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WangWeiye 2023-02-24 13:06:59 +08:00
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commit ef9314ee46
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2
工具/寻找阶段末尾空闲题号.ipynb
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"cells": [
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"outputs": [
{

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工具/批量添加题库字段数据.ipynb
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"cells": [
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.949\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.769\n",
"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.974\n",
"题号: 012837 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.949\n",
"题号: 012857 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.641\n",
"题号: 012858 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.923\n",
"题号: 012859 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.513\n",
"题号: 012839 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.487\n",
"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.590\n",
"题号: 012842 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.692\n",
"题号: 012843 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.641\n",
"题号: 014190 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.949\t0.333\n",
"题号: 014191 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.821\t0.718\n",
"题号: 012856 , 字段: usages 中已添加数据: 20230223\t2023届高三10班\t0.436\n",
"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三11班\t0.952\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三11班\t0.762\n",
"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三11班\t0.952\n",
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"题号: 012857 , 字段: usages 中已添加数据: 20230223\t2023届高三11班\t0.809\n",
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"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三12班\t0.950\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三12班\t0.800\n",
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"题号: 012839 , 字段: usages 中已添加数据: 20230223\t2023届高三12班\t0.600\n",
"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三12班\t0.750\n",
"题号: 012842 , 字段: usages 中已添加数据: 20230223\t2023届高三12班\t0.650\n",
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"题号: 012856 , 字段: usages 中已添加数据: 20230223\t2023届高三12班\t0.600\n",
"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t0.968\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t0.806\n",
"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t1.000\n",
"题号: 012837 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t0.968\n",
"题号: 012857 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t1.000\n",
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"题号: 012839 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t0.806\n",
"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t0.935\n",
"题号: 012842 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t0.677\n",
"题号: 012843 , 字段: usages 中已添加数据: 20230223\t2023届高三01班\t0.903\n",
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"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三02班\t0.806\n",
"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三02班\t0.935\n",
"题号: 012837 , 字段: usages 中已添加数据: 20230223\t2023届高三02班\t0.968\n",
"题号: 012857 , 字段: usages 中已添加数据: 20230223\t2023届高三02班\t0.903\n",
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"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三03班\t1.000\n",
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"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三03班\t0.966\n",
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"题号: 012857 , 字段: usages 中已添加数据: 20230223\t2023届高三03班\t0.897\n",
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"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三03班\t0.793\n",
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"题号: 012856 , 字段: usages 中已添加数据: 20230223\t2023届高三03班\t0.655\n",
"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三04班\t0.966\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三04班\t0.690\n",
"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三04班\t0.931\n",
