20221208 evening

This commit is contained in:
WangWeiye 2022-12-08 17:24:17 +08:00
parent 2f7b445a70
commit cf283c8a18
4 changed files with 1109 additions and 149 deletions

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@ -2,7 +2,7 @@
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@ -92,7 +92,7 @@
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@ -106,12 +106,12 @@
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@ -2,45 +2,134 @@
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"题号: 003400 , 字段: ans 中已修改数据: $(4,5)$\n",
"题号: 002329 , 字段: ans 中已修改数据: $\\dfrac{y^2}{25}+\\dfrac{x^2}{16}=1$或$\\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$\n",
"题号: 008873 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}{100}+\\dfrac{y^2}{64}=1$; (2) $\\dfrac{x^2}{6}+\\dfrac{y^2}{4}=1$; (3) $\\dfrac{x^2}8+\\dfrac{y^2}4=1$或$\\dfrac{y^2}8+\\dfrac{x^2}4=1$\n",
"题号: 002342 , 字段: ans 中已修改数据: $\\sqrt{3}-1$\n",
"题号: 010673 , 字段: ans 中已修改数据: $\\dfrac{x^2}{5.9^2}+\\dfrac{y^2}{5.8^2}=1$(以$1\\times 10^8\\text{km}$为单位)\n",
"题号: 002325 , 字段: ans 中已修改数据: $2x+4y-3=0$\n",
"题号: 004717 , 字段: ans 中已修改数据: B\n",
"题号: 002348 , 字段: ans 中已修改数据: $(-\\sqrt{5},0)$或$(\\sqrt{5},0)$\n",
"题号: 009985 , 字段: ans 中已修改数据: $6$\n",
"题号: 009830 , 字段: ans 中已修改数据: A\n",
"题号: 009832 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}{25}-\\dfrac{y^2}{3}=1$; (2) $\\dfrac{x^2}{16}-\\dfrac{y^2}9=1$\n",
"题号: 002372 , 字段: ans 中已修改数据: $\\dfrac{x^2}{64/9}-\\dfrac{y^2}4=1$\n",
"题号: 003431 , 字段: ans 中已修改数据: $3$\n",
"题号: 008952 , 字段: ans 中已修改数据: 斜率为$2$, 但是判别式小于零, 故直线不存在.\n",
"题号: 007380 , 字段: ans 中已修改数据: C\n",
"题号: 003666 , 字段: ans 中已修改数据: D\n",
"题号: 007455 , 字段: ans 中已修改数据: $120$\n",
"题号: 007502 , 字段: ans 中已修改数据: $20$\n",
"题号: 007521 , 字段: ans 中已修改数据: $2520$\n",
"题号: 010861 , 字段: ans 中已修改数据: $24$\n",
"题号: 009333 , 字段: ans 中已修改数据: $375$\n",
"题号: 007673 , 字段: ans 中已修改数据: $78120$\n",
"题号: 002537 , 字段: ans 中已修改数据: $3720$\n",
"题号: 002586 , 字段: ans 中已修改数据: $45213$, $88$\n",
"题号: 007432 , 字段: ans 中已修改数据: (1) $72$; (2) $72$; (3) $72$\n",
"题号: 002563 , 字段: ans 中已修改数据: $1-\\dfrac{1}{(n+1)!}$\n",
"题号: 009262 , 字段: ans 中已修改数据: (1) $6$; (2) $5$; (3) $4$\n",
"题号: 007476 , 字段: ans 中已修改数据: $3$或$6$\n",
"题号: 007494 , 字段: ans 中已修改数据: 证明略\n",
"题号: 003640 , 字段: ans 中已修改数据: $\\dfrac{27}{100}$\n",
"题号: 009351 , 字段: ans 中已修改数据: $\\dfrac{11}{21}$\n",
"题号: 003574 , 字段: ans 中已修改数据: $0.985$\n"
"题号: 002623 , 字段: usages 中已添加数据: 20221208\t2023届高三10班\t0.800\n",
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"题号: 004030 , 字段: usages 中已添加数据: 20221208\t2023届高三10班\t0.400\n",
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]
}
],

View File

@ -1,97 +1,365 @@
ans
usages
003400
$(4,5)$
002623
20221208 2023届高三10班 0.800
002329
$\dfrac{y^2}{25}+\dfrac{x^2}{16}=1$或$\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$
003764
20221208 2023届高三10班 1.000
008873
(1) $\dfrac{x^2}{100}+\dfrac{y^2}{64}=1$; (2) $\dfrac{x^2}{6}+\dfrac{y^2}{4}=1$; (3) $\dfrac{x^2}8+\dfrac{y^2}4=1$或$\dfrac{y^2}8+\dfrac{x^2}4=1$
007575
20221208 2023届高三10班 0.800
002342
$\sqrt{3}-1$
007528
20221208 2023届高三10班 0.714
010673
$\dfrac{x^2}{5.9^2}+\dfrac{y^2}{5.8^2}=1$(以$1\times 10^8\text{km}$为单位)
030495
20221208 2023届高三10班 0.629
002325
$2x+4y-3=0$
007630
20221208 2023届高三10班 0.971
004717
B
004342
20221208 2023届高三10班 0.943
002348
$(-\sqrt{5},0)$或$(\sqrt{5},0)$
007535
20221208 2023届高三10班 0.629
009985
$6$
007539
20221208 2023届高三10班 0.829
009830
A
007643
20221208 2023届高三10班 0.771
009832
(1) $\dfrac{x^2}{25}-\dfrac{y^2}{3}=1$; (2) $\dfrac{x^2}{16}-\dfrac{y^2}9=1$
004030
20221208 2023届高三10班 0.400
002372
$\dfrac{x^2}{64/9}-\dfrac{y^2}4=1$
002623
20221208 2023届高三11班 0.818
003431
$3$
003764
20221208 2023届高三11班 0.955
008952
斜率为$2$, 但是判别式小于零, 故直线不存在.
