diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb
index 1ab60d10..ff1b413c 100644
--- a/工具/寻找阶段末尾空闲题号.ipynb
+++ b/工具/寻找阶段末尾空闲题号.ipynb
@@ -11,7 +11,7 @@
      "text": [
       "首个空闲id: 14764 , 直至 020000\n",
       "首个空闲id: 22106 , 直至 030000\n",
-      "首个空闲id: 31358 , 直至 040000\n",
+      "首个空闲id: 31361 , 直至 040000\n",
       "首个空闲id: 40246 , 直至 999999\n"
      ]
     }
diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb
index 31531e06..77dea21c 100644
--- a/工具/批量题号选题pdf生成.ipynb
+++ b/工具/批量题号选题pdf生成.ipynb
@@ -9,9 +9,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "开始编译教师版本pdf文件:  临时文件/赋能31to42_教师用_20230323.tex\n",
+      "开始编译教师版本pdf文件:  临时文件/2022学年下学期高一高二材料_教师用_20230324.tex\n",
       "0\n",
-      "开始编译学生版本pdf文件:  临时文件/赋能31to42_学生用_20230323.tex\n",
+      "开始编译学生版本pdf文件:  临时文件/2022学年下学期高一高二材料_学生用_20230324.tex\n",
       "0\n"
      ]
     }
@@ -24,40 +24,34 @@
     "\"\"\"\n",
     "\n",
     "\"\"\"---设置是否在学生版中提供答案---\"\"\"\n",
-    "answered = True\n",
+    "answered = False\n",
     "\n",
     "\"\"\"---设置题目列表---\"\"\"\n",
     "#字典字段为文件名, 之后为内容的题号\n",
     "problems_dict = {\n",
-    "# \"2024届高二下学期周末卷01\":\"40001:40017\",\n",
-    "# \"2025届高一下学期周末卷01\":\"40018:40036\",\n",
-    "# \"2024届高二下学期周末卷02\":\"40037:40056\",\n",
-    "# \"2025届高一下学期周末卷02\":\"40057:40082\",\n",
-    "# \"2025届高一下学期周末卷03\":\"40083:40104\",\n",
-    "# \"2025届高一下学期周末卷03小测\":\"40105:40112\",\n",
-    "# \"2025届高一下学期周末卷04旧版\":\"40113:40130\",\n",
-    "# \"2025届高一下学期周末卷04小测\":\"40131:40139\",\n",
-    "# \"2024届高二下学期周末卷03\":\"40140:40160\",\n",
-    "# \"2024届高二上学期期末考试\":\"31267:31287\",\n",
-    "# \"2025届高一上学期期末考试\":\"31288:31308\",\n",
-    "# \"2024届高二下学期周末卷04\":\"40161:40180\",\n",
-    "# \"2025届高一下学期周末卷04\":\"40181:40201\",\n",
-    "# \"2024届高二下学期周末卷05\":\"40202:40225\",\n",
-    "# \"2025届高一下学期周末卷05\":\"40226:40245\",\n",
-    "# \"2024届空间向量校本作业\":\"22048:22083\",\n",
-    "# \"2024届二项式定理校本作业\":\"22084:22105\"\n",
-    "\"赋能31\":\"636:645\",\n",
-    "\"赋能32\":\"646:655\",\n",
-    "\"赋能33\":\"656:665\",\n",
-    "\"赋能34\":\"666:675\",\n",
-    "\"赋能35\":\"676:685\",\n",
-    "\"赋能36\":\"686:695\",\n",
-    "\"赋能37\":\"696:705\",\n",
-    "\"赋能38\":\"706:715\",\n",
-    "\"赋能39\":\"716:725\",\n",
-    "\"赋能40\":\"726:735\",\n",
-    "\"赋能41\":\"736:745\",\n",
-    "\"赋能42\":\"746:755\"\n",
+    "\"2024届高二下学期周末卷01\":\"40001:40017\",\n",
+    "\"2025届高一下学期周末卷01\":\"40018:40036\",\n",
+    "\"2024届高二下学期周末卷02\":\"40037:40056\",\n",
+    "\"2025届高一下学期周末卷02\":\"40057:40082\",\n",
+    "\"2025届高一下学期周末卷03\":\"40083:40104\",\n",
+    "\"2025届高一下学期周末卷03小测\":\"40105:40112\",\n",
+    "\"2025届高一下学期周末卷04旧版\":\"40113:40130\",\n",
+    "\"2025届高一下学期周末卷04小测\":\"40131:40139\",\n",
+    "\"2024届高二下学期周末卷03\":\"40140:40160\",\n",
+    "\"2024届高二上学期期末考试\":\"31267:31287\",\n",
+    "\"2025届高一上学期期末考试\":\"31288:31308\",\n",
+    "\"2024届高二下学期周末卷04\":\"40161:40180\",\n",
+    "\"2025届高一下学期周末卷04\":\"40181:40201\",\n",
+    "\"2024届高二下学期周末卷05\":\"40202:40225\",\n",
+    "\"2025届高一下学期周末卷05\":\"40226:40245\",\n",
+    "\"2024届空间向量校本作业\":\"22048:22083\",\n",
+    "\"2024届二项式定理校本作业\":\"22084:22105\",\n",
+    "\"2025届高一下学期周末卷05小测\":\"40246:40255\",\n",
+    "\"2025届高一下学期周末卷06\":\"40256:40273\",\n",
+    "\"2025届高一下学期周末卷06小测\":\"40274:40282\",\n",
+    "\"2025届高一下学期期中复习一(集合逻辑不等式)\":\"40283:40298\",\n",
+    "\"2024届高二下学期周末卷06\":\"40299:40316\",\n",
+    "\"2024届高二下学期周末卷07\":\"40317:40335\"\n",
     "\n",
     "}\n",
     "\n",
@@ -66,7 +60,7 @@
     "\"\"\"---设置文件保存路径---\"\"\"\n",
     "#目录和文件的分隔务必用/\n",
     "directory = \"临时文件/\"\n",
-    "filename = \"赋能31to42\"\n",
+    "filename = \"2022学年下学期高一高二材料\"\n",
     "\"\"\"---设置文件名结束---\"\"\"\n",
     "if directory[-1] != \"/\":\n",
     "    directory += \"/\"\n",
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 0a70e22f..f98424ea 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
@@ -7,10 +7,10 @@
    "outputs": [],
    "source": [
     "#修改起始id,出处,文件名\n",
-    "starting_id = 31358\n",
-    "raworigin = \"自拟题目\"\n",
-    "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目9.tex\"\n",
-    "editor = \"20230323\\t王伟叶\"\n",
+    "starting_id = 40246\n",
+    "raworigin = \"\"\n",
+    "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目10.tex\"\n",
+    "editor = \"20230324\\t王伟叶\"\n",
     "indexed = False\n"
    ]
   },
@@ -23,8 +23,96 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "添加题号031358, 来源: 自拟题目\n",
-      "添加题号031359, 来源: 自拟题目\n"
