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This commit is contained in:
WangWeiye 2022-12-20 11:59:20 +08:00
parent 29991913dd
commit 67651b8d4d
7 changed files with 313 additions and 333 deletions
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6
工具/关键字筛选题号.ipynb
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@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"outputs": [
{
@ -11,7 +11,7 @@
"0"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -21,7 +21,7 @@
"\n",
"\"\"\"---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---\"\"\"\n",
"keywords_dict_table = [\n",
" {\"origin\":[\"2023\"],\"origin2\":[\"青浦\"]}\n",
" {\"origin\":[\"2023\"],\"origin2\":[\"松江\"]}\n",
"]\n",
"\"\"\"---关键字设置完毕---\"\"\"\n",
"# 示例： keywords_dict_table = [\n",

194
工具/寻找tex文件中未赋答案的题目.ipynb
View File

@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 3,
"metadata": {},
"outputs": [
{
@ -99,202 +99,14 @@
"2022届上海春季高考.tex\n",
"2023届嘉定区一模.tex\n",
"2023届宝山区一模.tex\n",
"012655\n",
"\n",
"\n",
"012656\n",
"\n",
"\n",
"012657\n",
"\n",
"\n",
"012658\n",
"\n",
"\n",
"012659\n",
"\n",
"\n",
"012660\n",
"\n",
"\n",
"012661\n",
"\n",
"\n",
"012662\n",
"\n",
"\n",
"012663\n",
"\n",
"\n",
"012664\n",
"\n",
"\n",
"012665\n",
"\n",
"\n",
"012666\n",
"\n",
"\n",
"012667\n",
"\n",
"\n",
"012668\n",
"\n",
"\n",
"012669\n",
"\n",
"\n",
"012670\n",
"\n",
"\n",
"012671\n",
"\n",
"\n",
"012672\n",
"\n",
"\n",
"012673\n",
"\n",
"\n",
"012674\n",
"\n",
"\n",
"012675\n",
"\n",
"\n",
"2023届崇明区一模.tex\n",
"2023届徐汇区一模.tex\n",
"012634\n",
"\n",
"\n",
"012635\n",
"\n",
"\n",
"012636\n",
"\n",
"\n",
"012637\n",
"\n",
"\n",
"012638\n",
"\n",
"\n",
"012639\n",
"\n",
"\n",
"012640\n",
"\n",
"\n",
"012641\n",
"\n",
"\n",
"012642\n",
"\n",
"\n",
"012643\n",
"\n",
"\n",
"012644\n",
"\n",
"\n",
"012645\n",
"\n",
"\n",
"012646\n",
"\n",
"\n",
"012647\n",
"\n",
"\n",
"012648\n",
"\n",
"\n",
"012649\n",
"\n",
"\n",
"012650\n",
"\n",
"\n",
"012651\n",
"\n",
"\n",
"012652\n",
"\n",
"\n",
"012653\n",
"\n",
"\n",
"012654\n",
"\n",
"\n",
"2023届普陀区一模.tex\n",
"012592\n",
"\n",
"\n",
"012593\n",
"\n",
"\n",
"012594\n",
"\n",
"\n",
"012595\n",
"\n",
"\n",
"012596\n",
"\n",
"\n",
"012597\n",
"\n",
"\n",
"012598\n",
"\n",
"\n",
"012599\n",
"\n",
"\n",
"012600\n",
"\n",
"\n",
"012601\n",
"\n",
"\n",
"012602\n",
"\n",
"\n",
"012603\n",
"\n",
"\n",
"012604\n",
"\n",
"\n",
"012605\n",
"\n",
"\n",
"012606\n",
"\n",
"\n",
"012607\n",
"\n",
"\n",
"012608\n",
"\n",
"\n",
"012609\n",
"\n",
"\n",
"012610\n",
"\n",
"\n",
"012611\n",
"\n",
"\n",
"012612\n",
"\n",
"\n",
"2023届杨浦区一模.tex\n",
"2023届松江区一模.tex\n",
"2023届长宁区一模.tex\n",
"2023届闵行区一模.tex\n"
"2023届闵行区一模.tex\n",
"2023届青浦区一模.tex\n"
]
}
],

86
工具/批量添加题库字段数据.ipynb
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@ -2,34 +2,76 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"题号: 012655 , 字段: ans 中已修改数据: $\\{2\\}$\n",
"题号: 012656 , 字段: ans 中已修改数据: $(-1,1)$\n",
