diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index d893f15b..d41cc3f7 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -3839,7 +3839,9 @@ "008380", "031239" ], - "related": [], + "related": [ + "024723" + ], "remark": "", "space": "4em", "unrelated": [] @@ -4161,7 +4163,9 @@ "same": [ "008395" ], - "related": [], + "related": [ + "024724" + ], "remark": "", "space": "4em", "unrelated": [] @@ -292403,7 +292407,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024725" + ], "remark": "", "space": "4em", "unrelated": [] @@ -684284,6 +684290,87 @@ "space": "4em", "unrelated": [] }, + "024723": { + "id": "024723", + "content": "已知$\\tan \\alpha=3$, 则$\\dfrac 1{\\sin^2\\alpha+2\\sin \\alpha\\cos \\alpha}=$\\blank{50}.", + "objs": [ + "K0304003B" + ], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "教材复习题-20240311修改", + "edit": [ + "20220624\t王伟叶, 余利成", + "20240311\t吴轩萍" + ], + "same": [], + "related": [ + "000100" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024724": { + "id": "024724", + "content": "已知$\\alpha$是第二象限的角, 且$\\sin \\alpha=\\dfrac{\\sqrt {15}}4$, 则$\\dfrac{\\sin (\\alpha+\\dfrac{\\pi}{4})}{1+\\sin 2\\alpha+\\cos 2\\alpha}=$\\blank{50}.", + "objs": [ + "K0304003B", + "K0310002B", + "K0312003B" + ], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "教材复习题-20240311修改", + "edit": [ + "20220624\t王伟叶, 余利成", + "20240311\t吴轩萍" + ], + "same": [], + "related": [ + "000111" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024725": { + "id": "024725", + "content": "已知$\\sin \\alpha=-\\dfrac 14$, $\\alpha\\in (\\pi , \\dfrac{3\\pi} 2)$, $\\cos \\beta=\\dfrac 45$, $\\beta\\in (\\dfrac{3\\pi} 2, 2\\pi)$, 则$\\alpha+\\beta$是第\\blank{20}象限的角.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第二册习题-20240311修改", + "edit": [ + "20220806\t王伟叶", + "20240311\t吴轩萍" + ], + "same": [], + "related": [ + "010249" + ], + "remark": "", + "space": "", + "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