录入2024届高三124分守护卷1题目
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"space": "",
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"unrelated": []
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},
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"022801": {
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"id": "022801",
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"content": "设全集 $U=\\mathbf{R}$, 若 $A=\\{x | \\dfrac{2 x-1}{x}>1\\}$, 则 $\\overline{A}=$\\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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\t毛培菁"
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],
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"same": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022802": {
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"id": "022802",
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"content": "若复数 $z=\\dfrac{3-\\mathrm{i}}{1+\\mathrm{i}}$ ($\\mathrm{i}$ 为虚数单位), 则 $|z|=$\\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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022803": {
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"id": "022803",
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"content": "设 $x>0$, 则 $x+\\dfrac{2}{x+1}$ 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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022804": {
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"id": "022804",
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"content": "若函数 $f(x)=\\sin ^2(\\omega x)$, $\\omega \\neq 0$ 的最小正周期为 $\\pi$, 则 $\\omega=$\\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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022805": {
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"id": "022805",
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"content": "设等差数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 若 $a_2+a_7=12$, $S_4=8$, 则 $a_n=$\\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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022806": {
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"id": "022806",
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"content": "抛物线 $x^2=6 y$ 的焦点到直线 $3 x+4 y-1=0$ 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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022807": {
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"id": "022807",
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"content": "设 $(2 x-1)(x-1)^6=a_0+a_1 x+a_2 x^2+\\cdots+a_7 x^7$, 则 $a_5=$\\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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022808": {
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"id": "022808",
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"content": "已知 $m, n$ 是平面 $\\alpha$ 外的两条不同直线. 给出三个论断: \\textcircled{1} $m \\perp n$; \\textcircled{2} $n \\parallel \\alpha$; \\textcircled{3} $m \\perp \\alpha$. 以其中两个论断作为条件, 余下的一个论断作为结论, 写出一个正确的命题 (论断用序号表示): \\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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022809": {
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"id": "022809",
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"content": "如图, $F_1$、$F_2$ 分别是双曲线 $C: \\dfrac{x^2}{a^2}-y^2=1$ 的左、右焦点, 过 $F_2$ 的直线与双曲线 $C$ 的两条渐近线分别交于 $A$、$B$ 两点, 若 $\\overrightarrow{F_2A}=\\overrightarrow{AB}$, $\\overrightarrow{F_1B}\\cdot \\overrightarrow{F_2B}=0$,则双曲线 $C$ 的焦距 $|F_1F_2|$ 为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw ({-2/sqrt(3)},2) -- ({2/sqrt(3)},-2) ({2/sqrt(3)},2) -- ({-2/sqrt(3)},-2);\n\\filldraw (-1,0) circle (0.03) node [below] {$F_1$} coordinate (F_1);\n\\filldraw (1,0) circle (0.03) node [below] {$F_2$} coordinate (F_2);\n\\draw (-0.5,{sqrt(3)/2}) node [above] {$B$} coordinate (B);\n\\draw (0.25,{sqrt(3)/4}) node [above] {$A$} coordinate (A);\n\\draw (F_1)--(B)--(F_2);\n\\draw [domain = -2:2] plot ({sqrt(1/4+\\x*\\x/3)},\\x);\n\\draw [domain = -2:2] plot ({-sqrt(1/4+\\x*\\x/3)},\\x);\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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022810": {
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"id": "022810",
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"content": "设 $x \\in \\mathbf{R}$, 则``$|x-1|<1$''是``$x^2<4$''的\\bracket{20} .\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}",
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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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022811": {
