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 323578f4..859cf89f 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
@@ -400,3 +400,6 @@
 20240304-212023 高三下学期周末卷04
 032107:032127
 
+20240306-140205 高三下学期初态测试
+032128:032148
+
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 15451f10..a6d30823 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -140558,7 +140558,8 @@
         ],
         "same": [],
         "related": [
-            "023005"
+            "023005",
+            "032140"
         ],
         "remark": "",
         "space": "",
@@ -188290,7 +188291,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "032146"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -373857,7 +373860,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "032132"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -710232,7 +710237,9 @@
             "20230108\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "032129"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -738838,6 +738845,434 @@
         "space": "4em",
         "unrelated": []
     },
+    "032128": {
+        "id": "032128",
+        "content": "不等式 $1-\\dfrac{1}{x}\\leq 0$ 的解集为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题1",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032129": {
+        "id": "032129",
+        "content": "底面半径长为 1 , 母线长为 $\\sqrt{2}$ 的圆锥的体积为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题2",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "031008"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032130": {
+        "id": "032130",
+        "content": "已知复数 $z=2 \\mathrm{i}$, 则 $\\overline{z}+\\dfrac{1}{z}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题3",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032131": {
+        "id": "032131",
+        "content": "已知 $\\tan \\alpha=\\dfrac{1}{2}$, 则 $\\dfrac{\\sin (\\dfrac{\\pi}{2}+2 \\alpha)-1}{\\cos ^2 \\alpha}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题4",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032132": {
+        "id": "032132",
+        "content": "抛物线 $y=x^2$ 的准线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题5",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "013090"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032133": {
+        "id": "032133",
+        "content": "已知 $(2 x-1)^{10}=a_0+a_1(x-2)+a_2(x-2)^2+\\cdots+a_{10}(x-2)^{10}$, 则 $a_0-a_1+a_2-a_3+\\cdots+a_{10}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题6",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032134": {
+        "id": "032134",
+        "content": "已知函数 $y=2 \\sin (\\omega x+\\dfrac{\\pi}{3})$ 在区间 $[0, \\dfrac{\\pi}{2}]$ 上的最大值为 2 , 则正数 $\\omega$ 的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题7",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032135": {
+        "id": "032135",
+        "content": "上海国际电影节影片展映期间, 某影院准备在周日的某放映厅安排放映 4 部电影, 两部纪录片和两部悬疑片, 当天白天有 5 个时段可供放映 (5 个连续的场次), 则两部悬疑片不相邻 (中间隔空场也叫不相邻), 且当天最先放映的一定是悬疑片的排片方法有\\blank{50}种 (结果用数字表示).",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题8",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032136": {
+        "id": "032136",
+        "content": "已知点 $A(-3,1)$、$B(1,-3)$, 直线 $l_1: a x-y-2 a+5=0$ 与 $l_2: x+a y-3 a-4=0$ 交于点 $M$, 则 $\\overrightarrow{MA}\\cdot \\overrightarrow{MB}$ 的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题9",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032137": {
+        "id": "032137",
