diff --git a/工具/关键字筛选题号.py b/工具/关键字筛选题号.py index 61116d19..d3d43565 100644 --- a/工具/关键字筛选题号.py +++ b/工具/关键字筛选题号.py @@ -2,7 +2,7 @@ import os,re,json """---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---""" keywords_dict_table = [ - {"origin":["崇明"],"origin2":["二模"]} + {"origin":["2025"],"origin2":["校本"],"origin3":["高一下"]} ] """---关键字设置完毕---""" # 示例： keywords_dict_table = [ diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py index aa3b802d..c7fd3626 100644 --- a/工具/批量收录题目.py +++ b/工具/批量收录题目.py @@ -1,8 +1,8 @@ #修改起始id,出处,文件名 -starting_id = 14805 +starting_id = 14826 raworigin = "" filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目9.tex" -editor = "20230407\t王伟叶" +editor = "202304010\t王伟叶" indexed = True import os,re,json diff --git a/工具/批量生成题目pdf.py b/工具/批量生成题目pdf.py index 864c5192..3e784d13 100644 --- a/工具/批量生成题目pdf.py +++ b/工具/批量生成题目pdf.py @@ -11,7 +11,7 @@ answered = True #目录和文件的分隔务必用/ directory = "临时文件/" # filename = "高三二模前易错题" -filename = "赋能" +filename = "2022学年度下学期高一高二新增题目及校本作业" """---设置文件名结束---""" """---设置题目列表---""" @@ -19,7 +19,7 @@ filename = "赋能" problems_dict = { - +"2025届高一下学期校本作业":"21441:22047", "2024届高二下学期周末卷01":"40001:40017", "2025届高一下学期周末卷01":"40018:40036", "2024届高二下学期周末卷02":"40037:40056", @@ -49,7 +49,9 @@ problems_dict = { "2025届高一下学期周末卷02小测":"40387:40395", "2025届高一下学期周末卷07":"40396:40413", "2025届高一下学期周末卷07小测":"40414:40421", -"2025届高一下学期周末卷08":"40527:40551" +"2025届高一下学期周末卷08":"40527:40551", +"2024届高二下学期周末卷08":"40570:40587", +"2024届高二下学期周末卷09":"40588:40604" } diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 0d7fdc60..cb1bf7b1 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,418 +1,69 @@ ans -021441 -错误, 正确, 错误, 错误 - - -021442 -D - - -021443 -C - - -021444 -A - - -021445 -C - - -021446 -D - - -021447 -$-390^\circ$ - - -021448 -$304^\circ$, $-56^\circ$ - - -021449 -$-144^\circ$ - - -021450 -二, 四 - - -021451 -(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$ - - -021452 -\begin{tikzpicture}[>=latex] -\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle; -\draw (30:2) -- (0,0) -- (60:2); -\draw [->] (-2,0) -- (2,0) node [below] {$x$}; -\draw [->] (0,-2) -- (0,2) node [left] {$y$}; -\draw (0,0) node [below left] {$O$}; -\end{tikzpicture} - - -021453 -$-1290^{\circ}$;第二象限 - - -021454 -(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. - - -021455 -(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. - - -021456 -C - - -021457 -B - - -021458 -$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$ - - -021459 -(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$ - - -021460 -$\sqrt{3}$ - - -021461 -(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$ - - -021462 -(1)$16\pi+\frac{2\pi}{3}$,二;\\ -(2)$-18\pi+\frac{4\pi}{3}$,三;\\ -(3)$-2\pi+\frac{7\pi}{5}$,三;\\ -(4)$-2\pi+\frac{3\pi}{4}$,二. - - -021463 -$\frac{1}{2}$ - - -021464 -(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$. - - -021465 -(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ -(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ -(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\ -(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$. - - -021466 -(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$. - - -021467 -(1) 第四象限；第四象限；\\ -(2) 第二象限或者第四象限；第一象限或第二象限或者$y$轴正半轴. - - -021468 -$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$ - - -021469 -\begin{tabular}{|c|c|c|c|c|c|} -\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\ -\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\ -\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\ -\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\ -\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\ -\hline -\end{tabular} - - -040018 -(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\pi}{6}$; (3) $\dfrac{\pi}{10}$; (4) $\dfrac{\pi}{3}$; (5) $\dfrac{5\pi}{12}$; (6) $\dfrac{\pi}{15}$ - - -040019 -(1) $60^{\circ}$; (2) $36^{\circ}$; (3) $45^{\circ}$; (4) $75^{\circ}$; (5) $40^{\circ}$; (6) $54^{\circ}$ - - -040020 -(1) $2k\pi+\dfrac{\pi}{2}$; (2) $2k\pi+\dfrac{3\pi}{2}$; (3) $2k\pi+\dfrac{7\pi}{6}$; (4) $k\pi+\dfrac{\pi}{4}$; (5) $\dfrac{k\pi}{2}+\dfrac{\pi}{6}$ - - -040021 -(1) $k \times 360^{\circ}+60^{\circ}$;\\ -(2) $k \times 360^{\circ}+330^{\circ}$; \\ -(3) $k \times 360^{\circ}-210^{\circ}$; \\ -(4) $k \times 180^{\circ}-45^{\circ}$; \\ -(5) $k \times 90^{\circ}+50^{\circ}$ - - -040022 -(1) $330^{\circ}$; (2) $240^{\circ}$; (3) $210^{\circ}$; (4) $300^{\circ}$ - - -040023 -(1) $\dfrac{4\pi}{3}$; (2) $\dfrac{11\pi}{6}$; (3) $10-2\pi$; (4) $-10+4\pi$ - - -040024 -$18$ - - -040025 -$3$,$-2$ - - -040026 -(1) $1037$; (2) $-4k+53$; (3) $500$ - - -040027 -$-2n+10$ - - -040028 -15 - - -040029 -$7$ - - -040030 -$(4,\dfrac{14}{3}]$ - - -040031 -$2n-1$ - - -040032 -$(3,\dfrac{35}{9})$或$(\dfrac{35}{9},3)$ - - -040033 -$200$ - - -040034 -略 - - -040035 -$a_n=\begin{cases}1, & n=1,\\ 2n, & n=2k, \\ 2n-2, & n=2k+1\end{cases}$($k\in \mathbf{N}$, $k\ge 1$) - - -040036 -$6n-3$ - - -040057 -$\dfrac{19}{28}\sqrt{7}$ - - -040058 -$\dfrac{79}{156}$ - - -040059 -$2$ - - -040060 -$-\dfrac{\sqrt{1-m^2}}{m}$ - - -040061 -$-\dfrac{1}{5}, \dfrac{1}{5}$ - - -040062 -$-\dfrac{1}{3}, 3$ - - -040063 -$\dfrac{1}{2}, -2$ - - -040064 -$\dfrac{\sqrt{6}}{3}$ - - -040065 -$\dfrac{1}{3}, -\dfrac{9}{4}$ - - -040066 -$\dfrac{1}{3}, \dfrac{7}{9}$ - - -040067 -$\pm\dfrac{\sqrt{2}}{3}$ - - -040068 -$\dfrac{1}{4}, \dfrac{2}{5}$ - - -040069 -$\dfrac{1-\sqrt{17}}{4}$ - - -040070 -(1) 三； (2) 三 - - -040071 -(1) $[-\dfrac{1}{2},\dfrac{1}{2})\cup\{1\}$; (2) $[-\dfrac{\pi}{3},\dfrac{\pi}{3})$; (3) $\{-\dfrac{1}{2}\}$ - - -040072 -(1) $-\tan \alpha-\cot \alpha$; (2) $-\dfrac{\sqrt{2}}{\sin \alpha}$; (3) $-1$; (4) $0$ - - -040073 -略 - - -040074 -$-\dfrac{10}{9}$ - - -040075 -$a_n=\dfrac{1}{3n-2}$ - - -040076 -$a_n=\dfrac{1}{n}$ - - -040077 -$(n-\dfrac{4}{5})5^n$ - - -040078 -$2^{n+1}-3$ - - -040079 -$1078$ - - -040080 -$S_n=\begin{cases}\dfrac{n^2}{2}+n-\dfrac 23+\dfrac 23\cdot 2^n, & n\text{为偶数},\\ \dfrac{n^2}{2}-\dfrac 76+\dfrac 23\cdot 2^{n+1}, & n\text{为奇数} \end{cases}$ - - -040081 -(1) 略； (2) $n^2$ - - -040082 -(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$ - - -040083 -$\dfrac{\sqrt{3}}{2}$ - - -040084 -$0$ - - -040085 -$\{0,-2\pi\}$ - - -040086 -$-\dfrac{\pi}6,\dfrac 56\pi$ - - -040087 -$\cot \alpha$ - - -040088 -$7+4\sqrt{3}$ - - -040089 -$\dfrac{\sqrt{2}-\sqrt{6}}{4}$ - - -040090 -$\dfrac{\sqrt{3}+\sqrt{35}}{12}$ - - -040091 -$\dfrac 12$ - - -040092 +14826 $5$ +14827 +$\dfrac 43$ -040093 -$-\dfrac 12$ +14828 +$\{1\}$ +14829 +$\pi$ -040094 -$\dfrac{\pi}{12}$ +14830 +$\dfrac 14$ +14831 +$1$ -040095 -$\{x|x=\pm\frac 23 \pi+2k\pi,k \in \mathbf{Z}\}$ +14832 +$3$ +14833 +$\dfrac 52$ -040096 -$\dfrac 43 \pi$ +14834 +$2\pi$ +14835 +$0.9$ -040097 -$\textcircled{4}$ +14836 +$2\sqrt{2}$ +14837 +$(0,4)$ -040098 +14838 +B + +14839 +B + +14840 C +14841 +D -040099 -$\dfrac{-2\sqrt{2}-\sqrt{3}}6$ +14842 +(1) 相交; (2) $5\sqrt{5}+8$ +14843 +(1) $f(x)=\dfrac{\sqrt{2}}2\sin (2x+\dfrac\pi 4)+\dfrac 12$, 最大值为$\dfrac{1+\sqrt{2}}2$, 当且仅当$x=\dfrac\pi 8+k\pi$, $k\in \mathbf{Z}$时取得; (2) $A=\dfrac\pi 4$, $B=\dfrac\pi 3$, $AC=\sqrt{6}$ -040100 -$-\dfrac 7{25}$ - - -040101 -$-\dfrac {\pi}3$ - - -040102 -$(-\dfrac {12}{13}, \dfrac{5}{13})$ - - -040103 -$(\dfrac {5-12\sqrt{3}}{2}, \dfrac{12-5\sqrt{3}}{2})$ - - -040104 -略 +14844 +(1) 中位数$M=42.5$, 列联表如下: \begin{tabular}{|c|c|c|} +\hline & 超过$M$& 不超过$M$\\ +\hline 上班时间 & 10 & 10 \\ +\hline 下班时间 & 11 & 9\\ +\hline +\end{tabular}; (2) $\chi^2=0.1$, 无显著差异 +14845 +(1) $P(4a^{\frac 13},4a^{\frac 23})$; (2) $1$; (3) $2\sqrt{2}$或$\dfrac{\sqrt{2}}4$ +14846 +(1) 证明略 (2) $(\pi,\pi+3\sqrt{3}]$; (3) 证明略, 反之不一定成立, 如取$a_n$是常数$a$, 满足$a+2\sin a=\pi$(这样的$a$有三个) diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index 43f1724c..c06c70e8 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1,8 +1 @@ -014805,014806,014807,014808,014809,014810,014811,014812,014813,014814,014815,014816,014817,014818,014819,014820,014821,014822,014823,014824,014825,030608,030632,030636,030679,030715,030757,030836,030856,030895,030927,030955,030977,031022,031040,031115,031136,031149 - - -未使用题号: -030608,030632,030636,030679,030715,030757,030836,030856,030895,030927,030955,030977,031022,031040,031115,031136,031149 - -已使用题号: -014805,014806,014807,014808,014809,014810,014811,014812,014813,014814,014815,014816,014817,014818,014819,014820,014821,014822,014823,014824,014825 \ No newline at end of file +021441,021442,021443,021444,021445,021446,021447,021448,021449,021450,021451,021452,021453,021454,021455,021456,021457,021458,021459,021460,021461,021462,021463,021464,021465,021466,021467,021468,021469,021470,021471,021472,021473,021474,021475,021476,021477,021478,021479,021480,021481,021482,021483,021484,021485,021486,021487,021488,021489,021490,021491,021492,021493,021494,021495,021496,021497,021498,021499,021500,021501,021502,021503,021504,021505,021506,021507,021508,021509,021510,021511,021512,021513,021514,021515,021516,021517,021518,021519,021520,021521,021522,021523,021524,021525,021526,021527,021528,021529,021530,021531,021532,021533,021534,021535,021536,021537,021538,021539,021540,021541,021542,021543,021544,021545,021546,021547,021548,021549,021550,021551,021552,021553,021554,021555,021556,021557,021558,021559,021560,021561,021562,021563,021564,021565,021566,021567,021568,021569,021570,021571,021572,021573,021574,021575,021576,021577,021578,021579,021580,021581,021582,021583,021584,021585,021586,021587,021588,021589,021590,021591,021592,021593,021594,021595,021596,021597,021598,021599,021600,021601,021602,021603,021604,021605,021606,021607,021608,021609,021610,021611,021612,021613,021614,021615,021616,021617,021618,021619,021620,021621,021622,021623,021624,021625,021626,021627,021628,021629,021630,021631,021632,021633,021634,021635,021636,021637,021638,021639,021640,021641,021642,021643,021644,021645,021646,021647,021648,021649,021650,021651,021652,021653,021654,021655,021656,021657,021658,021659,021660,021661,021662,021663,021664,021665,021666,021667,021668,021669,021670,021671,021672,021673,021674,021675,021676,021677,021678,021679,021680,021681,021682,021683,021684,021685,021686,021687,021688,021689,021690,021691,021692,021693,021694,021695,021696,021697,021698,021699,021700,021701,021702,021703,021704,021705,021706,021707,021708,021709,021710,021711,021712,021713,021714,021715,021716,021717,021718,021719,021720,021721,021722,021723,021724,021725,021726,021727,021728,021729,021730,021731,021732,021733,021734,021735,021736,021737,021738,021739,021740,021741,021742,021743,021744,021745,021746,021747,021748,021749,021750,021751,021752,021753,021754,021755,021756,021757,021758,021759,021760,021761,021762,021763,021764,021765,021766,021767,021768,021769,021770,021771,021772,021773,021774,021775,021776,021777,021778,021779,021780,021781,021782,021783,021784,021785,021786,021787,021788,021789,021790,021791,021792,021793,021794,021795,021796,021797,021798,021799,021800,021801,021802,021803,021804,021805,021806,021807,021808,021809,021810,021811,021812,021813,021814,021815,021816,021817,021818,021819,021820,021821,021822,021823,021824,021825,021826,021827,021828,021829,021830,021831,021832,021833,021834,021835,021836,021837,021838,021839,021840,021841,021842,021843,021844,021845,021846,021847,021848,021849,021850,021851,021852,021853,021854,021855,021856,021857,021858,021859,021860,021861,021862,021863,021864,021865,021866,021867,021868,021869,021870,021871,021872,021873,021874,021875,021876,021877,021878,021879,021880,021881,021882,021883,021884,021885,021886,021887,021888,021889,021890,021891,021892,021893,021894,021895,021896,021897,021898,021899,021900,021901,021902,021903,021904,021905,021906,021907,021908,021909,021910,021911,021912,021913,021914,021915,021916,021917,021918,021919,021920,021921,021922,021923,021924,021925,021926,021927,021928,021929,021930,021931,021932,021933,021934,021935,021936,021937,021938,021939,021940,021941,021942,021943,021944,021945,021946,021947,021948,021949,021950,021951,021952,021