+      "添加题号040246, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040247, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040248, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040249, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040250, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040251, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040252, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040253, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040254, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040255, 来源: 2025届高一下学期周末卷05小测\n",
+      "添加题号040256, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040257, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040258, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040259, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040260, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040261, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040262, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040263, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040264, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040265, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040266, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040267, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040268, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040269, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040270, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040271, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040272, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040273, 来源: 2025届高一下学期周末卷06\n",
+      "添加题号040274, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040275, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040276, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040277, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040278, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040279, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040280, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040281, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040282, 来源: 2025届高一下学期周末卷06小测\n",
+      "添加题号040283, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040284, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040285, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040286, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040287, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040288, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040289, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040290, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040291, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040292, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040293, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040294, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040295, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040296, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040297, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040298, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n",
+      "添加题号040299, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040300, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040301, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040302, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040303, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040304, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040305, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040306, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040307, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040308, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040309, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040310, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040311, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040312, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040313, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040314, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040315, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040316, 来源: 2024届高二下学期周末卷06\n",
+      "添加题号040317, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040318, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040319, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040320, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040321, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040322, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040323, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040324, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040325, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040326, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040327, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040328, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040329, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040330, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040331, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040332, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040333, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040334, 来源: 2024届高二下学期周末卷07\n",
+      "添加题号040335, 来源: 2024届高二下学期周末卷07\n"
      ]
     }
    ],
diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb
index a5df3238..f36c673d 100644
--- a/工具/识别题库中尚未标注的题目类型.ipynb
+++ b/工具/识别题库中尚未标注的题目类型.ipynb
@@ -9,66 +9,96 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "022048 解答题\n",
-      "022049 解答题\n",
-      "022050 解答题\n",
-      "022051 解答题\n",
-      "022052 解答题\n",
-      "022053 解答题\n",
-      "022054 解答题\n",
-      "022055 解答题\n",
-      "022056 解答题\n",
-      "022057 解答题\n",
-      "022058 填空题\n",
-      "022059 解答题\n",
-      "022060 解答题\n",
-      "022061 解答题\n",
-      "022062 解答题\n",
-      "022063 解答题\n",
-      "022064 解答题\n",
-      "022065 解答题\n",
-      "022066 解答题\n",
-      "022067 解答题\n",
-      "022068 解答题\n",
-      "022069 解答题\n",
-      "022070 解答题\n",
-      "022071 解答题\n",
-      "022072 解答题\n",
-      "022073 解答题\n",
-      "022074 解答题\n",
-      "022075 解答题\n",
-      "022076 解答题\n",
-      "022077 解答题\n",
-      "022078 解答题\n",
-      "022079 解答题\n",
-      "022080 解答题\n",
-      "022081 解答题\n",
-      "022082 解答题\n",
-      "022083 解答题\n",
-      "022084 解答题\n",
-      "022085 解答题\n",
-      "022086 解答题\n",
-      "022087 解答题\n",
-      "022088 选择题\n",
-      "022089 解答题\n",
-      "022090 解答题\n",
-      "022091 解答题\n",
-      "022092 解答题\n",
-      "022093 解答题\n",
-      "022094 解答题\n",
-      "022095 填空题\n",
-      "022096 选择题\n",
-      "022097 解答题\n",
-      "022098 解答题\n",
-      "022099 解答题\n",
-      "022100 解答题\n",
-      "022101 解答题\n",
-      "022102 解答题\n",
-      "022103 解答题\n",
-      "022104 解答题\n",
-      "022105 解答题\n",
-      "031358 填空题\n",
-      "031359 填空题\n"
+      "040246 填空题\n",
+      "040247 填空题\n",
+      "040248 填空题\n",
+      "040249 填空题\n",
+      "040250 填空题\n",
+      "040251 填空题\n",
+      "040252 填空题\n",
+      "040253 填空题\n",
+      "040254 解答题\n",
+      "040255 解答题\n",
+      "040256 填空题\n",
+      "040257 填空题\n",
+      "040258 填空题\n",
+      "040259 填空题\n",
+      "040260 填空题\n",
+      "040261 填空题\n",
+      "040262 填空题\n",
+      "040263 填空题\n",
+      "040264 解答题\n",
+      "040265 解答题\n",
+      "040266 填空题\n",
+      "040267 填空题\n",
+      "040268 填空题\n",
+      "040269 填空题\n",
+      "040270 填空题\n",
+      "040271 填空题\n",
+      "040272 填空题\n",
+      "040273 填空题\n",
+      "040274 填空题\n",
+      "040275 填空题\n",
+      "040276 填空题\n",
+      "040277 填空题\n",
+      "040278 填空题\n",
+      "040279 填空题\n",
+      "040280 填空题\n",
+      "040281 填空题\n",
+      "040282 解答题\n",
+      "040283 解答题\n",
+      "040284 解答题\n",
+      "040285 解答题\n",
+      "040286 解答题\n",
+      "040287 解答题\n",
+      "040288 解答题\n",
+      "040289 解答题\n",
+      "040290 解答题\n",
+      "040291 填空题\n",
+      "040292 填空题\n",
+      "040293 选择题\n",
+      "040294 解答题\n",
+      "040295 解答题\n",
+      "040296 解答题\n",
+      "040297 解答题\n",
+      "040298 解答题\n",
+      "040299 填空题\n",
+      "040300 填空题\n",
+      "040301 填空题\n",
+      "040302 填空题\n",
+      "040303 填空题\n",
+      "040304 填空题\n",
+      "040305 填空题\n",
+      "040306 填空题\n",
+      "040307 填空题\n",
+      "040308 填空题\n",
+      "040309 填空题\n",
+      "040310 填空题\n",
+      "040311 解答题\n",
+      "040312 解答题\n",
+      "040313 解答题\n",
+      "040314 解答题\n",
+      "040315 解答题\n",
+      "040316 解答题\n",
+      "040317 填空题\n",
+      "040318 填空题\n",
+      "040319 填空题\n",
+      "040320 填空题\n",
+      "040321 填空题\n",
+      "040322 填空题\n",
+      "040323 填空题\n",
+      "040324 填空题\n",
+      "040325 填空题\n",
+      "040326 填空题\n",
+      "040327 填空题\n",
+      "040328 填空题\n",
+      "040329 填空题\n",
+      "040330 选择题\n",
+      "040331 选择题\n",
+      "040332 解答题\n",
+      "040333 解答题\n",
+      "040334 解答题\n",
+      "040335 解答题\n"
