录入2024届高三基础赋能卷12部分题目

题库0.3/Problems.json

@@ -342235,7 +342235,9 @@
             "20221215\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "019994"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -353370,7 +353372,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "019991"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -520107,7 +520111,9 @@
             "20231102\t余利成"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "019990"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -521515,6 +521521,172 @@
         "space": "",
         "unrelated": []
     },
+    "019988": {
+        "id": "019988",
+        "content": "已知集合 $A=\\{-1,0,1,2\\}$, $B=(-\\infty, 0]$, 则 $A \\cap B=$\\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": []
+    },
+    "019989": {
+        "id": "019989",
+        "content": "在平面直角坐标系 $xOy$ 中, 角 $\\theta$ 以射线 $Ox$ 为始边, 其终边与以原点为圆心的单位圆交于点 $(\\dfrac{3}{5}, \\dfrac{4}{5})$, 则 $\\tan \\theta=$\\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": []
+    },
+    "019990": {
+        "id": "019990",
+        "content": "已知直角三角形 $ABC$ 中, $\\angle A=90^{\\circ}$, $AB=3$, $AC=4$, 则 $\\triangle ABC$ 绕直线 $AC$ 旋转一周所得几何体的体积为\\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": [
+            "019920"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019991": {
+        "id": "019991",
+        "content": "已知无穷等比数列 $\\{a_n\\}$ 的前 $n$ 项和的极限为 $1$ , 则首项 $a_1$ 的取值范围是\\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": [
+            "012955"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019992": {
+        "id": "019992",
+        "content": "设 $0<\\omega<6$, $f(x)=\\sin \\omega x$. 将函数 $y=f(x)$ 的图像向左平移 $\\dfrac{2 \\pi}{3}$ 单位后, 所得函数图像与原来函数的图像重合, 则 $\\omega=$\\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": []
+    },
+    "019993": {
+        "id": "019993",
+        "content": "在 $\\triangle ABC$ 中, 角 $A, B, C$ 的对边分别为 $a, b, c$, 面积为 $S$. 若 $a^2+c^2-b^2=S$, 则角 $B$ 的大小为\\blank{50}(用反正切表示).",
+        "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": []
+    },
+    "019994": {
+        "id": "019994",
+        "content": "设 $n$ 是正整数. 则``$n=4$''是``$(x+\\dfrac{1}{x})^n$ 的二项展开式中存在常数项''的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充要条件}{既不充分也不必要条件}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231103\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "012563"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019995": {
+        "id": "019995",
+        "content": "焦点在 $x$ 轴上, 焦距为 $4$, 长轴长为 $10$ 的椭圆的标准方程为\\bracket{20}.\n\\fourch{$\\dfrac{x^2}{100}+\\dfrac{y^2}{84}=1$}{$\\dfrac{x^2}{100}+\\dfrac{y^2}{96}=1$}{$\\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$}{$\\dfrac{x^2}{25}+\\dfrac{y^2}{21}=1$}",
+        "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.",