收录高三寒假作业29新题
This commit is contained in:
parent
82ffefabdc
commit
4bc73da291
|
|
@ -85,3 +85,6 @@
|
|||
20240125-112538
|
||||
023844:023847
|
||||
|
||||
20240125-113548
|
||||
023848:023855
|
||||
|
||||
|
|
|
|||
|
|
@ -270116,7 +270116,9 @@
|
|||
"20220730\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"related": [
|
||||
"023849"
|
||||
],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
|
|
@ -643476,6 +643478,168 @@
|
|||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"023848": {
|
||||
"id": "023848",
|
||||
"content": "在边长为 $1$ 的正六边形 $ABCDEF$ 中, $|\\overrightarrow{BA}+\\overrightarrow{CD}+\\overrightarrow{EF}|=$\\blank{50}.",
|
||||
"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": []
|
||||
},
|
||||
"023849": {
|
||||
"id": "023849",
|
||||
"content": "已知平行四边形 $ABCD$ 的对角线 $AC$ 和 $BD$ 相交于 $O$, 且 $\\overrightarrow{OA}=\\overrightarrow{a}$, $\\overrightarrow{OB}=\\overrightarrow{b}$, 则 $\\overrightarrow{BC}$ 用 $\\overrightarrow{a}, \\overrightarrow{b}$ 表示为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"009629"
|
||||
],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"023850": {
|
||||
"id": "023850",
|
||||
"content": "设 $\\overrightarrow{a}, \\overrightarrow{b}$ 是不共线的两个平面向量, 已知 $\\overrightarrow{PQ}=\\overrightarrow{a}+\\sin \\alpha \\cdot \\overrightarrow{b}$, 其中 $\\alpha \\in(0,2 \\pi)$, $\\overrightarrow{QR}=2 \\overrightarrow{a}-\\overrightarrow{b}$. 若 $P$、$Q$、$R$ 三点共线, 则角 $\\alpha$ 的值为\\blank{50}.",
|
||||
"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": []
|
||||
},
|
||||
"023851": {
|
||||
"id": "023851",
|
||||
"content": "设向量 $\\overrightarrow{a}, \\overrightarrow{b}$ 不共线, 且 $\\overrightarrow{c}=\\lambda \\overrightarrow{a}+\\overrightarrow{b}$, $\\overrightarrow{d}=\\overrightarrow{a}+(2 \\lambda-1) \\overrightarrow{b}$, 若 $\\overrightarrow{c}$ 与 $\\overrightarrow{d}$ 同向, 则实数 $\\lambda=$\\blank{50}.",
|
||||
"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": []
|
||||
},
|
||||
"023852": {
|
||||
"id": "023852",
|
||||
"content": "如图, 已知等边三角形 $ABC$ 内接于圆 $O$, $D$ 为线段 $OA$ 的中点, 若 $\\overrightarrow{BA}=\\overrightarrow{a}$, $\\overrightarrow{BC}=\\overrightarrow{b}$, 则 $\\overrightarrow{BD}$ 用 $\\overrightarrow{a}, \\overrightarrow{b}$ 表示为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.5]\n\\filldraw (0,0) circle (0.02) node [right] {$O$} coordinate (O);\n\\draw (O) circle (1);\n\\draw (90:1) node [above] {$A$} coordinate (A);\n\\draw (210:1) node [below left] {$B$} coordinate (B);\n\\draw (-30:1) node [below right] {$C$} coordinate (C);\n\\draw ($(B)!0.5!(C)$) node [below] {$E$} coordinate (E);\n\\draw ($(A)!0.5!(O)$) node [below right] {$D$} coordinate (D);\n\\draw (A)--(B)--(C)--cycle(A)--(E)(B)--(D);\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": []
|
||||
},
|
||||
"023853": {
|
||||
"id": "023853",
|
||||
"content": "在等腰梯形 $ABCD$ 中, $\\overrightarrow{AB}=2 \\overrightarrow{DC}$, 点 $E$ 是线段 $BC$ 的中点, 若 $\\overrightarrow{AE}=\\lambda \\overrightarrow{AB}+\\mu \\overrightarrow{AD}$, 则 $\\lambda=$\\blank{50}, $\\mu=$\\blank{50}.",
|
||||
"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": []
|
||||
},
|
||||
"023854": {
|
||||
"id": "023854",
|
||||
"content": "在 $\\triangle ABC$ 中, $D$、$E$ 分别为 $BC$、$AC$ 边上的中点, $G$ 为 $BE$ 上一点, 且 $GB=2GE$, 设 $\\overrightarrow{AB}=\\overrightarrow{a}$, $\\overrightarrow{AC}=\\overrightarrow{b}$, 则 $\\overrightarrow{AG}$ 可用 $\\overrightarrow{a}, \\overrightarrow{b}$ 表示为\\blank{50}.",
|
||||
"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": []
|
||||
},
|
||||
"023855": {
|
||||
"id": "023855",
|
||||
"content": "已知 $O$、$A$、$B$ 是不共线的三点, 且 $\\overrightarrow{OP}=m \\overrightarrow{OA}+n \\overrightarrow{OB}$($m, n \\in \\mathbf{R}$).\\\\\n(1) 若 $m+n=1$, 求证: $A$、$P$、$B$ 三点共线;\\\\\n(2) 若 $A$、$P$、$B$ 三点共线, 求证: $m+n=1$.",
|
||||
"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.",
|
||||
|
|
|
|||
Reference in New Issue