"题号: 012657 , 字段: ans 中已修改数据: $\\sqrt{5}$\n",
"题号: 012658 , 字段: ans 中已修改数据: $5$\n",
"题号: 012659 , 字段: ans 中已修改数据: $3$\n",
"题号: 012660 , 字段: ans 中已修改数据: $0.3$\n",
"题号: 012661 , 字段: ans 中已修改数据: $\\dfrac{\\sqrt{3}}3\\pi$\n",
"题号: 012662 , 字段: ans 中已修改数据: $2$\n",
"题号: 012663 , 字段: ans 中已修改数据: $96$\n",
"题号: 012664 , 字段: ans 中已修改数据: $\\dfrac 53$\n",
"题号: 012665 , 字段: ans 中已修改数据: $60^\\circ$\n",
"题号: 012666 , 字段: ans 中已修改数据: $2021$\n",
"题号: 012667 , 字段: ans 中已修改数据: B\n",
"题号: 012668 , 字段: ans 中已修改数据: A\n",
"题号: 012669 , 字段: ans 中已修改数据: C\n",
"题号: 012670 , 字段: ans 中已修改数据: B\n",
"题号: 012671 , 字段: ans 中已修改数据: (1) $[k\\pi-\\dfrac{5\\pi}{12},k\\pi+\\dfrac\\pi{12}]$, $k\\in \\mathbf{Z}$; (2) $\\sqrt{13}$或$\\sqrt{61}$\n",
"题号: 012672 , 字段: ans 中已修改数据: (1) 证明略; (2) $a_n=3^n-2$; (3) $a_1+a_3+a_5+a_7+a_9=22133$\n",
"题号: 012673 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\arccos \\dfrac{\\sqrt{10}}{10}$; (3) $\\dfrac 13$\n",
"题号: 012674 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}{12}+\\dfrac{y^2}4=1$; (2) $3+2\\sqrt{3}$; (3) 存在, $m$的取值范围为$[-\\dfrac{\\sqrt{3}}3,0)$\n",
"题号: 012675 , 字段: ans 中已修改数据: (1) 当$a=0$时, $f(x)$是偶函数; 当$a\\ne 0$时, $f(x)$既不是奇函数又不是偶函数; (2) $(-1,\\dfrac 5{27})$; (3) $[2\\ln 2-2,1]$\n"
"题号: 012634 , 字段: ans 中已修改数据: $\\{0\\}$\n",
"题号: 012635 , 字段: ans 中已修改数据: $2$\n",
"题号: 012636 , 字段: ans 中已修改数据: $[-2,1]$\n",
"题号: 012637 , 字段: ans 中已修改数据: $\\pi$\n",
"题号: 012638 , 字段: ans 中已修改数据: $(-1,1)$\n",
"题号: 012639 , 字段: ans 中已修改数据: $-672$\n",
"题号: 012640 , 字段: ans 中已修改数据: $1$\n",
"题号: 012641 , 字段: ans 中已修改数据: $4$\n",
"题号: 012642 , 字段: ans 中已修改数据: $\\dfrac 29$\n",
"题号: 012643 , 字段: ans 中已修改数据: $2\\sqrt{3}$\n",
"题号: 012644 , 字段: ans 中已修改数据: $(-\\infty,-\\dfrac{182}3)$\n",
"题号: 012645 , 字段: ans 中已修改数据: $\\dfrac{29}{13}$\n",
"题号: 012646 , 字段: ans 中已修改数据: C\n",
"题号: 012647 , 字段: ans 中已修改数据: C\n",
"题号: 012648 , 字段: ans 中已修改数据: B\n",
"题号: 012649 , 字段: ans 中已修改数据: D\n",
"题号: 012650 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\arcsin \\dfrac{\\sqrt{15}}{15}$\n",
"题号: 012651 , 字段: ans 中已修改数据: (1) $y+1=0$; (2) 当$0<a<1$时, 函数$y=f(x)$在$(0,1]$及$[\\dfrac 1a,+\\infty)$上严格增, 在$[1,\\dfrac 1a]$上严格减; 当$a=1$时, 函数$y=f(x)$在$(0,+\\infty)$上严格增\n",
"题号: 012652 , 字段: ans 中已修改数据: (1) $200+100\\sqrt{3}$米; (2) $2022$万元\n",
"题号: 012653 , 字段: ans 中已修改数据: (1) $\\lambda_1=2$; (2) $x^2+y^2=1$或$x^2-3y^2=1$; (3) 存在, $x_2=1$\n",
"题号: 012654 , 字段: ans 中已修改数据: (1) $b_1=1$, $b_2=2$, $b_3=3$, $b_4=4$; (2) 存在, $k$的最小值为$17$; (3) 证明略\n",
"题号: 012592 , 字段: ans 中已修改数据: $1$\n",
"题号: 012593 , 字段: ans 中已修改数据: $2$\n",
"题号: 012594 , 字段: ans 中已修改数据: $(1,+\\infty)$\n",
"题号: 012595 , 字段: ans 中已修改数据: $0$\n",
"题号: 012596 , 字段: ans 中已修改数据: $\\pi$\n",
"题号: 012597 , 字段: ans 中已修改数据: $16$\n",
"题号: 012598 , 字段: ans 中已修改数据: $60^\\circ$\n",
"题号: 012599 , 字段: ans 中已修改数据: $\\dfrac 35$\n",
"题号: 012600 , 字段: ans 中已修改数据: $0$\n",
"题号: 012601 , 字段: ans 中已修改数据: $2$\n",
"题号: 012602 , 字段: ans 中已修改数据: $\\dfrac 34$\n",
"题号: 012603 , 字段: ans 中已修改数据: $k\\le 5+3\\sqrt{2}$\n",
