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录入高二寒假作业7新题

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wangweiye7840 2024-02-04 14:17:31 +08:00
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3
工具v2/文本文件/新题收录列表.txt
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@ -337,3 +337,6 @@
20240204-133650 高二寒假作业6
024489:024496,040399,030028,013015,024497,013014,024498:024500,013033,016087
20240204-141708 高二寒假作业7
024501:024502,022875,024503:024512,008994,009009,024513:024514,009070

398
题库0.3/Problems.json
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@ -31841,7 +31841,9 @@
"20220624\t朱敏慧, 王伟叶"
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@ -62893,7 +62895,9 @@
"20220625\t王伟叶"
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@ -65483,7 +65487,9 @@
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@ -243979,7 +243985,8 @@
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@ -254657,7 +254664,9 @@
"002000",
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@ -255357,7 +255366,9 @@
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@ -255900,7 +255911,9 @@
"20220726\t王伟叶"
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@ -255944,7 +255957,9 @@
"20220726\t王伟叶"
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@ -292157,7 +292172,9 @@
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@ -447272,7 +447289,9 @@
"20230503\t王伟叶"
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@ -489530,7 +489549,9 @@
"20230606\t王伟叶"
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@ -500467,7 +500488,9 @@
"20230705\t王伟叶"
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@ -590659,7 +590682,9 @@
"20230209\t王伟叶"
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@ -591194,7 +591219,9 @@
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@ -593499,7 +593526,9 @@
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@ -593888,7 +593917,9 @@
"010393",
"002000"
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@ -594591,7 +594622,9 @@
"20230209\t王伟叶"
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@ -595376,7 +595409,9 @@
"20230209\t王伟叶"
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@ -595546,7 +595581,9 @@
"20230209\t王伟叶"
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@ -595602,7 +595639,9 @@
"20230209\t王伟叶"
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@ -663492,6 +663531,318 @@
"space": "4em",
"unrelated": []
},
"024501": {
"id": "024501",
"content": "若非零向量 $\\overrightarrow{a}, \\overrightarrow{b}$ 满足 $|\\overrightarrow{a}+\\overrightarrow{b}|=|\\overrightarrow{a}-\\overrightarrow{b}|$, 则 $\\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 所成角的大小为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"016139"
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"remark": "",
"space": "",
"unrelated": []
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"024502": {
"id": "024502",
"content": "已知 $|\\overrightarrow{a}|=|\\overrightarrow{b}|=2$, $\\overrightarrow{a}, \\overrightarrow{b}$ 的夹角为 $60^{\\circ}$, 则 $\\overrightarrow{a}+\\overrightarrow{b}$ 在 $\\overrightarrow{a}$ 方向上的投影为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
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"same": [],
"related": [
"021759",
"040696"
],
"remark": "",
"space": "",
"unrelated": []
},
"024503": {
"id": "024503",
"content": "如果 $\\overrightarrow{AP}=\\dfrac{1}{3}\\overrightarrow{PB}$, 且有 $\\overrightarrow{PB}=\\lambda \\overrightarrow{BA}$, 那么实数 $\\lambda$ 的值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"021743",
"000883"
],
"remark": "",
"space": "",
"unrelated": []
},
"024504": {
"id": "024504",
"content": "已知点 $A$ 的坐标为 $(3,-2)$, 点 $B$ 在 $y$ 轴上, 且 $|\\overrightarrow{AB}|=3 \\sqrt{2}$, 则 $\\overrightarrow{AB}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024505": {
"id": "024505",
"content": "已知 $z=m^2+2 m-15+\\dfrac{m^2-5 m+6}{m^2-25}\\mathrm{i}$.\\\\\n(1) 当且仅当实数 $m=$\\blank{50}时, $z$ 是实数;\\\\\n(2) 当且仅当实数 $m=$\\blank{50}时, $z$ 是纯虚数.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
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"related": [
"008980",
"021844",
"002000",
"010393"
],
"remark": "",
"space": "",
"unrelated": []
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"024506": {
"id": "024506",
"content": "已知关于 $x$ 的方程 $x^2+k x+3=0$($k \\in \\mathbf{R}$) 有两个虚根 $\\alpha$ 和 $\\beta$, 且 $|\\alpha-\\beta|=2 \\sqrt{2}$, 则 $k=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"20240204\t杨懿荔"
],
