From 57084e2414f745f42d4723e74f938ec0c9f5698f Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Wed, 22 Feb 2023 19:49:31 +0800 Subject: [PATCH] =?UTF-8?q?20230222=20=E4=BF=AE=E5=A4=8D=E4=B8=80=E4=B8=AA?= =?UTF-8?q?=E9=A2=98=E5=BA=93=E7=9A=84=E9=97=AE=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 256 ------------------------------------------ 1 file changed, 256 deletions(-) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index b27d4777..5e821609 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -431208,262 +431208,6 @@ "remark": "", "space": "" }, - "031237": { - "id": "031237", - "content": "从编号分别为$1$、$2$、$3$、$4$、$5$、$6$的$6$个大小与质地相同的小球中随机取出$3$个, 则恰有$2$个小球编号相邻的概率为\\blank{50}.", - "objs": [ - "K0803002B", - "K0818001X" - ], - "tags": [ - "第八单元", - "概率" - ], - "genre": "填空题", - "ans": "", - "solution": "", - "duration": -1, - "usages": [], - "origin": "教材复习题-20230220修改", - "edit": [ - "20220624\t王伟叶, 余利成", - "20230220\t王伟叶" - ], - "same": [], - "related": [ - "000221" - ], - "remark": "", - "space": "" - }, - "031238": { - "id": "031238", - "content": "在$(\\sqrt x+\\dfrac 1{\\sqrt[3]x})^{100}$的展开式中, 有理项有\\blank{50}项.", - "objs": [ - "K0819002X" - ], - "tags": [ - "第八单元", - "二项式定理" - ], - "genre": "填空题", - "ans": "有$17$项是有理项", - "solution": "考虑$(x^{\\frac 12}+x^{-\\frac 13})^{100}$展开式的通项$T_{r+1}=\\mathrm{C}_{100}^rx^{\\frac{100-r}2}\\cdot (x^{-\\frac 13})^r=\\mathrm{C}_{100}^rx^{50-\\dfrac{3r}6}$.\n令$r=6k$($k\\in \\mathbf{Z}$), 则$0\\le 6k\\le 100$, 即$r=0,6,12,\\cdots ,96$.\n因此共有$17$个有理项.", - "duration": -1, - "usages": [], - "origin": "代数精编第九章排列组合-20230220修改", - "edit": [ - "20220720\t王伟叶", - "20230220\t王伟叶" - ], - "same": [], - "related": [ - "007528" - ], - "remark": "", - "space": "" - }, - "031239": { - "id": "031239", - "content": "已知$\\tan \\alpha =3$, 则$\\dfrac 1{\\sin ^2\\alpha +2\\sin \\alpha \\cos \\alpha}$的值为\\blank{50}.", - "objs": [], - "tags": [ - "第三单元" - ], - "genre": "填空题", - "ans": "", - "solution": "", - "duration": -1, - "usages": [], - "origin": "二期课改练习册高一第二学期-20230220修改", - "edit": [ - "20220726\t王伟叶", - "20230220\t王伟叶" - ], - "same": [], - "related": [ - "009553", - "008380" - ], - "remark": "", - "space": "" - }, - "031240": { - "id": "031240", - "content": "设向量$\\overrightarrow a$、$\\overrightarrow b$满足$|\\overrightarrow a|=5$, $|\\overrightarrow b|=6$, $(\\overrightarrow a+\\overrightarrow b)\\cdot \\overrightarrow b=21$, 则$\\langle \\overrightarrow a, \\overrightarrow b\\rangle =$\\blank{50}.", - "objs": [], - "tags": [ - "第五单元" - ], - "genre": "填空题", - "ans": "", - "solution": "", - "duration": -1, - "usages": [], - "origin": "新教材必修第二册课堂练习-20230220修改", - "edit": [ - "20220730\t王伟叶", - "20230220\t王伟叶" - ], - "same": [], - "related": [ - "009626" - ], - "remark": "", - "space": "" - }, - "031241": { - "id": "031241", - "content": "函数$y=\\dfrac{x^2+7}{\\sqrt{x^2+4}}$的值域是\\blank{50}.", - "objs": [], - "tags": [ - "第二单元" - ], - "genre": "填空题", - "ans": "", - "solution": "", - "duration": -1, - "usages": [], - "origin": "2022届高三第二轮复习讲义-20230222修改", - "edit": [ - "20230118\t王伟叶", - "20230222\t王伟叶" - ], - "same": [], - "related": [ - "012847" - ], - "remark": "", - "space": "" - }, - "031242": { - "id": "031242", - "content": "已知$f(x)=\\begin{cases}(2-a) x+1, & x<1, \\\\ 2ax, & x \\geq 1\\end{cases}$满足: 对任意$x_1 \\neq x_2$, 都有$\\dfrac{f(x_1)-f(x_2)}{x_1-x_2}>0$成立, 则实数$a$的取值范围是\\blank{50}.", - "objs": [], - "tags": [ - "第二单元" - ], - "genre": "填空题", - "ans": "", - "solution": "", - "duration": -1, - "usages": [], - "origin": "2022届高三第二轮复习讲义-20230222修改", - "edit": [ - "20230118\t王伟叶", - "20230222\t王伟叶" - ], - "same": [], - "related": [ - "012851" - ], - "remark": "", - "space": "" - }, - "031237": { - "id": "031237", - "content": "从编号分别为$1$、$2$、$3$、$4$、$5$、$6$的$6$个大小与质地相同的小球中随机取出$3$个, 则恰有$2$个小球编号相邻的概率为\\blank{50}.", - "objs": [ - "K0803002B", - "K0818001X" - ], - "tags": [ - "第八单元", - "概率" - ], - "genre": "填空题", - "ans": "", - "solution": "", - "duration": -1, - "usages": [], - "origin": "教材复习题-20230220修改", - "edit": [ - "20220624\t王伟叶, 余利成", - "20230220\t王伟叶" - ], - "same": [], - "related": [ - "000221" - ], - "remark": "", - "space": "" - }, - "031238": { - "id": "031238", - "content": "在$(\\sqrt x+\\dfrac 1{\\sqrt[3]x})^{100}$的展开式中, 有理项有\\blank{50}项.", - "objs": [ - "K0819002X" - ], - "tags": [ - "第八单元", - "二项式定理" - ], - "genre": "填空题", - "ans": "有$17$项是有理项", - "solution": "考虑$(x^{\\frac 12}+x^{-\\frac 13})^{100}$展开式的通项$T_{r+1}=\\mathrm{C}_{100}^rx^{\\frac{100-r}2}\\cdot (x^{-\\frac 13})^r=\\mathrm{C}_{100}^rx^{50-\\dfrac{3r}6}$.\n令$r=6k$($k\\in \\mathbf{Z}$), 则$0\\le 6k\\le 100$, 即$r=0,6,12,\\cdots ,96$.\n因此共有$17$个有理项.", - "duration": -1, - "usages": [], - "origin": "代数精编第九章排列组合-20230220修改", - "edit": [ - "20220720\t王伟叶", - "20230220\t王伟叶" - ], - "same": [], - "related": [ - "007528" - ], - "remark": "", - "space": "" - }, - "031239": { - "id": "031239", - "content": "已知$\\tan \\alpha =3$, 则$\\dfrac 1{\\sin ^2\\alpha +2\\sin \\alpha \\cos \\alpha}$的值为\\blank{50}.", - "objs": [], - "tags": [ - "第三单元" - ], - "genre": "填空题", - "ans": "", - "solution": "", - "duration": -1, - "usages": [], - "origin": "二期课改练习册高一第二学期-20230220修改", - "edit": [ - "20220726\t王伟叶", - "20230220\t王伟叶" - ], - "same": [], - "related": [ - "009553", - "008380" - ], - "remark": "", - "space": "" - }, - "031240": { - "id": "031240", - "content": "设向量$\\overrightarrow a$、$\\overrightarrow b$满足$|\\overrightarrow a|=5$, $|\\overrightarrow b|=6$, $(\\overrightarrow a+\\overrightarrow b)\\cdot \\overrightarrow b=21$, 则$\\langle \\overrightarrow a, \\overrightarrow b\\rangle =$\\blank{50}.", - "objs": [], - "tags": [ - "第五单元" - ], - "genre": "填空题", - "ans": "", - "solution": "", - "duration": -1, - "usages": [], - "origin": "新教材必修第二册课堂练习-20230220修改", - "edit": [ - "20220730\t王伟叶", - "20230220\t王伟叶" - ], - "same": [], - "related": [ - "009626" - ], - "remark": "", - "space": "" - }, "031241": { "id": "031241", "content": "函数$y=\\dfrac{x^2+7}{\\sqrt{x^2+4}}$的值域是\\blank{50}.",