From f10f95c041edca29317610073959f85b75f6db75 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Mon, 1 Jan 2024 09:45:29 +0800 Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A02026=E5=B1=8A=E9=AB=98?= =?UTF-8?q?=E4=B8=80=E8=AE=B2=E4=B9=89=E9=83=A8=E5=88=86=E9=A2=98=E7=9B=AE?= =?UTF-8?q?=E7=9A=84=E7=AD=94=E6=A1=88?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 1302 ++++++++++++++++++++--------------------- 1 file changed, 651 insertions(+), 651 deletions(-) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 78fe58fc..a2fe5dea 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -1551,7 +1551,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略, 等号成立的条件为$a=\\pm b$", "solution": "", "duration": -1, "usages": [ @@ -1868,7 +1868,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{3}{2}$", "solution": "", "duration": -1, "usages": [ @@ -1949,7 +1949,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$1-\\lg a$", "solution": "", "duration": -1, "usages": [ @@ -2130,7 +2130,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -2178,7 +2178,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{1}{1-2^x}$", "solution": "", "duration": -1, "usages": [ @@ -2506,7 +2506,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$1$或$-1$", "solution": "", "duration": -1, "usages": [ @@ -2744,7 +2744,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(\\dfrac{3}{5},1)$", "solution": "", "duration": -1, "usages": [ @@ -3425,7 +3425,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$f(x)=x^2+3+|x-1|+|x+1|$, $g(x)=|x-1|-|x+1|$", "solution": "", "duration": -1, "usages": [ @@ -40114,7 +40114,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-1,1)$", "solution": "", "duration": -1, "usages": [ @@ -40218,7 +40218,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "第一、第四", "solution": "", "duration": -1, "usages": [ @@ -40608,7 +40608,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -42306,7 +42306,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$, $3$", "solution": "", "duration": -1, "usages": [ @@ -44475,7 +44475,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "不一定, 如$y=1-x^2$, $x\\in [0,1]$, $(0,1)$和$(1,0)$都是公共点", "solution": "", "duration": -1, "usages": [ @@ -91739,7 +91739,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$y=1+2^{-x}$, $x\\in \\mathbf{R}$", "solution": "", "duration": -1, "usages": [ @@ -91831,7 +91831,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{x+3}{2x-4}$", "solution": "", "duration": -1, "usages": [ @@ -263254,7 +263254,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-1,5]$; (2) $(-3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -263283,7 +263283,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 正确, 根据定义; (2) 不正确, 如$A=\\varnothing$, $B=\\{1\\}$, $C=\\{2\\}$; (3) 正确, $A$中每个元素都在$B$中, $B$中每个元素都在$C$中, 故$A$中每个元素都在$C$中. 另一方面, 因$A\\subset B$, 所以存在$x$使得$x\\in B$, 但$x\\not\\in A$, 所以$x\\in C$, 但$x\\not\\in A$, 所以$A\\subset C$", "solution": "", "duration": -1, "usages": [], @@ -263308,7 +263308,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\subset$; (2) $\\supset$; (3) $=$", "solution": "", "duration": -1, "usages": [], @@ -263332,7 +263332,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\{a,b\\}$, $\\{a,c\\}$, $\\{a,d\\}$, $\\{a,b,c\\}$, $\\{a,b,d\\}$, $\\{a,c,d\\}$", "solution": "", "duration": -1, "usages": [], @@ -263407,7 +263407,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(A\\cap B)\\cup C=(A\\cup C)\\cap (B\\cup C)=\\{2,3,4,5,6\\}$; (2) $(A\\cup B)\\cap C=(A\\cap C)\\cup (B\\cap C)=\\{3,4,5,6\\}$", "solution": "", "duration": -1, "usages": [], @@ -263455,7 +263455,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 假命题, $2$; (2) 真命题, 由定义; (3) 假命题, $0$不是集合; (4) 假命题, 如$A=B=\\{1\\}$", "solution": "", "duration": -1, "usages": [], @@ -263479,7 +263479,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\alpha\\Rightarrow \\beta$; (2) $\\beta\\Rightarrow \\alpha$", "solution": "", "duration": -1, "usages": [], @@ -263504,7 +263504,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) 必要非充分; (2) 充分非必要; (3) 充要", "solution": "", "duration": -1, "usages": [], @@ -263529,7 +263529,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[4,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -263755,7 +263755,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 假, 如$a=1$, $b=0$, $c=100$, $d=0$; (2) 假, 如$a=-1$, $b=-1$, $c=0$; (3) 真, 根据符号的定义; (4) 假, 如$a=2$, $b=1$, $c=\\dfrac{1}{2}$, $d=1$; (5) 假, 如$a=-1$, $b=-1$, $c=1$, $d=-1$", "solution": "", "duration": -1, "usages": [], @@ -264307,7 +264307,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{2}{3}$", "solution": "", "duration": -1, "usages": [], @@ -264331,7 +264331,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\pm \\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -264355,7 +264355,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-4$; (2) $b-a$", "solution": "", "duration": -1, "usages": [ @@ -264393,7 +264393,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $10$; (2) $\\dfrac{1}{4}$", "solution": "", "duration": -1, "usages": [], @@ -264417,7 +264417,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a^{\\frac{59}{15}}$; (2) $a^{\\frac{4}{9}}$", "solution": "", "duration": -1, "usages": [], @@ -264441,7 +264441,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a^6$; (2) $-6b^{\\frac{1}{6}}$", "solution": "", "duration": -1, "usages": [], @@ -264465,7 +264465,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -264489,7 +264489,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -264537,7 +264537,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $16$; (2) $2$", "solution": "", "duration": -1, "usages": [], @@ -264561,7 +264561,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $A+B$; (2) $2A+\\dfrac{1}{2}B$", "solution": "", "duration": -1, "usages": [], @@ -264585,7 +264585,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $1$; (2) $\\dfrac{2}{3}$; (3) $-1$", "solution": "", "duration": -1, "usages": [], @@ -264610,7 +264610,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$3b+2a$", "solution": "", "duration": -1, "usages": [], @@ -264634,7 +264634,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-\\dfrac{2}{3}$; (2) $1$; (3) $18$; (4) $-2$", "solution": "", "duration": -1, "usages": [], @@ -264659,7 +264659,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$5+\\dfrac{1}{a}$", "solution": "", "duration": -1, "usages": [], @@ -264685,7 +264685,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -264817,7 +264817,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2.5^{-3}>3.1^{-3}$; (2) $1.7^{\\frac 32}>1.6^{\\frac 32}$", "solution": "", "duration": -1, "usages": [], @@ -264879,7 +264879,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 幂函数; (2) 幂函数; (3) 指数函数; (4) 幂函数; (5) 指数函数; (6) 指数函数", "solution": "", "duration": -1, "usages": [], @@ -264903,7 +264903,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\mathbf{R}$; (2) $(-\\infty,2)\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -264928,7 +264928,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,5.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:{ln(5.5)/ln(4)}, samples = 100] plot (\\x,{exp(\\x*ln(4))}) node [right] {$y=4^x$};\n\\draw [domain = {ln(5.5)/ln(0.25)}:3, samples = 100] plot (\\x,{exp(\\x*ln(0.25))}) node [right] {$y=(\\frac{1}{4})^x$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -264952,7 +264952,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $1.4^{0.3}<1.4^{0.4}$; (2) $0.3^{1.4}>0.3^{1.5}$; (3) 当$a>1$时, $a^{-3. 14}>(\\dfrac 1a)^\\pi$; 当$0=latex,scale = 0.5]\n\\draw [->] (-0.5,0) -- (5.5,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.001:5, samples = 100] plot (\\x,{ln(\\x)/ln(10)}) node [right] {$y=\\lg x$};\n\\draw [domain = 0.001:5, samples = 100] plot (\\x,{ln(\\x)/ln(0.1)}) node [below right] {$y=\\log_{\\frac{1}{10}} x$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -265150,7 +265150,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(2,0)$", "solution": "", "duration": -1, "usages": [], @@ -265176,7 +265176,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\log_{0.2}3>\\log_{0.2}6$; (2) $\\log_{0.2}3>\\log_{0.3}3$", "solution": "", "duration": -1, "usages": [], @@ -265200,7 +265200,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -265224,7 +265224,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=0.99988^t$; (2) 至少经过$87$年", "solution": "", "duration": -1, "usages": [], @@ -265248,7 +265248,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -265274,7 +265274,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,-3]\\cup [2,+\\infty)$; (2) $[1,2)\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -265333,7 +265333,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[1,+\\infty)$; (2) $[-\\dfrac{1}{3},1]$", "solution": "", "duration": -1, "usages": [], @@ -265419,7 +265419,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "都不一定, 如$y=0$, $x\\in \\{-1,1\\}$", "solution": "", "duration": -1, "usages": [], @@ -265443,7 +265443,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) \\begin{tikzpicture}[>=latex, samples = 200]\n\\draw [->] (-3,0) -- (0,0) node [above left] {$O$} -- (3,0) node [below right] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw [domain = -3:0, dashed] plot (\\x , {-\\x * \\x * \\x / 8+ \\x * \\x /8 +\\x});\n\\draw [domain = -3:0] plot (-\\x , {-\\x * \\x * \\x / 8+ \\x * \\x /8 +\\x});\n\\end{tikzpicture}\\\\\n(2) \\begin{tikzpicture}[>=latex, samples = 200]\n\\draw [->] (-3,0) -- (0,0) node [below left] {$O$} -- (3,0) node [below right] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw [domain = 0:3, dashed] plot (\\x, {sin(\\x * 60) * \\x - 0.5});\n\\draw [domain = 0:3] plot (-\\x, {sin(\\x * 60) * \\x - 0.5});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -265467,7 +265467,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 证明略", "solution": "", "duration": -1, "usages": [], @@ -265491,7 +265491,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 偶函数, 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; (4) 既是奇函数, 又是偶函数, 理由略", "solution": "", "duration": -1, "usages": [], @@ -265515,7 +265515,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 不存在, 理由略; (2) 存在($a=0$), 理由略", "solution": "", "duration": -1, "usages": [], @@ -265611,7 +265611,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "如$y=-x^2-2x$", "solution": "", "duration": -1, "usages": [], @@ -265636,7 +265636,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 在$[-2,1]$和$[2,3]$上是严格增函数; 