From 3507aeffdb02eff079d7d605dfed9f2459bb277e Mon Sep 17 00:00:00 2001
From: WangWeiye <kj_wangweiye@126.com>
Date: Thu, 6 Apr 2023 19:05:35 +0800
Subject: [PATCH] 20230406 evening

---
 工具/修改题目数据库.py     |   2 +-
 工具/文本文件/metadata.txt | 238 +------------------------
 工具/添加关联题目.py       |   4 +-
 工具/讲义生成.py           |   7 +-
 题库0.3/Problems.json      | 352 +++++++++++++++++++++++++++++++++----
 5 files changed, 327 insertions(+), 276 deletions(-)

diff --git a/工具/修改题目数据库.py b/工具/修改题目数据库.py
index 569bc8ad..11629a5f 100644
--- a/工具/修改题目数据库.py
+++ b/工具/修改题目数据库.py
@@ -1,6 +1,6 @@
 import os,re,json
 """这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块"""
-problems = "10000,10003"
+problems = "40070"
 
 def generate_number_set(string,dict):
     string = re.sub(r"[\n\s]","",string)
diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt
index d572ede5..ef3b7bec 100644
--- a/工具/文本文件/metadata.txt
+++ b/工具/文本文件/metadata.txt
@@ -1,235 +1,3 @@
-usages
-001050
-20220906	2023届高三2班	0.871
-
-009446
-20220906	2023届高三2班	0.355
-
-001072
-20220906	2023届高三2班	0.774
-
-010060
-20220906	2023届高三2班	0.742
-
-000033
-20220906	2023届高三2班	0.903
-
-001073
-20220906	2023届高三2班	0.935
-
-000023
-20220906	2023届高三2班	0.774
-
-002773
-20220906	2023届高三2班	0.742
-
-002775
-20220906	2023届高三2班	0.645
-
-002784
-20220906	2023届高三2班	0.903
-
-007991
-20220906	2023届高三2班	0.581
-
-005150
-20220906	2023届高三2班	0.903
-
-002790
-20220906	2023届高三2班	0.774
-
-002791
-20220906	2023届高三2班	0.774
-
-000757
-20220906	2023届高三2班	0.968
-
-002793
-20220906	2023届高三2班	0.968
-
-000389
-20220906	2023届高三2班	0.871
-
-002800
-20220906	2023届高三2班	0.903
-
-000778
-20220907	2023届高三2班	0.750
-
-001262
-20220907	2023届高三2班	0.656
-
-000342
-20220907	2023届高三2班	0.125
-
-001238
-20220907	2023届高三2班	0.906
-
-001239
-20220907	2023届高三2班	0.875
-
-001242
-20220907	2023届高三2班	0.844
-
-002831
-20220907	2023届高三2班	0.594	0.406
-
-002968
-20220907	2023届高三2班	0.531	0.063
-
-009508
-20220907	2023届高三2班	1.000
-
-003936
-20220907	2023届高三2班	0.906
-
-007984
-20220907	2023届高三2班	1.000
-
-009511
-20220907	2023届高三2班	0.844
-
-005508
-20220907	2023届高三2班	0.844
-
-000734
