录入高一高二期中考试试题
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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 = "14808"
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problems = "40504"
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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 = 15227
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starting_id = 15248
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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 = "20230414\t王伟叶"
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editor = "20230418\t王伟叶"
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indexed = True
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import os,re,json
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@ -88,6 +88,8 @@ problems_dict = {
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"2025届高一下学期周末卷07小测":"40414:40421",
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"2025届高一下学期周末卷08":"40527:40551",
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"2024届高二下学期周末卷08":"40570:40587",
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"2024届高二下学期周末卷09":"40588:40604"
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"2024届高二下学期周末卷09":"40588:40604",
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"2024届高二下学期期中考试":"15248:15268",
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"2025届高一下学期区期中统考试题":"15269:15289"
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}
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@ -376203,6 +376203,804 @@
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"remark": "",
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"space": "12ex"
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},
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"015248": {
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"id": "015248",
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"content": "向量$\\overrightarrow {a}=(3,0,1)$的模$|\\overrightarrow {a}|=$\\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": "2024届高二下学期期中考试试题1",
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"edit": [
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"20230418\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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"015249": {
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"id": "015249",
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"content": "函数$y=\\ln x$的导函数的定义域为\\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": "2024届高二下学期期中考试试题2",
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"edit": [
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"20230418\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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"015250": {
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"id": "015250",
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"content": "根据二项式定理, $(1+x)^{10}$的二项展开式共有\\blank{50}项.",
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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": "2024届高二下学期期中考试试题3",
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"edit": [
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"20230418\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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"015251": {
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"id": "015251",
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"content": "设$m, n \\in \\mathbf{R}$, 若向量$\\overrightarrow {a}=(2,-1,3)$与向量$\\overrightarrow {b}=(m, 2, n)$平行, 则$m+n=$\\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": "2024届高二下学期期中考试试题4",
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"edit": [
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"20230418\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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"015252": {
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"id": "015252",
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"content": "已知函数$f(x)=\\cos (x-\\dfrac{\\pi}{3})$, 则函数$y=f(x)$的导函数$f'(x)=$\\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": "2024届高二下学期期中考试试题5",
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"edit": [
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"20230418\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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"015253": {