953,021954,021955,021956,021957,021958,021959,021960,021961,021962,021963,021964,021965,021966,021967,021968,021969,021970,021971,021972,021973,021974,021975,021976,021977,021978,021979,021980,021981,021982,021983,021984,021985,021986,021987,021988,021989,021990,021991,021992,021993,021994,021995,021996,021997,021998,021999,022000,022001,022002,022003,022004,022005,022006,022007,022008,022009,022010,022011,022012,022013,022014,022015,022016,022017,022018,022019,022020,022021,022022,022023,022024,022025,022026,022027,022028,022029,022030,022031,022032,022033,022034,022035,022036,022037,022038,022039,022040,022041,022042,022043,022044,022045,022046,022047 \ No newline at end of file diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index df25abfd..cd5093ce 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -365575,6 +365575,405 @@ "remark": "", "space": "12ex" }, + "014826": { + "id": "014826", + "content": "已知复数$z=3+4 \\mathrm{i}$, 其中$\\mathrm{i}$是虚数单位, 则$|z|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$5$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题1", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014827": { + "id": "014827", + "content": "双曲线$\\dfrac{x^2}{9}-\\dfrac{y^2}{7}=1$的离心率为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac 43$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题2", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014828": { + "id": "014828", + "content": "已知$A=\\{x | \\dfrac{x-1}{x} \\leq 0\\}$, $B=\\{x | x \\geq 1\\}$, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\{1\\}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题3", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014829": { + "id": "014829", + "content": "函数$y=\\sin 2 x$的最小正周期为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\pi$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题4", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014830": { + "id": "014830", + "content": "$\\triangle ABC$是边长为$1$的等边三角形, 点$M$为边$AB$的中点, 则$\\overrightarrow{AC} \\cdot \\overrightarrow{AM}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac 14$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题5", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014831": { + "id": "014831", + "content": "已知函数$y=2 x+\\dfrac{1}{8 x}$, 定义域为$(0,+\\infty)$, 则该函数的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$1$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题6", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014832": { + "id": "014832", + "content": "已知$n \\in \\mathbf{N}$, 若$\\mathrm{C}_6^n=\\mathrm{P}_5^2$, 则$n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$3$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题7", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014833": { + "id": "014833", + "content": "已知数列$\\{a_n\\}$的通项公式为$a_n=\\begin{cases}2 n, & n=1, \\\\ 2^{-n}, & n \\geq 2,\\end{cases}$ 前$n$项和为$S_n$, 则$\\displaystyle\\lim _{n \\to+\\infty} S_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac 52$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题8", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014834": { + "id": "014834", + "content": "已知四棱锥$P-ABCD$的底面是边长为$\\sqrt{2}$的正方形, 侧棱长均为$\\sqrt{5}$. 若点$A$、$B$、$C$、$D$在圆柱的一个底面圆周上, 点$P$在圆柱的另一个底面内, 则该圆柱的体积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$2\\pi$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题9", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014835": { + "id": "014835", + "content": "已知某产品的一类部件由供应商$A$和$B$提供, 占比分别为$\\dfrac{1}{3}$和$\\dfrac{2}{3}$, 供应商$A$提供的部件的良品率为$0.96$, 若该部件的总体良品率为$0.92$, 则供应商$B$提供的部件的良品率为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$0.9$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题10", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014836": { + "id": "014836", + "content": "如图, 线段$AB$的长为$8$, 点$C$在线段$AB$上, $AC=2$. 点$P$为线段$CB$上任意一点, 点$A$绕着点$C$顺时针旋转, 点$B$绕着点$P$逆时针旋转. 