录入回忆版2024届春考试题
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"space": "4em",
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"unrelated": []
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},
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"023535": {
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"id": "023535",
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"content": "函数 $f(x)=\\log _2 x$ 的定义域为\\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届春季高考试题1",
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"edit": [
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"20240108\t王伟叶"
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023536": {
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"id": "023536",
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"content": "直线 $x-y+1=0$ 的倾斜角为\\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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"usages": [],
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"origin": "2024届春季高考试题2",
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"edit": [
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"20240108\t王伟叶"
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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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"023537": {
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"id": "023537",
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"content": "若复数 $z$ 满足 $\\dfrac{z}{1+\\mathrm{i}}=\\mathrm{i}$ ($\\mathrm{i}$ 为虚数单位), 则 $\\overline{z}=$\\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届春季高考试题3",
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"edit": [
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"20240108\t王伟叶"
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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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"023538": {
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"id": "023538",
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"content": "在 $(x-1)^6$ 的二项展开式中, $x^4$ 项的系数为\\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届春季高考试题4",
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"edit": [
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"20240108\t王伟叶"
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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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"023539": {
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"id": "023539",
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"content": "在 $\\triangle ABC$ 中, 若 $BC=2$, $\\angle A=45^{\\circ}$, $\\angle B=30^{\\circ}$, 则 $AC=$\\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届春季高考试题5",
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"edit": [
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"20240108\t王伟叶"
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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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"023540": {
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"id": "023540",
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"content": "在等差数列 $\\{a_n\\}$ 中, $a_n=n+c$, $S_n$ 是数列 $\\{a_n\\}$ 的前 $n$ 项和, 若 $S_7<0$, 则 $c$ 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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"usages": [],
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"origin": "2024届春季高考试题6",
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"edit": [
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"20240108\t王伟叶"
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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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"023541": {
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"id": "023541",
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"content": "已知实数 $a b=1$, 则 $4 a^2+9 b^2$ 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届春季高考试题7",
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"edit": [
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"20240108\t王伟叶"
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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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"023542": {
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"id": "023542",
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"content": "在 $\\triangle ABC$ 中, $AB=5$, $AC=7$, $BC=6$, 若以 $B$、$C$ 为焦点, 且过 $A$ 点的双曲线的离心率 $e=$\\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届春季高考试题8",
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"edit": [
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"20240108\t王伟叶"
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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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"023543": {
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"id": "023543",
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"content": "已知 $f(x)=x^2$, $g(x)=\\begin{cases}f(x),& x \\geq 0,\\\\-f(-x),& x<0,\\end{cases}$ 则 $g(x) \\leq 2-x$ 的解集为\\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届春季高考试题9",
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"edit": [
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"20240108\t王伟叶"
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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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"023544": {
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"id": "023544",