      ]
     }
    ],
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 1978fa71..90cfaf58 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -449169,5 +449169,1715 @@
         "related": [],
         "remark": "",
         "space": "12ex"
+    },
+    "040246": {
+        "id": "040246",
+        "content": "若$\\sin \\alpha: \\sin \\dfrac{\\alpha}{2}=6: 5$, 则$\\cos \\alpha=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040247": {
+        "id": "040247",
+        "content": "计算: $(\\cos \\dfrac{\\pi}{8}+\\sin \\dfrac{\\pi}{8})(\\cos ^3 \\dfrac{\\pi}{8}-\\sin ^3 \\dfrac{\\pi}{8})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040248": {
+        "id": "040248",
+        "content": "在$\\triangle ABC$中, 若$a=7$, $b=14$, $A=30^{\\circ}$, 则$B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040249": {
+        "id": "040249",
+        "content": "已知$\\tan 35^{\\circ}=a$, 用$a$表示$\\dfrac{\\cos 20^{\\circ}}{1-\\sin 20^{\\circ}}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040250": {
+        "id": "040250",
+        "content": "已知$\\alpha$、$\\beta \\in(0, \\pi)$, $\\tan \\dfrac{\\alpha}{2}=\\dfrac{1}{2}$, $\\sin (\\alpha+\\beta)=\\dfrac{5}{13}$, 则$\\cos \\beta$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040251": {
+        "id": "040251",
+        "content": "已知$\\sin (\\dfrac{\\pi}{4}-\\alpha)=\\dfrac{5}{13}$, $\\alpha \\in(0, \\dfrac{\\pi}{4})$, 则$\\dfrac{\\cos 2 \\alpha}{\\cos (\\dfrac{\\pi}{4}+\\alpha)}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040252": {
+        "id": "040252",
+        "content": "在$\\triangle ABC$中, 已知$a=4$, $b=3$, $c=3 \\sqrt{5}$, 则$\\sin C$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040253": {
+        "id": "040253",
+        "content": "在$\\triangle ABC$中, 若$\\cos ^2B-\\cos ^2C=\\sin ^2A$, 则此三角形的形状为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040254": {
+        "id": "040254",
+        "content": "在$\\triangle ABC$中, 若$S_{\\triangle ABC}=\\dfrac{1}{2}$, $a c=2$, $\\sin A=\\cos C$, 求角$A$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040255": {
+        "id": "040255",
+        "content": "已知$\\tan \\dfrac{\\alpha+\\beta}{2}=\\dfrac{\\sqrt{3}}{2}$, 求$\\cos 2 \\alpha \\cdot \\cos 2 \\beta-\\cos ^2(\\alpha-\\beta)$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040256": {
+        "id": "040256",
+        "content": "若$\\dfrac{a}{\\cos A}=\\dfrac{b}{\\cos B}=\\dfrac{c}{\\cos C}$, 则$\\triangle ABC$的形状是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040257": {
+        "id": "040257",
+        "content": "若$a \\sin A=b \\sin B$, 则$\\triangle ABC$的形状是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040258": {
+        "id": "040258",
+        "content": "若$a \\cdot \\cos A=b \\cdot \\cos B$, 则$\\triangle ABC$的形状是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040259": {
+        "id": "040259",
+        "content": "在$\\triangle ABC$中, $a^2+b^2-c^2=a b \\cdot \\cot C$. 若$\\triangle ABC$是锐角三角形, 则角$C=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040260": {
+        "id": "040260",
+        "content": "在$\\triangle ABC$中, $a^2+b^2-c^2=a b \\cdot \\cot C$. 若$\\triangle ABC$不是锐角三角形, 则角$C=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040261": {
+        "id": "040261",
+        "content": "在$\\triangle ABC$中, $a=8$, $b=10$, $C=60^\\circ$, 则此三角形外接圆半径是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040262": {
+        "id": "040262",
+        "content": "已知$\\triangle ABC$的外接圆的半径、$\\triangle ABC$的面积均为$1$, 则$\\sin A \\sin B \\sin C=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040263": {
+        "id": "040263",
+        "content": "在$\\triangle ABC$中, $b=2 \\sqrt{2}$, $a=2$. 若$A=\\theta$, 即$\\theta$使得$\\triangle ABC$存在, 则$\\theta$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040264": {
+        "id": "040264",
+        "content": "在$\\triangle ABC$中, $a$、$b$、$c$分别为内角$A$、$B$、$C$的对边, 且满足$2 a \\sin A=(2 b+c) \\sin B+(2 c+b) \\sin C$.\\\\\n(1) 求$A$的大小;\\\\\n(2) 若$\\sin B+\\sin C=1$, 试判断$\\triangle ABC$的形状.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040265": {
+        "id": "040265",
+        "content": "在某地区的平面规划图中(如图), 三点$A, B, C$分别表示三个街区, $\\angle ABC=\\dfrac{\\pi}{3}$. 现准备在线段$AB$上的点$D$处建一个停车场, 它到街区$B$的距离为$1$, 到街区$A, C$的距离相等.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (4,0) node [right] {$B$} coordinate (B);\n\\filldraw (3,0) node [below] {$D$} coordinate (D) circle (0.03);\n\\draw (B) ++ (120:{(1+sqrt(33))/2}) node [above] {$C$} coordinate (C);\n\\draw (A)--(B)--(C)--cycle(C)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 若线段$AD$的长为$3$, 求$\\sin \\angle BCD$的值;\\\\\n(2) 若$\\triangle BCD$的面积为$\\sqrt{3}$, 求点$A$到直线$BC$的距离.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040266": {