若它们恰重合于点$D$, 则$\\triangle CDP$的面积的最大值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0) node [below] {$C$} coordinate (C);\n\\draw (8,0) node [right] {$B$} coordinate (B);\n\\draw (5.5,0) node [below] {$P$} coordinate (P);\n\\draw ({24/7},{4*sqrt(6)/7}) node [above] {$D$} coordinate (D);\n\\draw (A)--(B)(C)--(D)--(P);\n\\draw [dashed] (A) arc (180:{atan(2*sqrt(6)/5)}:2);\n\\draw [dashed] (B) arc (0:{180-atan(8*sqrt(6)/29)}:2.5);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$2\\sqrt{2}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题11", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014837": { + "id": "014837", + "content": "若关于$x$的函数$y=\\dfrac{x^3+a}{\\mathrm{e}^x}$在$\\mathbf{R}$上存在极小值($\\mathrm{e}$为自然对数的底数), 则实数$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$(0,4)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题12", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014838": { + "id": "014838", + "content": "设$a \\in \\mathbf{R}$, 则``$a<1$''是``$a^2=latex]\n\\def\\l{2}\n\\def\\m{2}\n\\def\\n{{sqrt(5)}}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(B)!0.5!(C)$) node [right] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(C1)$) node [right] {$F$} coordinate (F);\n\\draw [dashed] (A)--(E)--(D1)--(F);\n\\end{tikzpicture}\n\\end{center}\n(1) 判断直线$AE$与$D_1F$的关系, 并说明理由;\\\\\n(2) 若直线$D_1E$与底面$ABCD$所成角为$\\dfrac{\\pi}{4}$, 求四棱柱$ABCD-A_1B_1C_1D_1$的全面积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 相交; (2) $5\\sqrt{5}+8$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题17", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "014843": { + "id": "014843", + "content": "已知向量$\\overrightarrow {a}=(\\sin x, 1+\\cos 2 x)$, $\\overrightarrow {b}=(\\cos x, \\dfrac{1}{2})$, $f(x)=\\overrightarrow {a} \\cdot \\overrightarrow {b}$.\\\\\n(1) 求函数$y=f(x)$的最大值及相应$x$的值;\\\\\n(2) 在$\\triangle ABC$中, 角$A$为锐角, 且$A+B=\\dfrac{7 \\pi}{12}$, $f(A)=1$, $BC=2$, 求边$AC$的长.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $f(x)=\\dfrac{\\sqrt{2}}2\\sin (2x+\\dfrac\\pi 4)+\\dfrac 12$, 最大值为$\\dfrac{1+\\sqrt{2}}2$, 当且仅当$x=\\dfrac\\pi 8+k\\pi$, $k\\in \\mathbf{Z}$时取得; (2) $A=\\dfrac\\pi 4$, $B=\\dfrac\\pi 3$, $AC=\\sqrt{6}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题18", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "014844": { + "id": "014844", + "content": "李先生是一名上班族, 为了比较上下班的通勤时间, 记录了$20$天个工作日内, 家里到单位的上班时间以及同路线返程的下班时间(单位: 分钟), 如下茎叶图显示两类时间的共$40$个记录:\n\\begin{center}\n\\begin{tabular}{cccccccccccc|c|ccccccccccc}\n\\multicolumn{12}{r|}{上班时间} & & \\multicolumn{11}{l}{下班时间} \\\\\n& & & & & & & & 9 & 8 & 8 & 7 & 3 & 6 & 7 & 8 & 8 & 8 & 9 \\\\\n6 & 5 & 4 & 4 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 & 4 & 0 & 0 & 1 & 3 & 3 & 3 & 3 & 4 & 4 & 5 & 5 \\\\\n& & & & & & & & 4 & 2 & 2 & 1 & 5 & 1 & 7\\\\\n& & & & & & & & & & & & 6 & 4\n\\end{tabular}\n\\end{center}\n(1) 求出这$40$个通勤记录的中位数$M$, 并完成下列$2 \\times 2$列联表:\n\\begin{center}\n\\begin{tabular}{|l|l|l|}\n\\hline & 超过$M$& 不超过$M$\\\\\n\\hline 上班时间 & & \\\\\n\\hline 下班时间 & & \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(2) 根据列联表中的数据, 请问上下班的通勤时间是否有显著差异? 并说明理由.\\\\\n附: $\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)}$, $n=a+b+c+d$, $P(\\chi^2 \\geq 3.841) \\approx 0.05$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 中位数$M=42.5$, 列联表如下: \\begin{tabular}{|c|c|c|}\n\\hline & 超过$M$& 不超过$M$\\\\\n\\hline 上班时间 & 10 & 10 \\\\\n\\hline 下班时间 & 11 & 9\\\\\n\\hline\n\\end{tabular}; (2) $\\chi^2=0.1$, 无显著差异", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题19", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "014845": { + "id": "014845", + "content": "若直线和抛物线的对称轴不平行且与抛物线只有一个公共点, 则称该直线是抛物线在该点处的切线, 该公共点为切点. 已知抛物线$C_1: y^2=4 a x$和$C_2: x^2=4 y$, 其中$a>0$. $C_1$与$C_2$在第一象限内的交点为$P$. $C_1$与$C_2$在点$P$处的切线分别为$l_1$和$l_2$, 定义$l_1$和$l_2$的夹角为曲线$C_1$、$C_2$的夹角.\\\\\n(1) 求点$P$的坐标;\\\\\n(2) 若$C_1$、$C_2$的夹角为$\\arctan \\dfrac{3}{4}$, 求$a$的值;\\\\\n(3) 若直线$l_3$既是$C_1$也是$C_2$的切线, 切点分别为$Q$、$R$, 当$\\triangle PQR$为直角三角形时, 求出相应的$a$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $P(4a^{\\frac 13},4a^{\\frac 23})$; (2) $1$; (3) $2\\sqrt{2}$或$\\dfrac{\\sqrt{2}}4$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题20", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "014846": { + "id": "014846", + "content": "已知$f(x)=x+2 \\sin x$, 等差数列$\\{a_n\\}$的前$n$项和为$S_n$, 记$T_n=\\displaystyle\\sum_{i=1}^n f(a_1)$.