diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index f92fc4e7..852fab2c 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -18673,7 +18673,8 @@ "008484", "008487", "011055", - "011647" + "011647", + "019965" ], "remark": "", "space": "", @@ -32562,7 +32563,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "019964" + ], "remark": "", "space": "", "unrelated": [] @@ -331198,7 +331201,9 @@ "20221209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "019965" + ], "remark": "", "space": "", "unrelated": [] @@ -336408,7 +336413,9 @@ "20221212\t王伟叶" ], "same": [], - "related": [], + "related": [ + "019964" + ], "remark": "", "space": "", "unrelated": [] @@ -521004,6 +521011,153 @@ "space": "", "unrelated": [] }, + "019964": { + "id": "019964", + "content": "抛物线 $y^2=4 x$ 的准线方程是\\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": [ + "000979", + "031118", + "012354" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "019965": { + "id": "019965", + "content": "计算: $\\displaystyle\\lim_{n\\to+\\infty}\\dfrac{2 n-1}{3 n+2}=$\\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": [ + "000546", + "012183" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "019966": { + "id": "019966", + "content": "已知 $\\sin \\alpha=\\dfrac{\\sqrt{5}}{5}$, 则 $\\sin ^4 \\alpha-\\cos ^4 \\alpha$ 的值为\\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": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019967": { + "id": "019967", + "content": "等比数列 $\\{a_n\\}$ 的首项 $a_1=1$, 公比为 $\\dfrac{1}{3}$, 则 $\\displaystyle\\lim _{n \\to+\\infty}(a_1+a_3+a_5+\\cdots a_{2 n-1})=$\\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": [] + }, + "019968": { + "id": "019968", + "content": "已知 $\\cos \\alpha-\\sin \\alpha=\\dfrac{\\sqrt{2}}{3}$, 则 $\\cos (\\dfrac{\\pi}{2}-2 \\alpha)=$\\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": [] + }, + "019969": { + "id": "019969", + "content": "在复平面内, 复数 $z=\\sin 2+\\mathrm{i}\\cos 2$ ($\\mathrm{i}$ 为虚数单位) 对应的点位于\\bracket{20}.\n\\fourch{第一象限}{第二象限}{第三象限}{第四象限}", + "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": [] + }, + "019970": { + "id": "019970", + "content": "已知椭圆的标准方程为 $\\dfrac{x^2}{16}+\\dfrac{y^2}{4}=1$, 则其焦距为\\bracket{20} .\n\\fourch{$\\sqrt{2}$}{$2 \\sqrt{2}$}{$2 \\sqrt{3}$}{$4 \\sqrt{3}$}", + "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.", @@ -625402,7 +625556,9 @@ "20230108\t王伟叶" ], "same": [], - "related": [], + "related": [ + "019964" + ], "remark": "", "space": "", "unrelated": []