diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index cd370159..0772834e 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -319360,7 +319360,9 @@ "20220819\t王伟叶" ], "same": [], - "related": [], + "related": [ + "022800" + ], "remark": "", "space": "", "unrelated": [] @@ -603737,6 +603739,33 @@ "space": "", "unrelated": [] }, + "022800": { + "id": "022800", + "content": "已知点$O(0,0)$、$Q_0(0,1)$和$R_0(3,1)$, 记$Q_0R_0$的中点为$P_1$, 取$Q_0P_1$和$P_1R_0$中的一条, 记其端点为$Q_1$、$R_1$, 使之满足$(|OQ_1|-2)(|OR_1|-2)<0$; 记$Q_1R_1$的中点为$P_2$, 取$Q_1P_2$和$P_2R_1$中的一条, 记其端点为$Q_2$、$R_2$, 使之满足$(|OQ_2|-2)(|OR_2|-2)<0$; 依次下去, 得到点$P_1,P_2,\\cdots ,P_n,\\cdots$, 则线段$Q_0P_n$的长度将``无限趋近''于一个确定的值$a$, $a=$\\blank{50}.", + "objs": [], + "tags": [ + "第七单元", + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海2011年秋季高考试题14-20231120修改", + "edit": [ + "20220819\t王伟叶", + "20231120\t王伟叶", + "20231120\t王伟叶" + ], + "same": [], + "related": [ + "011614" + ], + "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