007575
20221208 2023届高三11班 0.727
007380
C
007528
20221208 2023届高三11班 0.773
003666
D
030495
20221208 2023届高三11班 0.591
007455
$120$
007630
20221208 2023届高三11班 0.818
007502
$20$
004342
20221208 2023届高三11班 0.636
007521
$2520$
007535
20221208 2023届高三11班 0.409
010861
$24$
007539
20221208 2023届高三11班 0.727
009333
$375$
007643
20221208 2023届高三11班 0.409
007673
$78120$
004030
20221208 2023届高三11班 0.318
002537
$3720$
002623
20221208 2023届高三12班 0.917
002586
$45213$, $88$
003764
20221208 2023届高三12班 1.000
007432
(1) $72$; (2) $72$; (3) $72$
007575
20221208 2023届高三12班 0.833
002563
$1-\dfrac{1}{(n+1)!}$
007528
20221208 2023届高三12班 0.792
009262
(1) $6$; (2) $5$; (3) $4$
030495
20221208 2023届高三12班 0.750
007476
$3$或$6$
007630
20221208 2023届高三12班 0.917
007494
证明略
004342
20221208 2023届高三12班 0.875
003640
$\dfrac{27}{100}$
007535
20221208 2023届高三12班 0.750
009351
$\dfrac{11}{21}$
007539
20221208 2023届高三12班 0.792
007643
20221208 2023届高三12班 0.500
004030
20221208 2023届高三12班 0.292
002623
20221208 2023届高三01班 0.840
003764
20221208 2023届高三01班 1.000
007575
20221208 2023届高三01班 1.000
007528
20221208 2023届高三01班 0.960
030495
20221208 2023届高三01班 0.480
007630
20221208 2023届高三01班 0.920
004342
20221208 2023届高三01班 0.800
007535
20221208 2023届高三01班 0.880
007539
20221208 2023届高三01班 0.920
007643
20221208 2023届高三01班 0.800
004030
20221208 2023届高三01班 0.880
002623
20221208 2023届高三03班 0.923
003764
20221208 2023届高三03班 1.000
007575
20221208 2023届高三03班 0.846
007528
20221208 2023届高三03班 0.885
030495
20221208 2023届高三03班 0.577
007630
20221208 2023届高三03班 0.731
004342
20221208 2023届高三03班 0.808
007535
20221208 2023届高三03班 0.846
007539
20221208 2023届高三03班 0.808
007643
20221208 2023届高三03班 0.615
004030
20221208 2023届高三03班 0.692
002623
20221208 2023届高三04班 0.923
003764
20221208 2023届高三04班 1.000
007575
20221208 2023届高三04班 0.885
007528
20221208 2023届高三04班 0.538
030495
20221208 2023届高三04班 0.308
007630
20221208 2023届高三04班 0.654
004342
20221208 2023届高三04班 0.846
007535
20221208 2023届高三04班 0.808
007539
20221208 2023届高三04班 0.654
007643
20221208 2023届高三04班 0.115
004030
20221208 2023届高三04班 0.615
002623
20221208 2023届高三05班 0.897
003764
20221208 2023届高三05班 0.974
007575
20221208 2023届高三05班 0.872
007528
20221208 2023届高三05班 0.744
030495
20221208 2023届高三05班 0.821
007630
20221208 2023届高三05班 0.949
004342
20221208 2023届高三05班 0.923
007535
20221208 2023届高三05班 0.795
007539
20221208 2023届高三05班 0.846
007643
20221208 2023届高三05班 0.769
004030
20221208 2023届高三05班 0.487
002623
20221208 2023届高三06班 0.949
003764
20221208 2023届高三06班 1.000
007575
20221208 2023届高三06班 0.795
007528
20221208 2023届高三06班 0.692
030495
20221208 2023届高三06班 0.538
007630
20221208 2023届高三06班 0.923
004342
20221208 2023届高三06班 0.949
007535
20221208 2023届高三06班 0.795
007539
20221208 2023届高三06班 0.846
007643
20221208 2023届高三06班 0.872
004030
20221208 2023届高三06班 0.564
002623
20221208 2023届高三07班 0.929
003764
20221208 2023届高三07班 0.964
007575
20221208 2023届高三07班 0.929
007528
20221208 2023届高三07班 0.679
030495
20221208 2023届高三07班 0.179
007630
20221208 2023届高三07班 0.857
004342
20221208 2023届高三07班 0.857
007535
20221208 2023届高三07班 0.714
007539
20221208 2023届高三07班 0.750
007643
20221208 2023届高三07班 0.107
004030
20221208 2023届高三07班 0.607
002623
20221208 2023届高三08班 0.857
003764
20221208 2023届高三08班 1.000
007575
20221208 2023届高三08班 0.929
007528
20221208 2023届高三08班 0.750
030495
20221208 2023届高三08班 0.286
007630
20221208 2023届高三08班 0.714
