收录徐汇区2023届二模试题
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import os,re,json
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"""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"""
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problems = "593"
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problems = "15229"
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def generate_number_set(string,dict):
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string = re.sub(r"[\n\s]","",string)
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@ -1,8 +1,8 @@
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#修改起始id,出处,文件名
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starting_id = 15248
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starting_id = 15290
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raworigin = ""
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filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目11.tex"
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editor = "20230418\t王伟叶"
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editor = "20230419\t王伟叶"
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indexed = True
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import os,re,json
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@ -34,7 +34,7 @@ problems_dict = {
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"第九单元":"014791,014797,014811,014812,014823,014844,015009,015026,015035,015051,015077,015094,015098,015106,015119,015130,015141,015145,015151,015177,015197,015203,015219"
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}
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20230414 2023届高三二模(15区, 缺徐汇)
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20230414 2023届高三二模
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problems_dict = {
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"2023届高三杨浦区二模试题":"14784:14804",
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"2023届高三崇明区二模试题":"14805:14825",
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@ -51,6 +51,7 @@ problems_dict = {
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"2023届长宁区高三二模试题":"15185:15205",
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"2023届松江区高三二模试题":"15206:15226",
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"2023届奉贤区高三二模试题":"15227:15247",
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"2023届徐汇区高三二模试题":"15290:15310"
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}
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20230418 2022学年第二学期高一高二材料收集
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@ -377274,6 +377274,405 @@
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"remark": "",
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"space": "12ex"
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},
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"015290": {
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"id": "015290",
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"content": "已知集合$A=\\{x \\| x |<3\\}$, $B=\\{x | y=\\sqrt{2-x}\\}$, 则$A \\cup B=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题1",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015291": {
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"id": "015291",
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"content": "若角$\\alpha$的终边过点$P(4,-3)$, 则$\\sin (\\dfrac{3 \\pi}{2}+\\alpha)=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题2",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015292": {
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"id": "015292",
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"content": "抽取某校高一年级$10$名女生, 测得她们的身高 (单位: $\\text{cm}$) 数据如下: $163$, $165$, $161$, $157$, $162$, $165$, $158$, $155$, $164$, $162$, 据此估计该校高一年级女生身高的第$25$百分位数是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题3",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015293": {
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"id": "015293",
