diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 170cadf0..7c4c3447 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -361,3 +361,6 @@ 20240222-151626 高二下学期周末卷02 040956,023839,040957:040970 +20240224-134951 2024年空中课堂必修第一册补充例题与习题 +024597:024598,014651,024599:024602,000007:000008,000025,000027,000029,000009,000014:000016,000031,000037,000039:000040,024603:024604,000052:000053,000056:000058,000062:000065,000067,000069:000073,024605:024609,000048,000054:000055,000061,000066,000081:000084,000087:000088,007939,000090,024610,030726,024611:024612,007924,000077:000080,000085:000086 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index c0e86ca0..5836003d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -1398,7 +1398,9 @@ "20220624\t王伟叶, 余利成" ], "same": [], - "related": [], + "related": [ + "024599" + ], "remark": "", "space": "4em", "unrelated": [] @@ -224582,7 +224584,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024604" + ], "remark": "", "space": "4em", "unrelated": [] @@ -396474,7 +396478,9 @@ "20230131\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024602" + ], "remark": "", "space": "", "unrelated": [] @@ -667907,6 +667913,332 @@ "space": "", "unrelated": [] }, + "024597": { + "id": "024597", + "content": "用符号``$\\in$''``$\\notin$''``$\\supset$''或``$\\subset$''填空:\\\\\n(1) $0$\\blank{30}$\\varnothing$;\\\\\n(2) $\\{x | x \\geq 1\\}$\\blank{30}$\\{x |(x-1)^2=0\\}; $\\\\\n(3) 设集合 $B$ 为全集 $U$ 的一个非空子集, 若 $A \\subset B$, 则 $A \\cap \\overline{B}$\\blank{30}$B$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024598": { + "id": "024598", + "content": "已知 $x$、$y$、$z \\in \\mathbf{R}$, 那么``$x$、$y$、$z$ 中至少有一个大于 1''是``$x+y+z>3$''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": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024599": { + "id": "024599", + "content": "解下列不等式:\\\\\n(1) $\\dfrac{1-x}{x+2}\\geq 0$;\\\\\n(2) $|x-1|<2$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [ + "000036" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024600": { + "id": "024600", + "content": "设 $a \\in \\mathbf{R}$, 已知全集 $U=\\mathbf{R}$, 集合 $A=\\{x | x^2-2 a x+a^2-4 \\leq 0\\}$, $B=\\{x|| x-1|+| x-4 |>3\\}$.\\\\\n(1) 当 $a=3$ 时, 求 $A \\cap B$;\\\\\n(2) 若``$x \\in A$''是``$x \\in \\overline{B}$''的必要非充分条件, 求 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024601": { + "id": "024601", + "content": "设 $a \\in \\mathbf{R}$, 已知关于 $x$ 的不等式 $(a^2-1) x^2-(a-1) x-1<0$ 的解集是 $\\mathbf{R}$, 求 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024602": { + "id": "024602", + "content": "(1) 已知 $x<\\dfrac{5}{4}$, 求 $4 x-2+\\dfrac{1}{4 x-5}$ 的最大值;\\\\\n(2) 已知 $x>0$, $y>0$, 且 $\\dfrac{1}{x}+\\dfrac{9}{y}=1$, 求 $x+y$ 的最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [ + "014148" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024603": { + "id": "024603", + "content": "若一个非空数集 $F$ 满足: 对任意实数 $a, b \\in F$, 有 $a+b, a-b, a b \\in F$,且当 $b \\neq 0$ 时, 有 $\\dfrac{a}{b}\\in F$, 则称 $F$ 为一个数域. 