004342
20221208 2023届高三08班 0.821
007535
20221208 2023届高三08班 0.536
007539
20221208 2023届高三08班 0.893
007643
20221208 2023届高三08班 0.500
004030
20221208 2023届高三08班 0.536
002623
20221208 2023届高三09班 0.857
003764
20221208 2023届高三09班 0.964
007575
20221208 2023届高三09班 0.821
007528
20221208 2023届高三09班 0.679
030495
20221208 2023届高三09班 0.536
007630
20221208 2023届高三09班 0.893
004342
20221208 2023届高三09班 0.643
007535
20221208 2023届高三09班 0.429
007539
20221208 2023届高三09班 0.714
007643
20221208 2023届高三09班 0.464
004030
20221208 2023届高三09班 0.143
003574
$0.985$

View File

@ -24950,7 +24950,19 @@
"solution": "",
"duration": -1,
"usages": [
"20220607\t2022届高三01班\t0.767"
"20220607\t2022届高三01班\t0.767",
"20221208\t2023届高三10班\t0.946",
"20221208\t2023届高三11班\t0.905",
"20221208\t2023届高三12班\t0.900",
"20221208\t2023届高三01班\t0.933",
"20221208\t2023届高三02班\t0.833",
"20221208\t2023届高三03班\t0.808",
"20221208\t2023届高三04班\t0.963",
"20221208\t2023届高三05班\t0.923",
"20221208\t2023届高三06班\t0.972",
"20221208\t2023届高三07班\t0.920",
"20221208\t2023届高三08班\t0.926",
"20221208\t2023届高三09班\t0.840"
],
"origin": "赋能练习",
"edit": [
@ -64048,7 +64060,20 @@
"ans": "$2x+4y-3=0$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.730",
"20221208\t2023届高三11班\t0.714",
"20221208\t2023届高三12班\t0.850",
"20221208\t2023届高三01班\t0.733",
"20221208\t2023届高三02班\t0.833",
"20221208\t2023届高三03班\t0.808",
"20221208\t2023届高三04班\t0.259",
"20221208\t2023届高三05班\t0.795",
"20221208\t2023届高三06班\t0.833",
"20221208\t2023届高三07班\t0.200",
"20221208\t2023届高三08班\t0.778",
"20221208\t2023届高三09班\t0.720"
],
"origin": "2016届创新班作业\t3161-椭圆[2]",
"edit": [
"20220625\t王伟叶"
@ -64145,7 +64170,20 @@
"ans": "$\\dfrac{y^2}{25}+\\dfrac{x^2}{16}=1$或$\\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.892",
"20221208\t2023届高三11班\t0.857",
"20221208\t2023届高三12班\t0.800",
"20221208\t2023届高三01班\t0.833",
"20221208\t2023届高三02班\t0.667",
"20221208\t2023届高三03班\t0.923",
"20221208\t2023届高三04班\t0.815",
"20221208\t2023届高三05班\t0.821",
"20221208\t2023届高三06班\t0.944",
"20221208\t2023届高三07班\t0.760",
"20221208\t2023届高三08班\t0.852",
"20221208\t2023届高三09班\t0.680"
],
"origin": "2016届创新班作业\t3162-椭圆[3]",
"edit": [
"20220625\t王伟叶"
@ -64457,7 +64495,20 @@
"ans": "$\\sqrt{3}-1$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.811",
"20221208\t2023届高三11班\t0.667",
"20221208\t2023届高三12班\t0.850",
"20221208\t2023届高三01班\t0.833",
"20221208\t2023届高三02班\t0.700",
"20221208\t2023届高三03班\t0.846",
"20221208\t2023届高三04班\t0.852",
"20221208\t2023届高三05班\t0.897",
"20221208\t2023届高三06班\t0.917",
"20221208\t2023届高三07班\t0.880",
"20221208\t2023届高三08班\t0.815",
"20221208\t2023届高三09班\t0.680"
],
"origin": "2016届创新班作业\t3163-椭圆[4]",
"edit": [
"20220625\t王伟叶"
@ -64602,7 +64653,20 @@
"ans": "$(-\\sqrt{5},0)$或$(\\sqrt{5},0)$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.919",
"20221208\t2023届高三11班\t1.000",
"20221208\t2023届高三12班\t0.950",
"20221208\t2023届高三01班\t0.967",
"20221208\t2023届高三02班\t0.833",
"20221208\t2023届高三03班\t0.885",
"20221208\t2023届高三04班\t0.963",
"20221208\t2023届高三05班\t0.692",
"20221208\t2023届高三06班\t0.917",
"20221208\t2023届高三07班\t0.920",
"20221208\t2023届高三08班\t0.963",
"20221208\t2023届高三09班\t0.920"
],
"origin": "2016届创新班作业\t3164-双曲线[1]",
"edit": [
"20220625\t王伟叶"
@ -65193,7 +65257,20 @@
"ans": "$\\dfrac{x^2}{64/9}-\\dfrac{y^2}4=1$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.757",
"20221208\t2023届高三11班\t0.524",
