收录高三寒假作业45新题

工具v2/文本文件/新题收录列表.txt

@@ -133,3 +133,6 @@
 20240125-123201
 023954:023956,016816,023957:023959
 
+20240125-123757
+023960:023965
+

题库0.3/Problems.json

@@ -645864,6 +645864,126 @@
         "space": "4em",
         "unrelated": []
     },
+    "023960": {
+        "id": "023960",
+        "content": "函数 $f(x)=\\sqrt{x+3}+\\log _2(6-x)$ 的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023961": {
+        "id": "023961",
+        "content": "已知函数 $f(x)=\\sqrt{-x^2+2 x+3}$, 则函数 $f(3 x-2)$ 的定义域为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023962": {
+        "id": "023962",
+        "content": "已知 $f(\\dfrac{1}{2}x-1)=2 x-5$, 且 $f(a)=6$, 则 $a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023963": {
+        "id": "023963",
+        "content": "已知 $f(2 x+1)=x^2-2 x$, 则 $f(3)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023964": {
+        "id": "023964",
+        "content": "高斯是德国著名的数学家, 近代数学奠基者之一, 享有``数学王子''的称号, 用其名字命名的``高斯函数''为设 $x \\in \\mathbf{R}$, 用 $[x]$ 表示不超过 $x$ 的最大整数, 则 $y=[x]$ 称为高斯函数.例如: $[-2.1]=-3$, $[3.1]=3$, 已知函数 $f(x)=\\dfrac{2^x+3}{2^x+1}$, 则函数 $y=[f(x)]$ 的值域为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023965": {
+        "id": "023965",
+        "content": "行驶中的汽车在刹车时由于惯性作用, 要继续往前滑行一段距离才能停下, 这段距离叫做刹车距离. 在某种路面上, 某种型号汽车的刹车距离 $y(\\mathrm{m})$ 与汽车的车速 $x(\\mathrm{km}/ \\mathrm{h})$ 满足下列关系: $y=\\dfrac{x^2}{200}+m x+n(m$、$n$ 是常数 $)$. 下图是根据多次实验数据绘制的刹车距离 $y(m)$ 与汽车的车速 $x(\\mathrm{km}/ \\mathrm{h})$ 的关系图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.05, yscale = 0.05]\n\\draw [->] (-10,0) -- (100,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,50) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:100, samples = 100] plot (\\x,{\\x*\\x/200+\\x/100});\n\\foreach \\i/\\j in {40/8.4,60/18.6,80/32.8}\n{\\draw [dashed] (\\i,0) node [below] {$\\i$} -- (\\i,\\j) -- (0,\\j) node [left] {$\\j$};}; \n\\end{tikzpicture}\n\\end{center}\n(1) 求出 $y$ 关于 $x$ 的函数表达式;\\\\\n(2) 如果要求刹车距离不超过 $25.2 m$, 求行驶的最大速度.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "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.",