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"id": "015253",
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"content": "设$a \\in \\mathbf{R}$, 若$1$是函数$f(x)=a x+\\ln x$的一个驻点, 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": "2024届高二下学期期中考试试题6",
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"edit": [
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"20230418\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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"015254": {
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"id": "015254",
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"content": "在$(\\sqrt[3]{x}+\\dfrac{2}{x})^8$的二项展开式中, 常数项为\\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": "2024届高二下学期期中考试试题7",
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"edit": [
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"20230418\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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"015255": {
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"id": "015255",
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"content": "若圆的参数方程为$\\begin{cases}x=3 \\sin \\theta+4 \\cos \\theta, \\\\ y=4 \\sin \\theta-3 \\cos \\theta\\end{cases}$($\\theta$为参数), 则此圆的半径为\\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": "2024届高二下学期期中考试试题8",
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"edit": [
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"20230418\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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"015256": {
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"id": "015256",
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"content": "在极坐标系中, 圆$\\rho=8 \\sin \\theta$的圆心到直线$\\theta=\\dfrac{\\pi}{4}$($\\rho \\in \\mathbf{R}$)的距离为\\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": "2024届高二下学期期中考试试题9",
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"edit": [
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"20230418\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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"015257": {
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"id": "015257",
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"content": "设$a \\in \\mathbf{R}$, 若关于$x$的方程$a \\mathrm{e}^x=x^2$有三个实数解, 则$a$的取值范围为\\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": "2024届高二下学期期中考试试题10",
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"edit": [
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"20230418\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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"015258": {
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"id": "015258",
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"content": "定义域和值域都是$\\mathbf{R}$的连续函数$y=f(x)$恰有$17$个驻点, 连续的导函数$y=f'(x)$在定义域$\\mathbf{R}$上被这些驻点分割成$18$个小区间, 其中恰有$9$个区间能使$f'(x)>0$恒成立, 若记$y=f(x)$的零点个数为$n$, 则$n$的最大值为\\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": "2024届高二下学期期中考试试题11",
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"edit": [
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"20230418\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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"015259": {
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"id": "015259",
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"content": "在空间中, $O$是一个定点, $\\overrightarrow{OA}$、$\\overrightarrow{OB}$、$\\overrightarrow{OC}$是给定的三个不共面的向量, 且它们两两之间的夹角都是锐角. 若向量$\\overrightarrow{OP}$满足$|\\overrightarrow{OA} \\cdot \\overrightarrow{OP}|=|\\overrightarrow{OA}|$, $|\\overrightarrow{OB} \\cdot \\overrightarrow{OP}|=2|\\overrightarrow{OB}|$, $|\\overrightarrow{OC} \\cdot \\overrightarrow{OP}|=3|\\overrightarrow{OC}|$, 则满足题意的点$P$的个数为\\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": "2024届高二下学期期中考试试题12",
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"edit": [
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"20230418\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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"015260": {
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"id": "015260",
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"content": "在$(a+b)^{10}$的二项展开式中, 第$3$项为\\bracket{20}.\n\\fourch{$\\mathrm{C}_{10}^2 a^8 b^2$}{$\\mathrm{C}_{10}^2 a^2 b^8$}{$\\mathrm{C}_{10}^3 a^7 b^3$}{$\\mathrm{C}_{10}^3 a^3 b^7$}",
