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录入静安普陀闵行长宁松江区2023届二模答案 以及 修改题目15056的一个错误

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2
工具/latex界面修改题目内容.py
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@ -1,6 +1,6 @@
import os,re,json import os,re,json
"""这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭""" """这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭"""
problems = "15202" problems = "15056"
editor = "王伟叶" editor = "王伟叶"
def generate_number_set(string,dict): def generate_number_set(string,dict):

414
工具/文本文件/metadata.txt
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@ -1,196 +1,320 @@
ans ans
15059 15122
$\{3,5\}$ $\{0,1,2\}$
15060 15123
$1$
15124
$\sqrt{5}$
15125
$\dfrac{x^2}{\frac{11}3}+\dfrac{y^2}{\frac{11}2}=1$($\dfrac{3x^2}{11}+\dfrac{2y^2}{11}=1$)
15126
$-\dfrac 23$
15127
$3$
15128
$(0,\dfrac 12]$
15129
$(\dfrac 14,\dfrac{\sqrt{3}}4)$
15130
$y=0.186x+11.571$
15131
$\dfrac{\sqrt{2}}2$
15132
$95.4$(或者$95.5$也可以)
15133
$1+2\lg 2$
15134
C
15135
B
15136
A
15137
D
15138
(1) 证明略; (2) $2^{n+2}-4-3n$
15139
(1) $\dfrac 23$; (2) 证明略
15140
(1) $2\sqrt{3}$; (2) $\sqrt{2}$
15141
(1) 分布为$\begin{pmatrix}0 & 1 & 2 \\ \dfrac 15 & \dfrac 35 & \dfrac 15\end{pmatrix}$, 期望为$1$; (2) $\chi^2\approx 0.595$, 脑瘤病患在左右侧的部位与习惯在哪一侧接听手机电话无关
15142
(1) $2x-y-2\ln 2=0$; (2) $-a-\dfrac 12$; (3) 有且仅有一个零点
15143
$(-1,1)$
15144
$\pi$ $\pi$
15061 15145
$81$ $2$
15062 15146
$-5$ $9$
15063 15147
$(x-1)^2+y^2=4$ $(-\infty,0)\cup [\dfrac 13,+\infty)$
15064 15148
$40$ $-\dfrac 17$
15065 15149
$-2$ $36\pi$
15066 15150
$(300+100\sqrt{2})\pi$ $14$
15067 15151
$\dfrac{2\pi}{3}$ $68$
15068 15152
$\dfrac{11}{32}$ $3$
15069 15153
$4$ $(-\dfrac 12,0)$
15070 15154
$[-2,2]$ $3\sqrt{5}$
15071 15155
B
15072
A A
15073 15156
D D
15074 15157
C
15075
(1) $\dfrac{16}{65}$; (2) 周长为$32$, 面积为$24$
15076
(1) 证明略; (2) 距离为$\dfrac{\sqrt{2}}2$, 所成角为$\arcsin\dfrac{\sqrt{10}}{10}$
15077
(1) \begin{tabular}{|c|c|c|c|} \hline & 生产标兵 & 非生产标兵 & 总计\\\hline
$35$周岁及以上组 & $20$ & $60$ & $80$\\\hline
$35$周岁以下组 & $30$ & $50$ & $80$ \\\hline
总计& $50$ & $110$ & $160$ \\ \hline
\end{tabular}, $\chi^2\approx 2.91$, 因此没有$95\%$的把握认为是否为生产标兵与工人所在的年龄有关; (2) 估计该厂工人中$35$周岁以下占$40\%$, 该厂生产标兵中$35$周岁以下占$50\%$
15078
(1) $y=\pm 2\sqrt{2}x$; (2) 最大值为$\dfrac 14$, 此时$\angle AF_1B$的正切值为$-\dfrac{24}{7}$; (3) 证明略
15079
(1) $h_1(x)$是, $h_2(x)$不是; (2) $y=ax^2+(4-2a)x+a$($0<a<2$); (3) $2\sqrt{3}$
15080
平行或相交
15081
$5$
15082
$(\sqrt{3},0)$
15083
$\sqrt{3}x-y+\sqrt{3}+3=0$
15084
$[3,+\infty)$
15085
$16\pi$
15086
$(-\dfrac 12,\dfrac 23)\cup (3,+\infty)$
15087
$0$
15088
$100\sqrt{2}$
15089
$(-\dfrac 1{11},-\dfrac 1{19})$
15090
$\dfrac{\sqrt{10}}5$
15091
$[0,\dfrac\pi 3]\cup [\dfrac{2\pi}3,\pi]$
15092
C
15093
C
15094
B B
15095 15158
D D
15096 15159
(1) 最小正周期为$\pi$, 对称轴的方程为$x=\dfrac\pi 6+\dfrac{k\pi}2$, $k\in \mathbf{Z}$; (2) $(0,\dfrac 32]$ (1) 证明略; (2) $8\sqrt{3}$
15097 15160
(1) 证明略; (2) $\dfrac{\sqrt{5}}3$ (1) $[1,+\infty)$; (2) $10216$
`1
15098
(1) $a=0.26$, $b=0.38$; (2) $\dfrac 23$; (3) $X$的分布为$\begin{pmatrix} 0 & 1 & 2 \\ \dfrac 5{14} & \dfrac{15}{28} & \dfrac 3{28} \end{pmatrix}$, 期望为$\dfrac 34$
15099 15161
(1) $x_3^2+\dfrac 14$; (2) $(-1,1)$; (3) 证明略 (1) $\dfrac 13$; (2) $1.2$
15100 15162
(1) 证明略; (2) $1$; (3) 证明略 (1) $2$; (2) $(-1,\dfrac 74)$; (3) 是定值$\sqrt{6}$
15163
(1) $(1,+\infty)$; (2) $[-1,\dfrac 32]$; (3) 证明略
15101 15164
$\{0,2\}$ $\{-1,1\}$
15102 15165
$(2,+\infty)$ $10$
15103 15166
$3-\mathrm{i}$ $\dfrac 12$
15104 15167
$5$ $18\pi$
15105 15168
$\dfrac 17$ $2$
15106 15169
$32.5$ $0.2$
15107 15170
$12$
15171
$\dfrac 14$
15172
$[-2,+\infty)$
15173
$\sqrt{2}$
15174
$[\dfrac 76,\dfrac{15}2]$
15175
$\dfrac{-3\pm \sqrt{6}}6$
15176
D
15177
C
15178
B
15179
C
15180
(1) $\dfrac 13$; (2) $8\sqrt{2}$
15181
(1) 证明略; (2) $\dfrac{4\sqrt{21}}{21}$
15182
(1) $0.01998$; (2) 分布为$\begin{pmatrix}0 & 1 & 2 & 3 \\ 0.00000 & 0.00030 & 0.02940 & 0.97030 \end{pmatrix}$, 期望为$2.97$
15183