+        "id": "040266",
+        "content": "函数$y=\\sqrt{\\sin x-\\dfrac{1}{2}}$的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040267": {
+        "id": "040267",
+        "content": "函数$y=\\sqrt{\\sin x}+\\dfrac{1}{\\sqrt{9-x^2}}$的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040268": {
+        "id": "040268",
+        "content": "函数$y=\\cos (\\dfrac{\\pi x}{2}-\\dfrac{1}{4})$的最小正周期是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040269": {
+        "id": "040269",
+        "content": "函数$y=|\\sin x|$的最小正周期是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040270": {
+        "id": "040270",
+        "content": "函数$y=|1+2 \\sin 2 x|$的最小正周期是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040271": {
+        "id": "040271",
+        "content": "函数$y=|\\sin x|+|\\cos x|$的最小正周期是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040272": {
+        "id": "040272",
+        "content": "若函数$y=f(x)$满足$f(x)+f(x+1)=0$, 且当$x \\in[0,1)$时, $f(x)=\\sin x+1$, 则$f(7.5)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040273": {
+        "id": "040273",
+        "content": "下列函数中是周期函数的有\\blank{50}.\\\\\n\\textcircled{1} $y=\\sin |x|$; \\textcircled{2} $y=\\cos |x|$; \\textcircled{3} $y=\\sin x+2 \\cos x$; \\textcircled{4} $y=x+\\sin x$; \\textcircled{5} $y=\\sin ^2 x$.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040274": {
+        "id": "040274",
+        "content": "若$\\dfrac{a}{\\sin A}=\\dfrac{b}{\\cos B}=\\dfrac{c}{\\cos C}$, 则$\\triangle ABC$的形状是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040275": {
+        "id": "040275",
+        "content": "函数$y=\\sqrt{\\sin x-\\cos x}$的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040276": {
+        "id": "040276",
+        "content": "函数$y=\\cos (\\dfrac{x}{2}-\\dfrac{\\pi}{4})$的最小正周期是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040277": {
+        "id": "040277",
+        "content": "函数$y=|\\sin 2 x|$的最小正周期是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040278": {
+        "id": "040278",
+        "content": "在$\\triangle ABC$中, 角$A, B, C$所对的边分别是$a, b, c$. $\\tan A=1$, $\\tan B=2$, $c=3$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040279": {
+        "id": "040279",
+        "content": "在$\\triangle ABC$中, $a=\\sqrt{5}$, $b=\\sqrt{7}$, $c=2 \\sqrt{3}$, 则$b c \\cos A+c a \\cos B+a b \\cos C=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040280": {
+        "id": "040280",
+        "content": "在$\\triangle ABC$中, $A=60^\\circ$, 且最长边长和最短边长分别是方程$x^2-6 x+7=0$的两个根, 则此三角形的周长是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040281": {
+        "id": "040281",
+        "content": "对于$\\triangle ABC$, 下列四个命题中, 正确命题的序号是\\blank{50}.\\\\\n\\textcircled{1} 若$\\sin A=\\cos B$, 则$\\triangle ABC$总是直角三角形; \\textcircled{2} 若$\\sin 2A=\\sin 2B$, 则$\\triangle ABC$总是等腰三角形;\n\\textcircled{3} 若$\\tan A \\tan B<1$, 则$\\triangle ABC$总是钝角三角形; \\textcircled{4} 若$\\cos (A-B) \\cos (A-C)=1$, 则$\\triangle ABC$总是等边三角形.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040282": {
+        "id": "040282",
+        "content": "在$\\triangle ABC$中, 内角$A, B, C$所对的边长分别是$a, b, c$.\\\\\n(1) 若$a=4, C=\\dfrac{\\pi}{3}$, 且$\\triangle ABC$的面积$S=\\sqrt{3}$, 求$b, c$的值;\\\\\n(2) 若$\\sin (B+A)+\\sin (B-A)=\\sin 2A$, 试判断$\\triangle ABC$的形状",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷06小测",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040283": {
+        "id": "040283",
+        "content": "已知集合$S=\\{x | x=2 n+1, n \\in \\mathbf{Z}\\}$, $T=\\{x | x=4 n \\pm 1, n \\in \\mathbf{Z}\\}$, 问$S$、$T$之间的关系如何? 并证明.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040284": {
+        "id": "040284",
+        "content": "已知命题$p$: ``对任意$x \\in[-1,1]$, 不等式$x^2-x-m<0$''是真命题.\\\\\n(1) 求实数$m$的范围;\\\\\n(2) 若命题$q$: ``$-4<m-a<4$''是命题$p$的充分不必要条件, 求实数$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040285": {
+        "id": "040285",
+        "content": "已知$c>0$, 设$p$: 函数$y=c^x$在$\\mathbf{R}$上严格单调递减; $q$: 不等式$x+|x-2 c|>1$的解集是$\\mathbf{R}$, 如果$p$和$q$中有且只有一个正确, 求实数$c$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040286": {
+        "id": "040286",
+        "content": "已知``存在$x \\in\\{x |-1<x<1\\}$, 使等式$x^2-x-m=0$成立''是真命题, 且实数$m$的取值范围$A$.\\\\\n(1) 求$A$;\\\\\n(2) 设不等式$(x-a)(x+a-2)<0$的解集为$B$, 若$x \\in B$是$x \\in A$的必要条件, 求实数$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040287": {