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"题号: 012858 , 字段: usages 中已添加数据: 20230223\t2023届高三04班\t0.966\n",
"题号: 012859 , 字段: usages 中已添加数据: 20230223\t2023届高三04班\t0.724\n",
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"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三04班\t0.828\n",
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"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三05班\t0.763\n",
"题号: 012842 , 字段: usages 中已添加数据: 20230223\t2023届高三05班\t0.842\n",
"题号: 012843 , 字段: usages 中已添加数据: 20230223\t2023届高三05班\t0.816\n",
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"题号: 012856 , 字段: usages 中已添加数据: 20230223\t2023届高三05班\t0.474\n",
"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三06班\t0.925\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三06班\t0.750\n",
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"题号: 012857 , 字段: usages 中已添加数据: 20230223\t2023届高三06班\t0.825\n",
"题号: 012858 , 字段: usages 中已添加数据: 20230223\t2023届高三06班\t0.950\n",
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"题号: 012839 , 字段: usages 中已添加数据: 20230223\t2023届高三06班\t0.700\n",
"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三06班\t0.725\n",
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"题号: 014190 , 字段: usages 中已添加数据: 20230223\t2023届高三06班\t0.925\t0.675\n",
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"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三07班\t0.939\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三07班\t0.697\n",
"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三07班\t0.909\n",
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"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三07班\t0.515\n",
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"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三08班\t0.900\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三08班\t0.733\n",
"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三08班\t1.000\n",
"题号: 012837 , 字段: usages 中已添加数据: 20230223\t2023届高三08班\t1.000\n",
"题号: 012857 , 字段: usages 中已添加数据: 20230223\t2023届高三08班\t0.967\n",
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"题号: 012841 , 字段: usages 中已添加数据: 20230223\t2023届高三08班\t0.833\n",
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"题号: 014191 , 字段: usages 中已添加数据: 20230223\t2023届高三08班\t0.933\t0.933\n",
"题号: 012856 , 字段: usages 中已添加数据: 20230223\t2023届高三08班\t0.700\n",
"题号: 012834 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t1.000\n",
"题号: 012835 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t0.656\n",
"题号: 012836 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t0.938\n",
"题号: 012837 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t0.906\n",
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"题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t1.000\n",
"题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.931\n",
"题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t1.000\n",
"题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.724\n",
"题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.724\n",
"题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.621\n",
"题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.793\n",
"题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.414\n",
"题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.931\t0.690\n",
"题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.724\t0.414\n",
"题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.935\n",
"题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.968\n",
"题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.677\n",
"题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.839\n",
"题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.419\n",
"题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.645\n",
"题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.935\n",
"题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.968\n",
"题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.645\n",
"题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.677\n",
"题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.742\n",
"题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.806\n",
