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录入第二轮讲义15课前课后使用结果

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WangWeiye 2023-04-14 09:53:14 +08:00
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题库0.3/Problems.json
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@ -321687,7 +321687,16 @@
"ans": "$3018$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.632",
"20230403\t2023届高三12班\t0.714",
"20230403\t2023届高三02班\t0.800",
"20230403\t2023届高三04班\t0.708",
"20230403\t2023届高三05班\t0.811",
"20230403\t2023届高三07班\t0.852",
"20230403\t2023届高三08班\t0.920",
"20230403\t2023届高三09班\t0.741"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -321902,7 +321911,16 @@
"ans": "$\\dfrac{n}{n+1}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.737",
"20230403\t2023届高三12班\t0.857",
"20230403\t2023届高三02班\t0.733",
"20230403\t2023届高三04班\t0.792",
"20230403\t2023届高三05班\t0.838",
"20230403\t2023届高三07班\t0.630",
"20230403\t2023届高三08班\t0.840",
"20230403\t2023届高三09班\t0.741"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322001,7 +322019,18 @@
"ans": "$1830$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.524",
"20230411\t2023届高三12班\t0.900",
"20230411\t2023届高三02班\t0.645",
"20230411\t2023届高三03班\t0.800",
"20230411\t2023届高三04班\t0.615",
"20230411\t2023届高三05班\t0.694",
"20230411\t2023届高三06班\t0.692",
"20230411\t2023届高三07班\t0.633",
"20230411\t2023届高三08班\t0.682",
"20230411\t2023届高三09班\t0.630"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322043,7 +322072,18 @@
"ans": "(1) $b_n=\\begin{cases} 2^{\\frac 32 n}, & n=2k, \\\\ 2^{\\frac{3n-1}2} & n=2k-1\\end{cases}$($k$为正整数); (2) $S_n=\\begin{cases} \\dfrac{10}{7}\\cdot 2^{\\frac 32 n}-\\dfrac{10}{7}, & n=2k, \\\\ \\dfrac{3}{7}\\cdot 2^{\\frac{3n+3}2}-\\dfrac{10}{7} & n=2k-1\\end{cases}$($k$为正整数)",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.857\t0.286",
"20230411\t2023届高三12班\t0.950\t0.350",
"20230411\t2023届高三02班\t0.871\t0.484",
"20230411\t2023届高三03班\t0.720\t0.440",
"20230411\t2023届高三04班\t0.731\t0.423",
"20230411\t2023届高三05班\t0.889\t0.611",
"20230411\t2023届高三06班\t0.846\t0.513",
"20230411\t2023届高三07班\t0.867\t0.433",
"20230411\t2023届高三08班\t0.318\t0.227",
"20230411\t2023届高三09班\t0.630\t0.074"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322106,7 +322146,16 @@
"ans": "$\\dfrac{2}{19}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.737",
"20230403\t2023届高三12班\t0.762",
"20230403\t2023届高三02班\t0.833",
"20230403\t2023届高三04班\t0.917",
"20230403\t2023届高三05班\t0.865",
"20230403\t2023届高三07班\t0.852",
"20230403\t2023届高三08班\t0.880",
"20230403\t2023届高三09班\t0.741"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322127,7 +322176,16 @@
"ans": "$\\begin{cases} 2, & n=1, \\\\ 2^{n-1} & n\\ge 2\\end{cases}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.737",
"20230403\t2023届高三12班\t0.429",
"20230403\t2023届高三02班\t0.800",
"20230403\t2023届高三04班\t0.958",
"20230403\t2023届高三05班\t0.649",
"20230403\t2023届高三07班\t0.481",
"20230403\t2023届高三08班\t0.920",
"20230403\t2023届高三09班\t0.593"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322232,7 +322290,16 @@
