=4$上运动, 以$OA$、$OB$为两边作平行四边形$OACB$, 则动点$C$的轨迹方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040013": { + "id": "040013", + "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+y^2=1$($a>1$)的左、右焦点分别是$F_1$、$F_2$, 点$P$是椭圆$C$上的一点且在第一象限, $\\triangle PF_1F_2$的周长为$4+2 \\sqrt{3}$. 过点$P$作椭圆$C$的切线$l$, 分别与$x$轴和$y$轴交于$A$、$B$两点, $O$为坐标原点. 当点$P$在椭圆$C$上移动时, $\\triangle AOB$面积的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040014": { + "id": "040014", + "content": "已知椭圆$C: \\dfrac{x^2}{2}+y^2=1$, 过点$A(0,2)$的直线$l$交椭圆$C$于不同的两点$P$、$Q$. 若$\\overrightarrow{AQ}=\\lambda \\overrightarrow{AP}$, 则实数$\\lambda$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040015": { + "id": "040015", + "content": "在平面直角坐标系$x O y$中, 若直线$y=k x+1$与抛物线$x^2=2 y$相交于$A$、$B$两点.\\\\\n(1) 求$\\overrightarrow{OA} \\cdot \\overrightarrow{OB}$的值;\\\\\n(2) 若$\\triangle AOB$的面积为$2$, 求实数$k$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040016": { + "id": "040016", + "content": "已知两圆$C_1: (x-2)^2+y^2=54$, $C_2: (x+2)^2+y^2=6$, 动圆$M$在圆$C_1$内部且和圆$C_1$内切、和圆$C_2$外切.\\\\\n(1) 求动圆圆心$M$的轨迹$C$的方程;\\\\\n(2) 过点$A(3,0)$的直线与(1)中的曲线$C$交于$P$、$Q$两点, 点$P$关于$x$轴对称的点为$R$, 求$\\triangle ARQ$面积的最大值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040017": { + "id": "040017", + "content": "已知斜率为$k$的直线$l$经过抛物线$C: y^2=4 x$的焦点$F$, 且与抛物线$C$交于不同的两点$A(x_1, y_1)$、$B(x_2, y_2)$.\\\\\n(1) 若点$A$和$B$到抛物线准线的距离分别为$\\dfrac{3}{2}$和$3$, 求$|AB|$;\\\\\n(2) 若$|AF|+|AB|=2|BF|$, 求$k$的值;\\\\\n(3) 点$M(t, 0), t>0$, 对任意确定的实数$k$, 若$\\triangle AMB$是以$AB$为斜边的直角三角形, 判断符合条件的点$M$有几个, 并说明理由.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040018": { + "id": "040018", + "content": "请将下列的角的单位从角度制化为弧度制:\\\\\n(1) $45^{\\circ}=$\\blank{50};\n(2) $30^{\\circ}=$\\blank{50};\n(3) $18^{\\circ}=$\\blank{50};\n(4) $60^{\\circ}=$\\blank{50};\n(5) $75^{\\circ}=$\\blank{50};\n(6) $12^{\\circ}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040019": { + "id": "040019", + "content": "请将下列的角的单位从弧度制化为角度制:\\\\\n(1) $\\dfrac{\\pi}{3}=$\\blank{50};\n(2) $\\dfrac{\\pi}{5}=$\\blank{50};\n(3) $\\dfrac{\\pi}{4}=$\\blank{50};\n(4) $\\dfrac{5 \\pi}{12}=$\\blank{50};\n(5) $\\dfrac{2 \\pi}{9}=$\\blank{50};\n(6) $\\dfrac{3 \\pi}{10}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040020": { + "id": "040020", + "content": "请将下列的角的单位从角度制化为弧度制:\\\\\n(1) 设$k \\in \\mathbf{Z}$, 则角$k \\times 360^{\\circ}+90^{\\circ}=$\\blank{50};\\\\\n(2) 设$k \\in \\mathbf{Z}$, 则角$k \\times 360^{\\circ}+270^{\\circ}=$\\blank{50};\\\\\n(3) 设$k \\in \\mathbf{Z}$, 则角$k \\times 360^{\\circ}+210^{\\circ}=$\\blank{50};\\\\\n(4) 设$k \\in \\mathbf{Z}$, 则角$k \\times 180^{\\circ}+45^{\\circ}=$\\blank{50};\\\\\n(5) 设$k \\in \\mathbf{Z}$, 则角$k \\times 90^{\\circ}+30^{\\circ}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040021": { + "id": "040021", + "content": "请将下列的角的单位从弧度制化为角度制:\\\\\n(1) 设$k \\in \\mathbf{Z}$, 则角$2 k \\pi+\\dfrac{\\pi}{3}=$\\blank{50};\\\\\n(2) 设$k \\in \\mathbf{Z}$, 则角$2 k \\pi+\\dfrac{11 \\pi}{6}=$\\blank{50};\\\\\n(3) 设$k \\in \\mathbf{Z}$, 则角$2 k \\pi-\\dfrac{7 \\pi}{6}=$\\blank{50};\\\\\n(4) 设$k \\in \\mathbf{Z}$, 则角$k \\pi-\\dfrac{\\pi}{4}=$\\blank{50};\\\\\n(5) 设$k \\in \\mathbf{Z}$, 则角$k \\cdot \\dfrac{\\pi}{2}+\\dfrac{5 \\pi}{18}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040022": { + "id": "040022", + "content": "下面的各个角$\\beta$与角$\\alpha(0^{\\circ} \\leq \\alpha<360^{\\circ})$的终边重合, 请你写出相应的角$\\alpha$.