"题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.484\n",
"题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.871\t0.290\n",
"题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.903\t0.452\n"
]
}
],

708
工具/文本文件/metadata.txt
View File

@ -1,506 +1,542 @@
usages
012834
20230223 2023届高三10班 0.949
012881
20230224 2023届高三10班 0.944
012835
20230223 2023届高三10班 0.769
012882
20230224 2023届高三10班 0.833
012836
20230223 2023届高三10班 0.974
012883
20230224 2023届高三10班 0.806
012837
20230223 2023届高三10班 0.949
012884
20230224 2023届高三10班 0.917
012857
20230223 2023届高三10班 0.641
012885
20230224 2023届高三10班 0.444
012858
20230223 2023届高三10班 0.923
012887
20230224 2023届高三10班 0.722
012859
20230223 2023届高三10班 0.513
012905
20230224 2023届高三10班 0.889
012839
20230223 2023届高三10班 0.487
012906
20230224 2023届高三10班 0.944
012841
20230223 2023届高三10班 0.590
012907
20230224 2023届高三10班 0.806
012842
20230223 2023届高三10班 0.692
012908
20230224 2023届高三10班 0.611
012843
20230223 2023届高三10班 0.641
012912
20230224 2023届高三10班 0.389
014190
20230223 2023届高三10班 0.949 0.333
012913
20230224 2023届高三10班 0.750
014191
20230223 2023届高三10班 0.821 0.718
012901
20230224 2023届高三10班 0.389
012856
20230223 2023届高三10班 0.436
012902
20230224 2023届高三10班 1.000 0.556
012834
20230223 2023届高三11班 0.952
012903
20230224 2023届高三10班 0.806 0.250
012835
20230223 2023届高三11班 0.762
012881
20230224 2023届高三11班 0.857
012836
20230223 2023届高三11班 0.952
012882
20230224 2023届高三11班 0.857
012837
20230223 2023届高三11班 0.952
012883
20230224 2023届高三11班 0.857
012857
20230223 2023届高三11班 0.809
012884
20230224 2023届高三11班 0.905
012858
20230223 2023届高三11班 0.905
012885
20230224 2023届高三11班 0.571
012859
20230223 2023届高三11班 0.809
012887
20230224 2023届高三11班 0.667
012839
20230223 2023届高三11班 0.476
012905
20230224 2023届高三11班 0.905
012841
20230223 2023届高三11班 0.714
012906
20230224 2023届高三11班 0.857
012842
20230223 2023届高三11班 0.476
012907
20230224 2023届高三11班 0.667
012843
20230223 2023届高三11班 0.571
012908
20230224 2023届高三11班 0.571
014190
20230223 2023届高三11班 0.238 0.191
012912
20230224 2023届高三11班 0.381
014191
20230223 2023届高三11班 0.857 0.762
012913
20230224 2023届高三11班 0.476
012856
20230223 2023届高三11班 0.333
012901
20230224 2023届高三11班 0.524
012834
20230223 2023届高三12班 0.950
012902
20230224 2023届高三11班 0.048 0.238
012835
20230223 2023届高三12班 0.800
012903
20230224 2023届高三11班 0.762 0.238
012836
20230223 2023届高三12班 1.000
012881
20230224 2023届高三12班 1.000
012837
20230223 2023届高三12班 0.950
012882
20230224 2023届高三12班 0.955
012857
20230223 2023届高三12班 0.750
012883
20230224 2023届高三12班 0.909
012858
20230223 2023届高三12班 0.950
012884
20230224 2023届高三12班 0.818
012859
20230223 2023届高三12班 0.750
012885
20230224 2023届高三12班 0.364
012839
20230223 2023届高三12班 0.600
012887
20230224 2023届高三12班 0.682
012841
20230223 2023届高三12班 0.750
012905
20230224 2023届高三12班 1.000
012842
20230223 2023届高三12班 0.650
012906
20230224 2023届高三12班 1.000
012843
20230223 2023届高三12班 0.750
012907
20230224 2023届高三12班 0.818
014190
20230223 2023届高三12班 1.000 0.500
012908
20230224 2023届高三12班 0.818
014191
20230223 2023届高三12班 0.850 0.650
012912
20230224 2023届高三12班 0.591
012856
20230223 2023届高三12班 0.600
012913
20230224 2023届高三12班 0.545
012834
20230223 2023届高三01班 0.968
012901
20230224 2023届高三12班 0.682
012835
20230223 2023届高三01班 0.806
012902
20230224 2023届高三12班 0.909 0.636
012836
20230223 2023届高三01班 1.000
012903
20230224 2023届高三12班 0.864 0.227
012837
20230223 2023届高三01班 0.968
012881
20230224 2023届高三01班 1.000
012857
20230223 2023届高三01班 1.000
012882
20230224 2023届高三01班 0.852
012858
20230223 2023届高三01班 1.000
012883
20230224 2023届高三01班 0.926
012859
20230223 2023届高三01班 0.871
012884
20230224 2023届高三01班 1.000
012839
20230223 2023届高三01班 0.806
012885
20230224 2023届高三01班 0.963
012841
20230223 2023届高三01班 0.935
012887
20230224 2023届高三01班 0.852
012842
20230223 2023届高三01班 0.677
012905
20230224 2023届高三01班 0.963
012843
20230223 2023届高三01班 0.903
012906
20230224 2023届高三01班 1.000
014190
20230223 2023届高三01班 0.968 0.806
012907
20230224 2023届高三01班 0.926
014191
20230223 2023届高三01班 0.968 1.000
012908
20230224 2023届高三01班 0.926
012856
20230223 2023届高三01班 0.742
012912
20230224 2023届高三01班 0.926
012834
20230223 2023届高三02班 0.968
012913
20230224 2023届高三01班 0.963
012835
20230223 2023届高三02班 0.806
012901
