From 264a9c0d42e86fbe189783cdfe59a645573a78ad Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Sat, 21 Oct 2023 11:27:33 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A52024=E5=B1=8A=E9=AB=98?= =?UTF-8?q?=E4=B8=89=E4=B8=8A=E5=AD=A6=E6=9C=9F=E6=B5=8B=E9=AA=8C=E5=9B=9B?= =?UTF-8?q?=E9=81=93=E9=A2=98=E5=BA=93=E5=A4=96=E8=AF=95=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 80 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 80 insertions(+) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 98087bf0..bf2f01f0 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -517848,6 +517848,86 @@ "space": "", "unrelated": [] }, + "019880": { + "id": "019880", + "content": "某展馆现有一块三角形区域可以布展, 经过测量其三边长分别为 $14$、$10$、$6$ (单位: $\\text{m}$), 且该区域的租金为每天 40 元 $/ \\text{m}^2$. 若租用上述区域 5 天, 则仅场地的租用费约需\\blank{50}元. (结果保留整数)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231021\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019881": { + "id": "019881", + "content": "已知平面向量 $\\overrightarrow{a}, \\overrightarrow{b}, \\overrightarrow{c}$, 对任意实数 $t$, 都有 $|\\overrightarrow{b}-t \\overrightarrow{a}| \\geq|\\overrightarrow{b}-\\overrightarrow{a}|$, $|\\overrightarrow{b}-t \\overrightarrow{c}| \\geq|\\overrightarrow{b}-\\overrightarrow{c}|$ 成立. 若 $|\\overrightarrow{a}|=3$, $|\\overrightarrow{c}|=2$, $|\\overrightarrow{a}-\\overrightarrow{c}|=\\sqrt{7}$, 则 $|\\overrightarrow{b}|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231021\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019882": { + "id": "019882", + "content": "如图, 设 $ABCDEF$ 是半径为 $1$ 的圆 $O$ 内接正六边形, $M$ 是圆 $O$ 上的动点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\filldraw (0,0) circle (0.03) node [below right] {$O$} coordinate (O);\n\\draw (O) circle (2);\n\\foreach \\i/\\j/\\k in {90/A/above,150/B/left,210/C/left,270/D/below,330/E/right,30/F/right}\n{\\draw (\\i:2) node [\\k] {$\\j$} coordinate (\\j);};\n\\draw (A)--(B)--(C)--(D)--(E)--(F)--cycle;\n\\end{tikzpicture}\n\\end{center}\n(1) 求 $|\\overrightarrow{AB}+\\overrightarrow{BD}+\\overrightarrow{DF}-\\overrightarrow{AM}|$ 的最大值;\\\\\n(2) 求证: $\\overrightarrow{MA}^2+\\overrightarrow{MC}^2+\\overrightarrow{ME}^2$ 为定值;\\\\\n(3) 已知 $P$ 是正六边形 $ABCDEF$ 内的任意一点(包含边界), 设 $\\overrightarrow{OP}=x \\overrightarrow{OE}+y \\overrightarrow{OF}$ ($x, y$ 是实数 ), 请问 $x-y$ 是否存在最小值? 若存在, 请求出这个最小值, 否则请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231021\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "019883": { + "id": "019883", + "content": "(1) 判断 $f_1(x)=x^2-4 x,$($x \\in[1,4]$) 与 $f_2(x)=|x-1|+|x-2|,$($x \\in[1,4]$) 是否是增函数?\\\\\n(2) 已知函数 $g(x)=2^x+\\dfrac{a}{2^{x-1}}$ 在 $[2,4]$ 上为增函数, 求实数 $a$ 的取值范围.\\\\\n(3) 已知函数 $h(x)$ 在 $[0,1]$ 上为增函数, 且满足条件: \\textcircled{1} $h(0)=0$, \\textcircled{2} $h(\\dfrac{x}{3})=\\dfrac{1}{2}h(x)$, \\textcircled{3} $h(1-x)=1-h(x)$, 求 $h(\\dfrac{1}{2024})$ 的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231021\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "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.",