+        "id": "040287",
+        "content": "解关于$x$的不等式$[(m+3) x-1](x+1)>0$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040288": {
+        "id": "040288",
+        "content": "解不等式组$\\begin{cases}x<0, \\\\ \\dfrac{3-x}{3+x}>|\\dfrac{2-x}{2+x}|.\\end{cases}$",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040289": {
+        "id": "040289",
+        "content": "设不等式$x^2-2 a x+a+2 \\leq 0$的解集为$M$, 若$M \\subseteq[1,4]$, 求实数$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040290": {
+        "id": "040290",
+        "content": "求使$\\sqrt{x}+\\sqrt{y} \\leq a \\sqrt{x+y}$, ($x>0$, $y>0$)恒成立的$a$的最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040291": {
+        "id": "040291",
+        "content": "若集合$A=\\{a, b, 2\\}$, 集合$B=\\{2, b^2, 2 a\\}$, $a$、$b \\in \\mathbf{R}$, 且$A=B$, 则实数$b=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040292": {
+        "id": "040292",
+        "content": "王昌龄《从军行》中有``黄沙百战穿金甲, 不破楼兰终不还''之句, 其中``攻破楼兰''是``返回家乡''的\\blank{50}条件.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040293": {
+        "id": "040293",
+        "content": "设集合$P_1=\\{x | x^2+a x+1>0\\}$, $P_2=\\{x | x^2+a x+2>0\\}$, $Q_1=\\{x | x^2+x+b>0\\}$, $Q_2=\\{x | x^2+2 x+b>0\\}$, 其中$a$、$b \\in \\mathbf{R}$, 下列说法正确的是\\bracket{20}.\n\\onech{对任意$a$, $P_1$是$P_2$的子集; 对任意$b$, $Q_1$不是$Q_2$的子集}{对任意$a$, $P_1$是$P_2$的子集; 存在$b$, 使得$Q_1$是$Q_2$的子集}{存在$a$, 使得$P_1$不是$P_2$的子集; 对任意$b$,  $Q_1$不是$Q_2$的子集}{存在$a$, $P_1$不是$P_2$的子集; 存在$b$, 使得$Q_1$是$Q_2$的子集}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040294": {
+        "id": "040294",
+        "content": "已知$A=\\{x | \\dfrac{x^2+3 x+2}{x-1}>0\\}$, $B=\\{x | x^2+a x+b \\leq 0\\}$, 且有$A \\cup B=\\{x | x+2>0\\}$, $A \\cap B=\\{x | 1<x \\leq 3\\}$, 求实数$a$、$b$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040295": {
+        "id": "040295",
+        "content": "设集合$A=\\{x | 0<a x+1 \\leq 5\\}$, $B=(-\\dfrac{1}{2}, 2]$.\\\\\n(1) $A$、$B$是否能相等? 若能, 求出$a$的值, 若不能, 说明理由;\\\\\n(2) 已知$p: x \\in A$, $q: x \\in B$, 且$p$是$q$的充分不必要条件, 求实数$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040296": {
+        "id": "040296",
+        "content": "解不等式$\\log _a(x-\\dfrac{1}{x})>1$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040297": {
+        "id": "040297",
+        "content": "若$x>0, y>0, x+y=1$, 求证: $(1+\\dfrac{1}{x})(1+\\dfrac{1}{y}) \\geq 9$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040298": {
+        "id": "040298",
+        "content": "已知三数$a$、$b$、$c$满足$a+b+c=1$, $a^2+b^2+c^2=1$, 且$a>b>c$.\\\\\n(1) 求$a+b$的取值范围;\\\\\n(2) $a^2+b^2$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期期中复习一(集合逻辑不等式)",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040299": {
+        "id": "040299",
+        "content": "已知函数$f(x)$的导函数为$f'(x)$, 且满足$f(x)=2 x f'(\\mathrm{e})+\\ln x$, 则$f'(\\mathrm{e})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040300": {
+        "id": "040300",
+        "content": "设函数$f(x)$在$\\mathbf{R}$上存在导函数$f'(x)$, $f(x)$的图像在点$M(1, f(1))$处的切线方程为$y=\\dfrac{1}{2} x+2$, 那么$f(1)+f'(1)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040301": {
+        "id": "040301",
+        "content": "曲线$y=x \\mathrm{e}^x+2 x+1$在点$(0,1)$处的切线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040302": {
+        "id": "040302",
+        "content": "曲线$y=(x-1) \\mathrm{e}^x$在$(1,0)$处的切线与坐标轴围成的三角形面积为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040303": {
+        "id": "040303",
+        "content": "若$f(x)=-\\dfrac{1}{2} x^2+a \\ln (x+2)$在$[-1,+\\infty)$上是减函数, 则实数$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040304": {
+        "id": "040304",
+        "content": "如图, 水以恒速(即单位时间内注入水的体积相同)注入下面四种底面积相同的容器中, 试分别找出各容器对应的水面高度$h$与时间$t$的函数图像\\blank{50}.\n\\begin{center}\n\\textcircled{1}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,2) ellipse (1 and 0.25);\n\\draw (-1,0) arc (180:360:1 and 0.25);\n\\draw [dashed] (-1,0) arc (180:0:1 and 0.25);\n\\draw (-1,0) --++ (0,2) (1,0) --++ (0,2);\n\\end{tikzpicture}\n\\textcircled{2}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,2) ellipse (2 and 0.5);\n\\draw (-1,0) arc (180:360:1 and 0.25);\n\\draw [dashed] (-1,0) arc (180:0:1 and 0.25);\n\\draw (-1,0) --++ (-1,2) (1,0) --++ (1,2);\n\\end{tikzpicture}\n\\textcircled{3}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,2) ellipse (1 and 0.25);\n\\draw (-2,0) arc (180:360:2 and 0.5);\n\\draw [dashed] (-2,0) arc (180:0:2 and 0.5);\n\\draw (-2,0) --++ (1,2) (2,0) --++ (-1,2);\n\\end{tikzpicture}\n\\textcircled{4}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,2) ellipse (1 and 0.25);\n\\draw (-1.5,1) arc (180:360:1.5 and 0.375);\n\\draw [dashed] (-1.5,1) arc (180:0:1.5 and 0.375);\n\\draw (-1,0) arc (180:360:1 and 0.25);\n\\draw [dashed] (-1,0) arc (180:0:1 and 0.25);\n\\draw (-1,0) --++ (-0.5,1) --++ (0.5,1) (1,0) --++ (0.5,1) --++ (-0.5,1);\n\\end{tikzpicture}\n\\end{center}\n\\begin{center}\n(I)\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (1.5,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2.5) node [left] {$h$};\n\\draw [domain = 0:2] plot ({1/3*(3-1.5*\\x+0.5*0.5*\\x*\\x)*\\x},\\x);\n\\end{tikzpicture}\n(II)\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (2.5,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2.5) node [left] {$h$};\n\\draw [domain = 0:2] plot (\\x,\\x);\n\\end{tikzpicture}\n(III)\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3.5,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2.5) node [left] {$h$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:1] plot ({1/3*(3+1.5*\\x+0.5*0.5*\\x*\\x)*\\x},\\x);\n\\draw [domain = 1:2] plot ({9.5/3-1/3*(3+1.5*(2-\\x)+0.5*0.5*(2-\\x)*(2-\\x))*(2-\\x)},\\x);\n\\end{tikzpicture}\\\\\n(IV)\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (5,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2.5) node [left] {$h$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2] plot ({1/3*(3+1.5*\\x+0.5*0.5*\\x*\\x)*\\x},\\x);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040305": {
+        "id": "040305",
+        "content": "如图为函数$f(x)$的导函数的图像, 则下列判断正确的有\\blank{50}.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-3.5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:1, samples = 100] plot (\\x,{2*sin((\\x+1)/2*90)});\n\\draw [domain = 1:5, samples = 100] plot (\\x,{2*sin((\\x-4)*90)});\n\\foreach \\i/\\j in {-3/below,-2/below,-1/above,1/below,2/below,3/above,4/below} \n{\\draw (\\i,0.2) -- (\\i,0) node [\\j] {$\\i$};};\n\\draw [dashed] (1,2) -- (1,0) (3,-2) -- (3,0);\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} $f(x)$在$(-3,1)$上单调递增; \\textcircled{2} $x=-1$是$f(x)$的极小值点; \\textcircled{3} $f(x)$在$(2,4)$上单调递减, 在$(-1,2)$上单调递增; \\textcircled{4} $x=2$是$f(x)$的极小值点.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040306": {
+        "id": "040306",
+        "content": "已知函数$f(x)=\\dfrac{1}{2} x-\\sin x$在$[0, \\dfrac{\\pi}{2}]$上的极小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040307": {
+        "id": "040307",
+        "content": "已知函数$f(x)=a \\sqrt{x}+\\ln x$在$x=1$处取得极值, 则实数$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040308": {
+        "id": "040308",
+        "content": "函数$f(x)=x^3-a x^2+b x$在$x=1$处有极值为$4$, 则$a-b$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040309": {
+        "id": "040309",
+        "content": "已知函数$f(x)=x^3+3 a x^2+b x+a^2$, 若$x=-1$时, $f(x)$取得极值$0$, 则$a b=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040310": {
+        "id": "040310",
+        "content": "已知函数$f(x)=x^2(x-a)$, 若$x=2$为$f(x)$的极值点, 则此时$f(x)$的极小值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040311": {
+        "id": "040311",
+        "content": "已知函数$f(x)=\\dfrac{x^2-a}{\\mathrm{e}^x}$, 是否存在实数$a$使得$x=1$是函数$f(x)$的一个极值点, 若存在求出$a$的值, 否则说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040312": {
+        "id": "040312",
+        "content": "设函数$f(x)=x^3+x^2-x-2$.\\\\\n(1) 求$f(x)$在$x=-2$处的切线方程;\\\\\n(2) 求$f(x)$的极小值点和极大值点.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040313": {
+        "id": "040313",
+        "content": "已知函数$f(x)=(-x^2+a x) \\mathrm{e}^x$, $a \\in \\mathbf{R}$.\\\\\n(1) 若$f'(0)=1$时, 求实数$a$的值;\\\\\n(2) 若函数$f(x)$在$(-1,1)$上单调递增, 求实数$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040314": {
+        "id": "040314",
+        "content": "如图, 有一块半椭圆形钢板, 其长半轴长为$2 r$, 短半轴长为$r$, 计划将此钢板切割成等腰梯形的形状, 下底$AB$是半椭圆的短轴, 上底$CD$的端点在椭圆上, 记$CD=2 x$, 梯形面积为$S$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (1.5,0) arc (0:180:1.5 and 3) -- (1.5,0);\n\\draw (1.5,0) node [below right] {$B$} coordinate (B);\n\\draw (-1.5,0) node [below left] {$A$} coordinate (A);\n\\draw (50:1.5 and 3) node [above right] {$C$} coordinate (C);\n\\draw (130:1.5 and 3) node [above left] {$D$} coordinate (D);\n\\draw (B)--(C)--(D)--(A);\n\\draw (1.5,0) --++ (0.6,0) (0,3) --++ (2.1,0);\n\\draw [<->] (1.8,0) -- (1.8,3) node [midway, fill = white] {$2r$};\n\\draw (1.5,0) --++ (0,-0.6) (-1.5,0) --++ (0,-0.6);\n\\draw [<->] (-1.5,-0.3) -- (1.5,-0.3) node [midway, fill = white] {$2r$};\n\\end{tikzpicture}\n\\end{center}\n(1) 求面积$S$以$x$为自变量的函数式, 并写出其定义域;\\\\\n(2) 求面积$S$的最大值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040315": {
