收录2023届金山区二模试题
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#修改起始id,出处,文件名
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starting_id = 15017
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starting_id = 15038
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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 = "202304012\t王伟叶"
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@ -369604,6 +369604,405 @@
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"remark": "",
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"space": "12ex"
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},
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"015038": {
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"id": "015038",
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"content": "已知集合$A=\\{-1,0\\}$, 集合$B=\\{2, a\\}$, 若$A \\cap B=\\{0\\}$, 则$a=$\\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届金山区高三二模试题1",
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"edit": [
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"202304012\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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"015039": {
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"id": "015039",
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"content": "若实数$x$满足不等式$x^2-3 x+2<0$, 则$x$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届金山区高三二模试题2",
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"edit": [
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"202304012\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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"015040": {
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"id": "015040",
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"content": "双曲线$\\dfrac{x^2}{9}-\\dfrac{y^2}{16}=1$的渐近线方程是\\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届金山区高三二模试题3",
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"edit": [
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"202304012\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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"015041": {
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"id": "015041",
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"content": "已知向量$\\overrightarrow {a}=(0,1,0)$, 向量$\\overrightarrow {b}=(1,1,0)$, 则$\\overrightarrow {a}$与$\\overrightarrow {b}$的夹角的大小为\\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届金山区高三二模试题4",
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"edit": [
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"202304012\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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"015042": {
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"id": "015042",
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"content": "在$(2+x)^5$的二项展开式中, $x^4$项的系数为\\blank{50}(结果用数值表示).",
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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届金山区高三二模试题5",
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"edit": [
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"202304012\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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"015043": {
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"id": "015043",
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"content": "若复数$z=2+\\mathrm{i}$($\\mathrm{i}$是虚数单位), 则$z \\cdot \\overline {z}-z=$\\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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"edit": [
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"202304012\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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"015044": {
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"id": "015044",
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"content": "已知$y=f(x)$是定义域为$\\mathbf{R}$的奇函数, 当$x \\geq 0$时, $f(x)=2 x^3+2^x-1$, 则$f(-2)=$\\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届金山区高三二模试题7",
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"edit": [
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"202304012\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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"015045": {
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"id": "015045",
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"content": "掷一颗骰子, 令事件$A=\\{1,2,3\\}$, $B=\\{1,2,5,6\\}$, 则$P(A | B)=$\\blank{50}(结果用数值表示).",
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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届金山区高三二模试题8",
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"edit": [
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"202304012\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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"015046": {
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"id": "015046",
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"content": "已知正实数$a$、$b$满足$\\dfrac{1}{a}+\\dfrac{2}{b}=1$, 则$2 a+b$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": "2023届金山区高三二模试题9",
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"edit": [
