录入2023空中课堂高三复习课32题目

工具/latex界面修改题目内容.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"""
-problems = "13475"
+problems = "15305"
 editor = "王伟叶"
 
 def generate_number_set(string,dict):

工具/关键字筛选题号.py

@@ -2,7 +2,7 @@ import os,re,json
 
 """---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---"""
 keywords_dict_table = [
-    {"origin":[r"一模"],"origin2":["2023"],"origin3":[r"试题(9|10|11|15|19)"]}
+    {"origin":[r"2023"],"content":["内切球为"]}
 ]
 """---关键字设置完毕---"""
 # 示例： keywords_dict_table = [

工具/批量收录题目.py

@@ -1,8 +1,8 @@
 #修改起始id,出处,文件名
-starting_id = 40667
+starting_id = 15332
 raworigin = ""
 filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex"
-editor = "20230428\t王伟叶"
+editor = "20230501\t王伟叶"
 indexed = False
 
 import os,re,json

工具/文本文件/题号筛选.txt

@@ -1,10 +1 @@
-15080:15100
-
-
-
-
-未使用题号:
-
-
-已使用题号:
-015080,015081,015082,015083,015084,015085,015086,015087,015088,015089,015090,015091,015092,015093,015094,015095,015096,015097,015098,015099,015100
+015305

工具/题号选题pdf生成.py

@@ -7,7 +7,7 @@ import os,re,time,json,sys
 """---设置题目列表---"""
 #留空为编译全题库, a为读取文本文件中的题号筛选.txt文件生成题库
 problems = r"""
-21529
+a
 """
 """---设置题目列表结束---"""
 