在$[-3,-2]$和$[1,2]$上是严格减函数; (2) 在$[-\\pi,-\\dfrac{\\pi}{2}]$和$[\\dfrac{\\pi}{2},\\pi]$上是严格增函数, 在$[-\\dfrac{\\pi}{2},\\dfrac{\\pi}{2}]$上是严格减函数", "solution": "", "duration": -1, "usages": [], @@ -265660,7 +265660,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "在$[-2,-1]$上是严格减函数, 在$[-1,2]$上是严格增函数, 理由略", "solution": "", "duration": -1, "usages": [], @@ -265756,7 +265756,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 最大值为$1$, 最小值不存在; (2) 最大值为$1$, 最小值为$-3$; (3) 最大值不存在, 最小值为$-8$; (4) 最大值为$0$, 最小值为$-6$", "solution": "", "duration": -1, "usages": [], @@ -265780,7 +265780,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\begin{cases}5, & -21000\\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -266010,7 +266010,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$[0,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -266034,7 +266034,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=\\dfrac{x-2}{3}$, $x\\in \\mathbf{R}$; (2) $y=-\\dfrac{3}{x}$, $x\\in \\{x|x\\ne 0\\}$; (3) $y=-\\sqrt{x}$, $x\\in [0,+\\infty)$; (4) $y=(x-1)^2$, $x\\in [1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -266059,7 +266059,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "存在反函数, 反函数为$y=\\begin{cases}x, & -1\\le x\\le 0, \\\\ 1-x, & 0=latex,scale = 0.3]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:{exp(ln(3)/5)}, samples = 100] plot ({\\x*\\x*\\x*\\x*\\x},\\x) plot ({-\\x*\\x*\\x*\\x*\\x},-\\x);\n\\end{tikzpicture}; (2) $\\{x|x\\in\\mathbf{R}, \\ x\\in 0\\}$, 大致图像为\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.5:2, samples = 100] plot (\\x,{exp(-2*ln(\\x))}) plot (-\\x,{exp(-2*ln(\\x))});\n\\end{tikzpicture}; (3) $(0,+\\infty)$, 大致图像为\\begin{tikzpicture}[>=latex,scale = 0.3]\n\\draw [->] (-0.5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.6:1.45, samples = 100] plot ({\\x*\\x*\\x*\\x},{1/\\x/\\x/\\x});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [ @@ -281854,7 +281854,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "约$3086\\text{cm}^3/\\text{s}$", "solution": "", "duration": -1, "usages": [ @@ -281891,7 +281891,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $3.1^{-\\frac 12}>3.2^{-\\frac 12}$; (2) $(a+2)^{\\frac 13}>a^{\\frac 13}$", "solution": "", "duration": -1, "usages": [ @@ -282001,7 +282001,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "一、二", "solution": "", "duration": -1, "usages": [ @@ -282147,7 +282147,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "存在, $a$的值为$-1$或$0$", "solution": "", "duration": -1, "usages": [ @@ -282208,7 +282208,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,3]$; (2) $(-\\infty,0)\\cup (0,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -282246,7 +282246,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,4.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:3, samples = 100] plot (\\x,{exp(\\x*ln(1.5))}) node [right] {\\textcircled{1}};\n\\draw [domain = -3:3, samples = 100] plot (\\x,{exp(\\x*ln(2/3))}) node [right] {\\textcircled{2}} plot (\\x,{exp(\\x*ln(2/3))-1}) node [right] {\\textcircled{3}};\n\\draw [dashed] (-3,-1) -- (3,-1);\n\\end{tikzpicture}, \\textcircled{1}与\\textcircled{2}关于$y$轴对称, \\textcircled{2}向下平移$1$个单位得到\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -282284,7 +282284,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(2,3)$", "solution": "", "duration": -1, "usages": [], @@ -282308,7 +282308,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(2,1)$", "solution": "", "duration": -1, "usages": [], @@ -282332,7 +282332,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $1.2^{2.6}<1.2^{2.61}$; (2) $(\\sqrt 3)^{-\\frac 13}>(\\dfrac{\\sqrt 3}3)^\\frac 12$", "solution": "", "duration": -1, "usages": [ @@ -282369,7 +282369,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(1,3)$; (2) $[16,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -282406,7 +282406,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -282443,7 +282443,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "约$81$台", "solution": "", "duration": -1, "usages": [ @@ -282480,7 +282480,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -282504,7 +282504,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -282541,7 +282541,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,-\\sqrt{2})\\cup (\\sqrt{2},+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -282578,7 +282578,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$3^{2x}<3^x<3^{-x}$", "solution": "", "duration": -1, "usages": [], @@ -282602,7 +282602,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,0)\\cup (5,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -282664,7 +282664,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-12,+\\infty)$; (2) $\\mathbf{R}$", "solution": "", "duration": -1, "usages": [ @@ -282700,7 +282700,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [ @@ -282736,7 +282736,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex]\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 [domain = {1/9}:2, samples = 100] plot (\\x,{ln(\\x)/ln(3)}) node [right] {\\textcircled{1}};\n\\draw [domain = {1/9}:2, samples = 100] plot (\\x,{ln(\\x)/ln(1/3)}) node [right] {\\textcircled{2}};\n\\draw [domain = {1/9}:2, samples = 100] plot ({ln(\\x)/ln(1/3)},\\x) node [above] {\\textcircled{3}};\n\\end{tikzpicture}; \\textcircled{1}的图像与\\textcircled{2}的图像关于$x$轴对称, \\textcircled{2}的图像与\\textcircled{3}的图像关于直线$y=x$对称, \\textcircled{1}的图像绕原点逆时针旋转$90^\\circ$后得到\\textcircled{3}的图像", "solution": "", "duration": -1, "usages": [ @@ -282873,7 +282873,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -282911,7 +282911,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a>1$时, 定义域为$(-\\infty,1)$; 当$01$时, $mn$; (3) $m0$时, 定义域为$(-\\infty,-a)\\cup (-a,a)\\cup (a,+\\infty)$; (2) 当$a<0$时, 定义域为$(-\\infty,a]\\cup [0,+\\infty)$; 当$a=0$时, 定义域为$\\mathbf{R}$; 当$a>0$时, 定义域为$(-\\infty,0]\\cup [a,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -283244,7 +283244,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -283286,7 +283286,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 证明略", "solution": "", "duration": -1, "usages": [ @@ -283323,7 +283323,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 证明略", "solution": "", "duration": -1, "usages": [ @@ -283360,7 +283360,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 奇函数, 理由略; (2) 偶函数, 理由略; (3) 既不是奇函数, 又不是偶函数, 理由略; (4) 既不是奇函数, 又不是偶函数, 理由略; (5) 奇函数, 理由略", "solution": "", "duration": -1, "usages": [ @@ -283387,7 +283387,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -283472,7 +283472,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "最大值为$-2$, 最小值为$-3$", "solution": "", "duration": -1, "usages": [ @@ -283511,7 +283511,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$8$", "solution": "", "duration": -1, "usages": [ @@ -283575,7 +283575,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 奇函数, 理由略; (2) 偶函数, 理由略", "solution": "", "duration": -1, "usages": [ @@ -283635,7 +283635,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:3, samples = 100] plot (\\x,{\\x*\\x-2*abs(\\x)});\n\\end{tikzpicture}\\\\\n定义域为$\\mathbf{R}$, 是偶函数, 在$(-\\infty,-1]$和$[0,1]$上是严格减函数, 在$[-1,0]$和$[1,+\\infty)$上是严格增函数, 最小值为$-1$", "solution": "", "duration": -1, "usages": [ @@ -283757,7 +283757,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y_{\\min}=\\begin{cases}0, & t\\le 2, \\\\ 2^{t+1}-8, & 2\\le t<4 \\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -283800,7 +283800,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "定义域为$\\{1,2,3,4\\}$, 图像: \\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (0,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,0.2) -- (0.3,0.3) -- (0,0.4) -- (-0.3,0.5) -- (0,0.6) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed] (0.1,0.1) -- (4.5,4.5);\n\\foreach \\i/\\j/\\k in {1/1/10,2/2/12,3/3/14,4/4/16}\n{\\draw [dashed] (\\i,0) node [below] {$\\i$} --++ (0,\\j) -- (0,\\j) node [left] {$\\k$};\n\\filldraw (\\i,\\j) circle (0.06);};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [ @@ -283945,7 +283945,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $P=\\dfrac{2}{3}v^2$, $v\\in (0,48]$; (2) $y=\\dfrac{200}{3}v+\\dfrac{86400}{v}$, $v\\in (0,48]$; (3) 船速为$36$海里/小时时所需总费用最少", "solution": "", "duration": -1, "usages": [ @@ -284007,7 +284007,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=10600-200x$, $x\\in \\{4,5,6,7,8,9,10\\}$", "solution": "", "duration": -1, "usages": [ @@ -284139,7 +284139,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "不存在, 理由略", "solution": "", "duration": -1, "usages": [ @@ -284178,7 +284178,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=-\\sqrt[3]{x}$, $x\\in \\mathbf{R}$; (2) $y=\\dfrac{2x}{1-x}$, $x\\in \\{x|x\\ne 1\\}$; (3) $y=-\\sqrt{x-1}$, $x\\in (1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -284227,7 +284227,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=\\lg (x-1)$, $x\\in (1,+\\infty)$; (2) $y=2^x-1$, $x\\in \\mathbf{R}$; (3) $y=2^{x-1}$, $x\\in \\mathbf{R}$", "solution": "", "duration": -1, "usages": [ @@ -284264,7 +284264,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$16$", "solution": "", "duration": -1, "usages": [ @@ -298180,7 +298180,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $29$; (2) $10$; (3) $3$; (4) $\\dfrac{23}{2}$", "solution": "", "duration": -1, "usages": [], @@ -298204,7 +298204,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -298376,7 +298376,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 是的, 理由略; (2) 是的, 理由略", "solution": "", "duration": -1, "usages": [], @@ -298402,7 +298402,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $80$; (2) $\\displaystyle_{i=1}^{10} a_{2i}=320$", "solution": "", "duration": -1, "usages": [], @@ -298426,7 +298426,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$-4$", "solution": "", "duration": -1, "usages": [], @@ -298570,7 +298570,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 是的, 理由略; (2) 不一定, 当$q\\ne -1$(且$q\\ne 0$)时, 是等比数列; 当$q=-1$时, 不是等比数列", "solution": "", "duration": -1, "usages": [], @@ -298594,7 +298594,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -298645,7 +298645,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "约$13.1\\%$", "solution": "", "duration": -1, "usages": [], @@ -298669,7 +298669,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $605$; (2) $\\dfrac{255}{16}$; (3) $-\\dfrac{4095}{3072}$; (4) $24$", "solution": "", "duration": -1, "usages": [ @@ -298730,7 +298730,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $299.609375\\text{m}$; (2) 不会超过, 理由略", "solution": "", "duration": -1, "usages": [], @@ -298856,7 +298856,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\dfrac{9-(\\frac{4}{9})^n}{5}$; (3) $6\\pi$", "solution": "", "duration": -1, "usages": [], @@ -298919,7 +298919,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "是的, 第$15$项", "solution": "", "duration": -1, "usages": [], @@ -299019,7 +299019,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$a_n=2^{\\frac{n(n-1)}{2}}$", "solution": "", "duration": -1, "usages": [], @@ -299071,7 +299071,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $73$个; (2) $a_n=8a_{n-1}$", "solution": "", "duration": -1, "usages": [], @@ -299145,7 +299145,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -299352,7 +299352,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -325051,7 +325051,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 是集合, 是空集; (2) 不是集合, 对象是否在其中不确定; (3) 不是集合, 未确定``哪一部分''; (4) 是集合, 对象是否在其中是确定的", "solution": "", "duration": -1, "usages": [], @@ -325075,7 +325075,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 是无限集, 正整数有无穷多个; (2) 是有限集, 因为是有限集$\\{1,2,3,\\cdots,600\\}$的一部分组成的; (3) 是有限集, 地球上出现过的人的数量是有限的; (4) 是无限集, 到$A$的距离为$\\dfrac{1}{2},\\dfrac{1}{3},\\dfrac{1}{4},\\cdots$的点就已经是无穷多个了", "solution": "", "duration": -1, "usages": [], @@ -325100,7 +325100,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\in$; (2) $\\in$; (3) $\\not\\in$; (4) $\\in$", "solution": "", "duration": -1, "usages": [], @@ -325125,7 +325125,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\in$; (2) $\\not\\in$; (3) $\\in$; (4) $\\in$; (5) $\\not\\in$; (6) $\\not\\in$", "solution": "", "duration": -1, "usages": [], @@ -325149,7 +325149,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 是集合, 是有限集; (2) 是集合, 是无限集; (3) 不是集合, ``影响力比较大''定义模糊, 无法明确界定; (4) 是集合, 是有限集; (5) 是集合, 是无限集; (6) 是集合, 是无限集", "solution": "", "duration": -1, "usages": [], @@ -325174,7 +325174,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -325200,7 +325200,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$a=4$", "solution": "", "duration": -1, "usages": [ @@ -325239,7 +325239,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{1,2,3,\\cdots,10\\}$; (2) $\\{1,2,3,4\\}$; (3) $\\{3,4,5,6,7\\}$", "solution": "", "duration": -1, "usages": [], @@ -325265,7 +325265,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $A=\\{2,4,6,8\\}$; (2) $B=\\{x|x=2m, \\ m\\in \\mathbf{Z}\\}$; (3) $C=\\{x|\\dfrac{x-2}{3}\\in \\mathbf{Z}, \\ x\\in \\mathbf{N}\\}$; (4) $D=\\{x|x=3m+2, \\ m\\in \\mathbf{Z}\\}$; (5) $E=\\{(x,y)|xy<0\\}$", "solution": "", "duration": -1, "usages": [], @@ -325290,7 +325290,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[1,2)$; (2) $(-\\infty,3]$", "solution": "", "duration": -1, "usages": [], @@ -325317,7 +325317,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 描述法, $A=\\{0,3,4,5,7,8,9,12\\}$; (2) 列举法, $B=\\{(x,y)|x^2=y^2=1\\}$", "solution": "", "duration": -1, "usages": [], @@ -325339,7 +325339,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -325363,7 +325363,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -325390,7 +325390,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\begin{cases}x=2, \\\\ y=6\\end{cases}$或$\\begin{cases}x=4, \\\\ y=0.\\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -325416,7 +325416,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $B\\subset A$; (2) $C\\subset D$; (3) $E\\subset F$", "solution": "", "duration": -1, "usages": [], @@ -325441,7 +325441,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "所有子集为$\\varnothing,\\{a\\},\\{b\\},\\{c\\},\\{a,b\\},\\{a,c\\},\\{b,c\\},\\{a,b,c\\}$, 除$\\{a,b,c\\}$外其余七个均为真子集", "solution": "", "duration": -1, "usages": [], @@ -325465,7 +325465,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -325491,7 +325491,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\varnothing$, $\\{0\\}$, $\\{2\\}$, $\\{0,2\\}$", "solution": "", "duration": -1, "usages": [], @@ -325515,7 +325515,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -325544,7 +325544,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$A\\cap B=(-2,-1)\\cup (1,2)$; (2) $A\\cup B=(-3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -325568,7 +325568,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\{(2,1)\\}$", "solution": "", "duration": -1, "usages": [], @@ -325590,7 +325590,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\{3\\}$, $\\{1,3\\}$, $\\{2,3\\}$, $\\{1,2,3\\}$", "solution": "", "duration": -1, "usages": [], @@ -325612,7 +325612,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\overline{A\\cup B}=\\{e\\}$, $\\overline A\\cap \\overline B=\\{e\\}$, $\\overline{A\\cap B}=\\{a,b,d,e\\}$, $\\overline A\\cup \\overline B=\\{a,b,d,e\\}$", "solution": "", "duration": -1, "usages": [], @@ -325680,7 +325680,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\{0,2,4,6,8,9,10\\}$", "solution": "", "duration": -1, "usages": [], @@ -325704,7 +325704,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(\\overline{A}\\cup B)\\cup (A\\cap \\overline{B})$; (2) $(A\\cap \\overline{B}\\cap \\overline{C})\\cup (A\\cap B\\cap C)$", "solution": "", "duration": -1, "usages": [], @@ -325726,7 +325726,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 是真命题, $n=10k+5=5(2k+1)$, $k\\in \\mathbf{N}$; (2) 是假命题, 如一副三角板的两块; (3) 不是命题, 无法判断真假; (4) 是假命题, 两个角都是$90^\\circ$时它们既互补, 又相等; (5) 是真命题, 是全等三角形的判定定理; (6) 不是命题, 无法判断真假; (7) 不是命题, 无法判断真假(是``开语句'', 当$x$的值确定后, 就是命题了)", "solution": "", "duration": -1, "usages": [], @@ -325748,7 +325748,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 假命题, $2$; (2) 真命题, $A+B=180^\\circ$, $A=B$, 故$A=90^\\circ$; (3) 假命题, 如$A=B=\\{1\\}$", "solution": "", "duration": -1, "usages": [], @@ -325770,7 +325770,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 若一个三角形是等腰三角形, 则它的两底角相等. 成立; (2) 若$n$是素数, 则$n$是奇数. 不成立; (3) 若两个角是对顶角, 则它们相等. 成立", "solution": "", "duration": -1, "usages": [], @@ -325792,7 +325792,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}, \\textcircled{1}\\textcircled{3}", "solution": "", "duration": -1, "usages": [], @@ -325815,7 +325815,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,0]$", "solution": "", "duration": -1, "usages": [], @@ -325837,7 +325837,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-1,0)\\cup [3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -325861,7 +325861,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 充分非必要, 正方形的四个内角都是直角, 但是长为$2$, 宽为$1$的矩形不是正方形, 它的四个内角也都是直角; (2) 必要非充分, 当$x=\\sqrt{2}$时, $x^2$是有理数, $x$不是有理数, 而当$x=\\dfrac{p}{q}$($p,q\\in \\mathbf{Z}$)时, $x^2=\\dfrac{p^2}{q^2}$也是有理数", "solution": "", "duration": -1, "usages": [], @@ -325883,7 +325883,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -325905,7 +325905,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "通过枚举发现它们等价", "solution": "", "duration": -1, "usages": [], @@ -325949,7 +325949,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "反证法, 证明略", "solution": "", "duration": -1, "usages": [], @@ -325973,7 +325973,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "反证法, 证明略", "solution": "", "duration": -1, "usages": [], @@ -325995,7 +325995,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -326020,7 +326020,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -326042,7 +326042,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -326072,7 +326072,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -326094,7 +326094,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -326322,7 +326322,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -326596,7 +326596,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -326618,7 +326618,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -327805,7 +327805,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-\\dfrac{1}{2}$; (2) $\\pm 3$", "solution": "", "duration": -1, "usages": [], @@ -327827,7 +327827,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-2$; (2) $2$", "solution": "", "duration": -1, "usages": [], @@ -327851,7 +327851,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-2023$或$-1$", "solution": "", "duration": -1, "usages": [], @@ -327873,7 +327873,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\begin{cases}a-b, & a\\ge b, \\\\ b-a, & a=latex]\n\\draw [->] (0,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2, samples = 100] plot ({\\x*\\x},\\x);\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -328473,7 +328473,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{4}", "solution": "", "duration": -1, "usages": [ @@ -328508,7 +328508,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -328543,7 +328543,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2.5^{-2}<1.8^{-2}$; (2) $1.32^{\\frac{4}{5}}<(-\\sqrt{2})^{\\frac{4}{5}}$", "solution": "", "duration": -1, "usages": [], @@ -328565,7 +328565,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\dfrac{1}{x}$的图像向右平移$2$个单位后得到$y=\\dfrac{1}{x-2}$的图像, 理由略, 大致图像为\\\\\n\\begin{tikzpicture}[>=latex, scale = 0.25]\n\\draw [->] (-8,0) -- (8,0) node [below] {$x$};\n\\draw [->] (0,-8) -- (0,8) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$};\n\\draw [domain = 0.125:8, samples = 100, thin] plot (\\x,1/\\x) plot (-\\x,-1/\\x);\n\\draw [domain = 0.125:6, samples = 100, thick] plot (\\x+2,1/\\x);\n\\draw [domain = 0.125:10, samples = 100, thick] plot (-\\x+2,-1/\\x);\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -328589,7 +328589,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\dfrac{1}{x}$的图像向上平移$1$个单位后得到$y=\\dfrac{x-1}{x-2}$的图像, 理由略, 大致图像为\\\\\n\\begin{tikzpicture}[>=latex, scale = 0.25]\n\\draw [->] (-8,0) -- (8,0) node [below] {$x$};\n\\draw [->] (0,-8) -- (0,8) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$};\n\\draw [domain = 0.125:6, samples = 100, thin] plot (\\x+2,1/\\x);\n\\draw [domain = 0.125:10, samples = 100, thin] plot (-\\x+2,-1/\\x);\n\\draw [domain = {15/7}:8, samples = 100, thick] plot (\\x,{(\\x-1)/(\\x-2)});\n\\draw [domain = -8:{17/9}, samples = 100, thick] plot (\\x,{(\\x-1)/(\\x-2)});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -328613,7 +328613,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -328657,7 +328657,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=3^x$", "solution": "", "duration": -1, "usages": [], @@ -328681,7 +328681,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,5.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:{ln(5.5)/ln(2)}, samples = 100] plot (\\x,{exp(\\x*ln(2))}) node [right] {$y=2^x$};\n\\draw [domain = -3:{ln(5.5)/ln(3)}, samples = 100] plot (\\x,{exp(\\x*ln(3))}) node [above] {$y=3^x$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -328703,7 +328703,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,5.