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"202304012\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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"015047": {
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"id": "015047",
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"content": "若函数$y=\\sin (\\omega x-\\dfrac{\\pi}{3})$(常数$\\omega>0$)在区间$(0, \\pi)$没有最值, 则$\\omega$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届金山区高三二模试题10",
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"edit": [
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"202304012\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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"015048": {
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"id": "015048",
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"content": "已知函数$y=f(x)$和$y=g(x)$的表达式分别为$f(x)=\\sqrt{-x^2-4 x}$, $g(x)=x|x^2-a|$, 若对任意$x_1 \\in[1, \\sqrt{2}]$, 总存在$x_2 \\in[-3,0]$, 使得$g(x_1)<f(x_2)$, 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": "2023届金山区高三二模试题11",
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"edit": [
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"202304012\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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"015049": {
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"id": "015049",
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"content": "已知$\\overrightarrow {a}$、$\\overrightarrow {b}$、$\\overrightarrow {c}$、$\\overrightarrow {d}$都是平面向量, 且$|\\overrightarrow {a}|=|2 \\overrightarrow {a}-\\overrightarrow {b}|=|5 \\overrightarrow {a}-\\overrightarrow {c}|=1$, 若$\\langle\\overrightarrow {a}, \\overrightarrow {d}\\rangle=\\dfrac{\\pi}{4}$, 则$|\\overrightarrow {b}-\\overrightarrow {d}|+|\\overrightarrow {c}-\\overrightarrow {d}|$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": "2023届金山区高三二模试题12",
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"edit": [
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"202304012\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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"015050": {
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"id": "015050",
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"content": "若实数$a$、$b$满足$a^2>b^2>0$, 则下列不等式中成立的是\\bracket{20}.\n\\fourch{$a>b$}{$2^a>2^b$}{$a>|b|$}{$\\log _2 a^2>\\log _2 b^2$}",
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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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"edit": [
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"202304012\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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"015051": {
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"id": "015051",
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"content": "某社区通过公益讲座宣传交通法规. 为了解讲座效果, 随机抽取$10$位居民, 分别在讲座前、\n后各回答一份交通法规知识问卷, 满分为$100$分. 他们得分的茎叶图如图所示 (``叶''是个位数字), 则下列选项叙述错误的是\\bracket{20}.\n\\begin{center}\n\\begin{tabular}{ccc|c|cccc} \n\\multicolumn{3}{r|}{讲座前} & & \\multicolumn{4}{l}{讲座后} \\\\\n& 5 & 0 & 5 & & & & \\\\\n5 & 0 & 0 & 6 & & & & \\\\\n5 & 0 & 0 & 7 & & & & \\\\\n& & 0 & 8 & 0 & 5 & 5 & 5 \\\\\n& & 0 & 9 & 0 & 0 & 5 & 5 \\\\\n& & & 10 & 0 & 0 & &\n\\end{tabular}\n\\end{center}\n\\twoch{讲座后的答卷得分整体上高于讲座前的得分}{讲座前的答卷得分分布较讲座后分散}{讲座后答卷得分的第$80$百分位数为$95$}{讲座前答卷得分的极差大于讲座后得分的极差}",
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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届金山区高三二模试题14",
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"edit": [
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"202304012\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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"015052": {
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"id": "015052",
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"content": "如图, 在矩形$ABCD$中, $E$、$F$分别为边$AD$、$BC$上的点, 且$AD=3AE$, $BC=3BF$, 设$P$、$Q$分别为线段$AF$、$CE$的中点, 将四边形$ABFE$沿着直线$EF$进行翻折, 使得点$A$不在平面$CDEF$上, 在这一过程中, 下列关系不能恒成立的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (1,0) node [below] {$F$} coordinate (F);\n\\draw (3,0) node [right] {$C$} coordinate (C);\n\\draw (3,2) node [right] {$D$} coordinate (D);\n\\draw (1,2) node [above] {$E$} coordinate (E);\n\\draw (0,2) node [left] {$A$} coordinate (A);\n\\draw (B) rectangle (D) (E)--(F)(A)--(F)(E)--(C);\n\\filldraw ($(A)!0.5!(F)$) node [left] {$P$} coordinate (P) circle (0.03);\n\\filldraw ($(C)!0.5!(E)$) node [left] {$Q$} coordinate (Q) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n\\twoch{直线$AB\\parallel$直线$CD$}{直线$PQ\\parallel$直线$ED$}{直线$AB \\perp$直线$PQ$}{直线$PQ\\parallel$平面$ADE$}",
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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届金山区高三二模试题15",
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"edit": [
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"202304012\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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"015053": {
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"id": "015053",
