收录高三寒假作业31新题
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20240125-113926
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023856:023864
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20240125-114309
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023865:023872
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@ -62364,7 +62364,9 @@
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"20220625\t王伟叶"
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"023870"
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"remark": "",
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"space": "4em",
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"unrelated": []
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"20220806\t王伟叶"
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],
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"related": [],
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"related": [
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"023866"
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"remark": "",
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"space": "4em",
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"20230209\t王伟叶"
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],
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"same": [],
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"related": [],
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"related": [
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"023870"
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"remark": "",
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"space": "4em",
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@ -643844,6 +643850,172 @@
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"space": "4em",
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"unrelated": []
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},
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"023865": {
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"id": "023865",
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"content": "如图, 已知 $BC=3BP$, $CA=3CQ$, 设 $\\overrightarrow{AB}=\\overrightarrow{c}$, $\\overrightarrow{BC}=\\overrightarrow{a}$, 用 $\\overrightarrow{a}$、$\\overrightarrow{c}$ 表示: $\\overrightarrow{PA}=$\\blank{50}. $\\overrightarrow{PQ}=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (3,0.5) node [right] {$A$} coordinate (A);\n\\draw (2,2) node [above] {$C$} coordinate (C);\n\\draw ($(B)!{1/3}!(C)$) node [above left] {$P$} coordinate (P);\n\\draw ($(C)!{1/3}!(A)$) node [above right] {$Q$} coordinate (Q);\n\\draw (A)--(B)--(C)--cycle(Q)--(P)--(A);\n\\end{tikzpicture}\n\\end{center}",
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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": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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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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"023866": {
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"id": "023866",
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"content": "设 $\\overrightarrow{a}=(1,2)$, $\\overrightarrow{b}=(x, 1)$, $\\overrightarrow{u}=\\overrightarrow{a}+2 \\overrightarrow{b}$, $\\overrightarrow{v}=2 \\overrightarrow{a}+\\overrightarrow{b}$, 若 $\\overrightarrow{u}$ 与 $\\overrightarrow{v}$ 平行, 则实数 $x=$\\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": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [
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"031520",
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"010364"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023867": {
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"id": "023867",
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"content": "对于非零向量 $\\overrightarrow{a}$ 和 $\\overrightarrow{b}$, ``$\\overrightarrow{a}$ 和 $\\overrightarrow{b}$ 垂直''是``$|\\overrightarrow{a}+\\overrightarrow{b}|=|\\overrightarrow{a}-\\overrightarrow{b}|$''的\\blank{50}条件.",
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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": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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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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"023868": {
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"id": "023868",
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"content": "在平面直角坐标系 $x O y$ 中, 已知 $A(1,0)$、$B(0,1), C$ 为坐标平面内第一象限的点, 且 $\\angle AOC=\\dfrac{\\pi}{4}$, $|OC|=2$, 若 $\\overrightarrow{OC}=\\lambda \\overrightarrow{OA}+\\mu \\overrightarrow{OB}$, 则 $\\lambda+\\mu=$\\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": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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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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"023869": {
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"id": "023869",
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"content": "已知 $|\\overrightarrow{a}|=|\\overrightarrow{b}|=2, \\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 的夹角为 $60^{\\circ}$, 若 $\\overrightarrow{OP}=3 \\overrightarrow{a}+2 \\overrightarrow{b}$, $\\overrightarrow{OQ}=-2 \\overrightarrow{a}+3 \\overrightarrow{b}$, 则 $P$、$Q$ 两点之间的距离为\\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": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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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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"023870": {
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"id": "023870",
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"content": "如图, 经过 $\\triangle OAB$ 的重心 $G$ 的直线与 $OA$、$OB$ 分别交于点 $P$、$Q$, 若 $\\overrightarrow{OP}=m \\overrightarrow{OA}$, $\\overrightarrow{OQ}=n \\overrightarrow{OB}$($m, n \\in \\mathbf{R}$), 则 $\\dfrac{1}{n}+\\dfrac{1}{m}$ 的值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$A$} coordinate (A);\n\\draw (3,0) node [below] {$B$} coordinate (B);\n\\draw (2,2.5) node [above] {$O$} coordinate (O);\n\\filldraw ($1/3*(A)+1/3*(B)+1/3*(O)$) node [below] {$G$} coordinate (G) circle (0.03);\n\\draw (0,0.7) coordinate (S);\n\\draw ($(S)!2!(G)$) coordinate (T);\n\\path [name path = PQ, draw] (S)--(T);\n\\path [name path = AOB, draw] (A)--(O)--(B)--cycle;\n\\path [name intersections = {of = PQ and AOB, by = {P,Q}}];\n\\draw (P) node [above] {$P$};\n\\draw (Q) node [above] {$Q$};\n\\end{tikzpicture}\n\\end{center}",
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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": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [
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"001907",
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"021822"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023871": {
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"id": "023871",
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"content": "已知向量 $\\overrightarrow{OA}$、$\\overrightarrow{OB}$ 的夹角为 $\\dfrac{\\pi}{3},|\\overrightarrow{OA}|=4$, $|\\overrightarrow{OB}|=1$, 若点 $M$ 在直线 $OB$ 上, 则 $|\\overrightarrow{OA}-\\overrightarrow{OM}|$ 的最小值为\\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": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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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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"023872": {
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"id": "023872",
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"content": "已知向量 $\\overrightarrow{a}=(2,-1)$, $\\overrightarrow{b}=(2 m, 3 n)$ (其中 $m, n$ 是非零实数).\\\\\n(1) 若 $\\overrightarrow{a}\\perp \\overrightarrow{b}$, 求 $\\dfrac{m}{n}$ 的值;\\\\\n(2) 若 $\\overrightarrow{a}\\parallel \\overrightarrow{b}$, 求 $\\dfrac{m}{n}$ 的值;\\\\\n(3) 若 $\\langle\\overrightarrow{a}, \\overrightarrow{b}\\rangle=\\arctan 2$, 求 $\\dfrac{m}{n}$ 的值;\\\\\n(4) 当 $\\dfrac{m}{n}$ 取 (3) 中所求得的值时, 是否总有 $\\langle\\overrightarrow{a}, \\overrightarrow{b}\\rangle=\\arctan 2$? 请说明理由.",
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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": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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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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"030001": {
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"id": "030001",
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"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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"20230730\t王伟叶"
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],
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"same": [],
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"related": [],
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"related": [
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"023866"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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