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"related": [
"009034",
"021892",
"021898"
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"remark": "",
"space": "",
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"024507": {
"id": "024507",
"content": "计算: (1) $\\mathrm{i}+\\mathrm{i}^2+\\mathrm{i}^3+\\cdots +\\mathrm{i}^{200}=$\\blank{50};\\\\\n(2) $(1+\\mathrm{i})^{10}-(1-\\mathrm{i})^{10}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"009011",
"021832"
],
"remark": "",
"space": "",
"unrelated": []
},
"024508": {
"id": "024508",
"content": "计算:\\\\\n(1) $|\\dfrac{(\\sqrt{5}-2 \\mathrm{i})(1+\\sqrt{3}\\mathrm{i})^2}{\\sqrt{13}+\\sqrt{23}\\mathrm{i}}|$\\\\\n(2) $(\\sqrt{3}+\\mathrm{i})^8$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"021866"
],
"remark": "",
"space": "4em",
"unrelated": []
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"024509": {
"id": "024509",
"content": "已知 $\\overrightarrow{a}=(2,-3)$, $\\overrightarrow{b}$ 满足 $\\overrightarrow{b}\\parallel \\overrightarrow{a}$, 且 $\\overrightarrow{a}\\cdot \\overrightarrow{b}=-28$, 则 $\\overrightarrow{b}$ 的坐标为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
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"024510": {
"id": "024510",
"content": "在直角坐标系中, 点 $A(-4,3)$ 为三角形 $\\triangle ABO$ 的直角顶点. 已知 $|\\overrightarrow{AB}|=2|\\overrightarrow{OA}|$, 且 $B$ 的纵坐标大于零, 则 $\\overrightarrow{AB}$ 的坐标是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
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"space": "",
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"024511": {
"id": "024511",
"content": "如图所示, 平面内有三个向量 $\\overrightarrow{OA}, \\overrightarrow{OB}, \\overrightarrow{OC}$, 其中 $\\overrightarrow{OA}, \\overrightarrow{OB}$ 的夹角为 $120^{\\circ}$, $\\overrightarrow{OA}, \\overrightarrow{OC}$ 的夹角为 $30^{\\circ}$, 且 $|\\overrightarrow{OA}|=|\\overrightarrow{OB}|=1$, $|\\overrightarrow{OC}|=2 \\sqrt{3}$, 若 $\\overrightarrow{OC}=\\lambda \\overrightarrow{OA}+\\mu \\overrightarrow{OB}$($\\lambda, \\mu \\in \\mathbf{R}$), 则 $\\lambda+\\mu=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (1,0) node [below] {$A$} coordinate (A);\n\\draw (120:1) node [left] {$B$} coordinate (B);\n\\draw (30:{2*sqrt(3)}) node [right] {$C$} coordinate (C);\n\\foreach \\i in {A,B,C}\n{\\draw [->] (O)--(\\i);};\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"018497",
"008578",
"030105"
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"024512": {
"id": "024512",
"content": "已知向量 $\\overrightarrow{OA}=(3,-4)$, $\\overrightarrow{OB}=(6,-3)$, $\\overrightarrow{OC}=(5-m,-4-m)$, 若 $\\triangle ABC$ 是直角三角形, 则数 $m$ 的值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"001916"
],
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"space": "",
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"024513": {
"id": "024513",
"content": "已知关于 $x$ 的方程 $x^2+k x+k^2-2 k=0$($k \\in \\mathbf{R}$) 有一个模为 $1$ 的根, 求 $k$ 的值.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
"related": [
"009036",
"018018",
"021900"
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"remark": "",
"space": "4em",
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"024514": {
"id": "024514",
"content": "如图所示, $PQ$ 过 $\\triangle ABC$ 的重心 $G$, 设 $\\overrightarrow{AB}=\\overrightarrow{a}$, $\\overrightarrow{AC}=\\overrightarrow{b}$, 若 $\\overrightarrow{AP}=m \\overrightarrow{a}$, $\\overrightarrow{AQ}=n \\overrightarrow{b}$, 求证: $\\dfrac{1}{m}+\\dfrac{1}{n}=3$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$B$} coordinate (B);\n\\draw (2,0) node [below] {$C$} coordinate (C);\n\\draw (1.2,2) node [above] {$A$} coordinate (A);\n\\draw ($1/3*(A)+1/3*(B)+1/3*(C)$) node [below right] {$G$} coordinate (G);\n\\draw (A)--(B)--(C)--cycle(A)--($(A)!{3/2}!(G)$) node [below] {$D$} coordinate (D);\n\\draw ($(A)!{3/4}!(B)$) node [left] {$P$} coordinate (P);\n\\draw ($(A)!{3/5}!(C)$) node [right] {$Q$} coordinate (Q);\n\\draw (P)--(Q);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240204\t杨懿荔"
],
"same": [],
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"remark": "",
"space": "4em",
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"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.",
@ -667469,7 +667820,8 @@
],
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@ -737922,7 +738274,9 @@
"same": [
"021759"
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"related": [
"024502"
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