"题号: 012604 , 字段: ans 中已修改数据: C\n",
"题号: 012605 , 字段: ans 中已修改数据: D\n",
"题号: 012606 , 字段: ans 中已修改数据: B\n",
"题号: 012607 , 字段: ans 中已修改数据: A\n",
"题号: 012608 , 字段: ans 中已修改数据: (1) $\\dfrac {2\\pi}3$; (2) $S=\\sin(\\theta-\\dfrac\\pi 3)+\\dfrac{\\sqrt{3}}2$, $\\theta\\in (0,\\pi)$, $S$的最大值为$1+\\dfrac{\\sqrt{3}}2$\n",
"题号: 012609 , 字段: ans 中已修改数据: (1) $58$; (2) $m=2^{k-1}$, 理由略\n",
"题号: 012610 , 字段: ans 中已修改数据: (1) 证明略; (2) $18$米\n",
"题号: 012611 , 字段: ans 中已修改数据: (1) 值为$\\dfrac 23$, 是定值; (2) $\\dfrac{20}3$; (3) $k_1=\\dfrac{\\sqrt{30}}6$时, $|k_1-k_2|$取到最小值$\\dfrac{\\sqrt{30}}3$\n",
"题号: 012612 , 字段: ans 中已修改数据: (1) 具有性质$M$, 理由略; (2) 存在, $c$的范围为$(0,+\\infty)$; (3) $3$\n",
"题号: 012529 , 字段: ans 中已修改数据: $\\{2,3,4\\}$\n",
"题号: 012530 , 字段: ans 中已修改数据: $-1$\n",
"题号: 012531 , 字段: ans 中已修改数据: $23$\n",
"题号: 012532 , 字段: ans 中已修改数据: $(-3,2)$\n",
"题号: 012533 , 字段: ans 中已修改数据: $\\dfrac 65$\n",
"题号: 012534 , 字段: ans 中已修改数据: $\\dfrac\\pi 4$\n",
"题号: 012535 , 字段: ans 中已修改数据: $3$\n",
"题号: 012536 , 字段: ans 中已修改数据: $\\dfrac 23$\n",
"题号: 012537 , 字段: ans 中已修改数据: $2\\sqrt{30}$\n",
"题号: 012538 , 字段: ans 中已修改数据: $-\\dfrac 35$\n",
"题号: 012539 , 字段: ans 中已修改数据: $\\dfrac{125\\pi}{48}$\n",
"题号: 012540 , 字段: ans 中已修改数据: $(\\dfrac{13}{15},\\dfrac 76)$\n",
"题号: 012541 , 字段: ans 中已修改数据: D\n",
"题号: 012542 , 字段: ans 中已修改数据: A\n",
"题号: 012543 , 字段: ans 中已修改数据: B\n",
"题号: 012544 , 字段: ans 中已修改数据: D\n",
"题号: 012545 , 字段: ans 中已修改数据: (1) $[k\\pi-\\dfrac\\pi 6,k\\pi+\\dfrac\\pi 3]$, $k\\in \\mathbf{Z}$; (2) 最大值为$\\dfrac{\\sqrt{3}-1}2$, 最小值为$-\\dfrac 32$\n",
"题号: 012546 , 字段: ans 中已修改数据: (1) 证明略; (2) 证明略\n",
"题号: 012547 , 字段: ans 中已修改数据: (1) $2480$人; (2) $11$月$11$日新感染者人数最多, 为$630$人\n",
"题号: 012548 , 字段: ans 中已修改数据: (1) $\\dfrac{\\sqrt{2}}2$; (2) 过定点$(\\dfrac 23,0)$; (3) $\\dfrac 19$\n",
"题号: 012549 , 字段: ans 中已修改数据: (1) $5$; (2) 在定直线$y=2x$上; (3) 当且仅当$a=-\\dfrac 2{\\mathrm{e}}$时存在, $k=3$, $x_0=2$\n"
]
}
],

216
工具/文本文件/metadata.txt
View File

@ -1,64 +1,190 @@
ans
012655
$\{2\}$
012634
$\{0\}$
012656
$(-1,1)$
012657
$\sqrt{5}$
012658
$5$
012659
$3$
012660
$0.3$
012661
$\dfrac{\sqrt{3}}3\pi$
012662
012635
$2$
012663
$96$
012636
$[-2,1]$
012664
$\dfrac 53$
012637
$\pi$
012665
$60^\circ$
012638
$(-1,1)$
012666
$2021$
012639
$-672$
012667
B
012640
$1$
012668
A
012641
$4$
012669
012642
$\dfrac 29$
012643
$2\sqrt{3}$
012644
$(-\infty,-\dfrac{182}3)$
012645
$\dfrac{29}{13}$
012646
C
012670
012647
C
012648
B
012671
(1) $[k\pi-\dfrac{5\pi}{12},k\pi+\dfrac\pi{12}]$, $k\in \mathbf{Z}$; (2) $\sqrt{13}$或$\sqrt{61}$
012649
D
012672
(1) 证明略; (2) $a_n=3^n-2$; (3) $a_1+a_3+a_5+a_7+a_9=22133$
012650
(1) 证明略; (2) $\arcsin \dfrac{\sqrt{15}}{15}$
012673
(1) 证明略; (2) $\arccos \dfrac{\sqrt{10}}{10}$; (3) $\dfrac 13$
012651
(1) $y+1=0$; (2) 当$0<a<1$时, 函数$y=f(x)$在$(0,1]$及$[\dfrac 1a,+\infty)$上严格增, 在$[1,\dfrac 1a]$上严格减; 当$a=1$时, 函数$y=f(x)$在$(0,+\infty)$上严格增
012674
(1) $\dfrac{x^2}{12}+\dfrac{y^2}4=1$; (2) $3+2\sqrt{3}$; (3) 存在, $m$的取值范围为$[-\dfrac{\sqrt{3}}3,0)$
