diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index a864368a..9d5f22f4 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -223,3 +223,6 @@ 20240125-152122 024198:024200,000465,024201:024205,019538,024206:024210 +20240125-152725 +024211:024215,011270,024216,011102,024217:024218,004157,024219:024222 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 37ab0e8e..11a28ac6 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -342012,7 +342012,9 @@ "20221209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024214" + ], "remark": "", "space": "", "unrelated": [] @@ -359191,7 +359193,9 @@ "same": [ "023569" ], - "related": [], + "related": [ + "024212" + ], "remark": "", "space": "", "unrelated": [] @@ -431876,7 +431880,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024214" + ], "remark": "", "space": "", "unrelated": [] @@ -547795,7 +547801,8 @@ ], "same": [], "related": [ - "019898" + "019898", + "024215" ], "remark": "", "space": "", @@ -637463,7 +637470,9 @@ "same": [ "012836" ], - "related": [], + "related": [ + "024212" + ], "remark": "", "space": "", "unrelated": [] @@ -651211,6 +651220,254 @@ "space": "4em", "unrelated": [] }, + "024211": { + "id": "024211", + "content": "函数 $y=\\dfrac{(x-2)^0}{x+1}+\\log _x(x+2)$ 的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024212": { + "id": "024212", + "content": "``$a=1$''是``函数 $f(x)=|x-a|$ 在区间 $[1,+\\infty)$ 上为严格增函数''的\\blank{50}条件.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "012836", + "023569" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024213": { + "id": "024213", + "content": "函数 $y=|x+1|+\\sqrt{x^2-4 x+4}$ 的值域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024214": { + "id": "024214", + "content": "若函数 $f(x)=3^x+\\dfrac{a}{3^x+1}$ 最小值为 $\\dfrac{5}{3}$, 则 $a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "012252", + "015549" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024215": { + "id": "024215", + "content": "函数 $y=\\log _{0.7}(6-x-x^2)$ 的严格增区间为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "020482" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024216": { + "id": "024216", + "content": "$f(x)$ 是定义在 $\\mathbf{R}$ 上的奇函数, 且 $f(x+1)=\\dfrac{1+f(x)}{1-f(x)}$, ($f(x) \\neq 0,1$). 若 $f(1)=3$, 则 $f(2025)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024217": { + "id": "024217", + "content": "若 $p$: $\\log _2x<0$, $q$: $x<1$, 则 $p$ 是 $q$ 成立的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024218": { + "id": "024218", + "content": "若定义在 $\\mathbf{R}$ 上的奇函数 $f(x)$ 在 $(0,+\\infty)$ 上是严格增函数, 又 $f(-3)=0$, 则不等式 $x f(x)<0$ 的解集为\\bracket{20}.\n\\fourch{$(-3,0) \\cup(0,3)$}{$(-\\infty,-3) \\cup$$(3,+\\infty)$}{$(-3,0) \\cup$$(3,+\\infty)$}{$(-\\infty,-3) \\cup(0,3)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024219": { + "id": "024219", + "content": "(1) 已知 $x \\in[\\dfrac{1}{27}, 9]$, 求函数 $y=\\log _3\\dfrac{x}{27}\\cdot \\log _33 x$ 的最大值和最小值;\\\\\n(2) 已知 $a>0$ 且 $a \\neq 1$, 关于 $x$ 的方程 $a^{2 x}-2 k a^x+k+2=0$ 有实数解, 求实数 $k$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024220": { + "id": "024220", + "content": "设 $a>0$ 且 $a \\neq 1$, $t \\in R$, 已知函数 $f(x)=\\log _a(x+1)$, $g(x)=2 \\log _a(2 x+t)$.\\\\\n(1) 当 $t=-1$ 时, 求不等式 $f(x) \\leq g(x)$ 的解;\\\\\n(2) 若函数 $F(x)=a^{f(x)}+t x^2-2 t+1$ 在区间 $(-1,2]$ 上有零点, 求实数 $t$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024221": { + "id": "024221", + "content": "某生态基地种植某中药材的年固定成本为 $250$ 万元, 每产出 $x$ 吨需另外投入可变成本 $h(x)$ 万元, 已知 $h(x)=\\begin{cases}a x^2+49 x,& x \\in(0,50],\\\\51 x+\\dfrac{13635}{2 x+1}-860,& x \\in(50,100] .\\end{cases}$ 通过市场分析, 该中药材可以每吨 $50$ 万元的价格全部售完. 设基地种植该中药材年利润为 $y$ 万元, 当基地产出该中药材 $40$ 吨时, 年利润为 $190$ 万元.\\\\\n(1) 求实数 $a$ 的值;\\\\\n(2) 求年利润 $y$ 的最大值 (精确到 $0.1$ 万元), 并求此时的年产量 (精确到 $0.1$ 吨).", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024222": { + "id": "024222", + "content": "对于定义域为 $D$ 的函数 $y=f(x)$, 如果存在区间 $[m, n] \\subseteq D$, 同时满足:\\\\\n(1) $f(x)$ 在 $[m, n]$ 内是单调函数;\\\\\n(2) 当定义域是 $[m, n]$ 时, $f(x)$ 的值域也是 $[m, n]$. 则称 $[m, n]$ 是该函数的``和谐区间''.\\\\\n(1) 求证: 函数 $y=g(x)=3-\\dfrac{5}{x}$ 不存在``和谐区间'';\\\\\n(2) 已知: 函数 $y=\\dfrac{(a^2+a) x-1}{a^2x},$($a \\in \\mathbf{R}$, $a \\neq 0$) 有``和谐区间''$[m, n]$, 当 $a$ 变化时, 求出 $n-m$ 的最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0