+        "content": "已知定义在$(0,+\\infty)$ 上的函数$y=f(x)$, 且$f(x)=\\begin{cases}\\sin x,&  x \\in(0,\\dfrac{\\pi}{2}]\\\\f'(x-\\dfrac{\\pi}{2}),&  x \\in(\\dfrac{\\pi}{2},+\\infty),\\end{cases}$, 则函数 $y=f(x)-\\log _{2024}x$ 的零点个数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题10",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032138": {
+        "id": "032138",
+        "content": "如图所示, 图 1 中涂色小正方形个数 $a_1=1$, 图 2 中涂色小正方形个数 $a_2=5$, 图 3 中涂色小正方形个数 $a_3=29$, 图 4 中涂色小正方形个数 $a_4=185$, 按照图中所示规律则 $a_5=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.25]\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,0) rectangle ++ (1,1);};\n\\foreach \\i in {0,1}\n{\\draw (\\i,-13) -- (\\i,14);};\n\\foreach \\i in {-13,-12,...,14}\n{\\draw (0,\\i) -- (1,\\i);};\n\\draw (0,-15) node {图 1};\n\\end{tikzpicture}\n\\hspace{1em}\n\\begin{tikzpicture}[>=latex, scale = 0.25]\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,1) rectangle ++ (1,1);};\n\\foreach \\i in {-1,0,1}\n{\\filldraw [pattern = north east lines] (\\i,0) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,-1) rectangle ++ (1,1);};\n\\foreach \\i in {-1,0,...,2}\n{\\draw (\\i,-13) -- (\\i,14);};\n\\foreach \\i in {-13,-12,...,14}\n{\\draw (-1,\\i) -- (2,\\i);};\n\\draw (0,-15) node {图 2};\n\\end{tikzpicture}\n\\hspace{1em}\n\\begin{tikzpicture}[>=latex, scale = 0.25]\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,4) rectangle ++ (1,1);};\n\\foreach \\i in {-1,0,1}\n{\\filldraw [pattern = north east lines] (\\i,3) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,2) rectangle ++ (1,1);};\n\\foreach \\i in {-3,-1,0,1,3}\n{\\filldraw [pattern = north east lines] (\\i,1) rectangle ++ (1,1);};\n\\foreach \\i in {-4,-3,...,4}\n{\\filldraw [pattern = north east lines] (\\i,0) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,-4) rectangle ++ (1,1);};\n\\foreach \\i in {-1,0,1}\n{\\filldraw [pattern = north east lines] (\\i,-3) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,-2) rectangle ++ (1,1);};\n\\foreach \\i in {-3,-1,0,1,3}\n{\\filldraw [pattern = north east lines] (\\i,-1) rectangle ++ (1,1);};\n\\foreach \\i in {-4,-3,...,5}\n{\\draw (\\i,-13) -- (\\i,14);};\n\\foreach \\i in {-13,-12,...,14}\n{\\draw (-4,\\i) -- (5,\\i);};\n\\draw (0,-15) node {图 3};\n\\end{tikzpicture}\n\\hspace{1em}\n\\begin{tikzpicture}[>=latex, scale = 0.25]\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,13) rectangle ++ (1,1);};\n\\foreach \\i in {-1,0,1}\n{\\filldraw [pattern = north east lines] (\\i,12) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,11) rectangle ++ (1,1);};\n\\foreach \\i in {-3,-1,0,1,3}\n{\\filldraw [pattern = north east lines] (\\i,10) rectangle ++ (1,1);};\n\\foreach \\i in {-4,-3,...,4}\n{\\filldraw [pattern = north east lines] (\\i,9) rectangle ++ (1,1);};\n\\foreach \\i in {-3,-1,0,1,3}\n{\\filldraw [pattern = north east lines] (\\i,8) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,7) rectangle ++ (1,1);};\n\\foreach \\i in {-1,0,1}\n{\\filldraw [pattern = north east lines] (\\i,6) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,5) rectangle ++ (1,1);};\n\\foreach \\i in {-9,-3,-1,0,1,3,9}\n{\\filldraw [pattern = north east lines] (\\i,4) rectangle ++ (1,1);};\n\\foreach \\i in {-10,-9,-8,-4,-3,-2,-1,0,1,2,3,4,8,9,10}\n{\\filldraw [pattern = north east lines] (\\i,3) rectangle ++ (1,1);};\n\\foreach \\i in {-9,-3,-2,-1,0,1,2,3,9}\n{\\filldraw [pattern = north east lines] (\\i,2) rectangle ++ (1,1);};\n\\foreach \\i in {-12,-10,-9,-8,-6,-4,-3,-2,-1,0,1,2,3,4,6,8,9,10,12}\n{\\filldraw [pattern = north east lines] (\\i,1) rectangle ++ (1,1);};\n\\foreach \\i in {-13,-12,...,13}\n{\\filldraw [pattern = north east lines] (\\i,0) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,-13) rectangle ++ (1,1);};\n\\foreach \\i in {-1,0,1}\n{\\filldraw [pattern = north east lines] (\\i,-12) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,-11) rectangle ++ (1,1);};\n\\foreach \\i in {-3,-1,0,1,3}\n{\\filldraw [pattern = north east lines] (\\i,-10) rectangle ++ (1,1);};\n\\foreach \\i in {-4,-3,...,4}\n{\\filldraw [pattern = north east lines] (\\i,-9) rectangle ++ (1,1);};\n\\foreach \\i in {-3,-1,0,1,3}\n{\\filldraw [pattern = north east lines] (\\i,-8) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,-7) rectangle ++ (1,1);};\n\\foreach \\i in {-1,0,1}\n{\\filldraw [pattern = north east lines] (\\i,-6) rectangle ++ (1,1);};\n\\foreach \\i in {0}\n{\\filldraw [pattern = north east lines] (\\i,-5) rectangle ++ (1,1);};\n\\foreach \\i in {-9,-3,-1,0,1,3,9}\n{\\filldraw [pattern = north east lines] (\\i,-4) rectangle ++ (1,1);};\n\\foreach \\i in {-10,-9,-8,-4,-3,-2,-1,0,1,2,3,4,8,9,10}\n{\\filldraw [pattern = north east lines] (\\i,-3) rectangle ++ (1,1);};\n\\foreach \\i in {-9,-3,-2,-1,0,1,2,3,9}\n{\\filldraw [pattern = north east lines] (\\i,-2) rectangle ++ (1,1);};\n\\foreach \\i in {-12,-10,-9,-8,-6,-4,-3,-2,-1,0,1,2,3,4,6,8,9,10,12}\n{\\filldraw [pattern = north east lines] (\\i,-1) rectangle ++ (1,1);};\n\\foreach \\i in {-13,-12,...,14}\n{\\draw (\\i,-13) -- (\\i,14) (-13,\\i)--(14,\\i);};\n\\draw (0,-15) node {图 4};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题11",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032139": {
+        "id": "032139",
+        "content": "已知实数 $a, b$, 若对任意 $\\theta \\in \\mathbf{R}$, 不等式 $|a \\cos \\theta+b \\sin \\theta|+|a \\sin \\theta-b \\cos \\theta| \\leq 5 \\sqrt{2}$ 恒成立, 则 $|3 a+4 b|-|3 a-4 b|$ 的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题12",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032140": {
+        "id": "032140",
+        "content": "若 $1+\\mathrm{i}$ 是关于 $x$ 的方程 $x^2+p x+q=0$ 的一个根 (其中 $\\mathrm{i}$ 为虚数单位, $p, q \\in \\mathbf{R}$ ), 则 $q$ 的值为\\bracket{20}.\n\\fourch{$\\sqrt{2}$}{2}{-2}{1}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题13",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "004503"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032141": {
+        "id": "032141",
+        "content": "已知 $\\overrightarrow{a}, \\overrightarrow{b}$ 是两个不共线的单位向量, $\\overrightarrow{c}=\\lambda \\overrightarrow{a}+\\mu \\overrightarrow{b}$($\\lambda, \\mu \\in \\mathbf{R}$), 则``$\\lambda<0$ 且 $\\mu<0$''是``$\\overrightarrow{c}\\cdot(\\overrightarrow{a}+\\overrightarrow{b})<0$''的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{既不充分也不必要条件}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题14",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032142": {
+        "id": "032142",
+        "content": "已知直线 $l: a x+b y+c=0$, 点 $A(x_1, y_1)$、$B(x_2, y_2)$, 设 $a x_1+b y_1+c=\\delta_1$, $a x_2+b y_2+c=\\delta_2$, 下列条件中可以推出直线 $l$ 与线段 $AB$ 的延长线相交的是\\bracket{20}.\n\\fourch{$\\dfrac{\\delta_1}{\\delta_2}=1$}{$\\dfrac{\\delta_1}{\\delta_2}=0$}{$\\dfrac{\\delta_1}{\\delta_2}>1$}{$\\dfrac{\\delta_1}{\\delta_2}<0$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题15",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032143": {
+        "id": "032143",