012652
(1) $200+100\sqrt{3}$米; (2) $2022$万元
012675
(1) 当$a=0$时, $f(x)$是偶函数; 当$a\ne 0$时, $f(x)$既不是奇函数又不是偶函数; (2) $(-1,\dfrac 5{27})$; (3) $[2\ln 2-2,1]$
012653
(1) $\lambda_1=2$; (2) $x^2+y^2=1$或$x^2-3y^2=1$; (3) 存在, $x_2=1$
012654
(1) $b_1=1$, $b_2=2$, $b_3=3$, $b_4=4$; (2) 存在, $k$的最小值为$17$; (3) 证明略
012592
$1$
012593
$2$
012594
$(1,+\infty)$
012595
$0$
012596
$\pi$
012597
$16$
012598
$60^\circ$
012599
$\dfrac 35$
012600
$0$
012601
$2$
012602
$\dfrac 34$
012603
$k\le 5+3\sqrt{2}$
012604
C
012605
D
012606
B
012607
A
012608
(1) $\dfrac {2\pi}3$; (2) $S=\sin(\theta-\dfrac\pi 3)+\dfrac{\sqrt{3}}2$, $\theta\in (0,\pi)$, $S$的最大值为$1+\dfrac{\sqrt{3}}2$
012609
(1) $58$; (2) $m=2^{k-1}$, 理由略
012610
(1) 证明略; (2) $18$米
012611
(1) 值为$\dfrac 23$, 是定值; (2) $\dfrac{20}3$; (3) $k_1=\dfrac{\sqrt{30}}6$时, $|k_1-k_2|$取到最小值$\dfrac{\sqrt{30}}3$
012612
(1) 具有性质$M$, 理由略; (2) 存在, $c$的范围为$(0,+\infty)$; (3) $3$
012529
$\{2,3,4\}$
012530
$-1$
012531
$23$
012532
$(-3,2)$
012533
$\dfrac 65$
012534
$\dfrac\pi 4$
012535
$3$
012536
$\dfrac 23$
012537
$2\sqrt{30}$
012538
$-\dfrac 35$
012539
$\dfrac{125\pi}{48}$
012540
$(\dfrac{13}{15},\dfrac 76)$
012541
D
012542
A
012543
B
012544
D
012545
(1) $[k\pi-\dfrac\pi 6,k\pi+\dfrac\pi 3]$, $k\in \mathbf{Z}$; (2) 最大值为$\dfrac{\sqrt{3}-1}2$, 最小值为$-\dfrac 32$
012546
(1) 证明略; (2) 证明略
012547
(1) $2480$人; (2) $11$月$11$日新感染者人数最多, 为$630$人
012548
(1) $\dfrac{\sqrt{2}}2$; (2) 过定点$(\dfrac 23,0)$; (3) $\dfrac 19$
012549
(1) $5$; (2) 在定直线$y=2x$上; (3) 当且仅当$a=-\dfrac 2{\mathrm{e}}$时存在, $k=3$, $x_0=2$

2
工具/文本文件/题号筛选.txt
View File

@ -1 +1 @@
012529,012530,012531,012532,012533,012534,012535,012536,012537,012538,012539,012540,012541,012542,012543,012544,012545,012546,012547,012548,012549
012287,012288,012289,012290,012291,012292,012293,012294,012295,012296,012297,012298,012299,012300,012301,012302,012303,012304,012305,012306,012307

16
工具/题号选题pdf生成.ipynb
View File

@ -2,16 +2,16 @@
"cells": [
{
"cell_type": "code",
"execution_count": 9,
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"开始编译教师版本pdf文件: 临时文件/2019余_教师用_20221219.tex\n",
"开始编译教师版本pdf文件: 临时文件/松江_教师用_20221220.tex\n",
"0\n",
"开始编译学生版本pdf文件: 临时文件/2019余_学生用_20221219.tex\n",
"开始编译学生版本pdf文件: 临时文件/松江_学生用_20221220.tex\n",
"0\n"
]
}
@ -26,14 +26,14 @@
"\"\"\"---设置题目列表---\"\"\"\n",
"#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n",
"problems = r\"\"\"\n",
"12308:12319,12320:12323,12324:12328\n",
"a\n",
"\n",
"\"\"\"\n",
"\"\"\"---设置题目列表结束---\"\"\"\n",
"\n",
"\"\"\"---设置文件名---\"\"\"\n",
"#目录和文件的分隔务必用/\n",
"filename = \"临时文件/2019余\"\n",
"filename = \"临时文件/松江\"\n",
"\"\"\"---设置文件名结束---\"\"\"\n",
"\n",
"\n",
@ -174,7 +174,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "mathdept",
"display_name": "Python 3.8.15 ('mathdept')",
"language": "python",
"name": "python3"
},
@ -188,12 +188,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.15"
"version": "3.8.15"
