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 c8e6a696..a0c65d5e 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 @@ -430,3 +430,6 @@ 20240312-151353 高一下学期周末卷05预选 040238,024726 +20240312-152115 高二下周末卷04 +041073,011075,002376,041074:041078,002112,002409,041079:041087 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 89215526..308cd30e 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -28951,7 +28951,9 @@ "20220624\t朱敏慧, 王伟叶" ], "same": [], - "related": [], + "related": [ + "041079" + ], "remark": "", "space": "", "unrelated": [] @@ -75490,7 +75492,8 @@ ], "same": [], "related": [ - "008901" + "008901", + "041073" ], "remark": "", "space": "", @@ -77597,7 +77600,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "041084" + ], "remark": "", "space": "4em", "unrelated": [] @@ -78223,7 +78228,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "041079" + ], "remark": "", "space": "", "unrelated": [] @@ -254422,7 +254429,8 @@ "021229" ], "related": [ - "002310" + "002310", + "041073" ], "remark": "", "space": "4em", @@ -303392,7 +303400,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "041075" + ], "remark": "", "space": "4em", "unrelated": [] @@ -303729,7 +303739,8 @@ "021229" ], "related": [ - "015316" + "015316", + "041073" ], "remark": "", "space": "4em", @@ -398219,7 +398230,8 @@ ], "same": [], "related": [ - "023699" + "023699", + "041073" ], "remark": "", "space": "", @@ -398264,7 +398276,9 @@ "20230128\t王伟叶" ], "same": [], - "related": [], + "related": [ + "041079" + ], "remark": "", "space": "", "unrelated": [] @@ -462417,7 +462431,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "041075" + ], "remark": "", "space": "", "unrelated": [] @@ -497765,7 +497781,9 @@ "20230606\t王伟叶" ], "same": [], - "related": [], + "related": [ + "041079" + ], "remark": "", "space": "4em", "unrelated": [] @@ -533614,7 +533632,9 @@ "20230730\t王伟叶" ], "same": [], - "related": [], + "related": [ + "041087" + ], "remark": "", "space": "4em", "unrelated": [] @@ -587706,7 +587726,9 @@ "008901", "010677" ], - "related": [], + "related": [ + "041073" + ], "remark": "", "space": "4em", "unrelated": [] @@ -638525,7 +638547,9 @@ "20231124\t毛培菁" ], "same": [], - "related": [], + "related": [ + "041080" + ], "remark": "", "space": "", "unrelated": [] @@ -701272,7 +701296,9 @@ "20221120\t朱敏慧" ], "same": [], - "related": [], + "related": [ + "041075" + ], "remark": "", "space": "", "unrelated": [] @@ -770447,7 +770473,9 @@ "20240224\t杨懿荔" ], "same": [], - "related": [], + "related": [ + "041079" + ], "remark": "", "space": "4em", "unrelated": [] @@ -771922,5 +771950,327 @@ "remark": "", "space": "4em", "unrelated": [] + }, + "041073": { + "id": "041073", + "content": "若方程 $\\dfrac{x^2}{m+2}+\\dfrac{y^2}{2 m-1}=1$ 表示的曲线是双曲线, 则实数 $m$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [ + "008901", + "021229", + "010677", + "013985", + "002310" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "041074": { + "id": "041074", + "content": "双曲线 $\\dfrac{x^2}{4}-y^2=1$ 的斜率为 2 的弦的中点的轨迹方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041075": { + "id": "041075", + "content": "已知实数 $x, y$ 满足 $y=\\sqrt{x^2+1}$, 则 $\\dfrac{y}{x}$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [ + "030481", + "010665", + "016426" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "041076": { + "id": "041076", + "content": "若点 $O$ 和点 $F(-2,0)$ 分别是双曲线 $\\dfrac{x^2}{a^2}-y^2=1$($a>0$) 的中心和左焦点, 点 $P$ 为双曲线右支上的任意一点, 则 $\\overrightarrow{OP}\\cdot \\overrightarrow{FP}$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041077": { + "id": "041077", + "content": "设 $F_1$、$F_2$ 分别为双曲线 $x^2-\\dfrac{y^2}{9}=1$ 的左、右焦点. 