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"content": "命题``若$x>a$, 则$\\dfrac{x-1}{x}>0$''是真命题, 实数$a$的取值范围是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题4",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015294": {
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"id": "015294",
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"content": "在正项等比数列$\\{a_n\\}$中, $a_5^2+2 a_6 a_8+a_9^2=100$, 则$a_5+a_9=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题5",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015295": {
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"id": "015295",
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"content": "设一组样本数据$x_1, x_2, \\cdots, x_n$的方差为$0.01$, 则数据$10 x_1, 10 x_2, \\cdots, 10 x_n$的方差为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题6",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015296": {
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"id": "015296",
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"content": "如图所示, 圆锥$SO$的底面圆半径$OA=1$, 侧面的平面展开图的面积为$3 \\pi$, 则此圆锥的体积为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw (0,0) node [left] {$O$} coordinate (O);\n\\draw (1,0) node [below] {$A$} coordinate (A);\n\\draw (0,{2*sqrt(2)}) node [above left] {$S$} coordinate (S);\n\\draw (A) arc ({-acos(1/3)}:{-acos(1/3)+120}:3) node [above] {$B$} coordinate (B);\n\\draw (A)--(S)--(-1,0) arc (180:360:1 and 0.25) (B)--(S);\n\\draw [dashed] (S)--(O)--(A) arc (0:180:1 and 0.25);\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题7",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015297": {
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"id": "015297",
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"content": "若$(1+x)(1-2 x)^{2023}=a_0+a_1 x+a_2 x^2+\\cdots+a_{2024} x^{2024}$, $a_1 \\in \\mathbf{R}$($i=0,1,2, \\cdots, 2024$), 则$a_1+a_2+\\cdots+a_{2004}=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题8",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015298": {
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"id": "015298",
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"content": "己知双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的左焦点为$F(-1,0)$, 过$F$且与$x$轴垂直的直线与\n双曲线交于$A$、$B$两点, $O$为坐标原点, $\\triangle AOB$的面积为$\\dfrac{3}{2}$, 则$F$到双曲线的浙近线距离为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题9",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015299": {
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"id": "015299",
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"content": "甲、乙、丙、丁四名同学互不影响地报名参加高中社会实践活动, 高中社会实践活动共有博物馆讲解、养老院慰问、交通宣传、超市导购四个项目, 每人限报其中一项, 记事件$A$为``$4$名同学所报项目各不相同'', 事件$B$为``只有甲同学一人报交通宣传项目, 则$P(A | B)=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题10",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015300": {
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"id": "015300",
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"content": "已知函数$f(x)=x+\\dfrac{a}{x}+b$, $x \\in[b,+\\infty)$, 其中$b>0$, $a \\in \\mathbf{R}$, 若$f(x)$的最小值为$2$, 则实数$a$的取值范周是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题11",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015301": {
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"id": "015301",
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"content": "已知数列$\\{a_n\\}$溚足: 对于任意$n \\in \\mathbf{N}$, $n\\ge 1$, 有$a_n \\in(0, \\dfrac{\\pi}{2})$, 且$a_1=\\dfrac{\\pi}{4}$, $f(a_{n+1})=\\sqrt{f'(a_n)}$, 其中$f(x)=\\tan x$. 若$b_n=\\dfrac{(-1)^n}{\\tan a_{n+1}-\\tan a_n}$, 数列$\\{b_n\\}$的前$n$项和为$T_n$, 则$T_{120}=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题12",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015302": {
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"id": "015302",
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"content": "已知$z \\in \\mathbf{C}$, 则``$z+\\overline {z}=0$''是``$\\mathrm{z}$为纯虚数''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届徐汇区高三二模试题13",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015303": {
