20221202 afternoon

This commit is contained in:
Wang Weiye 2022-12-02 13:10:18 +08:00
parent 4a7a32cde2
commit 412074cb34
6 changed files with 441 additions and 51 deletions

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@ -11,7 +11,7 @@
"text": [ "text": [
"首个空闲id: 12096 , 直至 020000\n", "首个空闲id: 12096 , 直至 020000\n",
"首个空闲id: 20227 , 直至 030000\n", "首个空闲id: 20227 , 直至 030000\n",
"首个空闲id: 30483 , 直至 999999\n" "首个空闲id: 30496 , 直至 999999\n"
] ]
} }
], ],

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@ -2,20 +2,20 @@
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"#修改起始id,出处,文件名\n", "#修改起始id,出处,文件名\n",
"starting_id = 30485\n", "starting_id = 12096\n",
"origin = \"空中课堂必修第三册复习课例题\"\n", "origin = \"2023届高三上学期考试院提供适应性测试卷\"\n",
"filename = r\"C:\\Users\\Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目5.tex\"\n",
"editor = \"20221127\\t王伟叶\"" "editor = \"20221202\\t王伟叶\""
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@ -70,8 +70,8 @@
" pid = str(id).zfill(6)\n", " pid = str(id).zfill(6)\n",
" if pid in pro_dict:\n", " if pid in pro_dict:\n",
" duplicate_flag = True\n", " duplicate_flag = True\n",
" NewProblem = CreateNewProblem(id = pid, content = p, origin = origin , dict = pro_dict,editor = editor)\n", " # NewProblem = CreateNewProblem(id = pid, content = p, origin = origin , dict = pro_dict,editor = editor)\n",
" # NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n", " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n",
" pro_dict[pid] = NewProblem\n", " pro_dict[pid] = NewProblem\n",
" id += 1\n", " id += 1\n",
"\n", "\n",
@ -101,7 +101,7 @@
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@ -115,12 +115,12 @@
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@ -9,36 +9,27 @@
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"012075 填空题\n", "012096 填空题\n",
"012076 填空题\n", "012097 填空题\n",
"012077 填空题\n", "012098 填空题\n",
"012078 填空题\n", "012099 填空题\n",
"012079 填空题\n", "012100 填空题\n",
"012080 填空题\n", "012101 填空题\n",
"012081 填空题\n", "012102 填空题\n",
"012082 填空题\n", "012103 填空题\n",
"012083 填空题\n", "012104 填空题\n",
"012084 填空题\n", "012105 填空题\n",
"012085 填空题\n", "012106 填空题\n",
"012086 填空题\n", "012107 填空题\n",
"012087 选择题\n", "012108 选择题\n",
"012088 选择题\n", "012109 选择题\n",
"012089 选择题\n", "012110 选择题\n",
"012090 选择题\n", "012111 选择题\n",
"012091 解答题\n", "012112 解答题\n",
"012092 解答题\n", "012113 解答题\n",
"012093 解答题\n", "012114 解答题\n",
"012094 解答题\n", "012115 解答题\n",
"012095 解答题\n", "012116 解答题\n"
"030485 解答题\n",
"030486 解答题\n",
"030487 解答题\n",
"030488 解答题\n",
"030489 解答题\n",
"030490 解答题\n",
"030491 解答题\n",
"030492 解答题\n",
"030493 解答题\n"
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@ -480,7 +480,7 @@
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@ -456,7 +456,7 @@
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@ -298029,6 +298029,405 @@
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"content": "已知集合$A=\\{x|\\dfrac{2x}{x-1}\\le 1\\}$, $B=\\{-1,0,1,2\\}$, 则$A\\cap B=$\\blank{50}.",
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"content": "在空间直角坐标系中, 点$A(1,2,-3)$关于$xOz$平面对称的点的坐标是$\\blank{50}$.",
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"content": "已知$m\\in \\mathbf{R}$, 直线$l_1:\\sqrt{3}x-y+7=0$, $l_2:mx+y-1=0$. 若$l_1\\parallel l_2$, 则$l_1$与$l_2$之间的距离为\\blank{50}.",