(1) 离心率为$\dfrac{\sqrt{5}}2$, 渐近线方程为$y=\pm \dfrac 12 x$; (2) $1$; (3) 证明略
15184
(1) $-4$; (2) 存在切线$l_2$与$l_1$垂直, 理由略; (3) $(\dfrac{3-\sqrt{5}}{2},\dfrac 12]\cup [2,\dfrac{3+\sqrt{5}}{2})$
15185
$\{2,4\}$
15186
$(-\infty,1)$
15187
$0.2$
15188
$(1,+\infty)$
15189
$\dfrac{2\sqrt{2}}3\pi$
15190
$1$
15191
$0.8$
15192
$4$ $4$
15108 15193
$(-\infty,-5]\cup \{0\}\cup [5,+\infty)$ $3$
15109 15194
$\dfrac 65$ $[-1,1]$
15110 15195
$48\pi$ $3$
15111 15196
$\dfrac{x^2}3-y^2=1$ $\dfrac{\sqrt{21}}{14}$
15112 15197
$\dfrac 52$
15113
A
15114
D D
15115 15198
A
15199
C C
15116 15200
B B
15117 15201
(1) $\begin{cases}2, & n=1, \\ 2^{n-1}, & n\ge 2;\end{cases}$ (2) $m=11$ (1) 证明略; (2) 分布为$\begin{pmatrix} 0 & 1 & 2 \\ \dfrac 3{10} & \dfrac 35 & \dfrac{1}{10}\end{pmatrix}$, 期望为$\dfrac 45$
15118 15202
(1) 证明略; (2) $\dfrac{\sqrt{3}}4$ (1) 证明略; (2) $60^\circ$
15203
(1) $\lambda \approx 29.21$, 估计到$2023$年底该地新能源汽车保有量约$40.3$万辆; (2) $\hat{\lambda}\approx 29.67$, $\hat{r}\approx 0.32$
15204
(1) $\dfrac{x^2}4+\dfrac{y^2}3=1$; (2) $1$; (3) 值恒为$-3$, 证明略
15205
(1) 振幅为$\sqrt{2}$, 周期为$2\pi$, 初相位为$\dfrac{\pi}{4}$; (2) $(\dfrac{\pi}{3},\dfrac{5\pi}3]$; (3) $(0,1)$
15119 15206
(1) $\chi^2\approx 35.4$, 有$99.9\%$的把握认为电解电容质量与铝箔质量有关; (2) 约为$0.846$ $\{1\}$
15120 15207
(1)$\dfrac{x^2}2+y^2=1$; (2) $x\pm \dfrac{\sqrt{14}}7y-1=0$; (3) 证明略 $5$
15121 15208
(1) 在$(-\pi,0]$和$[\pi,2\pi]$上均为严格增函数, 在$[0,\pi]$和$[2\pi,3\pi)$上均为严格减函数, 极小值为$-\dfrac{1}{\mathrm{e}^\pi}$, 极大值为$1$与$\dfrac{1}{\mathrm{e}^{2\pi}}$; (2) $(-\infty,2]$; (3) 证明略 $-1$
15209
$0.94$
15210
$-\dfrac{24}{7}$
15211
$28$
15212
$50$
15213
$\dfrac 13$
15214
$\dfrac 8{11}$
15215
$9$
15216
$\dfrac{\sqrt{2}}2$
15217
$\sqrt{15}a$
15218
B
15219
B
15220
C
15221
B
15222
(1) $\dfrac \pi 3$; (2) $\dfrac 32$
15223
(1) 证明略; (2) $\arctan\dfrac{2\sqrt{5}}5$
15224
(1) $43.3$亿元; (2) (i) 全款购车两年后资产总额为$0.0322a$万元, 分期付款购车两年后资产总额为$0.0233a$万元, 应选择全款购车; (ii) $a<21.2134$, 这一措施对购买A, B, C车型有效
15225
(1) $C_1:\dfrac{x^2}2+y^2=1$, $C_2:\dfrac{x^2}2-y^2=1$; (2) $y=\dfrac 12 x$或$y=-\dfrac 12 x$; (3) $2$
15226
(1) $g(x)=f(h(x))$; (2) 导函数为$2(2x)^{2x}(1+\ln (2x))$, 最小值为$(\dfrac 1{\mathrm{e}})^{\frac 1{\mathrm{e}}}$; (3) 证明略

215
题库0.3/Problems.json
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@ -371093,7 +371093,7 @@
}, },
"015056": { "015056": {
"id": "015056", "id": "015056",
"content": "某网站计划$4$月份订购草莓在网络销售, 每天的进货量相同, 成本价为每盒$15$元. 决定每盒售价为$20$元, 未售出的草莓降价处理, 每盒$10$元. 假设当天进货能全部售完. 根据销售经验, 每天的购买量与网站每天的浏览量(单位: 万次) 有关. 为确定草莓的进货量, 相关人员统计了前两年$4$月份(共$60$天)网站每天的浏览量(单位: 万次)、购买草莓的数量(单位: 盒) 以及达到该流量的天数, 如下表所示:\n\\begin{center} \n\\begin{tabular}{|c|c|c|}\n\\hline 每天的浏览量 &$(0,1)$& {$[1,+\\infty)$} \\\\\n\\hline 每天的购买量 & 600 & 900 \\\\\n\\hline 天数 & 36 & 24 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n以每天的浏览量位于各区间的频率代替浏览量位于该区间的概率.\n(1) 求$4$月份草苺一天的购买量$X$(单位: 盒)的分布;\\\\\n(2) 设$4$月份销售草莓一天的利润为$Y$(单位: 元), 一天的进货量为$n$(单位: 盒), $n$为正整数且$n \\in[600,900]$, 当$n$为多少时, $Y$的期望达到最大值, 并求此最大值.", "content": "某网站计划$4$月份订购草莓在网络销售, 每天的进货量相同, 成本价为每盒$15$元. 决定每盒售价为$20$元, 未售出的草莓降价处理, 每盒$10$元. 假设当天进货能全部售完. 根据销售经验, 每天的购买量与网站每天的浏览量(单位: 万次) 有关. 为确定草莓的进货量, 相关人员统计了前两年$4$月份(共$60$天)网站每天的浏览量(单位: 万次)、购买草莓的数量(单位: 盒) 以及达到该流量的天数, 如下表所示:\n\\begin{center} \n\\begin{tabular}{|c|c|c|}\n\\hline 每天的浏览量 &$(0,1)$& {$[1,+\\infty)$} \\\\\n\\hline 每天的购买量 & 600 & 900 \\\\\n\\hline 天数 & 36 & 24 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n以每天的浏览量位于各区间的频率代替浏览量位于该区间的概率.\\\\\n(1) 求$4$月份草苺一天的购买量$X$(单位: 盒)的分布;\\\\\n(2) 设$4$月份销售草莓一天的利润为$Y$(单位: 元), 一天的进货量为$n$(单位: 盒), $n$为正整数且$n \\in[600,900]$, 当$n$为多少时, $Y$的期望达到最大值, 并求此最大值.",
"objs": [], "objs": [],
"tags": [ "tags": [
"第八单元" "第八单元"
@ -371105,7 +371105,8 @@
"usages": [], "usages": [],
"origin": "2023届金山区高三二模试题19", "origin": "2023届金山区高三二模试题19",
"edit": [ "edit": [
"20230413\t王伟叶" "20230413\t王伟叶",
"20230414\t王伟叶"
], ],
"same": [], "same": [],
"related": [], "related": [],
@ -372486,7 +372487,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\{0,1,2\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372507,7 +372508,7 @@