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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": "2024届高二下学期期中考试试题13",
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"edit": [
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"20230418\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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"015261": {
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"id": "015261",
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"content": "下列以$t$为参数的参数方程中, 能够表示方程$x y=1$的是\\bracket{20}.\n\\fourch{$\\begin{cases}x=t^{\\frac{1}{2}}, \\\\ y=t^{-\\frac{1}{2}}\\end{cases}$}{$\\begin{cases}x=\\sin t, \\\\ y=\\dfrac{1}{\\sin t}\\end{cases}$}{$\\begin{cases}x=\\cos t, \\\\ y=\\dfrac{1}{\\cos t}\\end{cases}$}{$\\begin{cases}x=\\tan t, \\\\ y=\\dfrac{1}{\\tan t}\\end{cases}$}",
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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": "2024届高二下学期期中考试试题14",
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"edit": [
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"20230418\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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"015262": {
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"id": "015262",
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"content": "计算: $\\displaystyle\\lim _{h \\to 0} \\dfrac{\\sin 2(x+h)-\\sin (2 x)}{h}=$\\bracket{20}.\n\\fourch{$0$}{$\\cos 2 x$}{$2 \\cos x$}{$2 \\cos 2 x$}",
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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": "2024届高二下学期期中考试试题15",
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"edit": [
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"20230418\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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"015263": {
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"id": "015263",
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"content": "设函数$y=f(x)$在定义域$D$上的导数值均存在, 其导函数为$y=f'(x)$, 关于这两个函数的图像, 有如下两个命题:\\\\\n命题$p$: 若$y=f'(x)$的图像关于直线$x=x_0$对称, 则$y=f(x)$的图像也关于直线$x=x_0$对称;\\\\\n命题$q$: 若$y=f'(x)$是减函数, 且其图像向右方无限延伸时会与$x$轴无限趋近, 则函数$y=f(x)$是增函数, 且其图像向右方无限延伸时也会存在一条平行或重合于$x$轴的直线$l$, 使得$y=f(x)$的图像与$l$无限趋近.\\\\\n下列判断正确的是\\bracket{20}.\n\\twoch{$p$和$q$都是真命题}{$p$和$q$都是假命题}{$p$是真命题, $q$是假命题}{$p$是假命题, $q$是真命题}",
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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": "2024届高二下学期期中考试试题16",
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"edit": [
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"20230418\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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"015264": {
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"id": "015264",
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"content": "已知函数$f(x)=\\mathrm{e}^x-x$, $x \\in \\mathbf{R}$.\\\\\n(1) 求$f'(0)$的值, 并写出该函数在点$(0, f(0))$处的切线方程;\\\\\n(2) 求函数$y=f(x)$在区间$[-1,1]$上的最大值和最小值.",
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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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||||
"origin": "2024届高二下学期期中考试试题17",
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"edit": [
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"20230418\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": "12ex"
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},
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"015265": {
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"id": "015265",
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"content": "如图, 在三棱锥$P-ABC$中, $PA \\perp$平面$ABC$, $\\angle BAC=90^{\\circ}$, $|AB|=|AP|=|AC|=2$, $M$、$N$分别为$PA$、$PC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = {(215:0.5cm)}]\n\\draw (0,0,0) node [below] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\draw (0,0,2) node [below] {$B$} coordinate (B);\n\\draw ($(A)!0.5!(P)$) node [above right] {$M$} coordinate (M);\n\\draw ($(P)!0.5!(C)$) node [right] {$N$} coordinate (N);\n\\draw (P)--(B)--(C)--cycle(B)--(N);\n\\draw [dashed] (B)--(M)--(N)(P)--(A)--(B)(A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$BN$与平面$ABC$所成角的大小;\\\\\n(2) 求平面$MNB$与平面$ABC$所成二面角的大小.",
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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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||||