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"id": "015303",
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"content": "某社区通过公益讲座宣传中国非物质文化遗产保护知识. 为了解讲座效果, 随机抽取$10$位社区居民, 让他们在讲座前和讲座后各回答一份相关知识问卷, 这$10$位社区居民在讲座前和讲座后问卷答题的正确率如下图. 则下列选项正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.7, yscale = 0.08]\n\\draw [->] (0,55) -- (11,55);\n\\draw [->] (0,55) -- (0,56) -- (0.2,57) -- (-0.2,58) -- (0,59) -- (0,105);\n\\draw (0,55) node [below left] {$O$};\n\\foreach \\i in {1,2,...,10}\n{\\draw (\\i,55.5) -- (\\i,55) node [below] {$\\i$};};\n\\foreach \\i in {60,65,...,100}\n{\\draw [dotted] (10.5,\\i) -- (0,\\i) node [left] {$\\i\\%$};};\n\\draw (5.5,45) node {居民编号};\n\\draw (-2,80) node [rotate = 90] {正确率};\n\\filldraw (12,70) circle (0.05 and {7/16}) ++ (1,0) node {讲座后};\n\\filldraw (12,80) node {\\tiny$\\times$} node {\\tiny$+$} ++ (1,0) node {讲座前};\n\\foreach \\i/\\j/\\k in {1/65/90,2/60/85,3/70/80,4/60/90,5/65/85,6/75/85,7/90/95,8/85/100,9/80/85,10/95/100}\n{\\filldraw (\\i,\\j) node {\\tiny$\\times$} node {\\tiny$+$} (\\i,\\k) circle (0.05 and {7/16});};\n\\end{tikzpicture}\n\\end{center}\n\\onech{讲座前问卷答题的正确率的中位数小于$70 \\%$}{讲座后问卷答题的正确率的平均数大于$85 \\%$}{讲座前问卷答题的正确率的标准差小于讲座后正确率的标准差}{讲座后问卷答题的正确率的极差大于讲座前正确率的极差}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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||||
"origin": "2023届徐汇区高三二模试题14",
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"edit": [
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||||
"20230419\t王伟叶"
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],
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||||
"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015304": {
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"id": "015304",
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"content": "设函数$f(x)=\\begin{cases}-x^2-2 x, x \\leq 0, \\\\ |\\ln x|, x>0,\\end{cases}$ 现有如下命题: \\textcircled{1} 若方程$f(x)=a$有四个不同的实根$x_1$、$x_2$、$x_3$、$x_4$, 则$x_1 \\cdot x_2 \\cdot x_3 \\cdot x_4$的取值范围是$(0,1)$; \\textcircled{2} 方程$f^2(x)-(a+\\dfrac{1}{a}) f(x)+1=0$的不同实根的个数只能是$1 , 2 , 3 , 8$, 下列判断正确的是\\bracket{20}.\n\\twoch{\\textcircled{1}和\\textcircled{2}均为真命题}{\\textcircled{1}和\\textcircled{2}均为假命题}{\\textcircled{1}为真命题, \\textcircled{2}为假命题}{\\textcircled{1}为假命题, \\textcircled{2}为真命题}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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||||
"usages": [],
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||||
"origin": "2023届徐汇区高三二模试题15",
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"edit": [
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"20230419\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"015305": {
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"id": "015305",
|
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"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": "",
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||||
"duration": -1,
|
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"usages": [],
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"20230419\t王伟叶"
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"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015306": {
|
||||
"id": "015306",
|
||||
"content": "雅言传承文明, 经典滋润人生, 中国的经典诗文是中华民族精神文明的重要组成部分. 某社区拟开展``诵读国学经典, 积淀文化底蕴''活动. 为了调查不同年龄人对此项活动所持的态度, 研究人员随机抽取了$300$人, 并将所得结果统计如下表所示.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline 分组区间 & {$[20,30)$} & {$[30,40)$} & {$[40,50)$} & {$[50,60)$} & {$[60,70]$} \\\\\n\\hline 人数 & 30 & 75 & 105 & 60 & 30 \\\\\n\\hline 支持态度人数 & 24 & 66 & 90 & 42 & 18 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1)完成下列$2 \\times 2$列联表, 并判断是否有$95 \\%$的把握认为年龄与所持态度有关;\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 年龄在$50$周岁及以上 & 年龄在$50$周岁以下 & 总计 \\\\\n\\hline 支持态度人数 & & & \\\\\n\\hline 不支持态度人数 & & & \\\\\n\\hline 总计 & & & \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(2) 以 (1) 中的频率估计概率, 若在该地区所有年龄在$50$周岁及以上的人中随机抽取$4$人, 记$X$为$4$人中持支持态度的人数, 求$X$的分布以及数学期望.\\\\\n参考数据: $P(\\chi^2 \\geq 3.841) \\approx 0.05$, 参考公式: $\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)}$.",
