收录2026届高一上学期随堂练习03题目

题库0.3/Problems.json

@@ -583016,6 +583016,186 @@
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+    "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 $\\dfrac{3 x^2+2 x+2}{x^2+x+1}<k$, 对于一切 $x \\in \\mathbf{R}$ 都成立, 则实数 $k$ 的取值范围为\\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": []
+    },
+    "022692": {
+        "id": "022692",
+        "content": "一元二次不等式 $a x^2+b x+c>0$ 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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",