diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 43cb0da0..be1253cd 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -18159,7 +18159,8 @@ "same": [], "related": [ "000410", - "004747" + "004747", + "019960" ], "remark": "", "space": "", @@ -25334,7 +25335,9 @@ "20230410\t徐慧" ], "same": [], - "related": [], + "related": [ + "019956" + ], "remark": "", "space": "", "unrelated": [] @@ -300164,7 +300167,8 @@ "000410", "004686", "004727", - "004747" + "004747", + "019960" ], "remark": "", "space": "", @@ -300390,7 +300394,9 @@ "20220817\t王伟叶" ], "same": [], - "related": [], + "related": [ + "019962" + ], "remark": "", "space": "", "unrelated": [] @@ -318861,7 +318867,9 @@ "20220819\t王伟叶" ], "same": [], - "related": [], + "related": [ + "019961" + ], "remark": "", "space": "", "unrelated": [] @@ -399471,7 +399479,9 @@ "20230312\t王伟叶" ], "same": [], - "related": [], + "related": [ + "019961" + ], "remark": "", "space": "", "unrelated": [] @@ -442276,7 +442286,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "019961" + ], "remark": "", "space": "", "unrelated": [] @@ -520820,6 +520832,177 @@ "space": "", "unrelated": [] }, + "019956": { + "id": "019956", + "content": "已知全集 $U=\\mathbf{R}$, 集合 $A=\\{x | x^2-3 x \\geq 0\\}$, 则 $\\overline{A}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [ + "000736" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "019957": { + "id": "019957", + "content": "设函数 $y=f(x)$ 是奇函数. 若 $f(-2)+f(-1)-3=f(1)+f(2)+3$, 则 $f(\\mathrm{l})+f(2)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019958": { + "id": "019958", + "content": "若复数 $z$ 满足 $(1+2 i) z=4+3 i (i$ 是虚数单位 $)$, 则 $z=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019959": { + "id": "019959", + "content": "等比数列 $\\{a_n\\}$ 中, $a_1+a_2=1$, $a_5+a_6=16$, 则 $a_9+a_{10}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019960": { + "id": "019960", + "content": "$(1-2 x)^5$ 的展开式中 $x^3$ 项的系数为 (用数字作答)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [ + "000532", + "010990" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "019961": { + "id": "019961", + "content": "已知两条直线 $l_1: 4 x+2 y-3=0$ 和 $l_2: 2 x+y+1=0$, 则 $l_1$ 与 $l_2$ 的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [ + "016463", + "011718", + "014701" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "019962": { + "id": "019962", + "content": "若 $a, b$ 为实数, 则``$a<-1$''是``$\\dfrac{1}{a}>-1$''的\\bracket{20}.\n\\fourch{充要条件}{充分非必要条件}{必要非充分条件}{既非充分也非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [ + "010998" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "019963": { + "id": "019963", + "content": "已知 $a$、$b$ 为两条不同的直线, $\\alpha$、$\\beta$ 为两个不同的平面, $\\alpha \\bigcap \\beta=a$, $a \\parallel b$, 则下列结论不可能成立的是\\bracket{20}.\n\\fourch{$b \\subset \\beta$, 且 $b \\parallel \\alpha$}{$b \\subset \\alpha$, 且 $b \\parallel \\beta$}{$b \\parallel \\alpha$, 且 $b \\parallel \\beta$}{$b$ 与 $\\alpha$、$\\beta$ 都相交}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231103\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",