20230224 noon

This commit is contained in:
WangWeiye 2023-02-24 13:06:59 +08:00
parent 82006b0f4e
commit ef9314ee46
6 changed files with 1211 additions and 548 deletions

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"cells": [ "cells": [
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 4,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {

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"cells": [ "cells": [
{ {
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"execution_count": 3, "execution_count": 4,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
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"题号: 012842 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t0.562\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: 012843 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t0.562\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: 014190 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t0.969\t0.531\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: 014191 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t0.906\t0.688\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: 012856 , 字段: usages 中已添加数据: 20230223\t2023届高三09班\t0.469\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"
] ]
} }
], ],

View File

@ -1,506 +1,542 @@
usages usages
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20230223 2023届高三10班 0.949 20230224 2023届高三10班 0.944
012835 012882
20230223 2023届高三10班 0.769 20230224 2023届高三10班 0.833
012836 012883
20230223 2023届高三10班 0.974 20230224 2023届高三10班 0.806
012837 012884
20230223 2023届高三10班 0.949 20230224 2023届高三10班 0.917
012857 012885
20230223 2023届高三10班 0.641 20230224 2023届高三10班 0.444
012858 012887
20230223 2023届高三10班 0.923 20230224 2023届高三10班 0.722
012859 012905
20230223 2023届高三10班 0.513 20230224 2023届高三10班 0.889
012839 012906
20230223 2023届高三10班 0.487 20230224 2023届高三10班 0.944
012841 012907
20230223 2023届高三10班 0.590 20230224 2023届高三10班 0.806
012842 012908
20230223 2023届高三10班 0.692 20230224 2023届高三10班 0.611
012843 012912
20230223 2023届高三10班 0.641 20230224 2023届高三10班 0.389
014190 012913
20230223 2023届高三10班 0.949 0.333 20230224 2023届高三10班 0.750
014191 012901
20230223 2023届高三10班 0.821 0.718 20230224 2023届高三10班 0.389
012856 012902
20230223 2023届高三10班 0.436 20230224 2023届高三10班 1.000 0.556
012834 012903
20230223 2023届高三11班 0.952 20230224 2023届高三10班 0.806 0.250
012835 012881
20230223 2023届高三11班 0.762 20230224 2023届高三11班 0.857
012836 012882
20230223 2023届高三11班 0.952 20230224 2023届高三11班 0.857
012837 012883
20230223 2023届高三11班 0.952 20230224 2023届高三11班 0.857
012857 012884
20230223 2023届高三11班 0.809 20230224 2023届高三11班 0.905
012858 012885
20230223 2023届高三11班 0.905 20230224 2023届高三11班 0.571
012859 012887
20230223 2023届高三11班 0.809 20230224 2023届高三11班 0.667
012839 012905
20230223 2023届高三11班 0.476 20230224 2023届高三11班 0.905
012841 012906
20230223 2023届高三11班 0.714 20230224 2023届高三11班 0.857
012842 012907
20230223 2023届高三11班 0.476 20230224 2023届高三11班 0.667
012843 012908
20230223 2023届高三11班 0.571 20230224 2023届高三11班 0.571
014190 012912
20230223 2023届高三11班 0.238 0.191 20230224 2023届高三11班 0.381
014191 012913
20230223 2023届高三11班 0.857 0.762 20230224 2023届高三11班 0.476
012856 012901
20230223 2023届高三11班 0.333 20230224 2023届高三11班 0.524
012834 012902
20230223 2023届高三12班 0.950 20230224 2023届高三11班 0.048 0.238
012835 012903
20230223 2023届高三12班 0.800 20230224 2023届高三11班 0.762 0.238
012836 012881
20230223 2023届高三12班 1.000 20230224 2023届高三12班 1.000
012837 012882
20230223 2023届高三12班 0.950 20230224 2023届高三12班 0.955
012857 012883
20230223 2023届高三12班 0.750 20230224 2023届高三12班 0.909