\\\\\n(1) 设$\\beta=1410^{\\circ}$, 则角$\\alpha=$\\blank{100};\\\\\n(2) 设$\\beta=-120^{\\circ}$, 则角$\\alpha=$\\blank{100};\\\\\n(3) 设$\\beta=2010^{\\circ}$, 则角$\\alpha=$\\blank{100};\\\\\n. (4) 设$\\beta=-420^{\\circ}$, 则角$\\alpha=$\\blank{100}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040023": { + "id": "040023", + "content": "下面的各个角与角$\\alpha(\\alpha \\in[0,2 \\pi))$的终边重合, 请你写出相应的角$\\alpha$.\\\\0\n(1) 设$\\beta=\\dfrac{22}{3} \\pi$, 则角$\\alpha=$\\blank{100};\\\\\n(2) 设$\\beta=-\\dfrac{13}{6} \\pi$, 则角$\\alpha=$\\blank{100};\\\\\n(3) 设$\\beta=10$, 则角$\\alpha=$\\blank{100};\\\\\n(4) 设$\\beta=-10$, 则角$\\alpha=$\\blank{100}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040024": { + "id": "040024", + "content": "在等差数列$\\{a_n\\}$中, $a_5=6, a_{10}=12$, 则$a_{15}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040025": { + "id": "040025", + "content": "若数列$\\{a_n\\}$为等差数列, $a_5=9, a_{11}=-3$, 则$a_8=$\\blank{50}, 公差$d=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040026": { + "id": "040026", + "content": "等差数列$\\{a_n\\}$中, $a_1=51, a_2=49$.\\\\\n(1) 设$-2021$是数列$\\{a_n\\}$的的第$m$项, 则$m=$\\blank{50};\\\\\n(2) 数列$\\{a_n\\}$中的偶数项依次构成数列$\\{b_n\\}$, 则$\\{b_n\\}$的第$k$项$b_k=$\\blank{50};\\\\\n(3) 设数列$\\{a_n\\}$在区间$[-999,0]$内共有$t$项, 则$t=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040027": { + "id": "040027", + "content": "等差数列$\\{a_n\\}$的公差小于 0 , 且有$a_2 \\cdot a_4=12, a_2+a_4=8$, 则通项$a_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040028": { + "id": "040028", + "content": "等差数列$\\{a_n\\}$中, $a_3+a_4+a_{10}+a_{11}=20$, 则$a_5+a_7+a_9=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040029": { + "id": "040029", + "content": "在首项为 40 , 公差为$-7$的等差数列$\\{a_n\\}$中, 绝对值最小的项的序数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040030": { + "id": "040030", + "content": "设常数$d \\in \\mathbf{R}$. 已知等差数列$\\{a_n\\}$的公差是$d$, 首项$a_1=1$. 若$a_8$是第一个比$29$大的项, 则$d$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040031": { + "id": "040031", + "content": "已知数列$\\{a_n\\}$的前$n$项和为$S_n$, 根据$S_n$, 求$\\{a_n\\}$的通项公式.\n(1) 若$S_n=n^2$, 则$a_n=$\\blank{50};\\\\\n(2) 若$S_n=n^2+1$, 则$a_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040032": { + "id": "040032", + "content": "设常数$m, n \\in \\mathbf{R}$. 已知关于$x$的方程$(x^2-4 x+m)(x^2-4 x+n)=0$的四个根组成一个首项为$1$的等差数列, 则数对$(m, n)$为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040033": { + "id": "040033", + "content": "数列$\\{a_n\\}$对于任意正整数$p, q$, 恒有$a_p+a_q=a_{p+q}$, 若$a_1=2$, 则$a_{100}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040034": { + "id": "040034", + "content": "已知数列$\\{a_n\\}$中, $a_n=3^n-n$, 求证: 数列$\\{a_n\\}$是严格增数列.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040035": { + "id": "040035", + "content": "已知数列$\\{a_n\\}$的前$n$项和为$S_n, S_n=\\begin{cases}n^2,& n=2 k-1, \\\\ n^2+1,& n=2 k,\\end{cases}$ ($k \\in \\mathbf{N}$, $k\\ge 1$), 求$\\{a_n\\}$的通项公式.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040036": { + "id": "040036", + "content": "已知数列$\\{a_n\\}$和$\\{b_n\\}$的通项公式分别是$a_n=2 n+1, b_n=3 n$, $n \\in \\mathbf{N}$, $n\\ge 1$. 将集合$\\{x | x=a_n,\\ n \\in \\mathbf{N}, \\ n\\ge 1\\} \\cap \\{x | x=b_n,\\ n \\in \\mathbf{N}, \\ n\\ge 1\\}$中的元素从小到大依次排列, 构成数列$c_1, c_2, \\cdots, c_n, \\cdots$, 求数列$\\{c_n\\}$的通项公式.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷01", + "edit": [ + "20230218\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" } } \ No newline at end of file