From 7e64581161249f8b6836840818812eab3636d355 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Fri, 24 Nov 2023 14:42:26 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A52024=E5=B1=8A124=E5=88=86?= =?UTF-8?q?=E5=AE=88=E6=8A=A4=E5=8D=B76=E9=A2=98=E7=9B=AE?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 360 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 360 insertions(+) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 1a1ebac7..b3eb1403 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -605285,6 +605285,366 @@ "space": "4em", "unrelated": [] }, + "022871": { + "id": "022871", + "content": "已知集合 $A=\\{-3,-1,0,1,2\\}$, $B=\\{x|| x |>1\\}$, 则 $A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022872": { + "id": "022872", + "content": "复数 $\\dfrac{5}{\\mathrm{i}-2}$ 的共轭复数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022873": { + "id": "022873", + "content": "2023 年女排世界杯共有 12 支参赛球队, 赛制采用 12 支队伍单循环, 两两捉对殿杀一场定胜负, 依次进行, 则此次杯赛共有\\blank{50}场比赛.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022874": { + "id": "022874", + "content": "已知 $0=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$E$} coordinate (E);\n\\draw (0.8,0,{-sqrt(3)}) node [right] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(E)$) node [below] {$B$} coordinate (B);\n\\draw ($(A)!0.5!(F)$) node [above left] {$C$} coordinate (C);\n\\draw (1.2,2.5,0) node [above] {$D$} coordinate (D);\n\\draw ($(A)!0.5!(D)$) node [left] {$A_1$} coordinate (A_1);\n\\draw ($(E)!0.5!(D)$) node [right] {$B_1$} coordinate (B_1);\n\\draw ($(F)!0.5!(D)$) node [left] {$C_1$} coordinate (C_1);\n\\draw (A)--(E)--(D)--cycle(B)--(B_1)--(A_1);\n\\draw [dashed] (A)--(F)--(E)(F)--(D)(B)--(C)--(C_1)(A_1)--(C_1)--(B_1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022880": { + "id": "022880", + "content": "若函数$f(x)=|x-a| \\cdot|x-3 a|$, $x \\in[0,1]$ 的值域为 $[0, f(1)]$, 则实数 $a$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022881": { + "id": "022881", + "content": "已知直线 $l$ 的斜率为 $2$, 则直线 $l$ 的一个法向量为\\bracket{20} .\n\\fourch{$(1,2)$}{$(2,1)$}{$(1,-2)$}{$(2,-1)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022882": { + "id": "022882", + "content": "命题``若 $x>a$, 则 $\\dfrac{x-1}{x}>0$''是真命题, 实数 $a$ 的取值范围是\\bracket{20} .\n\\fourch{($0,+\\infty$)}{($-\\infty, 1]$}{$[1,+\\infty$)}{$(-\\infty, 0]$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022883": { + "id": "022883", + "content": "在正四面体 $A-BCD$ 中, 点 $P$ 为 $\\triangle BCD$ 所在平面上的动点, 若 $AP$ 与 $AB$ 所成角为定值 $\\theta$, $\\theta \\in(0, \\dfrac{\\pi}{4})$, 则动点 $P$ 的轨迹是\\bracket{20} .\n\\fourch{圆}{椭圆}{双曲线}{抛物线}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022884": { + "id": "022884", + "content": "如图, 在一个圆锥内作一个内接圆柱 (圆柱的下底面在圆锥的底面上, 上底面的圆在圆锥的侧面上), 圆锥的母线长为 $4$, $AB$、$CD$ 是底面的两条直径,且 $AB=4$, $AB \\perp CD$, 圆柱与圆锥的公共点 $F$ 恰好为其所在母线 $PA$ 的中点, 点 $O$ 是底面的圆心.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw (-2,0) node [left] {$A$} coordinate (A) arc (180:360:2 and 0.5) node [right] {$B$} coordinate (B);\n\\draw (0,{2*sqrt(3)}) node [above] {$P$} coordinate (P);\n\\draw ($(P)!0.5!