"ans": "$\\begin{cases} 2, & n=1, \\\\ -\\dfrac{1}{3^{n-1}} & n\\ge 2\\end{cases}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.210",
"20230403\t2023届高三12班\t0.333",
"20230403\t2023届高三02班\t0.333",
"20230403\t2023届高三04班\t0.375",
"20230403\t2023届高三05班\t0.460",
"20230403\t2023届高三07班\t0.222",
"20230403\t2023届高三08班\t0.360",
"20230403\t2023届高三09班\t0.148"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322460,7 +322527,18 @@
"ans": "$\\begin{cases} 4, & n=1, \\\\ 2 & n\\ge 2\\end{cases}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.809",
"20230411\t2023届高三12班\t0.650",
"20230411\t2023届高三02班\t0.839",
"20230411\t2023届高三03班\t0.880",
"20230411\t2023届高三04班\t0.962",
"20230411\t2023届高三05班\t0.583",
"20230411\t2023届高三06班\t0.872",
"20230411\t2023届高三07班\t0.633",
"20230411\t2023届高三08班\t0.591",
"20230411\t2023届高三09班\t0.741"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322523,7 +322601,18 @@
"ans": "$\\begin{cases} 1, & n=1, \\\\ 2^{n-2} & n\\ge 2\\end{cases}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.524",
"20230411\t2023届高三12班\t0.450",
"20230411\t2023届高三02班\t0.903",
"20230411\t2023届高三03班\t0.840",
"20230411\t2023届高三04班\t0.885",
"20230411\t2023届高三05班\t0.556",
"20230411\t2023届高三06班\t0.692",
"20230411\t2023届高三07班\t0.767",
"20230411\t2023届高三08班\t0.500",
"20230411\t2023届高三09班\t0.741"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322684,7 +322773,16 @@
"ans": "$8$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.947\t0.947",
"20230403\t2023届高三12班\t0.857\t0.905",
"20230403\t2023届高三02班\t0.900\t0.933",
"20230403\t2023届高三04班\t0.833\t0.958",
"20230403\t2023届高三05班\t0.973\t0.973",
"20230403\t2023届高三07班\t0.926\t1.000",
"20230403\t2023届高三08班\t0.960\t0.920",
"20230403\t2023届高三09班\t0.963\t0.963"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322828,7 +322926,16 @@
"ans": "(1) 最大项为$a_{10}-b_{10}=8976$; (2) $\\{1,2,3,\\cdots,13\\}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.947\t0.737",
"20230403\t2023届高三12班\t0.857\t0.857",
"20230403\t2023届高三02班\t0.700\t0.733",
"20230403\t2023届高三04班\t0.583\t0.667",
"20230403\t2023届高三05班\t0.811\t0.811",
"20230403\t2023届高三07班\t0.741\t0.778",
"20230403\t2023届高三08班\t0.720\t0.760",
"20230403\t2023届高三09班\t0.778\t0.852"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322946,7 +323053,16 @@
"ans": "$2^{\\frac{n(n-1)}{2}}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.842",
"20230403\t2023届高三12班\t0.809",
"20230403\t2023届高三02班\t0.700",
"20230403\t2023届高三04班\t0.833",
"20230403\t2023届高三05班\t0.757",
"20230403\t2023届高三07班\t0.852",
"20230403\t2023届高三08班\t0.960",
"20230403\t2023届高三09班\t0.778"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322967,7 +323083,18 @@
"ans": "$0$; $-\\dfrac{63}{256}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.952\t0.952",
"20230411\t2023届高三12班\t1.000\t0.850",
"20230411\t2023届高三02班\t1.000\t0.903",
"20230411\t2023届高三03班\t0.960\t0.920",
"20230411\t2023届高三04班\t1.000\t0.846",
"20230411\t2023届高三05班\t0.972\t0.861",
"20230411\t2023届高三06班\t0.949\t0.846",
"20230411\t2023届高三07班\t0.967\t0.900",
"20230411\t2023届高三08班\t0.955\t0.636",
"20230411\t2023届高三09班\t1.000\t0.778"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -322988,7 +323115,16 @@
