收录高三寒假作业37新题

工具v2/文本文件/新题收录列表.txt

@@ -109,3 +109,6 @@
 20240125-115808
 023906:023910,023151
 
+20240125-120258
+023911:023914,019177,023915,020862,023916
+

题库0.3/Problems.json

@@ -644841,6 +644841,126 @@
         "space": "4em",
         "unrelated": []
     },
+    "023911": {
+        "id": "023911",
+        "content": "如图, 试用适当的符号表示下列点、直线和平面之间的关系:\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) --++ (3,0) --++ (-1.5,1.5) --++ (-3,0) node [below right = 0 and 0.4] {$\\beta$} --cycle;\n\\draw (3,0) --++ (-1.5,-1.5) --++ (-3,0) node [above right = 0 and 0.4] {$\\alpha$} -- (0,0);\n\\draw (1,0) node [above] {$D$} coordinate (D) --++ (-135:1.5) node [right] {$C$} coordinate (C);\n\\draw (2,0) node [below] {$B$} coordinate (B) --++ (135:1.5) node [right] {$A$} coordinate (A);\n\\end{tikzpicture}\n\\end{center}\n(1) 点 $C$ 与平面 $\\beta$:\\blank{100};\\\\\n(2) 点 $A$ 与平面 $\\alpha$:\\blank{100};\\\\\n(3) 直线 $AB$ 与平面 $\\alpha$:\\blank{100};\\\\\n(4) 直线 $CD$ 与平面 $\\alpha$:\\blank{100};\\\\\n(5) 平面 $\\alpha$ 与平面 $\\beta$:\\blank{100}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023912": {
+        "id": "023912",
+        "content": "下列所有正确命题的序号是\\blank{50}.\\\\\n\\textcircled{1} 过三点确定一个平面;\\\\\n\\textcircled{2} 四边形是平面图形;\\\\\n\\textcircled{3} 三条直线两两相交则确定一个平面;\\\\\n\\textcircled{4} 两个相交平面把空间分成四个区域.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023913": {
+        "id": "023913",
+        "content": "下图是正方体或四面体, 若 $P$、$Q$、$R$、$S$ 分别是所在棱的中点, 则这四个点共面的图共有\\blank{50}个.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0)  coordinate (A);\n\\draw (A) ++ (\\l,0,0)  coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l)  coordinate (C);\n\\draw (A) ++ (0,0,-\\l)  coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0)  coordinate (A_1);\n\\draw (B) ++ (0,\\l,0)  coordinate (B_1);\n\\draw (C) ++ (0,\\l,0)  coordinate (C_1);\n\\draw (D) ++ (0,\\l,0)  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\\draw ($(C)!0.5!(C_1)$) node [right] {$R$} coordinate (R);\n\\draw ($(C_1)!0.5!(D_1)$) node [above] {$S$} coordinate (S);\n\\draw ($(D_1)!0.5!(A_1)$) node [left] {$P$} coordinate (P);\n\\draw ($(A)!0.5!(A_1)$) node [left] {$Q$} coordinate (Q);\n\\foreach \\i in {P,Q,R,S}\n{\\filldraw (\\i) circle (0.03);};\n\\draw (1.2,-0.8) node {\\textcircled{1}};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0)  coordinate (A);\n\\draw (A) ++ (\\l,0,0)  coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l)  coordinate (C);\n\\draw (A) ++ (0,0,-\\l)  coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0)  coordinate (A_1);\n\\draw (B) ++ (0,\\l,0)  coordinate (B_1);\n\\draw (C) ++ (0,\\l,0)  coordinate (C_1);\n\\draw (D) ++ (0,\\l,0)  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\\draw ($(C)!0.5!(B)$) node [right] {$R$} coordinate (R);\n\\draw ($(C_1)!0.5!(D_1)$) node [above] {$S$} coordinate (S);\n\\draw ($(D_1)!0.5!(A_1)$) node [left] {$P$} coordinate (P);\n\\draw ($(A)!0.5!(B)$) node [below] {$Q$} coordinate (Q);\n\\foreach \\i in {P,Q,R,S}\n{\\filldraw (\\i) circle (0.03);};\n\\draw (1.2,-0.8) node {\\textcircled{2}};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex, z = {(-120:0.5cm)}]\n\\draw (0,0,0) coordinate (A);\n\\draw (2,0,0) coordinate (B);\n\\draw (1,0,{-sqrt(3)}) coordinate (C);\n\\draw ($1/3*(A)+1/3*(B)+1/3*(C)$) ++ (0,{2*sqrt(6)/3},0) coordinate (D);\n\\draw (A)--(B)--(D)--cycle;\n\\draw [dashed] (A)--(C)--(B)(C)--(D);\n\\draw ($(C)!0.5!