|
||||
"objs": [],
|
||||
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|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
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||||
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|
||||
"20230419\t王伟叶"
|
||||
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||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015307": {
|
||||
"id": "015307",
|
||||
"content": "已知向量$\\overrightarrow {m}=(2 \\sqrt{3} \\cos \\dfrac{x}{2},-2 \\sin \\dfrac{x}{2})$, $\\overrightarrow {n}=(\\cos \\dfrac{x}{2}, \\cos \\dfrac{x}{2})$, 函数$y=f(x)=\\overrightarrow {m} \\cdot \\overrightarrow {n}$.\\\\\n(1) 设$\\theta \\in[-\\dfrac{\\pi}{2}, \\dfrac{\\pi}{2}]$, 且$f(\\theta)=\\sqrt{3}+1$, 求$\\theta$的值;\\\\\n(2) 在$\\triangle ABC$中, $AB=1$, $f(C)=\\sqrt{3}+1$, 且$\\triangle ABC$的面积为$\\dfrac{\\sqrt{3}}{2}$, 求$\\sin A+\\sin B$的值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届徐汇区高三二模试题18",
|
||||
"edit": [
|
||||
"20230419\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
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|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015308": {
|
||||
"id": "015308",
|
||||
"content": "如图, 在直三棱柱$ABC-A_1B_1C_1$中, $\\angle BAC=90^{\\circ}$, $AB=AC=a$, $AA_1=b$, 点$E$、$F$分別在棱$BB_1$、$CC_1$上, 且$BE=\\dfrac{1}{3} BB_1$, $C_1F=\\dfrac{1}{3} CC_1$. 设$\\lambda=\\dfrac{b}{a}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,-1) node [below] {$A$} coordinate (A);\n\\draw (1,0,0) node [right] {$C$} coordinate (C);\n\\draw (-1,0,0) node [left] {$B$} coordinate (B);\n\\draw (A) ++ (0,3,0) node [above] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,3,0) node [left] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,3,0) node [right] {$C_1$} coordinate (C_1);\n\\draw ($(B)!{1/3}!(B_1)$) node [left] {$E$} coordinate (E);\n\\draw ($(C)!{2/3}!(C_1)$) node [right] {$F$} coordinate (F);\n\\draw (B)--(C)--(C_1)--(A_1)--(B_1)--cycle(B_1)--(C_1) (E)--(F);\n\\draw [dashed] (A)--(E)(A)--(F)(A_1)--(E)(A_1)--(F)(A)--(A_1)(B)--(A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 当$\\lambda=3$时, 求异面直线$AE$与$A_1F$所成的角的大小;\\\\\n(2) 当平面$AEF \\perp$平面$A_1EF$时, 求$\\lambda$的值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届徐汇区高三二模试题19",
|
||||
"edit": [
|
||||
"20230419\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015309": {
|
||||
"id": "015309",
|
||||
"content": "已知椭圆$C: \\dfrac{x^2}{t}+y^2=1$($t>1$)的左、右焦点分别为$F_1, F_2$, 直线$l: y=k x+m$($m \\neq 0$)与椭圆$C$交于$M$、$N$两点 ($M$点在$N$点的上方), 与$y$轴交于点$E$.\\\\\n(1) 当$t=2$时, 点$A$为椭圆$C$上除顶点外任一点, 求$\\triangle AF_1F_2$的周长;\\\\\n(2) 当$t=3$且直线$l$过点$D(-1,0)$时, 设$\\overrightarrow{EM}=\\lambda \\overrightarrow{DM}$, $\\overrightarrow{EN}=\\mu \\overrightarrow{DN}$, 求证: $\\lambda+\\mu$为定值, 并求出该值;\\\\\n(3) 若椭圆$C$的离心率为$\\dfrac{\\sqrt{3}}{2}$, 当$k$为何值时, $|OM|^2+|ON|^2$恒为定值? 并求此时$\\triangle MON$面积的最大值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届徐汇区高三二模试题20",
|
||||
"edit": [
|
||||
"20230419\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015310": {
|
||||
"id": "015310",
|
||||
"content": "已知常数$k$为非零整数, 若函数$y=f(x)$, $x \\in[0,1]$满足: 对任意$x_1, x_2 \\in[0,1]$, $|f(x_1)-f(x_2)| \\leq|(x_1+1)^k-(x_2+1)^k|$, 则称函数$y=f(x)$为$L(k)$函数.\\\\\n(1) 函数$y=2 x$, $x \\in[0,1]$是否为$L(2)$函数? 请说明理由;\\\\\n(2) 若$y=f(x)$为$L(1)$函数, 图像在$x \\in [0,1]$是一条连续的曲线, $f(0)=0$, $f(1)=\\dfrac{1}{2}$, 且$f(x)$在区间$(0,1)$上仅存在一个极值点, 分别记$f(x)_{\\max}$、$f(x)_{\\min}$为函数$y=f(x)$的最大、最小值, 求$f(x)_{\\max}-f(x)_{\\min}$的取值范围;\\\\\n(3) 若$a>0$, $f(x)=0.05 x^2+0.1 x+a \\ln (x+1)$, 且$y=f(x)$为$L(-1)$函数, $g(x)=f'(x)$, 对任意$x, y \\in[0,1]$, 恒有$|g(x)-g(y)| \\leq M$, 记$M$的最小值为$M(a)$, 求$a$的取值范围及$M(a)$关于$a$的表达式.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届徐汇区高三二模试题21",
|
||||
"edit": [
|
||||
"20230419\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"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.",
|
||||
|
|
|
|||
Reference in New Issue