录入2024届高三124分守护卷4题目
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"space": "4em",
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"unrelated": []
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"022840": {
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"id": "022840",
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"content": "已知集合 $A=\\{x | x-1 \\geq 0\\}$, $B=\\{0,1,2\\}$, 则 $A \\cap B=$\\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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022841": {
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"id": "022841",
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"content": "在单位圆中, $60^{\\circ}$ 的圆心角所对的弧长为\\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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022842": {
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"id": "022842",
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"content": "若直线 $l_1$ 和 $l_2$ 的倾斜角分别为 $32^{\\circ}$ 和 $152^{\\circ}$, 则 $l_1$ 与 $l_2$ 的夹角为\\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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022843": {
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"id": "022843",
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"content": "若直线 $l$ 的一个法向量为 $\\overrightarrow{n}=(2,1)$, 则直线 $l$ 的斜率 $k=$\\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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022844": {
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"id": "022844",
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"content": "设某种细胞每隔一小时就会分裂一次, 每个细胞分裂为两个细胞. 则 $7$ 小时后, $1$ 个此种细胞将分裂为\\blank{50}个.",
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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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022845": {
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"id": "022845",
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"content": "设 $\\triangle ABC$ 是等腰直角三角形, 斜边 $AB=2$. 现将 $\\triangle ABC$ (及其内部)绕斜边 $AB$ 所在的直线旋转一周形成一个旋转体, 则该旋转体的体积为\\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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022846": {
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"id": "022846",
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"content": "如图, 在平行四边形 $ABCD$ 中, $AB=2$, $AD=1$, 则 $\\overrightarrow{AC}\\cdot \\overrightarrow{BD}$ 的值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$A$} coordinate (A);\n\\draw (2,0) node [below] {$B$} coordinate (B);\n\\draw (B) ++ (60:1) node [above] {$C$} coordinate (C);\n\\draw (A) ++ (60:1) node [above] {$D$} coordinate (D);\n\\draw (A)--(B)--(C)--(D)--cycle(A)--(C)(B)--(D);\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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022847": {
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"id": "022847",
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"content": "若双曲线的一个顶点坐标为 $(3,0)$, 焦距为 10 , 则它的标准方程是\\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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022848": {
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"id": "022848",
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"content": "在无穷等比数列 $\\{a_n\\}$ 中, 若 $\\displaystyle\\lim _{n \\to +\\infty}(a_1+a_2+\\cdots+a_n)=\\dfrac{1}{3}$,则 $a_1$ 的取值范围是\\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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022849": {
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"id": "022849",
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"content": "函数 $y=\\dfrac{a x+b}{c x+d}$ 的大致图像如图, 若函数图像经过 $(0,-1)$ 和 $(-4,3)$ 两点, 且 $x=-1$ 和 $y=2$ 是其两条渐近线, 则 $a: b: c: d=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.3]\n\\draw [->] (-8,0) -- (8,0) node [below] {$x$};\n\\draw [->] (0,-8) -- (0,8) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -8:{-3/2},samples = 100] plot (\\x,{2-3/(\\x+1)});\n\\draw [domain = {-7/10}:8,samples = 100] plot (\\x,{2-3/(\\x+1)});\n\\draw [dashed] (-1,-8) -- (-1,8) (-8,2) -- (8,2);\n\\draw (-1,0) node [below left] {$-1$};\n\\draw (0,2) node [above right] {$2$};\n\\filldraw (-1,2) circle (0.1);\n\\filldraw (0,-1) circle (0.1) node [below right] {$(-1,0)$};\n\\filldraw (-4,3) circle (0.1) node [above left] {$(-4,3)$};\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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"20231124\t毛培菁"
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022850": {
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"id": "022850",
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"content": "设双曲线 $\\dfrac{x^2}{a^2}-\\dfrac{y^2}{a+1}=1$ 的两个焦点为 $F_1$、$F_2$, 点 $P$\n在双曲线上, 若 $PF_1 \\perp PF_2$, 则点 $P$ 到坐标原点 $O$ 的距离的最小值为\\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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"20231124\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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"022851": {
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"id": "022851",
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"content": "设 $a, b, c \\in \\mathbf{R}$, 则``$a, b, c$ 构成等差数列''是``$2 b=a+c$''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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"20231124\t毛培菁"
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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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"022852": {