"第四单元" "第四单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$1$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372528,7 +372529,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\sqrt{5}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372549,7 +372550,7 @@
"第七单元" "第七单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{x^2}{\\frac{11}3}+\\dfrac{y^2}{\\frac{11}2}=1$($\\dfrac{3x^2}{11}+\\dfrac{2y^2}{11}=1$)",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372570,7 +372571,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-\\dfrac 23$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372591,7 +372592,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$3$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372612,7 +372613,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(0,\\dfrac 12]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372633,7 +372634,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(\\dfrac 14,\\dfrac{\\sqrt{3}}4)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372654,7 +372655,7 @@
"第九单元" "第九单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$y=0.186x+11.571$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372675,7 +372676,7 @@
"第六单元" "第六单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{\\sqrt{2}}2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372696,7 +372697,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$95.4$(或者$95.5$也可以)",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372717,7 +372718,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$1+2\\lg 2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372738,7 +372739,7 @@
"第六单元" "第六单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "C",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372759,7 +372760,7 @@
"第二单元" "第二单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372780,7 +372781,7 @@
"第七单元" "第七单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "A",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372801,7 +372802,7 @@
"第二单元" "第二单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "D",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372822,7 +372823,7 @@
"第四单元" "第四单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 证明略; (2) $2^{n+2}-4-3n$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372843,7 +372844,7 @@
"第六单元" "第六单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\dfrac 23$; (2) 证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372864,7 +372865,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $2\\sqrt{3}$; (2) $\\sqrt{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372885,7 +372886,7 @@
"第九单元" "第九单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 分布为$\\begin{pmatrix}0 & 1 & 2 \\\\ \\dfrac 15 & \\dfrac 35 & \\dfrac 15\\end{pmatrix}$, 期望为$1$; (2) $\\chi^2\\approx 0.595$, 脑瘤病患在左右侧的部位与习惯在哪一侧接听手机电话无关",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372906,7 +372907,7 @@
"第二单元" "第二单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $2x-y-2\\ln 2=0$; (2) $-a-\\dfrac 12$; (3) 有且仅有一个零点",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372927,7 +372928,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(-1,1)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372948,7 +372949,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\pi$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372969,7 +372970,7 @@
"第九单元" "第九单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -372990,7 +372991,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$9$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373011,7 +373012,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(-\\infty,0)\\cup [\\dfrac 13,+\\infty)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373032,7 +373033,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-\\dfrac 17$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373053,7 +373054,7 @@