(A)$) node [left] {$F$} coordinate (F);\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (60:2 and 0.5) node [above left] {$D$} coordinate (D);\n\\draw (240:2 and 0.5) node [below] {$C$} coordinate (C);\n\\draw (A)--(P)--(B)(C)--(P)(F) arc (180:360:1 and 0.25);\n\\draw [dashed] (F)--++(0,{-sqrt(3)})(F)++(2,0)--++(0,{-sqrt(3)}) arc (0:360:1 and 0.25);\n\\draw [dashed] (F) arc (180:0:1 and 0.25)(F)--(O)(A)--(B)(C)--(D)(A) arc (180:0:2 and 0.5);\n\\end{tikzpicture}\n\\end{center}\n(1) 求圆柱的侧面积;\\\\\n(2) 求异面直线 $OF$ 和 $PC$ 所成的角的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "022885": { + "id": "022885", + "content": "已知函数 $f(x)=2^x+\\dfrac{a}{2^x}$.\\\\\n(1) 若 $f(x)$ 为奇函数, 求 $a$ 的值;\\\\\n(2) 若 $f(x)<3$ 在 $x \\in[1,3]$ 上恒成立, 求实数 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "022886": { + "id": "022886", + "content": "某地实行垃圾分类后, 政府决定为 $A, B, C$ 三个小区建造一座垃圾处理站 $M$, 集中处理三个小区的湿垃圾. 已知 $A$ 在 $B$ 的正西方向, $C$ 在 $B$ 的北偏东 $30^{\\circ}$ 方向, $M$ 在 $B$ 的北偏西 $20^{\\circ}$ 方向, 且在 $C$ 的北偏西 $45^{\\circ}$ 方向, 小区 $A$ 与 $B$ 相距 $2 \\mathrm{km}, B$ 与 $C$ 相距 $3 \\mathrm{km}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0) node [below] {$B$} coordinate (B);\n\\draw (B)++(60:3) node [right] {$C$} coordinate (C);\n\\draw (A)--(B)--(C);\n\\draw (C)--++(135:{3/sin(25)*sin(50)}) node [left] {$M$} coordinate (M);\n\\draw (A)--(M)(B)--(M);\n\\draw [dashed] (B)--++ (0,2) coordinate (N);\n\\draw [dashed] (C)--++ (0,2) coordinate (P);\n\\draw pic [draw, \"$45^\\circ$\", angle eccentricity = 1.5] {angle = P--C--M};\n\\draw pic [draw, \"$30^\\circ$\", angle eccentricity = 2] {angle = C--B--N};\n\\draw pic [draw, \"$20^\\circ$\", angle eccentricity = 2, scale = 1.3] {angle = N--B--M};\n\\end{tikzpicture}\n\\end{center}\n(1) 求垃圾处理站 $M$ 与小区 $C$ 之间的距离;\\\\\n(2) 假设有大、小两种运输车, 车在往返各小区、处理站之间都是直线行驶, 一辆大车的行车费用为每公里 $a$ 元, 一辆小车的行车费用为每公里 $\\lambda a$ 元(其中 $\\lambda$ 为满足 $100 \\lambda$ 是 $[1,99]$ 内的正整数). 现有两种运输湿垃圾的方案:\\\\\n方案 1: 只用一辆大车运输, 从 $M$ 出发, 依次经 $A, B, C$再由 $C$ 返回到 $M$;\\\\\n方案 2: 先用两辆小车分别从 $A$、$C$ 运送到 $B$, 然后并各自返回到 $A$、$C$, 一辆大车从 $M$ 直接到 $B$ 再返回到 $M$.试比较哪种方案更合算? 请说明理由. (结果精确到小数点后两位)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "022887": { + "id": "022887", + "content": "已知抛物线 $\\Gamma: y^2=8 x$ 和圆 $\\Omega: x^2+y^2-4 x=0$, 抛物线 $\\Gamma$ 的焦点为 $F$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-1,0) -- (6,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -5:5] plot ({\\x*\\x/8},\\x);\n\\draw (2,0) circle (2);\n\\end{tikzpicture}\n\\end{center}\n(1) 求 $\\Omega$ 的圆心到 $\\Gamma$ 的准线的距离;\\\\\n(2) 若点 $T(x, y)$ 在抛物线 $\\Gamma$ 上, 且满足 $x \\in[1,4]$, 过点 $T$ 作圆 $\\Omega$ 的两条切线, 记切点为 $A$、$B$, 求四边形 $TAFB$ 的面积的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "022888": { + "id": "022888", + "content": "已知数列 $\\{a_n\\}$ 满足 $a_1=1$, $a_2=a$($a>1$), $|a_{n+2}-a_{n+1}|=|a_{n+1}-a_n|+d$($d>0$, $n \\in \\mathbf{N}$, $n \\geq 1$).\\\\\n(1) 当 $d=a=2$ 时, 写出 $a_4$ 所有可能的值;\\\\\n(2) 当 $d=1$ 时, 若 $a_{2 n}>a_{2 n-1}$ 且 $a_{2 n}>a_{2 n+1}$ 对任意 $n \\in \\mathbf{N}$, $n \\geq 1$ 恒成立, 求数列 $\\{a_n\\}$ 的通项公式.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高三上学期124分守护卷题目", + "edit": [ + "20231124\t毛培菁" + ], + "same": [], + "related": [], + "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