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 1e284eb5..7e2b9c31 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 @@ -211,3 +211,6 @@ 20240125-144022 024150:024157 +20240125-145904 +024158:024160,023657,024161:024170,011324 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 99dff688..de7058ec 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -71472,7 +71472,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024158" + ], "remark": "", "space": "", "unrelated": [] @@ -274562,7 +274564,9 @@ "20220730\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024158" + ], "remark": "", "space": "4em", "unrelated": [] @@ -307623,7 +307627,9 @@ "20220817\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024170" + ], "remark": "", "space": "4em", "unrelated": [] @@ -367079,7 +367085,9 @@ "20230118\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024159" + ], "remark": "", "space": "", "unrelated": [] @@ -373437,7 +373445,9 @@ "20230123\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024169" + ], "remark": "", "space": "4em", "unrelated": [] @@ -505655,7 +505665,9 @@ "20230707\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024158" + ], "remark": "", "space": "4em", "unrelated": [] @@ -639934,7 +639946,8 @@ ], "same": [], "related": [ - "040448" + "040448", + "024161" ], "remark": "", "space": "", @@ -650079,6 +650092,280 @@ "space": "4em", "unrelated": [] }, + "024158": { + "id": "024158", + "content": "若直线 $l_1:(2-m) x+3 y=4-2 m$ 与 $l_2: 2 x+(3+m) y=4$ 垂直, 则实数 $m$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "002198", + "018864", + "009799" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024159": { + "id": "024159", + "content": "直线 $(m+2) x-(2 m-1) y-(3 m-4)=0$($m \\in \\mathbf{R}$) 恒过点\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "013105" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024160": { + "id": "024160", + "content": "若在直线 $y=-2$ 上有点 $P$, 它到点 $A(-3,1)$ 和点 $B(5,-1)$ 的距离之和最小, 则点 $P$ 的坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024161": { + "id": "024161", + "content": "若函数 $f(x)=x^3+a x^2-x-9$ 在 $x=-1$ 处取得极值, 则 $f(1)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "023668" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024162": { + "id": "024162", + "content": "设曲线 $y=x^{n+1}$($n \\in \\mathbf{N}$, $n \\geq 1$) 在点 $(1,1)$ 处的切线与 $x$ 轴的交点的横坐标为 $x_n$, 则 $x_1 \\cdot x_2 \\cdot x_3 \\cdot x_4 \\cdots \\cdot x_{2022}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024163": { + "id": "024163", + "content": "当 $x=m$ 时, 函数 $f(x)=x^3-x^2+3 x-2 \\ln x$ 取得最小值, 则 $m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024164": { + "id": "024164", + "content": "函数 $y=f(x)$ 在定义域 $(-\\dfrac{3}{2}, 3)$ 内的图像如下图所示. 记 $y=f(x)$ 的导函数为 $y=f'(x)$, 则不等式 $f'(x) \\leq 0$ 的解集为\\blank{50}.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-1.1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw (-1.5,-1) -- (-1,0) sin ({-1/3},0.8) cos (0.5,0) sin (1,-0.5) cos ({4/3},0) sin (2,1.5) cos ({8/3},0) -- (3,-1);\n\\foreach \\i/\\j in {-1.5/-1,{-1/3}/0.8,1/-0.5,2/1.5,3/-1}\n{\\draw [dashed] (\\i,\\j) -- (\\i,0);};\n\\filldraw [fill = white] (-1.5,-1) circle (0.03) (3,-1) circle (0.03);\n\\draw (-1.5,0) node [above] {$-\\frac{3}{2}$};\n\\draw (-1,0) node [below] {$-1$};\n\\draw ({-1/3},0) node [below] {$-\\frac{1}{3}$};\n\\draw (1,0) node [above] {$1$};\n\\draw ({4/3},0) node [below] {$\\frac{4}{3}$};\n\\draw (2,0) node [below] {$2$};\n\\draw ({8/3},0) node [below] {$\\frac{8}{3}$};\n\\draw (3,0) node [above] {$3$};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "031990" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024165": { + "id": "024165", + "content": "设 $F_1$、$F_2$ 分别为椭圆 $\\Gamma: \\dfrac{x^2}{3}+y^2=1$ 的左、右焦点, 点 $A$、$B$ 在椭圆 $\\Gamma$ 上, 且不是椭圆的顶点. 