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添加一道新题和一个关联题并修改一个题面

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weiye.wang 2023-11-18 10:19:26 +08:00
parent f018ecd794
commit 6f436dafca
1 changed files with 49 additions and 3 deletions
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题库0.3/Problems.json
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@ -595136,7 +595136,9 @@
"20230905\t王伟叶" "20230905\t王伟叶"
], ],
"same": [], "same": [],
"related": [], "related": [
"022789"
],
"remark": "", "remark": "",
"space": "4em", "space": "4em",
"unrelated": [] "unrelated": []
@ -595583,7 +595585,7 @@
}, },
"022470": { "022470": {
"id": "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": [], "objs": [],
"tags": [], "tags": [],
"genre": "填空题", "genre": "填空题",
@ -595593,7 +595595,8 @@
"usages": [], "usages": [],
"origin": "2025届高一上学期周末卷13小测", "origin": "2025届高一上学期周末卷13小测",
"edit": [ "edit": [
"20230905\t王伟叶" "20230905\t王伟叶",
"20231118\t徐慧"
], ],
"same": [], "same": [],
"related": [], "related": [],
@ -603448,6 +603451,49 @@
"space": "4em", "space": "4em",
"unrelated": [] "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": { "030001": {
"id": "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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.", "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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",