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 new file mode 100644 index 00000000..f5d2b165 --- /dev/null +++ b/工具v2/文本文件/新题收录列表.txt @@ -0,0 +1,3 @@ +20240124-092236 +023638:023648,010830,023649 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 5af164ae..6d0d2418 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -123281,7 +123281,9 @@ "20220703\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023646" + ], "remark": "", "space": "4em", "unrelated": [] @@ -123329,7 +123331,9 @@ "20220703\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023649" + ], "remark": "", "space": "4em", "unrelated": [] @@ -277318,7 +277322,9 @@ "20220730\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023638" + ], "remark": "", "space": "4em", "unrelated": [] @@ -302155,7 +302161,9 @@ "edit": [ "20220806\t王伟叶" ], - "same": [], + "same": [ + "023641" + ], "related": [], "remark": "", "space": "4em", @@ -525847,7 +525855,9 @@ "20230730\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023646" + ], "remark": "", "space": "4em", "unrelated": [] @@ -574361,7 +574371,9 @@ "20230101\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023638" + ], "remark": "", "space": "4em", "unrelated": [] @@ -638916,6 +638928,257 @@ "space": "4em", "unrelated": [] }, + "023638": { + "id": "023638", + "content": "自由落体运动, 物体下落的距离 $S$ (单位: $\\mathrm{m}$) 与时间 $t$ (单位: $\\mathrm{s}$) 满足函数关系 $S(t)=5 t^2$. 试求物体在 $t=2$ 时的瞬时速度.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [ + "009905", + "021372" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023639": { + "id": "023639", + "content": "如图, 已知曲线 $y=\\sqrt{2-x^2}$($-\\sqrt{2}\\leq x \\leq \\sqrt{2}$) 上两点 $P(1,1)$、$Q(0, \\sqrt{2})$.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw ({sqrt(2)},0) arc (0:180:{sqrt(2)});\n\\draw (45:{sqrt(2)}) node [below] {$P$} coordinate (P);\n\\draw (0,{sqrt(2)}) node [below left] {$Q$} coordinate (Q);\n\\draw ($(P)!-0.5!(Q)$) -- ($(Q)!-0.5!(P)$);\n\\filldraw (P) circle (0.03) (Q) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n(1) 求割线 $PQ$ 的斜率;\\\\\n(2) 对正整数 $n$ , 令 $x_n=1-\\dfrac{1}{n}$, $y_n=\\sqrt{2-x_n^2}$, 在该曲线上取一系列点 $Q_n(x_n, y_n)$ , 借助现代信息技术, 适当地计算一些割线 $PQ_n$ 的斜率, 观察并总结当 $n$ 逐渐增大时, 割线 $PQ_n$ 的斜率的变化趋势.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023640": { + "id": "023640", + "content": "求常数函数 $y=C$ 的导数.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023641": { + "id": "023641", + "content": "是否存在实数$b$, 使得直线 $y=-x+b$ 是下列函数图像的切线? 如果存在, 请求出 $b$ 的值; 如果不存在, 请说明理由.\\\\\n(1) $f(x)=\\ln x$;\\\\\n(2) $f(x)=\\dfrac{1}{x}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [ + "040177", + "010813" + ], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023642": { + "id": "023642", + "content": "设 $f(x)=\\ln x$, 已知 $f(x)$ 的图像上有且只有三个点到直线 $y=x+a$ 的距离为 $\\sqrt{2}$, 求实数 $a$ 的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023643": { + "id": "023643", + "content": "已知曲线 $y=\\mathrm{e}^x$ 在点 $(x_1, \\mathrm{e}^{x_1})$ 处的切线与曲线 $y=\\ln x$ 在点 $(x_2, \\ln x_2)$ 处的切线相同, 求 $(x_1+1)(x_2-1)$ 的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023644": { + "id": "023644", + "content": "证明: 对函数 $y=f(x)$ 与任何常数 $C\\in \\mathbf{R}$, 都有 $(C f(x))'=C f'(x)$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023645": { + "id": "023645", + "content": "利用导数求函数 $f(x)=-3 x^2+6 x-1$ 在 $[0,3]$ 上的最大值与最小值. 从而一般化, 此处所得的结果与之前的认识是否一致? 哪种方法更简便?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023646": { + "id": "023646", + "content": "某种型号的汽车在匀速行驶中每小时的耗油量 $y$ (单位: $\\mathrm{L}$) 关于行驶速度 $x$ (单位: $\\mathrm{km}$/$\\mathrm{h}$) 满足函数关系 $y=\\dfrac{1}{128000}x^3-\\dfrac{3}{80}x+8$($0=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A);\n\\draw (2,0) node [below] {$B$} coordinate (B);\n\\draw (0,1) node [left] {$D$} coordinate (D);\n\\draw (2,1) node [above right] {$C$} coordinate (C);\n\\draw (D) ++ (0,{2*tan(35)}) node [above] {$Q$} coordinate (Q);\n\\draw (B) ++ ({1/tan(35)},0) node [right] {$P$} coordinate (P);\n\\fill [pattern = north east lines] (A)--(B)--(C)--(D)--cycle;\n\\draw (A) rectangle (C) (D)--(Q)--(P)--(B);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023648": { + "id": "023648", + "content": "在微积分中``以直代曲''是最基本、最朴素的思想方法, 中国古代科学家刘徽创立的``割圆术'', 用圆的外切正 $n$ 边形和内接正 $n$ 边形``内外夹逼''的办法求出了圆周率 $\\pi$ 的精度较高的近似值, 事实上就是用``以直代曲''的思想进行近似计算的, 它是我国最优秀的传统科学文化之一. 借用``以直代曲''的方法, 在切点附近、可以用函数图像的切线代替在切点附近的曲线来``近似计算''. 请用函数 $f(x)=\\mathrm{e}^x$``近似计算''$\\sqrt[2024]{\\mathrm{e}}$ 的值为\\blank{50}(结果用分数表示).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023649": { + "id": "023649", + "content": "某厂生产产品 $x$ 件的总成本为 $C(x)=1200+\\dfrac{2}{75}x^3$ (单位: 万元) . 已知产品单价 $P$ (单位: 万元) 和产品件数 $x$ 满足函数关系 $P^2=\\dfrac{k}{x}$, 且生产 $100$ 件这样的产品时, 单价定为 $50$ 万元. 问产量为多少件时, 总利润最大?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t严捷" + ], + "same": [], + "related": [ + "004012" + ], + "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