From e2f3d0548cf10b57a5bfc888ea19c001c638a144 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Mon, 4 Mar 2024 20:34:40 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E4=B8=8B?= =?UTF-8?q?=E5=AD=A6=E6=9C=9F=E5=91=A8=E6=9C=AB=E5=8D=B703=E6=96=B0?= =?UTF-8?q?=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 177 ++++++++++++++++++++++++++++++- 2 files changed, 177 insertions(+), 3 deletions(-) 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 8c470d42..caaa906e 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 @@ -394,3 +394,6 @@ 20240304-162932 高二下学期周末卷03 040965,041052:041058,002376,041059:041060,016660,041061:041062,021253,041063:041064 +20240304-203406 高三下学期周末卷03 +030642,022697,032099:032101,015043:015045,030872,015047,032102:032103,015050:015052,030870,032104:032105,015056:015057,032106 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 0756b42e..a336d1d7 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -427700,7 +427700,8 @@ ], "same": [], "related": [ - "040965" + "040965", + "032101" ], "remark": "", "space": "", @@ -427767,7 +427768,9 @@ "edit": [ "20230413\t王伟叶" ], - "same": [], + "same": [ + "032100" + ], "related": [ "024337" ], @@ -428306,7 +428309,9 @@ "20230413\t王伟叶" ], "same": [], - "related": [], + "related": [ + "032106" + ], "remark": "", "space": "4em", "unrelated": [] @@ -738077,6 +738082,172 @@ "space": "4em", "unrelated": [] }, + "032099": { + "id": "032099", + "content": "函数 $y=\\sin x+\\cos x$ 的最小正周期为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240304\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032100": { + "id": "032100", + "content": "在 $(2+x)^5$ 的二项展开式中, $x^4$ 项的系数的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240304\t毛培菁" + ], + "same": [ + "015042" + ], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032101": { + "id": "032101", + "content": "双曲线 $\\dfrac{x^2}{9}-\\dfrac{y^2}{16}=1$ 的倾斜角为钝角的渐近线方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240304\t毛培菁" + ], + "same": [], + "related": [ + "015040" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "032102": { + "id": "032102", + "content": "设 $a \\in \\mathbf{R}$, $f(x)=x|x^2-3 a|$, 若对任意 $x \\in[0, \\sqrt{2}]$, $f(x) \\leq 2$ 恒成立, 则 $a$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240304\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032103": { + "id": "032103", + "content": "已知 $\\overrightarrow{a}$、$\\overrightarrow{b}$、$\\overrightarrow{c}$、$\\overrightarrow{d}$ 都是平面向量, 且 $|\\overrightarrow{a}|=3$, $|\\overrightarrow{a}-\\overrightarrow{b}|=1$, $|5 \\overrightarrow{a}-\\overrightarrow{c}|=1,\\langle\\overrightarrow{a}$, $\\overrightarrow{d}\\rangle=\\dfrac{\\pi}{3}$,则 $|\\overrightarrow{b}-\\overrightarrow{d}|+|\\overrightarrow{c}-\\overrightarrow{d}|$ 的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240304\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "032104": { + "id": "032104", + "content": "如图, 四棱锥 $P-ABCD$ 的底面是矩形, $PD \\perp$ 底面 $ABCD, M$ 为 $BC$ 的中点, $AB=1$, $PD=1$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$D$} coordinate (D);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,0,{2*sqrt(2)}) node [left] {$A$} coordinate (A);\n\\draw (A) ++ (2,0,0) node [right] {$B$} coordinate (B);\n\\draw ($(B)!0.5!(C)$) node [right] {$M$} coordinate (M);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\draw (P)--(A)--(B)--(C)--cycle (P)--(B);\n\\draw [dashed] (A)--(D)--(C) (D)--(P) (A)--(M);\n\\end{tikzpicture}\n\\end{center}\n(1) 若 $\\angle MAB=\\dfrac{\\pi}{6}$, 求四棱锥 $P-ABCD$ 的体积;\\\\\n(2) 若直线 $PB$ 与平面 $ABCD$ 所成的角为 $\\dfrac{\\pi}{6}$,求异面直线 $AM$ 与 $PC$ 所成的角的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240304\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "032105": { + "id": "032105", + "content": "在 $\\triangle ABC$ 中, 角 $A, B, C$ 所对边的边长分别为 $a, b, c$, 已知 $a=2 \\sqrt{2}$, $C=45^{\\circ}$.\\\\\n(1) 若 $\\sin A=\\sqrt{2}\\sin B$, 求 $c$;\\\\\n(2) 若 $\\triangle ABC$ 是钝角三角形, 且在其三个内角中, 有一个角是另一个角的 2 倍, 求 $\\triangle ABC$的面积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240304\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "032106": { + "id": "032106", + "content": "若函数 $y=f(x)$ 在 $x=x_0$ 处取得极值, 且存在 $\\lambda \\in \\mathbf{R}$, 使得 $f(x_0)=\\lambda x_0$, 则称 $x_0$ 是函数 $y=f(x)$ 的``$\\lambda$ 相关点''.\\\\\n(1) 若函数 $y=x^2+2 x+2$ 存在``$\\lambda$ 相关点'', 求 $\\lambda$ 的值;\\\\\n(2) 设 $k \\in \\mathbf{R}$ , 若函数 $y=k x^2-2 \\ln x$ 存在``1 相关点'', 求 $k$ 的值;\\\\\n(3) 设 $a, b, c \\in \\mathbf{R}$ 且 $a \\neq 0$, $f(x)=a x^3+b x^2+c x$. 若函数 $y=f(x)$ 有两个不相等且均不为零的``2 相关点'', 过点 $P(1,2)$ 存在 3 条直线与曲线 $y=f(x)$ 相切, 求 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240304\t毛培菁" + ], + "same": [], + "related": [ + "015058" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, "040001": { "id": "040001", "content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",