20230224 2023届高三01班 0.741
012836
20230223 2023届高三02班 0.935
012902
20230224 2023届高三01班 1.000 0.741
012837
20230223 2023届高三02班 0.968
012903
20230224 2023届高三01班 0.889 0.852
012857
20230223 2023届高三02班 0.903
012881
20230224 2023届高三02班 0.938
012858
20230223 2023届高三02班 0.968
012882
20230224 2023届高三02班 0.844
012859
20230223 2023届高三02班 0.710
012883
20230224 2023届高三02班 0.875
012839
20230223 2023届高三02班 0.710
012884
20230224 2023届高三02班 0.875
012841
20230223 2023届高三02班 0.903
012885
20230224 2023届高三02班 0.812
012842
20230223 2023届高三02班 0.516
012887
20230224 2023届高三02班 0.875
012843
20230223 2023届高三02班 0.677
012905
20230224 2023届高三02班 0.906
014190
20230223 2023届高三02班 0.355 0.516
012906
20230224 2023届高三02班 1.000
014191
20230223 2023届高三02班 0.903 0.677
012907
20230224 2023届高三02班 0.906
012856
20230223 2023届高三02班 0.548
012908
20230224 2023届高三02班 0.812
012834
20230223 2023届高三03班 1.000
012912
20230224 2023届高三02班 0.688
012835
20230223 2023届高三03班 0.655
012913
20230224 2023届高三02班 0.719
012836
20230223 2023届高三03班 0.966
012901
20230224 2023届高三02班 0.719
012837
20230223 2023届高三03班 0.966
012902
20230224 2023届高三02班 0.688 0.594
012857
20230223 2023届高三03班 0.897
012903
20230224 2023届高三02班 0.656 0.594
012858
20230223 2023届高三03班 1.000
012881
20230224 2023届高三03班 0.923
012859
20230223 2023届高三03班 0.690
012882
20230224 2023届高三03班 0.769
012839
20230223 2023届高三03班 0.897
012883
20230224 2023届高三03班 0.808
012841
20230223 2023届高三03班 0.793
012884
20230224 2023届高三03班 0.923
012842
20230223 2023届高三03班 0.586
012885
20230224 2023届高三03班 0.923
012843
20230223 2023届高三03班 0.759
012887
20230224 2023届高三03班 0.692
014190
20230223 2023届高三03班 0.345 0.655
012905
20230224 2023届高三03班 0.923
014191
20230223 2023届高三03班 0.897 0.690
012906
20230224 2023届高三03班 0.923
012856
20230223 2023届高三03班 0.655
012907
20230224 2023届高三03班 0.923
012834
20230223 2023届高三04班 0.966
012908
20230224 2023届高三03班 0.962
012835
20230223 2023届高三04班 0.690
012912
20230224 2023届高三03班 0.462
012836
20230223 2023届高三04班 0.931
012913
20230224 2023届高三03班 0.692
012837
20230223 2023届高三04班 1.000
012901
20230224 2023届高三03班 0.346
012857
20230223 2023届高三04班 0.793
012902
20230224 2023届高三03班 0.923 0.654
012858
20230223 2023届高三04班 0.966
012903
20230224 2023届高三03班 0.808 0.500
012859
20230223 2023届高三04班 0.724
012881
20230224 2023届高三04班 0.967
012839
20230223 2023届高三04班 0.759
012882
20230224 2023届高三04班 0.833
012841
20230223 2023届高三04班 0.828
012883
20230224 2023届高三04班 0.833
012842
20230223 2023届高三04班 0.655
012884
20230224 2023届高三04班 0.933
012843
20230223 2023届高三04班 0.690
012885
20230224 2023届高三04班 0.867
014190
20230223 2023届高三04班 0.448 0.517
012887
20230224 2023届高三04班 0.600
014191
20230223 2023届高三04班 0.828 0.966
012905
20230224 2023届高三04班 0.900
012856
20230223 2023届高三04班 0.655
012906
20230224 2023届高三04班 0.933
012834
20230223 2023届高三05班 0.868
012907
20230224 2023届高三04班 0.833
012835
20230223 2023届高三05班 0.763
012908
20230224 2023届高三04班 0.833
012836
20230223 2023届高三05班 0.974
012912
20230224 2023届高三04班 0.800
012837
20230223 2023届高三05班 0.974
012913
20230224 2023届高三04班 0.800
012857
20230223 2023届高三05班 0.789
012901
20230224 2023届高三04班 0.567
012858
20230223 2023届高三05班 0.947
012902
20230224 2023届高三04班 0.900 0.567
012859
20230223 2023届高三05班 0.763
012903
20230224 2023届高三04班 0.467 0.433
012839
20230223 2023届高三05班 0.658
012881
20230224 2023届高三05班 0.975
012841
20230223 2023届高三05班 0.763
012882
20230224 2023届高三05班 0.875
012842
20230223 2023届高三05班 0.842
012883
20230224 2023届高三05班 0.900
012843
20230223 2023届高三05班 0.816
012884
20230224 2023届高三05班 0.850
014190
20230223 2023届高三05班 0.316 0.316
012885
20230224 2023届高三05班 0.750
014191
20230223 2023届高三05班 0.868 0.737
012887
20230224 2023届高三05班 0.800
012856
20230223 2023届高三05班 0.474
012905
20230224 2023届高三05班 0.900
012834
20230223 2023届高三06班 0.925
012906
20230224 2023届高三05班 0.925
012835
20230223 2023届高三06班 0.750
012907
20230224 2023届高三05班 0.825
012836
20230223 2023届高三06班 0.975
012908
20230224 2023届高三05班 0.775
012837
20230223 2023届高三06班 1.000
012912
20230224 2023届高三05班 0.600
012857
20230223 2023届高三06班 0.825
012913
20230224 2023届高三05班 0.850
012858
20230223 2023届高三06班 0.950
012901
20230224 2023届高三05班 0.650
012859
20230223 2023届高三06班 0.675
012902
20230224 2023届高三05班 0.650 0.375
012839
