录入华二高二期中考试卷试题
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@ -2,7 +2,7 @@ import os,re,json
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"""---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---"""
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keywords_dict_table = [
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{"origin":[r"高一下学期"],"origin2":[r"统考"]}
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{"origin":[r"交大附中"]}
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]
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"""---关键字设置完毕---"""
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# 示例: keywords_dict_table = [
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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 = 15311
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starting_id = 40605
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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 = "20230420\t王伟叶"
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filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex"
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editor = "20230423\t王伟叶"
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indexed = True
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import os,re,json
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@ -1 +1 @@
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015269:015289
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040464:040505
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@ -475069,5 +475069,404 @@
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"related": [],
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"remark": "",
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"space": "12ex"
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},
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"040605": {
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"id": "040605",
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"content": "四人互相传球, 由甲开始发球, 并作为第一次传球, 经过$3$次传球后, 球仍回到甲手中, 则不同的传球方式共有\\blank{50}种.",
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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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"remark": "",
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"space": ""
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},
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"040606": {
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"id": "040606",
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"content": "书架上某层有$8$本书, 新买$2$本插进去, 要保持原有$8$本书的顺序, 则有\\blank{50}种不同的插法. (具体数字作答)",
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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": "202304华二高二期中考试试题2",
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"edit": [
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"20230423\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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"040607": {
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"id": "040607",
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"content": "若$(x+1)^n$的展开式中第$3$项与第$9$项的二项式系数相等, 则$n=$\\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": "202304华二高二期中考试试题3",
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"edit": [
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"20230423\t王伟叶"
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],
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"same": [],
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"remark": "",
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"space": ""
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},
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"040608": {
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"id": "040608",
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"content": "$7$ 个志愿者的名额分给$3$个班, 每班至少一个名额, 则有\\blank{50}种不同的分配方法. (用数字作答)",
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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": "202304华二高二期中考试试题4",
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"edit": [
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"20230423\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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"040609": {
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"id": "040609",
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"content": "$A$、$B$、$C$、$D$、$E$五名同学站成一排合影, 若$A$不站在两端, $B$和$C$相邻, 则不同的站队方式共有\\blank{50}种. (用数字作答)",
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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": "202304华二高二期中考试试题5",
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"edit": [
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"20230423\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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"040610": {
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"id": "040610",
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"content": "设函数$f(x)=\\dfrac{1}{3} x^2-27 \\ln x$在区间$[a, 2 a+1]$上严格减, 则实数$a$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": "202304华二高二期中考试试题6",
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"edit": [
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"20230423\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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"040611": {
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"id": "040611",
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"content": "$6$ 位大学毕业生分配到$3$家单位, 每家单位至少录用$1$人, 则不同的分配方法共有\\blank{50}种.",
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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": "202304华二高二期中考试试题7",