"20221208\t2023届高三12班\t0.650",
"20221208\t2023届高三01班\t0.867",
"20221208\t2023届高三02班\t0.700",
"20221208\t2023届高三03班\t0.808",
"20221208\t2023届高三04班\t0.741",
"20221208\t2023届高三05班\t0.872",
"20221208\t2023届高三06班\t0.750",
"20221208\t2023届高三07班\t0.720",
"20221208\t2023届高三08班\t0.852",
"20221208\t2023届高三09班\t0.680"
],
"origin": "2016届创新班作业\t3166-双曲线[3]",
"edit": [
"20220625\t王伟叶"
@ -69803,7 +69880,19 @@
"duration": -1,
"usages": [
"2016届11班\t1.000",
"2016届12班\t0.974"
"2016届12班\t0.974",
"20221208\t2023届高三10班\t0.941",
"20221208\t2023届高三11班\t0.750",
"20221208\t2023届高三12班\t0.870",
"20221208\t2023届高三01班\t0.966",
"20221208\t2023届高三02班\t0.967",
"20221208\t2023届高三03班\t1.000",
"20221208\t2023届高三04班\t0.926",
"20221208\t2023届高三05班\t0.842",
"20221208\t2023届高三06班\t0.974",
"20221208\t2023届高三07班\t0.769",
"20221208\t2023届高三08班\t0.933",
"20221208\t2023届高三09班\t0.933"
],
"origin": "2016届创新班作业\t4114-排列与排列数",
"edit": [
@ -71188,7 +71277,19 @@
"duration": -1,
"usages": [
"2016届11班\t0.974",
"2016届12班\t0.974"
"2016届12班\t0.974",
"20221208\t2023届高三10班\t0.765",
"20221208\t2023届高三11班\t0.750",
"20221208\t2023届高三12班\t0.826",
"20221208\t2023届高三01班\t0.897",
"20221208\t2023届高三02班\t0.500",
"20221208\t2023届高三03班\t0.962",
"20221208\t2023届高三04班\t0.852",
"20221208\t2023届高三05班\t0.842",
"20221208\t2023届高三06班\t0.868",
"20221208\t2023届高三07班\t0.769",
"20221208\t2023届高三08班\t0.967",
"20221208\t2023届高三09班\t0.767"
],
"origin": "2016届创新班作业\t4117-计数问题实例",
"edit": [
@ -71266,7 +71367,19 @@
"duration": -1,
"usages": [
"2016届11班\t0.744",
"2016届12班\t0.816"
"2016届12班\t0.816",
"20221208\t2023届高三10班\t0.853",
"20221208\t2023届高三11班\t0.550",
"20221208\t2023届高三12班\t0.826",
"20221208\t2023届高三01班\t0.759",
"20221208\t2023届高三02班\t0.667",
"20221208\t2023届高三03班\t0.577",
"20221208\t2023届高三04班\t0.704",
"20221208\t2023届高三05班\t0.842",
"20221208\t2023届高三06班\t0.684",
"20221208\t2023届高三07班\t0.769",
"20221208\t2023届高三08班\t0.800",
"20221208\t2023届高三09班\t0.733"
],
"origin": "2016届创新班作业\t4117-计数问题实例",
"edit": [
@ -71753,7 +71866,19 @@
"duration": -1,
"usages": [
"2016届11班\t0.949",
"2016届12班\t0.892"
"2016届12班\t0.892",
"20221208\t2023届高三02班\t0.839",
"20221208\t2023届高三10班\t0.800",
"20221208\t2023届高三11班\t0.818",
"20221208\t2023届高三12班\t0.917",
"20221208\t2023届高三01班\t0.840",
"20221208\t2023届高三03班\t0.923",
"20221208\t2023届高三04班\t0.923",
"20221208\t2023届高三05班\t0.897",
"20221208\t2023届高三06班\t0.949",
"20221208\t2023届高三07班\t0.929",
"20221208\t2023届高三08班\t0.857",
"20221208\t2023届高三09班\t0.857"
],
"origin": "2016届创新班作业\t4119-二项式定理[2]",
"edit": [
@ -91698,7 +91823,20 @@
"ans": "$(4,5)$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.946",
"20221208\t2023届高三11班\t0.809",
"20221208\t2023届高三12班\t1.000",
"20221208\t2023届高三01班\t0.900",
"20221208\t2023届高三02班\t0.800",
"20221208\t2023届高三03班\t0.846",
"20221208\t2023届高三04班\t0.704",
"20221208\t2023届高三05班\t0.769",
"20221208\t2023届高三06班\t0.861",
"20221208\t2023届高三07班\t0.840",
"20221208\t2023届高三08班\t0.852",
"20221208\t2023届高三09班\t1.000"
],
"origin": "2022届高三第一轮复习讲义",
"edit": [
"20220701\t王伟叶"
@ -92458,7 +92596,20 @@
"ans": "$3$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.649",
"20221208\t2023届高三11班\t0.524",
"20221208\t2023届高三12班\t0.900",
"20221208\t2023届高三01班\t0.767",
"20221208\t2023届高三02班\t0.733",
"20221208\t2023届高三03班\t0.769",
"20221208\t2023届高三04班\t0.704",
"20221208\t2023届高三05班\t0.615",
"20221208\t2023届高三06班\t0.722",