"ans": "$33$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.632",
"20230403\t2023届高三12班\t0.905",
"20230403\t2023届高三02班\t0.667",
"20230403\t2023届高三04班\t0.750",
"20230403\t2023届高三05班\t0.757",
"20230403\t2023届高三07班\t0.667",
"20230403\t2023届高三08班\t0.760",
"20230403\t2023届高三09班\t0.630"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -323100,7 +323236,18 @@
"ans": "$4$或$5$或$32$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.619",
"20230411\t2023届高三12班\t0.700",
"20230411\t2023届高三02班\t0.710",
"20230411\t2023届高三03班\t0.520",
"20230411\t2023届高三04班\t0.731",
"20230411\t2023届高三05班\t0.722",
"20230411\t2023届高三06班\t0.897",
"20230411\t2023届高三07班\t0.800",
"20230411\t2023届高三08班\t0.591",
"20230411\t2023届高三09班\t0.815"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -323121,7 +323268,18 @@
"ans": "(1) $(a_1,a_2)=(0,0)$或$(1-\\sqrt{2},2-\\sqrt{2})$或$(1+\\sqrt{2},2+\\sqrt{2})$; (2) 当$n=7$时$T_n$最大, $T_7=7-\\dfrac{21}{2}\\lg 2$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.714\t0.191",
"20230411\t2023届高三12班\t0.800\t0.500",
"20230411\t2023届高三02班\t0.742\t0.581",
"20230411\t2023届高三03班\t0.800\t0.720",
"20230411\t2023届高三04班\t0.577\t0.231",
"20230411\t2023届高三05班\t0.889\t0.611",
"20230411\t2023届高三06班\t0.769\t0.487",
"20230411\t2023届高三07班\t0.600\t0.233",
"20230411\t2023届高三08班\t0.455\t0.455",
"20230411\t2023届高三09班\t0.815\t0.333"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -323478,7 +323636,18 @@
"ans": "$\\dfrac 34-\\dfrac{2n+3}{2(n^2+3n+2)}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.762",
"20230411\t2023届高三12班\t0.850",
"20230411\t2023届高三02班\t0.774",
"20230411\t2023届高三03班\t0.640",
"20230411\t2023届高三04班\t0.692",
"20230411\t2023届高三05班\t0.861",
"20230411\t2023届高三06班\t0.744",
"20230411\t2023届高三07班\t0.733",
"20230411\t2023届高三08班\t0.727",
"20230411\t2023届高三09班\t0.704"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -323520,7 +323689,16 @@
"ans": "$2999$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.789",
"20230403\t2023届高三12班\t0.667",
"20230403\t2023届高三02班\t0.867",
"20230403\t2023届高三04班\t0.958",
"20230403\t2023届高三05班\t0.784",
"20230403\t2023届高三07班\t0.815",
"20230403\t2023届高三08班\t0.920",
"20230403\t2023届高三09班\t0.741"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -323583,7 +323761,16 @@
"ans": "$2^{n+1}$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.579",
"20230403\t2023届高三12班\t0.809",
"20230403\t2023届高三02班\t0.867",
"20230403\t2023届高三04班\t0.792",
"20230403\t2023届高三05班\t0.784",
"20230403\t2023届高三07班\t0.778",
"20230403\t2023届高三08班\t0.960",
"20230403\t2023届高三09班\t0.741"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -323604,7 +323791,18 @@
"ans": "(1) $\\{f(n)\\}$是严格增数列, 证明略; (2) $(-1,0)\\cup (0,1)$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.762\t0.143",
"20230411\t2023届高三12班\t0.900\t0.250",
"20230411\t2023届高三02班\t0.806\t0.290",
"20230411\t2023届高三03班\t0.640\t0.120",
"20230411\t2023届高三04班\t0.692\t0.385",
"20230411\t2023届高三05班\t0.917\t0.306",
"20230411\t2023届高三06班\t0.821\t0.462",
"20230411\t2023届高三07班\t0.733\t0.167",
"20230411\t2023届高三08班\t0.909\t0.182",
"20230411\t2023届高三09班\t0.444\t0.296"
