添加2024届高三基础赋能卷1五道补充题

题库0.3/Problems.json

@@ -518012,6 +518012,106 @@
         "space": "",
         "unrelated": []
     },
+    "019887": {
+        "id": "019887",
+        "content": "在 $\\triangle ABC$ 中, 角 $A$、$B$、$C$ 所对的边分别是 $a$、$b$、$c$, 若 $a: b: c=2: 3: 4$, 则 $\\cos C=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231021\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019888": {
+        "id": "019888",
+        "content": "已知 $M$ 是三棱锥 $P-ABC$ 的棱 $PC$ 的中点, 设三棱锥 $P-ABC$ 的体积为 $1$, 则三棱锥 $N-PAB$ 的体积为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231021\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019889": {
+        "id": "019889",
+        "content": "设 $a>0$. 双曲线 $\\dfrac{x^2}{a^2}-y^2=1$ 的一个顶点与抛物线 $y^2=12 x$ 的焦点重合, 则 $a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231021\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019890": {
+        "id": "019890",
+        "content": "设 $a, b \\in \\mathbf{R}$, $\\mathrm{i}$ 表示虚数单位. 若 $|a+b \\mathrm{i}|=1$, 则 $a b$ 的范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231021\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019891": {
+        "id": "019891",
+        "content": "已知 $y=f(x)$ 是 $\\mathbf{R}$ 上的偶函数, 则``$x_1+x_2=0$''是``$f(x_1)-f(x_2)=0$''的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{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": [
+            "20231021\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.",