"20221208\t2023届高三07班\t0.720",
"20221208\t2023届高三08班\t0.667",
"20221208\t2023届高三09班\t0.720"
],
"origin": "2022届高三第一轮复习讲义",
"edit": [
"20220701\t王伟叶"
@ -95925,7 +96076,20 @@
"ans": "$\\mathrm{P}_{34-m}^8$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.882",
"20221208\t2023届高三11班\t0.700",
"20221208\t2023届高三12班\t0.913",
"20221208\t2023届高三01班\t1.000",
"20221208\t2023届高三02班\t0.667",
"20221208\t2023届高三03班\t0.846",
"20221208\t2023届高三04班\t0.741",
"20221208\t2023届高三05班\t0.868",
"20221208\t2023届高三06班\t0.842",
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],
"origin": "2022届高三第一轮复习讲义",
"edit": [
"20220701\t王伟叶"
@ -96245,7 +96409,20 @@
"ans": "$407$",
"solution": "",
"duration": -1,
"usages": [],
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],
"origin": "2022届高三第一轮复习讲义",
"edit": [
"20220701\t王伟叶"
@ -100787,7 +100964,20 @@
"ans": "$-2$",
"solution": "",
"duration": -1,
"usages": [],
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"origin": "2016年双基百分百",
"edit": [
"20220701\t王伟叶"
@ -107025,7 +107215,20 @@
"ans": "证明略",
"solution": "",
"duration": -1,
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"origin": "教材复习题",
"edit": [
"20220703\t王伟叶"
@ -107879,7 +108082,19 @@
"solution": "",
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"origin": "2022届高三下学期测验卷01第6题",
"edit": [
@ -115385,7 +115600,19 @@
"solution": "",
"duration": -1,
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"edit": [
@ -125710,7 +125937,19 @@
"solution": "",
"duration": -1,
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"origin": "2022届高三下期中区统考第15题",
"edit": [
@ -186970,7 +187209,20 @@
"ans": "$36$",
"solution": "设$4$件奖品为$a$, $b$, $c$, $d$, 显然, 要将它们分成$2, 1, 1$三组, 因此第一步是组合, 得$\\mathrm{C}_4^2$; 我们假定$\\{a,b\\}\\{c\\}\\{d\\}$ 是一种组合, 再让它们坐到甲、乙、丙三个位置上去, 因此第二步是排列, 得$\\mathrm{P}_3^3$.\n所以不同的奖励法共有$N=\\mathrm{C}_4^2\\mathrm{P}_3^3=36$(种).",
"duration": -1,
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -187082,7 +187334,20 @@
"ans": "B",
"solution": "",
"duration": -1,
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -187126,7 +187391,20 @@
"ans": "A",
"solution": "",
"duration": -1,
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -187192,7 +187470,20 @@
"ans": "$63$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20221208\t2023届高三11班\t0.700",
"20221208\t2023届高三12班\t0.696",
"20221208\t2023届高三01班\t0.724",
"20221208\t2023届高三02班\t0.933",
"20221208\t2023届高三03班\t0.731",
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -187302,7 +187593,20 @@
"ans": "$13$",
"solution": "",
"duration": -1,
"usages": [],
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"20221208\t2023届高三11班\t0.950",
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"20221208\t2023届高三02班\t0.900",
"20221208\t2023届高三03班\t0.962",
"20221208\t2023届高三04班\t0.852",
"20221208\t2023届高三05班\t0.868",
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],
"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -188356,7 +188660,20 @@
"ans": "(1) $37440$; (2) $4320$; (3) $14400$; (4) $6720$",
"solution": "",
"duration": -1,
"usages": [],
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"20221208\t2023届高三08班\t0.700\t0.900\t0.600\t0.700",
"20221208\t2023届高三09班\t0.800\t1.000\t0.733\t0.600"
],
"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -188887,7 +189204,20 @@
"ans": "$0$",
"solution": "",
"duration": -1,