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"orig_nbformat": 4,
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}
}
},

126
题库0.3/Problems.json
View File

@ -309329,7 +309329,7 @@
"第一单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\{2,3,4\\}$",
"solution": "",
"duration": -1,
"usages": [],
@ -309350,7 +309350,7 @@
"第五单元"
],
"genre": "填空题",
"ans": "",
"ans": "$-1$",
"solution": "",
"duration": -1,
"usages": [],
@ -309371,7 +309371,7 @@
"第四单元"
],
"genre": "填空题",
"ans": "",
"ans": "$23$",
"solution": "",
"duration": -1,
"usages": [],
@ -309392,7 +309392,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$(-3,2)$",
"solution": "",
"duration": -1,
"usages": [],
@ -309413,7 +309413,7 @@
"第九单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 65$",
"solution": "",
"duration": -1,
"usages": [],
@ -309434,7 +309434,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac\\pi 4$",
"solution": "",
"duration": -1,
"usages": [],
@ -309455,7 +309455,7 @@
"第八单元"
],
"genre": "填空题",
"ans": "",
"ans": "$3$",
"solution": "",
"duration": -1,
"usages": [],
@ -309476,7 +309476,7 @@
"第二单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 23$",
"solution": "",
"duration": -1,
"usages": [],
@ -309497,7 +309497,7 @@
"第七单元"
],
"genre": "填空题",
"ans": "",
"ans": "$2\\sqrt{30}$",
"solution": "",
"duration": -1,
"usages": [],
@ -309518,7 +309518,7 @@
"第三单元"
],
"genre": "填空题",
"ans": "",
"ans": "$-\\dfrac 35$",
"solution": "",
"duration": -1,
"usages": [],
@ -309539,7 +309539,7 @@
"第六单元"
],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{125\\pi}{48}$",
"solution": "",
"duration": -1,
"usages": [],
@ -309560,7 +309560,7 @@
"第四单元"
],
"genre": "填空题",
"ans": "",
"ans": "$(\\dfrac{13}{15},\\dfrac 76)$",
"solution": "",
"duration": -1,
"usages": [],
@ -309581,7 +309581,7 @@
"第一单元"
],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -309602,7 +309602,7 @@
"第六单元"
],
"genre": "选择题",
"ans": "",
"ans": "A",
"solution": "",
"duration": -1,
"usages": [],
@ -309623,7 +309623,7 @@
"第二单元"
],
"genre": "选择题",
"ans": "",
"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
@ -309644,7 +309644,7 @@
"第七单元"
],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -309665,7 +309665,7 @@
"第三单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $[k\\pi-\\dfrac\\pi 6,k\\pi+\\dfrac\\pi 3]$, $k\\in \\mathbf{Z}$; (2) 最大值为$\\dfrac{\\sqrt{3}-1}2$, 最小值为$-\\dfrac 32$",
"solution": "",
"duration": -1,
"usages": [],
@ -309686,7 +309686,7 @@
"第六单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) 证明略",
"solution": "",
"duration": -1,
"usages": [],
@ -309707,7 +309707,7 @@
"第四单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $2480$人; (2) $11$月$11$日新感染者人数最多, 为$630$人",
"solution": "",
"duration": -1,
"usages": [],
@ -309728,7 +309728,7 @@
"第七单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $\\dfrac{\\sqrt{2}}2$; (2) 过定点$(\\dfrac 23,0)$; (3) $\\dfrac 19$",
"solution": "",
"duration": -1,
"usages": [],
@ -309749,7 +309749,7 @@