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"012100": {
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"content": "为了解某校高三年级男生的体重, 从该校高三年级男生中抽取$17$名, 测得他们的体重数据如下(按从小到大的顺序排列, 单位: kg): $56\\ 56 \\ 57\\ 58\\ 59\\ 59\\ 61\\ 63\\ 64\\ 65\\ 66\\ 68\\ 69\\ 70\\ 73\\ 74\\ 83$\\\\\n据此估计该校高三年级男生体重的第$75$百分位数为\\blank{50}kg.",
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"012101": {
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"content": "设$a,b$为实数. 若关于$x$的方程$x^2+abx+b=0$的解集为$\\{1,3\\}$, 则$a=$\\blank{50}.",
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"content": "已知常数$m>0$. 在$(x+\\dfrac mx)^6$的二项展开式中, $x^2$项的系数是$\\dfrac{1}{x^2}$项的系数的$4$倍, 则$m=$\\blank{50}.",
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"content": "已知定义在$(-3,3)$上的奇函数$y=f(x)$的导函数是$f'(x)$, 当$x\\ge 0$时, $y=f(x)$的图像如图所示, 则关于$x$的不等式$\\dfrac{f'(x)}{x}>0$的解集为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=stealth, line cap = round, line join = round,scale = 0.6]\n\\draw [->] (-1,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:3] plot (\\x,{1-pow(\\x-1,2)});\n\\draw [dashed] (1,0) node [below] {$1$} -- (1,1) (3,-3) -- (3,0) node [below right] {$3$};\n\\draw (2,0) node [below left] {$2$};\n\\end{tikzpicture}\n\\end{center}",
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"012105": {
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"content": "第$14$届国际数学教育大会(ICME-14)于$2021$年$7$月$12$日至$18$日在上海举办, 已知张老师和李老师都在$7$天中随机选择了连续的$3$天参会, 则两位老师所选的日期恰好都不相同的概率为\\blank{50}.",
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"012106": {
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"content": "已知$A$、$B$、$C$是半径为$1$的球面上的三点, 若$AB=AC=1$, 则$BC$的最大值为\\blank{50}.",
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"012107": {
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"content": "设$a\\in \\mathbf{R}$, $m\\in \\mathbf{Z}$. 若存在唯一的$m$使得关于$x$的不等式组$\\dfrac 12 x^2-\\dfrac 12<m<x+a$有解, 则$a$的取值范围是\\blank{50}.",
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"content": "如图是$6$株圣女果植株挂果个数的茎叶图, 则$6$株圣女果植株挂果个数的中位数为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=stealth, line cap = round, line join = round]\n\\draw (0,0) node {$1$};\n\\draw (0,-0.5) node {$2$};\n\\draw (0,-1) node {$3$};\n\\draw (0.3,0) node {$6$};\n\\draw (0.6,0) node {$8$};\n\\draw (0.3,-0.5) node {$1$} (0.6,-0.5) node {$2$} (0.9,-0.5) node {$2$};\n\\draw (0.3,-1) node {$1$};\n\\draw (0.15,0.25) -- (0.15,-1.25);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$21$}{$21.5$}{$22$}{$22.5$}",
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"content": "已知双曲线$\\Gamma_1:\\dfrac{x^2}{a_1^2}-\\dfrac{y^2}{b_1^2}=1$($a_1>0$, $b_1>0$)与$\\Gamma_2:\\dfrac{x^2}{a_2^2}-\\dfrac{y^2}{b_2^2}=1$($a_2>0$, $b_2>0$)有共同的渐近线, 则它们一定有相等的\\bracket{20}.\n\\fourch{实轴长}{虚轴长}{焦距}{离心率}",
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"content": "已知数列$\\{a_n\\}$的前$n$项和为$S_n$, 若$S_{2023}=a_{2023}$, 则$\\{a_n\\}$不可能是\\bracket{20}. \n\\twoch{公差大于$0$的等差数列}{公差小于$0$的等差数列}{公比大于$0$的等比数列}{公比小于$0$的等比数列}",
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"content": "已知$\\omega \\in \\mathbf{R}$, $\\varphi \\in [0, 2\\pi)$. 若对任意实数$x$均有$\\sin x\\ge \\cos (\\omega x+\\varphi)$, 则满足条件的有序实数对$(\\omega , \\varphi)$的个数为\\bracket{20}. \n\\fourch{$1$个}{$2$个}{$3$个}{无数个}",
