录入25届周末卷题目至01
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"space": "4em",
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"unrelated": []
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},
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"023108": {
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"id": "023108",
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"content": "在空间中, 下列命题不成立的是\\bracket{20}.\n\\twoch{两组对边都平行的四边形是平行四边形}{一组对边平行且相等的四边形是平行四边形}{两组对边分别相等的四边形是平行四边形}{对角线互相平分的四边形是平行四边形}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023109": {
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"id": "023109",
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"content": "空间四点中, 如果其中任意三点都不共线, 那么经过其中三点的平面可能是\\blank{50}个, 也可能是\\blank{50}个.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023110": {
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"id": "023110",
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"content": "三个平面把空间分成最多\\blank{50}个部分, 最少\\blank{50}个部分.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023111": {
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"id": "023111",
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"content": "直线 $a$ 经过平面 $\\alpha$ 外一点 $M$, 用符号表示为: \\blank{100}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023112": {
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"id": "023112",
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"content": "空间四个平面两两相交, 以其交线个数为元素构成的集合是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023113": {
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"id": "023113",
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"content": "以下命题中真命题为\\bracket{20}.\n\\twoch{经过三点确定一个平面}{经过一条直线和一个点确定一个平面}{经过两条直线确定一个平面}{两两相交且不共点的三条直线确定一个平面}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023114": {
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"id": "023114",
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"content": "已知: 直线 $a$ 上的两点 $A$、$B$ 在平面 $\\alpha$ 内, 则下列四个结论中不正确的一个是\\bracket{20}.\n\\twoch{直线 $a$ 在平面 $\\alpha$ 内}{平面 $\\alpha$ 通过直线 $a$}{直线 $a$ 上只有这两点在平面 $\\alpha$ 内}{直线 $a$ 上的所有点都在平面 $\\alpha$ 内}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023115": {
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"id": "023115",
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"content": "下列说法中正确的是\\bracket{20}.\n\\onech{如果两个平面 $\\alpha$、$\\beta$ 有一条公共直线 $a$, 就说平面 $\\alpha$、$\\beta$ 相交, 并记作 $\\alpha \\cap \\beta=a$}{两平面 $\\alpha$、$\\beta$ 有一个公共点 $A$, 就说 $\\alpha$、$\\beta$ 相交于过 $A$ 的任意一条直线}{两平面 $\\alpha$、$\\beta$ 有一个公共点 $A$, 就说 $\\alpha$、$\\beta$ 相交于 $A$ 点, 并记作 $\\alpha \\cap \\beta=A$}{两平面 $ABC$ 与 $DBC$ 相交于线段 $BC$}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023116": {
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"id": "023116",
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"content": "如果一条直线与一个平面有一个公共点, 则这条直线上可能有\\blank{50}个点在这个平面内.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023117": {
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"id": "023117",
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"content": "空间四边形 $ABCD$ 中, 点 $E$、$F$、$G$ 分别是 $AB$、$BC$、$CD$、$DA$ 的中点, 那么四边形 $EFGH$ 的形状是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023118": {
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"id": "023118",
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"content": "空间有五个点, 如果其中任意四点都不共面, 那么经过其中三个点的平面最多有\\blank{50}个.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023119": {
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"id": "023119",
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"content": "给出下列条件: \\textcircled{1} 空间的任意三点; \\textcircled{2} 空间的任意两条直线; \\textcircled{3} 梯形的两条腰所在的直线; \\textcircled{4} 空间的任意一条直线和任意一个点; \\textcircled{5} 空间两两相交的三条直线. 其中不一定能独立确定一个平面的条件的序号是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023120": {
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"id": "023120",
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"content": "已知 $\\angle BAC=\\angle B_1A_1C_1$, $AB \\parallel A_1B_1$, 则 $AC$ 与 $A_1C_1$ 的位置关系是\\bracket{20} .\n\\fourch{相交}{异面}{平行}{以上均有可能}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023121": {
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"id": "023121",
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"content": "在如图所示的长方体 $ABCD-A_1B_1C_1D_1$ 中, 画出:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{4}\n\\def\\m{3}\n\\def\\n{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\end{tikzpicture}\n\\hspace*{3em}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{4}\n\\def\\m{3}\n\\def\\n{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 平面 $A_1C_1D$ 与平面 $B_1D_1A$ 的交线;\\\\\n(2) 平面 $A_1C_1B$ 与平面 $AB_1D_1$ 的交线.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "25届周末卷补充题目",
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"023122": {
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"id": "023122",
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"content": "在正方体 $ABCD-A_1B_1C_1D_1$ 中, 点 $E$、$F$、$G$、$H$、$P$、$Q$ 分别是$AB$、$BC$、$CC_1$、$C_1D_1$、$D_1A_1$、$A_1A$ 的中点. 求证: 点 $E$、$F$、$G$、$H$、$P$、$Q$ 六点共面.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"edit": [
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"20240105\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"023123": {
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"id": "023123",
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"content": "如图, 已知平面 $\\alpha \\cap$ 平面 $\\beta=$ 直线 $a$, 直线 $b \\subset \\alpha$, 直线 $c \\subset \\beta$, $b \\cap a=A$, $c \\parallel a$. 求证: $b$ 与 $c$是异面直线.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) -- (2,0,0) -- (2,0,2) -- (0,0,2) node [above right = 0 and 0.15] {$\\alpha$}-- cycle;\n\\draw (0,0,0) -- (-0.5,1,0) node [below right = 0 and 0.15] {$\\beta$} -- (1.5,1,0) -- (2,0,0);\n\\draw (0.2,0.5,0) --+ (1,0,0) node [above] {$c$};\n\\draw (0.5,0) node [below] {$a$};\n\\draw (1.5,0,0) --++ (0,0,1) node [right] {$b$};\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"20240105\t杨懿荔"
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"same": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"023124": {
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"id": "023124",
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"content": "将边长为 $10$ 的正三角形 $ABC$, 按斜二测画法在水平放置的平面上画出, 如图三角形 $A' B' C'$, 求 $A' C'$的长.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} --++ (2,0) node [right] {$C$} -- (60:2) node [above] {$A$}--cycle;\n\\end{tikzpicture}\n\\hspace*{3em}\n\\begin{tikzpicture}[>=latex, y = {(45:0.5cm)}]\n\\draw (0,0) node [left] {$B'$} --++ (2,0) node [right] {$C'$} -- (60:2) node [above] {$A'$} --cycle;\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"20240105\t杨懿荔"
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"same": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"023125": {
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"id": "023125",
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"content": "已知正方体 $ABCD-A_1B_1C_1D_1$ 的棱长为 $2$, $E$、$F$ 分别为 $AB$、$BC$ 的中点.\n画出过点 $E$、$F$、$D_1$ 的截面, 并求截面多边形的周长.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\filldraw ($(A)!0.5!(B)$) node [below] {$E$} coordinate (E) circle (0.03);\n\\filldraw ($(B)!0.5!(C)$) node [below] {$F$} coordinate (F) circle (0.03);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "25届周末卷补充题目",
|
||||
"edit": [
|
||||
"20240105\t杨懿荔"
|
||||
],
|
||||
"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.",
|
||||
|
|
|
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Reference in New Issue