20230223 2023届高三06班 0.700
012903
20230224 2023届高三05班 0.050 0.400
012841
20230223 2023届高三06班 0.725
012881
20230224 2023届高三06班 0.921
012842
20230223 2023届高三06班 0.775
012882
20230224 2023届高三06班 0.947
012843
20230223 2023届高三06班 0.775
012883
20230224 2023届高三06班 0.947
014190
20230223 2023届高三06班 0.925 0.675
012884
20230224 2023届高三06班 0.947
014191
20230223 2023届高三06班 0.925 0.875
012885
20230224 2023届高三06班 0.868
012856
20230223 2023届高三06班 0.650
012887
20230224 2023届高三06班 0.737
012834
20230223 2023届高三07班 0.939
012905
20230224 2023届高三06班 0.974
012835
20230223 2023届高三07班 0.697
012906
20230224 2023届高三06班 0.974
012836
20230223 2023届高三07班 0.909
012907
20230224 2023届高三06班 0.816
012837
20230223 2023届高三07班 0.909
012908
20230224 2023届高三06班 0.868
012857
20230223 2023届高三07班 0.758
012912
20230224 2023届高三06班 0.684
012858
20230223 2023届高三07班 0.849
012913
20230224 2023届高三06班 0.868
012859
20230223 2023届高三07班 0.879
012901
20230224 2023届高三06班 0.737
012839
20230223 2023届高三07班 0.576
012902
20230224 2023届高三06班 0.921 0.579
012841
20230223 2023届高三07班 0.515
012903
20230224 2023届高三06班 0.895 0.737
012842
20230223 2023届高三07班 0.697
012881
20230224 2023届高三07班 0.938
012843
20230223 2023届高三07班 0.697
012882
20230224 2023届高三07班 0.750
014190
20230223 2023届高三07班 0.242 0.364
012883
20230224 2023届高三07班 0.656
014191
20230223 2023届高三07班 0.879 0.788
012884
20230224 2023届高三07班 0.750
012856
20230223 2023届高三07班 0.545
012885
20230224 2023届高三07班 0.375
012834
20230223 2023届高三08班 0.900
012887
20230224 2023届高三07班 0.625
012835
20230223 2023届高三08班 0.733
012905
20230224 2023届高三07班 0.969
012836
20230223 2023届高三08班 1.000
012906
20230224 2023届高三07班 0.969
012837
20230223 2023届高三08班 1.000
012907
20230224 2023届高三07班 0.719
012857
20230223 2023届高三08班 0.967
012908
20230224 2023届高三07班 0.469
012858
20230223 2023届高三08班 0.933
012912
20230224 2023届高三07班 0.531
012859
20230223 2023届高三08班 0.833
012913
20230224 2023届高三07班 0.719
012839
20230223 2023届高三08班 0.833
012901
20230224 2023届高三07班 0.344
012841
20230223 2023届高三08班 0.833
012902
20230224 2023届高三07班 0.906 0.438
012842
20230223 2023届高三08班 0.600
012903
20230224 2023届高三07班 0.594 0.344
012843
20230223 2023届高三08班 0.467
012881
20230224 2023届高三08班 0.966
014190
20230223 2023届高三08班 0.433 0.600
012882
20230224 2023届高三08班 0.966
014191
20230223 2023届高三08班 0.933 0.933
012883
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52
工具/添加题目到数据库.ipynb
View File

@ -7,11 +7,11 @@
"outputs": [],
"source": [
"#修改起始id,出处,文件名\n",
"starting_id = 40037\n",
"raworigin = \"2024届高二下学期周末卷02\"\n",
"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\zmj.tex\"\n",
"editor = \"20230223\\t王伟叶\"\n",
"indexed = False\n"
"starting_id = 31244\n",
"raworigin = \"2023年教育部命题四省联考\"\n",
"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\四省.tex\"\n",
"editor = \"20230224\\t王伟叶\"\n",
"indexed = True\n"
]
},
{
@ -23,26 +23,28 @@
"name": "stdout",
"output_type": "stream",
"text": [
"添加题号040037, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040038, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040039, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040040, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040041, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040042, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040043, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040044, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040045, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040046, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040047, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040048, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040049, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040050, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040051, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040052, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040053, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040054, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040055, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n",
"添加题号040056, 来源: 2024届高二下学期周末卷022024届高二下学期周末卷02\n"
"添加题号031244, 来源: 2023年教育部命题四省联考试题1\n",
"添加题号031245, 来源: 2023年教育部命题四省联考试题2\n",
"添加题号031246, 来源: 2023年教育部命题四省联考试题3\n",