012858 012884
20230223 2023届高三12班 0.950 20230224 2023届高三12班 0.818
012859 012885
20230223 2023届高三12班 0.750 20230224 2023届高三12班 0.364
012839 012887
20230223 2023届高三12班 0.600 20230224 2023届高三12班 0.682
012841 012905
20230223 2023届高三12班 0.750 20230224 2023届高三12班 1.000
012842 012906
20230223 2023届高三12班 0.650 20230224 2023届高三12班 1.000
012843 012907
20230223 2023届高三12班 0.750 20230224 2023届高三12班 0.818
014190 012908
20230223 2023届高三12班 1.000 0.500 20230224 2023届高三12班 0.818
014191 012912
20230223 2023届高三12班 0.850 0.650 20230224 2023届高三12班 0.591
012856 012913
20230223 2023届高三12班 0.600 20230224 2023届高三12班 0.545
012834 012901
20230223 2023届高三01班 0.968 20230224 2023届高三12班 0.682
012835 012902
20230223 2023届高三01班 0.806 20230224 2023届高三12班 0.909 0.636
012836 012903
20230223 2023届高三01班 1.000 20230224 2023届高三12班 0.864 0.227
012837 012881
20230223 2023届高三01班 0.968 20230224 2023届高三01班 1.000
012857 012882
20230223 2023届高三01班 1.000 20230224 2023届高三01班 0.852
012858 012883
20230223 2023届高三01班 1.000 20230224 2023届高三01班 0.926
012859 012884
20230223 2023届高三01班 0.871 20230224 2023届高三01班 1.000
012839 012885
20230223 2023届高三01班 0.806 20230224 2023届高三01班 0.963
012841 012887
20230223 2023届高三01班 0.935 20230224 2023届高三01班 0.852
012842 012905
20230223 2023届高三01班 0.677 20230224 2023届高三01班 0.963
012843 012906
20230223 2023届高三01班 0.903 20230224 2023届高三01班 1.000
014190 012907
20230223 2023届高三01班 0.968 0.806 20230224 2023届高三01班 0.926
014191 012908
20230223 2023届高三01班 0.968 1.000 20230224 2023届高三01班 0.926
012856 012912
20230223 2023届高三01班 0.742 20230224 2023届高三01班 0.926
012834 012913
20230223 2023届高三02班 0.968 20230224 2023届高三01班 0.963
012835 012901
20230223 2023届高三02班 0.806 20230224 2023届高三01班 0.741
012836 012902
20230223 2023届高三02班 0.935 20230224 2023届高三01班 1.000 0.741
012837 012903
20230223 2023届高三02班 0.968 20230224 2023届高三01班 0.889 0.852
012857 012881
20230223 2023届高三02班 0.903 20230224 2023届高三02班 0.938
012858 012882
20230223 2023届高三02班 0.968 20230224 2023届高三02班 0.844
012859 012883
20230223 2023届高三02班 0.710 20230224 2023届高三02班 0.875
012839 012884
20230223 2023届高三02班 0.710 20230224 2023届高三02班 0.875
012841 012885
20230223 2023届高三02班 0.903 20230224 2023届高三02班 0.812
012842 012887
20230223 2023届高三02班 0.516 20230224 2023届高三02班 0.875
012843 012905
20230223 2023届高三02班 0.677 20230224 2023届高三02班 0.906
014190 012906
20230223 2023届高三02班 0.355 0.516 20230224 2023届高三02班 1.000
014191 012907
20230223 2023届高三02班 0.903 0.677 20230224 2023届高三02班 0.906
012856 012908
20230223 2023届高三02班 0.548 20230224 2023届高三02班 0.812
012834 012912
20230223 2023届高三03班 1.000 20230224 2023届高三02班 0.688
012835 012913
20230223 2023届高三03班 0.655 20230224 2023届高三02班 0.719
012836 012901
20230223 2023届高三03班 0.966 20230224 2023届高三02班 0.719
012837 012902
20230223 2023届高三03班 0.966 20230224 2023届高三02班 0.688 0.594
012857 012903
20230223 2023届高三03班 0.897 20230224 2023届高三02班 0.656 0.594
012858 012881
20230223 2023届高三03班 1.000 20230224 2023届高三03班 0.923
012859 012882
20230223 2023届高三03班 0.690 20230224 2023届高三03班 0.769
012839 012883
20230223 2023届高三03班 0.897 20230224 2023届高三03班 0.808
012841 012884
20230223 2023届高三03班 0.793 20230224 2023届高三03班 0.923
012842 012885
20230223 2023届高三03班 0.586 20230224 2023届高三03班 0.923
012843 012887
20230223 2023届高三03班 0.759 20230224 2023届高三03班 0.692
014190 012905
20230223 2023届高三03班 0.345 0.655 20230224 2023届高三03班 0.923
014191 012906
20230223 2023届高三03班 0.897 0.690 20230224 2023届高三03班 0.923
012856 012907
20230223 2023届高三03班 0.655 20230224 2023届高三03班 0.923
012834 012908
20230223 2023届高三04班 0.966 20230224 2023届高三03班 0.962
012835 012912
20230223 2023届高三04班 0.690 20230224 2023届高三03班 0.462
