diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 08d8b1a3..df7d7842 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -583016,6 +583016,186 @@ "space": "", "unrelated": [] }, + "022685": { + "id": "022685", + "content": "不等式 $x^2-16 x+64>0$ 的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2026届高一上学期随堂练习卷03", + "edit": [ + "20230925\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022686": { + "id": "022686", + "content": "不等式 $\\dfrac{2 x-1}{x-1}<0$ 的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2026届高一上学期随堂练习卷03", + "edit": [ + "20230925\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022687": { + "id": "022687", + "content": "不等式组 $\\begin{cases}x^2-16<0\\\\x^2-4 x+3 \\geq 0\\end{cases}$ 的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2026届高一上学期随堂练习卷03", + "edit": [ + "20230925\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022688": { + "id": "022688", + "content": "不等式 $\\dfrac{2 x+3}{2-x}\\geq 1$ 的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2026届高一上学期随堂练习卷03", + "edit": [ + "20230925\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022689": { + "id": "022689", + "content": "关于 $x$ 的方程 $2 x+k(x+3)=4$ 的解为正数, 则实数 $k$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2026届高一上学期随堂练习卷03", + "edit": [ + "20230925\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022690": { + "id": "022690", + "content": "已知关于 $x$ 的不等式 $2 x^2-2(a-1) x+(a+3)>0$ 的解集是 $\\mathbf{R}$, 则实数 $a$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2026届高一上学期随堂练习卷03", + "edit": [ + "20230925\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022691": { + "id": "022691", + "content": "不等式 $\\dfrac{3 x^2+2 x+2}{x^2+x+1}0$ 的解集是 $(-\\dfrac{1}{2}, 2)$ 对于 $a, b, c$ 有以下几个结论:\\\\\n\\textcircled{1} $a>0$; \\textcircled{2} $b>0$; \\textcircled{3} $c>0$; \\textcircled{4} $a+b+c>0$; \\textcircled{5} $a-b+c>0$.\\\\\n其中正确结论的序号是\\blank{50}(填上你认为所有正确命题的序号).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2026届高一上学期随堂练习卷03", + "edit": [ + "20230925\t严捷" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "022693": { + "id": "022693", + "content": "解关于 $x$ 的不等式 $\\dfrac{a x+a}{x+a+1}>0$, $a \\in \\mathbf{R}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2026届高一上学期随堂练习卷03", + "edit": [ + "20230925\t严捷" + ], + "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