添加2026届高一上学期第三次测验部分题目
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@ -519753,6 +519753,226 @@
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"space": "",
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"unrelated": []
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},
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"019905": {
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"id": "019905",
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"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}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019906": {
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"id": "019906",
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"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}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019907": {
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"id": "019907",
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"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}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019908": {
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"id": "019908",
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"content": "已知 $\\log _{14}7=a$, $14^b=5$, 则 $\\log _{35}28=$\\blank{50}.(用 $a, b$ 表示)",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019909": {
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"id": "019909",
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"content": "已知 $a^{\\frac{2}{3}}=\\dfrac{4}{9}$($a>0$), 则 $\\log _{\\frac{2}{3}}a=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019910": {
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"id": "019910",
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"content": "方程 $\\lg (x-1)+\\lg (3-x)=\\lg (2-x)$ 的解为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019911": {
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"id": "019911",
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"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}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019912": {
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"id": "019912",
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"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}}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019913": {
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"id": "019913",
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"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}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019914": {
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"id": "019914",
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"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.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"019915": {
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"id": "019915",
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"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.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231030\t严捷"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"020001": {
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"id": "020001",
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"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.",
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