012836 012913
20230223 2023届高三04班 0.931 20230224 2023届高三03班 0.692
012837 012901
20230223 2023届高三04班 1.000 20230224 2023届高三03班 0.346
012857 012902
20230223 2023届高三04班 0.793 20230224 2023届高三03班 0.923 0.654
012858 012903
20230223 2023届高三04班 0.966 20230224 2023届高三03班 0.808 0.500
012859 012881
20230223 2023届高三04班 0.724 20230224 2023届高三04班 0.967
012839 012882
20230223 2023届高三04班 0.759 20230224 2023届高三04班 0.833
012841 012883
20230223 2023届高三04班 0.828 20230224 2023届高三04班 0.833
012842 012884
20230223 2023届高三04班 0.655 20230224 2023届高三04班 0.933
012843 012885
20230223 2023届高三04班 0.690 20230224 2023届高三04班 0.867
014190 012887
20230223 2023届高三04班 0.448 0.517 20230224 2023届高三04班 0.600
014191 012905
20230223 2023届高三04班 0.828 0.966 20230224 2023届高三04班 0.900
012856 012906
20230223 2023届高三04班 0.655 20230224 2023届高三04班 0.933
012834 012907
20230223 2023届高三05班 0.868 20230224 2023届高三04班 0.833
012835 012908
20230223 2023届高三05班 0.763 20230224 2023届高三04班 0.833
012836 012912
20230223 2023届高三05班 0.974 20230224 2023届高三04班 0.800
012837 012913
20230223 2023届高三05班 0.974 20230224 2023届高三04班 0.800
012857 012901
20230223 2023届高三05班 0.789 20230224 2023届高三04班 0.567
012858 012902
20230223 2023届高三05班 0.947 20230224 2023届高三04班 0.900 0.567
012859 012903
20230223 2023届高三05班 0.763 20230224 2023届高三04班 0.467 0.433
012839 012881
20230223 2023届高三05班 0.658 20230224 2023届高三05班 0.975
012841 012882
20230223 2023届高三05班 0.763 20230224 2023届高三05班 0.875
012842 012883
20230223 2023届高三05班 0.842 20230224 2023届高三05班 0.900
012843 012884
20230223 2023届高三05班 0.816 20230224 2023届高三05班 0.850
014190 012885
20230223 2023届高三05班 0.316 0.316 20230224 2023届高三05班 0.750
014191 012887
20230223 2023届高三05班 0.868 0.737 20230224 2023届高三05班 0.800
012856 012905
20230223 2023届高三05班 0.474 20230224 2023届高三05班 0.900
012834 012906
20230223 2023届高三06班 0.925 20230224 2023届高三05班 0.925
012835 012907
20230223 2023届高三06班 0.750 20230224 2023届高三05班 0.825
012836 012908
20230223 2023届高三06班 0.975 20230224 2023届高三05班 0.775
012837 012912
20230223 2023届高三06班 1.000 20230224 2023届高三05班 0.600
012857 012913
20230223 2023届高三06班 0.825 20230224 2023届高三05班 0.850
012858 012901
20230223 2023届高三06班 0.950 20230224 2023届高三05班 0.650
012859 012902
20230223 2023届高三06班 0.675 20230224 2023届高三05班 0.650 0.375
012839 012903
20230223 2023届高三06班 0.700 20230224 2023届高三05班 0.050 0.400
012841 012881
20230223 2023届高三06班 0.725 20230224 2023届高三06班 0.921
012842 012882
20230223 2023届高三06班 0.775 20230224 2023届高三06班 0.947
012843 012883
20230223 2023届高三06班 0.775 20230224 2023届高三06班 0.947
014190 012884
20230223 2023届高三06班 0.925 0.675 20230224 2023届高三06班 0.947
014191 012885
20230223 2023届高三06班 0.925 0.875 20230224 2023届高三06班 0.868
012856 012887
20230223 2023届高三06班 0.650 20230224 2023届高三06班 0.737
012834 012905
20230223 2023届高三07班 0.939 20230224 2023届高三06班 0.974
012835 012906
20230223 2023届高三07班 0.697 20230224 2023届高三06班 0.974
012836 012907
20230223 2023届高三07班 0.909 20230224 2023届高三06班 0.816
012837 012908
20230223 2023届高三07班 0.909 20230224 2023届高三06班 0.868
012857 012912
20230223 2023届高三07班 0.758 20230224 2023届高三06班 0.684
012858 012913
20230223 2023届高三07班 0.849 20230224 2023届高三06班 0.868
012859 012901
20230223 2023届高三07班 0.879 20230224 2023届高三06班 0.737
012839 012902
20230223 2023届高三07班 0.576 20230224 2023届高三06班 0.921 0.579
012841 012903
20230223 2023届高三07班 0.515 20230224 2023届高三06班 0.895 0.737
012842 012881
20230223 2023届高三07班 0.697 20230224 2023届高三07班 0.938
012843 012882
20230223 2023届高三07班 0.697 20230224 2023届高三07班 0.750
014190 012883
20230223 2023届高三07班 0.242 0.364 20230224 2023届高三07班 0.656
014191 012884
20230223 2023届高三07班 0.879 0.788 20230224 2023届高三07班 0.750