"origin": "2024届高二下学期期中考试试题18",
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||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
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"related": [],
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"remark": "",
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"space": "12ex"
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},
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"015266": {
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"id": "015266",
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||||
"content": "设$a \\in \\mathbf{R}$. 函数$f(x)=a x^2+\\dfrac{6}{x}$, $x>0$.\\\\\n(1) 当$a=3$时, 求函数$y=f(x)$的单调区间;\\\\\n(2) 设常数$c>0$. 当$a=0$时, 关于$x$的不等式$f(x)+2 x^3 \\geq 13 c$在$[c,+\\infty)$恒成立, 求$c$的取值范围.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期期中考试试题19",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015267": {
|
||||
"id": "015267",
|
||||
"content": "设实数$m \\neq 0$. 对任意给定的实数$x$, 都有$(3+m x)^{99}=a_0+a_1 x+a_2 x^2+\\ldots+a_{99} x^{99}$.\\\\\n(1) 当$m=1$时, 求$a_{97}+a_{98}$的值;\\\\\n(2) 若$m$是整数, 且满足$6<\\dfrac{a_5}{a_4}<7$成立, 求$a_0+a_1+a_2+\\cdots+a_{99}$的值;\\\\\n(3) 当$m \\in(12,13)$时, 根据$m$的取值, 讨论$(3+m x)^{99}$的二项展开式中系数最大的项是第几项.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期期中考试试题20",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015268": {
|
||||
"id": "015268",
|
||||
"content": "设常数$\\lambda \\in(0,1)$. 在棱长为$1$的正方体$ABCD-A_1B_1C_1D_1$中, 点$Q$满足$\\overrightarrow{D_1Q}=\\lambda \\overrightarrow{D_1C_1}$, 点$M$、$N$分别为棱$AD$、$AB$上的动点 (均不与顶点重合), 且满足$|\\overrightarrow{AN}|=\\lambda|\\overrightarrow{DM}|$, 记$|\\overrightarrow{DM}|=a$. 以$A$为原点, 分别以$\\overrightarrow{AB}$、$\\overrightarrow{AD}$与$\\overrightarrow{AA_1}$的方向为$x$、$y$与$z$轴的正方向, 建立如图空间直角坐标系.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [left] {$B$} coordinate (B);\n\\draw (B) ++ (\\l,0,0) node [below right] {$C$} coordinate (C);\n\\draw (B) ++ (\\l,0,-\\l) node [above 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 (B) ++ (0,\\l,0) node [left] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above right] {$D_1$} coordinate (D1);\n\\draw (A) ++ (0,\\l,0) node [above left] {$A_1$} coordinate (A1);\n\\draw (B1) -- (C1) -- (D1) -- (A1) -- cycle;\n\\draw (B) -- (B1) (C) -- (C1) (D) -- (D1);\n\\draw [dashed] (A) -- (A1);\n\\draw [->] (B) -- ($(A)!1.4!(B)$) node [right] {$x$};\n\\draw [->] (D) -- ($(A)!1.4!(D)$) node [below] {$y$};\n\\draw [->] (A1) -- ($(A)!1.4!(A1)$) node [right] {$z$};\n\\filldraw ($(C1)!0.6!(D1)$) node [below] {$Q$} coordinate (Q) circle (0.03);\n\\filldraw ($(A)!0.6!(D)$) node [below left] {$M$} coordinate (M) circle (0.03);\n\\filldraw ($(A)!0.24!(B)$) node [left] {$N$} coordinate (N) circle (0.03);\n\\draw [dashed] (A1)--(M)--(N)--cycle;\n\\end{tikzpicture}\n\\end{center}\n(1) 用$\\lambda$和$a$表示点$M$、$N$、$Q$的坐标;\\\\\n(2) 设$a=\\dfrac{1}{2}$, 若$\\angle MA_1N=\\angle AMN$, 求常数$\\lambda$的值;\\\\\n(3) 记$Q$到平面$MA_1N$的距离为$h(a)$. 求证: 若关于$a$的方程$h(a)=\\dfrac{\\sqrt{5}}{2} \\lambda$在$(0,1)$上恰有两个不同的解, 则这两个解中至少有一个大于$\\dfrac{1}{2}$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期期中考试试题21",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015269": {
|
||||
"id": "015269",
|
||||
"content": "函数$y=\\log _2 x$的定义域是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题1",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015270": {
|
||||
"id": "015270",
|
||||
"content": "函数$y=2 \\sin 3 x+4$的最小正周期是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题2",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015271": {
|
||||
"id": "015271",
|
||||
"content": "已知集合$A=\\{1\\}$, $B=\\{x | x^2+2 x+a=0,\\ x \\in \\mathbf{R}\\}$, 且$A \\subset B$, 则实数$a$的值是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题3",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015272": {
|
||||
"id": "015272",
|
||||
"content": "扇形$OAB$所在圆的半径长为$1$ , $\\overset{\\frown}{AB}$所对的圆心角$\\angle AOB$大小为$\\dfrac{\\pi}{3}$, 则扇形$OAB$的面积为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题4",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015273": {
|
||||
"id": "015273",
|
||||
"content": "指数函数$y=(a-1)^x$在区间$[0,2]$上的最大值为$4$, 则实数$a$的值是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题5",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015274": {
|
||||
"id": "015274",
|
||||