-20220907	2023届高三2班	0.469
-
-002856
-20220907	2023届高三2班	0.781	0.906
-
-000474
-20220907	2023届高三2班	0.813
-
-002847
-20220907	2023届高三2班	0.844	0.938
-
-002851
-20220907	2023届高三2班	0.500	0.281
-
-001286
-20220907	2023届高三2班	0.906
-
-001292
-20220907	2023届高三2班	0.906
-
-010110
-20220907	2023届高三2班	1.000	1.000	0.875	0.906
-
-000058
-20220907	2023届高三2班	1.000
-
-010114
-20220907	2023届高三2班	0.844
-
-001296
-20220907	2023届高三2班	1.000
-
-005610
-20220907	2023届高三2班	0.906
-
-001353
-20220907	2023届高三2班	0.813
-
-001305
-20220907	2023届高三2班	0.813	0.813	0.969	0.969	0.969
-
-010125
-20220907	2023届高三2班	0.969
-
-001309
-20220907	2023届高三2班	1.000	0.750
-
-005123
-20220907	2023届高三2班	0.563
-
-005678
-20220907	2023届高三2班	0.469
-
-001340
-20220908	2023届高三2班	0.788	0.818	0.879	0.727	0.788
-
-002925
-20220908	2023届高三2班	0.939
-
-002911
-20220908	2023届高三2班	0.879
-
-002918
-20220908	2023届高三2班	0.727
-
-003815
-20220908	2023届高三2班	0.939
-
-005568
-20220908	2023届高三2班	0.939
-
-000954
-20220908	2023届高三2班	1.000
-
-001324
-20220908	2023届高三2班	0.879
-
-001326
-20220908	2023届高三2班	0.939	0.970
-
-002871
-20220908	2023届高三2班	0.818
-
-002878
-20220908	2023届高三2班	0.818	0.818
-
-002898
-20220908	2023届高三2班	0.727
-
-000362
-20220908	2023届高三2班	0.879
-
-001351
-20220908	2023届高三2班	0.848
-
-003747
-20220908	2023届高三2班	0.727
-
-005199
-20220908	2023届高三2班	0.970
-
-009490
-20220908	2023届高三2班	0.879
-
-009517
-20220909	2023届高三2班	0.656
-
-007941
-20220909	2023届高三2班	0.813
-
-000092
-20220909	2023届高三2班	0.625
-
-001270
-20220909	2023届高三2班	1.000	1.000	0.969	0.781
-
-002888
-20220909	2023届高三2班	0.719
-
-001331
-20220909	2023届高三2班	0.156
-
-002894
-20220909	2023届高三2班	0.844	0.750
-
-001211
-20220909	2023届高三2班	0.969	0.906	0.875	0.844	0.750
-
-001218
-20220909	2023届高三2班	0.906	0.750	0.625
-
-002893
-20220909	2023届高三2班	0.813
-
-002895
-20220909	2023届高三2班	0.688
-
-009522
-20220909	2023届高三2班	0.563	0.250
-
+remark
+14804
+(3) 中证明不可能小于$51$的核心是$max(a_{2n-1},a_{2n})$是严格增数列
\ No newline at end of file
diff --git a/工具/添加关联题目.py b/工具/添加关联题目.py
index 24c3bcba..84f39a26 100644
--- a/工具/添加关联题目.py
+++ b/工具/添加关联题目.py
@@ -1,8 +1,8 @@
 import os,re,json,time
 