012856 012885
20230223 2023届高三07班 0.545 20230224 2023届高三07班 0.375
012834 012887
20230223 2023届高三08班 0.900 20230224 2023届高三07班 0.625
012835 012905
20230223 2023届高三08班 0.733 20230224 2023届高三07班 0.969
012836 012906
20230223 2023届高三08班 1.000 20230224 2023届高三07班 0.969
012837 012907
20230223 2023届高三08班 1.000 20230224 2023届高三07班 0.719
012857 012908
20230223 2023届高三08班 0.967 20230224 2023届高三07班 0.469
012858 012912
20230223 2023届高三08班 0.933 20230224 2023届高三07班 0.531
012859 012913
20230223 2023届高三08班 0.833 20230224 2023届高三07班 0.719
012839 012901
20230223 2023届高三08班 0.833 20230224 2023届高三07班 0.344
012841 012902
20230223 2023届高三08班 0.833 20230224 2023届高三07班 0.906 0.438
012842 012903
20230223 2023届高三08班 0.600 20230224 2023届高三07班 0.594 0.344
012843 012881
20230223 2023届高三08班 0.467 20230224 2023届高三08班 0.966
014190 012882
20230223 2023届高三08班 0.433 0.600 20230224 2023届高三08班 0.966
014191 012883
20230223 2023届高三08班 0.933 0.933 20230224 2023届高三08班 0.862
012856 012884
20230223 2023届高三08班 0.700 20230224 2023届高三08班 0.862
012834 012885
20230223 2023届高三09班 1.000 20230224 2023届高三08班 0.828
012835 012887
20230223 2023届高三09班 0.656 20230224 2023届高三08班 1.000
012836 012905
20230223 2023届高三09班 0.938 20230224 2023届高三08班 0.931
012837 012906
20230223 2023届高三09班 0.906 20230224 2023届高三08班 1.000
012857 012907
20230223 2023届高三09班 0.719 20230224 2023届高三08班 0.724
012858 012908
20230223 2023届高三09班 0.875 20230224 2023届高三08班 0.724
012859 012912
20230223 2023届高三09班 0.844 20230224 2023届高三08班 0.621
012839 012913
20230223 2023届高三09班 0.531 20230224 2023届高三08班 0.793
012841 012901
20230223 2023届高三09班 0.688 20230224 2023届高三08班 0.414
012842 012902
20230223 2023届高三09班 0.562 20230224 2023届高三08班 0.931 0.690
012843 012903
20230223 2023届高三09班 0.562 20230224 2023届高三08班 0.724 0.414
014190 012881
20230223 2023届高三09班 0.969 0.531 20230224 2023届高三09班 0.935
014191 012882
20230223 2023届高三09班 0.906 0.688 20230224 2023届高三09班 0.968
012856 012883
20230223 2023届高三09班 0.469 20230224 2023届高三09班 0.677
012884
20230224 2023届高三09班 0.839
012885
20230224 2023届高三09班 0.419
012887
20230224 2023届高三09班 0.645
012905
20230224 2023届高三09班 0.935
012906
20230224 2023届高三09班 0.968
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20230224 2023届高三09班 0.645
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"20230224\t2023届高三01班\t0.926",
"20230224\t2023届高三02班\t0.812",
"20230224\t2023届高三03班\t0.962",
"20230224\t2023届高三04班\t0.833",
"20230224\t2023届高三05班\t0.775",
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"20230224\t2023届高三08班\t0.724",
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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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"031249": {
"id": "031249",
"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": {
"id": "031250",
"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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"031251": {
"id": "031251",
"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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"031252": {
"id": "031252",
"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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"031253": {
"id": "031253",
"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": {
"id": "031254",
"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": {
"id": "031256",
"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": {
"id": "031259",
"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": { "040001": {
"id": "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}", "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}",