"usages": [],
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"20221208\t2023届高三01班\t0.966",
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"20221208\t2023届高三05班\t0.921",
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"20221208\t2023届高三07班\t0.885",
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -188960,7 +189290,20 @@
"ans": "$5985$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20221208\t2023届高三11班\t0.650",
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"20221208\t2023届高三02班\t0.900",
"20221208\t2023届高三03班\t0.808",
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -190236,7 +190579,20 @@
"ans": "$120$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20221208\t2023届高三11班\t0.550",
"20221208\t2023届高三12班\t0.696",
"20221208\t2023届高三01班\t0.862",
"20221208\t2023届高三02班\t0.700",
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"20221208\t2023届高三04班\t0.444",
"20221208\t2023届高三05班\t0.632",
"20221208\t2023届高三06班\t0.553",
"20221208\t2023届高三07班\t0.692",
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -190742,7 +191098,20 @@
"ans": "有$17$项是有理项",
"solution": "考虑$(x^{\\frac 12}+x^{-\\frac 13})^{100}$展开式的通项$T_{r+1}=\\mathrm{C}_{100}^rx^{\\frac{100-r}2}\\cdot (x^{-\\frac 13})^r=\\mathrm{C}_{100}^rx^{50-\\dfrac{3r}6}$.\n令$r=6k$($k\\in \\mathbf{Z}$), 则$0\\le 6k\\le 100$, 即$r=0,6,12,\\cdots ,96$.\n因此共有$17$个有理项.",
"duration": -1,
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -190916,7 +191285,20 @@
"ans": "证明略",
"solution": "记$S_n=0\\mathrm{C}_n^0+1\\cdot \\mathrm{C}_n^1+2\\mathrm{C}_n^2+3\\mathrm{C}_n^3+\\cdots +(n-1)\\mathrm{C}_n^{n-1}+n\\mathrm{C}_n^n$,\n又$S_n=n\\mathrm{C}_n^n+(n-1)\\mathrm{C}_n^{n-1}+\\cdots +1\\cdot \\mathrm{C}_n^1+0\\mathrm{C}_n^0$,\n两式相加, 并利用$\\mathrm{C}_n^m=\\mathrm{C}_n^{n-m}$, 得$2S_n=n(\\mathrm{C}_n^0+\\mathrm{C}_n^1+\\mathrm{C}_n^2+\\cdots +\\mathrm{C}_n^n)=n\\cdot 2^n$,\n所以$S_n=n\\cdot 2^{n-1}$($n\\in \\mathbf{N}$).",
"duration": -1,
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"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -191014,7 +191396,20 @@
"ans": "余数为$8$",
"solution": "因为$53^{53}=(54-1)^{53}$\n\\blank{50}$=54^{53}-\\mathrm{C}_{53}^1\\cdot 54^{52}+\\mathrm{C}_{53}^2\\cdot 54^{51}-\\mathrm{C}_{53}^3\\cdot 54^{50}+\\cdots +\\mathrm{C}_{53}^{52}\\cdot 54-1$\n\\blank{50}$=9A-1=9A-9+8=9B+8$($A,B\\in \\mathbf{Z}$),\n所以所求余数为8.",
"duration": -1,
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"edit": [
"20220720\t王伟叶"
@ -191891,7 +192286,20 @@
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三02班\t0.839",
"20221208\t2023届高三10班\t0.800",
"20221208\t2023届高三11班\t0.727",
"20221208\t2023届高三12班\t0.833",
"20221208\t2023届高三01班\t1.000",
"20221208\t2023届高三03班\t0.846",
"20221208\t2023届高三04班\t0.885",
"20221208\t2023届高三05班\t0.872",
"20221208\t2023届高三06班\t0.795",
"20221208\t2023届高三07班\t0.929",
"20221208\t2023届高三08班\t0.929",
"20221208\t2023届高三09班\t0.821"
],
"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -193230,7 +193638,20 @@
"ans": "0",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三02班\t0.742",
"20221208\t2023届高三10班\t0.971",
"20221208\t2023届高三11班\t0.818",
"20221208\t2023届高三12班\t0.917",
"20221208\t2023届高三01班\t0.920",
"20221208\t2023届高三03班\t0.731",
"20221208\t2023届高三04班\t0.654",
"20221208\t2023届高三05班\t0.949",
"20221208\t2023届高三06班\t0.923",
"20221208\t2023届高三07班\t0.857",
"20221208\t2023届高三08班\t0.714",