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"content": "设$\\{a_n\\}$是项数为$n_0$的有穷数列, 其中$n_0 \\geq 2$. 当$n \\leq \\dfrac{n_0}{2}$时, $a_n=\\dfrac{1}{2^n}$, 且对任意正整数$n \\leq n_0$都有$a_n+a_{n_0+1-n}=0$. 给出下列两个命题: \\textcircled{1} 若对任意正整数$n \\leq n_0$都有$\\displaystyle\\sum_{i=1}^n a_i \\leq \\dfrac{511}{512}$, 则$n_0$的最大值为$18$; \\textcircled{2} 对于任意满足$1 \\leq s<t<n_0$的正整数$s$和$t$, 总存在不超过$n_0$的正整数$m$和$k$, 使得$a_m+a_k=\\displaystyle\\sum_{i=s+1}^t a_i$. 下列说法正确的是\\bracket{20}.\n\\twoch{\\textcircled{1}是真命题, \\textcircled{2}是假命题}{\\textcircled{1}是假命题, \\textcircled{2}是真命题}{\\textcircled{1}和\\textcircled{2}都是真命题}{\\textcircled{1}和\\textcircled{2}都是假命题}",
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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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||||
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"202304012\t王伟叶"
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],
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"space": ""
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},
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"015054": {
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"id": "015054",
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"content": "在$\\triangle ABC$中, 角$A$、$B$、$C$所对边的边长分别为$a$、$b$、$c$, 已知$a=2 \\sqrt{2}$, $C=45^{\\circ}$.\\\\\n(1) 若$\\sin A=\\sqrt{2} \\sin B$, 求$c$;\\\\\n(2) 若$B-A=15^{\\circ}$, 求$\\triangle ABC$的面积.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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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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||||
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"edit": [
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"202304012\t王伟叶"
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],
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"same": [],
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"remark": "",
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"space": "12ex"
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},
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"015055": {
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"id": "015055",
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"content": "如图, 在正三棱柱$ABC-A_1B_1C_1$中, 已知$AB=AA_1=2, D$是$AB$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\h{2}\n\\draw ({-\\l/2},0,0) node [left] {$C$} coordinate (C);\n\\draw (0,0,{\\l/2*sqrt(3)}) node [below] {$A$} coordinate (A);\n\\draw ({\\l/2},0,0) node [right] {$B$} coordinate (B);\n\\draw (C) ++ (0,\\h) node [left] {$C_1$} coordinate (C_1);\n\\draw (A) ++ (0,\\h) node [below right] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\h) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) -- (A) -- (B) (C) -- (C_1) (A) -- (A_1) (B) -- (B_1) (C_1) -- (A_1) -- (B_1) (C_1) -- (B_1);\n\\draw [dashed] (C) -- (B);\n\\draw ($(A)!0.5!(B)$) node [below] {$D$} coordinate (D);\n\\draw (D)--(B_1);\n\\draw [dashed] (D)--(C)--(B_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$CC_1$与$DB_1$所成的角的大小;\\\\\n(2) 求证: 平面$CDB_1 \\perp$平面$ABB_1A_1$, 并求点$B$到平面$CDB_1$的距离.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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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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||||
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"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015056": {
|
||||
"id": "015056",
|
||||
"content": "某网站计划$4$月份订购草莓在网络销售, 每天的进货量相同, 成本价为每盒$15$元. 决定每盒售价为$20$元, 未售出的草莓降价处理, 每盒$10$元. 假设当天进货能全部售完. 根据销售经验, 每天的购买量与网站每天的浏览量(单位: 万次) 有关. 为确定草莓的进货量, 相关人员统计了前两年$4$月份(共$60$天)网站每天的浏览量(单位: 万次)、购买草莓的数量(单位: 盒) 以及达到该流量的天数, 如下表所示:\n\\begin{center} \n\\begin{tabular}{|c|c|c|}\n\\hline 每天的浏览量 &$(0,1)$& {$[1,+\\infty)$} \\\\\n\\hline 每天的购买量 & 600 & 900 \\\\\n\\hline 天数 & 36 & 24 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n以每天的浏览量位于各区间的频率代替浏览量位于该区间的概率.\n(1) 求$4$月份草苺一天的购买量$X$(单位: 盒)的分布;\\\\\n(2) 设$4$月份销售草莓一天的利润为$Y$(单位: 元), 一天的进货量为$n$(单位: 盒), $n$为正整数且$n \\in[600,900]$, 当$n$为多少时, $Y$的期望达到最大值, 并求此最大值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届金山区高三二模试题19",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015057": {
|
||||
"id": "015057",
|
||||
"content": "已知椭圆$\\Gamma: \\dfrac{x^2}{4}+\\dfrac{y^2}{b^2}=1$($0<b<2$).\\\\\n(1) 已知椭圆$\\Gamma$的离心率为$\\dfrac{\\sqrt{3}}{2}$, 求椭圆$\\Gamma$的标准方程;\\\\\n(2) 已知直线$l$过椭圆$\\Gamma$的右焦点且垂直于$x$轴, 记$l$与$\\Gamma$的交点分别为$A$、$B$, $A$、$B$两点关于$y$轴的对称点分别为$A'$、$B'$, 若四边形$ABB' A'$是正方形, 求正方形$ABB' A'$的内切圆的方程;\\\\\n(3) 设$O$为坐标原点, $P$、$Q$两点都在椭圆$\\Gamma$上, 若$\\triangle OPQ$是等腰直角三角形, 其中$\\angle OPQ$是直角, 点$P$在第一象限, 且$O$、$P$、$Q$三点按顺时针方向排列, 求$b$的最大值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届金山区高三二模试题20",
|
||||
"edit": [
|
||||
"202304012\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015058": {
|
||||
"id": "015058",
|
||||
"content": "若函数$y=f(x)$在$x=x_0$处取得极值, 且$f(x_0)=\\lambda x_0$(常数$\\lambda \\in \\mathbf{R}$), 则称$x_0$是函数$y=f(x)$的``$\\lambda$相关点''.\\\\\n(1) 若函数$y=x^2+2 x+2$存在``$\\lambda$相关点'', 求$\\lambda$的值;\\\\\n(2) 若函数$y=k x^2-2 \\ln x$(常数$k \\in \\mathbf{R})$存在``$1$相关点'', 求$k$的值;\\\\\n(3) 设函数$y=f(x)$的表达式为$f(x)=a x^3+b x^2+c x$(常数$a$、$b$、$c \\in \\mathbf{R}$且$a \\neq 0$), 若函数$y=f(x)$有两个不相等且均不为零的``$2$相关点'', 过点$P(1,2)$存在$3$条直线与曲线$y=f(x)$相切, 求实数$a$的取值范围.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届金山区高三二模试题21",
|
||||
"edit": [
|
||||
"202304012\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