diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 98c72147..a0e5822b 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -164394,7 +164394,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "022957" + ], "remark": "", "space": "4em", "unrelated": [] @@ -608885,7 +608887,9 @@ "20231118\t徐慧" ], "same": [], - "related": [], + "related": [ + "022962" + ], "remark": "", "space": "", "unrelated": [] @@ -613677,6 +613681,250 @@ "space": "", "unrelated": [] }, + "022954": { + "id": "022954", + "content": "已知 $\\log _{18}9=a$, $18^b=5$, 则 $\\log _{36}45=$\\blank{50}.(用 $a, b$ 表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022955": { + "id": "022955", + "content": "若``$|x-1|>2 x-3$ \" 是``$x \\leq a$''成立的必要非充分条件, 则实数 $a$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022956": { + "id": "022956", + "content": "化简: $\\log _23 \\cdot \\log _34 \\cdot \\log _45 \\cdot \\log _56 \\cdot \\log _67 \\cdot \\log _7 m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022957": { + "id": "022957", + "content": "已知函数 $y=x^{n^2-2 n-3}$($n \\in \\mathbf{Z}$) 的图像与两坐标轴都无公共点, 且图像关于 $y$ 轴对称, 则 $n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "same": [], + "related": [ + "005471" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "022958": { + "id": "022958", + "content": "若 $00$, $a \\neq 1$. 若 $\\log _a 2<\\log _2 a$, 则实数 $a$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022962": { + "id": "022962", + "content": "函数 $f(x)=\\log _{\\frac{1}{3}}(x^2-6 x+5)$ 的单调减区间是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "same": [], + "related": [ + "022788" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "022963": { + "id": "022963", + "content": "已知 $a+\\lg a=10$, $b+10^b=10$, 则 $a+b$ 等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022964": { + "id": "022964", + "content": "函数 $f(x)=x^2-b x+c$ 满足 $f(1+x)=f(1-x)$, $f(0)=3$, 则 $f(b^2)$\\blank{20}$f(c^2)$. (填写你认为正确的大小关系)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022965": { + "id": "022965", + "content": "若 $2(\\log _{0.5}x)^2+7(\\log _{0.5}x)+3 \\leq 0$, 求 $f(x)=(\\log _2 \\dfrac{x}{2})(\\log _2 \\dfrac{x}{4})$ 的最大值和最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20231218\t朱敏慧" + ], + "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