],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -345123,7 +345321,16 @@
"ans": "$\\dfrac{2\\sqrt{3}}3$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.421",
"20230403\t2023届高三12班\t0.714",
"20230403\t2023届高三02班\t0.700",
"20230403\t2023届高三04班\t0.625",
"20230403\t2023届高三05班\t0.811",
"20230403\t2023届高三07班\t0.481",
"20230403\t2023届高三08班\t0.760",
"20230403\t2023届高三09班\t0.296"
],
"origin": "2020年空中课堂高三复习课17",
"edit": [
"20230128\t王伟叶"
@ -345313,7 +345520,18 @@
"ans": "$(-\\infty,-2]\\cup [2,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.381",
"20230411\t2023届高三12班\t0.800",
"20230411\t2023届高三02班\t0.548",
"20230411\t2023届高三03班\t0.680",
"20230411\t2023届高三04班\t0.808",
"20230411\t2023届高三05班\t0.889",
"20230411\t2023届高三06班\t0.821",
"20230411\t2023届高三07班\t0.567",
"20230411\t2023届高三08班\t0.636",
"20230411\t2023届高三09班\t0.667"
],
"origin": "2020年空中课堂高三复习课18",
"edit": [
"20230128\t王伟叶"
@ -345557,7 +345775,18 @@
"ans": "$9$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.809",
"20230411\t2023届高三12班\t0.900",
"20230411\t2023届高三02班\t0.806",
"20230411\t2023届高三03班\t0.920",
"20230411\t2023届高三04班\t0.885",
"20230411\t2023届高三05班\t0.944",
"20230411\t2023届高三06班\t0.923",
"20230411\t2023届高三07班\t0.900",
"20230411\t2023届高三08班\t0.909",
"20230411\t2023届高三09班\t0.926"
],
"origin": "2020年空中课堂高三复习课19",
"edit": [
"20230128\t王伟叶"
@ -345663,7 +345892,16 @@
"ans": "(1) $a_n=2^n+1$; (2) 证明略; (3) 证明略",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.842\t0.474\t0.053",
"20230403\t2023届高三12班\t0.714\t0.905\t0.095",
"20230403\t2023届高三02班\t0.967\t0.767\t0.333",
"20230403\t2023届高三04班\t0.958\t0.667\t0.250",
"20230403\t2023届高三05班\t0.946\t0.730\t0.135",
"20230403\t2023届高三07班\t0.926\t0.741\t0.111",
"20230403\t2023届高三08班\t0.600\t0.600\t0.160",
"20230403\t2023届高三09班\t0.444\t0.444\t0.000"
],
"origin": "2020年空中课堂高三复习课19",
"edit": [
"20230128\t王伟叶"
@ -359997,7 +360235,16 @@
"ans": "$(-\\infty,3)$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230403\t2023届高三11班\t0.737",
"20230403\t2023届高三12班\t0.714",
"20230403\t2023届高三02班\t0.800",
"20230403\t2023届高三04班\t0.625",
"20230403\t2023届高三05班\t0.649",
"20230403\t2023届高三07班\t0.556",
"20230403\t2023届高三08班\t0.760",
"20230403\t2023届高三09班\t0.630"
],
"origin": "2023年空中课堂高三复习课23",
"edit": [
"20230221\t王伟叶"
@ -360054,7 +360301,18 @@
"ans": "$3$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.905",
"20230411\t2023届高三12班\t0.900",
"20230411\t2023届高三02班\t0.935",
"20230411\t2023届高三03班\t0.960",
"20230411\t2023届高三04班\t0.962",
"20230411\t2023届高三05班\t0.917",
"20230411\t2023届高三06班\t0.974",
"20230411\t2023届高三07班\t0.867",
"20230411\t2023届高三08班\t0.955",
"20230411\t2023届高三09班\t0.889"
],
"origin": "2023年空中课堂高三复习课23",
"edit": [
"20230221\t王伟叶"
@ -360187,7 +360445,18 @@
"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230411\t2023届高三11班\t0.476",
"20230411\t2023届高三12班\t0.400",
"20230411\t2023届高三02班\t0.355",
"20230411\t2023届高三03班\t0.400",
"20230411\t2023届高三04班\t0.308",
"20230411\t2023届高三05班\t0.472",
"20230411\t2023届高三06班\t0.667",
"20230411\t2023届高三07班\t0.500",
"20230411\t2023届高三08班\t0.364",
"20230411\t2023届高三09班\t0.518"
],
"origin": "2023年空中课堂高三复习课23",
"edit": [
"20230221\t王伟叶"