diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index f8eeca61..4cac01d6 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -595136,7 +595136,9 @@ "20230905\t王伟叶" ], "same": [], - "related": [], + "related": [ + "022789" + ], "remark": "", "space": "4em", "unrelated": [] @@ -595583,7 +595585,7 @@ }, "022470": { "id": "022470", - "content": "函数 $y=2^{x^2+4 x-5}$ 的严格增区间为\\blank{50}.", + "content": "函数 $y=2^{x^2+4 x-5}$ 的单调增区间为\\blank{50}.", "objs": [], "tags": [], "genre": "填空题", @@ -595593,7 +595595,8 @@ "usages": [], "origin": "2025届高一上学期周末卷13小测", "edit": [ - "20230905\t王伟叶" + "20230905\t王伟叶", + "20231118\t徐慧" ], "same": [], "related": [], @@ -603448,6 +603451,49 @@ "space": "4em", "unrelated": [] }, + "022788": { + "id": "022788", + "content": "函数 $y=\\log_{\\frac{1}{2}}(x^2+4 x-5)$ 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": [ + "20231118\t徐慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022789": { + "id": "022789", + "content": "已知定义在区间 $(-1,1)$ 上的函数 $f(x)=\\dfrac{x+b}{1+x^2}$ 为奇函数.\\\\\n(1) 证明: 函数 $y=f(x)$ 在区间 $(-1,1)$ 上是严格增函数;\\\\\n(2) 解关于 $t$ 的不等式 $f(t-1)+f(t)<0$.", + "objs": [], + "tags": [], + "genre": "4em", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一上学期周末卷12小测-20231118修改", + "edit": [ + "20230905\t王伟叶", + "20231118\t徐慧" + ], + "same": [], + "related": [ + "022447" + ], + "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