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"id": "022811",
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"content": "已知函数 $f(x)=\\sqrt{3}\\sin (2 x+\\theta)+\\cos (2 x+\\theta)$ 为偶函数, 且在 $[0, \\dfrac{\\pi}{2}]$ 上为增函数, 则 $\\theta$的一个值可以是\\bracket{20} .\n\\fourch{$\\dfrac{\\pi}{6}$}{$\\dfrac{\\pi}{3}$}{$\\dfrac{2 \\pi}{3}$}{$-\\dfrac{2 \\pi}{3}$}",
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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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022812": {
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"id": "022812",
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"content": "已知函数 $f(x)=|x+2|$, $g(x)=|x+t|$, 定义函数 $F(x)=\\begin{cases}f(x),& f(x) \\leq g(x),\\\\ g(x),& f(x)>g(x) .\\end{cases}$ 若对任意的 $x \\in \\mathbf{R}$, 都有 $F(x)=F(2-x)$ 成立, 则 $t$ 的取值为 \\bracket{20}.\n\\fourch{$-4$}{$-2$}{$0$}{$2$}",
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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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022813": {
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"id": "022813",
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"content": "在 $\\triangle ABC$ 中, $a=8$, $b=6$, $\\cos A=-\\dfrac{1}{3}$. 求:\\\\\n(1) 角 $B$;\\\\\n(2) $BC$ 边上的高.",
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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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022814": {
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"id": "022814",
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"content": "如图, 在圆柱 $OO_1$ 中, 它的轴截面 $ABB_1A_1$ 是一个边长为 $2$ 的正方形, 点 $C$ 为棱 $BB_1$ 的中点, 点 $C_1$ 为弧 $A_1B_1$ 的中点. 求:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A) -- (0,2) node [left] {$A_1$} coordinate (A_1) (2,0) node [right] {$B$} coordinate (B) -- (2,2) node [right] {$B_1$} coordinate (B_1);\n\\draw (1,2) ellipse (1 and 0.25);\n\\filldraw (1,2) circle (0.03) node [above] {$O_1$} coordinate (O_1);\n\\filldraw (1,0) circle (0.03) node [below] {$O$} coordinate (O);\n\\draw (A) arc (180:360:1 and 0.25);\n\\draw [dashed] (A) arc (180:0:1 and 0.25) (A) -- (B);\n\\draw ($(B)!0.5!(B_1)$) node [right] {$C$} coordinate (C);\n\\draw (O_1) ++ ({cos(-110)},{0.25*sin(-110)}) node [below] {$C_1$} coordinate (C_1);\n\\draw [dashed] (A_1)--(C_1)--(O)--cycle (A_1)--(C)--(O) (C_1)--(C);\n\\draw (A_1) -- (B_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 异面直线 $OC$ 与 $A_1C_1$ 所成角的大小;\\\\\n(2) 直线 $CC_1$ 与圆柱 $OO_1$ 底面所成角的大小;\\\\\n(3) 三棱锥 $C_1-OA_1C$ 的体积.",
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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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022815": {
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"id": "022815",
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"content": "已知椭圆 $\\Gamma: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$) 的长轴长为 $2 \\sqrt{2}$, 右顶点到左焦点的距离为 $\\sqrt{2}+1$, 直线 $l: y=k x+m$ 与椭圆 $\\Gamma$ 交于 $A$、$B$ 两点.\\\\\n(1) 求椭圆 $\\Gamma$ 的方程;\\\\\n(2) 若 $A$ 为椭圆的上顶点, $M$ 为 $AB$ 中点, $O$ 为坐标原点, 连接 $OM$ 并延长交椭圆 $\\Gamma$ 于 $N, \\overrightarrow{ON}=\\dfrac{\\sqrt{6}}{2}\\overrightarrow{OM}$, 求实数 $k$ 的值.",
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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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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"022816": {
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"id": "022816",
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"content": "对给定正有理数 $\\dfrac{m_i}{n_i}, \\dfrac{m_j}{n_j}(i \\neq j ; i$、$j$ 为正整数; $m_i$、$n_i$、$m_j$、$n_j$ 为正整数且 $m_i=m_j$ 和 $n_i=n_j$不同时成立), 按以下规则 $P$ 排列: \\textcircled{1} 若 $m_i+n_i<m_j+n_j$, 则 $\\dfrac{m_i}{n_i}$ 排在 $\\dfrac{m_j}{n_j}$ 的前面; \\textcircled{2} 若 $m_i+n_i=m_j+n_j$ 且 $n_i<n_j$, 则 $\\dfrac{m_i}{n_i}$ 排在 $\\dfrac{m_j}{n_j}$ 的前面, 按此规则排列得到数列 $\\{a_n\\}$, (例如 $\\dfrac{1}{1}, \\dfrac{2}{1}, \\dfrac{1}{2}, \\cdots)$.\\\\\n(1) 依次写出数列 $\\{a_n\\}$ 的前 10 项;\\\\\n(2) 对数列 $\\{a_n\\}$ 中小于 $1$ 的各项, 按以下规则 $Q$ 排列: \\textcircled{1} 各项不做化简运算; \\textcircled{2} 分母小的项排在前面; \\textcircled{3} 分母相同的两项, 分子小的项排在前面, 得到数列 $\\{b_n\\}$, 求数列 $\\{b_n\\}$ 的前 $10$ 项的和 $S_{10}$, 前 $2023$ 项的和 $S_{2023}$.",
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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": "2024届高三上学期124分守护卷题目",
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"edit": [
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"20231123\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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Reference in New Issue