题库0.3/Problems.json

@@ -397868,6 +397868,406 @@
         "space": "4em",
         "unrelated": []
     },
+    "015332": {
+        "id": "015332",
+        "content": "若关于$x$的方程$(\\dfrac{1}{2})^x+m=\\sqrt{x+1}$在实数范围内有解, 则实数$m$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015333": {
+        "id": "015333",
+        "content": "设$a>0$, 已知第一象限的两个点$P_1(x_1, y_1)$, $P_2(x_2, y_2)$分别在双曲线$\\Gamma_1: \\dfrac{x^2}{a^2}-y^2=1$和$\\Gamma_2: a^2 x^2-y^2=1$的右\n支上, 则$\\dfrac{x_1 x_2}{y_1 y_2}$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015334": {
+        "id": "015334",
+        "content": "设复数$z_1, z_2$满足: $z_1=\\mathrm{i} \\cdot \\overline{z_2}$, 且$|z_1-1|=1$, 其中$\\mathrm{i}$是虚数单位, 则$|z_1-z_2|$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015335": {
+        "id": "015335",
+        "content": "已知定义域为区间$D$的函数$y=f(x)$, 其导函数为$y=f'(x)$, 满足: 对任意$x \\in D$, 都有$f'(x)<1$. 证明: 方程$f(x)-x=0$至多只有一个实数解.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "015336": {
+        "id": "015336",
+        "content": "设$S_n$是无穷数列$\\{a_n\\}$的前$n$项和, 若对任意正整数$n$, 不等式$\\dfrac{S_n}{n}<\\dfrac{S_{n+1}}{n+1}$恒成立, 则称数列$\\{a_n\\}$为和谐数列. 给出下列$3$个命题:\\\\\n\\textcircled{1} 若对任意正整数$n$, 均有$a_n<a_{n+1}$, 则$\\{a_n\\}$为和谐数列;\\\\\n\\textcircled{2} 若等差数列$\\{a_n\\}$是和谐数列, 则$S_n$一定存在最小值;\\\\\n\\textcircled{3} 存在首项和公比均为负数的等比数列$\\{a_n\\}$是和谐数列.\n以上$3$个命题中真命题的个数有\\bracket{20}个.\n\\fourch{0}{1}{2}{3}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015337": {
+        "id": "015337",
+        "content": "如图, 棱长为$2$的正方体$ABCD-A_1B_1C_1D_1$中, $E$为棱$CC_1$的中点, 点$P$、$Q$分别为面$A_1B_1C_1D_1$和线段$B_1C$上的动点, 则$\\triangle PEQ$周长的最小值为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(C)!0.5!(C1)$) node [right] {$E$} coordinate (E);\n\\draw ($(B1)!0.3!(C)$) node [below] {$Q$} coordinate (Q);\n\\draw ($1/3*(A1)+1/3*(B1)+1/3*(C1)$) node [left] {$P$} coordinate (P);\n\\draw (B1)--(C)(E)--(Q);;\n\\draw [dashed] (Q)--(P)--(E);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$2 \\sqrt{2}$}{$\\sqrt{10}$}{$\\sqrt{11}$}{$2 \\sqrt{3}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015338": {
+        "id": "015338",
+        "content": "已知椭圆$\\Gamma: \\dfrac{x^2}{2}+y^2=1$的右焦点为$F_2$, 过$F_2$作两条不重合的动直线$l_1$、$l_2$, 其中$l_1$与$\\Gamma$交于$A$、$B$两点, $l_2$与$\\Gamma$交于$C$、$D$两点, $M$、$N$分别是线段$AB$、$CD$的中点. 若直线$MN$过定点$(\\dfrac{2}{3}, 0)$, 试问$l_1$与$l_2$的夹角是否为定值? 如果是, 求出该定值; 如果不是, 请说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "015339": {
+        "id": "015339",
+        "content": "设定义域为$\\mathbf{R}$的函数$y=f(x)$是增函数, 且存在实数$u, v$, 使得$u<v$, 且$f(u)<f(v)$. 求证: $y=f(x)$不是周期函数.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "015340": {
+        "id": "015340",
+        "content": "设$m \\in \\mathbf{R}$, 已知方程组$\\begin{cases}x+m y=2 \\text {, } \\\\ m x+16 y=8\\end{cases}$无解, 则$m$的值等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015341": {
+        "id": "015341",
+        "content": "令$\\sin \\theta+\\cos \\theta=t$, 若$\\sin ^3 \\theta+\\cos ^3 \\theta=a_3 t^3+a_2 t^2+a_1 t+a_0$对一切$\\theta \\in \\mathbf{R}$恒成立, 则$a_0+a_1+a_2+a_3=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015342": {
+        "id": "015342",
+        "content": "在平面上, 已知$\\overrightarrow {a}$, $\\overrightarrow {b}$是两个不平行的单位向量, $O$为定点, 集合$\\Omega=\\{P | \\overrightarrow{OP}=\\lambda \\overrightarrow {a}+\\mu \\overrightarrow {b},\\ 0 \\leq \\lambda \\leq 1, \\ 0 \\leq \\mu \\leq 2\\}$若$\\Omega$中所有的点构成图形的面积为$1$, 则$\\overrightarrow {a}$与$\\overrightarrow {b}$夹角的大小是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015343": {
+        "id": "015343",
+        "content": "设$a \\in \\mathbf{R}$, 如果函数$y=f(x)$和$y=g(x)$的图像上分别存在点$M$和$N$关于$x$轴对称, 则称函数$y=f(x)$和$y=g(x)$具有$C$关系. 若函数$y=a \\sqrt{x-1}$和$y=-x-1$不具有$C$关系, 求$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "015344": {
+        "id": "015344",
+        "content": "设$x \\in \\mathbf{R}$, 则$\\lg x>\\ln x$的解集是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015345": {