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"edit": [
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"20230423\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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"040612": {
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"id": "040612",
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"content": "已知在四面体$V-ABC$中, $VA=VB=VC=2$, $AB=1$, $\\angle ACB=\\dfrac{\\pi}{6}$, 则该四面体外接球的表面积为\\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": "202304华二高二期中考试试题8",
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"edit": [
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"20230423\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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"040613": {
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"id": "040613",
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"content": "用 1、2、3、4、5 组成没有重复数字的五位数$\\overline{a b c d e}$, 其中满足$a>b>c$, 且$c<d<e$的五位数有$n$个, 则在$1+(1+x)^1+(1+x)^2+(1+x)^3+\\cdots+(1+x)^n$的展开式中, $x^2$的系数是\\blank{50}.(用数字作答)",
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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": "202304华二高二期中考试试题9",
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"edit": [
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"20230423\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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"040614": {
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"id": "040614",
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"content": "已知函数$f(x)$的导函数$f'(x)$的图像如图所示, 给出以下结论:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-3,0) -- (3.2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [above right] {$O$};\n\\foreach \\i in {-2,-1,1,2,3}\n{\\draw (\\i,0) -- (\\i,0.1) node [above] {$\\i$};};\n\\draw (-3,0.5) -- (-1,-0.5) -- (1,0) -- (3.2,-0.8);\n\\draw [dashed] (-1,0) -- (-1,-0.5) (3,0) -- (3,-0.75);\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} $f(x)$在区间$(-1,1)$上严格增;\\\\\n\\textcircled{2} $f(x)$的图像在$x=-2$处的切线斜率等于$0$;\\\\\n\\textcircled{3} $f(x)$在$x=1$处取得极大值;\\\\\n\\textcircled{4} $f'(x)$在$x=-1$处取得极小值.\\\\\n正确的序号是\\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": "202304华二高二期中考试试题10",
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"edit": [
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"20230423\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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"040615": {
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"id": "040615",
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"content": "平面直角坐标系$xOy$中, 已知点$M(2,-1)$, 若直线$l: 3 x-4 y+5=0$上总存在$P$、$Q$两点, 使得$\\angle PMQ \\geq \\dfrac{\\pi}{2}$恒成立, 则线段$PQ$长度的取值范围是\\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": "202304华二高二期中考试试题11",
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"edit": [
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"20230423\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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"040616": {
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"id": "040616",
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"content": "设$x_1$、$x_2$是函数$f(x)=a x^2-\\mathrm{e}^x$ ($a \\in \\mathbf{R}$)的两个极值点, 若$\\dfrac{x_2}{x_1} \\geq 2$, 则$a$的最小值为\\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": "202304华二高二期中考试试题12",
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"edit": [
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"20230423\t王伟叶"
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],
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"related": [],
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"remark": "",
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"space": ""
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},
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"040617": {
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"id": "040617",
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"content": "下列求导运算正确的是\\bracket{20}.\n\\twoch{$(\\ln x+\\dfrac{3}{x})'=\\dfrac{1}{x}+\\dfrac{3}{x^2}$}{$(x^2 \\mathrm{e}^x)'=2 x \\mathrm{e}^x$}{$(3^x \\cos 2 x)'=3^x(\\ln 3 \\cdot \\cos 2 x-2 \\sin 2 x)$}{$(\\ln \\dfrac{1}{2}+\\log _2 x)'=2+\\dfrac{1}{x \\ln 2}$}",
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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": "202304华二高二期中考试试题13",
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"edit": [
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"20230423\t王伟叶"
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],
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"remark": "",
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"space": ""
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},
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"040618": {
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"id": "040618",