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"id": "022852",
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"content": "设 $x, y \\in \\mathbf{R}$, 若复数 $\\dfrac{x+\\mathrm{i}}{y-\\mathrm{i}}$ 是纯虚数, 则点 $P(x, y)$ 一定满足\\bracket{20}.\n\\fourch{$y=x$}{$y=\\dfrac{1}{x}$}{$y=-x$}{$y=-\\dfrac{1}{x}$}",
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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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"remark": "",
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"space": "",
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"unrelated": []
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},
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"022853": {
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"id": "022853",
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"content": "若展开 $(a+1)(a+2)(a+3)(a+4)(a+5)$, 则展开式中 $a^3$ 的系数等于\\bracket{20} .\n\\onech{在 $1,2,3,4,5$ 中所有任取两个不同的数的乘积之和}{在 $1,2,3,4,5$ 中所有任取三个不同的数的乘积之和}{在 $1,2,3,4,5$ 中所有任取四个不同的数的乘积之和}{以上结论都不对}",
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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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"20231124\t毛培菁"
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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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"022854": {
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"id": "022854",
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"content": "如图, 在正六棱锥 $P-ABCDEF$ 中, 已知底边长为 $2$, 侧棱与底面所成角为 $60^{\\circ}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw ({-sqrt(3)},0,1) node [left] {$A$} coordinate (A);\n\\draw (0,0,2) node [below] {$B$} coordinate (B);\n\\draw ({sqrt(3)},0,1) node [right] {$C$} coordinate (C);\n\\draw ({sqrt(3)},0,-1) node [right] {$D$} coordinate (D);\n\\draw (0,0,-2) node [below] {$E$} coordinate (E);\n\\draw ({-sqrt(3)},0,-1) node [below] {$F$} coordinate (F);\n\\draw (0,{2*sqrt(3)},0) node [above] {$P$} coordinate (P);\n\\draw (A)--(B)--(C)--(D);\n\\foreach \\i in {A,B,C,D} {\\draw (P)--(\\i);};\n\\draw [dashed] (A)--(F)--(E)--(D);\n\\foreach \\i in {E,F} {\\draw [dashed] (P)--(\\i);};\n\\end{tikzpicture}\n\\end{center}\n(1) 求该六棱锥的体积 $V$;\\\\\n(2) 求证: $PA \\perp CE$.",
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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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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"022855": {
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"id": "022855",
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"content": "请解答以下问题:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) -- (2,0) arc (0:180:1);\n\\filldraw (1,0) circle (0.03) node [below] {$O$};\n\\draw (1.8,0) node [below] {$B$} -- (1.8,0.6) node [above right] {$C$} -- (0.2,0.6) node [above left] {$D$} -- (0.2,0) node [below] {$A$};\n\\draw (3,0) -- (7,0) arc (0:180:2 and 1);\n\\filldraw (5,0) circle (0.03) node [below] {$O$};\n\\draw (6.6,0) node [below] {$B$} -- (6.6,0.6) node [above right] {$C$} -- (3.4,0.6) node [above left] {$D$} -- (3.4,0) node [below] {$A$};\n\\end{tikzpicture}\n\\end{center}\n(1) 如左图, 要在一个半径为 $1$ 米的半圆形铁板中截取一块面积最大的矩形 $ABCD$, 如何截取? 并求出这个最大矩形的面积.\\\\\n(2) 如右图, 要在一个长半轴为 $2$ 米, 短半轴为 $1$ 米的半个椭圆形铁板中截取一块面积最大的矩形 $ABCD$, 如何截取? 并求出这个最大矩形的面积.",
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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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"20231124\t毛培菁"
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],
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"same": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"022856": {
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"id": "022856",
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"content": "设 $\\{a_n\\}$ 是等差数列, 公差为 $d$, 前 $n$ 项和为 $S_n$.\\\\\n(1) 设 $a_1=40$, $a_6=38$, 求 $S_n$ 的最大值;\\\\\n(2) 设 $a_1=1$, $b_n=2^{a_n}$($n \\in \\mathbf{N}$, $n \\geq 1$), 数列 $\\{b_n\\}$ 的前 $n$ 项和为 $T_n$. 且对任意的 $n \\in \\mathbf{N}$, $n \\geq 1$,都有 $T_n \\leq 20$, 求 $d$ 的取值范围.",
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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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],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"022857": {
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"id": "022857",
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"content": "已知抛物线 $\\Gamma$ 的准线方程为 $x+y+2=0$, 焦点为 $F(1,1)$.\\\\\n(1) 求证: 抛物线 $\\Gamma$ 上任意一点 $P$ 的坐标 $(x, y)$ 都满足方程 $x^2-2 x y+y^2-8 x-8 y=0$;\\\\\n(2) 请指出抛物线 $\\Gamma$ 的对称性和范围, 并运用以上方程证明你的结论.",
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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",
|
||||
"edit": [
|
||||
"20231124\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"022858": {
|
||||
"id": "022858",
|
||||
"content": "现定义: 设 $a$ 是非零实常数, 若对于任意的 $x \\in D$, 都有 $f(a-x)=f(a+x)$, 则称函数 $y=f(x)$ 为``关于 $a$ 的偶型函数''.\\\\\n(1) 请以三角函数为例, 写出一个``关于 2 的偶型函数''的解析式, 并给予证明;\\\\\n(2) 设定义域为 $\\mathbf{R}$ 的``关于 $a$ 的偶型函数''$y=f(x)$ 在区间 ($-\\infty, a$) 上严格增, 求证: $y=f(x)$ 在区间 ($a,+\\infty$) 上严格减.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高三上学期124分守护卷题目",
|
||||
"edit": [
|
||||
"20231124\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