有以下命题:\\\\\n\\textcircled{1} $0$ 是任何数域的元素; \\textcircled{2} 若数域 $F$ 有非零元素, 则 $2023 \\in F$; \\textcircled{3} 集合 $P=\\{x | x=3 k, k \\in \\mathbf{Z}\\}$ 为数域; \\textcircled{4} 有理数集为数域. 其中所有真命题的序号为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024604": { + "id": "024604", + "content": "建造一个容积为 16 立方米、深为 4 米的长方形无盖水池, 如果池底和池壁的造价每平方米分别为 60 元和 40 元. 请你设计一个方案, 使水池的造价最低, 并求出最低造价.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [ + "007826" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024605": { + "id": "024605", + "content": "已知实数 $x$ 满足 $x+\\log _2(2^x-31)=5$, 求 $x$ 的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024606": { + "id": "024606", + "content": "设 $m \\in \\mathbf{R}$, 若函数 $y=2^x-m$ 的图像上存在两点关于原点对称, 求 $m$ 的最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024607": { + "id": "024607", + "content": "(1)化简: $\\log _5[\\dfrac{1}{\\sqrt[4]{5}}\\times(5 \\sqrt{5})^3]$.\\\\\n(2) 已知 $2^a=5$, 用 $a$ 表示 $\\lg 0.8$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024608": { + "id": "024608", + "content": "(1)已知 $a$ 为实数, 比较 $(\\dfrac{2}{3})^a$ 与 $(\\dfrac{3}{2})^a$ 的大小.\\\\\n(2) 已知 $a$、$b$ 为实数, $3^a=2^b$, 比较 $a$ 与 $b$ 的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024609": { + "id": "024609", + "content": "在自由声场(开阔空间)条件下, 点声源的声波遵循球面发散规律,在与声源距离为 $r$ (单位: $\\mathrm{m}$) 处, 声音强度的衰减量 $\\Delta L=10 \\lg (\\dfrac{1}{4}\\pi r^2)$ (单位: $\\mathrm{dB})$.\\\\\n(1) 有两个距离某一声源分别为 $20 \\mathrm{m}$ 和 $50 \\mathrm{m}$ 的声音探测仪 $A$ 和 $B$, 它们的读数相差多少 $\\mathrm{dB}$ ? (结果精确到 $1 \\mathrm{dB}$ )\\\\\n(2) 已知某单一声源 $O$ 、两个声音探测仪 $C$ 与 $D$, 依次在同一条直线上, $C$ 与 $D$ 间的距离为 $400 \\mathrm{m}$. 假设两个探测仪的读数分别为 $61.05 \\mathrm{dB}$ 和 $47.07 \\mathrm{dB}$, 试求声源 $O$ 与探测仪 $C$ 的距离(结果精确到 $1 \\mathrm{m}$) 以及声源 $O$ 处的声音强度 (结果精确到 $1 \\mathrm{dB}$).", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024610": { + "id": "024610", + "content": "对于函数 $y=\\dfrac{4 x}{x^2+1}$, 该函数是否存在反函数? 若存在,请求其反函数; 若不存在, 请选定一个区间, 使该函数在该区间上存在反函数, 求其反函数, 并写出该反函数所满足的性质.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024611": { + "id": "024611", + "content": "请研究函数 $y=\\dfrac{4 x}{x^2+1}$ 的基本性质与图像.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024612": { + "id": "024612", + "content": "用水清洗一堆蔬菜上残留的农药, 对用一定量的水清洗一次的效果作如下假定: 用 1 个单位量的水可洗掉蔬菜上残留农药量的 $\\dfrac{1}{2}$, 用水越多洗掉的农药量也越多, 但总还有农药残留在蔬菜上. 设用 $x$ 单位量的水清洗以后, 蔬菜上残留的农药量与本次清洗前残留农药量之比为 $y, x$ 与 $y$ 之间满足函数关系 $y=f(x)$.\\\\\n(1) 试规定 $f(0)$ 的值, 并解释其实际意义;\\\\\n(2) 试根据假定写出函数 $y=f(x)$ 满足的一些条件和具有的性质;\\\\\n(3) 假设当 $y$ 降低到 $2 \\%$ 时蔬菜安全可用. 请判断函数 $y=\\dfrac{2}{2+x+x^3}$ 是否满足(2)所列出的所有条件? 如果满足, 你能用本单元所学习的方法求出当蔬菜安全可用时所用水的单位量吗?(结果精确到 $0.1$)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024年空中课堂必修第一册复习课例题与习题", + "edit": [ + "20240224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0