+        "id": "015345",
+        "content": "已知$y=f(x)$是定义域为$\\mathbf{R}$的奇函数, 且$x \\leq 0$时, $f(x)=\\mathrm{e}^x-1$, 其中$\\mathrm{e}$为自然对数的底数, 则$y=f(x)$的值域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015346": {
+        "id": "015346",
+        "content": "如图, 在$\\triangle ABC$中, 点$D$、$E$是线段$BC$上两个动点, 且$\\overrightarrow{AD}+\\overrightarrow{AE}=x \\overrightarrow{AB}+y \\overrightarrow{AC}$, 则$\\dfrac{1}{x}+\\dfrac{9}{y}$的最小值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (3,0) node [right] {$C$} coordinate (C);\n\\draw ($(B)!0.3!(C)$) node [below] {$D$} coordinate (D);\n\\draw ($(B)!0.65!(C)$) node [below] {$E$} coordinate (E);\n\\draw (1,2) node [above] {$A$} coordinate (A);\n\\draw [->] (A)--(B);\n\\draw [->] (A)--(C);\n\\draw [->] (A)--(D);\n\\draw [->] (A)--(E);\n\\draw (B)--(C);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015347": {
+        "id": "015347",
+        "content": "如图, 棱长为$2$的正方体$ABCD-A_1B_1C_1D_1$的内切球为球$O, E$、$F$分别是棱$AB$和棱$CC_1$的中点, $G$在棱$BC$上移动, 则下列命题正确的个数是\\bracket{20}.\\\\\n\\textcircled{1} 存在点$G$, 使$OD$垂直于平面$EFG$;\\\\\n\\textcircled{2} 对于任意点$G, OA$平行于平面$EFG$;\\\\\n\\textcircled{3} 直线$EF$被球$O$截得的弦长为$\\sqrt{2}$;\\\\\n\\textcircled{4} 过直线$EF$的平面截球$O$所得的所有截面圆中, 半径最小的圆的面积为$\\dfrac{\\pi}{2}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$B$} coordinate (B);\n\\draw (B) ++ (\\l,0,0) node [below right] {$C$} coordinate (C);\n\\draw (B) ++ (\\l,0,-\\l) node [right] {$D$} coordinate (D);\n\\draw (B) ++ (0,0,-\\l) node [above right] {$A$} coordinate (A);\n\\draw (B) -- (C) -- (D);\n\\draw [dashed] (B) -- (A) -- (D);\n\\draw (A) ++ (0,\\l,0) node [above] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [left] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [right] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (D) -- (D1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (A) -- (A1);\n\\filldraw ($(A1)!0.5!(C)$) node [right] {$O$} coordinate (O) circle (0.03);\n\\draw [dashed] (O) circle (1) ellipse (1 and 0.25);\n\\draw ($(A)!0.5!(B)$) node [left] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(C1)$) node [right] {$F$} coordinate (F);\n\\draw ($(B)!0.8!(C)$) node [below] {$G$} coordinate (G);\n\\draw (F)--(G);\n\\draw [dashed] (F)--(E)--(G);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{0}{1}{2}{3}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015348": {
+        "id": "015348",
+        "content": "设$a \\in \\mathbf{R}$, 若集合$A=\\{(x, y) |(x+y)^2+x+y-2 \\leq 0\\}$, $B=\\{(x, y) |(x-a)^2+(y-2 a-1)^2 \\leq a^2-1\\}$, \n且$A \\cap B \\neq \\varnothing$, 则$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015349": {
+        "id": "015349",
+        "content": "已知$a$、$b$、$\\alpha$、$\\beta \\in \\mathbf{R}$, 满足$\\sin \\alpha+\\cos \\beta=a$, $\\cos \\alpha+\\sin \\beta=b$, $0<a^2+b^2 \\leq 4$, 有以下$2$个结论:\\\\\n\\textcircled{1} 存在常数$a$, 使得满足条件的实数$b$存在, 且对任意满足条件的实数$b$, $\\sin (\\alpha+\\beta)$的值是一个常数;\\\\\n\\textcircled{2} 存在常数$b$, 使得满足条件的实数$a$存在, 且对任意满足条件的实数$a$, $\\cos (\\alpha-\\beta)$的值是一个常数.\\\\\n其中真命题的个数是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015350": {
+        "id": "015350",
+        "content": "已知数列$\\{a_n\\}$中, $a_2=3 a_1$, 记$\\{a_n\\}$的前$n$项和为$S_n$, 且满足$S_{n+1}+S_n+S_{n-1}=3 n^2+2$($n \\geq 2$, $n \\in \\mathbf{N}$). 若对任意正整数$n$, 都有$a_n<a_{n+1}$, 则首项$a_1$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "015351": {
+        "id": "015351",
+        "content": "已知$u \\in \\mathbf{R}$, 关于$x$的方程$\\sin ^2 x-\\dfrac{1}{2} \\sin x=u$的所有正实数解按从小到大的顺序排列后, 是否能构成等差数列? 若能, 求所有满足条件的$u$的值; 若不存在, 说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023年空中课堂高三复习课32",
+        "edit": [
+            "20230501\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "020001": {
         "id": "020001",
         "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",