(B)$) node [below] {$R$} coordinate (R);\n\\draw ($(A)!0.5!(C)$) node [below] {$S$} coordinate (S);\n\\draw ($(D)!0.5!(A)$) node [left] {$P$} coordinate (P);\n\\draw ($(D)!0.5!(B)$) node [right] {$Q$} coordinate (Q);\n\\foreach \\i in {P,Q,R,S}\n{\\filldraw (\\i) circle (0.03);};\n\\draw (1.2,-0.8) node {\\textcircled{3}};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex, z = {(-120:0.5cm)}]\n\\draw (0,0,0) coordinate (A);\n\\draw (2,0,0) coordinate (B);\n\\draw (1,0,{-sqrt(3)}) coordinate (C);\n\\draw ($1/3*(A)+1/3*(B)+1/3*(C)$) ++ (0,{2*sqrt(6)/3},0) coordinate (D);\n\\draw (A)--(B)--(D)--cycle;\n\\draw [dashed] (A)--(C)--(B)(C)--(D);\n\\draw ($(C)!0.5!(B)$) node [below] {$R$} coordinate (R);\n\\draw ($(A)!0.5!(B)$) node [below] {$S$} coordinate (S);\n\\draw ($(D)!0.5!(A)$) node [left] {$P$} coordinate (P);\n\\draw ($(D)!0.5!(B)$) node [right] {$Q$} coordinate (Q);\n\\foreach \\i in {P,Q,R,S}\n{\\filldraw (\\i) circle (0.03);};\n\\draw (1.2,-0.8) node {\\textcircled{4}};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023914": {
+        "id": "023914",
+        "content": "若 $A$、$B$、$C$ 表示不同的点, $l$ 表示直线, $\\alpha$、$\\beta$ 表示不同的平面, 则下列所有正确推理的序号为\\blank{50}.\\\\\n\\textcircled{1} $A \\in l$, $A \\in \\alpha$, $B \\in l$, $B \\in \\alpha \\Rightarrow l \\subset \\alpha$;\\\\\n\\textcircled{2} $A \\in \\alpha$, $A \\in \\beta$, $B \\in \\alpha$, $B \\in \\beta \\Rightarrow \\alpha \\cap \\beta=AB$;\\\\\n\\textcircled{3} $l$ 不在平面 $\\alpha$ 上, $A \\in l \\Rightarrow A \\notin \\alpha$;\\\\\n\\textcircled{4} $A \\in \\alpha$, $A \\in l, l$ 不在平面 $\\alpha$ 上 $\\Rightarrow l \\cap \\alpha=A$.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023915": {
+        "id": "023915",
+        "content": "下列命题中正确的是\\bracket{20}.\n\\onech{空间不同的三点确定一个平面}{空间两两相交的三条直线确定一个平面}{空间有三个角为直角的四边形一定是平面图形}{和同一条直线相交的三条平行直线一定在同一平面上}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023916": {
+        "id": "023916",
+        "content": "如图, 平面 $ABEF \\perp$ 平面 $ABCD$, 四边形 $ABEF$ 与四边形 $ABCD$ 都是直角梯形, $\\angle BAD=\\angle FAB=90^{\\circ}$, $BC \\parallel  AD$ 且 $BC=\\dfrac{1}{2}AD$, $BE \\parallel  AF$ 且 $BE=\\dfrac{1}{2}AF$, $G$、$H$ 分别为 $FA$、$FD$ 的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [below] {$A$} coordinate (A);\n\\draw (3,0,0) node [right] {$D$} coordinate (D);\n\\draw (0,3,0) node [above] {$F$} coordinate (F);\n\\draw (0,0,1.5) node [below] {$B$} coordinate (B);\n\\draw (B) ++ (1.5,0,0) node [below] {$C$} coordinate (C);\n\\draw (B) ++ (0,1.5,0) node [left] {$E$} coordinate (E);\n\\draw (B)--(C)--(D)--(F)--(E)--cycle(E)--(C);\n\\draw [dashed] (A)--(D)(A)--(F)(A)--(B);\n\\draw ($(A)!0.5!(F)$) node [above right] {$G$} coordinate (G);\n\\draw ($(F)!0.5!(D)$) node [above right] {$H$} coordinate (H);\n\\draw (C)--(H);\n\\draw [dashed] (B)--(G)--(H);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: 四边形 $BCHG$ 为平行四边形;\\\\\n(2) 判断 $C$、$D$、$F$、$E$ 四点是否共面? 为什么?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "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.",