若 $\\overrightarrow{F_1A}+\\lambda \\overrightarrow{F_2B}=\\overrightarrow{0}$, 且 $\\lambda>0$, 则实数 $\\lambda$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024166": { + "id": "024166", + "content": "在平面直角坐标系 $x O y$ 中, 过点 $P(-3, a)$ 作圆 $x^2+y^2-2 x=0$ 的两条切线, 切点分别为 $M(x_1, y_1)$、$N(x_2, y_2)$. 若 $(x_2-x_1)(x_2+x_1)+(y_2-y_1)(y_2+y_1-2)=0$, 则实数 $a$ 的值等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024167": { + "id": "024167", + "content": "已知双曲线 $C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>b>0$) 的离心率为 $\\sqrt{5}$, 虚轴长为 $4$ .\\\\\n(1) 求双曲线标准方程;\\\\\n(2) 过点 $(0,1)$ 、倾斜角为 $45^{\\circ}$ 的直线 $l$ 与双曲线 $C$ 相交于 $A$、$B$ 两点. 求 $\\triangle AOB$ 面积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024168": { + "id": "024168", + "content": "已知函数 $f(x)=x^2+\\ln x-a x$.\\\\\n(1) 当 $a=3$ 时, 求 $f(x)$ 的单调增区间;\\\\\n(2) 若 $f(x)$ 在 $(0,1)$ 上是严格减函数, 求实数 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024169": { + "id": "024169", + "content": "如图所示, $ABCD$ 是边长为 $60 \\mathrm{cm}$ 的正方形硬纸片, 切去阴影部分所示的四个全等的等腰直角三角形, 再沿虚线折起, 使得 $A$、$B$、$C$、$D$ 四个点重合于图中的点 $P$, 正好形成一个正四棱柱形状的包装盒, $E$、$F$ 在 $AB$ 上是被切去的等腰直角三角形斜边的两个端点, 设 $AE=FB=x \\mathrm{cm}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A) -- (2,0) node [right] {$B$} coordinate (B) -- (2,2) node [right] {$C$} coordinate (C) -- (0,2) node [left] {$D$} coordinate (D) -- cycle;\n\\filldraw [pattern = north east lines] (0.7,0) --++ (0.3,0.3) --++ (0.3,-0.3);\n\\filldraw [pattern = north east lines] (0.7,2) --++ (0.3,-0.3) --++ (0.3,0.3);\n\\filldraw [pattern = north east lines] (0,0.7) --++ (0.3,0.3) --++ (-0.3,0.3);\n\\filldraw [pattern = north east lines] (2,0.7) --++ (-0.3,0.3) --++ (0.3,0.3);\n\\draw [dashed] (0.7,0) -- (2,1.3) (2,0.7) -- (0.7,2) (1.3,2) -- (0,0.7) (0,1.3) -- (1.3,0);\n\\draw [dashed] (1.3,0) -- (2,0.7) (2,1.3) -- (1.3,2) (0.7,2) -- (0,1.3) (0,0.7) -- (0.7,0);\n\\draw (0.7,0) node [below] {$E$} coordinate (E);\n\\draw (1.3,0) node [below] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(E)$) node [below] {$x$};\n\\draw ($(B)!0.5!(F)$) node [below] {$x$};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) rectangle ({0.7*sqrt(2)},{0.3*sqrt(2)}) coordinate (T);\n\\draw (T) --++ (0.35,0.35) coordinate (D) --++ (0,{-0.3*sqrt(2)}) --++ (-0.35,-0.35);\n\\draw (T) ++ (0.35,0.35) --++ ({-0.7*sqrt(2)},0) coordinate (A) --++ (-0.35,-0.35) coordinate (B);\n\\path [name path = AT, draw] (A)--(T);\n\\path [name path = BD, draw] (B)--(D);\n\\path [name intersections = {of = AT and BD, by = P}];\n\\filldraw (P) circle (0.03) node [above] {$P$} coordinate (P);\n\\path (1,-1);\n\\end{tikzpicture}\n\\end{center}\n(1) 求包装盒的容积 $V(x)$ 关于 $x$ 的函数表达式, 并求出函数的定义域;\\\\\n(2) 当 $x$ 为多少时, 包装盒的容积 $V(x)(\\mathrm{cm})^3$ 最大? 并求出此时包装盒的高与底面边长的比值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "013346" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024170": { + "id": "024170", + "content": "已知椭圆 $\\Gamma: \\dfrac{x^2}{9}+\\dfrac{y^2}{4}=1$.\\\\\n(1) 若抛物线 $C$ 的焦点与椭圆 $\\Gamma$ 的焦点重合, 求抛物线 $C$ 的标准方程;\\\\\n(2) 若椭圆 $\\Gamma$ 的上顶点 $A$ 、右焦点 $F$ 及 $x$ 轴上一点 $M$ 构成直角三角形, 求点 $M$ 的坐标;", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "010984" + ], + "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