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],
"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶",
@ -193543,7 +193964,20 @@
"ans": "$a$的最小正值为$4$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三02班\t0.677",
"20221208\t2023届高三10班\t0.771",
"20221208\t2023届高三11班\t0.409",
"20221208\t2023届高三12班\t0.500",
"20221208\t2023届高三01班\t0.800",
"20221208\t2023届高三03班\t0.615",
"20221208\t2023届高三04班\t0.115",
"20221208\t2023届高三05班\t0.769",
"20221208\t2023届高三06班\t0.872",
"20221208\t2023届高三07班\t0.107",
"20221208\t2023届高三08班\t0.500",
"20221208\t2023届高三09班\t0.464"
],
"origin": "代数精编第九章排列组合",
"edit": [
"20220720\t王伟叶"
@ -222792,7 +223226,20 @@
"ans": "(1) $\\dfrac{x^2}{100}+\\dfrac{y^2}{64}=1$; (2) $\\dfrac{x^2}{6}+\\dfrac{y^2}{4}=1$; (3) $\\dfrac{x^2}8+\\dfrac{y^2}4=1$或$\\dfrac{y^2}8+\\dfrac{x^2}4=1$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.946\t0.946\t0.892",
"20221208\t2023届高三11班\t0.952\t0.762\t0.619",
"20221208\t2023届高三12班\t0.950\t0.700\t0.800",
"20221208\t2023届高三01班\t0.967\t0.900\t0.867",
"20221208\t2023届高三02班\t0.900\t0.867\t0.767",
"20221208\t2023届高三03班\t0.923\t1.000\t0.692",
"20221208\t2023届高三04班\t0.926\t0.963\t0.778",
"20221208\t2023届高三05班\t0.923\t0.846\t0.692",
"20221208\t2023届高三06班\t0.889\t0.972\t0.806",
"20221208\t2023届高三07班\t0.960\t0.960\t0.680",
"20221208\t2023届高三08班\t0.852\t0.889\t0.815",
"20221208\t2023届高三09班\t0.960\t0.880\t0.680"
],
"origin": "二期课改练习册高二第二学期",
"edit": [
"20220726\t王伟叶"
@ -224818,7 +225265,20 @@
"ans": "斜率为$2$, 但是判别式小于零, 故直线不存在.",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.351",
"20221208\t2023届高三11班\t0.381",
"20221208\t2023届高三12班\t0.500",
"20221208\t2023届高三01班\t0.833",
"20221208\t2023届高三02班\t0.567",
"20221208\t2023届高三03班\t0.577",
"20221208\t2023届高三04班\t0.444",
"20221208\t2023届高三05班\t0.692",
"20221208\t2023届高三06班\t0.611",
"20221208\t2023届高三07班\t0.520",
"20221208\t2023届高三08班\t0.370",
"20221208\t2023届高三09班\t0.400"
],
"origin": "二期课改练习册高二第二学期",
"edit": [
"20220726\t王伟叶"
@ -231595,7 +232055,20 @@
"ans": "$100$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.941",
"20221208\t2023届高三11班\t1.000",
"20221208\t2023届高三12班\t1.000",
"20221208\t2023届高三01班\t0.931",
"20221208\t2023届高三02班\t1.000",
"20221208\t2023届高三03班\t0.962",
"20221208\t2023届高三04班\t1.000",
"20221208\t2023届高三05班\t0.947",
"20221208\t2023届高三06班\t0.868",
"20221208\t2023届高三07班\t0.923",
"20221208\t2023届高三08班\t0.933",
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],
"origin": "二期课改练习册高三",
"edit": [
"20220726\t王伟叶"
@ -233918,7 +234391,20 @@
"ans": "$\\dfrac{3439}{10000}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.559",
"20221208\t2023届高三11班\t0.450",
"20221208\t2023届高三12班\t0.652",
"20221208\t2023届高三01班\t0.931",
"20221208\t2023届高三02班\t0.533",
"20221208\t2023届高三03班\t0.692",
"20221208\t2023届高三04班\t0.593",
"20221208\t2023届高三05班\t0.789",
"20221208\t2023届高三06班\t0.553",
"20221208\t2023届高三07班\t0.615",
"20221208\t2023届高三08班\t0.467",
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],
"origin": "二期课改练习册高三",
"edit": [
"20220726\t王伟叶"
@ -244984,7 +245470,20 @@
"ans": "A",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t1.000",
"20221208\t2023届高三11班\t1.000",
"20221208\t2023届高三12班\t1.000",
"20221208\t2023届高三01班\t1.000",
"20221208\t2023届高三02班\t0.967",
"20221208\t2023届高三03班\t0.962",
"20221208\t2023届高三04班\t0.889",
"20221208\t2023届高三05班\t0.974",
"20221208\t2023届高三06班\t1.000",