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {-ln(5.5)/ln(2)}:3, samples = 100] plot (\\x,{exp(\\x*ln(0.5))});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -328725,7 +328725,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=(\\dfrac{1}{3})^x$", "solution": "", "duration": -1, "usages": [], @@ -328747,7 +328747,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-5.5) -- (0,0.5) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -3:{ln(5.5)/ln(4)}, samples = 100] plot (\\x,{-exp(\\x*ln(4))});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -328769,7 +328769,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $1.7^{2.5}<1.7^3$; (2) $(\\frac{3}{4})^{\\frac{1}{6}}>(\\frac{4}{3})^{-\\frac{1}{5}}$; (3) 当$a>1$时, $a^{\\frac 12}>a^{\\frac 13}$; 当$01$且$b\\ge -1$", "solution": "", "duration": -1, "usages": [], @@ -328835,7 +328835,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-1,-1)$", "solution": "", "duration": -1, "usages": [], @@ -328857,7 +328857,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{4}{3}$", "solution": "", "duration": -1, "usages": [], @@ -328883,7 +328883,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$30$年后该物种的种群数量约为现有种群数量的$237$倍", "solution": "", "duration": -1, "usages": [], @@ -328905,7 +328905,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=(\\dfrac{1}{2})^{\\frac{x}{5730}}$", "solution": "", "duration": -1, "usages": [], @@ -328949,7 +328949,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$或$\\dfrac{1}{3}$", "solution": "", "duration": -1, "usages": [], @@ -328971,7 +328971,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=a(1+r)^x$; (2) $y=1000\\cdot(1+0.0225)^5\\approx 1118$元", "solution": "", "duration": -1, "usages": [], @@ -328993,7 +328993,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(1,+\\infty)$; (2) $(-\\infty,-1)\\cup (5,+\\infty)$; (3) $(-1,\\dfrac{1}{2})$", "solution": "", "duration": -1, "usages": [], @@ -329015,7 +329015,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-0.5,0) -- (5.5,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {1/8}:5, samples = 100] plot (\\x,{ln(\\x)/ln(1/2)}) node [right] {$y=\\log_{\\frac{1}{2}} x$};\n\\draw [domain = {1/27}:5, samples = 100] plot (\\x,{ln(\\x)/ln(1/3)}) node [right] {$y=\\log_{\\frac{1}{3}} x$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -329037,7 +329037,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "是的, 理由略", "solution": "", "duration": -1, "usages": [], @@ -329059,7 +329059,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(0,\\dfrac{1}{2})$", "solution": "", "duration": -1, "usages": [], @@ -329081,7 +329081,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -329125,7 +329125,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\log_25<\\log_26$; (2) 当$a>1$时, $\\log_a0.1<\\log_a0.2$; 当$0\\log_67$", "solution": "", "duration": -1, "usages": [], @@ -329147,7 +329147,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$99^{89}<89^{99}$", "solution": "", "duration": -1, "usages": [], @@ -329169,7 +329169,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -329191,7 +329191,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(0,\\dfrac{3}{4})\\cup (1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -329213,7 +329213,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -329235,7 +329235,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [], @@ -329259,7 +329259,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$53.6$倍", "solution": "", "duration": -1, "usages": [], @@ -329281,7 +329281,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "经过$33$年", "solution": "", "duration": -1, "usages": [], @@ -329303,7 +329303,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{1}{4}$", "solution": "", "duration": -1, "usages": [], @@ -329325,7 +329325,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "当$02\\log_x 2$; 当$1\\dfrac{4}{3}$时, $1+\\log_x 3>2\\log_x 2$", "solution": "", "duration": -1, "usages": [], @@ -329369,7 +329369,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-1,+\\infty)$; (2) $[-3,1)\\cup (1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -329391,7 +329391,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 不同, $-1$不在定义域中; (2) 是的, 定义域与对应关系均相同; (3) 不是, $x=-1$时, $y=1$", "solution": "", "duration": -1, "usages": [], @@ -329413,7 +329413,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(0,1)$", "solution": "", "duration": -1, "usages": [], @@ -329488,7 +329488,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -329524,7 +329524,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,\\dfrac{5}{4}]$", "solution": "", "duration": -1, "usages": [], @@ -329574,7 +329574,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\begin{cases}0, & 0\\le x < 2,\\\\ 1, & 2\\le x<4, \\\\ 2, & 4\\le x<6, \\\\ 3, & 6\\le x<8,\\\\ 4, & x=8\\end{cases}$, 图像: \\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-1,0) -- (8.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,4.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j in {1/2,2/4,3/6,4/8}\n{\\draw [dashed] ({2*\\i},0) node [below] {$\\j$} --++ (0,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\foreach \\i in {0,2,4,6}\n{\\draw [thick] (\\i,{\\i/2}) --++ (2,0);\n\\filldraw (\\i,{\\i/2}) circle (0.09);\n\\filldraw [fill = white] ({\\i+2},{\\i/2}) circle (0.09);};\n\\filldraw (8,4) circle (0.09);\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -329618,7 +329618,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$f(x)=2x+7$", "solution": "", "duration": -1, "usages": [], @@ -329640,7 +329640,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-2]\\cup [0,3]$", "solution": "", "duration": -1, "usages": [], @@ -329684,7 +329684,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -329719,7 +329719,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -329741,7 +329741,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -329763,7 +329763,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "存在, $y=0$($x\\in \\mathbf{R}$)", "solution": "", "duration": -1, "usages": [], @@ -329785,7 +329785,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [], @@ -329807,7 +329807,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $f(x)=\\dfrac{2^x-2^{-x}}{2}$, $g(x)=\\dfrac{2^x+2^{-x}}{2}$; (2) 总存在, $f(x)=\\dfrac{H(x)-H(-x)}{2}$, $g(x)=\\dfrac{H(x)+H(-x)}{2}$", "solution": "", "duration": -1, "usages": [], @@ -329853,7 +329853,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "奇函数, 理由略", "solution": "", "duration": -1, "usages": [], @@ -329920,7 +329920,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -329942,7 +329942,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -329964,7 +329964,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "是严格增函数, 证明略", "solution": "", "duration": -1, "usages": [], @@ -329986,7 +329986,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a>0$时, 在定义域上是严格减函数, 证明略; 当$a<0$时, 在定义域上是严格增函数, 证明略", "solution": "", "duration": -1, "usages": [], @@ -330008,7 +330008,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,3]$", "solution": "", "duration": -1, "usages": [], @@ -330030,7 +330030,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "在$[-2,1]$上是严格减函数, 在$[1,2]$上是严格增函数, 理由略", "solution": "", "duration": -1, "usages": [], @@ -330052,7 +330052,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "在$[1,2]$上是严格增函数, 理由略", "solution": "", "duration": -1, "usages": [], @@ -330184,7 +330184,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "最大值不存在, 最小值为$-\\dfrac{1}{8}$", "solution": "", "duration": -1, "usages": [], @@ -330206,7 +330206,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "最大值为$2$, 最小值为$1$", "solution": "", "duration": -1, "usages": [], @@ -330232,7 +330232,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y_{\\max}=\\begin{cases}1-a, & a\\le 0, \\\\ 1, & 0\\le a<2\\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -330291,7 +330291,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$g(t)=\\begin{cases}t^2+1, & t\\le 0, \\\\ 1, & 0\\le t\\le 1, \\\\ t^2-2t+2, & t\\ge 1\\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -330313,7 +330313,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$S=2x^2-(a+b)x+ab$, $x\\in (0,a)$", "solution": "", "duration": -1, "usages": [], @@ -330335,7 +330335,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$S=\\begin{cases}\\dfrac{1}{2}t^2, & 0=latex, scale = 0.3]\n\\draw [->] (-8,0) -- (8,0) node [below] {$x$};\n\\draw [->] (0,-8) -- (0,8) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -2:2, thin] plot (\\x,{\\x*\\x*\\x}) node [above] {$y=x^3$};\n\\draw [domain = -2:2, ultra thick] plot ({\\x*\\x*\\x},\\x) node [right] {$y=x^{\\frac{1}{3}}$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -330731,7 +330731,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$a=4$, $b=3$", "solution": "", "duration": -1, "usages": [], @@ -330753,7 +330753,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -330788,7 +330788,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -330832,7 +330832,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -489135,7 +489135,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-85$; (2) 是的, 第$100$项", "solution": "", "duration": -1, "usages": [], @@ -489157,7 +489157,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$37$个座位", "solution": "", "duration": -1, "usages": [], @@ -489179,7 +489179,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "是的, 证明略", "solution": "", "duration": -1, "usages": [], @@ -489223,7 +489223,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [], @@ -489245,7 +489245,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $260$; (2) $21.7$; (3) $4.9$", "solution": "", "duration": -1, "usages": [], @@ -489267,7 +489267,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "可以确定, $S_{30}=2730$", "solution": "", "duration": -1, "usages": [], @@ -489289,7 +489289,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a_n=2n+1$; (2) 证明略", "solution": "", "duration": -1, "usages": [], @@ -489311,7 +489311,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$2090$", "solution": "", "duration": -1, "usages": [], @@ -489333,7 +489333,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-96$; (2) $5\\cdot 2^{n-1}$", "solution": "", "duration": -1, "usages": [], @@ -489355,7 +489355,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "约$4$年", "solution": "", "duration": -1, "usages": [], @@ -489377,7 +489377,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略, 