+        "content": "已知四棱锥 $P-ABCD$ 的底面为矩形, $PD \\perp$ 平面 $ABCD$, 点 $Q$ 为侧棱 $PA$ (不含端点的线段)上动点, 则点 $Q$ 在平面 $PBC$ 上的射影在\\bracket{20}.\n\\fourch{棱 $PB$ 上}{$\\triangle PBC$ 内部}{$\\triangle PBC$ 外部}{不确定}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题16",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032144": {
+        "id": "032144",
+        "content": "如图, 在三棱锥 $A-BCD$ 中, $AB \\perp$ 平面 $BCD$, 平面 $ABC \\perp$ 平面 $ABD$, $AC=AD$, $AB=BD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [above left] {$B$} coordinate (B);\n\\draw ({sqrt(3)},0,1) node [right] {$D$} coordinate (D);\n\\draw (-1,0,{sqrt(3)}) node [left] {$C$} coordinate (C);\n\\draw (0,2,0) node [above] {$A$} coordinate (A);\n\\draw (C)--(D)--(A)--cycle;\n\\draw [dashed] (B)--(C)(B)--(D)(B)--(A);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $BC \\perp BD$;\\\\\n(2) 求二面角 $A-CD-B$ 的正切值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题17",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "032145": {
+        "id": "032145",
+        "content": "我们平时常用的视力表叫做对数视力表, 视力呈现为 $4.8,4.9,5.0,5.1$. 视力 $\\geq 5.0$ 为正常视力. 否则就是近视. 某校进行一次对学生视力与学习成绩的相关调查, 随机抽查了 100 名近视学生的成绩 (按照各科占一定权重计算而得的满分 100 分的综合成绩), 得到频率分布直方图如下:\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.1, yscale = 60]\n\\draw [->] (40,0) -- (44,0) -- (44.5,0.002) -- (45.5,-0.002) -- (46,0) -- (110,0) node [below] {成绩};\n\\draw [->] (40,0) -- (40,0.05) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (40,0) node [below left] {$O$};\n\\foreach \\i/\\j in {50/0.007,60/0.013,70/0.020,80/0.024,90/0.036}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (10,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {50/0.007,60/0.013,70/0.020,80/0.024,90/0.036}\n{\\draw [dashed] (\\i,\\j) -- (40,\\j) node [left] {$\\k$};};\n\\draw (100,0) node [below] {$100$};\n\\end{tikzpicture}\n\\end{center}\n(1) 估计该校近视学生学习成绩的第 85 百分位数;(精确到 $0.1$)\\\\\n(2) 已知该校学生的近视率为 $54 \\%$, 学生成绩的优秀率为 $36 \\%$ (成绩 $\\geq 85$ 分视作优秀),从该校学生中任选一人, 若此人的成绩为优秀, 求此人近视的概率. (以样本中的频率作为相应的概率)",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题18",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "032146": {
+        "id": "032146",
+        "content": "在 $\\triangle ABC$ 中, 若 $\\sin A=\\dfrac{\\sin B+\\sin C}{\\cos B+\\cos C}$.\\\\\n(1) 试判断 $\\triangle ABC$ 的形状;\\\\\n(2) 如果三角形面积等于 $4$ , 求三角形周长的最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题19",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "006323"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "032147": {
+        "id": "032147",
+        "content": "已知点 $A(2,2)$、$B(-2,2)$, 椭圆 $\\Gamma_1: \\dfrac{y^2}{9}+\\dfrac{x^2}{5}=1$ 与双曲线 $\\Gamma_2: \\dfrac{y^2}{a^2}-\\dfrac{x^2}{2}=1$ 有相同的焦点.\\\\\n(1) 求双曲线 $\\Gamma_2$ 的方程与离心率.\\\\\n(2) 点 $P(x_0, y_0)$ 为双曲线 $\\Gamma_2$ 的一部分 $\\dfrac{y^2}{a^2}-\\dfrac{x^2}{2}=1$($-\\dfrac{1}{2}\\leq x \\leq \\dfrac{1}{2}$ 且 $y>0$) 上的动点,证明: 点 $P$ 双曲线 $\\Gamma_2$ 的切线等分 $\\triangle OAB$ 的面积 ($O$ 为原点).\\\\\n(3) 设双曲线 $\\Gamma_2$ 的切线 $l$ 与椭圆 $\\Gamma_1$ 交于 $C$、$D$ 两点, 求动弦 $CD$ 中点 $M$ 的轨迹方程.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题20",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "032148": {
+        "id": "032148",
+        "content": "已知函数 $y=f(x)$ 的表达式为 $f(x)=\\ln x+a x^2-x+a+1$.\\\\\n(1) 当 $a=0$ 时, 证明 $f(x) \\leq 0$ ; \\\\\n(2) 当 $a>0$ 时, 讨论函数 $y=f(x)$ 的单调性;\\\\\n(3) 若 $f(x) \\leq \\mathrm{e}^x$ 对 $x \\in (0,+\\infty)$ 恒成立, 求实数 $a$ 的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高三下学期初态测试试题21",
+        "edit": [
+            "20240306\t毛培菁"
+        ],
+        "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}",