"第二单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) $5$; (2) 在定直线$y=2x$上; (3) 当且仅当$a=-\\dfrac 2{\\mathrm{e}}$时存在, $k=3$, $x_0=2$",
"solution": "",
"duration": -1,
"usages": [],
@ -310568,7 +310568,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$1$",
"solution": "",
"duration": -1,
"usages": [],
@ -310587,7 +310587,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$2$",
"solution": "",
"duration": -1,
"usages": [],
@ -310606,7 +310606,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(1,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [],
@ -310625,7 +310625,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$0$",
"solution": "",
"duration": -1,
"usages": [],
@ -310644,7 +310644,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\pi$",
"solution": "",
"duration": -1,
"usages": [],
@ -310663,7 +310663,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$16$",
"solution": "",
"duration": -1,
"usages": [],
@ -310682,7 +310682,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$60^\\circ$",
"solution": "",
"duration": -1,
"usages": [],
@ -310701,7 +310701,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 35$",
"solution": "",
"duration": -1,
"usages": [],
@ -310720,7 +310720,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$0$",
"solution": "",
"duration": -1,
"usages": [],
@ -310739,7 +310739,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$2$",
"solution": "",
"duration": -1,
"usages": [],
@ -310758,7 +310758,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 34$",
"solution": "",
"duration": -1,
"usages": [],
@ -310777,7 +310777,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$k\\le 5+3\\sqrt{2}$",
"solution": "",
"duration": -1,
"usages": [],
@ -310796,7 +310796,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
@ -310815,7 +310815,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -310834,7 +310834,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
@ -310853,7 +310853,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "A",
"solution": "",
"duration": -1,
"usages": [],
@ -310872,7 +310872,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $\\dfrac {2\\pi}3$; (2) $S=\\sin(\\theta-\\dfrac\\pi 3)+\\dfrac{\\sqrt{3}}2$, $\\theta\\in (0,\\pi)$, $S$的最大值为$1+\\dfrac{\\sqrt{3}}2$",
"solution": "",
"duration": -1,
"usages": [],
@ -310891,7 +310891,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $58$; (2) $m=2^{k-1}$, 理由略",
"solution": "",
"duration": -1,
"usages": [],
@ -310910,7 +310910,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) $18$米",
"solution": "",
"duration": -1,
"usages": [],
@ -310929,7 +310929,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 值为$\\dfrac 23$, 是定值; (2) $\\dfrac{20}3$; (3) $k_1=\\dfrac{\\sqrt{30}}6$时, $|k_1-k_2|$取到最小值$\\dfrac{\\sqrt{30}}3$",
"solution": "",
"duration": -1,
"usages": [],
@ -310948,7 +310948,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 具有性质$M$, 理由略; (2) 存在, $c$的范围为$(0,+\\infty)$; (3) $3$",