"第六单元" "第六单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$36\\pi$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373074,7 +373075,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$14$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373095,7 +373096,7 @@
"第九单元" "第九单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$68$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373116,7 +373117,7 @@
"第七单元" "第七单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$3$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373137,7 +373138,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(-\\dfrac 12,0)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373158,7 +373159,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$3\\sqrt{5}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373179,7 +373180,7 @@
"第一单元" "第一单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "A",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373200,7 +373201,7 @@
"第六单元" "第六单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "D",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373221,7 +373222,7 @@
"第七单元" "第七单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373242,7 +373243,7 @@
"第三单元" "第三单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "D",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373263,7 +373264,7 @@
"第六单元" "第六单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 证明略; (2) $8\\sqrt{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373284,7 +373285,7 @@
"第四单元" "第四单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $[1,+\\infty)$; (2) $10216$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373305,7 +373306,7 @@
"第八单元" "第八单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\dfrac 13$; (2) $1.2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373326,7 +373327,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $2$; (2) $(-1,\\dfrac 74)$; (3) 是定值$\\sqrt{6}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373347,7 +373348,7 @@
"第二单元" "第二单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $(1,+\\infty)$; (2) $[-1,\\dfrac 32]$; (3) 证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373368,7 +373369,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\{-1,1\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373389,7 +373390,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$10$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373410,7 +373411,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac 12$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373431,7 +373432,7 @@
"第六单元" "第六单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$18\\pi$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373452,7 +373453,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373473,7 +373474,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$0.2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373494,7 +373495,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$12$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373515,7 +373516,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac 14$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373536,7 +373537,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$[-2,+\\infty)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373557,7 +373558,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\sqrt{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373578,7 +373579,7 @@
"第七单元" "第七单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$[\\dfrac 76,\\dfrac{15}2]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373599,7 +373600,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{-3\\pm \\sqrt{6}}6$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373620,7 +373621,7 @@
"第二单元" "第二单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "D",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373641,7 +373642,7 @@