"添加题号031247, 来源: 2023年教育部命题四省联考试题4\n",
"添加题号031248, 来源: 2023年教育部命题四省联考试题5\n",
"添加题号031249, 来源: 2023年教育部命题四省联考试题6\n",
"添加题号031250, 来源: 2023年教育部命题四省联考试题7\n",
"添加题号031251, 来源: 2023年教育部命题四省联考试题8\n",
"添加题号031252, 来源: 2023年教育部命题四省联考试题9\n",
"添加题号031253, 来源: 2023年教育部命题四省联考试题10\n",
"添加题号031254, 来源: 2023年教育部命题四省联考试题11\n",
"添加题号031255, 来源: 2023年教育部命题四省联考试题12\n",
"添加题号031256, 来源: 2023年教育部命题四省联考试题13\n",
"添加题号031257, 来源: 2023年教育部命题四省联考试题14\n",
"添加题号031258, 来源: 2023年教育部命题四省联考试题15\n",
"添加题号031259, 来源: 2023年教育部命题四省联考试题16\n",
"添加题号031260, 来源: 2023年教育部命题四省联考试题17\n",
"添加题号031261, 来源: 2023年教育部命题四省联考试题18\n",
"添加题号031262, 来源: 2023年教育部命题四省联考试题19\n",
"添加题号031263, 来源: 2023年教育部命题四省联考试题20\n",
"添加题号031264, 来源: 2023年教育部命题四省联考试题21\n",
"添加题号031265, 来源: 2023年教育部命题四省联考试题22\n"
]
}
],

4
文本处理工具/剪贴板文本整理_mathpix.ipynb
View File

@ -384,7 +384,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "mathdept",
"display_name": "pythontest",
"language": "python",
"name": "python3"
},
@ -403,7 +403,7 @@
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
}
}
},

643
题库0.3/Problems.json
View File

@ -318556,7 +318556,20 @@
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"20230118\t王伟叶"
@ -318577,7 +318590,20 @@
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@ -318640,7 +318692,20 @@
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"content": "设$z=1+\\mathrm{i}$, 则$z^2-\\mathrm{i}=$\\bracket{20}.\n\\fourch{$\\mathrm{i}$}{$-\\mathrm{i}$}{$1$}{$-1$}",
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"content": "设集合$A=\\{2,3, a^2-2 a-3\\}$, $B=\\{0,3\\}$, $C=\\{2, a\\}$. 若$B \\subseteq A$, $A \\cap C=\\{2\\}$, 则$a=$\\bracket{20}.\n\\fourch{$-3$}{$-1$}{$1$}{$3$}",
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"content": "甲、乙、丙、丁四名教师带领学生参加校园植树活动, 教师随机分成三组, 每组至少一人, 则甲、乙在同一组的概率为\\bracket{20}.\n\\fourch{$\\dfrac{1}{6}$}{$\\dfrac{1}{4}$}{$\\dfrac{1}{3}$}{$\\dfrac{1}{2}$}",
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"content": "平面向量$\\overrightarrow{a}$与$\\overrightarrow{b}$相互垂直, 已知$\\overrightarrow{a}=(6,-8)$, $|\\overrightarrow{b}|=5$, 且$\\overrightarrow{b}$与向量$(1,0)$的夹角是钝角, 则$\\overrightarrow{b}=$\\bracket{20}.\n\\fourch{$(-3,-4)$}{$(4,3)$}{$(-4,3)$}{$(-4,-3)$}",
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"content": "已知点$A, B, C$为椭圆$D$的三个顶点, 若$\\triangle ABC$是正三角形, 则$D$的离心率是\\bracket{20}.\n\\fourch{$\\dfrac{1}{2}$}{$\\dfrac{2}{3}$}{$\\dfrac{\\sqrt{6}}{3}$}{$\\dfrac{\\sqrt{3}}{2}$}",
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"content": "三棱锥$A-BCD$中, $AC \\perp$平面$BCD$, $BD \\perp CD$. 若$AB=3, BD=1$, 则该三棱锥体积的最大值为\\bracket{20}.\n\\fourch{$2$}{$\\dfrac{4}{3}$}{$1$}{$\\dfrac{2}{3}$}",
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"031250": {
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"content": "设函数$f(x), g(x)$在$\\mathbf{R}$的导函数存在, 且$f'(x)<g'(x)$, 则当$x \\in(a, b)$时\\bracket{20}.\n\\twoch{$f(x)<g(x)$}{$f(x)>g(x)$}{$f(x)+g(a)<g(x)+f(a)$}{$f(x)+g(b)<g(x)+f(b)$}",
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"content": "已知$a, b, c$满足$a=\\log _5(2^b+3^b), c=\\log _3(5^b-2^b)$, 则\\bracket{20}.\n\\twoch{$|a-c| \\geq|b-c|$, $|a-b| \\geq|b-c|$}{$|a-c| \\geq|b-c|$, $|a-b| \\leq|b-c|$}{$|a-c| \\leq|b-c|$, $|a-b| \\geq|b-c|$}{$|a-c| \\leq|b-c|$, $|a-b| \\leq|b-c|$}",
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"content": "已知$f(x)$是定义在$\\mathbf{R}$上的偶函数, $g(x)$是定义在$\\mathbf{R}$上的奇函数, 且$f(x), g(x)$在$(-\\infty, 0]$单调递减, 则以以下各结论中, 正确的有\\blank{50}.\\\\\n\\textcircled{1} $f(f(1))<f(f(2))$; \\textcircled{2} $f(g(1))<f(g(2))$; \\textcircled{3} $g(f(1))<g(f(2))$; \\textcircled{4} $g(g(1))<g(g(2))$.",
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"content": "已知平面$\\alpha \\cap$平面$\\beta=l$, $B, D$是$l$上两点, 直线$AB \\subset \\alpha$且$AB \\cap l=B$, 直线$CD \\subset \\beta$且$CD \\cap l=D$. 下列结论中, 错误的有\\blank{50}.\\\\\n\\textcircled{1} 若$AB \\perp l, CD \\perp l$, 且$AB=CD$, 则$ABCD$是平行四边形;\\\\\n\\textcircled{2} 若$M$是$AB$中点, $N$是$CD$中点, 则$MN\\parallel AC$;\\\\\n\\textcircled{3} 若$\\alpha \\perp \\beta, AB \\perp l, AC \\perp l$, 则$CD$在$\\alpha$上的射影是$BD$;\\\\\n\\textcircled{4} 直线$AB, CD$所成角的大小与二面角$\\alpha-l-\\beta$的大小相等.",
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"031254": {