公比为$3^d$", "solution": "", "duration": -1, "usages": [], @@ -489399,7 +489399,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略, 公差为$\\lg q$", "solution": "", "duration": -1, "usages": [], @@ -489465,7 +489465,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{341}{128}$; (2) $\\dfrac{4921}{243}$", "solution": "", "duration": -1, "usages": [], @@ -489487,7 +489487,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$2^{n-2}$", "solution": "", "duration": -1, "usages": [], @@ -489509,7 +489509,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "当且仅当$a=-1$时, 数列$\\{a_n\\}$是等比数列", "solution": "", "duration": -1, "usages": [], @@ -489553,7 +489553,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a_n=2^{1-n}$; (2) $T_n=2-2^{1-n}+n(n+1)$", "solution": "", "duration": -1, "usages": [], @@ -489575,7 +489575,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "约$2029.66$元", "solution": "", "duration": -1, "usages": [], @@ -489598,7 +489598,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{29}{99}$; (2) $\\dfrac{427}{990}$", "solution": "", "duration": -1, "usages": [], @@ -489620,7 +489620,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "周长的和为$8+4\\sqrt{2}$, 面积的和为$2$", "solution": "", "duration": -1, "usages": [], @@ -489643,7 +489643,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{4}{3}$", "solution": "", "duration": -1, "usages": [], @@ -489687,7 +489687,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{32}{3}$", "solution": "", "duration": -1, "usages": [], @@ -489753,7 +489753,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-\\dfrac{1}{2},0,\\dfrac{1}{4},\\dfrac{2}{5},\\dfrac{1}{2}$; (2) $\\dfrac{1}{2},\\dfrac{5}{4},\\dfrac{7}{8},\\dfrac{17}{16},\\dfrac{31}{32}$", "solution": "", "duration": -1, "usages": [], @@ -489775,7 +489775,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 是的, 理由略; (2) 是的, 理由略", "solution": "", "duration": -1, "usages": [], @@ -489797,7 +489797,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "有最大项, 第$8$和第$9$项最大", "solution": "", "duration": -1, "usages": [], @@ -489841,7 +489841,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "当$0<|q|\\le 1$时有最大项; 当$|q|>1$时无最大项", "solution": "", "duration": -1, "usages": [], @@ -489863,7 +489863,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a_n=a_{n-1}+n$; (2) $a_n=\\dfrac{n^2+n+2}{2}$", "solution": "", "duration": -1, "usages": [], @@ -489885,7 +489885,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $a_n=2^n-1$", "solution": "", "duration": -1, "usages": [], @@ -489929,7 +489929,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $0$", "solution": "", "duration": -1, "usages": [], @@ -489951,7 +489951,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -490061,7 +490061,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "前四项依次为$1,2,3,4$, 猜通项公式为$a_n=n$, 证明略", "solution": "", "duration": -1, "usages": [], @@ -490083,7 +490083,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$a=\\dfrac{1}{3}$, $b=\\dfrac{1}{2}$, $c=\\dfrac{1}{6}$, 证明略", "solution": "", "duration": -1, "usages": [], @@ -490105,7 +490105,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$a_1=\\dfrac{1}{2}$, $a_2=\\dfrac{3}{4}$, $a_3=\\dfrac{7}{8}$, 猜$a_n=1-\\dfrac{1}{2^n}$, 证明略", "solution": "", "duration": -1, "usages": [], @@ -511575,7 +511575,7 @@ "第二单元" ], "genre": "4em", - "ans": "", + "ans": "定义域为$\\mathbf{R}$, 对称的理由略, 大致图像为\\begin{tikzpicture}[>=latex,scale = 0.2]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-8) -- (0,8) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2:2, samples = 100] plot (\\x,{\\x*\\x*\\x});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -511603,7 +511603,7 @@ "第二单元" ], "genre": "4em", - "ans": "", + "ans": "定义域为$\\{x|x\\in\\mathbf{R}, \\ x\\ne 0\\}$, 对称的理由略, 大致图像为\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.2:2, samples = 100] plot (\\x,{exp(-2/3*ln(\\x))}) plot (-\\x,{exp(-2/3*ln(\\x))});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -511632,7 +511632,7 @@ "幂函数" ], "genre": "解答题", - "ans": "", + "ans": "$st=1$", "solution": "", "duration": -1, "usages": [], @@ -512282,7 +512282,7 @@ "第四单元" ], "genre": "4em", - "ans": "", + "ans": "(1) 证明略; (2) $a_n=\\begin{cases}1, & n=1,\\\\ -\\dfrac{2}{4n^2-8n+3}, & n\\ge 2\\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -523290,7 +523290,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -523335,7 +523335,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -523355,7 +523355,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\dfrac{f(u)}{f(v)}=f(u-v)$", "solution": "", "duration": -1, "usages": [ @@ -523388,7 +523388,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -523408,7 +523408,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -523428,7 +523428,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $a=\\dfrac{2}{3}$, $f(x)=\\log_{\\frac{2}{3}}(2-\\dfrac{2}{3}x)$是严格增函数; (2) $(1,2)$", "solution": "", "duration": -1, "usages": [], @@ -523487,7 +523487,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -523507,7 +523507,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -524352,7 +524352,7 @@ "第一单元" ], "genre": "4em", - "ans": "", + "ans": "当$m>1$时, 解集为$(m^2+m+1,+\\infty)$; 当$m=1$时, 解集为$\\varnothing$; 当$m<1$时, 解集为$(-\\infty,m^2+m+1)$", "solution": "", "duration": -1, "usages": [], @@ -524380,7 +524380,7 @@ "第一单元" ], "genre": "4em", - "ans": "", + "ans": "(1) $(-\\infty,-\\dfrac{1}{6})\\cup (1,+\\infty)$; (2) $(-\\dfrac{1}{6},1)$", "solution": "", "duration": -1, "usages": [], @@ -525375,7 +525375,7 @@ "第三章" ], "genre": "4em", - "ans": "", + "ans": "(1) $\\dfrac{1}{3}$; (2) $\\dfrac{5}{6}$; (3) $\\dfrac{5}{3}$; (4) $2$", "solution": "", "duration": -1, "usages": [ @@ -525666,7 +525666,7 @@ "objs": [], "tags": [], "genre": "4em", - "ans": "", + "ans": "(1) 证明略; (2) 证明略", "solution": "", "duration": -1, "usages": [], @@ -525691,7 +525691,7 @@ "第二单元" ], "genre": "4em", - "ans": "", + "ans": "(1) \\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-3,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.13:4, samples = 100] plot ({\\x+1},{exp(-2/3*ln(\\x))}) plot ({-\\x+1},{exp(-2/3*ln(\\x))});\n\\end{tikzpicture}; (2) \\begin{tikzpicture}[>=latex, scale = 0.25]\n\\draw [->] (-2,0) -- (8,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2:2.5, samples = 100] plot (\\x,{(2*\\x-3)/(\\x-3)});\n\\draw [domain = {15/4}:8, samples = 100] plot (\\x,{(2*\\x-3)/(\\x-3)});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [ @@ -525728,7 +525728,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "(1) $\\mathbf{R}$; (2) $(-\\infty,\\dfrac{2}{3})\\cup (\\dfrac{2}{3},+\\infty)$; (3) $(-\\infty,0)\\cup (0,1)\\cup (1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -525764,7 +525764,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -525799,7 +525799,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "(1) $(2,3)$; (2) $[\\dfrac{1}{2},1)\\cup (1,+\\infty)$; (3) $(1,2)\\cup (2,3)$", "solution": "", "duration": -1, "usages": [ @@ -526423,7 +526423,7 @@ "第二单元" ], "genre": "4em", - "ans": "", + "ans": "当且仅当$x=0$时函数值最小, 最小值为$\\dfrac{1}{2}$", "solution": "", "duration": -1, "usages": [ @@ -526461,7 +526461,7 @@ "第二单元" ], "genre": "4em", - "ans": "", + "ans": "$[-1,1)$, 证明略", "solution": "", "duration": -1, "usages": [ @@ -526499,7 +526499,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "大, $-1$", "solution": "", "duration": -1, "usages": [ @@ -529236,7 +529236,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "$(0,\\dfrac{\\sqrt{2}}{2}]$", "solution": "", "duration": -1, "usages": [ @@ -529276,7 +529276,7 @@ "第二单元" ], "genre": "4em", - "ans": "", + "ans": "(1) \\begin{tikzpicture}[>=latex]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -3:3, samples = 100] plot (\\x,{1/(1+\\x*\\x)});\n\\end{tikzpicture}; (2) \\begin{tikzpicture}[>=latex]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -3:3, samples = 100] plot (\\x,{\\x/(1+\\x*\\x)});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -529301,7 +529301,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -529457,7 +529457,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{2,3,5,7,11\\}$; (2) $\\{-2,-1,0,1,2\\}$; (3) $\\{2,1,0,-3\\}$; (4) $\\{-1,0,3\\}$; (5) $\\{(-2,3),(-1,0),(0,-1),(1,0),(2,3)\\}$; (6) $\\{(0,5),(1,4),(2,3),(3,2),(4,1),(5,0)\\}$", "solution": "", "duration": -1, "usages": [ @@ -529494,7 +529494,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{x|x=2k+1, \\ k\\in \\mathbf{Z}\\}$; (2) $\\{x|x=3k+2, \\ k \\in \\mathbf{N}\\}$; (3) $\\{x|x=10\\}$; (4) $\\{x||x|>4, \\ x\\in \\mathbf{Z}\\}$; (5) $\\{(x,y)|x=0, \\ y\\in \\mathbf{R}\\}$; (6) $\\{(x,y)|y=2x+1, \\ x\\in \\mathbf{R}\\}$", "solution": "", "duration": -1, "usages": [ @@ -529531,7 +529531,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-2,7)$; (2) $[-2,7]$; (3) $[-2,7)$; (4) $(-\\infty,\\dfrac{5}{2})$; (5) $(-5,+\\infty)$; (6) $[0,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -529570,7 +529570,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{1,2,5,10\\}$; (2) $\\{n|n=10k, \\ k\\in \\mathbf{N}, k\\ge 1$; (3) $\\varnothing$; (4) $\\{(-1,2)\\}$; (5) $\\{(-3,5)\\}$", "solution": "", "duration": -1, "usages": [ @@ -529659,7 +529659,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$P=\\{0,6,14,21\\}$", "solution": "", "duration": -1, "usages": [ @@ -529696,7 +529696,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [ @@ -529786,7 +529786,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$-1$或$-\\dfrac{1}{2}$", "solution": "", "duration": -1, "usages": [ @@ -529897,7 +529897,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "6", "solution": "", "duration": -1, "usages": [ @@ -529936,7 +529936,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{2}", "solution": "", "duration": -1, "usages": [ @@ -529975,7 +529975,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{5}\\textcircled{6}", "solution": "", "duration": -1, "usages": [ @@ -530026,7 +530026,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -530228,7 +530228,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [ @@ -530373,7 +530373,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\{1\\}$", "solution": "", "duration": -1, "usages": [ @@ -530569,7 +530569,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{1\\}\\cup (\\dfrac{9}{8},+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -530606,7 +530606,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$7$", "solution": "", "duration": -1, "usages": [ @@ -530776,7 +530776,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{2\\}$, $\\{-4,-2,2\\}$", "solution": "", "duration": -1, "usages": [ @@ -530839,7 +530839,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{(2,0)\\}$, $\\{(x,y)|y=x^2-4\\text{ 或 }y=x^2+x-6, \\ x\\in \\mathbf{R}\\}$", "solution": "", "duration": -1, "usages": [ @@ -530877,7 +530877,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\mathbf{R}$", "solution": "", "duration": -1, "usages": [ @@ -530915,7 +530915,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,1)$, $\\varnothing$, $\\varnothing$, $\\varnothing$, $(-\\infty,1)\\cup (5,6]$, $(-\\infty,1)\\cup (5,6]$, $(-\\infty,6]$, $(-\\infty,6]$", "solution": "", "duration": -1, "usages": [ @@ -530979,7 +530979,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,1]$", "solution": "", "duration": -1, "usages": [ @@ -531019,7 +531019,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\varnothing$; (2) $(\\dfrac{1}{16},+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -531056,7 +531056,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\mathbf{R}$", "solution": "", "duration": -1, "usages": [ @@ -531168,7 +531168,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [ @@ -531308,7 +531308,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$[3,4)\\cup [5,\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -531383,7 +531383,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -531422,7 +531422,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$[2,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -531532,7 +531532,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{3}\\textcircled{6}", "solution": "", "duration": -1, "usages": [ @@ -531675,7 +531675,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) 否; (2) 否; (3) 是; (4) 否; (5) 否; (6) 是", "solution": "", "duration": -1, "usages": [ @@ -531781,7 +531781,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{4}", "solution": "", "duration": -1, "usages": [ @@ -531827,7 +531827,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,-4]$", "solution": "", "duration": -1, "usages": [ @@ -531895,7 +531895,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) \\textcircled{2}; (2) \\textcircled{1}; (3) \\textcircled{2}; (4) \\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -531932,7 +531932,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "充要, 充要", "solution": "", "duration": -1, "usages": [ @@ -531978,7 +531978,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(如) $x>10$, (如) $x>0$", "solution": "", "duration": -1, "usages": [ @@ -532061,7 +532061,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$a>0$", "solution": "", "duration": -1, "usages": [ @@ -532147,7 +532147,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -532185,7 +532185,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -532327,7 +532327,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) 真, $\\pi$不是无理数, 假; (2) 假, $2+1\\ne 4$, 真; (3) 假, 存在实数既不是正数、也不是负数, 真; (4) 假, 存在实数不是正数, 且存在实数不是负数, 真; (5) 假, 存在实数$x$, 使得$x^2+1\\ne 0$, 真; (6) 真, 对任意实数$x$, $x^2+1\\ne 0$, 真; (7) 假, 存在实数$k$, 使关于$x$的方程$x^2+x+k=0$无实数根, 真; (8) 真, 存在三角形, 其中至少有两个钝角, 假; (9) 真, 存在$a,b$满足$a>1$, $b>1$, 但$ab\\le 1$, 假; (10) 假, 存在能整除$2$的正整数不是质数, 真", "solution": "", "duration": -1, "usages": [ @@ -532393,7 +532393,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -532433,7 +532433,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -532476,7 +532476,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -539870,7 +539870,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "(1) $2$; (2) $-2$; (3) $4$; (4) $-3$; (5) $\\sqrt{3}-\\sqrt{2}$; (6) $|a-b|^3$", "solution": "", "duration": -1, "usages": [ @@ -539905,7 +539905,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "(1) $a^{\\frac{3}{4}}$; (2) $a^{\\frac{23}{5}}$; (3) $a^{\\frac{1}{2}}\\cdot b^{-\\frac{4}{3}}$; (4) $a^{\\frac{3}{4}}\\cdot b^{\\frac{11}{4}}$; (5) $2\\cdot 3^{-\\frac{1}{2}}\\cdot a^{-\\frac{1}{2}}\\cdot b^{-\\frac{3}{2}}$; (6) $|a-b|^{-\\frac{1}{3}}$", "solution": "", "duration": -1, "usages": [ @@ -540032,7 +540032,7 @@ "第三章" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -540067,7 +540067,7 @@ "第三章" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -540102,7 +540102,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "$|a|+2a$", "solution": "", "duration": -1, "usages": [ @@ -540183,7 +540183,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -540218,7 +540218,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "$2^{-\\frac{9}{4}}$", "solution": "", "duration": -1, "usages": [ @@ -540276,7 +540276,7 @@ "第三章" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -540380,7 +540380,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "$-2$", "solution": "", "duration": -1, "usages": [ @@ -540461,7 +540461,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "(1) $16^x=32$; (2) $\\sqrt{5}^4=x$; (3) $x^=9$($x>0$); (4) $16^{-\\frac{1}{4}}=\\dfrac{x}{2}$", "solution": "", "duration": -1, "usages": [ @@ -540496,7 +540496,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2$; (2) $-3$; (3) $-\\dfrac{1}{4}$; (4) $3$", "solution": "", "duration": -1, "usages": [ @@ -540532,7 +540532,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\pm \\dfrac{1}{2}$; (2) $-3$; (3) $\\dfrac{3}{2}$; (4) $2$", "solution": "", "duration": -1, "usages": [ @@ -540567,7 +540567,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "(1) $5$; (2) $1$; (3) $3$; (4) $7$", "solution": "", "duration": -1, "usages": [ @@ -540648,7 +540648,7 @@ "第三章" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -540683,7 +540683,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "$64$", "solution": "", "duration": -1, "usages": [ @@ -540718,7 +540718,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\mathbf{R}$; (2) $(-\\infty,-3)\\cup (1,+\\infty)$; (3) $(-2,+\\infty)$; (4) $(1,2)\\cup (2,3)$", "solution": "", "duration": -1, "usages": [ @@ -540753,7 +540753,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "$32$", "solution": "", "duration": -1, "usages": [ @@ -540788,7 +540788,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{5}{2}$; (2) $\\dfrac{5}{2}$; (3) $1$; (4) $1$", "solution": "", "duration": -1, "usages": [ @@ -540869,7 +540869,7 @@ "第三章" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -540905,7 +540905,7 @@ "第三章" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -540940,7 +540940,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "$a+b+1$", "solution": "", "duration": -1, "usages": [ @@ -540975,7 +540975,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "$1-\\dfrac{1}{2}m$", "solution": "", "duration": -1, "usages": [ @@ -541010,7 +541010,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "$\\{\\dfrac{1}{3},2,3\\}$", "solution": "", "duration": -1, "usages": [ @@ -541045,7 +541045,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{6}$", "solution": "", "duration": -1, "usages": [ @@ -541080,7 +541080,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -541173,7 +541173,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "(1) $1-a$; (2) $\\dfrac{b}{a}$; (3) $\\dfrac{2-2a}{2a_b}$", "solution": "", "duration": -1, "usages": [ @@ -541253,7 +541253,7 @@ "第三章" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{a+b-2}{2}$", "solution": "", "duration": -1, "usages": [ @@ -541324,7 +541324,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{3+a}{a+ab}$", "solution": "", "duration": -1, "usages": [ @@ -541381,7 +541381,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -541415,7 +541415,7 @@ "第三章" ], "genre": "解答题", - "ans": "", + "ans": "$-4$", "solution": "", "duration": -1, "usages": [ @@ -541470,7 +541470,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$或$3$", "solution": "", "duration": -1, "usages": [ @@ -541505,7 +541505,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -541527,7 +541527,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -541549,7 +541549,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -541571,7 +541571,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\mathbf{R}$, 大致图像为\\begin{tikzpicture}[>=latex,scale = 0.3]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:{exp(ln(3)/5)}, samples = 100] plot ({\\x*\\x*\\x*\\x*\\x},\\x) plot ({-\\x*\\x*\\x*\\x*\\x},-\\x);\n\\end{tikzpicture}; (2) $\\mathbf{R}$, 大致图像为\\begin{tikzpicture}[>=latex,scale = 0.3]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:1.5, samples = 100] plot ({\\x*\\x*\\x},{\\x*\\x*\\x*\\x}) plot ({-\\x*\\x*\\x},{\\x*\\x*\\x*\\x});\n\\end{tikzpicture}; (3) $(0,+\\infty)$, 大致图像为\\begin{tikzpicture}[>=latex,scale = 0.3]\n\\draw [->] (-0.5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.6:1.45, samples = 100] plot ({\\x*\\x*\\x*\\x},{1/\\x/\\x/\\x});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -541593,7 +541593,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$0,1$或$2$", "solution": "", "duration": -1, "usages": [], @@ -541615,7 +541615,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$[0,8]$", "solution": "", "duration": -1, "usages": [ @@ -541817,7 +541817,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -541851,7 +541851,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $(-0.2)^{\\frac 25}<(-0.3)^{\\frac 25}$; (2) $(-2)^{-\\frac 25}>3^{-\\frac 25}$; (3) $1.68^{0.8}<(-1.71)^{0.8}$; (4) $0.3^{-\\frac 12}<0.2^{-\\frac 12}$", "solution": "", "duration": -1, "usages": [ @@ -541975,7 +541975,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\dfrac{1}{3},3)$; (2) $(\\dfrac{1}{3},+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -542033,7 +542033,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{3}\\textcircled{5}\\textcircled{6}, \\textcircled{1}\\textcircled{2}\\textcircled{4}", "solution": "", "duration": -1, "usages": [ @@ -542068,7 +542068,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{3}\\textcircled{5}", "solution": "", "duration": -1, "usages": [ @@ -542127,7 +542127,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-2,3)$", "solution": "", "duration": -1, "usages": [ @@ -542162,7 +542162,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$y$轴, $(0,1)$", "solution": "", "duration": -1, "usages": [ @@ -542197,7 +542197,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,5.