\\\\\n(1) 求证: 函数$y=f(x)$的图像关于点$(\\pi, \\pi)$中心对称;\\\\\n(2) 若$a_1$、$a_2$、$a_3$是某三角形的三个内角, 求$T_3$的取值范围;\\\\\n(3) 若$S_{100}=100 \\pi$, 求证: $T_{100}=100 \\pi$. 反之是否成立? 并请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 证明略 (2) $(\\pi,\\pi+3\\sqrt{3}]$; (3) 证明略, 反之不一定成立, 如取$a_n$是常数$a$, 满足$a+2\\sin a=\\pi$(这样的$a$有三个)", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届高三嘉定区二模试题21", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.", @@ -460707,5 +461106,670 @@ "related": [], "remark": "", "space": "" + }, + "040570": { + "id": "040570", + "content": "$(x^3-2 x)^7$的展开式的第$4$项的系数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040571": { + "id": "040571", + "content": "$(x+\\dfrac{2}{\\sqrt{x}})^6$展开式中常数项是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040572": { + "id": "040572", + "content": "$(2 x-5 y)^{20}$的展开式中各项系数之和为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040573": { + "id": "040573", + "content": "$(x-1)^{11}$展开式中$x$的偶次项系数之和是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040574": { + "id": "040574", + "content": "若$\\mathrm{C}_n^0+2\\mathrm{C}_n^1+4\\mathrm{C}_n^2+\\cdots+2^n \\mathrm{C}_n^n=729$, 则$\\mathrm{C}_n^1+\\mathrm{C}_n^2+\\mathrm{C}_n^3+\\cdots+\\mathrm{C}_n^n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040575": { + "id": "040575", + "content": "若今天是星期五, 再过$3^{100}$天是星期\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040576": { + "id": "040576", + "content": "$(1+x+x^2)(1-x)^{10}$展开式中, 含$x^6$的项为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040577": { + "id": "040577", + "content": "求$(1+x)+(1+x)^2+\\cdots+(1+x)^{10}$展开式中$x^3$的系数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040578": { + "id": "040578", + "content": "三棱柱$ABC-A_1B_1C_1$中, 若$\\overrightarrow{CA}=\\overrightarrow{a}$, $\\overrightarrow{CB}=\\overrightarrow{b}$, $\\overrightarrow{CC_1}=\\overrightarrow{c}$, 则用$\\overrightarrow{a}$、$\\overrightarrow{b}$、$\\overrightarrow{c}$表示$\\overrightarrow{A_1B}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040579": { + "id": "040579", + "content": "若$\\overrightarrow {a}=2 \\overrightarrow{i}+2 \\overrightarrow {j}+x \\overrightarrow {k}$, $\\overrightarrow {b}=x \\overrightarrow{i}-3 \\overrightarrow {j}-5 \\overrightarrow {k}$, 且$\\overrightarrow {a}$与$\\overrightarrow {b}$垂直, 则实数$x=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040580": { + "id": "040580", + "content": "已知$\\overrightarrow {a}, \\overrightarrow {b}$为平面$\\alpha$内的两个不相等的向量, $\\overrightarrow {c}$在直线$l$上, 则``$\\overrightarrow {c} \\perp \\overrightarrow {a}$且$\\overrightarrow {c} \\perp \\overrightarrow {b}$''是``直线$l$垂直平面$\\alpha$''的\\blank{50}条件.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040581": { + "id": "040581", + "content": "已知$S$是$\\triangle ABC$所在平面外一点, $D$是$SC$的中点, 若$\\overrightarrow{BD}=x \\overrightarrow{AB}+y \\overrightarrow{AC}+z \\overrightarrow{AS}$, 则$x+y+z=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040582": { + "id": "040582", + "content": "已知向量$\\overrightarrow {a} \\perp \\overrightarrow{b}$, 向量$\\overrightarrow{c}$与$\\overrightarrow{a}$、$\\overrightarrow{b}$的夹角都是$60^\\circ$, 且$|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|=2$, $| \\overrightarrow{c}|=3$, 则$\\overrightarrow{a}$与$2\\overrightarrow {b}-\\overrightarrow{c}$的夹角的余弦值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040583": { + "id": "040583", + "content": "已知空间四边形$ABCD$的每条边和对角线的长都等于$1$, 点$E$、$F$分别是$AB$、$AD$的中点, 则$\\overrightarrow{EF} \\cdot \\overrightarrow{DC}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040584": { + "id": "040584", + "content": "如图, 一个结晶体的形状为平行六面体, 其中, 以顶点$A$为端点的三条棱长都等于$1$, 且它们彼此的夹角都是$60^{\\circ}$, 那么以这个顶点为端点的晶体的对角线的长为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 