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录入一些2026届的答案

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weiye.wang 2024-03-30 12:00:45 +08:00
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工具v2/文本文件/metadata.txt
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usages usages
032153
20240325 2024届高三07班 0.919 FORCE
20240325 2024届高三07班 0.970
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题库0.3/Problems.json
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@ -134081,7 +134081,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $AN=\\dfrac{4\\sqrt{3}}{3}\\sin\\theta$, $AM=\\dfrac{4\\sqrt{3}}{3}\\sin(\\theta+\\dfrac{\\pi}{3})$, $\\theta\\in (0,\\dfrac{2\\pi}{3})$; (2) 使$AM=AN=2\\text{km}$, 才能使工厂产生的噪声对居民的影响最小",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -274817,7 +274817,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\dfrac{1}{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -274839,7 +274839,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 奇函数, 理由略; (2) 奇函数, 理由略; (3) 既不是奇函数, 又不是偶函数, 理由略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -274861,7 +274861,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "最小正周期是$4\\pi$, 单调减区间为$[\\dfrac{\\pi}{3}+4k\\pi,\\dfrac{7\\pi}{3}+4k\\pi]$, $k\\in \\mathbf{Z}$, 单调增区间为$[-\\dfrac{5\\pi}{3}+4k\\pi,\\dfrac{\\pi}{3}+4k\\pi]$, $k\\in \\mathbf{Z}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -274883,7 +274883,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) \\begin{tikzpicture}[>=latex]\n\\draw [->] (-5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -5:5, samples = 100] plot (\\x,{sin(\\x/pi*180+30)});\n\\draw [dashed] (pi/3,0) node [below] {$\\frac{\\pi}{3}$}-- (pi/3,1) -- (0,1) node [left] {$1$};\n\\draw [dashed] (-2*pi/3,0) node [below] {$-\\frac{2\\pi}{3}$}-- (-2*pi/3,-1) -- (0,-1) node [right] {$-1$};\n\\end{tikzpicture}\\\\\n(2) \\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -5:5, samples = 100] plot (\\x,{3*sin(2*\\x/pi*180-60)});\n\\draw [dashed] (5*pi/12,0) node [below] {$\\frac{5\\pi}{12}$} --++ (0,3) -- (0,3) node [left] {$3$};\n\\draw [dashed] (-pi/12,0) node [above] {$\\frac{\\pi}{12}$} --++ (0,-3) -- (0,-3) node [right] {$-3$};\n\\end{tikzpicture}",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -274905,7 +274905,7 @@
"第三单元" "第三单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "D",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -274927,7 +274927,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$y=\\dfrac{3}{2}\\sin (2x+\\dfrac{\\pi}{6})$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -274950,7 +274950,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\{\\alpha|\\alpha = \\dfrac{\\pi}{3}+k\\pi, \\ k\\in \\mathbf{Z}\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -274972,7 +274972,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\tan (-\\dfrac 27\\pi )>\\tan (-\\dfrac 25\\pi )$, 理由略; (2) $\\cot 231^\\circ>\\cot 237^\\circ$, 理由略; (3) $\\tan (k\\pi -\\dfrac\\pi 3)<\\tan (k\\pi +\\dfrac\\pi 3)$, 理由略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -294288,7 +294288,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) \\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-0.5,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-3.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2*pi, samples = 100] plot (\\x,{cos(\\x/pi*180)*2-1});\n\\draw [dashed] (2*pi,1) -- (0,1) node [left] {$1$};\n\\draw [dashed] (2*pi,1) -- (2*pi,0) node [below] {$2\\pi$};\n\\draw [dashed] (pi,0) node [above] {$\\pi$} -- (pi,-3) -- (0,-3) node [left] {$-3$};\n\\end{tikzpicture}\\\\\n(2) \\begin{tikzpicture}[>=latex]\n\\draw [->] (-7,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -pi/2:pi/2, samples = 100] plot (\\x,{cos(\\x/pi*180)});\n\\draw [domain = pi/2:3*pi/2, samples = 100] plot (\\x,{-cos(\\x/pi*180)});\n\\draw [domain = 3*pi/2:7, samples = 100] plot (\\x,{cos(\\x/pi*180)});\n\\draw [domain = -3*pi/2:-pi/2, samples = 100] plot (\\x,{-cos(\\x/pi*180)});\n\\draw [domain = -7:-3*pi/2, samples = 100] plot (\\x,{cos(\\x/pi*180)});\n\\draw (pi/2,0) node [below] {$\\frac{\\pi}{2}$};\n\\draw (0,1) node [above left] {$1$};\n\\end{tikzpicture}",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -294334,7 +294334,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 最大值为$3$, 取得最大值时$x$的集合为$\\{x|x=k\\pi, \\ k\\in \\mathbf{Z}\\}$; 最小值为$\\dfrac{1}{3}$, 取得最小值时$x$的集合为$\\{x|x=\\dfrac{\\pi}{2}+k\\pi, \\ k\\in \\mathbf{Z}\\}$;\\\\\n(2) 最大值为$1$, 取得最大值时$x$的集合为$\\{x|x=2k\\pi, \\ k\\in \\mathbf{Z}\\}$; 最小值为$-\\dfrac{5}{4}$, 取最小值时$x$的集合为$\\{x|x=\\dfrac{2\\pi}{3}+2k\\pi\\text{ 或 }\\dfrac{4\\pi}{3}+2k\\pi, \\ k\\in \\mathbf{Z}\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -294502,7 +294502,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "振幅为$\\sqrt{2}$, 频率为$30\\pi$, 初始相位为$-\\dfrac{\\pi}{12}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -294570,7 +294570,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "\\begin{tikzpicture}[>=latex]\n\\draw [->] (-0.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:3.5, samples = 100] plot (\\x,{2*sin(\\x*180+45)});\n\\draw [dashed] (0.25,0) node [below] {$\\frac{1}{4}$} --++ (0,2) -- (0,2) node [left] {$2$};\n\\draw [dashed] (1.25,0) node [above] {$\\frac{5}{4}$} --++ (0,-2) -- (0,-2) node [left] {$-2$};\n\\end{tikzpicture}\\\\\n(1) 开始振动的位置在平衡位置上方$\\sqrt{2}\\text{cm}$处; (2) 最高点和最低点与平衡位置的距离都是$2$; (3) 经过$2\\text{s}$小球往复振动一次; (4) 每秒小球往复振动$0.5$次",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -294614,7 +294614,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$y=2\\cos(\\dfrac{1}{2} x+\\dfrac{5\\pi}{3})$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -294728,7 +294728,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 奇函数, 理由略; (2) 偶函数, 理由略; (3) 奇函数, 理由略; (4) 偶函数, 理由略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -326303,7 +326303,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $[0,\\dfrac{\\pi}{3}]$; (2) $\\dfrac{24}{25}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511631,7 +511631,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 最大值是$6$, 当且仅当$x=\\pi+2k\\pi$, $k\\in \\mathbf{Z}$时取到; 最小值是$-2$, 当且仅当$x=2k\\pi$, $k\\in \\mathbf{Z}$时取到;\\\\\n(2) 最大值是$1$, 当且仅大哥$x=0$时取到; 最小值是$-\\dfrac{1}{2}$, 当且仅当$x=-\\dfrac{4\\pi}{3}$时取到",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511653,7 +511653,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "最小正周期为$\\pi$, 单调增区间是$[k\\pi-\\dfrac{\\pi}{3}k\\pi+\\dfrac{\\pi}{6}]$, $k\\in \\mathbf{Z}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511697,7 +511697,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\{x|\\dfrac{\\pi}{2}+2k\\pi<x<\\dfrac{3\\pi}{2}+2k\\pi, \\ k\\in \\mathbf{Z}\\}$; (2) $\\{x|-\\dfrac{3\\pi}{4}+2k\\pi<x<\\dfrac{3\\pi}{4}+2k\\pi, \\ k\\in \\mathbf{Z}\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511719,7 +511719,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "\\begin{tikzpicture}[>=latex]\n\\draw [->] (-7,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -7:7, samples = 200, ultra thick] plot (\\x,{2*sin(\\x/pi*180)});\n\\draw [domain = -7:7, samples = 200, thick] plot (\\x,{1*sin(2*\\x/pi*180)});\n\\draw [domain = -7:7, samples = 200, dashed, ultra thick] plot (\\x,{sin(\\x/pi*180+90)});\n\\draw [domain = -7:7, samples = 200, dashed] plot (\\x,{sin(\\x/pi*180)});\n\\draw [dashed] (-6,-3) -- (-5.5,-3) node [right] {$y=\\sin x$};\n\\draw [ultra thick] (-3,-3) -- (-2.5,-3) node [right] {$y=2\\sin x$};\n\\draw [thick] (0,-3) -- (0.5,-3) node [right] {$y=\\sin 2x$};\n\\draw [ultra thick, dashed] (3,-3) -- (3.5,-3) node [right] {$y=\\sin (x+\\dfrac{\\pi}{2})$};\n\\end{tikzpicture}",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511741,7 +511741,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "大致图像: \\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-3.