"content": "函数$y=\\sin (x+\\dfrac{\\pi}{2})$的单调减区间是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题6",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015275": {
|
||||
"id": "015275",
|
||||
"content": "已知$y=f(x)$是定义域为$\\mathbf{R}$的奇函数, 当$x>0$时, $f(x)=1-2 x$, 则当$x<0$时, $y=f(x)$的表达式为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题7",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015276": {
|
||||
"id": "015276",
|
||||
"content": "方程$|x-3|+|x-4|=1$的解集是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题8",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015277": {
|
||||
"id": "015277",
|
||||
"content": "对任意实数$x$, 定义$[x]$表示小于等于$x$的最大整数, 例如$[1.8]=1$, $[-1.8]=-2$, 则方程$x^2-[x]-1=0$的解的个数是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题9",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015278": {
|
||||
"id": "015278",
|
||||
"content": "某河道水上游览航线一经开放就受到公众喜爱, 其中有一条航线是: 从码头A出发顺流而下到码头B, 然后不做停留原路返回到码头A(不计调头时间). 假设游船在静水中的船速恒定不变, 且整个航程中途不做停靠, 以下结论正确的是\\blank{50}(填序号).\\\\\n\\textcircled{1} 水流速度越大整个航程所需时间越长;\\\\\n\\textcircled{2} 水流速度越大整个航程所需时间越短;\\\\\n\\textcircled{3} 水流速度大小不会影响整个航程所需时间.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题10",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015279": {
|
||||
"id": "015279",
|
||||
"content": "已知函数$y=f(x)$的表达式是$f(x)=x^4+4^{|x|}$, 若$\\alpha \\in(0, \\pi)$, 且$f(\\sin \\alpha)<f(\\cos \\alpha)$成立, 则$\\alpha$的取值范围是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题11",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015280": {
|
||||
"id": "015280",
|
||||
"content": "已知函数$y=f(x)$的表达式是$f(x)=\\cos 2 x+a \\sin x$, 若对于任意$x \\in \\mathbf{R}$都满足$f(x) \\leq f(\\dfrac{\\pi}{2})$, 则实数$a$的取值范围是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题12",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015281": {
|
||||
"id": "015281",
|
||||
"content": "``$a>b$''是``$a^2>b^2$''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}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题13",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015282": {
|
||||
"id": "015282",
|
||||
"content": "函数$y=\\dfrac{\\ln |x|}{x}$的大致图像是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-3.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = 0.33:3.5, samples = 100] plot (\\x,{ln(\\x)/\\x});\n\\draw [domain = 0.33:3.5, samples = 100] plot (-\\x,{ln(\\x)/(-\\x)});\n\\foreach \\i in {1,2,3}\n{\\draw (\\i,0.2) -- (\\i,0) (-\\i,0.2) -- (-\\i,0);\n\\draw (0.2,\\i) -- (0,\\i) (0.2,-\\i) -- (0,-\\i);};\n\\draw (1,0) node [below] {$1$} (-1,0) node [below] {$-1$};\n\\draw (0,1) node [left] {$1$} (0,-1) node [left] {$-1$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-3.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = 0.33:3.5, samples = 100] plot (\\x,{ln(\\x)/\\x});\n\\draw [domain = 0.33:3.5, samples = 100] plot (-\\x,{-ln(\\x)/(-\\x)});\n\\foreach \\i in {1,2,3}\n{\\draw (\\i,0.2) -- (\\i,0) (-\\i,0.2) -- (-\\i,0);\n\\draw (0.2,\\i) -- (0,\\i) (0.2,-\\i) -- (0,-\\i);};\n\\draw (1,0) node [below] {$1$} (-1,0) node [below] {$-1$};\n\\draw (0,1) node [left] {$1$} (0,-1) node [left] {$-1$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-3.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = 0.33:3.5, samples = 100] plot (\\x,{-ln(\\x)/\\x});\n\\draw [domain = 0.33:3.5, samples = 100] plot (-\\x,{ln(\\x)/(-\\x)});\n\\foreach \\i in {1,2,3}\n{\\draw (\\i,0.2) -- (\\i,0) (-\\i,0.2) -- (-\\i,0);\n\\draw (0.2,\\i) -- (0,\\i) (0.2,-\\i) -- (0,-\\i);};\n\\draw (1,0) node [below] {$1$} (-1,0) node [below] {$-1$};\n\\draw (0,1) node [left] {$1$} (0,-1) node [left] {$-1$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-3.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = 0.33:3.5, samples = 100] plot (\\x,{-ln(\\x)/\\x});\n\\draw [domain = 0.33:3.5, samples = 100] plot (-\\x,{-ln(\\x)/(-\\x)});\n\\foreach \\i in {1,2,3}\n{\\draw (\\i,0.2) -- (\\i,0) (-\\i,0.2) -- (-\\i,0);\n\\draw (0.2,\\i) -- (0,\\i) (0.2,-\\i) -- (0,-\\i);};\n\\draw (1,0) node [below] {$1$} (-1,0) node [below] {$-1$};\n\\draw (0,1) node [left] {$1$} (0,-1) node [left] {$-1$};\n\\end{tikzpicture}}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题14",
|
||||
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|
||||
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|
||||
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|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015283": {
|
||||
"id": "015283",
|
||||