 """---设置原题目id与新题目id列表, 新id的数目不能小于旧id的数目---"""
-old_ids = "601"
-new_ids = "50000"
+old_ids = "12213,248,31233,282,8912,9784"
+new_ids = "31386:40000"
 """---设置完毕---"""
 """---完成编辑后记得运行第二个单元格---"""
 
diff --git a/工具/讲义生成.py b/工具/讲义生成.py
index dd339d42..3a059f8f 100644
--- a/工具/讲义生成.py
+++ b/工具/讲义生成.py
@@ -5,12 +5,13 @@ import os,re,json,time,sys
 """2: 测验卷与周末卷(填空题, 选择题, 解答题)"""
 """3: 日常选题讲义(一个section)"""
 
-paper_type = 2 # 随后设置一下后续的讲义标题
+paper_type = 1 # 随后设置一下后续的讲义标题
 
 """---设置题块编号---"""
 
 problems = [
-"14784:14795","14796:14799","14800:14804"
+"000363,000625,002372,003421,010951,31386,012255,013097,013118,031323,31387,008866,012199,012548,013134","000960,002162,013063,002418,013982,014505,031229,031388,010958,31389,31390,31391,002268"
+
 ]
 
 """---设置结束---"""
@@ -19,7 +20,7 @@ problems = [
 if paper_type == 1:
     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)
     template_file = "模板文件/复习讲义模板.txt" #设置模板文件名
-    exec_list = [("标题数字待处理","06"),("标题文字待处理","概率与统计")] #设置讲义标题
+    exec_list = [("标题数字待处理","04"),("标题文字待处理","易错题-解析几何")] #设置讲义标题
     destination_file = "临时文件/"+exec_list[0][1]+"_"+exec_list[1][1] # 设置输出文件名
 elif paper_type == 2:
     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)
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 4e68e3b8..f5cee484 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -6547,7 +6547,9 @@
             "20220624\t王伟叶, 余利成"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "031387"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -7481,7 +7483,8 @@
         ],
         "related": [
             "010685",
-            "008930"
+            "008930",
+            "031389"
         ],
         "remark": "",
         "space": "12ex"
@@ -87922,7 +87925,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "031385"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -176152,7 +176157,7 @@
     },
     "006793": {
         "id": "006793",
-        "content": "已知数列$\\{a_n\\}$的前$n$项和$S_n=4-4\\times 2^{-n}$($n\\in \\mathbf{N}^*$), 求证: $\\{a_n\\}$成等比数列.",
+        "content": "已知数列$\\{a_n\\}$的前$n$项和$S_n=4-4\\times 2^{-n}$($n\\in \\mathbf{N}$, $n \\ge 1$), 求证: $\\{a_n\\}$成等比数列.",
         "objs": [
             "K0403003X"
         ],
@@ -226144,7 +226149,9 @@
             "20220726\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "031390"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -246256,7 +246263,9 @@
             "20220730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "031391"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -270115,7 +270124,9 @@
             "20220806\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "031384"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -304552,7 +304563,9 @@
             "20221209\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "031386"
+        ],
         "remark": "",
         "space": ""
     },
@@ -321908,7 +321921,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "031382"
+        ],
         "remark": "",
         "space": ""
     },
@@ -322992,7 +323007,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "031383"
+        ],
         "remark": "",
         "space": ""
     },
@@ -364746,7 +364763,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{3\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364765,7 +364782,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{24}{25}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364784,7 +364801,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-n+10$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364803,7 +364820,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$80$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364822,7 +364839,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{3}{3x-2}$($x<\\dfrac 23$)",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364841,7 +364858,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$12\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364860,7 +364877,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,1]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364879,7 +364896,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$107$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364898,7 +364915,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}4$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364917,7 +364934,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{7}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364936,7 +364953,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[\\dfrac 13,\\dfrac 53)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364955,7 +364972,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364974,7 +364991,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -364993,7 +365010,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -365012,7 +365029,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -365031,7 +365048,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -365050,7 +365067,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $a=0.1$, $b=0.3$; (2) $P(B)=0.5$, $P(A\\cap B)=0.3$, $P(A)P(B)=0.25\\ne 0.3$, 不相互独立",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -365069,7 +365086,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{\\sqrt{3}}3$; (2) $\\dfrac\\pi 6$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -365088,7 +365105,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 约$5.6$千米($\\sqrt{31.25}$); (2) 约$6.2$平方千米($\\dfrac{32\\sqrt{3}}{9}$)",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -365107,7 +365124,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $a=8$; (2) $a=2$; (3) $[\\dfrac{4\\sqrt{7}-8}3,4)\\cup (4,+\\infty)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -365126,7 +365143,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $3,7,10,17$或$3,7,10,3$或$3,7,4,11$; (2) 不存在, 证明略; (3) $51$, 证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -365136,7 +365153,7 @@
         ],
         "same": [],
         "related": [],
-        "remark": "",
+        "remark": "(3) 中证明不可能小于$51$的核心是$max(a_{2n-1},a_{2n})$是严格增数列",
         "space": "12ex"
     },
     "020001": {
@@ -416374,7 +416391,7 @@
     },
     "030072": {
         "id": "030072",
-        "content": "若数列$\\{a_n\\}$的所有项都是正数, 且$\\sqrt{a_1}+\\sqrt{a_2}+\\cdots +\\sqrt{a_n}=n^2+3n$($n\\in \\mathbf{N}^*$), 则$\\dfrac{a_1}{2}+\\dfrac{a_2}{3}+\\cdots +\\dfrac{a_n}{n+1}=$\\blank{50}.",
+        "content": "若数列$\\{a_n\\}$的所有项都是正数, 且$\\sqrt{a_1}+\\sqrt{a_2}+\\cdots +\\sqrt{a_n}=n^2+3n$($n\\in \\mathbf{N}$, $n \\ge 1$), 则$\\dfrac{a_1}{2}+\\dfrac{a_2}{3}+\\cdots +\\dfrac{a_n}{n+1}=$\\blank{50}.",
         "objs": [
             "K0402005X",
             "K0402004X"
@@ -444769,7 +444786,8 @@
         ],
         "same": [],
         "related": [
-            "014003"
+            "014003",
+            "031388"
         ],
         "remark": "",
         "space": ""
@@ -448770,6 +448788,270 @@
         "remark": "",
         "space": "12ex"
     },
+    "031382": {
+        "id": "031382",
+        "content": "已知数列$\\{a_n\\}$满足$a_{n+2}-a_n=2^n$, $a_1=1$, $a_2=2$, 则$a_n=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第四单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第二轮复习讲义-20230406修改",
+        "edit": [
+            "20230118\t王伟叶",
+            "20230406\t刘亚东"
+        ],
+        "same": [],
+        "related": [
+            "012933"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "031383": {
+        "id": "031383",
+        "content": "设等差数列$\\{a_n\\}$的前$n$项和为$S_n$, 若$S_4 \\geq 10$, $S_5 \\leq 15$, 则$a_5$的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第四单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第二轮复习讲义-20230406修改",
+        "edit": [
+            "20230118\t王伟叶",
+            "20230406\t刘亚东"
+        ],
+        "same": [],
+        "related": [
+            "012979"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "031384": {
+        "id": "031384",
+        "content": "已知数列$\\{a_n\\}$的通项公式为$a_n=\\dfrac{n-\\sqrt {98}}{n-\\sqrt {97}}$, 试问: 该数列是否有最大项、最小项? 若有, 分别指出第几项最大、最小; 若没有, 试说明理由.",
+        "objs": [
+            "K0406002X",
+            "K0406005X"
+        ],
+        "tags": [
+            "第四单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材选择性必修第一册习题-20230406修改",
+        "edit": [
+            "20220806\t王伟叶",
+            "20230406\t刘亚东"
+        ],
+        "same": [],
+        "related": [
+            "010777"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031385": {
+        "id": "031385",
+        "content": "已知数列$\\{a_n\\}$的通项$a_n=(n-2)(\\dfrac{10}{11})^n$, 试问该数列有没有最大项与最小项? 若有, 求出最大项与最小项; 若没有, 说明理由.",
+        "objs": [
+            "K0406005X"
+        ],
+        "tags": [
+            "第四单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20230406修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20230406\t余利成"
+        ],
+        "same": [],
+        "related": [
+            "003210"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031386": {
+        "id": "031386",
+        "content": "已知$P$为椭圆$\\dfrac{x^2}4+\\dfrac{y^2}2=1$上的任意一点, $Q$与$P$关于$x$轴对称, $F_1$、$F_2$为椭圆的左、右焦点, 若有$\\overrightarrow{F_1 P} \\cdot \\overrightarrow{F_2P} \\leq 1$, 求向量$\\overrightarrow{F_1 P}$与$\\overrightarrow{F_2 Q}$夹角的取值范围.",