若点 $P$ 在双曲线上, 且 $\\overrightarrow{PF_1}\\cdot \\overrightarrow{PF_2}=0$,则 $|\\overrightarrow{PF}_1+\\overrightarrow{PF_2}|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041078": { + "id": "041078", + "content": "已知 $F$ 为双曲线 $C: \\dfrac{x^2}{9}-\\dfrac{y^2}{16}=1$ 的左焦点, $P$、$Q$ 为 $C$ 上的点, 若 $PQ$ 的长等于虚轴长的 2 倍, 点 $A(5,0)$ 在线段 $PQ$ 上, 则 $\\triangle PQF$ 的周长为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041079": { + "id": "041079", + "content": "已知抛物线顶点在原点, 焦点在 $y$ 轴上, 抛物线上一点 $(m,-3)$ 到焦点的距离为 5 , 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": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [ + "002408", + "013987", + "017966", + "041011", + "000783" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "041080": { + "id": "041080", + "content": "设抛物线的顶点坐标为 $(2,0)$, 准线方程为 $x=-1$, 则它的焦点坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [ + "022847" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "041081": { + "id": "041081", + "content": "科技公司组织技术人员进行某新项目研发, 技术人员将独立地进行项目中不同类型的实验甲、乙、丙, 已知实验甲、乙、丙成功的概率分别为 $\\dfrac{3}{4}$、$\\dfrac{2}{3}$ 和 $\\dfrac{1}{2}$, 对实验甲、乙、丙各进行一次, 则至少有一次成功的概率为\\blank{50}. (结果用最简分数表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041082": { + "id": "041082", + "content": "抗击疫情期间, 小志参与了社区志愿者工作. 现在要对服务时长排名前 $20 \\%$ 的志愿者进行表彰. 该社区的志愿者服务时长 (单位: 小时) 如下:\n\\\\\n\\begin{tabular}{rrrrrrrrrr}\n186.0 & 102.0 & 22.0 & 64.0 & 36.0 & 68.0 & 106.0 & 126.0 & 110.0 & 210.0 \\\\\n124.0 & 226.0 & 154.0 & 230.0 & 58.0 & 162.0 & 70.0 & 162.0 & 166.0 & 16.0\n\\end{tabular}\\\\\n根据以上数据, 该社区志愿者服务时长的第 80 百分位数是\\blank{50}. (精确到 $0.1$)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041083": { + "id": "041083", + "content": "给定抛物线 $y^2=2 x$, 设 $A(a, 0)(a>0), P$ 是抛物线上一点, 求 $|PA|$ 的最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "041084": { + "id": "041084", + "content": "已知双曲线的方程为 $x^2-\\dfrac{y^2}{2}=1$, 试问 : 是否存在被点 $M(1,1)$ 平分的弦? 如果存在,求出弦所在的直线方程; 如果不存在, 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [ + "002386" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "041085": { + "id": "041085", + "content": "为了纪念建党 100 周年, 某班举行党史知识答题竞赛, 其中 $A, B$ 两组各 6 名同学的答题成绩的统计数据茎叶图如下, 茎叶图中有一个数字记录模糊, 无法辨认, 用``{\\color{black}\\rule{0.3cm}{0.3cm}}''表示.\n\\begin{center}\n\\begin{tabular}{cccc|c|ccc}\n\\multicolumn{4}{r|}{A组} & & \\multicolumn{3}{l}{B组}\\\\\n\\hline\n& & 3 & 5 & 8 & 3 & 8 & 5 \\\\\n3 & 2 & {\\color{black}\\rule{0.3cm}{0.3cm}} & 1 & 9 & 2 & 4 & 8\n\\end{tabular}\n\\end{center}\n(1) 若 $\\mathrm{A}$ 组同学的平均成绩大于 $B$ 组同学的平均成绩, 分别求 $\\mathrm{A}, B$ 两组同学成绩的中位数;\\\\\n(2) 若 $\\mathrm{A}, B$ 两组同学的平均成绩相同, 分别求出 $\\mathrm{A}, B$\n两组同学成绩的方差 $s_A^2$ 和 $s_B^2$, 并由此分析两组同学的成绩;\\\\\n(3) 若从 $\\mathrm{A}$ 组 6 名同学中, 随机选取 3 名同学参加学校红歌合唱, 求选取的 3 名同学中既有成绩在 $[80,90)$ 分, 又有成绩在 $[90,100)$ 分的概率.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "041086": { + "id": "041086", + "content": "点 $P(3,0)$ 的直线 $l$ 与双曲线 $\\Gamma: \\dfrac{x^2}{a^2}-y^2=1$($a>0$) 交于 $A$、$B$ 两点.\\\\\n(1) 若直线 $l$ 斜率为 1 , 且点 $A$、$B$ 均在 $\\Gamma$ 的右支上, 求 $a$ 的取值范围;\\\\\n(2) 若 $a=1$, $|AB|=4 \\sqrt{2}$, 求直线 $l$ 的方程.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "041087": { + "id": "041087", + "content": "双曲线 $\\Gamma: \\dfrac{x^2}{3}-y^2=1$ 的左、右焦点分别为 $F_1$、$F_2$, 过 $F_2$ 作直线 $l$ 交 $y$ 轴于点 $Q$.\\\\\n(1) 当直线 $l$ 平行于 $\\Gamma$ 的一条渐近线时, 求点 $F_1$ 到直线 $l$ 的距离;\\\\\n(2) 当直线 $l$ 的斜率为 1 时, 在 $\\Gamma$ 的右支上是否存在点 $P$, 满足 $\\overrightarrow{F_1P}\\cdot \\overrightarrow{F_1Q}=0$ ? 若存在, 求出 $P$ 的坐标; 若不存在, 说明理由;\\\\\n(3) 若直线 $l$ 与 $\\Gamma$ 交于不同两点 $A$、$B$, 且 $\\Gamma$ 上存在一点 $M$, 满足 $\\overrightarrow{OA}+\\overrightarrow{OB}+4 \\overrightarrow{OM}=\\overrightarrow{0}$ (其中 $O$ 为坐标原点), 求直线 $l$ 的方程.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t蔡海鸾" + ], + "same": [], + "related": [ + "019514" + ], + "remark": "", + "space": "4em", + "unrelated": [] } } \ No newline at end of file