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -5:5, samples = 100] plot (\\x,{3*sin(2*\\x/pi*180+45)});\n\\foreach \\i in {-3,-2,-1,1,2,3}\n{\\draw (0.1,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\foreach \\i in {{-pi/8},{pi/8},{3*pi/8},{5*pi/8},{7*pi/8}}\n{\\draw (\\i,0.2) -- (\\i,0);};\n\\draw (-pi/8,0) node [above left] {$-\\frac{\\pi}{8}$};\n\\draw (pi/8,0) node [above] {$\\frac{\\pi}{8}$};\n\\draw (3*pi/8,0) node [above right] {$\\frac{3\\pi}{8}$};\n\\draw (5*pi/8,0) node [below] {$\\frac{5\\pi}{8}$};\n\\draw (7*pi/8,0) node [below right] {$\\frac{7\\pi}{8}$};\n\\end{tikzpicture}\\\\\n振幅为$3$, 频率为$\\dfrac{1}{\\pi}$, 初始相位为$\\dfrac{\\pi}{4}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511763,7 +511763,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "周期$T=0.02\\text{s}$, 频率$f=50\\text{Hz}$, 电流的最大值为$10\\text{A}$; $I_0=10$, $\\omega = 100\\pi$, $\\varphi = 0$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511785,7 +511785,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{4\\pi}{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511807,7 +511807,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\varphi=\\dfrac{\\pi}{2}$, $\\omega = \\dfrac{3}{4}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511829,7 +511829,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "定义域为$\\{x|x\\in \\mathbf{R}, \\ x\\ne 6k+1, \\ k\\in \\mathbf{Z}\\}$, 单调增区间为$(6k-5,6k+1)$, $k\\in \\mathbf{Z}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511851,7 +511851,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\dfrac{\\pi}{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511873,7 +511873,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$2\\sqrt{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -511895,7 +511895,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$n=3$, 在$(-\\dfrac{\\pi}{18}+\\dfrac{k\\pi}{3}, \\dfrac{5\\pi}{18}+\\dfrac{k\\pi}{3})$, $k\\in \\mathbf{Z}$上是严格增函数",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -662416,7 +662416,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{\\pi}{6}$, $\\pi$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -662438,7 +662438,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "在$[-\\dfrac{\\pi}{6},\\dfrac{\\pi}{3}]$上严格减, 在$[\\dfrac{\\pi}{3},\\dfrac{2\\pi}{3}]$上严格增, 值域为$[-1,1]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -690343,7 +690343,7 @@
"objs": [], "objs": [],
"tags": [], "tags": [],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\{x|x\\ne \\dfrac{\\pi}{6}+k\\pi, \\ k\\in \\mathbf{Z}\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -690365,7 +690365,7 @@
"objs": [], "objs": [],
"tags": [], "tags": [],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$[-1,\\dfrac{5}{4}]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -690385,7 +690385,7 @@
"objs": [], "objs": [],
"tags": [], "tags": [],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{5\\pi}{6}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -690405,7 +690405,7 @@
"objs": [], "objs": [],
"tags": [], "tags": [],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "充分非必要",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -690428,7 +690428,7 @@
"objs": [], "objs": [],
"tags": [], "tags": [],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$0$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -690448,7 +690448,7 @@
"objs": [], "objs": [],
"tags": [], "tags": [],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$[\\dfrac{13\\pi}{6},+\\infty)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -690521,7 +690521,7 @@
"objs": [], "objs": [],
"tags": [], "tags": [],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\pi$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -690546,7 +690546,7 @@
"objs": [], "objs": [],
"tags": [], "tags": [],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "面积$S=2\\sqrt{2}\\sin\\theta\\sin(\\dfrac{\\pi}{4}-\\theta)(=\\sqrt{2}\\sin(2\\theta+\\dfrac{\\pi}{4})-1)$, $\\theta\\in (0,\\dfrac{\\pi}{4})$, 面积的最大值为$\\sqrt{2}-1$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],