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"content": "在棱柱 $ABCD-A_1B_1C_1D_1$ 中, 底面 $ABCD$ 为平行四边形, $|AA_1|=3$, $|BD|=4$, 且 $\\overrightarrow{AB_1}\\cdot \\overrightarrow{BC}-\\overrightarrow{AD_1}\\cdot \\overrightarrow{DC}=5$, 则异面直线 $AA_1$ 与 $BD$ 的夹角为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\def\\l{4}\n\\def\\m{3}\n\\def\\n{3}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ ({\\l+0.4},0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0.4,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,-0.5) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\n,-0.5) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\n,-0.5) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\n,-0.5) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\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届春季高考试题10",
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"edit": [
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"20240108\t王伟叶"
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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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"023545": {
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"id": "023545",
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"content": "已知正方形展区 $ABCD$ 边长为 $1.2 \\mathrm{km}, E$ 距 $AB$、$AD$ 的距离都为 $0.2 \\mathrm{km}, F$ 距 $BC$、$CD$的距离都为 $0.4 \\mathrm{km}$, 若有一个圆形跑道经过 $E$、$F$ 两点, 且与 $AD$ 只有一个交点, 则圆形跑道的周长为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 2]\n\\draw (0,0) node [below left] {$A$} coordinate (A);\n\\draw (1.2,0) node [below right] {$B$} coordinate (B);\n\\draw (1.2,1.2) node [above right] {$C$} coordinate (C);\n\\draw (0,1.2) node [above left] {$D$} coordinate (D);\n\\draw (A)--(B)--(C)--(D)--cycle;\n\\filldraw (0.2,0.2) circle (0.015) node [right] {$E$} coordinate (E);\n\\filldraw (0.8,0.8) circle (0.015) node [right] {$F$} coordinate (F);\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届春季高考试题11",
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"edit": [
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"20240108\t王伟叶"
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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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"023546": {
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"id": "023546",
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"content": "已知 $a_1=2$, $a_2=4$, $a_3=8$, $a_4=16$, 若实数 $b_1$、$b_2$、$b_3$、$b_4$ 满足 $\\{a_i+a_j | 1 \\leq i<j \\leq 4\\}=\\{b_i+b_j | 1 \\leq i<j \\leq 4\\}$, 则有序数组 $(b_1, b_2, b_3, b_4)$ 有\\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届春季高考试题12",
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"edit": [
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"20240108\t王伟叶"
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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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"023547": {
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"id": "023547",
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"content": "已知 $a$、$b$、$c \\in \\mathbf{R}$, $b>c$, 则下列不等式恒成立的是\\bracket{20}.\n\\fourch{$a+b^2>a+c^2$}{$a^2+b>a^2+c$}{$a b^2>a c^2$}{$a^2 b>a^2 c$}",
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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届春季高考试题13",
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"edit": [
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"20240108\t王伟叶"
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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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"023548": {
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"id": "023548",
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"content": "空间中有两个不同的平面 $\\alpha$、$\\beta$, 两条不同的直线 $m$、$n$, 则下列说法正确的是\\bracket{20}.\n\\twoch{若 $\\alpha \\perp \\beta$, $m \\perp \\alpha$, $n \\perp \\beta$, 则 $m \\perp n$}{若 $\\alpha \\perp \\beta$, $m \\perp \\alpha$, $m \\perp n$, 则 $n \\perp \\beta$}{若 $\\alpha \\parallel \\beta$, $m \\parallel \\alpha$, $n \\parallel \\beta$, 则 $m \\parallel n$}{若 $\\alpha \\parallel \\beta$, $m \\parallel \\alpha$, $m \\parallel n$, 则 $n \\parallel \\beta$}",
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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届春季高考试题14",
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"edit": [
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"20240108\t王伟叶"
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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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"023549": {
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"id": "023549",
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"content": "有四个礼品盒. 已知前三个礼品盒中分别只装了一支钢笔、一本书以及一个笔袋, 第四个盒子中钢笔、书、笔袋都有. 现随机抽取一个盒子, 事件 $A$ 为抽中的盒子里面有钢笔, 事件 $B$ 为抽中的盒子里面有书, 事件 $C$ 为抽中的盒子里面有笔袋. 则下面正确的选项是 \\bracket{20}.\n\\fourch{$A$ 与 $B$ 互斥}{$A$ 与 $B$ 相互独立}{$A$ 与 $B \\cup C$ 互斥}{$A$ 与 $B \\cap C$ 独立}",
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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届春季高考试题15",
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"edit": [
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"20240108\t王伟叶"
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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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"023550": {
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"id": "023550",
