录入24届赋能补充题至9B

题库0.3/Problems.json

@@ -617592,6 +617592,166 @@
         "space": "",
         "unrelated": []
     },
+    "023049": {
+        "id": "023049",
+        "content": "设集合 $A=\\{2,3,4,12\\}$, $B=\\{0,1,2,3\\}$, 则 $A \\cup B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023050": {
+        "id": "023050",
+        "content": "双曲线 $x^2-\\dfrac{y^2}{2}=1$ 的渐近线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023051": {
+        "id": "023051",
+        "content": "若复数 $z=1-\\mathrm{i}$ ($\\mathrm{i}$ 为虚数单位), 则 $z^2$ 的共轭复数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023052": {
+        "id": "023052",
+        "content": "记等差数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$. 若 $a_5=1$, 则 $S_9=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023053": {
+        "id": "023053",
+        "content": "已知实数 $a>0$, $b>0$, 且 $a+b=4$, 则 $a^2+b^2$ 的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023054": {
+        "id": "023054",
+        "content": "已知圆锥的体积为 $\\dfrac{\\sqrt{3}}{3}\\pi$, 且母线与底面所成角为 $\\dfrac{\\pi}{3}$, 则该圆锥的表面积为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023055": {
+        "id": "023055",
+        "content": "设 $a \\in \\mathbf{R}$, 若 $(2+\\dfrac{a}{x})(1+x)^5$ 展开式中 $x^2$ 的系数为 $10$, 则 $a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023056": {
+        "id": "023056",
+        "content": "下列命题正确的是\\bracket{20} .\n\\onech{如果两条直线垂直于同一条直线, 那么这两条直线互相平行}{如果一条直线垂直于一个平面内的两条直线, 那么这条直线垂直于这个平面}{如果一条直线平行于一个平面内的一条直线, 那么这条直线平行于这个平面}{如果一个平面内的两条相交直线与另一个平面平行, 那么这两个平面互相平行}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",