"20221208\t2023届高三07班\t0.880",
"20221208\t2023届高三08班\t0.926",
"20221208\t2023届高三09班\t0.960"
],
"origin": "新教材选择性必修第一册课堂练习",
"edit": [
"20220730\t王伟叶"
@ -245035,7 +245534,20 @@
"ans": "(1) $\\dfrac{x^2}{25}-\\dfrac{y^2}{3}=1$; (2) $\\dfrac{x^2}{16}-\\dfrac{y^2}9=1$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.973\t0.946",
"20221208\t2023届高三11班\t0.952\t0.809",
"20221208\t2023届高三12班\t0.900\t0.900",
"20221208\t2023届高三01班\t0.967\t0.967",
"20221208\t2023届高三02班\t0.933\t0.833",
"20221208\t2023届高三03班\t0.885\t0.808",
"20221208\t2023届高三04班\t0.926\t0.852",
"20221208\t2023届高三05班\t0.949\t0.974",
"20221208\t2023届高三06班\t1.000\t0.972",
"20221208\t2023届高三07班\t0.840\t0.760",
"20221208\t2023届高三08班\t0.963\t0.852",
"20221208\t2023届高三09班\t1.000\t0.880"
],
"origin": "新教材选择性必修第一册课堂练习",
"edit": [
"20220730\t王伟叶"
@ -247550,7 +248062,20 @@
"ans": "$15$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.853",
"20221208\t2023届高三11班\t0.700",
"20221208\t2023届高三12班\t0.739",
"20221208\t2023届高三01班\t0.966",
"20221208\t2023届高三02班\t0.933",
"20221208\t2023届高三03班\t0.923",
"20221208\t2023届高三04班\t0.852",
"20221208\t2023届高三05班\t0.789",
"20221208\t2023届高三06班\t0.974",
"20221208\t2023届高三07班\t0.808",
"20221208\t2023届高三08班\t0.800",
"20221208\t2023届高三09班\t0.767"
],
"origin": "新教材选择性必修第二册课堂练习",
"edit": [
"20220730\t王伟叶"
@ -248651,7 +249176,20 @@
"ans": "$6$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20221208\t2023届高三10班\t0.946",
"20221208\t2023届高三11班\t1.000",
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"20221208\t2023届高三01班\t0.933",
"20221208\t2023届高三02班\t0.933",
"20221208\t2023届高三03班\t0.962",
"20221208\t2023届高三04班\t1.000",
"20221208\t2023届高三05班\t0.974",
"20221208\t2023届高三06班\t1.000",
"20221208\t2023届高三07班\t0.920",
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],
"origin": "上海2022年秋季高考试题2",
"edit": [
"20220730\t王伟叶"
@ -264916,7 +265454,20 @@
"ans": "$\\dfrac{x^2}{5.9^2}+\\dfrac{y^2}{5.8^2}=1$(以$1\\times 10^8\\text{km}$为单位)",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20221208\t2023届高三12班\t0.750",
"20221208\t2023届高三01班\t0.667",
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],
"origin": "新教材选择性必修第一册习题",
"edit": [
"20220806\t王伟叶"
@ -269662,7 +270213,20 @@
"ans": "$2174$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20221208\t2023届高三04班\t0.333",
"20221208\t2023届高三05班\t0.368",
"20221208\t2023届高三06班\t0.210",
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],
"origin": "新教材选择性必修第二册习题",
"edit": [
"20220806\t王伟叶"
@ -278849,7 +279413,20 @@
"ans": "$48$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20221208\t2023届高三11班\t0.500",
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],
"origin": "2022届高三上学期国庆卷4试题9",
"edit": [
"20220817\t王伟叶"
@ -288908,7 +289485,20 @@
"ans": "$\\dfrac 1{15}$",
"solution": "",
"duration": -1,
"usages": [],
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"20221208\t2023届高三02班\t1.000",
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"20221208\t2023届高三04班\t1.000",
"20221208\t2023届高三05班\t0.947",
"20221208\t2023届高三06班\t0.921",
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],
"origin": "上海2014年秋季高考试题10",
"edit": [
"20220819\t王伟叶"
@ -319046,7 +319636,20 @@
"ans": "$15360$",
"solution": "",
"duration": -1,
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],
"origin": "2022届杨浦高三基础考试题18-20221130修改",
"edit": [
"20221027\t王伟叶",