"solution": "",
"duration": -1,
"usages": [],
@ -311369,7 +311369,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\{0\\}$",
"solution": "",
"duration": -1,
"usages": [],
@ -311388,7 +311388,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$2$",
"solution": "",
"duration": -1,
"usages": [],
@ -311407,7 +311407,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$[-2,1]$",
"solution": "",
"duration": -1,
"usages": [],
@ -311426,7 +311426,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\pi$",
"solution": "",
"duration": -1,
"usages": [],
@ -311445,7 +311445,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(-1,1)$",
"solution": "",
"duration": -1,
"usages": [],
@ -311464,7 +311464,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$-672$",
"solution": "",
"duration": -1,
"usages": [],
@ -311483,7 +311483,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$1$",
"solution": "",
"duration": -1,
"usages": [],
@ -311502,7 +311502,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$4$",
"solution": "",
"duration": -1,
"usages": [],
@ -311521,7 +311521,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 29$",
"solution": "",
"duration": -1,
"usages": [],
@ -311540,7 +311540,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$2\\sqrt{3}$",
"solution": "",
"duration": -1,
"usages": [],
@ -311559,7 +311559,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,-\\dfrac{182}3)$",
"solution": "",
"duration": -1,
"usages": [],
@ -311578,7 +311578,7 @@
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{29}{13}$",
"solution": "",
"duration": -1,
"usages": [],
@ -311597,7 +311597,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
@ -311616,7 +311616,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
@ -311635,7 +311635,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "B",
"solution": "",
"duration": -1,
"usages": [],
@ -311654,7 +311654,7 @@
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
"usages": [],
@ -311673,7 +311673,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) $\\arcsin \\dfrac{\\sqrt{15}}{15}$",
"solution": "",
"duration": -1,
"usages": [],
@ -311692,7 +311692,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $y+1=0$; (2) 当$0<a<1$时, 函数$y=f(x)$在$(0,1]$及$[\\dfrac 1a,+\\infty)$上严格增, 在$[1,\\dfrac 1a]$上严格减; 当$a=1$时, 函数$y=f(x)$在$(0,+\\infty)$上严格增",
"solution": "",
"duration": -1,
"usages": [],
@ -311711,7 +311711,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $200+100\\sqrt{3}$米; (2) $2022$万元",
"solution": "",
"duration": -1,
"usages": [],
@ -311730,7 +311730,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $\\lambda_1=2$; (2) $x^2+y^2=1$或$x^2-3y^2=1$; (3) 存在, $x_2=1$",
"solution": "",
"duration": -1,
"usages": [],
@ -311749,7 +311749,7 @@
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"ans": "(1) $b_1=1$, $b_2=2$, $b_3=3$, $b_4=4$; (2) 存在, $k$的最小值为$17$; (3) 证明略",
"solution": "",
"duration": -1,
"usages": [],