"第九单元" "第九单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "C",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373662,7 +373663,7 @@
"第二单元" "第二单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373683,7 +373684,7 @@
"第四单元" "第四单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "C",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373704,7 +373705,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\dfrac 13$; (2) $8\\sqrt{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373725,7 +373726,7 @@
"第六单元" "第六单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 证明略; (2) $\\dfrac{4\\sqrt{21}}{21}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373746,7 +373747,7 @@
"第八单元" "第八单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $0.01998$; (2) 分布为$\\begin{pmatrix}0 & 1 & 2 & 3 \\\\ 0.00000 & 0.00030 & 0.02940 & 0.97030 \\end{pmatrix}$, 期望为$2.97$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373767,7 +373768,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 离心率为$\\dfrac{\\sqrt{5}}2$, 渐近线方程为$y=\\pm \\dfrac 12 x$; (2) $1$; (3) 证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373788,7 +373789,7 @@
"第二单元" "第二单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $-4$; (2) 存在切线$l_2$与$l_1$垂直, 理由略; (3) $(\\dfrac{3-\\sqrt{5}}{2},\\dfrac 12]\\cup [2,\\dfrac{3+\\sqrt{5}}{2})$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373809,7 +373810,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\{2,4\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373830,7 +373831,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(-\\infty,1)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373851,7 +373852,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$0.2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373872,7 +373873,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$(1,+\\infty)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373893,7 +373894,7 @@
"第六单元" "第六单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{2\\sqrt{2}}3\\pi$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373914,7 +373915,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$1$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373935,7 +373936,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$0.8$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373956,7 +373957,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$4$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373977,7 +373978,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$3$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -373998,7 +373999,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$[-1,1]$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374019,7 +374020,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$3$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374040,7 +374041,7 @@
"第七单元" "第七单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{\\sqrt{21}}{14}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374061,7 +374062,7 @@
"第九单元" "第九单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "D",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374082,7 +374083,7 @@
"第五单元" "第五单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "A",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374103,7 +374104,7 @@
"第六单元" "第六单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "C",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374124,7 +374125,7 @@
"第四单元" "第四单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374145,7 +374146,7 @@
"第八单元" "第八单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 证明略; (2) 分布为$\\begin{pmatrix} 0 & 1 & 2 \\\\ \\dfrac 3{10} & \\dfrac 35 & \\dfrac{1}{10}\\end{pmatrix}$, 期望为$\\dfrac 45$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374166,7 +374167,7 @@
"第六单元" "第六单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 证明略; (2) $60^\\circ$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374188,7 +374189,7 @@