2]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (1,0,0) node [right] {$B$} coordinate (B);\n\\draw ({1/2},0,{-sqrt(3)/2}) node [below] {$D$} coordinate (D);\n\\draw ($(B)+(D)-(A)$) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0.5,{sqrt(2/3)},{-1/2/sqrt(3)}) node [left] {$A_1$} coordinate (A_1);\n\\draw ($(B)+(A_1)-(A)$) node [above] {$B_1$} coordinate (B_1);\n\\draw ($(C)+(A_1)-(A)$) node [right] {$C_1$} coordinate (C_1);\n\\draw ($(D)+(A_1)-(A)$) node [above] {$D_1$} coordinate (D_1);\n\\draw (A)--(B)--(C)--(C_1)--(D_1)--(A_1)--cycle;\n\\draw (A_1)--(B_1)--(C_1)(B)--(B_1);\n\\draw [dashed] (A)--(C_1)(A)--(D)--(C)(D)--(D_1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040585": { + "id": "040585", + "content": "已知$(1-2 x)^7=a_0+a_1 x+a_2 x^2+\\cdots+a_7 x^7$, 求:\\\\\n(1) $a_1+a_2+\\cdots+a_7$;\\\\\n(2) $a_1+a_3+a_5+a_7$;\\\\\n(3) $|a_0|+|a_1|+\\cdots+|a_7|$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040586": { + "id": "040586", + "content": "已知$(\\sqrt{x}-\\dfrac{2}{x^2})^n$的展开式中, 第五项与第三项的系数之比为$56: 3$, 求展开式中所有的有理项.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040587": { + "id": "040587", + "content": "求$(5 x-2 y)^{20}$展开式中, 第几项的系数最小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷08", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040588": { + "id": "040588", + "content": "直三棱柱$ABC-A_1 B_1 C_1$中, 若$\\overrightarrow{CA}=\\overrightarrow {a}, \\overrightarrow{CB}=\\overrightarrow {b}, \\overrightarrow{CC_1}=\\overrightarrow {c}$, 则$\\overrightarrow{A_1B}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040589": { + "id": "040589", + "content": "设点$B$是点$A(2,-3,5)$关于$xOy$平面的对称点, 则$|\\overrightarrow{AB}|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040590": { + "id": "040590", + "content": "已知点$A$、$B$、$C$、$D$的坐标分别为$(-1,0,-1)$、$(-1,0,0)$、$(-2,-2,-2)$、$(-3,0,0)$, 则$\\overrightarrow{AB}$与$\\overrightarrow{CD}$的夹角为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040591": { + "id": "040591", + "content": "已知$A$、$B$、$C$三点的坐标分别为$A(4,1,3)$, $B(2,-5,1)$, $C(3,7, \\lambda)$, $\\overrightarrow{AB} \\perp \\overrightarrow{AC}$, 则$\\lambda$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040592": { + "id": "040592", + "content": "在长方体$ABCD-A' B' C' D'$中, $AB=2$, $AD=4$, $AA'=3$, $E$、$F$在棱$AA'$, 且$AE=EF=FA'$, $G$是$B' C'$的中点, 则直线$FG$与$EC'$所成角的大小是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040593": { + "id": "040593", + "content": "已知$\\overrightarrow {a}=(2,-1,3)$, $\\overrightarrow {b}=(-1,4,-2)$, $\\overrightarrow {c}=(7, \\lambda, 5)$, 若$\\overrightarrow {a}, \\overrightarrow {b}, \\overrightarrow {c}$三向量共面, 则实数$\\lambda$等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040594": { + "id": "040594", + "content": "在长方体$ABCD-A'B'C'D'$中, $AB=1$, $AD=2$, $AA'=3$, 则直线$A'C'$到平面$ACB'$的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040595": { + "id": "040595", + "content": "设$\\overrightarrow {a}=(a_1, a_2, a_3), \\overrightarrow {b}=(b_1, b_2, b_3)$, 且$\\overrightarrow {a} \\neq \\overrightarrow {b}$, 记$|\\overrightarrow {a}-\\overrightarrow {b}|=m$, 则$\\overrightarrow {a}-\\overrightarrow {b}$与$x$轴正方向的夹角的余弦值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040596": { + "id": "040596", + "content": "已知$\\overrightarrow{OA}=(1,2,3), \\overrightarrow{OB}=(2,1,2), \\overrightarrow{OP}=(1,1,2)$, 点$Q$在直线$OP$上运动, 则当$\\overrightarrow{QA} \\cdot \\overrightarrow{QB}$取得最小值时, 点$Q$的坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040597": { + "id": "040597", + "content": "设$A_1, A_2, A_3, A_4, A_5$是空间中给定的$5$个不同点, 则使$\\overrightarrow{MA_1}+\\overrightarrow{MA_2}+\\overrightarrow{MA_3}+\\overrightarrow{MA_4}+\\overrightarrow{MA_5}=\\overrightarrow{0}$成立的点$M$的个数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040598": { + "id": "040598", + "content": "已知平行六面体$ABCD-A'B'C'D'$中, $AB=4$, $AD=3$, $AA'=5$, $\\angle BAD=90^{\\circ}$, $\\angle BAA'=\\angle DAA'=60^{\\circ}$, 求$AC'$的长.