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 8b2dca9a..c2c98259 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 @@ -16,3 +16,6 @@ 20240124-194256 023677:023682 +20240124-202600 +023683:023688 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index adad1074..4022db0d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -248805,7 +248805,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023688" + ], "remark": "", "space": "4em", "unrelated": [] @@ -248931,7 +248933,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023687" + ], "remark": "", "space": "4em", "unrelated": [] @@ -365414,7 +365418,9 @@ "20230118\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023683" + ], "remark": "", "space": "", "unrelated": [] @@ -592865,7 +592871,9 @@ "20230209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023683" + ], "remark": "", "space": "", "unrelated": [] @@ -593485,7 +593493,9 @@ "20230209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023683" + ], "remark": "", "space": "", "unrelated": [] @@ -593955,7 +593965,9 @@ "20230209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023686" + ], "remark": "", "space": "", "unrelated": [] @@ -594211,7 +594223,9 @@ "20230209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023688" + ], "remark": "", "space": "4em", "unrelated": [] @@ -639881,6 +639895,137 @@ "space": "4em", "unrelated": [] }, + "023683": { + "id": "023683", + "content": "若直线 $l_1: x+m y+6=0$ 和 $l_2:(m-2) x+3 y+2 m=0$, 则当且仅当 $m \\in$\\blank{50}时, $l_1$ 与 $l_2$ 相交; 当且仅当 $m \\in$\\blank{50}时, $l_1$ 与 $l_2$ 平行.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [ + "021967", + "013058", + "021987" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023684": { + "id": "023684", + "content": "(1) 若直线 $l_1: 2 x+y-3=0$, $l_2: 3 x-2 y-4=0$, 则 $l_1$ 与 $l_2$ 的夹角为\\blank{50}.\\\\\n(2) 若平行直线 $l_1: 2 x+y-1=0$, $l_2: 2 x+y+1=0$, 则 $l_1$、$l_2$ 的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023685": { + "id": "023685", + "content": "(1) 过点 $P(1,1)$ 且与直线 $\\sqrt{3}x+y+1=0$ 的夹角为 $60^{\\circ}$ 的直线方程是\\blank{50}.\\\\\n(2) 若三条直线 $4 x+y+4=0$、$m x+y+1=0$、$x-y+1=0$ 不能围成三角形, 则 $m$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023686": { + "id": "023686", + "content": "若 $0 \\leq \\theta \\leq \\dfrac{\\pi}{2}$, 当点 $(1, \\cos \\theta)$ 到直线 $x \\sin \\theta+y \\cos \\theta-1=0$ 的距离是 $\\dfrac{1}{4}$, 则直线的倾斜角为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [ + "022002" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023687": { + "id": "023687", + "content": "设直线 $l$ 过点 $A(2,4)$, 它被两平行线 $x-y+1=0$ 和 $x-y-1=0$ 所截得的线段的中点在直线 $x+2 y-3=0$ 上, 则直线 $l$ 的方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [ + "008811" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023688": { + "id": "023688", + "content": "求经过点 $A(2,3)$, 且被两平行线 $3 x+4 y-7=0$ 和 $3 x+4 y+8=0$ 截得长为 $3 \\sqrt{2}$ 的线段所在直线方程.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [ + "008807", + "022010" + ], + "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