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"content": "设等差数列$\\{a_n\\}$的前$n$项和为$S_n$, 且$a_4=10$.\\\\\n(1) 若$S_{20}=590$, 求$\\{a_n\\}$的公差;\\\\\n(2) 若$a_1\\in \\mathbf{Z}$, 且$S_7$是数列$\\{S_n\\}$中最大的项, 求$a_1$所有可能的值.",
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"012113": {
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"content": "如图, 正四棱柱$ABCD-A_1B_1C_1D_1$的底面边长为$1$, 高为$2$, $AC$、$BD$相交于点$O$.\n\\begin{center}\n\\begin{tikzpicture}[>=stealth, line cap = round, line join = round, scale = 1.7]\n\\def\\l{1}\n\\def\\m{1}\n\\def\\n{2}\n\\draw (0,0,0) node [below left] {\\footnotesize $A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {\\footnotesize $B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {\\footnotesize $C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {\\footnotesize $D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {\\footnotesize $A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [above] {\\footnotesize $B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {\\footnotesize $C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {\\footnotesize $D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw (A1)-- (C1);\n\\draw [dashed] (A1) -- (D) (C1) -- (D) (A) -- (C) (B) -- (D);\n\\draw ($(A)!0.5!(C)$) node [below] {\\footnotesize $O$} coordinate (O);\n\\draw [dashed] (O) -- (B1);\n\\end{tikzpicture}\n\\end{center}\n(1)证明: 直线$B_1O$与平面$A_1C_1D$平行;\\\\\n(2)求三棱锥$O-A_1C_1D$的体积.",
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"012114": {
"id": "012114",
"content": "闲置房出租是增加社会住房供给量, 满足人们居住需求的重要途径. 王先生有一套住房以每月$7000$元的价格出租, 但合同租期本月到期. 房客直接向王先生提出希望从下月起续租三年, 并愿意每月支付$8000$元的租金. 王先生通过中介公司了解到: 该房屋所在小区的类似住宅, 目前的租金为每月$8000$-$9000$元, 在委托中介公司后, 一般$2$-$4$周左右可以\n找到承租人, 同时每次租赁交易成功后, 中介公司向出租方和承租方各收取一个月租金的$50\\%$作为中介费. 对于是否同意房客续租, 王先生需要作出决策.\\\\\n(1) 除了上述了解到的情况, 还有哪些因素王先生可能需要考虑? 写出这些因素(不超过$5$个);\\\\ \n(2) 为了简化问题, 请对相关因素作出合情假设, 由此帮助王先生作出决策, 并说明理由.",
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"012115": {
"id": "012115",
"content": "已知椭圆$\\Gamma:\\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的左、右焦点分别为$F_1,F_2$, 直线$l$的斜率为$k$, 在$y$轴上的截距为$m$.\\\\\n(1) 设$k=1$, 若$\\Gamma$的焦距为$2$, $l$过点$F_1$, 求$l$的方程;\\\\\n(2) 设$m=0$. 若$P(\\sqrt{3},\\dfrac 12)$是$\\Gamma$上的一点, 且$|\\overrightarrow{PF_1}|+|\\overrightarrow{PF_2}|=4$, $l$与$\\Gamma$交于不同的两点$A,B$, $Q$为$\\Gamma$的上顶点, 求$\\triangle ABQ$面积的最大值;\\\\\n(3) 设$\\overrightarrow{n}$是$l$的一个法向量, $M$是$l$上一点, 对于坐标平面内的点$N$, 定义$\\delta_N=\\dfrac{\\overrightarrow{n}\\cdot \\overrightarrow{MN}}{|\\overrightarrow{n}|}$. 用$a,b,k,m$表示$\\delta_{F_1}\\cdot \\delta_{F_2}$, 并利用$\\delta_{F_1}\\cdot \\delta_{F_2}$与$b^2$的大小关系, 提出一个关于$l$与$\\Gamma$位置关系的真命题, 给出该命题的证明.",
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"012116": {
"id": "012116",
"content": "已知$a\\in \\mathbf{R}$, 函数$f(x)=\\sin^2 x-a\\sin x$.\\\\\n(1) 当$a=2$时, 求$f(x)$的值域;\\\\\n(2) 若函数$y=f(x)-f(\\dfrac \\pi 2-x)$在区间$[0,\\dfrac\\pi 2]$上是严格增函数, 求$a$的最大值;\\\\\n(3) 设$a=\\dfrac 12$, $u\\in \\mathbf{R}$. 方程$f(x)=u$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; 若不能, 说明理由.",
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"020001": { "020001": {
"id": "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.", "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.",