+        "id": "040315",
+        "content": "已知函数$f(x)=\\dfrac{\\ln x+a x}{x}$, $a \\in \\mathbf{R}$.\\\\\n(1) 若$a=0$, 求$f(x)$的最大值;\\\\\n(2) 若$0<a<1$, 求证: $f(x)$有且只有一个零点.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040316": {
+        "id": "040316",
+        "content": "已知函数$f(x)=x^2 \\mathrm{e}^x$($\\mathrm{e}$为自然对数的底数).\\\\\n(1) 求函数$f(x)$的单调区间;\\\\\n(2) 若函数$g(x)=\\dfrac{x^2}{\\mathrm{e}^x}-m$有且仅有$2$个零点, 求实数$m$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷06",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040317": {
+        "id": "040317",
+        "content": "函数$y=\\dfrac{x}{1-\\cos x}$的在$x=\\dfrac{\\pi}{4}$处的导数值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040318": {
+        "id": "040318",
+        "content": "若函数$f(x)=2 \\ln x-\\dfrac{1}{x}$, $f'(x_0)=3$, 则$x_0=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040319": {
+        "id": "040319",
+        "content": "曲线$y=\\dfrac{x}{\\sin x}$在点$(\\dfrac{\\pi}{2}, \\dfrac{\\pi}{2})$处的切线方程是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040320": {
+        "id": "040320",
+        "content": "过原点且与曲线$y=-x \\ln x-1$相切的直线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040321": {
+        "id": "040321",
+        "content": "函数$f(x)=2 x^3+6 x^2+7$的递增区间是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040322": {
+        "id": "040322",
+        "content": "函数$f(x)=\\dfrac{\\ln x+1}{x}$的单调增区间为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040323": {
+        "id": "040323",
+        "content": "若函数$f(x)=a x^3-12 x+a$的减区间为$[-3,3]$, 则实数$a$的值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040324": {
+        "id": "040324",
+        "content": "已知函数$f(x)=x^2+a x-\\ln x$在$[2,3]$上是减函数, 则实数$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040325": {
+        "id": "040325",
+        "content": "已知函数$f(x)=x^3+m \\ln x$在区间$[2,3]$上不单调, 则实数$m$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040326": {
+        "id": "040326",
+        "content": "若二项式$(2 x+\\dfrac{a}{x})^7$的展开式中$\\dfrac{1}{x^3}$的系数是$84$, 则实数$a$的值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040327": {
+        "id": "040327",
+        "content": "若$(x^2+\\dfrac{1}{x^3})^n$展开式的各项系数之和为$256$, 则$n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040328": {
+        "id": "040328",
+        "content": "若二项式$(3 x+\\dfrac{1}{x \\sqrt{x}})^n$的展开式中含有常数项, 则正整数$n$的最小值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040329": {
+        "id": "040329",
+        "content": "已知三次函数$f(x)=\\dfrac{1}{3} a x^3+b x^2+x+c$无极值点, 且满足$a+\\dfrac{16}{b^2} \\leq 8$, 则$a^2-b^2=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040330": {
+        "id": "040330",
+        "content": "函数$y=x^3-3 x^2-9 x$($-2<x<2$)有\\bracket{20}.\n\\twoch{极大值为$5$, 无极小值}{极小值为$-27$, 无极大值}{极大值为$5$, 极小值为$-27$}{极大值为$5$, 极小值为$-11$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040331": {
+        "id": "040331",
+        "content": "在$(x^2+\\dfrac{1}{x})^6$的二项展开式中的常数项是第\\bracket{20}项.\n\\fourch{$3$}{$5$}{$4$}{$6$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040332": {
+        "id": "040332",
+        "content": "对于$(x+\\dfrac{a}{x})(2 x-\\dfrac{1}{x})^5$的展开式.\\\\\n(1) 若$a=0$, 求该展开式中含$x^2$项的系数;\\\\\n(2) 若该展开式中各项系数的和为$2$, 求该展开式中的常数项.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040333": {
+        "id": "040333",
+        "content": "已知函数$f(x)=x \\ln x+a x^2-1$, 且$f'(1)=-1$.\\\\\n(1) 求$f(x)$的解析式;\\\\\n(2) 若对于任意$x \\in(0,+\\infty)$, 都有$f(x)-m x \\leq-1$, 求$m$的最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040334": {
+        "id": "040334",
+        "content": "已知函数$f(x)=a(\\mathrm{e}^x-2)-x$.\\\\\n(1) 讨论函数$f(x)$的单调性;\\\\\n(2) 若不等式$f(x) \\geq 1-2 a$对任意$x \\in[-1,+\\infty)$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届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040335": {
+        "id": "040335",
+        "content": "已知函数$f(x)=x^3-a x^2+x+4$.\\\\\n(1) 求函数$f(x)$在$x=0$处的切线方程;\\\\\n(2) 若对任意的$x \\in(0,+\\infty), f(x)+f(-x) \\geq 4 \\ln x+8$恒成立, 求$a$的取值范围;\\\\\n(3) 当$a=3$时, 设函数$g(x)=f(x)-k x$, 对于任意的$k<1$, 试确定函数$g(x)$的零点个数, 并说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷07",
+        "edit": [
+            "20230324\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
     }
 }
\ No newline at end of file