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"content": "质点$P$和$Q$在以坐标原点$O$为圆心, 半径为$1$的$\\odot O$上逆时针作匀速圆周运动, 同时出发. $P$的角速度大小为$2 \\text{rad} / \\text{s}$, 起点为$\\odot O$与$x$轴正半轴的交点; $Q$的角速度大小为$5 \\text{rad} / \\text{s}$, 起点为射线$y=-\\sqrt{3} x$($x \\geq 0$)与$\\odot O$的交点. 则当$Q$与$P$重合时, 在以下各坐标中$Q$的坐标可以为\\blank{50}.\\\\\n\\textcircled{1} $(\\cos \\dfrac{2 \\pi}{9}, \\sin \\dfrac{2 \\pi}{9})$; \\textcircled{2} $(-\\cos \\dfrac{5 \\pi}{9},-\\sin \\dfrac{5 \\pi}{9})$; \\textcircled{3} $(\\cos \\dfrac{\\pi}{9},-\\sin \\dfrac{\\pi}{9})$; \\textcircled{4} $(-\\cos \\dfrac{\\pi}{9}, \\sin \\dfrac{\\pi}{9})$.",
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"031255": {
"id": "031255",
"content": "下图改编自李约瑟所著的《中国科学技术史》, 用于说明元代数学家郭守敬在编制《授时历》时所做的天文计算. 图中的$\\overset\\frown{AB}, \\overset\\frown{AC}, \\overset\\frown{BD}, \\overset\\frown{CD}$都是以$O$为圆心的圆弧, $CMNK$是为计算所做的矩形, 其中$M, N, K$分别在线段$OD, OB, OA$上, $MN \\perp OB$, $KN \\perp OB$. 记$\\alpha=\\angle AOB$, $\\beta=\\angle AOC$, $\\gamma=\\angle BOD$, $\\delta=\\angle COD$, 则下列各结论中正确的有\\blank{50}.\\\\\n\\textcircled{1} $\\sin \\beta=\\sin \\gamma \\cos \\delta$; \\textcircled{2} $\\cos \\beta=\\cos \\gamma \\cos \\delta$; \\textcircled{3} $\\sin \\alpha=\\dfrac{\\sin \\delta}{\\cos \\beta}$; \\textcircled{4} $\\cos \\alpha=\\dfrac{\\cos \\gamma \\cos \\delta}{\\cos \\beta}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 3]\n\\draw (0,0,0) node [left] {$O$} coordinate (O);\n\\draw ({sqrt(2)/2},0,{sqrt(2)/2}) node [below] {$A$} coordinate (A);\n\\draw ({sqrt(6)/4},{1/2},{sqrt(6)/4}) node [below right] {$C$} coordinate (C);\n\\draw ({sqrt(6)/4},0,{sqrt(6)/4}) node [above left] {$K$} coordinate (K);\n\\draw ({sqrt(6)/4},0,0) node [above right] {$N$} coordinate (N);\n\\draw ($(N)+(C)-(K)$) node [above] {$M$} coordinate (M);\n\\draw (1,0,0) node [right] {$B$} coordinate (B);\n\\draw ($(O)!{4/sqrt(10)}!(M)$) node [right] {$D$} coordinate (D);\n\\draw (O)--(A)(O)--(C)(O)--(D)(K)--(C)--(M);\n\\draw [dashed] (O)--(B)(M)--(N)--(K)(O)--++(0,1,0)(O)--++(0,0,1);\n\\draw [domain = 0:45] plot ({cos(\\x)},0,{sin(\\x)});\n\\draw [dashed, domain = 45:90] plot ({cos(\\x)},0,{sin(\\x)});\n\\draw [domain = 0:{acos(sqrt(6)/sqrt(10))}] plot ({cos(\\x)},{sin(\\x)},0);\n\\draw [dashed,domain = {acos(sqrt(6)/sqrt(10))}:90] plot ({cos(\\x)},{sin(\\x)},0);\n\\draw [dashed, domain = 0:90] plot (0,{cos(\\x)},{sin(\\x)});\n\\draw [domain = 0:30] plot ({sqrt(2)/2*cos(\\x)},{sin(\\x)},{sqrt(2)/2*cos(\\x)});\n\\draw [dashed, domain = 30:90] plot ({sqrt(2)/2*cos(\\x)},{sin(\\x)},{sqrt(2)/2*cos(\\x)});\n\\draw [domain = 0:{acos(sqrt(10)/4)}] plot ({sqrt(6)/sqrt(10)*cos(\\x)},{2/sqrt(10)*cos(\\x)},{sin(\\x)});\n\\draw [dashed, domain = {acos(sqrt(10)/4)}:90] plot ({sqrt(6)/sqrt(10)*cos(\\x)},{2/sqrt(10)*cos(\\x)},{sin(\\x)});\n\\end{tikzpicture}\n\\end{center}",
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"031256": {
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"content": "某工厂生产的产品的质量指标服从正态分布$N(100, \\sigma^2)$. 质量指标介于$99$至$101$之间''的产品为良品, 为使这种产品的良品率达到$95.45 \\%$, 则需调整生产工艺, 使得$\\sigma$至多为\\blank{50}. (若$X \\sim N(\\mu, \\sigma^2)$, 则$P\\{|X-\\mu|<2 \\sigma\\}=0.9545$)",
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"031257": {
"id": "031257",
"content": "若$P, Q$分别是抛物线$x^2=y$与圆$(x-3)^2+y^2=1$上的点, 则$|PQ|$的最小值为\\blank{50}.",
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"031258": {
"id": "031258",
"content": "数学家祖冲之曾给出圆周率$\\pi$的两个近似值: ``约率''$\\dfrac{22}{7}$与``密率''$\\dfrac{355}{113}$、它们可用``调日法''得到: 称小于$3.1415926$的近似值为弱率, 大于$3.1415927$的近似值为强率. 由$\\dfrac{3}{1}<\\pi<\\dfrac{4}{1}$, 取$3$为弱率, $4$为强率, 得$a_1=\\dfrac{3+4}{1+1}=\\dfrac{7}{2}$, 故$a_1$为强率, 与上一次的弱率$3$计算得$a_2=\\dfrac{3+7}{1+2}=\\dfrac{10}{3}$, 故$a_2$为强率, 继续计算, $\\cdots \\cdots$. 若某次得到的近似值为强率, 与上一次的弱率继续计算得到新的近似值; 若某次得到的近似值为弱率, 与上一次的强率继续计算得到新的近似值, 依此类推. 已知$a_m=\\dfrac{22}{7}$, 则$m=$\\blank{50}; $a_{8}=$\\blank{50}.",
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"031259": {
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"content": "如图为一个开关阵列, 每个开关只有``开''和``关''两种状态, 按其中一个开关$1$次, 将导致自身和所有相邻的开关改变状态. 例如, 按$(2,2)$将导致$(1,2),(2,1),(2,2),(2,3),(3,2)$改变状态. 如果要求只改变$(1,1)$的状态, 则需按开关的最少次数为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline$(1,1)$&$(1,2)$&$(1,3)$\\\\\n\\hline$(2,1)$&$(2,2)$&$(2,3)$\\\\\n\\hline$(3,1)$&$(3,2)$&$(3,3)$\\\\\n\\hline\n\\end{tabular}\n\\end{center}",