+        "objs": [],
+        "tags": [
+            "第七单元"
+        ],
+        "genre": "解答题",
+        "ans": "$[\\pi-\\arccos\\dfrac 13,\\pi]$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2019届春季高考试题11-20230406修改",
+        "edit": [
+            "20221209\t王伟叶",
+            "20230406\t周双"
+        ],
+        "same": [],
+        "related": [
+            "012213"
+        ],
+        "remark": "因过程较长, 从12213改为解答题, 内容不变",
+        "space": "12ex"
+    },
+    "031387": {
+        "id": "031387",
+        "content": "过点$(3, -2)$, 且在$x$轴、$y$轴上截距相等的直线的方程为\\blank{50}.",
+        "objs": [
+            "K0702001X",
+            "K0702002X"
+        ],
+        "tags": [
+            "第七单元",
+            "直线"
+        ],
+        "genre": "填空题",
+        "ans": "$y=-\\dfrac 23 x$或$y=-x+1$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "教材复习题-20230406修改",
+        "edit": [
+            "20220624\t王伟叶, 余利成",
+            "20230406\t周双"
+        ],
+        "same": [],
+        "related": [
+            "000248"
+        ],
+        "remark": "因答案能明显地反映出思考过程, 故从248改为填空题, 内容不变",
+        "space": ""
+    },
+    "031388": {
+        "id": "031388",
+        "content": "设抛物线$C: y^2=4 x$的焦点为$F$, 过$F$且斜率为$k(k>0)$的直线$l$与$C$交于$A$、$B$两点, $|AB|=8$. 求直线$l$的方程为及过点$A, B$且与抛物线$C$的准线相切的圆的方程.",
+        "objs": [],
+        "tags": [
+            "第七单元"
+        ],
+        "genre": "解答题",
+        "ans": "$y=x-1$; $(x-3)^2+(y-2)^2=16$或$(x-11)^2+(y+6)^2=144$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2020年空中课堂高三复习课22-20230214修改-20230406修改",
+        "edit": [
+            "20230128\t王伟叶",
+            "20230214\t吴惠群",
+            "20230406\t周双"
+        ],
+        "same": [],
+        "related": [
+            "014003",
+            "031233"
+        ],
+        "remark": "因过程较长, 从31233改为解答题, 内容不变",
+        "space": "24ex"
+    },
+    "031389": {
+        "id": "031389",
+        "content": "已知直线$y=ax-1$与曲线$y^2=2x$只有一个公共点, 则实数$a$的值为\\blank{50}.",
+        "objs": [
+            "K0720003X"
+        ],
+        "tags": [
+            "第七单元"
+        ],
+        "genre": "填空题",
+        "ans": "$a=0$或$-\\dfrac 12$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "教材复习题-20230406修改",
+        "edit": [
+            "20220624\t王伟叶, 余利成",
+            "20230406\t周双"
+        ],
+        "same": [],
+        "related": [
+            "010685",
+            "008930",
+            "000282"
+        ],
+        "remark": "因答案能明显地反映出思考过程, 故从282改为填空题, 内容不变",
+        "space": ""
+    },
+    "031390": {
+        "id": "031390",
+        "content": "已知双曲线的虚轴的长为$6$, 一条渐近线的方程为$3x-y=0$, 则此双曲线的标准方程为\\blank{50}.",
+        "objs": [
+            "K0717006X",
+            "K0716003X"
+        ],
+        "tags": [
+            "第七单元",
+            "双曲线"
+        ],
+        "genre": "填空题",
+        "ans": "$x^2-\\dfrac{y^2}9=1$或$\\dfrac{y^2}{81}-\\dfrac{x^2}9=1$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "二期课改练习册高二第二学期-20230406修改",
+        "edit": [
+            "20220726\t王伟叶",
+            "20230406\t周双"
+        ],
+        "same": [],
+        "related": [
+            "008912"
+        ],
+        "remark": "因过程不易书写, 意义不大, 故从8912改为填空题, 内容不变",
+        "space": ""
+    },
+    "031391": {
+        "id": "031391",
+        "content": "倾斜角是$\\dfrac{5\\pi} 6$, 且在$x$轴上的截距为$-1$的直线$l$的点斜式方程为\\blank{50}.",
+        "objs": [
+            "K0702001X",
+            "K0702004X",
+            "K0701002X"
+        ],
+        "tags": [
+            "第七单元",
+            "直线"
+        ],
+        "genre": "填空题",
+        "ans": "$y=-\\dfrac{\\sqrt 3}{3}(x+1)$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材选择性必修第一册课堂练习-20230406修改",
+        "edit": [
+            "20220730\t王伟叶",
+            "20230406\t周双"
+        ],
+        "same": [],
+        "related": [
+            "009784"
+        ],
+        "remark": "因题目简单, 故从9784改为填空题, 内容不变",
+        "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}",
@@ -450227,7 +450509,7 @@
     },
     "040070": {
         "id": "040070",
-        "content": "按要求填写象限:\\\\\n(1) 若$\\alpha$在第二象限, 则$\\dfrac{\\alpha}{3}$总不在第象限(填写``一''、``二''、``三''、``四''之一);\\\\\n(2) 若$-\\dfrac{\\pi}{2}<\\alpha<0$, 则点$(\\sin \\alpha, \\cot \\alpha)$总在第象限(填写``一''、``二''、``三''、``四''之一).",
+        "content": "按要求填写象限:\\\\\n(1) 若$\\alpha$在第二象限, 则$\\dfrac{\\alpha}{3}$总不在第\\blank{50}象限(填写``一''、``二''、``三''、``四''之一);\\\\\n(2) 若$-\\dfrac{\\pi}{2}<\\alpha<0$, 则点$(\\sin \\alpha, \\cot \\alpha)$总在第\\blank{50}象限(填写``一''、``二''、``三''、``四''之一).",
         "objs": [],
         "tags": [],
         "genre": "解答题",