From 64a7c8034cb6193932a907c849f441059ccb7da3 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Mon, 30 Oct 2023 20:39:21 +0800 Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A02026=E5=B1=8A=E9=AB=98?= =?UTF-8?q?=E4=B8=80=E4=B8=8A=E5=AD=A6=E6=9C=9F=E7=AC=AC=E4=B8=89=E6=AC=A1?= =?UTF-8?q?=E6=B5=8B=E9=AA=8C=E9=83=A8=E5=88=86=E9=A2=98=E7=9B=AE?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 220 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 220 insertions(+) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 8618d2ca..1bc5d238 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -519753,6 +519753,226 @@ "space": "", "unrelated": [] }, + "019905": { + "id": "019905", + "content": "函数 $y=a^{x-1}+2$($a>0$, $a \\neq 1$) 的图像恒过一定点, 此定点的坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019906": { + "id": "019906", + "content": "函数 $y=(m^2-m-1) x^{m^2-2 m-1}$ 是幂函数, 则 $m$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019907": { + "id": "019907", + "content": "设 $\\alpha \\in\\{-1,1, \\dfrac{1}{2}, 3\\}$, 则使函数 $y=x^\\alpha$ 的定义域为 $\\mathbf{R}$, 且图像关于原点对称的所有 $\\alpha$ 的取值集合为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019908": { + "id": "019908", + "content": "已知 $\\log _{14}7=a$, $14^b=5$, 则 $\\log _{35}28=$\\blank{50}.(用 $a, b$ 表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019909": { + "id": "019909", + "content": "已知 $a^{\\frac{2}{3}}=\\dfrac{4}{9}$($a>0$), 则 $\\log _{\\frac{2}{3}}a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019910": { + "id": "019910", + "content": "方程 $\\lg (x-1)+\\lg (3-x)=\\lg (2-x)$ 的解为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019911": { + "id": "019911", + "content": "若函数 $y=\\lg [(a^2-1) x^2+(a+1) x+1]$ 的定义域为 $\\mathbf{R}$, 则实数 $a$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019912": { + "id": "019912", + "content": "已知函数 $y=(x-a)(x-b)$ (其中 $a>b$) 的图像如图所示, 则函数 $y=a^x+b$ 的图像大致为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (1,0.1) -- (1,0) node [below] {$1$};\n\\draw (-1,0.1) -- (-1,0) node [above] {$-1$};\n\\draw [thick, domain = -2.4:1.4] plot (\\x,{(\\x-0.4)*(\\x+1.4)});\n\\end{tikzpicture}\n\\end{center}\n\\fourch{\\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0.1,1) -- (0,1) node [right] {$1$};\n\\draw [domain = -1.3:2,thick] plot (\\x,{exp(\\x*ln(0.4))-1.4});\n\\draw [dashed] (-2,-1.4) -- (2,-1.4);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0.1,1) -- (0,1) node [right] {$1$};\n\\draw [domain = -1.1:2,thick] plot (\\x,{exp(\\x*ln(0.4))-0.8});\n\\draw [dashed] (-2,-0.8) -- (2,-0.8);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0.1,1) -- (0,1) node [right] {$1$};\n\\draw [domain = -1.1:2,thick] plot (-\\x,{exp(\\x*ln(0.4))-0.8});\n\\draw [dashed] (-2,-0.8) -- (2,-0.8);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0.1,1) -- (0,1) node [right] {$1$};\n\\draw [domain = -1.3:2,thick] plot (-\\x,{exp(\\x*ln(0.4))-1.4});\n\\draw [dashed] (-2,-1.4) -- (2,-1.4);\n\\end{tikzpicture}}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019913": { + "id": "019913", + "content": "对于 $a>0$, $a \\neq 1$, 给出下列四个命题, 其中真命题是\\bracket{20}.\n\\onech{$\\log _a(1+a)$总是小于$\\log _a(1+\\dfrac{1}{a})$}{$\\log _a(1+a)$总是大于$\\log _a(1+\\dfrac{1}{a})$}{$a^{1+a}$总是小于$a^{1+\\frac{1}{a}}$}{$a^{1+a}, a^{1+\\frac{1}{a}}$ 的大小不能确定}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "019914": { + "id": "019914", + "content": "已知函数 $y=x^{-4}$ 和函数 $y=(x-1)^{-4}+2$, 指出这两个函数图像之间的关系,并在平面直角坐标系中作出函数 $y=(x-1)^{-4}+2$ 的大致图像.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "019915": { + "id": "019915", + "content": "已知 $2^x \\leq 256$ 且 $\\log _2 x \\geq \\dfrac{1}{2}$, 求函数 $f(x)=(\\log _2 x-1) \\cdot(\\log _{\\sqrt{2}}\\sqrt{x}-2)$的最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231030\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "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.",