"第九单元" "第九单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\lambda \\approx 29.21$, 估计到$2023$年底该地新能源汽车保有量约$40.3$万辆; (2) $\\hat{\\lambda}\\approx 29.67$, $\\hat{r}\\approx 0.32$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374209,7 +374210,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\dfrac{x^2}4+\\dfrac{y^2}3=1$; (2) $1$; (3) 值恒为$-3$, 证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374230,7 +374231,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 振幅为$\\sqrt{2}$, 周期为$2\\pi$, 初相位为$\\dfrac{\\pi}{4}$; (2) $(\\dfrac{\\pi}{3},\\dfrac{5\\pi}3]$; (3) $(0,1)$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374251,7 +374252,7 @@
"第一单元" "第一单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\{1\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374272,7 +374273,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$5$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374293,7 +374294,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-1$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374314,7 +374315,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$0.94$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374335,7 +374336,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-\\dfrac{24}{7}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374356,7 +374357,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$28$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374377,7 +374378,7 @@
"第六单元" "第六单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$50$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374398,7 +374399,7 @@
"第八单元" "第八单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac 13$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374419,7 +374420,7 @@
"第四单元" "第四单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac 8{11}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374440,7 +374441,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$9$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374461,7 +374462,7 @@
"第二单元" "第二单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{\\sqrt{2}}2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374482,7 +374483,7 @@
"第五单元" "第五单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\sqrt{15}a$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374503,7 +374504,7 @@
"第七单元" "第七单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374524,7 +374525,7 @@
"第九单元" "第九单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374545,7 +374546,7 @@
"第一单元" "第一单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "C",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374566,7 +374567,7 @@
"第二单元" "第二单元"
], ],
"genre": "选择题", "genre": "选择题",
"ans": "", "ans": "B",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374587,7 +374588,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\dfrac \\pi 3$; (2) $\\dfrac 32$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374608,7 +374609,7 @@
"第六单元" "第六单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 证明略; (2) $\\arctan\\dfrac{2\\sqrt{5}}5$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374629,7 +374630,7 @@
"第二单元" "第二单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $43.3$亿元; (2) (i) 全款购车两年后资产总额为$0.0322a$万元, 分期付款购车两年后资产总额为$0.0233a$万元, 应选择全款购车; (ii) $a<21.2134$, 这一措施对购买A, B, C车型有效",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374650,7 +374651,7 @@
"第七单元" "第七单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $C_1:\\dfrac{x^2}2+y^2=1$, $C_2:\\dfrac{x^2}2-y^2=1$; (2) $y=\\dfrac 12 x$或$y=-\\dfrac 12 x$; (3) $2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -374671,7 +374672,7 @@
"第二单元" "第二单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $g(x)=f(h(x))$; (2) 导函数为$2(2x)^{2x}(1+\\ln (2x))$, 最小值为$(\\dfrac 1{\\mathrm{e}})^{\\frac 1{\\mathrm{e}}}$; (3) 证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],