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"031260": {
"id": "031260",
"content": "如图, 四边形$ABCD$是圆柱底面的内接四边形, $AC$是圆柱的底面直径, $PC$是圆柱的母线, $E$是$AC$与$BD$的交点, $AB=AD$, $\\angle BAD=60^{\\circ}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-2,0) arc (180:360:2 and 0.5);\n\\draw [dashed] (-2,0) arc (180:0:2 and 0.5);\n\\draw (0,4) ellipse (2 and 0.5);\n\\draw (-2,0) -- (-2,4) (2,0) -- (2,4);\n\\draw (150:2 and 0.5) node [above] {$B$} coordinate (B);\n\\draw (30:2 and 0.5) node [below] {$D$} coordinate (D);\n\\draw (80:2 and 0.5) node [above right] {$C$} coordinate (C);\n\\draw (260:2 and 0.5) node [below] {$A$} coordinate (A);\n\\draw (C)++(0,4) node [above] {$P$} coordinate (P);\n\\draw ($(P)!0.25!(A)$) node [left] {$F$} coordinate (F);\n\\draw [dashed] (P)--(A)(P)--(B)(P)--(C)(P)--(D)(A)--(C)(B)--(D)(C)--(F)(D)--(F)(A)--(B)--(C)--(D)--cycle;\n\\path [name path = AC] (A)--(C);\n\\path [name path = BD] (B)--(D);\n\\path [name intersections = {of = AC and BD, by = E}];\n\\draw (E) node [below right] {$E$};\n\\end{tikzpicture}\n\\end{center}\n(1) 记圆柱的体积为$V_1$, 四棱锥$P-ABCD$的体积为$V_2$, 求$\\dfrac{V_1}{V_2}$;\\\\\n(2) 设点$F$在线段$AP$上, $PA=4PF$, $PC=4CE$, 求二面角$F-CD-P$的余弦值.",
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"031261": {
"id": "031261",
"content": "已知函数$f(x)=\\sin (\\omega x+\\varphi)$在区间$(\\dfrac{\\pi}{6}, \\dfrac{\\pi}{2})$单调, 其中$\\omega$为正整数, $|\\varphi|<\\dfrac{\\pi}{2}$, 且$f(\\dfrac{\\pi}{2})=f(\\dfrac{2 \\pi}{3})$.\\\\\n(1) 求$y=f(x)$图像的一条对称轴;\\\\\n(2) 若$f(\\dfrac{\\pi}{6})=\\dfrac{\\sqrt{3}}{2}$, 求$\\varphi$.",
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"origin": "2023年教育部命题四省联考试题18",
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"031262": {
"id": "031262",
"content": "记数列$\\{a_n\\}$的前$n$项和为$T_n$, 且$a_1=1$, $a_n=T_{n-1}$($n \\geq 2$).\\\\\n(1) 求数列$\\{a_n\\}$的通项公式:\\\\\n(2) 设$m$为整数, 且对任意$n \\in \\mathbf{N}$, $n \\ge 1$, $m \\geq \\dfrac{1}{a_1}+\\dfrac{2}{a_2}+\\cdots+\\dfrac{n}{a_n}$, 求$m$的最小值.",
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"origin": "2023年教育部命题四省联考试题19",
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"031263": {
"id": "031263",
"content": "一个池塘里的鱼的数目记为$N$, 从池塘里捞出$200$尾鱼, 并给鱼作上标识, 然后把鱼放回池塘里, 过一小段时间后再从池塘里拱出$500$尾鱼, $X$表示捞出的$500$尾鱼中有标识的鱼的数目.\\\\\n(1) 若$N=5000$, 求$X$的数学期望;\\\\\n(2) 已知捞出的$500$尾鱼中$15$尾有标识, 试给出$N$的估计值(以使得$P(X=15)$取大的$N$的值作为$N$的估计值).",
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"origin": "2023年教育部命题四省联考试题20",
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"031264": {
"id": "031264",
"content": "已知双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)过点$A(4 \\sqrt{2}, 3)$, 且焦距为$10$.\\\\\n(1) 求$C$的方程;\\\\\n(2) 已知点$B(4 \\sqrt{2},-3)$, $D(2 \\sqrt{2}, 0)$, $E$为线段$AB$上一点, 且直线$DE$交$C$于$G$, $H$两点. 证明: $\\dfrac{|GD|}{|GE|}=\\dfrac{|HD|}{|HE|}$.",
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"origin": "2023年教育部命题四省联考试题21",
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"031265": {
"id": "031265",
"content": "椭圆曲线加密算法运用于区块链.\\\\\n椭圆曲线$C=\\{(x, y) | y^2=x^3+a x+b,\\ 4 a^3+27 b^2 \\neq 0\\}$, $P \\in C$关于$x$轴的对称点记为 $\\tilde{C}$. $C$在点$P(x, y)$($y \\neq 0$)处的切线是指曲线$y=\\pm \\sqrt{x^3+a x+b}$在点$P$处的切线. 定义``$\\oplus$\" 运算满足:\\\\\n\\textcircled{1} 若$P \\in C$, $Q \\in C$, 且直线$PQ$与$C$有第三个交点$R$, 则$P \\oplus Q=\\tilde{R}$;\\\\\n\\textcircled{2} 若$P \\in C$, $Q \\in C$, 且$PQ$为$C$的切线, 切点为$P$, 则$P \\oplus Q=\\tilde{P}$;\\\\\n\\textcircled{3} 若$P \\in C$, 规定$P \\oplus \\tilde{P}=0^{\\circ}$, 且$P \\oplus 0^{\\circ}=0^{\\circ} \\oplus P=P$.\\\\\n(1) 当$4 a^3+27 b^2=0$时, 讨论函数$h(x)=x^3+a x+b$零点的个数;\\\\\n(2) 已知``$\\oplus$''运算满足交换律、结合律, 若$P \\in C$, $Q \\in C$, 且$PQ$为$C$的切线, 切点为$P$, 证明: $P \\oplus P=\\tilde{Q}$;\\\\(3) 已知$P(x_1, y_1) \\in C$, $Q(x_2, y_2) \\in C$, 且直线$PQ$与$C$有第三个交点, 求$P \\oplus Q$的坐标.",
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"origin": "2023年教育部命题四省联考试题22",
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"040001": {
"id": "040001",
"content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",