"content": "已知$\\triangle ABC$的三个内角$A$、$B$、$C$满足$\\sin C+\\sin (B-A)=\\sin 2A$, 则$\\triangle ABC$的形状是\\bracket{20}.\n\\twoch{等腰三角形}{直角三角形}{等腰直角三角形}{等腰三角形或直角三角形}",
|
||||
"objs": [],
|
||||
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|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题15",
|
||||
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|
||||
"20230418\t王伟叶"
|
||||
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|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015284": {
|
||||
"id": "015284",
|
||||
"content": "已知对任意正数$a$、$b$、$c$, 当$a+b+c=1$时, 都有$2^a+2^b+2^c<m$成立, 则实数$m$的取值范围是\\bracket{20}.\n\\fourch{$[3 \\sqrt[3]{2},+\\infty)$}{$(3 \\sqrt[3]{2},+\\infty)$}{$[4,+\\infty)$}{$(4,+\\infty)$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题16",
|
||||
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|
||||
"20230418\t王伟叶"
|
||||
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|
||||
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|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"015285": {
|
||||
"id": "015285",
|
||||
"content": "已知集合$A=\\{x|| x-2 | \\leq 1,\\ x \\in \\mathbf{R}\\}$、$B=\\{x | \\dfrac{x-3}{x+1}<0,\\ x \\in \\mathbf{R}\\}$, 求$A \\cap B$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题17",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015286": {
|
||||
"id": "015286",
|
||||
"content": "已知$\\cos \\theta=-\\dfrac{4}{5}$, $\\theta \\in(0, \\pi)$, 求下列各式的值:\\\\\n(1) $\\sin (\\dfrac{\\pi}{2}-\\theta) \\cdot \\tan (\\theta+\\pi)$;\\\\\n(2) $\\dfrac{1-\\sin 2 \\theta}{1+\\cos 2 \\theta}$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题18",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015287": {
|
||||
"id": "015287",
|
||||
"content": "如图, 四边形$ABCD$中, $AB=2, BC=1$, $\\cos \\angle ACB=\\dfrac{2 \\sqrt{7}}{7}, \\angle D=\\dfrac{\\pi}{3}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) coordinate (O);\n\\draw (O) ++ (-1,{2/sqrt(3)}) node [above] {$A$} coordinate (A);\n\\draw (O) ++ (1,{2/sqrt(3)}) node [above] {$B$} coordinate (B);\n\\draw (B) ++ (-60:1) node [right] {$C$} coordinate (C);\n\\draw (O) ++ (-100:{sqrt(7)/sqrt(3)}) node [below] {$D$} coordinate (D);\n\\draw (A)--(B)--(C)--(D)--cycle(A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求线段$AC$的长;\\\\\n(2) 求四边形$ABCD$面积的最大值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题19",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015288": {
|
||||
"id": "015288",
|
||||
"content": "在月亮和太阳的引力作用下, 海水水面发生的周期性涨落现象叫做潮汐. 一般早潮叫潮, 晩潮叫汐. 受潮汐影响, 港口的水深也会相应发生变化. 下图记录了某港口某一天整点时刻的水深$y$(单位: 米) 与时间$x$(单位: 时)的大致关系:\n假设$4$月份的每一天水深与时间的关系都符合图中所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-1,0) -- (25,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,13) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {1,2,...,24} \n{\\draw [dotted] (\\i,-1) -- (\\i,13);}\n\\foreach \\i in {1,2,...,48}\n{\\draw ({\\i/2},0.2) -- ({\\i/2},0);};\n\\foreach \\i in {2,4,...,24}\n{\\draw (\\i,0) node [below] {$\\i$};};\n\\foreach \\i in {1,2,...,12}\n{\\draw [dotted] (-1,\\i) -- (25,\\i);\n\\draw (0,\\i) node [left] {$\\i$};};\n\\foreach \\i in {1,2,...,24}\n{\\draw (0.2,{\\i/2}) -- (0,{\\i/2});};\n\\foreach \\i in {0,1,...,24}\n{\\filldraw (\\i,{8+3*sin((\\i-11)*30)}) circle (0.08);};\n\\end{tikzpicture}\n\\end{center}\n(1) 请运用函数模型$y=A \\sin (\\omega x+\\varphi)+h$($A>0$, $\\omega>0$,$-\\dfrac{\\pi}{2}<\\varphi<\\dfrac{\\pi}{2}$, $h \\in \\mathbf{R}$), 根据以上数据写出水深$y$与时间$x$的函数的近似表达式;\\\\\n(2) 根据该港口的安全条例, 要求船底与水底的距离必须不小于$3.5$米, 否则该船必须立即离港. 一艘船满载货物, 吃水 (即船底到水面的距离) $6$米, 计划明天进港卸货.\\\\\n(i) 求该船可以进港的时间段;\\\\\n(ii) 该船今天会到达港口附近, 明天$0$点可以及时进港并立即开始卸货. 已知卸货时吃水深度以每小时$0.3$米的速度匀速减少, 卸完货后空船吃水$3$米. 请设计一个卸货方案, 在保证严格遵守该港口安全条例的前提下, 使该船明天尽早完成卸货(不计停靠码头和驶离码头所需时间).",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题20",
|
||||
"edit": [
|
||||
"20230418\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
},
|
||||
"015289": {
|
||||
"id": "015289",
|
||||
"content": "已知函数$y=F(x)$与$y=f(x)$的定义域为$\\mathbf{R}$, 若对任意区间$[u, v] \\subseteq \\mathbf{R}$, 存在$p \\in[u, v]$且$q \\in[u, v]$, 使$f(p) \\leq \\dfrac{F(u)-F(v)}{u-v} \\leq f(q)$, 则称$y=f(x)$是$y=F(x)$的生成函数.\\\\\n(1) 求证: $f(x)=2 x$是$F(x)=x^2-3$的生成函数;\\\\\n(2) 若$f(x)=x^2+2$是$y=F(x)$的生成函数, 判断并证明$y=F(x)$的单调性;\\\\\n(3) 若$y=f(x)$是$y=F(x)$的生成函数, 实数$a \\neq 0$, 求$y=F(a x+b)$的一个生成函数.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期区期中统考试题21",
|
||||
"edit": [
|
||||
"20230418\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