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"content": "若函数 $y=f(x)$, $x \\in(n, n+1)$, $n \\in \\mathbf{N}$ 满足 $f(x+1)=f'(x)$, 则称函数 $y=f(x)$ 为延展函数. 已知延展函数 $y=g(x)$ 和函数 $y=h(x)$, 满足当 $x \\in(0,1)$ 时, $g(x)=\\mathrm{e}^x$, $h(x)=x^{10}$. 给定以下两个命题:\\\\\n\\textcircled{1} 存在直线 $y=k x+b$($k$、$b \\in \\mathbf{R}$, $k \\neq 0$) 与 $y=g(x)$ 的图像有无穷多个公共点;\\\\\n\\textcircled{2} 存在直线 $y=k x+b$($k$、$b \\in \\mathbf{R}$, $k \\neq 0$) 与 $y=h(x)$ 的图像有无穷多个公共点. \n则正确的选项是\\bracket{20}.\n\\twoch{\\textcircled{1}是真命题, \\textcircled{2}是真命题}{\\textcircled{1}是假命题, \\textcircled{2}是假命题}{\\textcircled{1}是真命题, \\textcircled{2}是假命题}{\\textcircled{1}是假命题, \\textcircled{2}是真命题}",
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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届春季高考试题16",
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"edit": [
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"20240108\t王伟叶"
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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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"023551": {
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"id": "023551",
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"content": "已知 $f(x)=\\sin (\\omega x+\\dfrac{\\pi}{3})$, $\\omega>0$.\\\\\n(1) 若 $\\omega=1$, 当 $x \\in[0, \\pi]$ 时, 求 $y=f(x)$ 的值域;\\\\\n(2) 已知 $a>\\pi$($a \\in \\mathbf{R}$), 且 $f(x)$ 的最小正周期为 $\\pi$, 若 $f(x)$ 在 $x \\in[\\pi, a]$ 上有三个零点, 求 $a$ 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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"origin": "2024届春季高考试题17",
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"edit": [
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"20240108\t王伟叶"
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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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"023552": {
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"id": "023552",
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"content": "如图, $PA$、$PB$、$PC$ 为圆锥的三条母线, 且 $AB=AC$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.5]\n\\draw (1,0) node [right] {$A$} coordinate (A);\n\\draw (0,{sqrt(2)}) node [above] {$P$} coordinate (P);\n\\draw (A) arc (0:-180:1 and 0.25) -- (P) --cycle;\n\\draw [dashed] (A) arc (0:180:1 and 0.25);\n\\draw (-110:1 and 0.25) node [below] {$B$} coordinate (B);\n\\draw (70:1 and 0.25) node [above right] {$C$} coordinate (C);\n\\draw (P)--(B);\n\\draw [dashed] (P)--(C)(A)--(B)--(C)--cycle;\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $PA \\perp BC$;\\\\\n(2) 若圆锥的侧面积为 $\\sqrt{3}\\pi$, $BC$ 为底面直径, $BC=2$, 求二面角 $B-PA-C$ 的大小.",
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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": "",
|
||||
"duration": -1,
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||||
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"origin": "2024届春季高考试题18",
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"20240108\t王伟叶"
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||||
"remark": "",
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||||
"space": "4em",
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||||
"unrelated": []
|
||||
},
|
||||
"023553": {
|
||||
"id": "023553",
|
||||
"content": "共有 $136$ 箱水果, 其中一级果 $102$ 箱, 二级果 $34$ 箱.\\\\\n(1) 从中随机挑出两箱水果, 则一级果、二级果各一箱的概率;\\\\\n(2) 按分层抽样抽出 $8$ 箱水果, 求一级果、二级果各几箱;\\\\\n(3) 抽出若干箱水果, 其中, 一级果 $120$ 个, 单果的平均质量为 $303.45$ 克, 方差为 $603.46$; 二级果 $48$ 个, 单果的平均质量为 $204.4$ 克, 方差为 $648.21$; 求 $168$ 个水果的平均数与方差, 并预估果园中水果的单果质量.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
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||||
"duration": -1,
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||||
"usages": [],
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||||
"origin": "2024届春季高考试题19",
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||||
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||||
"20240108\t王伟叶"
|
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||||
"remark": "",
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||||
"space": "4em",
|
||||
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|
||||
},
|
||||
"023554": {
|
||||
"id": "023554",
|
||||
"content": "在平面直角坐标系 $x O y$ 中, 已知点 $A$ 为椭圆 $\\Gamma: \\dfrac{x^2}{6}+\\dfrac{y^2}{2}=1$ 上一点, $F_1$、$F_2$ 分别为椭圆的左、右焦点.\\\\\n(1) 若点 $A$ 的横坐标为 $2$, 求 $|AF_1|$ 的长;\\\\\n(2) 设 $\\Gamma$ 的上、下顶点分别为 $M_1$、$M_2$, 记 $\\triangle AF_1F_2$ 的面积为 $S_1, \\triangle AM_1M_2$ 的面积为 $S_2$,若 $S_1 \\geq S_2$, 求 $|OA|$ 的取值范围;\\\\\n(3) 在 $x$ 轴上方, 设直线 $AF_2$ 与 $\\Gamma$ 交于点 $B$, 与 $y$ 轴交于点 $K, KF_1$ 延长线与 $\\Gamma$ 交于点 $C$,在 $x$ 轴上方是否存在点 $C$, 使得 $\\overrightarrow{F_1A}+\\overrightarrow{F_1B}+\\overrightarrow{F_1C}=\\lambda(\\overrightarrow{F_2A}+\\overrightarrow{F_2B}+\\overrightarrow{F_2C})$($\\lambda \\in \\mathbf{R}$) 成立?若存在, 请求出点 $C$ 的坐标; 若不存在, 请说明理由.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
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"origin": "2024届春季高考试题20",
|
||||
"edit": [
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||||
"20240108\t王伟叶"
|
||||
],
|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"023555": {
|
||||
"id": "023555",
|
||||
"content": "对于定义在 $\\mathbf{R}$ 上的函数 $f(x)$, 记集合 $M_a=\\{t | t=f(x)-f(a), x \\geq a\\}$, $L_a=\\{t | t=f(x)-f(a), x \\leq a\\}$.\\\\\n(1) 若 $f(x)=x^2+1$, 求 $M_1$ 和 $L_1$;\\\\\n(2) 若 $f(x)=x^3-3 x^2$, 求证: 对任意 $a \\in \\mathbf{R}$, 都有 $M_a \\subseteq[-4,+\\infty)$, 且存在 $a$,使得 $-4 \\in M_a$ ; \\\\\n(3) 已知定义在 $\\mathbf{R}$ 上的函数 $f(x)$ 有最小值. 证明:``$f(x)$ 是偶函数''是``对任意 $c>0$, 都有 $M_{-c}=L_c$''的充要条件.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届春季高考试题21",
|
||||
"edit": [
|
||||
"20240108\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
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|
||||
"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.",
|
||||
|
|
|
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Reference in New Issue