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"content": "函数$f(x)=\\dfrac{x-\\sin x}{\\mathrm{e}^x+\\mathrm{e}^{-x}}$在$[-\\pi, \\pi]$上的图像大致为\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex, xscale = 0.4, yscale = 5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-0.2) -- (0,0.2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain =-pi:pi, samples = 100] plot (\\x,{(\\x-sin(\\x/pi*180))/(exp(\\x)+exp(-\\x))});\n\\draw (0.3,0.1) -- (0,0.1) node [left] {$0.1$};\n\\draw (pi,0.02) -- (pi,0) node [below] {$\\pi$};\n\\draw (-pi,0.02) -- (-pi,0) node [below] {$-\\pi$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, xscale = 0.4, yscale = 5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-0.2) -- (0,0.2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain =-pi:pi, samples = 100] plot (\\x,{(\\x-1.5*sin(\\x/pi*180))/(exp(\\x)+exp(-\\x))});\n\\draw (0,0.1) -- (0.3,0.1) node [right] {$0.1$};\n\\draw (pi,0.02) -- (pi,0) node [below] {$\\pi$};\n\\draw (-pi,0.02) -- (-pi,0) node [below] {$-\\pi$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, xscale = 0.4, yscale = 5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-0.2) -- (0,0.2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain =-pi:pi, samples = 100] plot (\\x,{-(\\x-sin(\\x/pi*180))/(exp(\\x)+exp(-\\x))});\n\\draw (0.3,0.1) -- (0,0.1) node [left] {$0.1$};\n\\draw (pi,0.02) -- (pi,0) node [below] {$\\pi$};\n\\draw (-pi,0.02) -- (-pi,0) node [below] {$-\\pi$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, xscale = 0.4, yscale = 5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-0.2) -- (0,0.2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain =-pi:pi, samples = 100] plot (\\x,{sqrt(abs(\\x))/10-0.1});\n\\draw (0.3,0.1) -- (0,0.1) node [left] {$0.1$};\n\\draw (pi,0.02) -- (pi,0) node [below] {$\\pi$};\n\\draw (-pi,0.02) -- (-pi,0) node [below] {$-\\pi$};\n\\end{tikzpicture}}",
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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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"space": ""
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},
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"040619": {
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"id": "040619",
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"content": "设$(2 x-1)^5=a_0+a_1 x+a_2 x^2+a_3 x^3+a_4 x^4+a_5 x^5$, 则$|a_1|+2|a_2|+3|a_3|+4|a_4|+5|a_5|=$\\bracket{20}.\n\\fourch{$80$}{$242$}{$405$}{$810$}",
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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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||||
"duration": -1,
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||||
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||||
"origin": "202304华二高二期中考试试题15",
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"edit": [
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"20230423\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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"040620": {
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"id": "040620",
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"content": "点$P$为抛物线$C: y^2=4 x$准线上的点, 若存在过$P$的直线交抛物线$C$于$A$、$B$两点, 且$|PA|=|AB|$, 则称点$P$为``$\\Omega$点'', 那么下列结论中正确的是\\bracket{20}.\n\\onech{准线上的所有点都不是``$\\Omega$点''}{准线上的所有点都是``$\\Omega$点''}{准线上仅有有限个点是``$\\Omega$点''}{准线上有无穷多个点(不是所有的点)是``$\\Omega$点''}",
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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": "202304华二高二期中考试试题16",
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"edit": [
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"20230423\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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"040621": {
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"id": "040621",
|
||||
"content": "如图, 已知四棱锥$P-ABCD$的底面是菱形, 对角线$AC$、$BD$交于点$O$, $OA=3$, $OB=4$, $OP=3$, $OP \\perp$底面$ABCD$, 设点$M$满足$\\overrightarrow{PM}=\\dfrac{1}{2} \\overrightarrow{MC}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw (0,0,0) node [below] {$O$} coordinate (O);\n\\draw ({-3/sqrt(2)},0,{3/sqrt(2)}) node [below] {$A$} coordinate (A);\n\\draw ({2*sqrt(2)},0,{2*sqrt(2)}) node [below] {$B$} coordinate (B);\n\\draw ($(A)!2!(O)$) node [right] {$C$} coordinate (C);\n\\draw ($(B)!2!(O)$) node [left] {$D$} coordinate (D);\n\\draw (O) ++ (0,3,0) node [above] {$P$} coordinate (P);\n\\draw ($(P)!{1/3}!(C)$) node [right] {$M$} coordinate (M);\n\\draw (A)--(B)--(C)--(P)--cycle(P)--(B)(M)--(B)(P)--(D)--(A);\n\\draw [dashed] (A)--(C)(B)--(D)(P)--(O)(D)--(M)(D)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$PA$与平面$BDM$所成角的正弦值;\\\\\n(2) 求点$P$到平面$BDM$的距离.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "202304华二高二期中考试试题17",
|
||||
"edit": [
|
||||
"20230423\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"040622": {
|
||||
"id": "040622",
|
||||
"content": "对于代数式$(2 x-\\dfrac{1}{\\sqrt{x}})^5$,\\\\\n(1) 求其展开式中含$x^2$的项的系数;\\\\\n(2) 设该代数式的展开式中前三项的二项式系数的和为$M$, $(1+a x)^4$的展开式中各项系数的和为$N$, 若$M=N$, 求实数$a$的值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "202304华二高二期中考试试题18",
|
||||
"edit": [
|
||||
"20230423\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"040623": {
|
||||
"id": "040623",
|
||||
"content": "已知直线$l: y=k x$($k \\neq 0$)与圆$C: x^2+y^2-2 x-3=0$相交于$A$、$B$两点.\\\\\n(1) 若$|AB|=\\sqrt{13}$, 求$k$;\\\\\n(2) 在$x$轴上是否存在点$M$, 使得当$k$变化时, 总有直线$MA$、$MB$的斜率之和为 $0$ , 若存在, 求出点$M$的坐标; 若不存在, 说明理由.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "202304华二高二期中考试试题19",
|
||||
"edit": [
|
||||
"20230423\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"040624": {
|
||||
"id": "040624",
|
||||
"content": "已知椭圆$C: \\dfrac{x^2}{a^2}+y^2=1$($a>1$)的离心率为$\\dfrac{\\sqrt{3}}{2}$.\\\\\n(1) 求椭圆$C$的方程;\\\\\n(2) 若直线$l: y=k x-2$与椭圆$C$交于两个不同点$D$、$E$, 以线段$DE$为直径的圆经过原点, 求实数$k$的值;\\\\\n(3) 设$A$、$B$为椭圆$C$的左、右顶点, $H$为椭圆$C$上除$A$、$B$外任意一点, 线段$BH$的垂直平分线分别交直线$BH$和直线$AH$于点$P$和点$Q$, 分别过点$P$和$Q$作$x$轴的垂线, 垂足分别为$M$和$N$, 求证: 线段$MN$的长为定值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "202304华二高二期中考试试题20",
|
||||
"edit": [
|
||||
"20230423\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"040625": {
|
||||
"id": "040625",
|
||||
"content": "已知函数$f(x)=x-\\ln x-3$.\\\\\n(1) 求曲线$y=f(x)$在$x=1$处的切线方程;\\\\\n(2) 函数$f(x)$在区间$(k, k+1)$ ($k \\in \\mathbf{N}$)上有零点, 求$k$的值;\\\\\n(3) 记函数$g(x)=x^2-b x-3-f(x)$, 设$x_1$、$x_2$($x_1<x_2$)是函数$g(x)$的两个极值点, 若$b \\geq 2$, 且$g(x_1)-g(x_2) \\geq m$恒成立, 求实数$m$的最大值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "202304华二高二期中考试试题21",
|
||||
"edit": [
|
||||
"20230423\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
}
|
||||
}
|
||||
Reference in New Issue