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:{ln(5.5)/ln(3)}, samples = 100] plot (\\x,{exp(\\x*ln(3))}) node [right] {$y=3^x$};\n\\draw [domain = {ln(5.5)/ln(1/3)}:3, samples = 100] plot (\\x,{exp(\\x*ln(1/3))}) node [right] {$y=(\\frac{1}{3})^x$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [ @@ -542298,7 +542298,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,2)$", "solution": "", "duration": -1, "usages": [ @@ -542377,7 +542377,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -542412,7 +542412,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -542447,7 +542447,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -542482,7 +542482,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -542539,7 +542539,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $m>n$; (2) $m,n$同号时, $m>n$; $m,n$异号时, $mn$, 则$a>b$; 若$m=n$, 则$a=b$; 若$m1$时, $\\log_a 2a<\\log_a 3a$; 当$0\\log_a 3a$", "solution": "", "duration": -1, "usages": [ @@ -543832,7 +543832,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(2,4)$", "solution": "", "duration": -1, "usages": [ @@ -543952,7 +543952,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -544018,7 +544018,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "最大值为$2$, 最小值为$0$", "solution": "", "duration": -1, "usages": [ @@ -544084,7 +544084,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$m=latex,xscale = 0.1, yscale = 0.3]\n\\draw [->] (0,0) -- (50,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,9) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j in {6/4,16/5,22/6,28/7,34/8}\n{\\draw [dashed] (\\i,0) node [below] {$\\i$} --++ (0,\\j) -- (0,\\j) node [left] {$\\j$};};\n\\draw (0,3) node [left] {$3$};\n\\foreach \\i/\\j/\\k in {0/3/6,6/4/16,16/5/22,22/6/28,28/7/34}\n{\\draw (\\i,\\j) -- (\\k,\\j);\n\\filldraw [fill = white] (\\i,\\j) circle (0.45 and 0.15);\n\\filldraw (\\k,\\j) circle (0.45 and 0.15);\n};\n\\draw (34,8) -- (50,8);\n\\filldraw [fill = white] (34,8) circle (0.45 and 0.15);\n\\end{tikzpicture}; (2) 不能超过$22$千米", "solution": "", "duration": -1, "usages": [ @@ -544586,7 +544586,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [ @@ -544626,7 +544626,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{x}{x-1}$", "solution": "", "duration": -1, "usages": [ @@ -544666,7 +544666,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$8x^4-8x^2+1$", "solution": "", "duration": -1, "usages": [ @@ -544706,7 +544706,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[2,3]$", "solution": "", "duration": -1, "usages": [ @@ -544774,7 +544774,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-16,-1]\\cup (0,1)\\cup \\{2\\}$", "solution": "", "duration": -1, "usages": [ @@ -544814,7 +544814,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -544842,7 +544842,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\lg 5$; (2) $\\dfrac{1}{2}$", "solution": "", "duration": -1, "usages": [ @@ -544938,7 +544938,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\begin{cases}\\dfrac{\\sqrt{2}}{2}x, & x\\in [0,2], \\\\ 2\\sqrt{2}-\\dfrac{\\sqrt{2}}{2}x, & x\\in [2,4], \\\\ \\dfrac{\\sqrt{2}}{2}x-3\\sqrt{2}, & x\\in [4,6], \\\\ 4\\sqrt{2}-\\dfrac{\\sqrt{2}}{2}x, & x\\in [6,8],\\end{cases}$ 图像: \\begin{tikzpicture}[>=latex, xscale = 0.5]\n\\draw [->] (-0.5,0) -- (9,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed] (0,{sqrt(2)}) node [left] {$\\sqrt{2}$} -- (6,{sqrt(2)});\n\\draw [dashed] (2,0) -- (2,{sqrt(2)}) (6,0) -- (6,{sqrt(2)});\n\\foreach \\i in {2,4,6,8}\n{\\draw (\\i,0) node [below] {$\\i$};};\n\\draw (0,0) -- (2,{sqrt(2)}) -- (4,0) -- (6,{sqrt(2)}) -- (8,0);\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [ @@ -544966,7 +544966,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [ @@ -545007,7 +545007,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -545047,7 +545047,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "既是奇函数又是偶函数", "solution": "", "duration": -1, "usages": [ @@ -545109,7 +545109,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -545144,7 +545144,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -545209,7 +545209,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$f(x)=\\begin{cases}(x-1)^3+1, & x \\ge 0,\\\\ 1-(x+1)^3, & x<0\\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -545325,7 +545325,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "存在, $a=2$", "solution": "", "duration": -1, "usages": [ @@ -545438,7 +545438,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{3}$, $0$", "solution": "", "duration": -1, "usages": [ @@ -545500,7 +545500,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$f(\\sqrt{3})0$时, 在$(-\\infty,+\\infty)$上是严格增函数; 当$a<0$时, 在$(-\\infty,+\\infty)$上是严格减函数; (3) 在$[-3,2]$上是严格减函数, 在$[2,3]$上是严格增函数; (4) 当$a>0$时, 在$(-\\infty,-1]$上是严格减函数; 当$a<0$时, 在$(-\\infty,-1]$上是严格增函数", "solution": "", "duration": -1, "usages": [ @@ -546036,7 +546036,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[\\dfrac{1}{7},\\dfrac{1}{3})$", "solution": "", "duration": -1, "usages": [ @@ -546123,7 +546123,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-1,1)$; (2) 奇函数, 理由略; (3) 是定义域上的严格减函数, 理由略", "solution": "", "duration": -1, "usages": [ @@ -546185,7 +546185,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -546222,7 +546222,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -546282,7 +546282,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-2)\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -546319,7 +546319,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac{1}{2},+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -546356,7 +546356,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -546543,7 +546543,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(2,\\dfrac{12}{5})$", "solution": "", "duration": -1, "usages": [ @@ -546640,7 +546640,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$(a,b)=(1,0)$或$(-1,3)$", "solution": "", "duration": -1, "usages": [ @@ -546700,7 +546700,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\log_5 2$", "solution": "", "duration": -1, "usages": [ @@ -546986,7 +546986,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -547470,7 +547470,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-4,0) -- (6,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,6) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$};\n\\draw [dashed] (-4,-4) -- (6,6) (1,-4) -- (1,6);\n\\draw (1,0) node [fill = white, below] {$1$};\n\\draw [domain = {1/2* (-3 - sqrt(21))}:{1/2* (-3 + sqrt(21))}, samples = 100] plot (\\x,{\\x+1/(\\x-1)});\n\\draw [domain = {1/2* (7 - sqrt(21))}:{1/2* (7 + sqrt(21))}, samples = 100] plot (\\x,{\\x+1/(\\x-1)});\n\\end{tikzpicture}, 图像关于点$(1,1)$对称", "solution": "", "duration": -1, "usages": [ @@ -547574,7 +547574,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[1,2]$, $4$, $\\dfrac{29}{5}$", "solution": "", "duration": -1, "usages": [ @@ -548056,7 +548056,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$S=\\dfrac{C^2}{4\\pi}$, $C\\in (0,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -548094,7 +548094,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\sqrt{144-x^2}$, $x\\in (0,12)$", "solution": "", "duration": -1, "usages": [ @@ -548159,7 +548159,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$s=\\begin{cases}4t, & 0\\le t\\le 3, \\\\ 5t-3, & 3\\le t\\le 7\\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -548251,7 +548251,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=\\begin{cases}\\dfrac{1}{2} x, & x\\in [0,1], \\\\ \\dfrac{3}{2}-x, & x\\in [1,\\dfrac{3}{2}], \\\\ x-\\dfrac{3}{2}, & x\\in [\\dfrac{3}{2},3],\\\\ \\dfrac{3}{2}-\\dfrac{1}{2} x, & x\\in [2,3],\\end{cases}$ 图像: \\begin{tikzpicture}[>=latex]\n\\draw [->] (-0.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed] (1,0) -- (1,0.5) (2,0) -- (2,0.5) (0,0.5) -- (2,0.5);\n\\draw (0,0.5) node [left] {$\\frac{1}{2}$} (1.5,0) node [below] {$\\frac{3}{2}$};\n\\foreach \\i in {1,2,3}\n{\\draw (\\i,0) node [below] {$\\i$};};\n\\draw (0,0) -- (1,0.5) -- (1.5,0) -- (2,0.5) -- (3,0);\n\\end{tikzpicture}\\\\\n(2) $\\dfrac{1}{2}$或$\\dfrac{5}{4}$或$\\dfrac{7}{4}$或$\\dfrac{5}{2}$", "solution": "", "duration": -1, "usages": [ @@ -548421,7 +548421,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{-3\\pm \\sqrt{13}}{2}$", "solution": "", "duration": -1, "usages": [ @@ -548456,7 +548456,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{2\\}$", "solution": "", "duration": -1, "usages": [], @@ -548480,7 +548480,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,5)$", "solution": "", "duration": -1, "usages": [ @@ -548537,7 +548537,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,3)$", "solution": "", "duration": -1, "usages": [ @@ -548617,7 +548617,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "无整数解, 理由略", "solution": "", "duration": -1, "usages": [ @@ -548740,7 +548740,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$[-\\dfrac{3}{2},\\dfrac{2}{3})$", "solution": "", "duration": -1, "usages": [ @@ -548820,7 +548820,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(0,\\dfrac{1}{2})$", "solution": "", "duration": -1, "usages": [ @@ -548877,7 +548877,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,1]$", "solution": "", "duration": -1, "usages": [ @@ -548912,7 +548912,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "解集为$\\{1\\}$", "solution": "", "duration": -1, "usages": [ @@ -549103,7 +549103,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -549162,7 +549162,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -549197,7 +549197,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -549232,7 +549232,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -549267,7 +549267,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -549412,7 +549412,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $2n-1$; (2) $38$, $-16$; (3) $62$", "solution": "", "duration": -1, "usages": [ @@ -549447,7 +549447,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [ @@ -549504,7 +549504,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -549539,7 +549539,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$102$", "solution": "", "duration": -1, "usages": [ @@ -549574,7 +549574,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2n-3$", "solution": "", "duration": -1, "usages": [ @@ -549609,7 +549609,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$1,3,5$", "solution": "", "duration": -1, "usages": [ @@ -549688,7 +549688,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$1700$米", "solution": "", "duration": -1, "usages": [ @@ -549723,7 +549723,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $90$, $120$; (2) $3$; (3) $24$; (4) $\\dfrac{A+B}{2}$", "solution": "", "duration": -1, "usages": [ @@ -549758,7 +549758,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$6064$", "solution": "", "duration": -1, "usages": [ @@ -549793,7 +549793,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac{1}{8},\\dfrac{7}{48}]$", "solution": "", "duration": -1, "usages": [ @@ -549872,7 +549872,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -549995,7 +549995,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $11$; (2) $-360$; (3) $\\dfrac{17}{13}$; (4) $-\\dfrac{3}{2}$", "solution": "", "duration": -1, "usages": [ @@ -550074,7 +550074,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\dfrac{1}{2}$; (2) $9$", "solution": "", "duration": -1, "usages": [ @@ -550109,7 +550109,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\begin{cases}3, & n=1,\\\\ 2n, & n\\ge 2\\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -550200,7 +550200,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$23$", "solution": "", "duration": -1, "usages": [ @@ -550302,7 +550302,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -550447,7 +550447,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{9}{5}$", "solution": "", "duration": -1, "usages": [ @@ -550526,7 +550526,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$17$", "solution": "", "duration": -1, "usages": [ @@ -550627,7 +550627,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "\\begin{tabular}{|c|c|c|c|}\n\\hline$a_1$&$q$&$n$&$a_n$\\\\\n\\hline 9 & \\underline{$3$} & 4 & 243 \\\\\n\\hline \\underline{$\\dfrac{1}{2}$} &$-2$& 7 & 32 \\\\\n\\hline 4 &$\\dfrac 12$& \\underline{$8$} &$\\dfrac 1{32}$\\\\\n\\hline 3 &$\\dfrac 23$& 3 & \\underline{$\\dfrac{4}{3}$}\\\\\n\\hline\n\\end{tabular}", "solution": "", "duration": -1, "usages": [ @@ -550683,7 +550683,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$15\\cdot (-2)^n$", "solution": "", "duration": -1, "usages": [ @@ -550717,7 +550717,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pm 2$", "solution": "", "duration": -1, "usages": [ @@ -550751,7 +550751,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -550785,7 +550785,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2187$", "solution": "", "duration": -1, "usages": [ @@ -550819,7 +550819,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{5}-1}{2}$", "solution": "", "duration": -1, "usages": [ @@ -550853,7 +550853,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$48$或$-80$", "solution": "", "duration": -1, "usages": [ @@ -550909,7 +550909,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -551053,7 +551053,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$a_n=2^{5-2n}$或$a_n=2^{2n-3}$", "solution": "", "duration": -1, "usages": [ @@ -551109,7 +551109,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -551143,7 +551143,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -551199,7 +551199,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [ @@ -551234,7 +551234,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{255}{16}$", "solution": "", "duration": -1, "usages": [ @@ -551269,7 +551269,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\begin{cases}n, & q=1, \\\\ \\dfrac{q-q^{n+1}}{1-q}, & q\\ne 1 \\text{且} q\\ne 0\\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -551305,7 +551305,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [ @@ -551364,7 +551364,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{4^n+8}{3}$", "solution": "", "duration": -1, "usages": [ @@ -551399,7 +551399,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -551458,7 +551458,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$30$", "solution": "", "duration": -1, "usages": [ @@ -551537,7 +551537,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "不是, 是", "solution": "", "duration": -1, "usages": [ @@ -551682,7 +551682,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{3}$, $32$", "solution": "", "duration": -1, "usages": [ @@ -551719,7 +551719,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "如$(1,\\dfrac{1}{2})$($a_1>0$, $q\\in (0,1)$均可以)", "solution": "", "duration": -1, "usages": [ @@ -551777,7 +551777,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$10$", "solution": "", "duration": -1, "usages": [ @@ -551856,7 +551856,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{10}{3}$", "solution": "", "duration": -1, "usages": [ @@ -552001,7 +552001,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}\n\\hline$n$& 1 & 2 & 3 &$\\cdots$& 11 &$\\cdots$&\\underline{$21$}&$\\cdots$&\\underline{$100$} \\\\\n\\hline$a_n$&\\underline{$8$} &\\underline{$14$}&\\underline{$20$} &$\\cdots$& \\underline{$68$}&$\\cdots$& 128 &$\\cdots$& 602 \\\\\n\\hline\n\\end{tabular}", "solution": "", "duration": -1, "usages": [ @@ -552032,7 +552032,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$n^2-n+1$", "solution": "", "duration": -1, "usages": [ @@ -552085,7 +552085,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$672$", "solution": "", "duration": -1, "usages": [ @@ -552342,7 +552342,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2-\\dfrac{1}{2^{n-1}}$", "solution": "", "duration": -1, "usages": [ @@ -552377,7 +552377,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2^{n-1}\\cdot n$", "solution": "", "duration": -1, "usages": [ @@ -552412,7 +552412,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$3-2(\\dfrac{2}{3})^{n-1}$", "solution": "", "duration": -1, "usages": [ @@ -552447,7 +552447,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{2n-1}$", "solution": "", "duration": -1, "usages": [ @@ -552482,7 +552482,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$n^2+4n-4$", "solution": "", "duration": -1, "usages": [], @@ -552504,7 +552504,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$5^{\\frac{n(n-1)}{2}}$", "solution": "", "duration": -1, "usages": [], @@ -552549,7 +552549,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\begin{cases}2, & n=3k+1, \\\\ \\dfrac{1}{2}, & n=3k+2, \\\\ -1, & n = 3k+3\\end{cases}$($k\\in \\mathbf{N}$)", "solution": "", "duration": -1, "usages": [ @@ -552628,7 +552628,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$4\\cdot 3^{n-1}-5\\cdot 2^{n-1}$", "solution": "", "duration": -1, "usages": [], @@ -552650,7 +552650,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2^n}{2^n-1}$", "solution": "", "duration": -1, "usages": [], @@ -552696,7 +552696,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $a_n=\\sqrt{n}-\\sqrt{n-1}$", "solution": "", "duration": -1, "usages": [], @@ -553044,7 +553044,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$, $4$, $5$, $n$", "solution": "", "duration": -1, "usages": [ @@ -553100,7 +553100,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$(2n-1)^2$", "solution": "", "duration": -1, "usages": [ @@ -553176,7 +553176,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$n^3$", "solution": "", "duration": -1, "usages": [ @@ -553208,7 +553208,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2^nx+(2^n-1)$", "solution": "", "duration": -1, "usages": [ @@ -553240,7 +553240,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "存在, $a=\\dfrac{1}{4}$, $b=-\\dfrac{1}{4}$, 证明略", "solution": "", "duration": -1, "usages": [ @@ -553316,7 +553316,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -553382,7 +553382,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -553502,7 +553502,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$a_n=2-\\dfrac{1}{n}$", "solution": "", "duration": -1, "usages": [ @@ -553537,7 +553537,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$a_n=3\\cdot 2^{n-1}-2$", "solution": "", "duration": -1, "usages": [ @@ -553660,7 +553660,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$a_n=2^{2^{n-1}}$", "solution": "", "duration": -1, "usages": [ @@ -607664,7 +607664,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "存在(当$a=4$时)", "solution": "", "duration": -1, "usages": [], @@ -607684,7 +607684,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $19$; (2) 可能, $f(x)=\\begin{cases}2x^3-2^{-x}+1, & x<0,\\\\ 0, & x=0, \\\\ 2x^3+2^x-1, & x>0 \\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -607706,7 +607706,7 @@ "第二单元" ], "genre": "4em", - "ans": "", + "ans": "(1) 既不是奇函数, 又不是偶函数, 证明略; (2) 既不是奇函数, 又不是偶函数, 证明略; (3) 奇函数, 证明略", "solution": "", "duration": -1, "usages": [ @@ -609820,7 +609820,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -609840,7 +609840,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -609873,7 +609873,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -609906,7 +609906,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) 最大值不存在; 最小值为$-6$(当且仅当$x=2$时取); (2) 最大值为$3$(当且仅当$x=1$时取; 最小值不存在; (3) 最大值为$1$(当且仅当$x=-2$时取); 最小值为$-8$(当且仅当$x=1$时取); (4) 最大值为$5$(当且仅当$x=-2$时取), 最小值为$-3$(当且仅当$x=0$时取)", "solution": "", "duration": -1, "usages": [ @@ -609941,7 +609941,7 @@ "第二单元" ], "genre": "4em", - "ans": "", + "ans": "$[-1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -610872,7 +610872,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "$2.2$", "solution": "", "duration": -1, "usages": [ @@ -610910,7 +610910,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "$1.6$", "solution": "", "duration": -1, "usages": [ @@ -610949,7 +610949,7 @@ "第二单元" ], "genre": "", - "ans": "", + "ans": "$\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -614215,7 +614215,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -614335,7 +614335,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{17}{2}$; (2) $20$", "solution": "", "duration": -1, "usages": [], @@ -614355,7 +614355,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $10$; (2) $20$", "solution": "", "duration": -1, "usages": [], @@ -614839,7 +614839,7 @@ "第四单元" ], "genre": "", - "ans": "", + "ans": "$310$", "solution": "", "duration": -1, "usages": [ @@ -614877,7 +614877,7 @@ "第四单元" ], "genre": "4em", - "ans": "", + "ans": "$\\begin{cases}\\dfrac{a-a^{2n+3}}{1-a^2}, & a\\ne \\pm 1, \\\\ (n+1)a, & a = \\pm 1\\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -614916,7 +614916,7 @@ "第四单元" ], "genre": "", - "ans": "", + "ans": "(1) $a_n=4n$; (2) $a_n=\\dfrac{n}{n+1}$; (3) $a_n=(-1)^n\\cdot \\dfrac{1}{2n}$; (4) $a_n=(-1)^{n+1}\\cdot \\sqrt[3]{n}$; (5) $a_n=(-1)^{n+1}\\cdot \\dfrac{n+1}{n(n+2)}$", "solution": "", "duration": -1, "usages": [ @@ -614948,7 +614948,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $1$; (2) $\\dfrac{1}{4}$", "solution": "", "duration": -1, "usages": [ @@ -614981,7 +614981,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{325}{999}$; (2) $\\dfrac{291}{110}$", "solution": "", "duration": -1, "usages": [ @@ -615014,7 +615014,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{22}{9}$; (2) $\\dfrac{2}{55}$", "solution": "", "duration": -1, "usages": [ @@ -615049,7 +615049,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$a_1>a_2$, $a_2=a_3$, $a_3