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040599": { + "id": "040599", + "content": "如图, 已知四棱锥$P-ABCD$, 底面$ABCD$为矩形, $PA=AB=2$, $AD=2AB$, $PA \\perp$平面$ABCD$, $E, F$分别是$BC, PC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (4,0,0) node [right] {$D$} coordinate (D);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\draw (0,0,2) node [left] {$B$} coordinate (B);\n\\draw (4,0,2) node [right] {$C$} coordinate (C);\n\\draw ($(P)!0.5!(C)$) node [above] {$F$} coordinate (F);\n\\draw ($(B)!0.5!(C)$) node [below] {$E$} coordinate (E);\n\\draw (P)--(B)--(C)--(D)--cycle(E)--(F)(P)--(C);\n\\draw [dashed] (P)--(A)--(B)(A)--(D)(A)--(E)(A)--(C)(A)--(F);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$PD$与平面$AEF$所成的角的正弦值;\\\\\n(2) 求二面角$F-AE-D$的大小 (用反三角函数表示).", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040600": { + "id": "040600", + "content": "如图, 在直三棱柱$ABO-A_1B_1O_1$中, $OO_1=4$, $OA=4$, $OB=3$, $\\angle AOB=90^{\\circ}$, $D$是线段$A_1B_1$的中点, $P$是侧棱$BB_1$上的一点. 若$OP \\perp BD$, 求$OP$与底面$AOB$所成角的大小 (结果用反三角函数值表示). \n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw (0,0,0) node [above right] {$O$} coordinate (O);\n\\draw (4,0,0) node [above right] {$A$} coordinate (A);\n\\draw (0,0,3) node [left] {$B$} coordinate (B);\n\\draw (0,4,0) node [above right] {$O_1$} coordinate (O_1);\n\\draw ($(A)+(O_1)-(O)$) node [right] {$A_1$} coordinate (A_1);\n\\draw ($(B)+(O_1)-(O)$) node [left] {$B_1$} coordinate (B_1);\n\\draw ($(A_1)!0.5!(B_1)$) node [below] {$D$} coordinate (D);\n\\draw (B)++(0,1.25) node [left] {$P$} coordinate (P);\n\\draw (B)--(D);\n\\draw (B)--(A)--(A_1)--(O_1)--(B_1)--cycle(A_1)--(B_1);\n\\draw [dashed] (B)--(O)--(A)(O)--(O_1)(O)--(P);\n\\draw [->] (B)--($(O)!1.6!(B)$) node [left] {$x$} coordinate (x);\n\\draw [->] (A)--($(O)!1.3!(A)$) node [right] {$y$} coordinate (y);\n\\draw [->] (O_1)--($(O)!1.3!(O_1)$) node [left] {$z$} coordinate (z);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040601": { + "id": "040601", + "content": "正方体$AC_1$的棱长为$1$, $E$为$BB_1$的中点, $G$、$F$分别为对角线$AD_1$、$BD$的中点, $M$在$CD_1$上, 且$CM=\\dfrac{1}{4} CD_1$.\\\\\n(1) 求$EM$与$GF$所成的角;\\\\\n(2) 是否存在过$G$、$F$两点的截面, 使得$EF$垂直于此截面? 若存在, 求出与棱$D_1C_1$的交点的位置; 若不存在, 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040602": { + "id": "040602", + "content": "已知平行六面体$ABCD-A_1B_1C_1D_1$的底面$ABCD$是菱形, 且$\\angle C_1CB=\\angle C_1CD=\\angle BCD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 2]\n\\draw (0,0,0) node [below] {$C$} coordinate (C);\n\\draw (-1,0,0) node [below] {$B$} coordinate (B);\n\\draw ({cos(80)},0,{-sin(80)}) node [right] {$D$} coordinate (D);\n\\draw ($(B)+(D)-(C)$) node [below] {$A$} coordinate (A);\n\\draw (C) ++ ({1.3*sin(10)},{1.3*sqrt(1-sin(10)*sin(10)-tan(10)*tan(10)-2*sin(10)*tan(10)*tan(10)-sin(10)*sin(10)*tan(10)*tan(10))},{1.3*tan(10)*(1+sin(10))}) node [right] {$C_1$} coordinate (C_1);\n\\draw ($(C_1)-(C)+(D)$) node [right] {$D_1$} coordinate (D_1);\n\\draw ($(C_1)-(C)+(B)$) node [left] {$B_1$} coordinate (B_1);\n\\draw ($(C_1)-(C)+(A)$) node [above] {$A_1$} coordinate (A_1);\n\\draw (B)--(C)--(D)--(D_1)--(A_1)--(B_1)--cycle(B_1)--(C_1)--(D)(C)--(C_1)(D)--(C_1)--(D_1);\n\\draw [dashed] (B)--(D)(A_1)--(C)(B)--(C_1)(B)--(A)--(D)(A)--(A_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $CC_1 \\perp BD$;\\\\\n(2) 找出$|\\dfrac{CD}{CC_1}|$的一个比值, 使得$A_1 C \\perp$平面$C_1 BD$, 并予以证明.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040603": { + "id": "040603", + "content": "正三棱柱$ABC-A_1B_1C_1$中, $AB=2$, $AA_1=\\dfrac{\\sqrt{6}}{2}$, $O$为$AB$中点.\\\\\n(1) $P$点在棱$A_2B_1$上什么位置时, 异面直线$AP$与$A_1C$互相垂直;\\\\\n(2) 求平面$A_1CO$与侧面$B_1BCC_1$所成的锐二面角的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040604": { + "id": "040604", + "content": "在直三棱柱$ABC-A_1B_1C_1$中, 底面是等腰直角三角形, $\\angle ACB=90^{\\circ}$, 侧棱$AA_1=2$, $D$、$E$分别是$CC_1$与$A_1B$的中点, 点$E$在平面$ABD$上的射影是$\\triangle ABD$的重心$G$.\\\\\n(1) 求$A_1B$与平面$ABD$所成角的大小 (结果用反三角函数值表示);\\\\\n(2) 求点$A_1$到平面$AED$的距离.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷09", + "edit": [ + "202304010\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" } } \ No newline at end of file